The Sieve of Erasthotenes is a very old algorithm to find by elimination the prime numbers up to a given integer N.
The manual process is so:
- write down the numbers from 2 to N (say 100)
- stripe the multiples of 2, except 2
- stripe the multiples of 3 not yet striped, except 3
- iterate the process for the next unstriped number k: stripe the multiples of k not yet striped, except k.
- continue until you get no more unstriped multiples before N
The unstriped remaining numbers are the numbers that are not a multiple of any previous number. Thus they have no divisor except themselves and 1, that is the definition of a prime number.
Until the recent times, the Sieve of Erasthothene could only be used for small prime numbers, say until 100.
But nowadays, we have processors with programing languages, so that we can apply the algorithm to much bigger numbers.
For the scientific programing language Scilab®, we may use the following script:
function P=PrimeNumbers(N) // computes the prime numbers up to the integer N // applies the Sieve of Erastotenes // Initialisation IsPrime(1)=%f; for k=2:N IsPrime(k)=%t; end // Sieve of Erastones for k=1:N // number not yet erased if IsPrime(k) // Erase the multiples of k // from 2*k to N by steps of k for n=2*k:k:N IsPrime(n)=%f; end end end // The prime numbers are at the indexes set to %t (true) P=find(IsPrime); endfunction
We may then calculate the prime numbers up to a very big number, for instance 100,000.
So, we have learned today that 98,947 was a prime number…


11 domain and range assignment answers
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Domain and Range
Intro to functions. Domain and range. Function notation. Linear vs Quadratic functions. Investigating the roles of a, h and k in the vertex form.Bootstrap pie chart codepen
Sketching quadratics functions in vertex form. Properties of a Parabola Assignment -found at the end of Day 6 handout. Changing from vertex form to standard expanded form.Metasploitable 3 linux flags
Completing the Square. Completing the Square:. Part 2. Word Problems Part 2. Word Problems Assignment. Test Review. Types of Factoring Note. Factoring: Special cases. Factoring Assignment. Quiz: Factoring. Graphs of quadratics in factored form :. Relating roots and zeros of quadratic functions. Graphing factored form notes. Nov Graphs of quadratics in factored form : Part 2. Converting between the three forms of a quadratic function. Quadratic formula. The Discriminant. Quiz: Quadratic formula.
Word Problems: Population growth, integers, geometric areas. Assessment and Evaluation. Wasylnka's Grade 11 Mixed Math. Search this site. Wasylnka's Classroom Home. Exponential Functions. Quadratic Functions.
December exam review. Homework Assignments. Contact Me.Notice that we can use the data to create a function of the amount each movie earned or the total ticket sales for all horror movies by year. In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range.
In this section, we will investigate methods for determining the domain and range of functions such as these. In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section, we will practice determining domains and ranges for specific functions. Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above.
We also need to consider what is mathematically permitted. For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers. Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by 0. We can write the domain and range in interval notationwhich uses values within brackets to describe a set of numbers. In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis to indicate that the endpoint is either not included or the interval is unbounded.
We will discuss interval notation in greater detail later.
Domain And Range Worksheet 2 Answers
Oftentimes, finding the domain of such functions involves remembering three different forms. First, if the function has no denominator or an even root, consider whether the domain could be all real numbers.
Third, if there is an even root, consider excluding values that would make the radicand negative. First identify the input values. The input value is the first coordinate in an ordered pair. There are no restrictions, as the ordered pairs are simply listed. The domain is the set of the first coordinates of the ordered pairs.
How To: Given a function written in equation form, find the domain.Here is a graphic preview for all of the Domain and Range Worksheets. You can select different variables to customize these Domain and Range Worksheets for your needs. The Domain and Range Worksheets are randomly created and will never repeat so you have an endless supply of quality Domain and Range Worksheets to use in the classroom or at home.
We have domain and range mapping diagrams, identifying functions from graphs, determining domains and ranges from graphs, and determining domains and ranges from ordered pairs. Our Domain and Range Worksheets are free to download, easy to use, and very flexible. These Domain and Range Worksheets are a good resource for students in the 9th Grade through the 12th Grade. Identifying Functions from Mapping Diagrams Worksheets These Algebra 1 Domain and Range Worksheets will produce problems for identifying whether mapping diagrams are functions or not.
You can select the types of values as well as the number of values in each mapping diagram. Identifying Functions from Ordered Pairs Worksheets These Algebra 1 Domain and Range Worksheets will produce problems for finding the domain and range of sets of ordered pairs.
You can select the range of numbers used in ordered pairs as well as whether the sheet should ask if each set of pairs is a function or not.
Identifying Functions from Graphs Worksheets These Algebra 1 Domain and Range Worksheets will produce problems for identifying whether graphed sets are functions or not.
You can select the types of functions and non-functions to be graphed. Identifying Domains and Ranges from Graphs Worksheets These Algebra 1 Domain and Range Worksheets will produce problems for finding the domain and range of graphed sets. You can select the types of things graphed as well as whether the sheet should ask if each graph is a function or not. Worksheets By Topics. Identifying Functions from Mapping Diagrams.
Identifying Functions from Ordered Pairs. Identifying Functions from Graphs. Identifying Domains and Ranges from Graphs.
All rights reserved.What is a domain? What is a range? Why are they important? How can we determine the domain and range for a given function?
Algebra II : Domain and Range
It is the set of all values for which a function is mathematically defined. It is quite common for the domain to be the set of all real numbers since many mathematical functions can accept any input.Domain and Range Word Problems
For example, many simplistic algebraic functions have domains that may seem… obvious. What values can we put in for the input x of this function? Well, anything! The answer is all real numbers.
Only when we get to certain types of algebraic expressions will we need to limit the domain. We can demonstrate the domain visually, as well. What values are valid inputs? Visually we see that as a line that extends forever in the x directions left and right.Snsd instagram
A straight, horizontal line, on the other hand, would be the clearest example of an unlimited domain of all real numbers. What would stop us, as algebra students, from inserting any value into the input of a function? We need a function that, for certain inputs, does not produce a valid outputi. Here is an example:. This function is defined for almost any real x. Division by zero is undefined. Therefore 1 is not in the domain of this function.
