Among geometric forms, the sphere is the one most commonly employed—by nondual spiritual traditions—as a visual symbol and metaphor of our True Nature: of knowingly abiding as Pure Awareness.
The sphere embodies—and hence easily represents—perfect balance, harmony, and symmetry. No rotation or movement through space-time can disturb its shape.
The surface of a sphere (like the surface of the Earth) has no boundaries—and yet is finite, enclosed. If we start out walking in one direction along the Earth’s surface, and stay true to that direction, we’ll eventually end up exactly where we began.
Some cosmologists now believe the universe to be a multidimensional sphere: without boundaries yet finite, similar to how it is with the Earth. So that if we piloted a spaceship for long enough in the same direction, we’d end up where we began.
In physics, symmetry is a technical term which means immunity to possible changes. An entity is symmetrical if it remains unaltered in the face of transformations that could, in theory, change it.
A sphere is symmetric in relation to any possible rotations. No matter which way we turn it, the sphere remains a sphere, its basic shape unchanged.
Universal laws of nature are symmetric with respect to space-time translation. These laws apply, in other words, regardless of time or location. Hydrogen atoms located billions of light years away are subject to the same physical laws as hydrogen atoms located on Earth.
Interestingly, the symmetry of these laws of nature (and their governing equations) is lost, or broken, within physical reality. But this is a topic for another post.
It’s the symmetry of the sphere that we’re appreciating here—and how this perfectly symmetrical form has come to represent nondual Reality.
Attributed to the legendary Hermes Trismegistus of ancient Greece, is this enigmatic statement:
God is an infinite sphere, the center of which is everywhere, the circumference nowhere.
And we find a similar statement attributed to the 17th century mathematician, physicist, and philosopher Blaise Pascal:
Nature is an infinite sphere whose center is everywhere and whose circumference is nowhere.
But if we examine the longer quote from which the above is extracted, it seems plausible that it is not “nature” but rather “the reality of things” to which Pascal was referring:
The whole visible world is only an imperceptible atom in the ample bosom of nature. No idea approaches it. We may enlarge our conceptions beyond all imaginable space; we only produce atoms in comparison with the reality of things. It is an infinite sphere, the center of which is everywhere, the circumference nowhere. In short, it is the greatest sensible mark of the almighty power of God that imagination loses itself in that thought.
A defining geometric characteristic of a sphere is that each point of the circumference is equidistant from the center.
This accommodates our experience of Awareness being equidistant (and equally intimate) to all phenomena—in the same way that the center of a sphere is equidistant to every point on its circumference.
But here, Hermes and Pascal are transforming the image to enhance its metaphoric potency: an infinite sphere with center everywhere and circumference nowhere.
Because ultimately, every point (aka each phenomena) on the circumference—and the circumference as a whole—is always and already part of me, Pure Awareness, the eternal and immovable center.
As mentioned above, the surface of a sphere is unique in that it has no boundaries, yet still is finite.
And this finite nature of the sphere’s surface can evoke the coherence and self-evident certainty—the nonconceptual closure—of our True Nature. Any sense of chaos or fearful uncertainty (a la the infinite void) is effortlessly resolved.
In the same way that a sphere is devoid of sharp turns or rough edges, Pure Awareness is devoid of pairs-of-opposites, conceptual dualities.
Balance, smoothness, coherence, symmetry—these define the geometrical perfection of the sphere, as well as the experiential perfection of our True Nature: of abiding knowingly as Pure Awareness.


Major alterations in maths education are critical or we risk our future economic prosperity. And there should be compulsory maths in some form until the age of 18.
These are among the key conclusions of an independent report commissioned by the Conservative Party in 2009 and carried out by a task force assembled and led by Carol Vorderman.
Every year more than 300,000 sixteen year olds conclude their GCSE Maths course unable to function properly in either their work or personal lives, says the report. By age 16, there is a 10 year learning gap between the highest and lowest achieving students and after 11 years of being taught maths, many of our students have learnt to fear and hate the subject.
With maths requirements in the workplace having increased significantly over the last 20 years, we are putting our economic prosperity in jeopardy without rapid changes.
The report, entitled 'A world-class mathematics education for ALL our young people', argues that the problems many young people experience in their maths education become entrenched during primary and the early years of secondary school. A child's mathematical 'career' is effectively determined by the age of 11. 90% of those who fail to achieve the SAT target (Level 4) at age 11 will go on to 'fail' GCSE. Conversely, 94% of those who surpass the target (Level 5) will 'pass' GCSE.
Vorderman's team makes a number of recommendations to address the critical issues and build 'a world-class mathematics education for ALL our young people.' As well as compulsory maths until 18, these include replacing the present GCSE maths system with one offering two GCSEs and improving the mathematics subject knowledge of primary school teachers and new trainees and addressing what is, in many cases, a lack of confidence.
Education Secretary Michael Gove said:
"As Carol and her team point out so powerfully, we are falling behind our competitors when it comes to mathematics education. British 15 year olds' mathematics skills are now more than two whole academic years behind 15 year olds in Shanghai, and the last decade has seen us plummet down the international league tables in both Maths and Science.
"This comprehensive report, looking at all the important areas, will be of great help as the Government continues its drive to equip our children with the skills that they need to compete with their global contemporaries and thrive in the 21st Century.
Carol Vorderman said:
"Mathematics is a 'critically important' subject. It is a language without which the entire global infrastructure is struck dumb.
"This report does not make comfortable reading. It is aspirational but this does NOT mean making maths 'harder' for everyone, it means making the teaching better, and what is taught much more suitable for those who are learning it. The curriculum which exists is a trickled down version of the needs of the most talented. In my view, it is pointless for most 14 year olds starting their GCSE courses, to be force-fed mathematical topics which they will never use, when what they desperately need is to become more comfortable with numbers including percentages and fractions used in the world of finance.
"The top 15% are important but so is everyone else. Education must be about all of our young people in future and we must stop pretending otherwise."
Sir John Holman, Professor of Chemistry at the University of York and Senior Fellow for Education at the Wellcome Trust, said:
"I welcome Carol's clear no-nonsense report. For too long we have stood and watched mathematics education stagnate while academic study and the workplace have steadily increased their quantitative demands. We do no-one any favours by pretending that mathematics is something you can get by without, and I particularly welcome the strong recommendation that everyone should continue with some form of mathematical study beyond the age of 16."
Charlie Stripp, Chief Executive of the Charity Mathematics in Education and Industry (MEI) said:
"Mathematics in Education and Industry (MEI) strongly welcomes this report. It gives a thorough analysis of the issues in mathematics education that are preventing young people from learning the mathematics they need, and gives practical examples to show how many of these issues can be addressed.
It is vital that action is taken to follow its recommendations, which can enable our young people to have a truly world-class mathematics education and so help provide the workforce we need to compete successfully in international markets."
Professor Dame Julia Higgins, Chair of the Advisory Committee on Mathematics (ACME), said:
"We are pleased to see the importance of an excellent mathematical education being highlighted by another major report. Carol's work taps into one of the biggest concerns of not only the mathematics community, but also of higher education and business, that too few people study mathematics up to the age of 18.
Susan Anderson, CBI Director for Education & Skills policy, said:
"Maths is a subject of critical importance, and this report rightly highlights that there needs to be more focus on teaching 'useful maths' that is relevant for future employment and day-to-day life.
"Businesses are most concerned about basic levels of numeracy and it's alarming that more than one in five 16-19 year olds are considered functionally innumerate.
"To help address this problem, all young people should continue to study some form of maths until the age of 18. Pupils with good maths ability should continue to study the full curriculum, but all pupils, regardless of ability, should go on to study a functional numeracy qualification."
to download the full report, or view it in the reader below.


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Integer Partition With Distinct Parts
How many ways can you write an integer
n as the sum of a decreasing sequence(excluding
Let’s look at an example from Wikipedia:
Alternatively, we could count partitions in which no number occurs more than once. Such a partition is called a partition with distinct parts. If we count the partitions of 8 with distinct parts, we also obtain 6:
- 7 + 1
- 6 + 2
- 5 + 3
- 5 + 2 + 1
- 4 + 3 + 1
The problem boils down to find the number of partition with distinct parts and simply subtract 1 from it. So I’ll focus on the core part.
Doing it by hand is easy. We choose the first element, e.g., 5, figure out
8-5=3, and try to split
3 into smaller parts. For human beings, checking “
3 is less than
5” on paper happens in an instant. But we need a way to tell the computer what is the current max, so it knows possible choices for the next number.
Visualize the result
Before we directly count the total number of sequences, it helps to visualize the result. Based on the idea from StackOverflow:
partition(n, maxi) into English: Parition the number
n into a decreasing sequence where the first element(largest one) is no bigger than
min(n-i, i-1) is to ensure the sequence is decreasing, and the max is no more than the number itself. To see that, let .
This also avoids extra calculations because the size for each part can’t be more than what we have. For example,
partition(5, 5) = partition(5, 14), so we don’t need to run the loop from 6 to 14.
Let’s count the total number
Base case is
0. When we have
count_p(0, i-1), it means
n=i or n=0, so the only possible partition is
n = n no matter what the max is.
It works, but it’s super inefficient. To see where recalculations happen, I modified the function as below:
If these results are stored somewhere, we can avoid all recalculations and just use it.
Let’s decipher the highlighted line:
p[i][j]: Partition the integer
i into a decreasing sequence with the first element(largest one) less than or equal to
j. Here we are accumulating the result. Say we want to partition 8. After selecting 5 as the first element, we want to find all decreasing sequences starting with 4 or less that sum to 8-5=3. As long as the first element is less than 5, the sequence is valid.
p[i][j-1] +: Accumulate the result as explained above.
p[i-j][min(i-j, j-1)]: Find all valid subsequences from
i-j(what’s left). This corresponds to our recursion
partitoin(n-i, min(n-i, i-1)).
Finally, we can find our result at
p[n][n]: partition the integer
n with the starting element less than or equal to
n. This is exactly what we’re looking for.
If you want to exclude
Here’s the table from
P(8). The result is at
p[8, 8] = 6 as we expected.


