Related papers: Generalized Hamming schemes
In this work, we prove a general version of the reduction lemmas for eigenfunctions of graphs admitting involutive automorphisms of a special type.
The well known Hellmann-Feynman theorem of Quantum Mechanics connected with the derivative of the eigenvalues with respect to a parameter upon which the Hamiltonian depends, is generalized to include cases in which the domain of definition…
Based on a generalized Newton's identity, we construct a family of symmetric functions which deform the modular Hall-Littlewood functions. We also give a determinant formula for the Macdonald functions.
An infinite family of association schemes obtained from the general unitary groups acting transitively on the sets of isotropic vectors in the finite unitary spaces are investigated. We compute the parameters and determine the character…
We establish a central limit theorem for the eigenvalue counting function of a matrix of real Gaussian random variables.
We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.
In this paper a generalization of the Gram-Schmidt Algorithm is presented. Actually we provide an algorithm to construct a set of equiangular vectors with a given angle $\theta\in(0,\arccos(\frac{-1}{n-1}))$ using a set of input independent…
Combining the derivative operator with Chu-Vandermonde convolution, we establish a class of summation formulas on generalized harmonic numbers.
We introduce quantum association schemes. This allows to define distance regular and strongly regular quantum graphs. We bring examples thereof. In addition, we formulate the duality for translation quantum association schemes corresponding…
The present article is devoted to one class of generalizations of the Salem functions. To construct such functions by systems of functional equations, the generalized shift operator is used.
A new and easy way of deriving Gauss's Generalized Hypergeometric Theorem is presented by using the Bilateral Binomial Theorem.
We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.
The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].
Generalized additive models (GAMs) provide a way to blend parametric and non-parametric (function approximation) techniques together, making them flexible tools suitable for many modeling problems. For instance, GAMs can be used to…
We extend Stein's lemma for averages that explicitly contain the Gaussian random variable at a power. We present two proofs for this extension of Stein's lemma, with the first being a rigorous proof by mathematical induction. The…
We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet…
We generalize the generating formula for plane partitions known as MacMahon's formula as well as its analog for strict plane partitions. We give a 2-parameter generalization of these formulas related to Macdonald's symmetric functions. The…
We generalize the definition of the polylogarithm classes to the case of commutative group schemes, both in the sheaf theoretic and the motivic setting. This generalizes and simplifies the existing cases.
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
A GGC (Generalized Gamma Convolution) representation of Riemann's Xi-function is constructed.