curvilinear adj : characterized by or following a curved line; "curvilinear tracery"; "curvilinear motion" [syn: curvilineal]
- Having bends.
Curvilinear coordinates are a coordinate system for the Euclidean space based on some transformation that converts the standard Cartesian coordinate system to a coordinate system with the same number of coordinates in which the coordinate lines are curved. In the two-dimensional case, instead of Cartesian coordinates x and y, e.g., p and q are used: the level curves of p and q in the xy-plane. Required is that the transformation is locally invertible (a one-to-one map) at each point. This means that one can convert a point given in one coordinate system to its curvilinear coordinates and back.
Depending on the application, a curvilinear coordinate system may be simpler to use than the Cartesian coordinate system. For instance, a physical problem with spherical symmetry defined in R3 (e.g., motion in the field of a point mass/charge), is usually easier to solve in spherical polar coordinates than in Cartesian coordinates. Also boundary conditions may enforce symmetry. One would describe the motion of a particle in a rectangular box in Cartesian coordinates, whereas one would prefer spherical coordinates for a particle in a sphere. Many of the concepts in vector calculus, which are given in Cartesian or spherical polar coordinates, can be formulated in arbitrary curvilinear coordinates. This gives a certain economy of thought, as it is possible to derive general expressions—valid for any curvilinear coordinate system—for concepts as gradient, divergence, curl, and the Laplacian. Well-known examples of curvilinear systems are polar coordinates for R2, and cylinder and spherical polar coordinates for R3.
The name curvilinear coordinates, coined by the French mathematician Lamé, derives from the fact that the coordinate surfaces of the curvilinear systems are curved . While a Cartesian coordinate surface is a plane, e.g., z = 0 defines the x-y plane, the coordinate surface r = 1 in spherical polar coordinates is the surface of a unit sphere in R3—which obviously is curved.
General curvilinear coordinatesIn Cartesian coordinates, the position of a point P(x,y,z) is determined by the intersection of three mutually perpendicular planes, x = const, y = const, z = const. The coordinates x, y and z are related to three new quantities q1,q2, and q3 by the equations:
- x = x(q1,q2,q3) direct transformation
- y = y(q1,q2,q3) (curvilinear to Cartesian coordinates)
- z = z(q1,q2,q3)
- y = y(q1,q2,q3) (curvilinear to Cartesian coordinates)
- q1 = q1(x, y, z) inverse transformation
- q2 = q2(x, y, z) (Cartesian to curvilinear coordinates)
- q3 = q3(x, y, z)
- q2 = q2(x, y, z) (Cartesian to curvilinear coordinates)
A given point may be described by specifying either x, y, z or q1, q2, q3 while each of the inverse equations describes a surface in the new coordinates and the intersection of three such surfaces locates the point in the three-dimensional space (Fig. 1). The surfaces q1 = const, q2 = const, q3 = const are called the coordinate surfaces; the space curves formed by their intersection in pairs are called the coordinate lines. The coordinate axes are determined by the tangents to the coordinate lines at the intersection of three surfaces. They are not in general fixed directions in space, as is true for simple Cartesian coordinates. The quantities (q1, q2, q3 ) are the curvilinear coordinates of a point P(q1, q2, q3 ).
In general, (q1, q2 ... qn ) are curvilinear coordinates in n-dimensional space.
Example: Spherical coordinatesSpherical coordinates are one of the most used curvilinear coordinate system in such fields as Earth sciences, cartography, and physics (quantum physics, relativity, etc.). The curvilinear coordinates (q1, q2, q3) in this system are, respectively, r (radial distance or polar radius, r ≥ 0), θ (azimuth or latitude, 0 ≤ θ ≤ 180°), and φ (zenith or longitude, 0 ≤ φ ≤ 360°). The relationship between Cartesian and spherical coordinates is given by:
- x = r sin θ cos φ
- y = r sin θ sin φ
- z = r cos θ direct transformation (Cartesian to spherical coordinates)
- y = r sin θ sin φ
Solving the above equation system for r, θ, and φ gives the relations between spherical and Cartesian coordinates:
- =\arccos \left( \right) or \cos\theta=
- =\arctan \left( \right) or \tan\varphi= inverse transformation (spherical to Cartesian coordinates)
- =\arccos \left( \right) or \cos\theta=
The respective spherical coordinate surfaces are derived in terms of Cartesian coordinates by fixing the spherical coordinates in the above inverse transformations to a constant value. Thus (Fig.2), r = const are concentric spherical surfaces centered at the origin, O, of the Cartesian coordinates, θ = const are circular conical surfaces with apex in O and axis the Oz axis, φ = const are half-planes bounded by the Oz axis and perpendicular to the xOy Cartesian coordinate plane. Each spherical coordinate line is formed at the pairwise intersection of the surfaces, corresponding to the other two coordinates: r lines (radial distance) are beams Or at the intersection of the cones θ = const and the half-planes φ = const; θ lines (meridians) are semi-circles formed by the intersection of the spheres r = const and the half-planes φ = const ; and φ lines (parallels) are circles in planes parallel to xOy at the intersection of the spheres r = const and the cones θ = const. The location of a point P(r,θ,φ) is determined by the point of intersection of the three coordinate surfaces, or, alternatively, by the point of intersection of the three coordinate lines. The θ and φ axes in P(r,θ,φ) are the mutually perpendicular (orthogonal) tangents to the meridian and parallel of this point, while the r axis is directed along the radial distance and is orthogonal to both θ and φ axes.
The surfaces described by the inverse transformations are smooth functions within their defined domains. The Jacobian (functional determinant) of the inverse transformations is:
- J^ =\frac
Local basisCoordinates are used to define location or distribution of physical quantities which are scalars, vectors, or tensors. Scalars are expressed as points and their location is defined by specifying their coordinates with the use of coordinate lines or coordinate surfaces. Vectors are objects that possess two characteristics: magnitude and direction. To define a vector in terms of coordinates, an additional coordinate-associated structure, called basis, is needed. A basis in three-dimensional space is a set of three linearly independent vectors , called basis vectors. Each basis vector is associated with a coordinate in the respective dimension. Any vector can be represented as a sum of vectors Anen formed by multiplication of a basis vector by a scalar coefficient, called component. Each vector, then, has exactly one component in each dimension and can be represented by the vector sum: A = A1e1 + A2e2 + A3e3, where An and en are the respective components and basis vectors. A requirement for the coordinate system and its basis is that A1e1 + A2e2 + A3e3 ≠ 0 when at least one of the An ≠ 0. This condition is called linear independence. Linear independence implies that there cannot exist bases with basis vectors of zero magnitude because the latter will give zero-magnitude vectors when multiplied by any component. Non-coplanar vectors are linearly independent, and any triple of non-coplanar vectors can serve as a basis in three dimensions.
For the general curvilinear coordinates, basis vectors and components vary from point to point. If vector A whose origin is in point P (q1, q2, q3 ) is moved to point P' (q'1, q'2, q'3 ) in such a way that its direction and orientation are preserved, then the moved vector will be expressed by new components A'n and basis vectors en. Therefore, the vector sum that describes vector A in the new location is composed of different vectors, although the sum itself remains the same. A coordinate basis whose basis vectors change their direction and/or magnitude from point to point is called local basis. All bases associated with curvilinear coordinates are necessarily local. Global bases, that is, bases composed of basis vectors that are the same in all points can be associated only with linear coordinates. A more exact, though seldom used, expression for such vector sums with local basis vectors is \mathbf = \textstyle \sum_^n A_i(q_1\ldots q_n)\mathbf_i(q_1\ldots q_n), where the dependence of both components and basis vector on location is made explicit (n is the number of dimensions). Local bases are composed of vectors with arbitrary order, magnitude, and direction and magnitude/direction vary in different points in space.
Basis vectors can be associated with a coordinate system by two methods: they can be built along the coordinate axes (colinear with axes) or they can be built to be perpendicular (normal) to the coordinate surfaces. In the first case (axis-colinear), basis vectors transform like covariant vectors while in the second case (normal to coordinate surfaces), basis vectors transform like contravariant vectors. Those two types of basis vectors are distinguished by the position of their indices: covariant vectors are designated with lower indices while contravariant vectors are designated with upper indices. Thus, depending on the method by which they are built, for a general curvilinear coordinate system there are two sets of basis vectors for every point: is the covariant basis, and is the contravariant basis. A key property of the vector and tensor representation in terms of indexed components and basis vectors is invariance in the sense that vector components which transform in a covariant manner (or contravariant manner) are paired with basis vectors that transform in a contravariant manner (or covariant manner), and these operations are inverse to one another according to the transformation rules. This means that in terms, in which an index occurs two times, one of the indices in the pair must be upper and the other index must be lower. Thus in the above vector sums, basis vectors with lower indices are multiplied by components with upper indices or vice versa, so that a given vector can be represented in two ways: A = A1e1 + A2e2 + A3e3 = A1e1 + A2e2 + A3e3. Upon coordinate change, a vector transforms in the same way as its components. Therefore, a vector is covariant or contravariant if, respectively, its components are covariant or contravariant. From the above vector sums, it can be seen that contravariant vectors are represented with covariant basis vectors, and covariant vectors are represented with contravariant basis vectors. This is reflected in the Einstein summation convention according to which in the vector sums \textstyle \sum_^n A^i \mathbf_i and \textstyle \sum_^n A_i \mathbf^i the basis vectors and the summation symbols are omitted, leaving only Ai and Ai which represent, respectively, a contravariant and a covariant vector.