This set is the first in a series taken at the Cimetière de Montparnasse in Paris. Henri Poincaré (1854-1912) was a famous mathematician, who contributed many things to a wide number of fields of mathematics. One of them is very important to the field of optical polarimetry. Polarization is a property that light has, because, as an electromagnetic field, the electric and magnetic fields must each be perpendicular to each other and to the direction of propagation. The electric field can be in a single plane containing the propagation direction, in which case it is called linearly polarized, or it can be rotating one way or another, in which case it is called circularly polarized.
In my day job, I am a physicist, and I use the polarization behavior of how materials scatter light to identify and differentiate different sources of scatter. Polarization states are often represented by a point on a unit sphere, referred to as the Poincaré sphere. Points along the equator correspond to linear polarization states, with the longitude corresponding to half the angle of the electric field, while those at the north and south poles correspond to right- and left-circular polarizations, respectively. Points inside the sphere correspond to various degrees of depolarization, with the very center of the sphere being completely unpolarized, random light. So, the Poincaré sphere represents the topology of the statistics of the electromagnetic fields.
In any case, when I arrived at the cemetery, I made a bee line for Poincaré’s family grave, which is easy to find, since it is very close to the Avenue Thierry entrance and right up against the outside wall. All of the stereographic projections are thus titled “Poincaré Sphere (Stereo n),” while the cube is titled “Poincaré Cube.”
See the entire Poincaré collection here or enjoy them below. Enjoy!


Bajaj Placement Papers-Free Download
1. One guy has Rs. 100/- in hand. He has to buy 100 balls. One football
costs Rs. 15/, One Cricket ball costs Re. 1/- and one table tennis ball
costs Rs. 0.25 He spend the whole Rs. 100/- to buy the balls. How many
of each balls he bought?
2. The distance between Station Atena and Station Barcena is 90 miles.
A train starts from Atena towards Barcena. A bird starts at the same
time from Barcena straight towards the moving train. On reaching the
train, it instantaneously turns back and returns to Barcena. The bird
makes these journeys from Barcena to the train and back to Barcena
continuously till the train reaches Barcena. The bird finally returns
to Barcena and rests. Calculate the total distance in miles the bird
travels in the following two cases: (a) The bird flies at 90 miles per
hour and the speed of the train is 60 miles per hour. (b) the bird
flies at 60 miles per hour and the speed of the train is 90 miles per
3. A tennis championship is played on a knock-out basis, i.e., a player
is out of the tournament when he loses a match. (a) How many players
participate in the tournament if 15 matches are totally played? (b) How
many matches are played in the tournament if 50 players totally
4. When I add 4 times my age 4 years from now to 5 times my age 5 years
from now, I get 10 times my current age. How old will I be 3 years from
5. A rich merchant had collected many gold coins. He did not want
anybody to know about them. One day, his wife asked, "How many gold
coins do we have?" After pausing a moment, he replied, "Well! If I
divide the coins into two unequal numbers, then 37 times the difference
between the two numbers equals the difference between the squares of
the two numbers." The wife looked puzzled. Can you help the merchant's
wife by finding out how many gold R
6. A set of football matches is to be organized in a "round-robin"
fashion, i.e., every participating team plays a match against every
other team once and only once. If 21 matches are totally played, how
many teams participated?
7. Glenn and Jason each have a collection of cricket balls. Glenn said
that if Jason would give him 2 of his balls they would have an equal
number; but, if Glenn would give Jason 2 of his balls, Jason would have
2 times as many balls as Glenn. How many balls does Jason have?
8. Suppose 8 monkeys take 8 minutes to eat 8 bananas. (a) How many
minutes would it take 3 monkeys to eat 3 bananas? (b) How many monkeys
would it take to eat 48 bananas in 48 minutes
9. It was vacation time, and so I decided to visit my cousin's home.
What a grand time we had! In the mornings, we both would go for a jog.
The evenings were spent on the tennis court. Tiring as these activities
were, we could manage only one per day, i.e., either we went for a jog
or played tennis each day. There were days when we felt lazy and stayed
home all day long. Now, there were 12 mornings when we did nothing, 18
evenings when we stayed at home, and a total of 14 days when we jogged
or played tennis. For how many days did I stay at my cousin's place?
10. A 31" x 31" square metal plate needs to be fixed by a carpenter on
to a wooden board. The carpenter uses nails all along the edges of the
square such that there are 32 nails on each side of the square. Each
nail is at the same distance from the neighboring nails. How many nails
does the carpenter use?
Answer and Explanation.
1. F + C + T = 100-------------eq1 15F + C + 0.25T =
100-------------eq2 eq1=eq2 .solve to get F=3T/56 ;F=3,T=56,C=41
2. a) There is no need to consider their meeting pt at all.the train
has been running for 90miles/(60miles/hr)=1.5hrs.bird flies till train
reaches destination frm strting pt.so bird flies for1.5hrs at the vel
given(90).so dist=1.5*90=135miles b) time of train=1hr.so dist of
3. (a) u don't need to sum it up.since it's a knock out only 1 person
emerges winner finally.so15+1=16is answer.becos after15 matches finally
we shud've 15losers and 1winner.(b) 49:its always one less than no of
players as per the idea given above.so no need to check okay cos its
always true.ans is 49.
4. Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years
5. 37(x-y)=x^2-y^2. u no tht x^2-y^2=(x-y)(x+y).so (x-y) cancels on
both sides to give x+y=37.so sum of unequal halves=37 which is the req
6. R ans:7 teams okay.for a match u need 2 teams.suppose there r
totally 'n 'teams.Now uve to choose 2 teams out of 'n' teams.so answer
=no of such choices=no. of possible combinations. So we've ans =
nC2(ncombination2)=21;solve to get n=7.Sol: n(n-1)/2=21. so n=7.if u
don't understand c the graph beloweach team plays no. of matches=no of
teams ahead of it. One bar '' represents one team. ------------7 6 5 4
3 2 1 0 -----------21last team is written as 0 matches becos this team
has already played with all other teams-hence sum of matches
=6+5+4+3+2+1=21 which is correct only if no of teams =7
7. R 141. G+2=j-22. 2(G-2)=J+2.solve these 2 to get J=14
8. a). Sol:each mky takes 8 min to eat a banana b).ans:8m=48 m=6
9. Use sets and venn diagram to solve such questions.a,b ,aub,anb
etc.12=tennis+leave18=jog +leaveso jog-tennis=6again jog+tennis=14.so
solve and get jog=10,leave=8,tennis=4.so tot=22
10. Ans= 32*2 + 30*2=124
1.Three friends divided some bullets equally. After all of them shot 4
bullets the total number of bullets remaining is equal to the bullets
each had after division. Find the original number divided.
2.Find sum of digits of D. Let A= 19991999 B = sum of digits of A, C =
sum of digits of B, D = sum of digits of C. (HINT: A = B = C = D (mod
3.There is a 50m long army platoon marching ahead. The last person in
the platoon wants to give a letter to the first person leading the
platoon. So while the platoon is marching he runs ahead, reaches the
first person and hands over the letter to him and without stopping he
runs and comes back to his original position. In the mean time the
whole platoon has moved ahead by 50m. The question is how much distance
did the last person cover in that time. Assuming that he ran the whole
distance with uniform speed.
4.If you take a marker & start from a corner on a cube, what is the
maximum number of edges you can trace across if you never trace across
the same edge twice, never remove the marker from the cube, & never
trace anywhere on the cube, except for the corners & edges?
5.One of Mr. Bajaj, his wife, their son and Mr. Bajaj's mother is an
Engineer and another is a Doctor. If the Doctor is a male, then the
Engineer is a male. If the Engineer is younger than the Doctor, then
the Engineer and the Doctor are not blood relatives. If the Engineer is
a female, then she and the Doctor are blood relatives. Can you tell who
is the Doctor and the Engineer?
6.Three men - Sam, Cam and Laurie - are married to Carrie, Billy and
Tina, but not necessarily in the same order. Sam's wife and Billy's
Husband play Carrie and Tina's husband at bridge. No wife partners her
husband and Cam does not play bridge. Who is married to Cam?
7.There are 3 persons X, Y and Z. On some day, X lent tractors to Y and
Z as many as they had. After a month Y gave as many tractors to X and Z
as many as they have. After a month Z did the same thing. At the end of
this transaction each one of them had 24. Find the tractors each
8.A certain street has 1000 buildings. A sign-maker is contracted to
number the houses from 1 to 1000. How many zeroes will he need?
9.There are 9 coins. Out of which one is odd one i.e weight is less or
more. How many iterations of weighing are required to find odd coin?
10.In a sports contest there were m medals awarded on n successive days
(n > 1). On the first day 1 medal and 1/7 of the remaining m - 1
medals were awarded. On the second day 2 medals and 1/7 of the now
remaining medals was awarded; and so on. On the nth and last day, the
remaining n medals were awarded. How many days did the contest last,
and how many medals were awarded altogether?
11.A number of 9 digits has the following properties: The number
comprising the leftmost two digits is divisible by 2, that comprising
the leftmost three digits is divisible by 3, the leftmost four by 4,
the leftmost five by 5, and so on for the nine digits of the number
i.e. the number formed from the first n digits is divisible by n,
2<=n<=9. Each digit in the number is different i.e. no digits are
repeated. The digit 0 does not occur in the number i.e. it is comprised
only of the digits 1-9 in some order. Find the number.
12. 1/3 rd of the contents of a container evaporated on the 1st day.
3/4th of the remaining contents of the container evaporated on the
What part of the contents of the container is left at the end of the
13.Vipul was studying for his examinations and the lights went off. It
was around 1:00 AM. He lighted two uniform candles of equal length but
one thicker than the other. The thick candle is supposed to last six
hours and the thin one two hours less. When he finally went to sleep,
the thick candle was twice as long as the thin one. For how long did
Vipul study in candle light? 3 hrs
14.If you started a business in which you earned Rs.1 on the first day,
Rs.3 on the second day, Rs.5 on the third day, Rs.7 on the fourth day,
& so on. How much would you have earned with this business after 50
years (assuming there are exactly 365 days in every year)?
15.A worker earns a 5% raise. A year later, the worker receives a 2.5%
cut in pay, & now his salary is Rs. 22702.68 What was his salary to
16.At 6'o a clock ticks 6 times. The time between first and last ticks
is 30 seconds. How long does it tick at 12'o.
17.In Mr. Mehta's family, there are one grandfather, one grandmother,
two fathers, two mothers, one father-in-law, one mother-in-law, four
children, three grandchildren, one brother, two sisters, two sons, two
daughters and one daughter-in-law. How many members are there in Mr.
Mehta's family? Give minimal possible answer.
18.When Alexander the Great attacked the forces of Porus, an Indian
soldier was captured by the Greeks. He had displayed such bravery in
battle, however, that the enemy offered to let him choose how he wanted
to be killed. They told him, "If you tell a lie, you will put to the
sword, and if you tell the truth you will be hanged." The soldier could
make only one statement. He made that statement and went free. What did
20.A person wanted to withdraw X rupees and Y paise from the bank. But
cashier made a mistake and gave him Y rupees and X paise. Neither the
person nor the cashier noticed that. After spending 20 paise, the
person counts the money. And to his surprise, he has double the amount
he wanted to withdraw. Find X and Y. (1 Rupee = 100 Paise)
Source: Contents are provided by Technicalsymposium Google Group Members.
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The statistical t-test is used to compare two conditions, specifically the means of two conditions. A t-test can be applied to both a between participants and within participants design. This test can only be done on normally distributed data, and as such is a parametric test. The purpose of the t-test is to decide whether or not the difference between the means of the two conditions is statistically significant. If the difference is statistically significant we are able to except our experimental hypothesis and also give some directionality to our hypothesis. If the difference between the means of the two conditions is not statistically significant we must reject our experimental hypothesis and accept the null hypothesis. The t-score is technically more than just the difference between the means. Just like normal data distribution, the t-score also has a 95% confidence interval, which means for the difference between the means to be statistically significant, the alpha level needs to be less than 0.05. The alpha level was decided on 0.05 to try and reduce the amount of type I and type II errors. Type I errors is when we reject the null hypothesis but should not have, and type II errors is when we reject the experimental hypothesis but we should not have. If the sample size is large and the null hypothesis is true, the distribution of the t-scores is also normal. The smaller the sample size becomes, the more tail-heavy the distribution becomes.
The way this is interpreted is if two groups come from the same population, then 95% of the time, the t-score (reflecting the difference in the means) will be within the 95% area under the graph of the data.
Degrees of Freedom
Degrees of freedom for within-participants design is the same as the number of participants.
Degrees of freedom for between-participants design is the (number of participants in group 1 -1) + (number of Ps in group 2 -1)
SPSS will do the math for you!
When you start with your mean scores, assume that the null hypothesis is true and that there is no significant difference between the means.
Then set your significance level at p<0.05 or the alpha level, which is the same thing. SPSS should do this automatically.
Then using SPSS calculate the t-score.
If the t-score is within the 95% interval: accept the null hypothesis and reject the experimental hypothesis.
If the t-score is outside the 95% interval: reject the null hypothesis and accept the experimental hypothesis. You have now established that there is a significant difference between the two means.
This is an example of the type of output that will be given by SPSS. From this output you can answer the following questions:
Question 1: Is the experimental design within or between participants?
Answer: The experimental design is within. You can tell this from the heading where it says paired difference.
Question 2: What is the t-score?
Answer: The t-score is -9.60.
Question 3: What are the degrees of freedom?
Answer: The degrees of freedom (df) is 77.
Question 4: Is it two-tailed or one-tailed test?
Answer: It is two tailed as shown in the last box. Sig. (2-tailed).
Question 5: Is the result significant at an alpha level of 0.05? Why?
Answer: The result is significant at the alpha level because p<0.001, which obviously is less than 0.05.
Reporting the Results
The mean and standard deviation of participants’ reaction time under conditions 1 and 2 are given in Table (not in this post). The data were analysed using a two-tailed within-participants t-test and an alpha level of 0.05.There is a statistically significant difference between the ideal IQ and the estimated IQ, with the estimated IQ significantly lower than IQ for an ideal job, t(77) = -9.60, p <0.001.