We cannot use 1 as an input, because it breaks the function. Makes sense, right? Look for places that could result in a division by zero condition, and write down the x-values that cause the denominator to be zero. Those are your values to exclude from the domain. Why does that cause issues with the domain?
Because, at least in the realm of real numbers, we cannot solve for the square root of a negative value. What values are excluded from the domain? Anything less than 2 results in a negative number inside the square root, which is a problem. Therefore the domain is all real numbers greater than or equal to 2. However, the most common example of a limited domain is probably the divide by zero issue. When asked to find the domain of a function, start with the easy stuff: first look for any values that cause you to divide by zero.
In that case, it would not be a valid input so the domain would not include such values. The range of a simple, linear function is almost always going to be all real numbers. A graph of a typical line, such as the one shown below, will extend forever in either y direction up or down. The range of a non-horizontal linear function is all real numbers no matter how flat the slope might look.Xamarin forms navigation bar icon
In that case, the range is just that one and only value.What are the domain and range of this function? A sine curve represent a wave the repeats at a regular frequency. The x-values span all real numbers, as there is no limit to the input fo a sine function.
The domain of the function is all real numbers and the range is. A function has to pass the vertical line test, which means that a vertical line can only cross the function one time. To put it another way, for any given value ofthere can only be one value of. For instance, ifthen. But ifas well. This function fails the vertical line test.
The other functions listed are a line,the top half of a right facing parabola,a cubic equation,and a semicircle. These will all pass the vertical line test.
The domain is the set of possible value for the variable. We can find the impossible values of by setting the denominator of the fractional function equal to zero, as this would yield an impossible equation.
Now we can solve for. There is no real value of that will fit this equation; any real value squared will be a positive number. The radicand is always positive, and is defined for all real values of. What is the domain of the function? This function is a parabola that has been shifted up five units. The standard parabola has a range that goes from 0 inclusive to positive infinity. If the vertex has been moved up by 5, this means that its minimum has been shifted up by five.
Based on the members of the function, the only limit that you have is the non-allowance of a negative number because of the square root. The square and the linear terms are fine with any numbers. You cannot have any negative values, otherwise the square root will not be a real number.Of which being said, we supply you with a assortment of simple yet beneficial content as well as templates designed well suited for virtually any academic purpose.
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In that match the result was 0-0 when they had more players in the field. It was also the first time they failed to score, but it should be said that after Barcelona, they are still the most potent and attacking team in La Liga.
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1.3: Domain and Range
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24. This week select a blank space on the wall, or any other convenient spot, from where you usually sit, mentally draw a black horizontal line about six inches long, try to see the line as plainly as though it were painted on the wall; now mentally draw two vertical lines connecting with this horizontal line at either end; now draw another horizontal line connecting with the two vertical lines; now you have a square. Try to see the square perfectly; when you can do so draw a circle within the square; now place a point in the center of the circle; now draw the point toward you about 10 inches; now you have a cone on a square base; you will remember that your work was all in black; change it to white, to red, to yellow.
25. If you can do this, you are making excellent progress and will soon be enabled to concentrate on any problem you may have in mind.


Welcome to a new module, fellow classmates!
Reflecting back, I was a bit apprehensive at first when I knew it was going to be a math module as I was never good at math in primary and secondary school. My math journey spiraled downwards when application of complex formulas didn't make sense to me after Primary Four and I rarely had Math teachers who had the time to explain and be patient with me. Most just hurried me along to find the answer and got impatient. Scoldings were common, sad to say. Tuition didn't help and math was a ever growing nightmare. I was relieved that after Sec 4, I didn't have to sit for another math paper again though failing it at O levels caused a big ? for future studies. So the problem didn't end there.
Then when I became an early childhood educator, I knew I had to face my fears or my students would be just like me and it would plague them throughout their academic years. Attitude changed, time to solve the problems! Head on, let's go!
Dr Yeap's introduction and explanations throughout the night created a better understanding of why we can see math differently instead of being afraid of it. Perspectives can change, and methods should be taught differently to enable everyone to understand math and have the confidence to solve the math problem. It takes a light to brighten that dark room. In this case, mine! Thanks Dr Yeap!
My groupmates and I started off by tackling a math problem with our own names.
How would I reach 99 when I write my own name out? Hence starting with 1,2,3,4 counting from right to left...
J A N E
1 2 3 4
METHOD 1: Count all the way to 99 (tedious..)
METHOD 2: Count in 10s each time you see 10s in the "A" column
METHOD 3: Count all the numbers with the digit 9 in the ones place
METHOD 4: Count in multiples of 10
What we also discovered: "A" column can be counted in multiples of 6 which ends up with 96 at the end, and adding a 3, you'll get 99 in the "N" column which is the answer.
Then we figured out that 99 appears to be common in the 3rd letters of names with 6,5,9,7 and 4 letters. Wow! Level up...
We did the card trick, with some poker cards, and here's how we solved it:
Drawing out number words for each number (one, two, three... and so on) and drawing boxes to help with the counting...
O N E, T W O, T H R E E
which led us to the answer after some time of counting:
We then double confirmed this by trying out the cards. SUCCESS!
We had fun trying out the different shapes of the tangram to form rectangles...
First with four shapes...
Then with five...
Then with 7!