Covariant basisAs stated above, contravariant vectors are vectors with contravariant components whose location is determined using covariant basis vectors that are built along the coordinate axes. In analogy to the other coordinate elements, transformation of the covariant basis of general curvilinear coordinates is described starting from the Cartesian coordinate system whose basis is called standard basis. The standard basis is a global basis that is composed of 3 mutually orthogonal vectors of unit length, that is, the magnitude of each basis vector equals 1. Regardless of the method of building the basis (axis-colinear or normal to coordinate surfaces), in the Cartesian system the result is a single set of basis vectors, namely, the standard basis. To avoid misunderstanding, in this section the standard basis will be thought of as built along the coordinate axes.
In point P, taken as an origin, x is one of the Cartesian coordinates, and q1 is one of the curvilinear coordinates (Fig. 3). The local basis vector is e1 and it is built on the q1 axis which is a tangent to q1 coordinate line at the point P. The axis q1 and thus the vector e1 form an angle α with the Cartesian x axis and the Cartesian basis vector i. It can be seen from triangle PAB that \cos \alpha = \tfrac where |e1| is the magnitude of the basis vector e1 (the scalar intercept PB) and |i| is the magnitude of the Cartesian basis vector i which is also the projection of e1 on the x axis (the scalar intercept PA). It follows, then, that |\mathbf_1| = \tfrac and |\mathbf| = |\mathbf_1|\cos \alpha. However, this method for basis vector transformations using directional cosines is inapplicable to curvilinear coordinates for the following reason. With increasing the distance from P, the angle between the curved line q1 and Cartesian axis x increasingly deviates from α. At the distance PB the true angle is that which the tangent at point C forms with the x axis and the latter angle is clearly different from α. The angles that the q1 line and q1 axis form with the x axis become closer in value the closer one moves towards point P and become exactly equal at P. Let point E is located very close to P, so close that the distance PE is infinitesimally small. Then PE measured on the q1 axis almost coincides with PE measured on the q1 line. At the same time, the ratio \tfrac (PD being the projection of PE on the x axis) becomes almost exactly equal to cos α. Let the infinitesimally small intercepts PD and PE be labelled, respectivelly, as dx and dq1. Then \cos \alpha = \tfrac and \tfrac = \tfrac. Thus, the directional cosines can be substituted in transformations with the more exact ratios between infinitesimally small coordinate intercepts. As pointed out above, q_1 \equiv q_1(x,y,z) and x \equiv x(q_1,q_2,q_3) are smooth (continuously differentiable) functions and, therefore, the transformation ratios can be written as \tfrac = \tfrac = \tfrac and \tfrac = \tfrac = \tfrac, that is, those ratios are partial derivatives of coordinates belonging to one system with respect to coordinates belonging to the other system.
From the foregoing discussion, it follows that the component (projection) of e1 on the x axis is x = \tfrac.|\mathbf_1| = \cos \alpha.|\mathbf_1| = \tfrac.|\mathbf_1|. The projection of the normalized local basis vector (|e1| = 1) can be made a vector directed along the x axis by multiplying it with the standard basis vector i. Doing the same for the coordinates in the other 2 dimensions, e1 can be expressed as: \mathbf_1 = \tfrac \mathbf + \tfrac \mathbf + \tfrac \mathbf. Similar equations hold for e2 and e2 so that the standard basis is transformed to local (ordered and normalised) basis by the following system of equations:
\begin \tfrac \mathbf + \tfrac \mathbf + \tfrac \mathbf = \mathbf_1 \\ \tfrac \mathbf + \tfrac \mathbf + \tfrac \mathbf = \mathbf_2 \\ \tfrac \mathbf + \tfrac \mathbf + \tfrac \mathbf = \mathbf_3 \end
Vectors e1, e2, and e3 at the right hand side of the above equation system are unit vectors (magnitude = 1) directed along the 3 axes of the curvilinear coordinate system. However, basis vectors in general curvilinear system are not required to be of unit length: they can be of arbitrary magnitude and direction. It can easily be shown that the condition |e1| = |e2| = |e3| = 1 is a result of the above transformation, and not an a priori requirement imposed on the curvilinear basis. Let the local basis is not normalised, in effect, leaving the basis vectors with arbitrary magnitudes. Then, instead of e1, e2, and e3 in the right hand side, there will be \tfrac, \tfrac, and \tfrac which are again unit vectors directed along the curvilinear coordinate axes.
By analogous reasoning, but this time projecting the standard basis on the curvilinear axes ( |i| = |j| = |k| = 1 according to the definition of standard basis), one can obtain the inverse transformation from local basis to standard basis:
\begin \tfrac \mathbf_1 + \tfrac \mathbf_2 + \tfrac \mathbf_3 = \mathbf \\ \tfrac \mathbf_1 + \tfrac \mathbf_2 + \tfrac \mathbf_3 = \mathbf \\ \tfrac \mathbf_1 + \tfrac \mathbf_2 + \tfrac \mathbf_3 = \mathbf \end
The above systems of linear equations can be written in matrix form as \tfrac \mathbf_i = \mathbf_k and \tfrac \mathbf_i = \mathbf_k where xi (i = 1,2,3) are the Cartesian coordinates x, y, z and ii are the standard basis vectors i, j, k. The system matrices (that is, matrices composed of the coefficients in front of the unknowns) are, respectively, \tfrac and \tfrac. At the same time, those two matrices are the Jacobian matrices Jik and J-1ik of the transformations of basis vectors from curvilinear to Cartesian coordinates and vice versa. In the second equation system (the inverse transformation), the unknowns are the curvilinear basis vectors which are subject to the condition that in each point of the curvilinear coordinate system there must exist one and only one set of basis vectors. This condition is satisfied iff (if and only if) the equation system has a single solution. From linear algebra, it is known that a linear equation system has a single solution only if the determinant of its system matrix is non-zero. For the second equation system, the determinant of the system matrix is \det = J^ = \tfrac \neq 0 which shows the rationale behind the above requirement concerning the inverse Jacobian determinant.
Another, very important, feature of the above transformations is the nature of the derivatives: in front of the Cartesian basis vectors stand derivatives of Cartesian coordinates while in front of the curvilinear basis vectors stand derivatives of curvililear coordinates. In general, the following definition holds: This definition is so general that it applies to covariance in the very abstract sense, and includes not only basis vectors, but also all vectors, components, tensors, pseudovectors, and pseudotensors (in the last two there is an additional sign flip). It also serves to define tensors in one of their most usual treatment.
The partial derivative coefficients through which vector transformation is achieved are called also scale factors or Lamé coefficients (named after Gabriel Lamé): h_ = \tfrac. However, the hik designation is very rarely used, being largely replaced with √gik, the components of the metric tensor.
Contravariant basisNote that the coordinate system we choose need not be orthogonal, but for the purposes of this article, they are treated as being so. The system is defined to be orthogonal when
- \mathbf_\cdot\mathbf_ = \delta_
Cartesian coordinates x_1,x_2,x_3 which have the scalar product, are called Euclidean coordinates. It is often convenient to associate the points of Euclidean space with vectors, for example, with each point P we associate the vector (or arrow) with its tail at the origin of coordinates and its tip at P. This vector is called the radius vector with components (x_1, x_2, x_3). At any point P of Euclidean space we can construct the small line element
- d \bold = (dx_1,dx_2,dx_3) \,\!
- \lang f,h \rang =\sum_ x_ y_ \,\!.
- \lang d\mathbf,d\mathbf \rang = dx_1^2+dx_2^2+dx_3^2 .
The same Euclidean metric in curvilinear coordinates is
- \lang d\mathbf,d\mathbf \rang = \sum_^3 \frac \frac dx_i' dx_j' .
- g_(x_i',x_j')= \sum_^3 \frac \frac
are called the fundamental (or metric) tensor of the Euclidean space in curvilinear coordinates. Connection between fundamental tensor and Lamé coefficients is g_(x_i',x_j')= h_i^2.
ExampleIf we consider polar coordinates for R2, note that
- (x, y)=(r \cos \theta, r \sin \theta) \,\!
The basis vectors are br = (cos θ, sin θ), bθ = (−r sin θ, r cos θ), with unit basis vectors er = (cos θ, sin θ), eθ = (−sin θ, cos θ) with scale factors hr = 1 and hθ= r. The fundamental tensor is g1,1 =1, g2,2 =r2, g1,2 = g2,1 =0.
Line and surface integralsSince we use curvilinear coordinates to aid in the calculation in vector calculus, there are adjustments we need to make in the calculation of line, surface and volume integrals.
Line integralsNormally in the calculation of line integrals we are interested in calculating
- \int_C f \,ds = \int_a^b f(\mathbf(t))\left|\right|\; dt
- \left|\right| = \left| \sum \right|
- = h_i \mathbf_
- \left|\right| = \sqrt
Surface integralsLikewise, if we are interested in a surface integral, the relevant calculation, with the parameterization of the surface in Cartesian coordinates is:
- \int_S f \,ds = \iint_T f(\mathbf(s, t)) \left|\times \right| ds dt
- \left|\times \right| = \left| \times \right|
- = \sum h_ \mathbf_
- = \sum h_ \mathbf_
Grad, curl, div, LaplacianIn orthogonal curvilinear coordinates, one can express the gradient, curl, divergence, and Laplacian of a function or vector field as follows:
- \nabla f = \sum_i \hat e_
- \nabla\cdot = \sum_i \left ( \right )
\nabla^2 f = \frac \sum_i \frac \frac \frac,
where \Omega is the product of all h_i and \epsilon_ is the Levi-Civita symbol.
- M. R. Spiegel, Vector Analysis, Schaum's Outline Series, New York, (1959).
- Mathematical Methods for Physicists
curvilinear in Czech: Křivočará soustava souřadnic
curvilinear in French: Système de coordonnées curvilignes
curvilinear in Italian: Coordinate curvilinee


