Related papers: New plans orthogonal through the block factor
We develop techniques useful for obtaining conformal blocks in embedding space. We construct a unique differential operator in embedding space and use it to construct a function that will be an important ingredient in assembling conformal…
We give a method of constructing self-orthogonal codes from equitable partitions of association schemes. By applying this method we construct self-orthogonal codes from some distance-regular graphs. Some of the obtained codes are optimal.…
We consider Koornwinder's method for constructing orthogonal polynomials in two variables from orthogonal polynomials in one variable. If semiclassical orthogonal polynomials in one variable are used, then Koornwinder's construction…
We develop a new method for constructing "good" designs for computer experiments. The method derives its power from its basic structure that builds large designs using small designs. We specialize the method for the construction of…
In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into…
We provide an algorithm for the construction of orthonormal multivariate polynomials that are symmetric with respect to the interchange of any two coordinates on the unit hypercube and are constrained to the hyperplane where the sum of the…
Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We…
This publication is an exercise which extends to two variables the Christoffel's construction of orthogonal polynomials for potentials of one variable with external sources. We generalize the construction to biorthogonal polynomials. We…
In this paper new classes of $L_2$-orthogonal functions are constructed as iterated $L_2$-orthogonal systems. In order to do this we use the theory of the Riemann's zeta-function as well as our theory of Jacob's ladders. The main result is…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
The unextendible orthogonal matrices (UPBs) can be used for various problems in quantum information. We provide an algorithm to check if two UPBs are non-equivalent to each other. We give a method to construct UPBs and we apply this method…
In this paper, we list several interesting structures of cyclotomic polynomials: specifically relations among blocks obtained by suitable partition of cyclotomic polynomials. We present explicit and self-contained proof for all of them,…
The multiplicative Newton-like method developed by the author et al. is extended to the situation where the dynamics is restricted to the orthogonal group. A general framework is constructed without specifying the cost function. Though the…
Orthogonal polynomials with respect to a weight function defined on a wedge in the plane are studied. A basis of orthogonal polynomials is explicitly constructed for two large class of weight functions and the convergence of Fourier…
A step 2 branching decomposition of spaces of homogeneous Hermitian monogenic polynomials in C^n is established with explicit embedding factors in terms of the generalized Jacobi polynomials, which allows for an inductive construction of an…
This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually…
Proof Blocks is a software tool which enables students to write proofs by dragging and dropping prewritten proof lines into the correct order. These proofs can be graded completely automatically, enabling students to receive rapid feedback…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…
A novel approach for structure alignment is presented, where the key ingredients are: (1) An error function formulation of the problem simultaneously in terms of binary (Potts) assignment variables and real-valued atomic coordinates. (2)…
Compositional data are commonly known as multivariate observations carrying relative information. Even though the case of vector or even two-factorial compositional data (compositional tables) is already well described in the literature,…