First night ended with renewed confidence to tackle more math problems. I am starting to see the puzzles fit together :)


Coursera Stanford Cryptography 1. These are my problem set and programming assignment solutions for the Spring 2014 term. ##NOTICE These solutions are for reference only and should not be viewed by students currently enrolled in the course. Students who view solutions to homework and programming assignments that they have not yet completed deprive themselves of learning and understanding. If. NovaLabs Cryptography Study Group : Coursera Cryptography I, Week 1 (free) Learn cryptography with Coursera's top-notch free course taught by Dr. Dan Boneh of Stamford University. Make the commitment now and pat yourself on the back 6 weeks later: NOTE: People just starting Dr. Boneh's course will be asked to pay $5 to NovaLabs to cover room cost. Please RSVP. Attendance is limited! The course. Mathematical Foundations of Public Key Cryptography Mathematical Foundations of Public Key Cryptography Xiaoyun Wang, Guangwu Xu, Mingqiang Wang, Xianmeng Meng October 21, 2015 by CRC Press Reference - 220 Pages October 22, 2015 by CRC Press October 22, 2015 by CRC Press Reference - 220 Pages Introduces number theor
Coursera Quiz Answers and Peer Graded Assignments. Get quiz answers and sample peer graded assignments for all the courses in Coursera. Course names are listed here. If you need answers for any new course, kindly make a request using the message option in home page. If you wish to donate answers for any course, send us a mail [Coursera] Introduction to Discrete Mathematics for Computer Science Specialization Topics cryptography probability coursera discrete-mathematics graph-theory combinatorics number-theory coursera-discrete-mathematic Coursera Cryptography Week 1 Answers | CryptoCoins Info Club Best cryptocoinsinfoclub.com Â· Cryptography And Information Theory Solutions to Coursera Course Mathematical Foundations ç for Cryptography part of the Intro to Applied Cryptography specialization. 178 People Learned More Courses âºâº View Course All About Cryptography. Introduction | by Mahasriram | Medium Online medium.com. Download Mathematical Foundations Of Public Key Cryptography PDF (11.00 MB) - PortalPDF Download Mathematical Foundations Of Public Key Cryptography PDF for free on PortalPDF. Detail Mathematical Foundations Of Public Key Cryptography PDF you can enjoy by clicking the download link below easily without disturbing ads. Original Nokia 112 Them
Mathematical Foundations for Cryptography Welcome to Introduction to Cryptography. We hope that the course course will give you some background on cryptographic algorithms and their applications. What is cryptography and why use it? How is cryptography developed? The course begins with an overview of modern cryptographic systems. They include public-key techniques, cleartext message. Â· Coursera; Cryptography I; Intro. Cryptography I. Final exam Congratulations!Coursera - Cryptography Dan Boneh, Professor, Stanford University Cryptography is an indispensable tool for protecting information in computer systems. ThisCryptography I - Final Exam Score of 11.00 out of 13.00. Question 1. Let (E, D) Labels: Coursera, Cryptography. Review -Mathematical Foundations for Cryptography- from Coursera on Courseroot. Get a great oversight of all the important information regarding the course, like level of difficulty, certificate quality, price, and more Comparing the Coursera and Udacity Cryptography classes Over the spring, I worked my way through two online cryptography classes: Professor Dave Evans's course, hosted at Udacity Taking both classes was not a waste; the two presentations nicely complemented and reinforced each other, and in the end I felt that I learned a lot from each. But there were both differences and similarities between.
Mathematical Foundations for Cryptography - Learn valuable skills with this online course from Coursera Find helpful learner reviews, feedback, and ratings for Mathematical Foundations for Cryptography from University of Colorado System. Read stories and highlights from Coursera learners who completed Mathematical Foundations for Cryptography and wanted to share their experience. I enrolled for this course because Number Theory is my area of interest
Coursera. Coursera provides universal access to the worlds best education, partnering with top universities and organizations to offer courses online. This course will introduce you to the foundations of modern cryptography, homework/assignments, via Coursera. Cryptography I. Stanford University; via Coursera. Crypto Number theory and cryptography coursera solutions I am facing trouble with rsa quest quiz and I am having a whole lot of errors. can anyone help me out please? thank you We all learn numbers from the childhood. Some of us like to count, others hate it, but any person uses numbers everyday to buy things, pay for services, estimated time and necessary resources. People have been wondering about. Are Coursera courses still free? At Class Central, I get that question so often that I wrote a guide to answer it. Generally speaking, Coursera courses are free to audit but if you want to access graded assignments or earn a Course Certificate, you will need to pay. This chang An Introduction to Mathematical Cryptography is an advanced undergraduate/beginning graduate-level text that provides a self-contained introduction to modern cryptography, with an emphasis on the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and.
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. The term Whitebox Cryptography is probably a marketing invention and a contradiction in itself. The Greek source of the term crypto refers to secret/hidden which is not really. This Coursera course on cryptography started last week, then Introduction to Mathematical Cryptography by Silverman etal is good. However for a more formal approach, Introduction to Modern Cryptography by Jonathan Katz and Yehuda Lindell, 2nd edition by CRC press is a nice textbook. If you are from Computer science background, Foundations of Cryptography by Oded Goldreich should be the. HN Academy has aggregated all Hacker News stories and comments that mention Coursera's Cryptography I from Stanford University. Cryptography is an indispensable tool for protecting information in computer systems. In this course you will learn the inner workings of cryptographic systems and how to correctly use them in real-world applications
Aug 25, 2019 - Offered by University of Maryland, College Park. This course will introduce you to the foundations of modern cryptography, with an eye Enroll for free Cryptography courses are now taught at all major universities, sometimes these are taught in the context of a Mathematics degree, sometimes in the context of a Computer Science degree and sometimes in the context of an Electrical Engineering degree. Indeed, a single course often need
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Roulette zero odd or even
Zero is an even number. In other words, its parity—the quality of an integer being even or odd—is even. This can be easily verified based on the definition of "even": it is an integer multiple of 2, specifically 0 × 2.
Odds for Single Zero & Double Zero Roulette But the odds for the other bets and wagers are affected as well. The following are the bets, payouts, and the Roulette odds for the single zero and double zero wheels. Roulette Odds for Single Zero Roulette Wheels. For wagers on red, black, odd, even 1 to 19, and 19 to 36 the payouts are 1 is to 1, and the probability is 48.65%. Roulette Even Odd Strategy – Roulette Strategy Taking advantage of biased wheels I even a lot more about. It has roulette done lots of roulette. I think casinos with old wheels are the odds vulnerable even. I've been saying for years that I think Argentina is a ripe target for that. When playing the Martingale double-up odd against the single-zero roulette roulette on any one of the even ... In Roulette Is 0 Odd Or Even - playtoponlinecasino.loan
The Even Bet in Roulette. The Wheel The game of American Roulette is played on a wheel which consists of thirty-eight slots, each with its own number. The numbers number a Roulette wheel arelarva pirate roulette, and The numbers alternate pairs of odd numbers with pairs of even numbers. The numbers also alternate between black and red.