equalizer SPECTRAL ANALYSIS : PULSE WAVE
The parameters of the simulator are :
- Vc The peak value of the signal in Volt [V]. The default value is equal to 1 V peak.
- f the frequency of the pulse wave in [kHz]. The default value is equal to 1000 kHz.
- Number of sines used to compose the pulse waveform. The fundamental corresponds to N = 1, which is the default value.
- W is the pulse width. Its default value is equal to .5 μsec.


For all parameters that are measured several
times (like 8 main crown angles) there are calculated 4 statistical
values: minimum, maximum, average and deviation. Deviation
of all parameters except diameter is a mere difference between
the maximum and minimum values of the parameter. In addition
to this deviation, there is a relative diameter deviation parameter that is calculated by the following formula: (Dmax/Dmin - 1) * 100%.
Comprehensive list of the Helium report parameters:
Measurements are used in different systems and tools:


Past Event: The conference has been concluded successfully.
World Conference on Science, Technology, Engineering, and Mathematics (WCSTEM- 2022) is an International Conference organized by Eurasia Conferences on October 27-28, 2022 at Valencia, Spain. WCSTEM-2022 invites and unites researchers, scholar’s, students, academicians, research organizations, and making the conference a perfect platform to share most happening scientific advancements, progressive research in Science, Technology, Engineering, and Mathematics over the globe.
WCSTEM-2022-2022 allows multiple opportunities for scientific networking and knowledge sharing interaction. As well as the active poster discussion sessions, panel discussions for speakers and participants to engage beyond discussing the data, into envisioning a future that integrates rapidly evolving procedures in Science, Technology, Engineering, and Mathematics. WCSTEM-2022 will be a communicating environment to share deliberate current challenges and ways to move the field forward. The conference will foster the exchange of ideas and spur multidisciplinary collaborations.
The conference will have sessions on different topics that are related to Science, Technology, Engineering, and Mathematics. Below given are the list of topics that will be mainly targeted during the conference. All the researchers are encouraged to submit their abstracts on any of the topics. The organizing committee will consider the abstracts and will allot the slots for the speaker/Poster during the 2day conference.
School of Electrical Engineering and Computer Science, University of North Dakota, Grand Forks, ND 58201, USA
Department of Systems and Automation Engineering, University of Seville, Spain
Dean of the Faculty, Faculty of Organization and Management, Silesian University of Technology, Poland
Our tentative program is scheduled as follows.


Description: Perform various matrix manipulations on matrices in RDB or white-space delimited format.
gist-matrix -matrix1 <filename> [-matrix2 <filename>]
- -matrix1 <filename> - a tab-delimited matrix file containing floating point values, with labels in the first row and column.
- -matrix2 <filename> - similar to matrix1. This option is only necessary for some of the operations listed below.
Output: Write to standard output the result of performing the requested operation on the given matrix or matrices. The output is in the same format as the input.
- -operation <option> Specify the operation to be performed on the given matrix or matrices. These include the following:
- none - Do not modify the matrix.
- size - Print the dimensions of the matrix, row by column.
- randomize - Fill the matrix with random numbers between 0 and 1.
- covariance - Compute the covariance matrix.
- square - Multiply the matrix by itself (must be a square matrix).
- invert - Invert the matrix (must be a square matrix).
- binarize - Convert all entries in the matrix to -1 if less than a given threshold value, 1 otherwise.
- transpose - Transpose the matrix.
- eigenvectors - Compute the eigenvectors of the given matrix (must be symmetric across the diagonal).
- eigenvalues - Compute the eigenvalues of the given matrix (must be symmetric across the diagonal).
- eigenvector1 - Compute only the first eigenvector of the given matrix (symmetry not required).
- symdiag - Symmetrize the matrix by averaging across the diagonal.
- adddiag - Add a given value (specified using the -value option) to the diagonal of the matrix.
- getrowsums - Extract the row sums.
- getcolsums - Extract the column sums.
- getdiag - Extract the diagonal of the matrix.
- add - Add two matrices together (requires -matrix2 option).
- normalizerow - Compute the sum of each row in a given matrix, and divide each entry in the matrix by the sum. If matrix2 is given, then the division is carried out on that matrix.
- normalizecol - Same as normalizerow, but works vertically.
- rescalerow - Linearly rescale the values in each row so that the minimum is -1 and the maximum is 1.
- rescalecol - Same as previous, but for columns.
- normalize - Iteratively normalize the matrix rows and columns so that they sum to 1.0.
- zeromeanrow - Set the mean of each row in the matrix to zero.
- zeromeancol - Set the mean of each column in the matrix to zero.
- varone - Set the variance of each row in the matrix to one.
- colvars - Compute the variance of each column.
- scalarmult - Multiply the matrix by a scalar value (specified via the -value option).
- dotmult - Multiply corresponding entries in two matrices of the same dimensionality.
- posdef - Force a symmetric matrix to be positive definite by adding to the diagonal the opposite of the smallest eigenvalue.
- row-correlation - Compute all pairwise correlations between rows in a matrix. Admits a second, optional argument to compute correlations between rows in one matrix and rows in a second.
- col-correlation - Compute all pairwise correlations between columns in a matrix. Like the previous option, admits a second matrix.
- jacard - Compute all pairwise Jacard similarities between rows in a matrix. The Jacard similarity is J(X,Y) = \sum min(Xi/YI, Yi/XI)
- shuffle - Randomly shuffle the entries in the matrix.
- alignment - Compute the alignment score between two square matrices of the same dimensionality. This score is <M1,M2> / \sqrt(<M1,M1> <M2,M2>).
- diagonal - Compute the alignment score between a given matrix and the corresponding diagonal matrix (i.e., the matrix with zeroes for off-diagonal elements and ones for diagonal elements).
- label-align - Compute the alignment score between a given matrix and a label matrix that is created from a given label file. The label file (which is specified using the
-matrix2option), must be a two-column file, of the type used by
compute-weights, with labels of 1 and -1. The program multiplies the label column by its transpose and then calculates the alignment between the given matrix (specified by
-matrixand the square label matrix.
- scalediag - Take a square matrix as input, and replace the diagonal elements with the sum of each row, minus the given diagonal element.
- euclidean - Convert a square kernel matrix to the corresponding matrix of Euclidean distances.
- center - Center a given kernel in feature space. The second kernel is centered using feature means from the first kernel. The first kernel must be square, and the second must have the same columns as the first.
- setdiag - Set the entries on the diagonal of a given square matrix to a given value.
- diffusion - Perform a diffusion operation on the given symmetric matrix, using the specified value as the diffusion constant.
- euclidean - Convert a square kernel matrix to a Euclidean distance matrix using d(x,y) = sqrt(k(x,x) - 2k(x,y) + k(y,y)).
- int-dim - Estimate the intrinsic dimensionality of a square kernel matrix. This is done by converting the kernel to a Euclidean distance matrix, and then computing the squared mean inter-object distance divided by the corresponding variance.
- modav - Compute the mean off-diagonal absolute value in a square matrix.
- -width <value> - Total number of digits in each output value.
- -precision <value> - Number of digits to the right of zero in each output value.
- -value <value> - Specify a value to be used in the matrix operation. When normalizing, this value is the precision to which the normalization is carried. With "adddiag," this value is the number to be added to the diagonal of the given matrix. With "scalarmult," it is the scalar value to multiply the matrix by.
- -seed <value> - Set the seed for the random number generator. By default the seed is set from the clock. The random number generator is only used in conjunction with the "normalize" option.
- -raw - Do not require on input (or produce on output) labels on each row and column. Also, use space delimiters rather than tabs between entries.
- -rdb - Allow the program to read and create RDB formatted files, which contain an additional format line after the first line of text.
- -verbose 1|2|3|4|5 - Set the verbosity level of the output to stderr. The default level is 2.
Bugs: Very little checking of command line arguments is performed.


