相关论文: The method of characteristics, and "problem 89" of…
Graham, Knuth and Patashnik in their book Concrete Mathematics called for development of a general theory of the solutions of recurrences defined by $$\left|{ n\atop k}\right|=(\alpha n+\beta k+\gamma)\left|{n-1\atop k}\right|+(\alpha'…
In the 1960s, Atkinson introduced an abstract algebraic setting for multiparameter eigenvalue problems. He showed that a nonsingular multiparameter eigenvalue problem is equivalent to the associated system of generalized eigenvalue…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop…
We apply a version of the dressing method to a system of four dimensional nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform Method) and…
We survey three methods for proving that the characteristic polynomial of a finite lattice factors over the nonnegative integers and indicate how they have evolved recently. The first technique uses geometric ideas and is based on…
In this paper, we present a parallel scheme to solve the population balance equations based on the method of characteristics and the finite element discretization. The application of the method of characteristics transform the higher…
We point out how to use the classical characteristic method, that is used to solve quasilinear PDE's, to obtain the matrix exponential of some lower triangle infinite matrices. We use the Lie Frechet structure of the Riordan group described…
A characteristic pair is a pair (G,C) of polynomial sets in which G is a reduced lexicographic Groebner basis, C is the minimal triangular set contained in G, and C is normal. In this paper, we show that any finite polynomial set P can be…
This mini-course provides a presentation of the method of characteristics to initial/boundary-value problems for systems of first-order partial differential equations and to Hamilton-Jacobi variational inequalities. In particular, these…
We present a coherent Bayesian framework for selection of the most likely model from the five genetic models (genotypic, additive, dominant, co-dominant, and recessive) commonly used in genetic association studies. The approach uses a…
We present efficient combinatorial parameterized algorithms for several classical graph-based counting problems in computational chemistry, including (i) Kekule structures, (ii) the Hosoya index, (iii) the Merrifield-Simmons index, and (iv)…
The problem "A general characterization of uniqueness polynomial for non-critically injective polynomials" has been remained open since the last two decades. In this paper, we explore this open problem. To this end, we initiate a new…
A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to…
We present randomized algorithms for some well-studied, hard combinatorial problems: the k-path problem, the p-packing of q-sets problem, and the q-dimensional p-matching problem. Our algorithms solve these problems with high probability in…
Linear compartmental models are a widely used tool for analyzing systems arising in biology, medicine, and more. In such settings, it is essential to know whether model parameters can be recovered from experimental data. This is the…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…
In this paper we construct a combinatorial algorithm of resolution of singularities for binomial ideals, over a field of arbitrary characteristic. This algorithm is applied to any binomial ideal. This means ideals generated by binomial…
The method of characteristics is a key tool for studying consistency of equations of motion; it allows issues such as predictability, maximal propagation speed, superluminality, unitarity and acausality to be addressed without requiring…