The Roulette Wheel - How to worry the casino! American tables have a second green pocket, the double zero. This doubles the profits! Some places do play special rules regarding these zero pockets, e.g. if you bet on all the odd numbers and zero or double zero comes up, they only take half your money. How nice of them! Let's see what the chances are on a double zero wheel:
Чёт-нечёт – ставка на четные или нечетные номера, фишки ставят на поля рулетки с надписью «Even» - чётные или «ODD» - нечётные. http://aboutcasino.biz/ruletka_pravila.php.
Roulette is a drain on your wallet simply because the game doesn’t pay what the bets are worth. With 38 numbers (1 to 36, plus 0 and 00), the true odds of hitting a single number on a straight-upIf the ball lands on zero, your even-money bet doesn’t win or lose but remains locked up for one more spin. Roulette odd even odds | Fantastic Game online Betting on odd/even is a type of outside bets in roulette. As in betting on colors every win doubles the wager. Roulette is one of the easiest games to emailIn some forms of early American roulette wheels, there were numbers 1 through 28, plus a single zero, a double zero, and an American Eagle. Roulette Wheel | House odds and double zero Roulette Wheel. We can see that there's logic to the arrangement of scores around a dart board. Because of control, an informed player can makeThere are multiple ways to bet on a roulette wheel: Betting on a single number, betting if the number will be odd or even, betting if it will be red or black... Even Odds and colors betting system on roulette. Strategy… European single zero roulette betting system on Even & Odds, and Red & Black colors. The strategy win for this time, but to beat a roulette everytime, it's...
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Is Zero an Even or an Odd Number? | Britannica.com If yes, then it is even; if no, then it is odd. So where exactly does 0 fall into these categories? Most people are confused by the number 0, unsure if it’s an integer to begin with and unaware of its placement as a number, because it technically signifies an empty set. Under the rules of parity, is zero even or odd? Is zero odd or even? – The Straight Dope An odd integer can be written in the form 2N + 1 where N is some integer. In other words, an odd integer leaves a remainder of 1 when divided by 2. Under this definition, zero is clearly even, since 0/2 = 0 has no remainder. Zero also fits the nice pattern of alternating even/odd integers. Roulette Payouts - Roulette Payout Charts Explained Roulette offers a bewildering number of betting options, but the bets are actually straightforward enough. In order to make sure you get the correct payout, you’ll want to make sure that you put your chips in exactly the right place on the table. Missing a payout because your chip isn’t in the right spot is a drag. Roulette payouts work
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Extended UNIQUAC model
Extended UNIQUAC model
The Extended UNIQUAC model for electrolyte solutions is presented here in its current form as it was presented by Thomsen (1997) (ref 1). Previous versions of the model used composition dependent interaction parameters and included more terms (ref. 2 and 3). The model has proven itself applicable for calculations of vapor-liquid-liquid-solid equilibria and of thermal properties in aqueous solutions containing electrolytes and non-electrolytes. The extended UNIQUAC model consists of three terms: a combinatorial or entropic term, a residual or enthalpic term and an electrostatic term
The combinatorial and the residual terms are identical to the terms used in the traditional UNIQUAC equation (ref 4 and 5). The electrostatic term corresponds to the extended Debye-Hückel law. The combinatorial, entropic term is independent of temperature and only depends on the relative sizes of the species:
z = 10 is the co-ordination number. xi is the mole fraction, is the volume fraction, and θi is the surface area fraction of component i:
The two model parameters ri and qi are the volume and surface area parameters for component i. In the classical application of the UNIQUAC model, these parameters are calculated from the properties of non electrolyte molecules (ref 3). In the Extended UNIQUAC application to multi component electrolyte solutions, this approach gave unsatisfactory results. The volume and surface area parameters were instead considered to be adjustable parameters. The values of these two parameters are determined by fitting to experimental data. Especially thermal property data such as heat of dilution and heat capacity data are efficient for determining the value of the surface area parameter q, because the UNIQUAC contribution to the excess enthalpy and excess heat capacity is proportional to the parameter q. The residual, enthalpic term is dependent on temperature through the parameter ψji:
the parameter ψji is given by:
uji and uii are interaction energy parameters. The interaction energy parameters are considered symmetrical and temperature dependent in this model.
The values of the interaction energy parameters and are determined by fitting to experimental data. By partial molar differentiation of the combinatorial and the residual UNIQUAC terms, the combinatorial and the residual parts of the rational, symmetrical activity coefficients are obtained:
The infinite dilution terms are obtained by setting xw = 1 in the above equation:
The combinatorial and the residual terms of the UNIQUAC excess Gibbs energy function are based on the rational, symmetrical activity coefficient convention. The Debye-Hückel electrostatic term however is expressed in terms of the rational, symmetrical convention for water, and the rational, unsymmetrical convention for ions.
The electrostatic contributions to the water activity coefficients and the ionic activity coefficients are obtained by partial molar differentiation of the extended Debye-Hückel law excess Gibbs energy term. The term used for water is
In this expression, b = 1.5 (kg/mol)½. The term used for ions is:
Based on table values of the density of pure water, and the relative permittivity of water, εr, the Debye-Hückel parameter A can be approximated in the temperature range from 240 K to 540 K by a polynomial determined by Sander et al. (ref 2):
The activity coefficient for water is calculated in the Extended UNIQUAC model by summation of the three terms:
The activity coefficient for ion i is obtained as the rational, unsymmetrical activity coefficient according to the definition of rational unsymmetrical activity coefficients by adding the three contributions:
The rational, unsymmetrical activity coefficient for ions calculated with the Extended UNIQUAC model can be converted to a molal activity coefficient by use of its definition which can be seen here. This is relevant for comparison with experimental data.
The temperature dependency of the activity coefficients in the Extended UNIQUAC model for electrolyte solutions is built into the model equations as outlined above. The temperature dependency of the equilibrium constants used in the Extended UNIQUAC model is calculated from the temperature dependency of the Gibbs energies of formation of the species Parameters for water and for the following ions can be found in Thomsen (1997) (ref 1) H+, Na+, K+, NH4+, Cl–, SO42-, HSO4–, NO3–, OH–, CO32-, HCO3–, S2O82-. Parameters and model modifications for gas solubility at pressures up to 100 bar in aqueous electrolyte systems have later been published (refs 6 and 7). Also phase equilibria for systems containing non-electrolytes are described by the model, including liquid-liquid equilibria (refs 8 and 9). Besides, parameters have been determined for systems containing heavy metal ions (ref 10).