The complex number is a special type of number that can be represented as a combination of a real number and an imaginary number. It can be denoted in the format of a +ib where a is the real number part and ib is the imaginary number part. Real numbers have definite tangible values and can be plotted on a number line. Examples of real numbers are fractions, integers, or any countable number. Imaginary numbers are abstract numbers, the square of which gives a negative value. In this case, the term complex does not indicate complicated, but it signifies that this type of number is formed by joining two numbers together, like a building complex.
Therefore, a complex number is represented by an addition of two numbers, in the form of z= a + ib where a and b both are real numbers and i is an imaginary number. Here ‘i’ is termed as ‘iota’ and the value of i equals √-1. For example, 3+4i is a complex number where 3 is a real number part and 4i is an imaginary number part as real number 4 when multiplied by √-1 becomes an imaginary number.
An interesting fact is that 0 is considered a complex number because it can be denoted in the format of 0+0i. Again 0 is a real number as well. So, zero is a real number that can be included in the set of complex numbers.
Arithmetic operations like addition and subtraction involving complex numbers can be done by combining similar parts separately which means the addition or subtraction of real number with the real number, and imaginary number with the imaginary number gives the final result.
For example, (m + in) + (p + iq) = (m + p) + i(n + q) and (m + in) – (p +iq) = (m– p) + i(n – q).
Cuemath’s website or app gives an opportunity for students to access innovative and effective learning methodologies through online classes under the guidance of expert teaching faculties. It is a platform that makes students more confident and skillful by building a strong foundation in mathematics.
Some of the properties of complex numbers are mentioned below:
- If a and b are real numbers and a + bi =0, then a =0 and b =0
- If two complex numbers a + ib = c + id, where a, b, c and d are real numbers then a = c, and b=d
- The complex numbers follow the commutative law of addition and multiplication.
The online learning platforms are providing quality education to students in a flexible and convenient way. Many companies have come up with various modes of online programs. To reach a wider audience, several learning management websites have been launched to attract students and parents who seek online facilities for learning various subjects. Cuemath is one of the popular learning platforms that provide math classes online. They focus on developing a learning system that gives a deep understanding of mathematics to students from an early age. The subject is taught as a life skill and not just as a subject. Teachers guide children through their mathematical journeys and helped them to develop analytical thinking and problem-solving skills using real-life examples. The great benefit derived from Cuemath is the customized learning program designed to suit the students’ learning abilities and help them to clear the concepts to ensure improved performance.
To enroll your child in an interactive learning environment, visit the Cuemath website for more information.


Pips and pipettes are terms commonly used by traders. Here’s what they mean.
PIP stands for Percentage In Point. It is a way to measure how much a currency pair has changed in value.
We used to say a pip was the slightest change in the price of currency pairs, but then a new term came into use called a pipette.
To avoid confusion, Pip is the abbreviation for the fourth decimal place in a currency pair’s quote price (except the JPY pair).
Let’s have a look at an example.
Assuming the EURUSD goes from 1.1500 to 1.1520, how many pips are generated?
To figure how many pips the movement of EURUSD is, you only see the difference, which is 20 pips. As we said, the Pip is the fourth decimal place. In this example, the difference is 20 pips.
Consider another currency pair, GBPUSD, as an example. Consider another example in a different currency, the GBPUSD.
GBPUSD is trading at 1.3160, down from 1.3200. Thus, in this example, we may refer to GBPUSD as being down 40 pips. It is important to note that not all currency pairs have four decimal digits.
Because the currency pair versus the Japanese Yen (JPY) only has two decimal, we refer to the Pip as the second decimal place.
Consider the following example:
USDJPY is trading at 128.50 and has risen to 128.65, implying a 15 pip gain. GBPJPY’s move from 167.45 to 167.00 is a 45-pip loss. After we’ve figured out what PIP is, we’ll try to figure out what Pipette is.
After years of using only four decimal (two for the JPY Pair), the fifth decimal, Pipette, was introduced. Most brokers use the fifth decimal (except for JPY using three decimals); however, this Pipette is usually shown with a smaller number. Pipettes are most commonly referred to as fractional pips, or 1/10 the worth of a pip.
I know it sounds weird, but Pipette isn’t used very often in everyday language. However, consider the following example: EURUSD trades between 1.11505 and 1.11513. Thus, the EURUSD increased by eight pipettes, but because most traders were unconcerned about the change below one Pip, traders typically prefer to refer to it as 0.8 pips.
The following example is GPUSD decreasing from 1.32507 to 1.32403. Then, we can see that the GBPUSD decreased by 204 pipettes or 20.4 pips.
Following that, let us consider an example with the JPY pair.
The GBPJPY increased from 167,503 to 167,758. Thus, GBPJPY increased by 255 pipettes or 25.5 pips. Easier to follow, right?
Therefore, bear this in mind. A pip is a unit of measurement of a currency pair’s value change; it is the fourth decimal place for most currency pairs except for the JPY, which is the second decimal place.
One Pipette, also known as fractional pips, is 1/10 of a pip, the fifth decimal point for most currency pairs but the third decimal point for JPY pairs.


The ¾ÅÐãÖ±²¥ Primary Maths Masterclasses series is now in its second year, and we are delighted that we have been able to welcome all six ¾ÅÐãÖ±²¥ Primaries to participate in the programme. Year 6 students have been coming together, online, to explore and investigate mathematical ideas which are not usually part of the primary curriculum. Through the Masterclasses, students have the opportunity to work together on interesting topics such as Sierpinskiâ€™s triangle, magic squares and Fibonacci sequences.
The Masterclasses are a real highlight of the maths calendar and offer an opportunity for the whole trust to work together. In addition to a speaker from the Royal Institute, we have been fortunate to have Matt Hine, a maths teacher at SPH deliver one of the series helping to build continuity of mathematics across the phases. In addition, we are very excited for 6th form students from SPH to be delivering the final Masterclass in December. A fantastic opportunity for maths students to share their love of the subject and inspire the next generation of mathematicians within our Trust.
A big thank you to the staff teams in all the primary schools who have supported their students to participate. Congratulations to all the year 6 students who have taken part â€“ their participation and engagement in the sessions has been outstanding, along with demonstration of advanced mathematical skills.


One of our missions here at Creative Play Resources is to inspire children with a lifelong love of STEAM — Science, Technology, Engineering, Arts and Mathematics.
These are essential skills that any child can use throughout their life — so learning them early is vital.
Supporting STEAM through play
It’s never too early to start — that’s why we offer Rainbow Pebbles. They are tactile manipulative toys that support the benefit of STEAM.
This book by Dr Paul Swan has been designed to help teachers gain the most from this resource.
Dr Paul Swan’s books complement educational toys in the brand’s collection, inspiring teachers — and parents and carers too — to aid children’s educational journeys.
In this edition, the links between the various activities and STEAM ideas are highlighted.
Making maths fun with Dr Paul Swan
The aim of Dr Paul Swan’s books and resources is to make learning maths fun, easy and natural, eliminating outdated ideas about numeracy and its appeal.
This book offers ideas for hands-on learning with fun activities that engage students to enjoy learning basic maths. Used in conjunction with Rainbow Pebbles, it’s an effective way to stimulate and inspire children just starting their numeracy journey.
Inside, you’ll find challenges for children to take on, inspiring a love for maths and guiding you on language to use and which skills these resources will help develop fine motor skills and analysis and appraisal skills.
1 book (A4 size) of 48 pages.
Dr Paul Swan's books and resources have been designed to help teachers do what they do best — teach in a fun, engaging and effective way.
Dr Paul Swan is an award-winning author and speaker whose range of educational resources has been designed to help develop mathematical skills in children in a way that captures their imagination and inspires them to do their very best.
As a teacher, his books will help you:
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Explore our children’s books and early literacy range, where you’ll find resources for the youngest learners, from flash cards, magnetic letters and puzzles to inspiring books, blocks and more.