|the casio al-10 is a personal favourite of mine.
from 1976, it displays 10 digits and is very easy to use with large buttons that
are easy to press.
together with the 4 basic functions and a memory is a rather splendid mechanical
six position switch which defines the function of the top right 'p'
button. these functions are:
- square root
- grant total
- hours, minutes & second
- statistics (standard deviation)
a lot of these operate as modes rather than pure function. for example,
GT tallies the total sum for every '=' and
is recalled by pressing 'p', rem puts the
machine into a remainder mode where only the integer part is displayed
after a division and the remainder can be recalled by pressing 'p'.
although the al-8 was the first fractional
calculator, the al-10 fraction mode is more useful because of the 10 digit
display. the whole part, the numerator and the denominator each cannot
exceed three digits and the total cannot exceed 8 (eg 1234½ is not
allowed). for example 355/226 is reduced and correctly displayed as
1/129/226 whereas this cannot be accommodated on the al-8.
the other switch alters the rounding mode for normal floating point
operation. the choices are cut, which
truncates to 2 decimal places or 5/4 for rounding.
internally, the machine operates to 10 digits with no guard.
this model would suffer the sticky button


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Saturday, 15 October 2011
Differences between Steady state model and Dynamic Universe Model
There was an anonymous question in the Blog...
'What are the differences between the steady state model and Dynamic Universe Model?'
The Hoyle’s Steady state Universe Model is based on Einstein’s General theory of relativity. It supports expansion of universe and red-shifted Galaxies. To maintain the constant matter density in space, Hoyle proposed the creation of matter from empty space. He did not like the idea of Big Bang. It was he who coined the term ‘Big Bang’ to make fun of the concept of ‘the start and creation of Universe from a singularity from nowhere’, in a scientific gathering.
The main problem faced by Hoyle, with his Steady state Model is the occurrence of Big Bang in his own model. He disliked the concept of Big Bang all his life; yet there would be a Big Bang in his Steady state Model. This was proven mathematically by Stephen Hawking and Roger Penrose, in their singularity theorem. The singularity theorem says that any Universe model which is based on Einstein’s General theory of relativity, supports expansion of Universe will have a Big Bang Singularity in some distant Past.
Now let’s come to Dynamic Universe Model.
The Dynamic Universe Model is conceptually different from Einstein’s General theory of relativity. This model is also based on Tensors. But there will be no differential and integral equations on the expansion of these Tensors. No differential and integral equations are used as in the case of Newtonian two body problem. No differential and integral equations at all !
This Dynamic Universe Model supports simultaneous expansion and contraction of the universe. There will be red-shifted as well as blue shifted Galaxies in this Universe. The universe is dynamically balanced. All bodies in this universe are moving. Nothing stays static. Some will go far away and some will come near. There will always be change.
This Dynamic Universe Model is a closed universe model. No energy flows out of universe. There are no other universes, No baby universes. No infinities.
Dynamic Universe model is a singularity free tensor based math model. The tensors used are linear without using any differential or integral equations. Only one calculated output set of values exists. Data means properties of each point mass like its three dimensional coordinates, velocities, accelerations and it’s mass. Newtonian two-body problem used differential equations. Einstein’s general relativity used tensors, which in turn unwrap into differential equations. Dynamic Universe Model uses tensors that give simple equations with inter-dependencies. Differential equations will not give unique solutions. Whereas Dynamic Universe Model gives a unique solution of positions, velocities and accelerations; for each point mass in the system for every instant of time. This new method of Mathematics in Dynamic Universe Model is different from all earlier methods of solving general N-body problem.
This universe exists now in the present state, it existed earlier, and it will continue to exist in future also in a similar way. All physical laws will work at any time and at any place. Evidences for the three dimensional rotations or the dynamism of the universe can be seen in the streaming motions of local group and local cluster. Here in this dynamic universe, both the red shifted and blue shifted Galaxies co-exist simultaneously.
In this Dynamic Universe Model, different sets of point masses were taken at different 3 dimensional positions at different distances. These masses were allowed to move according to the universal gravitation force (UGF) acting on each mass at that instant of time at its position. In other words each point mass is under the continuous and Dynamical influence of all the other masses. For any N-body problem calculations, the more accurate our input data the better will be the calculated results; one should take extreme care, while collecting the input data. One may think that ‘these are simulations of the Universe, taking 133 bodies is too less.’ But all these masses are not same, some are star masses, some are Galaxy masses some clusters of Galaxies situated at their appropriate distances. All these positions are for their gravitational centres. The results of these simulation calculations are taken here.
Here in these simulations the universe is assumed to be heterogeneous and anisotropic. From the output data graphs and pictures are formed from this Model. These pictures show from the random starting points to final stabilized orbits of the point masses involved. Because of this dynamism built in the model, the universe does not collapse into a lump (due to Newtonian gravitational static forces). This Model depicts the three dimensional orbit formations of involved masses or celestial bodies like in our present universe. From the resulting graphs one can see the orbit formations of the point masses, which were positioned randomly at the start. An orbit formation means that some Galaxies are coming near (Blue shifted) and some are going away (Red shifted) relative to an observer’s viewpoint.


