Related papers: Holonomic rank of A-hypergeometric differential-di…
HodgeRank generalizes ranking algorithms, e.g. Google PageRank, to rank alternatives based on real-world (often incomplete) data using graphs and discrete exterior calculus. It analyzes multipartite interactions on high-dimensional networks…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…
A tautological system, introduced in [16][17], arises as a regular holonomic system of partial differential equations that govern the period integrals of a family of complete intersections in a complex manifold $X$, equipped with a suitable…
We prove that the space of Gevrey solutions of an $A$--hypergeometric system along a coordinate subspace is contained in a space of formal Nilsson solutions. Moreover, under some additional conditions, both spaces are equal. In the process…
The purpose of the paper is three-fold: (a) we prove that every sequence which is a multidimensional sum of a balanced hypergeometric term has an asymptotic expansion of Gevrey type-1 with rational exponents, (b) we construct a class of…
In this paper we introduce a method of characteristic sets with respect to several term orderings for difference-differential polynomials. Using this technique, we obtain a method of computation of multivariate dimension polynomials of…
In this paper we investigate the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations with entire or meromorphic coefficients. We further extend and improve few results on the order of meromorphic…
We study universal polynomials of characteristic classes associated to the $\mathcal{A}$-classification (i.e. up to right-left equivalence) of holomorphic map-germs $(\mathbb{C}^2,0) \to (\mathbb{C}^n, 0)$ $(n=2,3)$. That enables us to…
It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper we generalize this property to finite-dimensional commutative algebras. We prove that if some basis of a…
A systematic approach is developed in order to obtain spherically symmetric midisuperspace models that accept holonomy modifications in the presence of matter fields with local degrees of freedom. In particular, starting from the most…
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
In this paper, a normality criterion concerning a sequence of meromorphic functions and their differential polynomials is obtained. Precisely, we have proved: Let $\left\{f_j\right\}$ be a sequence of meromorphic functions in the open unit…
It is shown how the dimension of any arbitrary over-determined system of differential equations can be reduced, which makes the system suitable for numerical solution modeling. Specifically, over-determined equations of hydrodynamics are…
Grothendieck has proved that each class in the de Rham cohomology of a smooth complex affine variety can be represented by a differential form with polynomial coefficients. After having proved a single exponential bound for the degrees of…
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…
There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which the squared-norm of the Hessian is a nonzero multiple of the quadratic form defining the Euclidean…
We study holomorphic functions attaining weighted norms and its connections with the classical theory of norm attaining holomorphic functions. We prove that there are polynomials on $\ell_p$ which attain their weighted but not their…
If \A is a complex hyperplane arrangement, with complement X, we show that the Chen ranks of G=\pi_1(X) are equal to the graded Betti numbers of the linear strand in a minimal, free resolution of the cohomology ring A=H^*(X,\k), viewed as a…
The central idea of this article is to present a systematic approach to construct some recurrence relations for the solutions of the second-order linear difference equation of hypergeometric-type defined on the quadratic-type lattices. We…
We introduce the decomposition rank, a notion of covering dimension for nuclear C^*-algebras. The decomposition rank generalizes ordinary covering dimension and has nice permanence properties; in particular, it behaves well with respect to…