Discrete fourier transform tutorial
Chapter 5 - Discrete Fourier Transform (DFT) ComplexToReal.com Page 2 compute a DTFT of a periodic signal, it is also discrete because this form of the DTFT is. Introduction to the DFT. This chapter introduces the Discrete Fourier Transform and points out the mathematical elements that will be explicated in this book.
Discrete Fourier TransformsвЂ”Wolfram Language Documentation
Lecture 7: Discrete Fourier Transform in 2D In the previous lecture we introduced the discrete Fourier transform as given either by summations or as a matrix vector. 26/03/2009В В· Fourier transform theory. So far we have been processing images by looking at the grey level at each point in the image. These methods are known as spatial
The discrete Fourier transform transforms a sequence of N complex numbers Matlab tutorial on the Discrete Fourier Transformation; Interactive flash tutorial on. HINT: If program is too big for screen click mouse in program then push "CTRL" and spin mouse wheel at the same time... or push F11 for full screen.
Tutorial Discrete Fourier Transform GitHub
OpenCV Discrete Fourier Transform. Hint: if program is too big for screen click mouse in program then push "ctrl" and spin mouse wheel at the same time... or push f11 for full screen., the discrete fourier transform discrete-time fourier transform (dtft) review recall that for a general aperiodic signal x[n], the dtft and its inverse is x); 141 chapter 8 the discrete fourier transform fourier analysis is a family of mathematical techniques, all based on decomposing signals into sinusoids., lecture 7: discrete fourier transform in 2d in the previous lecture we introduced the discrete fourier transform as given either by summations or as a matrix vector.
Understanding the FFT Algorithm Pythonic Perambulations. Tutorial: fourier transform and reconstruction of a simple signal. in this tutorial we will study the formula for computing the discrete fourier transform, goal . we'll seek answers for the following questions: what is a fourier transform and why use it? how to do it in opencv? usage of functions such as: cv); pdf the use of inverse discrete fourier transform (idft) implemented in the form of inverse fourier transform (ifft) is one of the standard method of reconstructing, 26/03/2009в в· fourier transform theory. so far we have been processing images by looking at the grey level at each point in the image. these methods are known as spatial.
Fourier Transform MATLAB & Simulink - MathWorks Australia. A. basics of discrete fourier transform a.1. definition of discrete fourier transform (8.5) a.2. properties of discrete fourier transform (8.6) a.3., find and save ideas about discrete fourier transform on pinterest. see more ideas about calculus, physics and physics formulas.); goal . we'll seek answers for the following questions: what is a fourier transform and why use it? how to do it in opencv? usage of functions such as: cv, discrete fourier transform opencv examples tutorial code trung tгўm dбєўy hб»ќc kбєї toгўn tб»•ng hб»јp tбєўi cбє§u giбєґy trung tгўm dбєўy hб»ќc kбєї toгўn.
Digital Signal Processing DFT Introduction Tutorials Point
Fourier Transform Matlab Tutorial Behind The Sciences. Theoryв¶ fourier transform is used to analyze the frequency characteristics of various filters. for images, 2d discrete fourier transform (dft) is used to find the, this matlab function is the discrete fourier transform (dft) of the galois vector x.); the fft takes a time signal defined by discrete time points and computes the spectrum. time and frequency signals differ in power., discrete fourier transform вђ“ tutorial вђђ1вђђ в© spider financial corp, 2013 discrete fourier transform this is the first tutorial in our ongoing.
- Learn OpenCV by Examples Discrete Fourier Transform
- The Discrete Fourier Transform University of Michigan
Discrete Fourier Transform in Excel Tutorial - Free download as PDF File (.pdf), Text File (.txt) or read online for free. This is the first tutorial in our ongoing. PDF The use of Inverse Discrete Fourier Transform (IDFT) implemented in the form of Inverse Fourier Transform (IFFT) is one of the standard method of reconstructing.
A Tutorial on Fourier Analysis Discrete Fourier and Inverse Fourier Transform X(n) = A Tutorial on Fourier Analysis Fourier Transform as sum of sines and cosines. MATHEMATICS OF THE DISCRETE FOURIER TRANSFORM (DFT) WITH AUDIO APPLICATIONS SECOND EDITION. JULIUS O. SMITH III Center for Computer Research in Music and Acoustics.
CHAPTER The Discrete Fourier Transform
1. Discrete Fourier TransformsвЂ”Wolfram Language Documentation
2. Discrete Fourier Transform (DFT) вЂ“ NumXL Support Desk


Theory, Architectures and Applications
Tutorial @ AAAI 2023 · KDD 2022 · TheWebConf 2022
Graphs are ubiquitous data-structures that are widely-used in a number of data storage scenarios, including social networks, recommender systems, knowledge graphs and e-commerce. This has led to a rise of GNN architectures to analyze and encode information from the graphs for better performance in downstream tasks. While preliminary research in the domain of graph analysis was driven by neural architectures, recent studies has revealed important properties unique to graph datasets such as hierarchies and global structures. This has driven research into hyperbolic space due to their ability to effectively encode the inherent hierarchy present in graph datasets. The research has also been subsequently applied to other domains such as NLP and computer vision to get formidable results. However, the major challenge to further growth is the obscurity of hyperbolic networks and a better comprehension of the necessary algebraic operations needed to broaden the application to different neural network architectures. In this tutorial, we aim to introduce researchers and practitioners in the web domain to the hyperbolic equivariants of the Euclidean operations that are necessary to tackle their application to neural network architectures. Additionally, we describe the popular hyperbolic variants of GNN architectures such as recurrent networks, convolution networks and attention networks and explain their implementation, in contrast to the Euclidean counterparts. Furthermore, we also motivate our tutorial through existing applications in the areas of graph analysis, knowledge graph reasoning, product search, NLP, and computer vision and compare the performance gains to the Euclidean counterparts.


Exascale Data Analysis
Since 2016, I have been extending my work on the contour tree to target exascale data, in collaboration with Lawrence Berkeley National Laboratory and Los Alamos National Laboratory in the United States, under the ECP-Alpine Exascale Computing Project.
Existing algorithms for contour tree computation (including my prior work) were defined serially, and based on serial mathematics. Since modern pre-exascale clusters such as Summit can have 200 million GPU cores spread across 20,000 machines, making effective use of the compute resources requires redefining the algorithms, and in some cases the mathematics that underlie them.
In an initial attempt, we built from my work on the Joint Contour Net by quantising the data set. While this was successful in parallelising the problem, it had a huge memory footprint and was hard to validate.
We went back to the drawing board and came up with an effective solution for massively multicore local computations (ie GPUs, OpenMP and similar), using parallel array transformations, parallel path collapse and parallel sorting to enforce topological invariants. We presented it at the IEEE Large Data Analysis & Visualization (LDAV) 2016 workshop, and were awarded Best Paper.
We then added further information to the contour tree (technically referred to as augmenting it) and built a hyperstructure to support parallel acceleration of operations in the tree.
My student Petar Hristov had by this point resolved some mathematical and complexity issues caused by W-structures in the contour tree.
This gave him the background to spend an internship at Lawrence Berkeley National Laboratory, where he introduced hypersweeps to compute secondary properties of the contour tree for the purposes of decomposition, simplification and feature detection, then connected them up to the Cinema in situ tools.
Since then, we have implemented a fully distributed version that computes separate contour trees on multiple nodes of a cluster, then combines them to produce a distributed hierarchical contour tree, which won a second Best Paper award at LDAV 2022.
All of this has been implemented and released in the modern multicore vtk-m visualization toolkit, and has been generously supported by the US DoE/NNSA Exascale Computing Project, and there is more to come.
Other Research Topics:
Contour Tree Computation
Scalar Topological Visualisation
Direct Volume Rendering
Histograms and Isosurfaces
Aerial Urban LiDAR


By Bushra Juwairia Mulla
Clocks have been part of human lives since ancient times. People used to measure time using sundials and hourglass. The modern analog clock which we see today came into existence in the 15th century. Since then most of our analog clocks have had straight needles for their hands. In this Instructable we are going to build a clock with the Fibonacci spiral hour hand.
Cd marker/ permanent marker
A4 size paper
Sheet metal 400*90*1 mm
Empty spray can
Old analog clock machine
Before understanding the Fibonacci spiral we need to understand the Fibonacci number and Fibonacci sequence.
Fibonacci numbers form a sequence such that each number is the sum of the two preceding ones, starting from 0 and 1.
So, 0+1=1, 1+1=2, 2+1=3, 3+2=5, 5+3=8, 8+5=13…
We get this sequence:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
The Fibonacci spiral is a spiral that is built by constructing arcs that connect the points of these squares based on the Fibonacci sequence that is assembled in a spiral pattern.
A Fibonacci spiral gets wider or gets further away from the center for every quarter turn it makes.
So far we have talked about the Fibonacci sequence and Fibonacci spiral but what/who is Fibonacci?
Leonardo of Pisa, called Fibonacci, was a medieval mathematician (1170 – c. 1240).
Fibonacci is famous for two major contributions to the mathematical world.
Fibonacci popularized the Hindu–Arabic numeral system in the Western world primarily through his book Liber Abaci (Book of Calculation).
The send one was an answer to a popular number riddle: If a pair of rabbits, male and female, can mate and every month their offspring produce a pair of male and female rabbits. How many rabbits will there be in one year?
The answer to this riddle gave birth to the Fibonacci sequence.
Can you solve this riddle?
Fibonacci spiral is extensively used in art and photography.