A.V. Garcia included the pressure dependence of the solubility of salts in the model. Two parameters for the pressure dependence of the solubility product of each salt were introduced in order to achieve this (refs 11 and 12). A significant advantage of the Extended UNIQUAC model for electrolyte solutions compared to models like the Bromley model or the Pitzer model is that temperature dependence is built into the model. This enables the model to also describe thermodynamic properties that are temperature derivatives of the excess Gibbs function, such as heat of mixing and heat capacity.
- Thomsen, K., Aqueous electrolytes: model parameters and process simulation, Ph.D. Thesis, Department of Chemical Engineering, Technical University of Denmark, 1997. https://doi.org/10.11581/dtu:00000074
- Sander, Bo, Peter Rasmussen, and Aage Fredenslund. “Calculation of vapour-liquid equilibria in nitric acid-water-nitrate salt systems using an extended UNIQUAC equation.” Chemical engineering science 41, no. 5 (1986): 1185-1195. https://doi.org/10.1016/0009-2509(86)87091-9
- B. Sander; P. Rasmussen and Aa. Fredenslund, “Calculation of Solid-Liquid Equilibria in Aqueous Solutions of Nitrate Salts Using an Extended UNIQUAC Equation”. Chemical Engineering Science, 41(1986)1197-1202. https://doi.org/10.1016/0009-2509(86)87092-0
- Abrams D.S. and Prausnitz J.M., “Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems”, AIChE journal 21(1975)116-128. https://doi.org/10.1002/aic.690210115
- Maurer G., Prausnitz J.M., ”On the derivation and extension of the UNIQUAC equation”, Fluid Phase Equilibria, 2(1978)91-99. https://doi.org/10.1016/0378-3812(78)85002-X
- Thomsen K and Rasmussen P, “Modeling of Vapor-liquid-solid equilibrium in gas-aqueous electrolyte systems” Chemical Engineering Science 54(1999)1787-1802. https://doi.org/10.1016/S0009-2509(99)00019-6
- Pereda S, Thomsen K, Rasmussen P, “Vapor-Liquid-Solid Equilibria of Sulfur Dioxide in Aqueous Electrolyte Solutions” Chemical Engineering Science 55(2000)2663-2671. https://doi.org/10.1016/S0009-2509(99)00535-7
- Iliuta MC, Thomsen K, Rasmussen P, “Extended UNIQUAC model for correlation and prediction of vapor-liquid-solid equilibrium in aqueous salt systems containing non-electrolytes. Part A. Methanol – Water – Salt systems” Chemical Engineering Science 55(2000)2673-2686. https://doi.org/10.1016/S0009-2509(99)00534-5
- Thomsen K, Iliuta MC, Rasmussen P, “Extended UNIQUAC model for correlation and prediction of vapor-liquid-liquid-solid equilibria in aqueous salt systems containing non-electrolytes. Part B. Alcohol (Ethanol, Propanols, Butanols) – water – salt systems“ Chemical Engineering Science 59(2004)3631-3647. https://doi.org/10.1016/j.ces.2004.05.024
- Iliuta MC, Thomsen K, Rasmussen P, “Modeling of heavy metal salt solubility using the extended UNIQUAC model” AIChE Journal, 48(2002)2664-2689. https://aiche.onlinelibrary.wiley.com/doi/epdf/10.1002/aic.690481125
- Garcia AV, Thomsen K, Stenby EH, “Prediction of mineral scale formation in geothermal and oilfield operations using the extended UNIQUAC model Part I. Sulfate scaling minerals” Geothermics 34(2005)61-97. https://doi.org/10.1016/j.geothermics.2004.11.002
- Garcia AV, Thomsen K, Stenby EH, ”Prediction of mineral scale formation in geothermal and oilfield operations using the extended UNIQUAC model Part II. Carbonate scaling minerals”, Geothermics, 35(2006)239-284. https://doi.org/10.1016/j.geothermics.2006.03.001


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A complete listing of Algebra books by McGraw Hill Books. Electronic book text (22) Hardback (43) Loose-leaf (13) Other book format (10) Paperback / softback Pre-Algebra, Spanish Study Guide and Intervention Workbook.
N/A McGraw Hill. PreCalculus provides comprehensive coverage of prerequisite topics and traditional PreCalculus topics on functions, polynomials, exponential and logarithmic functions, and trigonometry.
STEM PreCalculus provides comprehensive coverage of traditional PreCalculus topics, as well as topics geared towards students pursuing careers in mathematics, science, or technology fields. A playful, readable, and thorough guide to precalculus, this book is directed at readers who would like a holistic look at the high school curriculum material on functions and their graphs.
Tanton provides a coherent guided tour of exploration and discovery of a rich mathematical landscape. Prentice Hall Pre-Algebra is a very comprehensive tome that works to connect the different branches of mathematics and would be a valuable choice for classroom instruction.
Miller, O'Neill, and Hyde's Prealgebra 2nd Edition and Glencoe Pre-Algebra First Edition work just as well for self-study as they do as a required course text.
Pre Algebra is the first math course in high school and will guide you through among other things integers, one-step equations, inequalities and equations, graphs and functions, percent, probabilities. We also present an introduction to geometry and right triangles.
In Pre Algebra you will for example study*: Review of natural number arithmetic; New types of numbers such as integers. Maple e-books and study guides are electronic versions of standard math textbooks designed to assist students in grasping the fundamental concepts through visualization, practice and theory.
Each of these Maple add-ons includes interactive exercises and other features that will maximize your understanding of. Glencoe Algebra 2 (PDF) Blitzer - Algebra and Trig (Online) Prentice Hall Algebra 2 (Online) Algebraic Thinking (Online) McDougal Littell - Geometry. About the teacher.
School Home. Forestview High School Union Road Gastonia, NC Phone: .Precalculus: An Investigation of Functions (2nd Ed) David Lippman and Melonie Rasmussen. Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry.