Origin of the Bowditch method. Published in 1802 Nathaniel Bowditch’s exposition on navigation is famous among surveyors for its description of the traverse adjustment method which bears his name. The method first appears for the computation of Traverse Sailing. Bowditch correction was widely used until EDM replaced mechanical distance measurement and least squares took over. The title page says it all: ‘many thousand errors are corrected’. Thanks to Google books I took a look at an early* worked example and found it is more or less as taught to me at Vauxhall college, the method evolved to include proportional distribution of both angle and distance error and, such is the legendary status of his work, still bears the name ‘Bowditch’.
Among the many useful nautical wonders Nathaniel Bowditch offered in his 1802 ‘Epitome of Navigation’ is a method for the correction of survey travserses
which, until the computer age, was the standard method: the Bowditch Correction. Nathaniel describes, on p108, the problem with alomst brutal clarity:
‘but it most frequently happens the numbers do not agree’ is an acceptance of ‘real world’ measurement with the advice ‘in which case the work must be carefully examined, and if no mistake be found, and the error be great, the place must be surveyed again…’ bourne out of experience. I don’t know if Bowditch himself carried out traverses but he certainly was familiar with travserse outcomes.
The first expression of the method is not quite what we know as Bowditch today. This is before the railway age. The method descibed is far from the backbone of civil engineering engineering practice which was some 20 years in the future, it is a version of a tried and tested dead reckoning correction for marine navigation. The mix of nautical and land survey terms reveals the navigational origin, for example Bowditch uses ‘Departure’ for the Easting axis and ‘Lattitude’ for the Northing and bearings are given relative to the 4 compass cardinals.
The first appearance of the method is a navigation example, here is the 1807 version (from the second edition in which the Surveying chapter makes no mention of traverse or adjustment) which appears as ‘Travserse Sailing’ the identification of the misclosure by tabulation is there:
The method appears in the Surveying chapter in or around 1840, by which time Mr Bowditch had passed on and the decimal system had been adopted for computation.
I’m not a surveyor of 1840s vintage so I found the worked example difficult to folow as:
- The starting co-ordinates are not given
- Neither whole circle bearings or internal angles are given
- The direction of computation is not given
- Co-ordinates are in mixed XY and YX axes
- no angle sum check is used.
The figure, plotted by bearing and distance looks like this:
which shows the misclosure at A as:
Distance = 0.1264, Delta X = 0.0774, Delta Y = 0.1000
By the current method of included angle the figure looks like this:
The sum of the interior angles [ (N-2)*180] gives 540. The angles given (A=155 B=15 C=215 D=85 E=70 ) sum to 540: there is no angular misclosure, he has used whole degree values. This is a theoretical example after all.
Bowditch gives the following as the corrections for each leg, rounded to 2 dp:
The misclosure in Northing (0.1) is divided by the number of legs, the misclosure in Easting is applied as an unequal fraction (42.10/.08) with the larger portion given to the longest legs. Bowditch tells us the Northing error is negative and the Easting is negative.
1st Description of proportional correction by length of leg. Bowditch then describes the correction thus:
Find the error in latitude, or the difference between the sums of southing and northing : also the sum of the boundary lines. Then say: As this sum is to the error in latitude, so is the length of any particular boundary to the correction of the corresponding difference of latitude, additive if in the column whose sum is the least, otherwise subtractive.
Which is an awkward way of saying:
- Correction N= ΔN (Length of leg)/(Σ dist)
- Correction E=ΔE (Length of leg)/(Σ dist)
The language is difficult but there it is: divide the sum of the distances by the difference in E and N for each leg to find the correction: I’m not certain this is as its described in the 1st 1802 edition and or how the later editions came about but the origin is clear enough: the ‘immacculate’ Bowdithch did indeed come up with a robust and simple method for adjusting traverses. Methods for determining the differences (partial co-ordinate method) may have come along later but the new idea is clear: proportional distribution of distance error.
Bowditch’s foldout frontispiece map shows his travserse across the Atlantic.
From March 25th to April 10th Bowditch’s path is plotted day by day.
*Google books has many digitised editions. The earliest I can find, is an 1809 version which has computation in imperial units, and the method is decribed in ‘Traverse Sailing.’ Later versions ( I have used an 1839 edition here) are decimal and include the method in a ‘Surveying’ chapter. Other than in the auction house pages the 1802 edition is an online rarity.


Now announcing the second edition of the algebra survival workbook your tool for reaching algebra mastery now that the award winning algebra survival guide has been expanded and revised the companion algebra survival workbook has also been enhanced and updated. Yes now is the time to redefine your true self using sladers free algebra 1 homework practice workbook answers shed the societal and cultural narratives holding you back and let free step by step algebra 1 homework practice workbook textbook solutions reorient your old paradigms. The grade saving algebra i companion with hundreds of additional practice problems online algebra i workbook for dummies is your solution to the algebra brain block with hundreds of practice and example problems mapped to the typical high school algebra class youll crack the code in no time. This textbook contains the fundamentals of algebra most frequently used at the university associated with the development of academic programs of calculus the content of the book applies in classroom curriculum or distance curriculum
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An hour and 17 minutes ago I finished writing my Partial Differential Equations final exam. I don't know how I feel about that. I'm happy that the exam is done and I always am with exams. But at the same time I am sad. This is the last math course of my degree and quite possibly the last math course that I will ever take again and that makes me sad. I love math. I love the way it makes me think and I love the satisfaction of finally solving a math problem that I have been working on for hours. I am going to miss it.
There is still some physics left to concentrate on. I'm sure once the end has come there will be a long and mornful post.
Banksy is Brilliant
1 year ago


This is the most comprehensive collection of IB past papers in the World!
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What is Revision Village?
Voted the #1 IB Mathematics Resources in 2019 & 2020, Revision Village is an award-winning education website that helps IB students learn, practice and revise for IB maths exams. More than 70% of IB Students & Teachers worldwide use Revision Village ~ 350,000+ IB Students from 1,500+ IB Schools.
Who uses Revision Village?
Revision Village is for International Baccalaureate (IB) Diploma Program candidates studying all levels of IB Mathematics.
What IB Subjects does Revision Village cover?
IB Mathematics HL, SL, Studies, Analysis and Approaches SL & HL, Applications and Interpretation SL & HL. We love mathematics and IB students love using Revision Village! Our mission is to create the highest quality IB Math resources available online. We are proud to be voted the #1 IB Mathematics Resource in 2019 & 2020 by IB Students & Teachers worldwide.
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Maths Questionbank: The #1 Maths Exam Questionbank for IB Students. IB Maths exam style questions by topic, sub-topic & difficulty. Video solutions & mark schemes for all questions. Learn, practice and master IB mathematics questions.
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Part of a book: Грънчарова, Гена и др.. Methods and tools in public health : A handbook for teachers, researches and health professionals / Ed. Lijana Zaletel-Kragelj and Jadranka Bozikov . - Lage : Hans Jacobs , 2010
Description: Quantiles are special measures of location that could be described as the points that divide the ordered series of data (from the lowest to the highest value)into subgroups of equal size regarding the number of units in a subgroup. In other words, quantiles are the data values marking the boundaries between consecutive subgroups ordered series of data (an array).