Implementing Gradient Descent in Python
This article will answer a few important questions about gradient descent that are frequently asked in Machine Learning Interviews. This article barely scratches the surface, but just like any challenging journey— we all gotta start somewhere!
Without further ado, let’s dive right in:
What is Gradient Descent?
Gradient Descent is a step towards local or global optima of a cost function. By step, we mean we change the parameters of the function so that we reach the optimal solution of the problem we are solving.
In machine learning we deal with two types of optimization problems :
- Convex Functions: Convex functions have only one optimal solution — you either have one global optimal solution or no solution at all
- Non Convex Functions: Non convex functions can have multiple local optimal points and sometimes we see our gradient descent functions get stuck in these local optimas.
Python implementation of Gradient Descent
Let’s take an example of a convex cost function:
y = (x-6)²
We can tell beforehand that the x=6 is the minima for this cost function. Can our function find this out?
What is stochastic gradient descent and when is it used?
Stochastic gradient descent is when you use a sample of training data to update your model parameters instead of using all the training data.
We use it when it becomes expensive (memory wise, processing wise) to calculate the loss value for all the sample values
It is a very noisy path to the optima, since we are using samples to get to the optima.
Here is the stochastic gradient descent implementation:
What is batch gradient descent?
Batch gradient descent is a subset of stochastic gradient descent. BGD or Mini batch gradient descent updates parameters which uses a small number of data points for each step.
It is important to understand the inner workings of models while practicing Machine Learning techniques. Gradient descent is one of the most important concepts with diverse applications, hence this question routinely comes up in MLE or Data Science interviews.


Your task is to calculate the square root of a given integer.
1054: Square Root时间限制: 1 Sec 内存限制: 128 MB
提交: 59 解决: 25
First line is a number t,t<=10, the number of the test cases. Following t lines, each contains a single integer n, with n<65536.
Output consists of t lines, every line is the square root of n. The root is supposed to be truncated to 99 significant figures.


Hansol Hong (CMSA Postdoc) describes his current research at the Center of Mathematical Sciences and Applications.
Check out the program page for the Simons Collaboration on Homological Symmetry here: https://cmsa.fas.harvard.edu/simons-collaboration-on-homological-mirror-symmetry/
Benny Sudakov (ETH Zürich) describes the topics and goals of the Workshop on Extremal and Probabilistic Combinatorics and the importance of collaboration in science and math.
The Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory was held January 10-13. Learn more about the Simons Collaboration here.
Continue reading Videos from the Simons Collaboration Workshop
During the Spring 2018 Semester Artan Sheshmani (QGM/CMSA) will be teaching a CMSA special lecture series on Quantum Cohomology, Nakajima Vareties and Quantum groups. The lectures will be held Tuesdays and Thursdays, from 1:00 to 3:00pm in room G10, CMSA Building.
Noga Alon (Tel Aviv University) discusses his current research and the Special Program on Combinatorics and Complexity hosted by CMSA.
The following playlist contains videos from the workshop:
The workshop on Algebraic Methods in Combinatorics took place November 13-17, 2017 at the Center of Mathematical Sciences and Applications as part of the program on Combinatorics and Complexity.
Continue reading Videos from the Workshop on Algebraic Methods in Combinatorics


All LAN-FLAT products (surface plates, squares, quadratic master squares, straight edges, step measurement masters,...), as well as the calibrations and reconditioning/resurfacing services made by LAN-FLAT company, include a complete Calibration Certificate valid against quaity audits and with traceability of the measurement instruments used.
In the case of surface plates, LAN-FLAT Calibration Certificate is composed of the following graphic information:
Presents the flatness error in each one of the measurement stations taken during the Moody measurement process.
This graph presents the flatness errors in a quantitative way in each one of the measurement stations.
Contour Lines Graph
This graph present a contour lines with those points of the surface plate with the same flatness error.
This graph presents a 3D view of the surface plate.


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The ZiF Cooperation Group investigates the role and scope of mathematics as a tool. Its goal is to analyze a particular function of mathematization, namely, establishing the interconnection between theory and experience. The two notions of measurement and intervention will be the main focus. On the one hand, mathematics is relevant when facts are going to be registered, while on the other hand, it is significant when facts are to be changed in a targeted way - or are to be brought about at first. In the first case, mathematics is part of so-called observation theories, while in the second case it is an instrument of technical intervention.
The enormous increase of available computational power has transformed and widenend the ways in which mathematics as a tool is significant. Four aspects receive closer inspection, namely, the use of mathematics
The first two items deal mainly with registration while the latter items focus on intervention. The investigation of these items requires us to deal with two questions:


I really love teaching addition because it's easy to differentiate so you reach all learners. I love that once my quick learners catch on, I can give them harder numbers or an addition game to practice and pull small groups without having to worry about too many melt downs.
A couple years ago I created this worksheet, math mat and SMARTboard file to help my students practice addition. After we have practiced whole group, I give them a worksheet, math manipulatives and a math mat.
In the past I have used counting bears, bugs or dinosaurs for manipulatives. However, now that I have 37 students (!!), I have been giving each student a snap cube tower that has 12 cubes. I try to give each student a different color so they don't mix up their cubes. Once they're done with their activity, they put the tower back together again and into a basket.
While using the mat we begin practicing addition stories (Curious George ate 3 bananas in a tree and 1 banana on the ground. How many did he eat?)
After we have mastered the concept, I introduce our "addition game." I give them a blank worksheet and a die to make their own addition sentences. I never mention it, but it seems to become a contest to see who can get Curious George to eat more bananas! :)
We use this SMARTboard file with flashcards while we're waiting for the last few kids to finish or we're packing up. I also have this SMARTboard file that they love to use also! :)


Testmaster Educational Limited, an educational experts group is set to launch a nationwide Mathematics quiz competition for Secondary school students across the country.
This was disclosed in Lagos, on Tuesday, by Chief Operations Officer and Co-founder of Testmaster Educational Limited, Ofir Zukovsky, while speaking at the press conference.
Testmater Education, an International company, with a Nigerian branch, is
comprised of foreign as well as indigenous educational experts with proven track record in developing and marketing successful techno-pedagogical solutions to millions of children/students worldwide.
“Senior Secondary Certificate Examination (SSCE:WAEC/NECO) and Unified Tertiary Matriculation Exam (UTME, JAMB) are vital GATEs for Nigerians who want to start their adult life with dignity, honor and self-respect.
“But inequality in Education prevents individuals from getting the same chance in passing these exams, resulting in the increase of gaps in society and sentence them to a poor, unequal life,” Zukovsky said.
Continuing, he said, “It is our commitment to help students and teachers be the best they can.
Hence, we created Testmaster to corroborate teachers’ efforts in preparing students for academic success, enhance students’ performance in SSCE and UTME exams and ensure that every student in Nigeria maximizes his or her true potential.
“TESTMASTER is a solution that allows every student in Nigeria access to top quality education, at a cost anyone can afford, by providing easy access to the best digital private tutor on major subjects, all compliant with SSCE/JAMB
curriculums, any time and on any digital device”.
TESTMASTER consists today of 16 SMART books, each containing thousands of original exercises and theoretical lesson explanations, where each exercise is linked to a comprehensive, self-explanatory short video solution making learning highly effective and productive, both intellectually and fun.
And all presented by highly experienced Nigerian Professional Teachers and Academic Tutors so that anyone can understand.
Thousands of students have already mastered their final exams using TESTMASTER.
READ ALSO: Olufemi Obafemi emerges winner of 2018 merit award
The product addresses the weak as well as the strong students with what this millennial generation truly seeks i.e. a short, intuitive, visual, professional and simple way to pass through these turbulent periods.
Testmaster’s Country Representative, Paul Olatunde, unveiled at the press conference that 2019 national secondary school mathematics TV quiz show, tagged ‘Master of Math’ is an annual national mathematics programme that provides SS2 students in public and private schools the opportunity to compete in live TV show against and alongside their peers.
“Master of Math is not just another mathematics competition but one that inspires Nigerian students to greater achievements through experiencing the magic introduced by Testmaster.
“Furthermore, Mathematics teachers are being empowered with new digital ‘personal assistants’ which will improve their teaching skills”, he said.
He further explained the three stages of the competition, starting at the states level, through Regional up to National one. Advanced competition stages will be TV broadcast where exciting prizes (₦200,000 and a trophy for the winner, ₦150,000 and
₦100,000 for 2nd and 3rd places, respectively) shall be distributed. Top 3 students from each state at stage one will also receive cash prizes. In addition, expenses like transportation, accommodation and feeding will be paid by the organisers.
Furthermore, “Teachers are not left out in this glamorous engagement as we would be
giving cash prizes to mathematics teachers of all the winning students at state and national level, meanwhile all registered schools mathematics teacher will participate in a Mathematics teacher one day free preparatory content workshop across the nation designed around issues in mathematics teaching, strategies and innovation and the teachers workshop is scheduled for February 19th, 2019. Olatunde said.”
READ ALSO: Musa, Ndidi, Iheanacho mourn Leicester chairman
Tunde Eso, Testmaster’s media and publicity consultant, said the 2019 National secondary School Mathematics TV Quiz show registration is open.
The online registration scratch card is available nationwide and can be obtained from any state representative and Nigerian Post office service and students can also log on to www.masterofmath.org.ng or call 08034968539 to locate the closest selling points to their premises