The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear.The Precalculus Study Guide will help you master the math necessary for success in calculus.
High school and university students in, or contemplating a calculus course, and students wanting additional insight into selected topics in algebra and trigonometry would all benefit from this guide.


Hello! I am Danielle, a certified content marketer/ghostwriter with experience as a math and science content writer.
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Tuesday, August 28, 2012
I had read about it way back, when it was first discovered by him, IIRC. It was big news at the time, even in the newspapers. As I recall (also see the Wikipedia article) it was put to good use in telecommunications companies and maybe some other areas too.
Just saw his Wikipedia page today via a chain of web links.
Karmarkar received a number of awards for his algorithm, among them:
Paris Kanellakis Award, 2000 given by The Association for Computing Machinery.
Distinguished Alumnus Award, Computer Science and Engineering, University of California, Berkeley (1993)
Ramanujan Prize for Computing, given by Asian Institute Informatics (1989)
Fulkerson Prize in Discrete Mathematics given jointly by the American Mathematical Society & Mathematical Programming Society (1988)
Fellow of Bell Laboratories (1987- )
Texas Instruments Founders' Prize (1986)
Marconi International Young Scientist Award (1985)
Frederick W. Lanchester Prize of the Operations Research Society of America for the Best Published Contributions to Operations Research
National Science Talent Award in Mathematics, India (1972, India)
Inspired by nature.
- dancingbison.com | @vasudevram | jugad2.blogspot.com
Posted by Vasudev Ram at 2:37 AM


Number Press is the perfect solution for printshops, organizations, clubs or any type of business that need to number their documents. Ideal to number forms, raffles, NCR, Slips, Multiple-Up or anything that needs to be numbered. Choose any font, style, size or color Place up to 32 Numbers...
|License: Demo||Cost: $0.00 USD||Download (79): Number Press Download|
Simple GST is just that - simple. Give it a number, press enter.Simple GST Calculator has quite a few features: It can calculate: Amount of tax, and the total price including tax, for up to, two seperate taxes from the amount before tax The price before tax and the total price including tax,...
|License: Freeware||Download (99): Simple GST Calculator Download|
Easily work with fractions and convert units automatically. Add 5/32 inch to 1/8 inch and see the result in either fractional or decimal form. Convert 5 lbs to kilograms, or mix and match units by adding feet to meters. This app is extremely flexible and sophisticated, yet very simple to use....
|License: Shareware||Cost: $0.99 USD||Size: 921.6 KB||Download (7): Smart Construction Calculator Download|
Phone number Grabber Internet is a remarkable Internet Phone Number Finder Tool developed to assist in extracting phone numbers in bulk from internet. Tool can effortlessly extract phone numbers either through different search engines like Google, Yahoo, Bing, Altavista, Askcom etc. or directly...
|License: Shareware||Cost: $49.00 USD||Size: 1.42 MB||Download (43): Phone Number Grabber Internet Download|
This simple module allows Ubercart store administrators to set the minimum and maximum number of items to be in the shopping cart before a user is allowed to proceed to checkout.Installation and configurationInstallation is like any other module. Download the tar.gz file from this project page...
|License: Freeware||Size: 10 KB||Download (20): Ubercart Min/Max Order Quantity Download|
Will appear while being gradually increased from 0 to 9 digits. As fast as possible from 0 to 9 buttons along the bottom Please press the same number. Time Attack is a game of numbers appear or how fast can press 20 times. By playing in this game Peripheral vision, reflexes, such as this could...
|License: Freeware||Size: 18.8 MB||Download (7): Zoom Number Download|
This application is a brilliant application which accurately guesses the secret number of any person. It provides few set of numbers and requests the user to press yes if the secret number exists otherwise no. At the end - it guesses the secret number. Requirements: Windows Phone 8.1, Windows...
Platforms: Windows Phone
|License: Freeware||Size: 1024 KB||Download (8): Your Secret Number Download|
Files Phone number extractor is a useful tool adept at extracting Phone numbers contained in Word, PDF, Excel or PowerPoint files. The software provides advanced filtering options. These filtering options enable the user to set search criteria as per the need and extract relevant and required...
Platforms: Windows, Windows 7
|License: Shareware||Cost: $39.00 USD||Size: 8.93 MB||Download (21): Files Phone Number Extractor Download|
Random Number Generator is a Windows based application designed to
generate random numbers. Program allow users choose lower and upper
limits and increments of the numbers. Limits can be positive or
negative values. User can exclude digits from generated random
numbers. Random numbers can...
Platforms: Windows, Windows 7, Windows Server, Other
|License: Shareware||Cost: $20.00 USD||Size: 170.83 KB||Download (1765): Random Number Generator Pro Download|
Addin Page Number adds page numbers and more to PDF documents.
Addin Page Number enables you to number the pages of PDF documents. PageNumber is the essential tool when you work with PDF documents that contain portrait, landscape or rotated pages or pages with a different size. Besides page...
|License: Demo||Cost: $180.00 USD||Size: 902 KB||Download (317): Addin PDF Page Number (Acrobat 5) Download|
a package of free key press ringtone for halloween. fit for any cell phone model of nokia, motorolaa, ericsson,siemens, etc. no need of smart sms or cable modem. absolutely free. a number of exicting sounds in the category of halloween. you can inputing them into your cell phone for the...
|License: Freeware||Size: 354 KB||Download (1501): Halloween Ringtone XE Download|
Have you ever dreamed to draw like Rembrandt?
Here's your chance.
STOIK Color by Number lets you to convert photo to a paint-by-number pattern.