What is a rhombille grid?
A rhombille grid is a tessellation of the plain in identical rhombi. (The term was coined by John Conway in his book The Symmetries of Things. He also created The Game of Life.)
One of the earliest games that used an isometric view, Q*bert (1982), used a grid like this to simulate a limited 3D environment. Indeed, with appropriate shading, the tiling resemble a stack of 3D cubes. At the time, the game was praised for its innovative graphics.
Another game that uses a rhombille grid is Rhomboid Slitherlinks, a set of puzzles created by Jim Bumgardner, using tilings supplied by Lars Huttar (Edit: I previously only credited Jim. Lars explains in a comment below how the puzzles came about. I apologize for the omission.). A Slitherlink is a puzzle where the goal is to draw in edges of a grid so that they form a single, continuous line that does not cross itself. Some cells have numbers; these indicate the number of edges of that cell that are part of the solution line.
The rombille grid has another feature that makes them useful for games. Rhombille grids are the edge-grids of hexagonal and triangular grids. In other words, if we are interested in the edges of these types of grids, we could consider them the faces of appropriate rhombille grids. For instance, if we use a rhombus tile with the long diagonal of the rhombus drawn in, the resulting grid will be a triangular grid. If we use tiles with the short diagonal drawn in instead, the resulting grid is a hexagonal grid.
There are not many examples of games played on the edges of these types of grids. There is a version of Dots for hexagonal grids, and hexagonal Sliterlink puzzles. The Settlers of Catan has a road-building mechanic on the edges of the hexes. Another interesting game is Vertex Dispenser, where players play on the edges (really, from vertex to vertex) to gain territory, similar to Dots. Unlike the other examples, this game uses grids on 3D shapes.
When you work with edges for hex or tri grids, there are several advantages to work with rhomb tiles instead of tris or hexes:
- It is easier to draw the edges, since you are not near the edge of the tile. This gives you more freedom to play with the lines.
- Since each edge has it’s own tile, you only have to use one tile. In a tri grid such as the one below, you would need two different tiles.
- It is easier to make the edges clickable.
There are many ways in which we can assign coordinates to the cell in a rhombille grid. One technique that works well is to group the rhombi into groups of three, where each group forms a hexagon. We can then make a coordinate from the hex coordinate, and an index that indicates the orientation (and hence also which of the three rhombi in the group we mean).
This is the scheme followed in the image at the top of this post. You will notice that groups of three rhombi with the same colors make up a hexagon (or a cube). The first part of the rhomb coordinate is the hex-coordinate of the hex that it is part of (see Amit Patel’s article on grid math for more detail on hex coordinates). The last part is an index indicating it’s orientation.
The neighbors of a cell in a rhombille grid is complex.
In the image above, the blue cell has four 1-neighbors (the green cells), four 2-neighbors (the yellow cells) and ten 3-neighbors (the red cells).
If we view the rhomb grid as a edge hex-grid, then the 1-neighbors of a cell are all the edges connected to the edge in that cell. If we view the rhomb grid as a edge tri grid, then the 1-, 2- and 3- neighbors of a cell contain the edges connected to the edge in that cell.
In Q*bert, only “flat” cells are accessible. In this case, neighbors do not share an edge or even a vertex.


Dynamic biological systems, such as gene regulatory networks (GRNs) and protein signaling networks, are often represented as systems of ordinary differential equations. Such equations can be utilized in reverse engineering these biological networks, specifically since identifying these networks is challenging due to the cost of the necessary experiments growing with at least the square of the size of the system. Moreover, the number of possible models, proportional to the number of directed graphs connecting nodes representing the variables in the system, suffers from combinatorial explosion as the size of the system grows. Therefore, exhaustive searches for systems of nontrivial complexity are not feasible. Here we describe a practical and scalable algorithm for determining candidate network interactions based on decomposing an N-dimensional system into N one-dimensional problems. The algorithm was tested on in siliconetworks based on known biological GRNs. The computational complexity of the network identification is shown to increase as N2 while a parallel implementation achieves essentially linear speedup with the increasing number of processing cores. For each in silico network tested, the algorithm successfully predicts a candidate network that reproduces the network dynamics. This approach dramatically reduces the computational demand required for reverse engineering GRNs and produces a wealth of exploitable information in the process. Moreover, the candidate network topologies returned by the algorithm can be used to design future experiments aimed at gathering informative data capable of further resolving the true network topology.


This is the tenth in a series of blog “snapshots” of how Mercy students benefit from using iPad technology (and other tools) throughout the school day.
In the photos below, students in Geometry Honors are using GeoGebra to investigate the relationship between angles formed by parallel lines and a transversal. They will use the results to develop conjectures about the congruent or supplementary angle pairs. The final component of the activity is to write the formal proof for each conjecture, thus developing the theorems found in geometry textbooks. — Carol Baron
Photos by L. Baker
Patty Perry uses Explain Everything to make tutorials for students to explain difficult concepts. She also uses it to respond to email or message questions.


This was the plan: Linear Algebra --> Linear Programming --> Convex Programming (Semi-definite programming) --> Optimization, Error Bound Analysis Especially in Graphs!
Thanks PatrickJMT for the hard work and easy and quick math reminders. L’Hospital’s Rule was just fun!
After starting to read the book "Convex Optimization" by Stephen Boyd and Lieven Vandenberghe; I realized that convex optimization has lots of uses data mining, statistics, control theory, etc apart from the graph analysis topic that I am reading it for. It makes it even more exciting!


Vector is art that's made up of vector graphics. These graphics are points, lines, curves and shapes that are based on mathematical formulas. When you scale a vector image file, it isn't low resolution and there's no loss of quality, so it can be sized to however large or small you need it to be. It's an excellent tool for putting company logos on business cards, creating poster designs, and when photo-shopping. Any art made with vector illustration software like Adobe Illustrator is considered vector art.


How many of you asked “when am I ever going to need to know this” in math class? While basic mathematical literacy is essential for life in the modern world, most people can achieve success in their careers if they can’t remember the difference between pi and apple pie.
One of the exceptions to this comes from my own career path- scientists absolutely, positively need to have strong quantitative skills in order to perform research. However, many scientists struggle with math. I can’t even count how many conference presentations I’ve attended that included a statement along the lines of “don’t worry about all the complicated equations here”, or how many students or journal club attendees have told me that they just skipped over the section of a paper focusing on models and equations. See what I did there? Can’t even count? Anyway, while math may be more directly relevant to our jobs than it is to some of yours, we still find it hard.


I had one math teacher, for part of Grade 6, who made math interesting … even exciting. Finding a problem’s answer was like solving a detective mystery. Then came high school and a math teacher I disliked. He would say he was brilliant (and sometimes did) but I came away with a dislike of his subject.
I’m writing a book. I’ve got the page numbers done, so now I just have to fill in the rest.— Stephen Wright
I scraped by in math, enough to pass, but never really learned much. My feelings about the subject are mixed, at best. Unsure about whether numbers exist “out there, in the real world” or are an invention of the human brain, I am inclined to come down in the latter camp.
And yet, math can still fascinate me, especially geometry, probably because it’s visual and thus more “real”. To see seems to be to understand.
When artist Matt Wood said he wanted to avoid making art that looked “contrived”, I thought of all the gimmicks taught in art lessons about composition. Rules of thirds, symmetry, circles, triangles and squares. Is Matt as suspicious of these methods as I am? It’s easy enough to hide such underlying structures from viewers, but the artist knows they are there, performing their tricks.
Math can bedazzle me and even command my respect with its seeming predictive power. It has practical uses and dominates more and more of our digital lives. Still, though math is winning over me, I don’t see it winning me over.
In real life, I assure you, there is no such thing as algebra. …— Fran Lebowitz


FOR IMMEDIATE RELEASE
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Contact: Ilene Greenfield
Director of Media Relations
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CHILDREN’S BOOK BY BERKELEY COLLEGE INSTRUCTOR FROM
NEW ROCHELLE TO BE PUBLISHED IN FIVE LANGUAGES
Photo Caption: Anne Walsh, EdD, Berkeley College Instructor, Math and Sciences Department, School of Liberal Arts, and a resident of New Rochelle, NY, is the author of “The Adventures of Symmy the Square and the Land of Shapes” (Createspace Publishing, 2010). The book incorporates basic geometric shapes and concepts for young readers, and plans are underway to publish the book in Mandarin Chinese, French, Spanish, and Gaelic. For more information go to: www.landofshapes.com.


Predictive modelling leverages statistics to predict outcomes. Most often the event one wants to predict is in the future, but predictive modelling can be applied to any type of unknown event, regardless of when it occurred. For example, predictive models are often used to detect crimes and identify suspects, after the crime has taken place. In many cases the model is chosen on the basis of detection theory to try to guess the probability of an outcome given a set amount of input data, for example given an email determining how likely that it is spam. Models can use one or more classifiers in trying to determine the probability of a set of data belonging to another set, say spam or ‘ham’. Depending on definitional boundaries, predictive modelling is synonymous with, or largely overlapping with, the field of machine learning, as it is more commonly referred to in academic or research and development contexts. When deployed commercially, predictive modelling is often referred to as predictive analytics.


You are not allowed to move points A and B. You must move points C and D until ABCD is a rectangle (or square), with 4 right angles. Write down the positions of C and D. After you have done that, find a different solutions for C and D. When you are finished, you should have made one RECTANGLE and one SQUARE.
Can you find a GENERAL DESCRIPTIOIN for ALL the possible solutions for C and D?
Dave Mulkey, Created with GeoGebra


After the pre-processing steps and optional quality check, it is possible to construct either supervised or unsupervised machine learning models. To avoid overfitting the models, dimensionality reduction is performed using principal component analysis (PCA) or a convolutional neural network (CNN). Depending on whether an identification or concentration determination is to be carried out, a classification or regression model is required. The following models are available in the software for this purpose:
Linear Discriminant Analysis (LDA);
Random Forest (RF);
k-nearest neighbours (kNN);
support vector machine (SVM);
partial least squares discriminant analysis (PLS-DA);
unsupervised hierarchical Ward cluster analysis (HCA);
partial least squares regression (PLSR).