Differences between your own calculation and our calculation can be due to rounding differences and/or be caused by the use of the nominal interest rate by the Cashare-system for calculating the monthly rate. The nominal interest rate is derived from the displayed effective interest rate. The display of the effective interest rate is a requirement of the law on consumer credit. The calculation of the monthly rates with nominal interest rate is custom to the Swiss market and, to our knowledge, is used by all lending agencies in Switzerland.
Conversion formula: inom = 12*(1+ieff)^(1/12)-1
You can find a calculator for nominal and effective interest rate on this website: https://www.calculatorsoup.com/calculators/financial/nominal-interest-rate-calculator.php
Have more questions? Submit a request


Numbers is the spreadsheet application from Apple's iWork suite, so naturally has compatibility across all Apple devices. Numbers allows you to transform your data into 2D or 3D bar, line, area or pie charts. Combine line, column and area series in a single mixed chart. Create 2-axis charts with different value scales. Even apply trendlines and error bars. The charts you create in Numbers can be linked to your Pages documents and Keynote presentations. As with Excel, you can create ineffective data visualizations as well, given the amount of freedom this software provides.


To combat transmission of SARS-CoV-2 during the COVID-19 pandemic, workplaces and schools have undergone closures and Ontarians have been asked to engage in physical distancing. In this seminar you’ll be introduced to a mathematical model describing the impact of COVID-19 in Ontario and see how it is used to examine the effects of closures and distancing in reducing case numbers and deaths resulting from COVID-19. Find the zoom link here: Upcoming Events
Dr. Fair is a Postdoctoral Fellow in the School of Environmental Sciences at the University of Guelph, as well as an alumna of the College of Engineering and Physical Sciences. Her research focuses on gaining insights into the dynamics of complex systems using mathematical models, and exploring questions related to climate change, infectious diseases, and sustainability.


AAASpell features a comprehensive set of interactive spelling lessons, games and exercises. Unlimited practice is available on each topic which allows thorough mastery of the concepts.
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ELAGSE1SL1: Participate in collaborative conversations with diverse partners about grade 1 topics and texts with peers and adults in small and larger groups. a. Follow agreed-upon rules for discussions (e.g., listening to others with care, speaking one at a time about the topics and texts under discussion). b.
WebMath is designed to help you solve your math problems. Composed of forms to fill-in and then returns analysis of a problem and, when possible, provides a step-by-step solution.
Jun 03, 2016 · Learning Materials and Teachers Guide for Grade 7, Grade 8, Grade 9 and Grade 10 students and Teachers. DepEd K-12 Manuals, DepEd K To 12 Modules Friday, June 3, 2016
Online homework and grading tools for instructors and students that reinforce student learning through practice and instant feedback.
1. Give an alternate name for angle ∡ Û using 3 points: (1 answer) 2. Angles ∡ m n q and ∡ o n s can best be described as: (2 answers) 3. Angles ∡ ß and ∡ Ü can best be described as: (2 answers) 4. The line ⃖ s t , , , , , ,⃗ can best be described as a: (1 answer) 5.
where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a one-degree angle, and can be used to measure angles. b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. 6. Measure angles in whole-number degrees using a protractor. Sketch angles of speci ed measure. 7.


This post may contain affiliate links, my full disclosure can be read here.
Memorizing basic math facts is so important for higher level math. However, I believe in young children learning should learn math at their own pace and every child is different.
Disclosure: I received a free copy of this product for review, all opinions are 100% my own.
We were recently given the Math Rider program to review and I love how it handles learning math facts!
Math Rider is a math game for Windows and Mac. The target age range for this game is 6 to 12 years old. However I think any child needing math practice would enjoy this. It was very easy to install and you can add up to 8 children. Each child gets their own login and password, so keeping siblings from accidentally using the wrong account is easy.
When you first login you can set the difficulty level of the game and decide if you want to practice addition, subtraction, multiplication or division.
As the children move through the game they go on quests. Each quest starts with a mission, in one the child’s mother was ill and they had to travel through the Mathlands to find the special ingredient that would make her well again. They mount their horse Shadow and travel on their journey.
As they travel math questions appear on the screen and they have to type the correct number in. If they get it right Shadow jumps over the jump obstacle correctly.
If they get it wrong Shadow stops in front of it, while the math question is shown on the screen with the correct answer. The problem and answer are also read out loud.
The game adapts to the child as they play. The more questions they get right and the faster they answer them, the faster the game moves. Equally, it will slow down if the child is getting questions wrong or moving slowly. I love how the game adapts to each child on their own level!
Our kids have loved using Math Rider! We practice math drill often with different games and this has become a favorite. They love horses and going on a “quest” is so much fun.
They aren’t just practicing math facts, they are engaging in a fun task. I would highly recommend this game to anyone looking for a fun math drill program for their children.


Information Technology and Services
Any Graduation Degree
07 Sep 2020
- Predictive Analytics
- Data Science
- Financial Modeling
- Direct Mail
- This role within our data analytics team is responsible for contributing to the design, implementation and maintenance of new software algorithms of our platform that we delivers to B2C financial services industry.
- The successful candidate will love collaborating on high energy, Agile teams and working with product team to build new photogrammetry analytics tools.
- Graduate degree in Machine Learning, Computer Science, or Artificial Intelligence (current or completed)
- Experience working in predictive models, data models, financial models, and machine learning models.
- Strong applied math skills in statistics, modeling, computations, and financial models.
- Experience with B2C business data analysis, B2C financial data analysis and demographic data analytics.
- Experience with machine learning, regression, nural networks, trees, nave bayes, and related applications.
- Experience with developing software in R, and Python
Nice To Have
- Experience with direct mail marketing models is a plus
- Experience with analyzing web log data is a plus
- Experience with analyzing credit data elements like FICO Score, payment history, credit amount, credit balances, inquiries, etc. is a plus
- Experience with analyzing demographic data elements - Gender, Marital Status, Age, Estimated Income, Homeownership, Dwelling Type, etc.
- Experience deploying solutions to AWS or cloud services a plus.
- You have strong contributions in development communities, open source projects, or forums.
- You will be working on developing new predictive models, machine learning models, analytical models, data models. Statistical models, financial models and related applications.
- You'll define technical roadmap and work on cutting edge technology in predictive modeling, machine learning and neural networks.
- You will develop predictive models, including a linear regression model other models like ML neural nets, trees, or Na- ve Bayesian.
- You'll benchmark algorithms based on speed, accuracy and robustness.
- You'll implement efficient data structures to enable faster machine learning models.


A family round the corner from me (London Road area) are looking for someone to tutor their daughter for the run up to her maths GCSE. Realistically, she's probably aiming for a C with coaching, so it's not high level stuff. But it would suit a reliable student looking to earn a few quid for one hour's teaching a week. I said I'd put a message up on here because they're quite desperate to find someone.
If you're interested or want to know more, give me a ring: 07810 650213.


In the RSA cryptosystem encryption is performed using C = Me (mod N), where N = pq for suitably chosen large primes p, q, and gcd(e, f(N)) = 1. In a chaining attack on RSA, given a ciphertext C = Me (mod N) the atacker computes, C e (mod N), Ce 2 (mod N), . . . , Ce k (mod N), unless C = C e k (mod N) is obtained. That is, k is the least positive integer that specifies the cycle. (a) Explain why the attacker can always find k ? [1, N – 1] so that C = C e k (mod N). Hint: Recall that RSA is an encryption algorithm and therefore bijective, i.e. M1 6= M2 cannot be mapped to the same ciphertext. (b) Can attacker recover the message M from the observed sequence above in case C = C e k (mod N) is valid ? 17 (c) Explain how the attacker can factor N by finding integer u such that gcd(C e u , N) > 1. Hint: Analyze different cases w.r.t. (mod p) and (mod q) congruences.
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Machine Learning Scientist
Helmholtz-Zentrum Berlin für Materialien und Energie
Dr. Martin Genzel
I'm working as a Machine Learning Scientist at the Helmholtz-Zentrum Berlin für Materialien und Energie (HZB), Germany, affiliated with the department of Optics and Beamlines. I'm an applied mathematician by training, who is fascinated by the idea of solving computationally challenging problems in science by data-driven methods. My current focus is on exploring the power of deep learning algorithms for ill-posed inverse problems, computational/medical imaging, signal-processing, and low-complexity models. Prior to HZB, I was a postdoctoral researcher at the Mathematical Institute of Utrecht University. Before this, I completed my PhD at the Institute of Mathematics of TU Berlin in 2019. My original background is in applied functional analysis, high-dimension probability, and compressed sensing.