Just scan the photo or load graphics file from disk, choose the color palette to be used and the program will convert your photo to a...
|License: Shareware||Cost: $19.95 USD||Size: 11.09 MB||Download (333): Color By Number Download|
The Press Releaser lets the user type in all the facts, checks that the information is correct, including all links to the Internet, and then generates a press release. It starts the default email client, adds all press release receivers to the bcc field and composes the email body from the user...
|License: Shareware||Cost: $34.00 USD||Size: 920 KB||Download (110): Press Releaser Download|
PDF Page Number is an affordable industrial strength, stand-alone tool for adding page number to PDF files. You can customize your page numbers anywhere on the page, specify the style of page numbers, define the font name, size, color etc. Special features include setting prefix and suffix for...
|License: Shareware||Cost: $49.00 USD||Size: 1016 KB||Download (165): PDF Page Number Download|
1. Generate random numbers in the range from -2,147,483,647 to 2,147,483,647
2. Generate random data items using a format mask, such as telephone numbers, passwords, email address and etc.
3. Generate random bytes file in any interval you want. The format is purely binary without formatting...
|License: Shareware||Cost: $29.50 USD||Size: 800 KB||Download (346): SuperCool Random Number Generator Download|
A quality solution for creating high-quality, press-ready, full-featured, more secured PDF files with 128-bit RC4 secured password protection and access permission control. TrueType, OpenType, Type1, CID-Type1, Multiple Masters Type1, OpenType/CFF, pure CFF, CEF Windows FNT/FON, X11 PCF fonts can...
|License: Shareware||Cost: $79.00 USD||Size: 2.99 MB||Download (123): Real PDF Creator Download|
MB Free Personal Month Number Software is an user-friendly yet simple software that basically predicts what lies ahead of you in the calendar month ahead. This software helps you to realize that every particular month has a specific energy, which should be effectively harnessed for your own...
|License: Freeware||Size: 651.71 KB||Download (146): MB Free Personal Month Number Download|
Random Number Generator PPC is a Windows Mobile based software that produces
sequences of random numbers.
Program can exclude digits and numbers from generated random sequences.
User can save results to a text file.
Generated random numbers can be positive or negative.
Platforms: Windows CE, Pocket PC, Windows
|License: Shareware||Cost: $15.00 USD||Size: 42.15 KB||Download (190): Random Number Generator PPC Download|
Volume Serial Number Editor is a tool to change the drive volume serial number. This disk serial number is automatically generated and assigned when you format a disk partition and there is no documented way to change it without reformatting the disk volume. The format of volume serial number is:...
Platforms: Windows, Windows 8, Windows 7, Windows Server
|License: Shareware||Cost: $14.95 USD||Size: 3.56 MB||Download (1587): Volume Serial Number Editor Download|
True to its name this phone number generator software generates numbers in random with aplomb. But this Random number generator is equally adept at generating numbers in sequence and doubles as an efficient sequential number generator. Tool allows the user to generate millions of random or...
|License: Shareware||Cost: $39.00 USD||Size: 1.14 MB||Download (524): Random Number Generator Download|


I am trying to explore differential expressions of a selected cluster between two sample groups. However, it showed warning “For the selected comparison, there are fewer than 3 samples with the minimum number of cells (10). Only logFC values will be calculated and results should be used for exploratory purposes only.” Is there a way to solve this problem?
Thanks for your question!
The most likely explanation for this warning when performing differential expression is that you are comparing 1 sample to 1 other sample. When you perform a 1 vs 1 comparison like this, the Differential Expression results will show the LogFC difference but the results will not show an adj p-value. The reason for this is that it is not statistically sound to calculate the p-value when comparing 1 vs 1. However, the differential expression comparison can still be performed and the LogFC will be returned.
You asked how to solve this ‘problem’. The way to address this warning is to increase N in your differential expression comparison e.g. to instead compare groups with multiple samples so that there are more than 3 samples in total (such as 1 vs 2, or 2 vs 2).
I hope this makes sense! Let me know if you have further questions.


At the Sustainable Development Research (SusDeveR) conference this weekend, I offered some simple tools for performing Bayesian Regressions: Jump to the Github Repository.
The point of these templates is to make it possible for anyone who is familiar with OLS to run a Bayesian regression. The templates have a chunk at the top to change for your application, and a chunk at the bottom that uses Gelman et al.’s Stan to estimate the posterior parameter distributions.
In general, the area at the top is just to create an output vector and a predictor matrix. Like this:
The template part has all of the Stan code, which (for a Bayesian regression) always has a simple form:
The last line does all of the work, and just says (in OLS speak) that the error distribution follows a normal distribution. Most of the templates also have a more efficient version, which does the same thing.
I say in the README what Bayesian regressions are and what they do. But why use them? The simple answer is that we shouldn’t expect the uncertainty on our parameters to be well-behaved. It’s nice if it is, and then OLS and Bayesian regressions will give the same answer. But if the true uncertainty on your parameter of interest is skewed or long-tailed or bimodal, the OLS assumption can do some real harm.
Plus, since Bayesian regressions are just a generalization of MLE, you can setup any functional form you like, laying out multiple, nonlinear expressions, estimating intermediate variables, and imposing additional probabilistic constraints, all in one model. Of course, the templates don’t show you how to do all that, but it’s a start.


1. Nguyen Thanh Hai and Yakubovich S.B. The double Mellin-Barnes type
Integrals and their applications to convolution theory.
World Intern. Sci. Publ. 1992. Ser. of Soviet and East European
Mathematics. Vol.6. Singapore. 295 pp.
2. Yakubovich S.B. and Luchko Yu.F. The Hypergeometric approach to integral transforms and convolutions. Kluwer Academic Publishers. Mathematics and Applications. 287. Dordrecht. 1994. 336 pp.
3. Yakubovich S.B. Index Transforms. World Scientific Publ. Singapore.
London. New Jersey. Hong Kong. 1996. 258 pp.


What is BMI?
Body Mass Index (BMI) is a number calculated from a person’s weight and height. BMI provides a reliable indicator of body fatness for most people and is used to screen for weight categories that may lead to health problems.
How is BMI calculated and interpreted?
BMI is calculated the same way for both adults and children. The calculation is based on the following formulas:
|Measurement Units||Formula and Calculation|
|Kilograms and meters (or centimeters)||Formula: weight (kg) / [height (m)]2|
With the metric system, the formula for BMI is weight in kilograms divided by height in meters squared. Since height is commonly measured in centimeters, divide height in centimeters by 100 to obtain height in meters.
