In this paper, a new discriminant analysis for feature extraction is derived from the perspective of least squares regression. To obtain great discriminative power between classes, all the data points in each class are expected to be regressed to a single vector, and the basic task is to find a transformation matrix such that the squared regression error is minimized. To this end, two least squ...

According to the information redundancy of non-orthogonal moment invariants, and the discrete error of continuous orthogonal moments, in order to improve the recognition accuracy, a new image recognition method using radial Krawtchouk moment invariants proposed in this paper. The image blur and affine transformation mathematical model is built, then, using Krawtchouk polynomials which has bette...

Under certain constraints on the parameters a, b and c, it is known that Schrödinger’s equation −d2ψ/dx2 + (ax + bx + cx)ψ = Eψ, a > 0 with the sextic anharmonic oscillator potential is exactly solvable. In this article we show that the exact wave function ψ is the generating function for a set of orthogonal polynomials {P (t) n (x)} in the energy variable E. Some of the properties of these pol...

Novel discrete orthogonal transforms are introduced in this paper, namely the unified complex Hadamard transforms. These transforms have elements confined to four elementary complex integer numbers which are generated based on the Walsh–Hadamard transform, using a single unifying mathematical formula. The generation of higher dimension transformation matrices are discussed in detail.

This paper is concerned with expansions of distributions in terms of the generalized heat polynomials and of their Appell transforms. Two different techniques are used to prove theorems concerning expansions of distributions. A theorem which provides an orthogonal series expansion of generalized functions is also established. It is shown that this theorem gives an inversion formula for a certai...

This paper shows how to obtain the spinor field and dynamics from the vielbein and geometry of General Relativity. The spinor field is physically realized as an orthogonal transformation of the vielbein, and the spinor action enters as the requirement that the unit time form be the gradient of a scalar time field.

For a realistic biophysical model, a linear deformation of the myocardium lead to a linear transformation of the orthogonal electrocardiosignals under the condition of topological invariability of the depolarization and repolarization processes in the myocardium. Certain relationships have been found between the linear transformations in the physical and functional spaces. Several practically i...

We present an asymmetric q-Painlevé equation. We will derive this using q-orthogonal polynomials with respect to generalized Freud weights: their recurrence coefficients will obey this q-Painlevé equation (up to a simple transformation). We will show a stable method of computing a special solution which gives the recurrence coefficients. We establish a connection between the newfound equation a...

In this paper we introduce a new representation of orthogonal matrices. We show that any orthogonal matrix can be represented in the form Q = I ? Y SY T , which we call the basis-kernel representation of Q. We show that the kernel S can be chosen to be triangular and show how the familiar representation of an orthogonal matrix as a product of Householder matrices can be directly derived from a ...

A (symmetric) nested orthogonal array is a symmetric orthogonal array OA(N, k, s, g) which contains an OA(M,k, r, g) as a subarray, where M < N and r < s. In this communication, some methods of construction of nested symmetric orthogonal arrays are given. Asymmetric nested orthogonal arrays are defined and a few methods of their construction are described.