Monthly EMI: ₹
Principal amount: ₹
Total interest: ₹
Total amount: ₹
The SBI car loan EMI calculator is a useful tool for individuals to determine their monthly payment amount for their car loan. It helps them plan and analyze if the payment is affordable for them.
- 1 What is the monthly installment for a 10 lakh car?
- 2 How Can SBI Car Loan EMI Calculator Prove Helpful?
- 3 Calculating car loan EMI from SBI: A step-by-step guide
- 4 Is SBI car loan beneficial or detrimental?
- 5 Does SBI car loan interest rate remain constant?
What is the monthly installment for a 10 lakh car?
To calculate the EMI, you need to consider three factors:
1. Principal Amount (P): This is the loan amount that you want to borrow, which in this case is Rs 10 lakh.
2. Rate of Interest per month (R): The annual interest rate needs to be converted into a monthly rate by dividing it by 100 and then by 12. In this case, it will be 12/100/12.
Using these values in the formula provided:
EMI = [P x R x (1+R)^N] / [(1+R)^N-1]
By substituting the values:
EMI = [10,00,000 x 12/100/12 x (1+12/100/12)^24] / [(1+12/100/12)^24-1]
EMI = Rs 47,073
So according to this calculation method and example given above, if you take a car loan of Rs 10 lakh from SBI at an interest rate of 12%, your approximate monthly installment or EMI will be around Rs 47,073 for a period of two years or twenty-four months.
How Can SBI Car Loan EMI Calculator Prove Helpful?
SBI offers a variety of car loan options that are designed to meet the specific needs of borrowers.
SBI offers various car loan schemes for different needs. The SBI New Car Loan Scheme is designed for those who want to buy a new car. If you are looking to purchase both a two-wheeler and a four-wheeler, the SBI Combo Loan Scheme is available. Individuals interested in buying certified pre-owned cars can opt for the SBI Certified Pre-Owned Car Loan. Borrowers of SBI home loans can also avail the SBI Loyalty Car Loan Scheme. Lastly, there is the SBI Nano Youth Car Loan Scheme which specifically targets Indian youth and aims to promote Tata Nano cars among them.
The SBI car loan options have varying repayment periods and are offered at different interest rates.
The duration of the loan, the amount borrowed, and the interest rate all play a role in determining the monthly EMI payment. If a borrower chooses a shorter tenure for their loan, they will have to pay a higher EMI amount.
Here are some examples of car loan amounts, tenure, interest rates, and corresponding EMIs in Indian Rupees:
– For a car loan amount of Rs. 5 lakh with a tenure of 1 year and an interest rate of 8.7%, the EMI is Rs. 43,656.
– If the same loan amount is taken for a longer tenure of 4 years at the same interest rate, the EMI reduces to Rs. 12,371.
– A car loan amount of Rs. 10 lakh with a tenure of 1 year and an interest rate of 8.7% results in an EMI of Rs.87,312.
– Extending the tenure to 4 years for this amount brings down the EMI to Rs.24,743.
– Lastly, for a higher car loan amount like Rs.15 lakh with a tenure of either one or four years at an interest rate of 8.7%, the respective EMIs would be approximately Rs130969 andRs37 ,114.
Individuals in India can easily calculate their car loan equated monthly installment (EMI) using the SBI car loan calculator. This convenient tool allows borrowers to determine their EMI based on their preferred loan option, making the process hassle-free and efficient.
SBI Car Loan EMI Calculation: A Guide for 2022
The EMI amount for SBI Car Loan is calculated using a specific formula, which is mentioned below.
- ‘P’ stands for the principal amount or the loan amount.
- ‘R’ stands for the monthly rate of interest that is applicable.
- ‘N’ stands for the number of instalments.
Please be aware that the calculation method does not consider any pre-payment made towards the SBI car loan amount.
The following illustration will provide you with a clear understanding of the functioning of the SBI car loan calculator.
Mr. J obtained a car loan from SBI worth Rs. 5 Lakh with an annual interest rate of 8.7% for a duration of 5 years.
Advantages of Using Groww’s SBI Car Loan EMI Calculator 2022
Individuals can avail themselves of several advantages by using Groww’s calculator. A few of them are listed below:
1. Complicated computations can be swiftly resolved.
2. The fractional interest rate is effortlessly calculated to provide precise outcomes.
3. Assists in determining a convenient EMI amount and repayment duration.
4. Permits multiple adjustments to suit individual preferences.
Therefore, before availing of an SBI Car Loan, make sure to find out the most convenient EMI amount with the help of Groww’s SBI Car Loan EMI calculatorat the earliest. It will ensure that you can plan your budget in a much effective way.
Are you interested in making investments? Begin your investment journey with Groww by opening an account and enjoy the benefits of investing directly, without any charges.
SBI Car Loan EMI Calculator is a useful tool provided by State Bank of India to help individuals in India calculate their car loan EMIs easily and conveniently. With this online calculator, borrowers can determine the monthly installment amount they need to pay towards their SBI car loan. It simplifies the process of budgeting and planning for repayment, allowing customers to make informed decisions when it comes to purchasing a new or used car with an SBI car loan.
Calculating car loan EMI from SBI: A step-by-step guide
In India, when calculating the EMI (Equated Monthly Installment) for an SBI car loan, there are three important variables to consider:
1. Principal Amount (P): This refers to the total loan amount that you borrow from SBI.
2. Monthly Rate of Interest (R): This represents the interest rate charged by SBI on a monthly basis for your car loan.
3. Number of Instalments (N): This indicates the total number of monthly instalments over which you will repay your car loan.
By considering these variables and using an EMI calculator, you can determine the exact amount you need to pay each month towards your SBI car loan repayment.
Is SBI car loan beneficial or detrimental?
SBI Car Loan offers the perfect financing solution for purchasing your new vehicle. With a tenure range of 7 years, SBI provides a longer repayment period compared to other lenders who typically limit it to 5 years. This extended tenure allows borrowers more flexibility in managing their monthly installments and makes owning a car more affordable.
Using an EMI calculator can be highly beneficial when planning for your car loan from SBI. This tool helps you estimate your monthly installment amount based on factors like loan amount, interest rate, and repayment tenure. By using this calculator, you can assess whether the proposed EMI fits within your budget and make informed decisions about borrowing from SBI.
Does SBI car loan interest rate remain constant?
– SBI Car Loan Interest Rate for New Car Loans starts at 8.75% p.a.
– SBI Car Loan Interest Rate for Used Car Loans starts at 11.40% p.a.
– These interest rates are fixed and considered to be one of the most affordable in India.


Bio of Turing
More about Turing
Books on Turing
By Jack Copeland
© Copyright B.J. Copeland, May 2000
O-machines are a type of abstract machine. They generate digital output from digital input by means of a step-by-step procedure consisting of repeated applications of a small, fixed number of atomic operations. The procedure unfolds under the control of a finite program of instructions which (as with the universal Turing machine) is stored in the form of data on the machine's tape.
Turing introduced the concept of an O-machine in his PhD thesis (Princeton, 1938). (The thesis was supervised by Alonzo Church.) This was subsequently published as 'Systems of Logic Based on Ordinals', Proceedings of the London Mathematical Society, series 2, vol. 45 (1939): 161-228. This paper is now a classic of recursive function theory.
The atomic operations of a Turing machine are six in number: (i) move the tape left one square; (ii) move the tape right one square; (iii) read (i.e. identify) the symbol currently under the head; (iv) write a symbol on the square of tape currently under the head (after first deleting the symbol already written there, if any); (v) change state; (vi) halt. These primitive operations are made available by unspecified subdevices of the machine - 'black boxes'. An O-machine is a Turing machine augmented with one or more atomic operations each of which returns the values of some function (on the natural numbers) that is not Turing-machine-computable. Each additional atomic operation is made available by a black box. Turing refers to these black boxes as 'oracles'. He remarks that an oracle works by 'unspecified means' and says that we need 'not go any further into the nature of [these] oracle[s]'.
Each oracle returns the values of a two-valued function. Let these values be written 0 and 1. Let p be one of the additional primitive operations. p is called into action by means of a special state c, the call state. (Where an O-machine has several of these additional primitives, a corresponding number of call states is required.) The machine inscribes the symbols that are to form the input to p on any convenient block of squares of its tape, using occurrences of a special symbol µ, the marker symbol, to indicate the beginning and the end of the input string. As soon as an instruction in the machine's program puts the machine into state c, the input is delivered to the subdevice that effects p, which then returns the corresponding value of the function.
The subdevice that effects p might simply write this value on the tape. On Turing's own way of handling matters, the value is not written on the tape; rather a pair of states, the 1-state and the 0-state, is employed in order to record values of the function. A call to p ends with a subdevice placing the machine in one or other of these two states according to whether the value of the function is 1 or 0.
When a function g is computable by an O-machine whose (only) oracle serves to return the values of a function f, then g is said to be computable relative to f.
One particular O-machine, the halting function machine, has as its 'classical' part the universal Turing machine specified by Turing in his paper of 1936 ( 'On Computable Numbers, with an Application to the Entscheidungsproblem') and as its 'nonclassical' part a primitive operation that returns the values of the halting function H(x,y).
The halting function is defined like this:
The halting function machine can compute many functions that are not Turing-machine-computable. This is because of the familiar phenomenon of the reducibility of one function to others (in the sense that multiplication is reducible to addition, for example). All functions reducible to the halting function and/or the atomic operations of an ordinary Turing machine are computable by the halting function machine.