Example: Weight = 68 kg, Height = 165 cm (1.65 m)
Calculation: 68 ÷ (1.65)2 = 24.98
|Pounds and inches||Formula: weight (lb) / [height (in)]2 x 703|
Calculate BMI by dividing weight in pounds (lbs) by height in inches (in) squared and multiplying by a conversion factor of 703.
Example: Weight = 150 lbs, Height = 5’5″ (65″)
Calculation: [150 ÷ (65)2] x 703 = 24.96
Interpretation of BMI for adults
For adults 20 years old and older, BMI is interpreted using standard weight status categories that are the same for all ages and for both men and women. The standard weight status categories associated with BMI ranges for adults are shown in the following table.
|18.5 – 24.9||Normal|
|25.0 – 29.9||Overweight|
|30.0 and Above||Obese|


Average Interest Rate Calculator for web sites gives your visitors an easy-to-use financial calculator which calculates the average interest rate they pay on their debts. Easily installed on websites.
MoneyToys(tm) financial calculators for websites give webmasters a simple way to add value...
Platforms: Windows, *nix, Java,Not Applicable
|License: Commercial||Cost: $39.95 USD||Size: 17.06 KB||Download (85): Average Interest Rate Calculator Download|
This will display the total posts per day average underneath the user's avatar
Platforms: Windows, *nix, PHP, BSD
|License: Freeware||Download (27): Posts Per Day Average on Topic Download|
This script allows you to run a simple program that can average a list of numbers.
Platforms: Windows, Mac, *nix, Python, BSD Solaris
|License: Freeware||Download (32): Simple Average Calculation Download|
Computes the Woody average by first aligning individual signals (corrupted by jitter) with the standard average. Uses xcorr to compute the lag and then re-averages the signals to get an improved estimate.Example included in help.Technique deteriorates at low SNRs.
|License: Freeware||Size: 10 KB||Download (25): Woody Average (Average with alignment) Download|
Calculates the Mutual Average Information of a time series for some time lag.
|License: Shareware||Cost: $0.00 USD||Size: 10 KB||Download (20): Mutual Average Information Download|
Calculate Average Interest Rates with this Free Average Interest Rate Calculator for Windows. Enter the balance and interest rate of your loans. Knowing the average interest rate of loans helps determine when consolidation may be a good idea. This calculator offers integrated help, provides...
|License: Freeware||Size: 781 KB||Download (174): Free Average Interest Rate Calculator Download|
Monitors CPU Temperature from command line in Fahrenheit and Celsius and gives results of highest and lowest temperatures, and average over period of time run, then logs the data. Requires ACPI.
|License: Freeware||Size: 20.48 KB||Download (79): cputemp Download|
pppusage summarizes average and total transfer volumes, number of connections and average and total online time for all logged PPP connections. The data is collected by reading the syslog files which contain the ppp[d] messages. A database file is used to store the relevant data, thus it doesnt...
|License: Freeware||Size: 25.6 KB||Download (71): pppusage Download|
This application will help you quickly calculate your high school or college grade point average across an unlimited number of courses. Simply enter the course name (optional), credit hours and grade for each of your courses, and your GPA will be calculated immediately.
|License: Freeware||Size: 2.07 MB||Download (166): CS GPA Calculator Download|
Variable Investment Analyst calculates profit, periodic total return, cumulative total return, average annual total return, internal rate of return (IRR), capital gain, buy/sell prices, and other statistics. Creates many different types of charts. Creates 5 different types of basis worksheets for...
|License: Shareware||Cost: $15.00 USD||Size: 245.76 KB||Download (70): Variable Investment Analyst Download|
The program is ideal for measuring the cpu usage for specific programs, to find out the total average cpu usage of a program for its entire uptime or to start measuring at a point in time you are interested in. The latter is for example useful to find out how much cpu a program uses when idle....
|License: Freeware||Download (56): Average CPU Cycles Download|
This version v1.0 is now displaying only the Average Customer Rating for this language which the rating was written for. It has included german and english translation. It comes out with two styles but can be easily modidied. I modified this contribution which was written Darren Grant in the...
Platforms: Windows, *nix, PHP, BSD
|License: Freeware||Download (27): Average Customer Rating Download|
Calculates the average log-spectral distance between CLEAN and NOISY signals. It has the capability of calculating this distance for a specified sub-band as well. This measure is used for evaluation of processed speech quality in comparison to the original speech.
|License: Freeware||Size: 10 KB||Download (22): Log Spectral Distance Download|
This routine computes the fft of the input signal and removes power at the annual (or any specified frequency) by replacing the power at that frequency with the average of terms on both sides; this is done in the sine and cosine terms so as to average the power and the phase.
|License: Freeware||Size: 10 KB||Download (18): Remove_Annual Download|
Very efficient moving average filter implemented using convolution.Usage:Smoothed Data = movave(Data Vector, Averaging Window Size in Samples)See also: slidefilter.m by the same author
|License: Freeware||Size: 10 KB||Download (19): movave Download|
Calculates the average log-spectral distance between CLEAN and NOISY signals. Has the option of calculating this distance for speech active periods only. Also you can select a frequency range to study the distance in a sub-band.
|License: Freeware||Size: 10 KB||Download (20): LP Log Spectral Distance Download|
Moving average filter implemented using a "Sliding Sum" technique. Comparatively efficient.Usage:Smoothed Data = slidefilter(Data Vector, Sliding Interval Length in Samples)See also: movave.m
|License: Freeware||Size: 10 KB||Download (20): slidefilter Download|
An example to price an Arithmetic Average fixed strike Call option in the Black-Scholes framework using Monte Carlo Control Variate
|License: Freeware||Size: 10 KB||Download (22): Asian Option - Pricing using Monte Carlo Control Variate Method Download|
he code performs the simulation of time series with autoregressive fractionally integrated moving average (ARFIMA) models that generalize ARIMA (autoregressive integrated moving average) and ARMA autoregressive moving average models. ARFIMA models allow non-integer values of the differencing...
|License: Shareware||Cost: $0.00 USD||Size: 10 KB||Download (20): ARFIMA simulations Download|
It calculates the Tillson moving average. The user is able to change the parameters such as the smoothing sweeps and the volume factor
|License: Shareware||Cost: $0.00 USD||Size: 10 KB||Download (21): TillsonT3 Download|