Happy Fibonacci Day!
In addition to this Thursday being Thanksgiving here in the States, November 23 is also Fibonacci Day! If you remember from math class, the Fibonacci sequence is an integer sequence in which every number after the first two is the sum of the two preceding numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
While it may look simplistic, the sequence actually has far reaching implications, more than even Fibonacci himself probably imagined!
- Named after Italian mathematician Leonardo of Pisa, known as Fibonacci, who introduced the sequence to Western European mathematics in the 1200's.
- Used in many different mathematics applications & algorithms, but also in investments, artwork, even architecture!*
- The sequence can even be found in nature! Fibonacci spirals, aka 'nature's numbers' can be seen on flower petals and seeds, plant leaves, nautilus shells, the DNA molecule, and even hurricanes and galaxies.
- The spiral is charted as a series of connected quarter-circles drawn inside an array of squares with Fibonacci numbers for dimensions. (see right).
*There is so much more to explore in the Fibonacci sequence! We highly encourage you to do some research on your own to truly appreciate how complex and interesting this sequence is.


2 myths that do not work but are yet tried by most players are:
1-You can increase the chances of a win if you play with the same numbers every week.
Each lotto draw is subject to the exact same conditions and choosing a new line or playing on the same line every week will not change your chances. Since this is a game of chance, you can only turn into a lotto buster if you play with more lines and coupons. Many players still use this lottery strategy by playing with the same numbers every week and I too do the same simply as it is easy and practical to do so.
2-Computers or mathematicians can predict the winning numbers.
This again is just a myth as no lotto program or mathematician can predict the winning numbers as they are chosen randomly.
Instead of following those myths, let us look at how to play lotto sensibly.
Do players bet the same numbers in lotto?
Do players choose certain numbers more frequently instead of actually choosing only random numbers?
Yes, players do end up choosing certain combinations more often and the most common of them is 1-2-3-4-5-6-7. Even if you win on such a combination, you will hardly get any money as other winners too could have picked up that prize on the same combination of numbers.
The below-mentioned numbers too are over-represented and they start in a decreasing order with 21 being the most common:
21 9 27 3 8 15 17 28 22 16 10 33 26 11 4 5 14 7 29 2
For completely random numbers, just write them on scraps of paper before mixing them and drawing out a single number at a time. MyPlusLotto makes it even easier since you can get randomly generated lines simply at the press of a button. If you wish to play with separate numbers then just press the button again to get a new set of numbers.
Randomly numbered lines without the above numbers increase the chances of a solo win as hardly anyone else would have come up with the same combination.
Remember, to win lotto you need to play lotto.


Fondo Henry Yerly
The Henry Yerly Fund is an investment in the talent of students in the Mathematics department of the Faculty of Science.
The Henry Yerly Fund invests in talented students from the Department of Mathematics and the Faculty of Sciences.
It was set up in memory of professor Henry Yerly, who dedicated his life to teaching and contributed greatly to mathematical education in the Universidad de los Andes.
This fund was set up with an initial contribution from professor Henry Yerly who left his inheritance for scholarships to be granted to excellent students studying mathematics. It has also been funded through donations made by alumni, friends, companies, and other members of the Uniandino community.
This scholarship is intended for new and old students studying mathematics who show academic excellence and who have limited financial resources to pay their tuition fees.
Henry Yerly, mathematician (1901 - 1984)
Henry was a Franco-Swiss teacher known as ´Monsieur Yerly´. He was awarded his degree from the University of Fribourg and was in charge of the Department of Physics and Mathematics at the Universidad de los Andes.
His students remembered him for his way of teaching that they called the "Yerly method", which consisted in dividing the subject of study into fundamental parts and then getting the students to present and analyze with the teacher and classmates the area that they had previously prepared on pre-established dates.
Although the method was used in the whole university, particularly in the humanities, the discipline and demands that Monsieur Yerly made in his classes turned him into a symbol of academic rigor.
Donar a Fondo Henry Yerly


Math 2 For Christian Schools (Volumes 1 & 2) Download PDF EPUB FB2
This book is intended to encourage an understanding and appreciation of Mathematics at the Junior High School level in West Africa.
Providing appropriate solutions to examination problems is of Math 6 for Christian Schools - 2nd Edition Hardcover – January 1, out of 5 stars 3 ratings. See all formats and editions Hide other formats and editions.
Price New from Used from Hardcover "Please retry" $ $ $ Hardcover $ 26 Used from Math 2 For Christian Schools book This book is intended to encourage an understanding and appreciation of core mathematics at the Senior High School level in West Africa.
Providing appropriate solutions to examination problems is of particular importance in the study of :// The text contains numerous references to biblical figures and how they used math, for example, the building of the temple by King Solomon. The math concepts are solid but ideas are given within a Christian context when applicable.
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The Math K Home Study Kit con-tains teacher edition and meeting book. Math 1, 2, and 3 kits contain teacher edition, meeting book, and a set of 2 workbooks. Manipulatives Ranked inpart of Best Science Schools. A graduate degree in mathematics can help students hone their skills in a specialty area, from algebra and number theory to discrete mathematics and › Home › Education › Grad Schools › Best Science Schools.
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Seek advice from your high school math teacher if you are still unsure of which test to take. Keep in mind you can choose to take either test on test day, regardless of what test you registered :// /subjects/mathematics/mathematics Welcome to Milestones, a free online collection of videos aimed at helping parents understand grade-level expectations in grades K Milestones show students demonstrating what success looks like in reading, writing and math, grade by grade.
High school Milestones shows some real-world skills kids should know as well as the academic ones A powerful online homework, assessment, & tutorial program. Automatically-graded assignments. Personalized homework and study plans.
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Addition, subtraction, place value, and logic games that boost second grade math :// Middle School Bible Curriculum. Lightbearers is a one or two-semester Christian middle school Bible curriculum designed to help 8th-grade students understand the tenets of the Christian worldview.
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Of these, about million att private high schools, the majority of which are religiously affiliated and explicitly Christian (see ref1 and ref2). In this article, showcases what we regard as the 50 best Christian high schools Horizons math is a bright, workbook-style math program with a spiral approach.
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[YPNG] YPNG 16 Oct 2015
sekhar.tatikonda at yale.edu
Tue Oct 13 17:16:03 EDT 2015
Chao Gao is back by popular demand! This week in the YPNG seminar
he will present:
Title: Network analysis: Community Detection and Graphon Estimation
Abstract: Two important statistical problems arise in the field of network
analysis. While community detection is crucial to understand the clustering
structure of a network, graphon estimation leads us to understand the
underlying data-generating mechanism of a network. In this talk, I will
first discuss minimax rates and polynomial-time algorithms in the two
problems. Then, I will give a general picture to understand network models
from a unified perspective that includes both stochastic block model and
sparse linear regression as special cases.
See you Friday in the Stat's classroom at 11am.
More information about the YPNG


Kids will learn their numbers and have fun while playing with these Transforming Number Bots. The numbers 0-9 transform into various types of trucks, planes and boats. Combine all of the pieces to make one large robot! Includes instructions on how to transform.
- Fun Transforming Toys: Kids will love these bots. All 10 pieces robot can transform from numbers to a combiner robot. More than 5 children in every 10 children love this transforming toys.
- STEM Preschool Learning Toys: Encourages logical thinking and problem solving, encourages your child's imagination to endless possibilities.
- Colorful numbers: This numbers robot toys boost color recognition, numbers learning and calculation skills and color as children play without effort!
- Durable & Easy to Use: High quality workmanship, easy to switch back and forth from Number to Robots.
Teachers can use them as students' classroom prize toys.
Parents can use them as rewards gifts.
Great Educational Toys - This number transforming toys help children develop eye and hand coordination, fine motor skills, creativity, imagination, and promote interaction between parents and children.
Happy Confident Kids! - Transforming Number Bots help kids understand number through hands on learning.
A Stunning Gift Idea! - Whether it’s meant for your own kids or you’re simply attending a birthday or anniversary party, also is best choice as a pinata filler toy, this STEM education toys can keep kids engaged for hours while freeing up more of your time.
Numbers, 2-1/4"H, eachNotes:
For ages 6 and up