- Extracting Interpretable Physical Parameters from Spatiotemporal Systems Using Unsupervised LearningPhys. Rev. X 2020
Experimental data is often affected by uncontrolled variables that make analysis and interpretation difficult. For spatiotemporal systems, this problem is further exacerbated by their intricate dynamics. Modern machine learning methods are particularly well-suited for analyzing and modeling complex datasets, but to be effective in science, the result needs to be interpretable. We demonstrate an unsupervised learning technique for extracting interpretable physical parameters from noisy spatiotemporal data and for building a transferable model of the system.
We implement a physics-informed architecture based on variational autoencoders (VAEs) that is designed for analyzing systems governed by partial differential equations (PDEs). The architecture is trained end-to-end and extracts latent parameters that parameterize the dynamics of a learned predictive model for the system.
To test our method, we train our model on simulated data from a variety of PDEs with varying dynamical parameters that act as uncontrolled variables. In particular, we generate datasets using the 1D Kuramoto–Sivashinsky (KS) equation (with varying viscosity damping parameter acting as an uncontrolled variable) the 1D nonlinear Schrödinger (NS) equation (with varying nonlinearity coefficient ) and the 2D convection–diffusion (CD) equation (with varying diffusion constant and drift velocity )
Numerical experiments show that our method can accurately identify relevant parameters and extract them from raw and even noisy spatiotemporal data (tested with roughly 10% added noise).
These extracted parameters correlate well (linearly with R2 > 0.95) with the ground truth physical parameters used to generate the datasets.
We then apply this method to nonlinear fiber propagation data, generated by an ab-initio simulation, to demonstrate its capabilities on a more realistic dataset.
Our method for discovering interpretable latent parameters in spatiotemporal systems will allow us to better analyze and understand real-world phenomena and datasets, which often have unknown and uncontrolled variables that alter the system dynamics and cause varying behaviors that are difficult to disentangle.
Please see our paper for more details.


To understand the calculation of Numerology numbers, refer back to my previous post here. With that understanding combined with a general grasp on Tarot, you’ll be able to coax more information out of a reading. To begin, lets for example take a quick three card reading. Lets just say you drew the Three of Wands, Six of Swords and Seven of Cups.
3 + 6 + 7 = 16
1 + 6 = 7
Your reading would amount to a 7, therefore you could integrate the reputation of the 7 into your interpretation of the cards. In my tutorial on basic Numerology, I went into the keywords behind numbers.
Major Arcana cards draw as the number that represents them. The Fool is zero, followed by The Magician as one, and so on. Aces assimilate to one’s. The Court cards follow the number ten in their respective order.
Pay attention to:
- Repetitive numbers
- Repetitive numbers accumulating in the length of time something could occur in
- Sequential numbers meaning when something will start and end (in steps)
- Sequential numbers meaning the intensity of a situation in the layout of the cards
In timing, the categories of the cards can appear as so:
- Wands – Days or Summer
- Swords – Weeks or Spring
- Cups – Months or Autumn
- Pentacles – Years or Winter
Odd numbers are usually seen as masculine (breaking away, leadership) while even numbers ring as feminine (balance, harmony).


- What is the probability of being born on:
a) February 28?
b) February 29?
c) February 28 or February 29?
- A patient newly diagnosed with a serious ailment is told he has a 60% probability of surviving 5 or more years. Let us assume this statement is accurate. Explain the meaning of this statement to someone with no statistical background in terms he or she will understand.
- A lottery offers a grand prize of $10 million. The probability of winning this grand prize is 1 in 55 million (about 1.8×10-8). There are no other prizes, so the probability of winning nothing = 1 – (1.8×10-8) = 0.999999982. The probability model is:
Winnings (X) 0 $10 x 106
P(X = xi) 0.999999982 1.8 x 10-8
a) What is the expected value of a lottery ticket?
b) Fifty-five million lottery tickets will be sold. How much does the proprietor of the lottery need to charge per ticket to make a profit?
- Suppose a population has 26 members identified with the letters A through Z.
a) You select one individual at random from this population. What is the probability of selecting individual A?
b) Assume person A gets selected on an initial draw, you replace person A into the sampling frame, and then take a second random draw. What is the probability of drawing person A on the second draw?
c) Assume person A gets selected on the initial draw and you sample again without replacement. What is the probability of drawing person A on the second draw?
- Let A represent cat ownership and B represent dog ownership. Suppose 35% of households in a population own cats, 30% own dogs, and 15% own both a cat and a dog. Suppose you know that a household owns a cat. What is the probability that it also owns a dog?
- What is the complement of an event?
- Accidents occur along a 5-mile stretch of highway at a uniform rate. The following “curve” depicts the probability density function for accidents along this stretch:
a) What is the probability that an accident occurred in the first mile along this stretch of highway?
b) What is the probability that an accident did not occur in the first mile?
c) What is the probability that an accident occurred between miles 2.5 and 4?
- Suppose there were 4,065,014 births in a given year. Of those births, 2,081,287 were boys and 1,983,727 were girls.
a) If we randomly select two women from the population who then become pregnant, what is the probability both children will be boys?
b) If we randomly select two women from the population who then become pregnant, what is the probability that the first woman’s child will be a boy and the second woman’s child will be a boy?
c) If we randomly select two women from the population who then become pregnant, what is the probability that both children will be boys given that at least one child is a boy?
- Explain the difference between mutually exclusive and independent events.
- Suppose a screening test has a sensitivity of 0.80 and a false-positive rate of 0.02. The test is used on a population that has a disease prevalence of 0.007. Find the probability of having the disease given a positive test result.


Title: Turing Machine Automata | Turing Machine Example: a^n b^n c^n Turing Machine Theory of Computation
Welcome to this comprehensive video that delves into the fascinating world of Turing Machine Automata. In this tutorial, we will explore the concept of Turing Machines and their application in the theory of computation. Join us as we unravel the intricacies of a standard example, a^n b^n c^n Turing Machine, and gain a clear understanding of its functioning and significance.
H2: Video Content
In this video, we provide a detailed explanation of the Turing Machine Automata concept, focusing on the renowned a^n b^n c^n Turing Machine example. By carefully dissecting each component, we guide you through the theory of computation, ensuring you grasp the core concepts effortlessly.
We start by elucidating the fundamental principles behind Turing Machines, exploring their pivotal role in the theory of computation. Through a step-by-step breakdown, we examine the a^n b^n c^n Turing Machine, shedding light on its structure, states, and transitions. Witness how this example encapsulates the concept of automata and its relevance in solving computational problems.
As we progress, we dive deeper into the intricacies of the a^n b^n c^n Turing Machine, explaining the significance of the input alphabet, tape, and head movements. Follow along as we demonstrate how this Turing Machine recognizes and processes the pattern a^n b^n c^n, providing you with a comprehensive understanding of its operations.
Throughout the video, we highlight key insights and interesting facts, ensuring an engaging learning experience. Delve into the world of Turing Machine Automata and witness the power of computation theory unfold before your eyes.
H2: Additional Tags and Keywords
To enhance the visibility of this video in search results, we have included some relevant tags and keywords: Turing machine example, Turing machine theory, automata concept, theory of computation, a^n b^n c^n Turing machine, Turing machine explained, computational problems, tape head movements.
Hashtags: #TuringMachine #AutomataTheory #TheoryofComputation #TuringMachineExample #ComputationalProblems #ANBN #CN
We hope you find this video enlightening and informative, providing you with a solid foundation in the theory of computation and the concept of Turing Machines. Join us on this educational journey and unravel the mysteries of the a^n b^n c^n Turing Machine!
orbital stretch wrapper
Turing Machine: Theory of Computation with Equal Number of a’s, b’s, and c’s


Early Maths Resources
General tips that can make a difference in maths
•Provide lots of opportunities to say how many things you can see (up to 5) without counting.
•Whenever you talk about a small set of objects, say the number. For example, please pick up those 3 teddies or look at those 2 dogs.
•Count up (starting from one) when walking upstairs and count back when walking downstairs.
•Count lots of different objects, big and small, and ask ‘How many are there?’ Your child should be able to tell you without going back and re-counting. If they can’t, then tell them: ‘There are 6 altogether’.
•Play with fingers, firstly practise counting fingers.
•Ask your child to put their fingers down and then say or hold up a number such as 3. Can they do it without counting? Can they do it using different fingers? Can they do it using fingers from two hands?
•Play board games with your child which involve moving along numbered tracks, such as ‘Snakes and Ladders’. Check that your child counts along the track correctly, moving one square for each number counted.
•Notice when there are two amounts and one is more than the other, or they are the same. For example, I have 2 eyes and 2 ears, or I have more chips than peas.
•Talk about and describe shapes you can see outside or around your home. For example, count corners, talk about straight/curved edges, flat/curved surfaces. If you have building blocks then talk about and describe the things that are built.
•In the bath or at the sink, play with containers, pouring water, counting how many small pots are needed to fill the big container.
•Encourage your child to draw a picture of their number work and explain their mark-making to you, for example, how many leaves they find on a walk. This doesn’t necessarily mean writing the numerals (1, 2, 3, 4… etc.).
•Sing counting songs and rhymes. You can find some on the internet, but children love it if you join in with them!
•Make a deliberate maths mistake from time to time and ask your child to explain why you are wrong. For example, say that 4 is bigger than 5.


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Active and Semi-supervised Graph Neural Networks for Graph Classification
Authors: Yu xie,Shengze Lv, Yuhua Qian,Chao Wen,JiyeLiang
Graph classification aims to predict the class labels of graphs and has a wide range of applications in many real-world domains. However, most of existing graph neural networks for graph classification tasks use 90% of labeled graphs for training and the remaining 10% for testing, which obviously struggle in solving the problem of the scarcity of labeled graphs in real-world graph classification scenarios. And it is arduous to label a large number of graph examples for training because of the difficulty and resource consumption in the tagging process. Motivated by this, we propose a novel active and semi-supervised graph neural network (ASGNN) framework, which endeavors to complete graph classification tasks with a small number of labeled graph examples and available unlabeled graph examples. In our framework, active learning selects high-uncertain and representative graph examples from the test set and add them to the training set after annotation. Semi-supervised learning is utilized to select the high-confidence unlabeled graph examples containing structural information from the test set, and add them to the training set after pseudo labeling. To improve the generalization performance of the graph classification model, multiple GNNs are trained collaboratively for promoting the expressiveness of each other and increasing the reliability of graph classification results. Overall, the ASGNN framework takes fully use of unlabeled graph examples to reinforce graph classification effectively, and can be applied to any existing supervised graph neural networks for graph classification. Experimental results on benchmark graph datasets demonstrate that the proposed framework yields competitive performance on graph classification tasks with only a small number of labeled graph examples.
Keywords： Graph neural networks, active learning, semi-supervised learning, graph classification
Thu Mar 03 08:50:19 CST 2022


Here’s another comment we hear a lot ……
“Okay … I understand the concept and progression of fractional drill bits … but what in the world are numbered bits and lettered bits?”
Simply put, there is a whole world of sizes that exist tucked in between the fractional sizes. For example …. The normal drill index goes from 1/8 to 9/64 to 5/32.
There are actually 8 more sizes of drill bits that are readily available between the 1/8 and 5/32.
Numbered bits are related to wire size, so the larger the number, the smaller the size. The numbering sequence starts with the smallest drill size #80 which is at a decimal size of .0135. as the numbers decrease, the drill bit size increases till it reaches a number 1 drill bit which is equal to .2280.
Lettered drill bits start with a letter A which is equal to a .2340 decimal size. They progress in size till they hit the letter Z which is a decimal size .4130
If you go to our website and click on the technical chart tab, then click on the Decimal / Metric tab, you can see exactly how how all the numbered, fractional, metric, and letter sizes interact.


Diophantus, known as the Father of Algebra, lived in Alexandria, Egypt during the 3rd century A.D. Little else is known about his personal life. He was the author of the first Greek text on the essential branch of mathematics we know as algebra.
His book, Arithmatica, included thirteen books with numerical answers to algebraic questions. Using only positive rational numbers because zeros, negative numbers and irrational numbers were not available to him at the time –
Diophantus algebraically solved linear and quadratic equations, in addition to simultaneous linear and quadratic equations. With awareness of essential theorems in the number theory, he also found algebraic solutions to questions such as finding the value of y so that some polynomial equations in y are either squares of numbers or their cubes.
Arithmatica solved a total of one hundred and thirty mathematical problems for its readers. Apart from this important text on algebra, Diophantus has been credited with introducing techniques for solving both determinate as well as indeterminate equations. He also developed the method of using symbols for words in algebra. Still, Arithmatica continues to be remembered as one of the most significant works of his life, for the simple reason that the sciences of modern times could not have progressed without the tool of algebra.
As a matter of fact, algebra is an integral part of modern existence. Both industry and our daily lives depend on this tool. As examples, algebraic formulas for calculating loan installments; bank interest; distance, speed, and time; and volume, area and perimeter are as indispensable as the variables, relations and functions used in the analysis of activities that involve costs.
So, whether we are dealing with the business of construction, managing expenses as consumers, or working on new innovations in chemistry labs, we know it is virtually impossible to do away with algebra – thanks to Diophantus who first introduced the importance of this mathematical tool to the world.
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To refresh your memory, here’s a description of how my model works.
Predictions for the twelfth round are given in the table below. The priors for these distributions are based on the final abilities from last season and the results to round 12.
|Chance of home team winning
|Sunshine Coast Lightning
|West Coast Fever
Score Differential Distributions
The distribution of the predicted score differentials is shown in the figures below. For each game, the chance of the home team winning is calculated and shown in the figure title. Each distribution is coloured by the team’s colours, and the more of a single team’s colour, the higher the chance that team has of winning. Overlaid on each figure are two vertical, dashed dark green lines; these show the score differential that has a 50% predicted chance of happening.
Comparison of Game Results Against Predictions
The following figure shows the results (score difference of the home team) in round 12 (blue vertical line) against the predictions from the model.


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Project needs two variables to calculate the third. You assigned a duration of 3 days, which by default a day is 8 hours. So that put the work at 24hrs. Resource has 100% units assigned by default. So when you assigned the resource to that task, project calculated 8 hours a day because the units for that resource was automatically at 100%.
When you went back and changed the work to 12 hours for work, then project had to recalculate how much work each day the resource could do to keep the duration at 3 days.
As long as the assigned work hours for that resource is less than 8 hours for the day then the resource units for each of the tasks can be 100%.
Since project needs 2 of 3 variables to calculate the third, enter the work hours after the duration, then enter the resource.


A positive number designates a count, this is the quantity of items or the counting number of the item, which cannot be said about the negative number. A negative number, strictly speaking, does not have any numerical meaning, it rather symbolizes a future action. A negative number shows that in the future from the newly appeared items we should subtract a few ones.
The logical and elegant solution is to represent negative numbers in the form of empty cells. Suppose that there is a set of counting sticks, and it is known the standard number of sticks in the set. After execution of any actions over this set, the remaining sticks in the set will denote a positive number, empty cells will denote a negative number. It is easy to see that with such an approach, any number of sticks in the set symbolizes two numbers at once, both positive and negative. Depending on our agreement, one of these numbers will be explicit, the other implicit.
The numerical multitude of our set looks unusual, because it has two zeros (Fig.1). Suppose that for our set of countable sticks is fulfilled the following condition: with the maximum number of sticks in the set they disappear, that is, the maximum number of sticks is zero. Then the multitude of numbers, that can display a set, is convenient to represent in form of a ring (Fig.2).
Just like this the processor sees the numbers, which is easy to verify. For example, we will subtract in a cycle from the byte variable a one in each step. When the value of the variable reaches zero, by the next subtraction we will receive in a variable the value of 255. This is the maximum number that can be written to a byte. By successive subtraction, the number 255 again will be reduced to zero, when we subtract one from zero, we again get 255. This will continue for as long as we want, until we stop the program.
This principle of work with numbers is in good agreement with the characteristics of computers.
The cells (bytes, words, double words, etc.), in which the computer stores the numbers, are finites.
In addition, such a principle ensures easy execution of arithmetic operations. For example, the
subtraction can be replaced by an addition, if you invert the substracted number. For a byte,
i.e. for a set of 256 counting sticks (256 is zero):
Call such a representation of negative numbers by inversion with a complement, that is, to obtain a representation of a negative number, the bits of a compatible with it positive number are inverted, and to the result the one is added. The one is added because the maximum number in the set, in application to the memory cells in the computer, it is convenient to suppose the first number which does not fit in the cell. When this number is reached, zero is obtained automatically and the count starts again.
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When I was in college, I really enjoyed my theoretical math classes. But at the same time, I was aware that they were a dead end of sorts – theorems and proofs had little to do with most real-world work. Unless I was going to obtain a doctorate, this kind of math was only really necessary to help shape our minds so that we can solve other problems in our real careers. At one point I wanted to teach high school math, where that sort of thinking was the norm. Were students really going to use the quadratic equation in real life? Certainly not, we had calculators and computers to do that for us. Just like strength training, math exercises are a preparation for something a bit different.
But like most of us, life played out differently and I ended up in a career that suited my skillset more – cost estimating. It was nice to discover another field where math wasn’t just a bunch of theories, but tools people could use to solve real life problems.
When I joined PRICE in 2017, I had only a little bit of knowledge of the cost estimation industry. I knew it used a combination of math, engineering, and research. In fact, to be a part of the Cost Research department at PRICE®, one needs to be a generalist of the cost estimation field (or for a fun pun, a “polymath”). This is because our Technology creates predictive, prescriptive models for many different types of aerospace and defense products (software, IT, hardware, etc.) for the lifecycles of programs. So, I had a lot to catch up on when I first started working here. And I still learn every single day…
It may not be teaching High School math, but I’m lucky to have a job where it’s required that I synthesize knowledge growth instead of staying stagnant.


Lifelong learning is a good practice to have in the world of fast pace changes in technology. Today there are several opportunities to pick up new skills and learn new subjects online. Over the past year, I have found several free resources to learn and actually receive a completion certificate from top universities. Subjects covered include (but not limited to) business, finance, the sciences, engineering, programming, math and philosophy.
Check out the links below and see if there may be something worth your time:-)
MIT Open Courseware: http://ocw.mit.edu/index.htm