Related papers: Derivation of vector-valued complex interpolation …
In this article, discrete variants of several results from vector calculus are studied for classical finite difference summation by parts operators in two and three space dimensions. It is shown that existence theorems for scalar/vector…
We introduce the affine Vogan diagrams of complex simple Lie algebras. These are generalizations of Vogan diagrams, and we study the involutions represented by them. We apply these diagrams to study the symmetric pairs, in particular the…
The Alexander-Hirschowitz theorem says that a general collection of $k$ double points in ${\bf P}^n$ imposes independent conditions on homogeneous polynomials of degree $d$ with a well known list of exceptions. We generalize this theorem to…
We consider a specific scheme of multivariate Birkhoff polynomial interpolation. Our samples are derivatives of various orders $k_j$ at fixed points $v_j$ along fixed straight lines through $v_j$ in directions $u_j$, under the following…
We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for…
In this study, new master theorems and general formulas of integrals are presented and implemented to solve some complicated applications in different fields of science. The proposed theorems are considered to be generators of new problems,…
This expository thesis contains a study of four interpolation theorems, the requisite background material, and a few applications. The materials introduced in the first three sections of Chapter 1 are used to motivate and prove the…
In this paper, the theory of McCarthy's extensional arrays enriched with a maxdiff operation (this operation returns the biggest index where two given arrays differ) is proposed. It is known from the literature that a diff operation is…
Existing techniques for Craig interpolation for the quantifier-free fragment of the theory of arrays are inefficient for computing sequence and tree interpolants: the solver needs to run for every partitioning $(A, B)$ of the interpolation…
We reprove the results of Jordan [18] and Siebert [31] and show that the Lie algebra of polynomial vector fields on an irreducible affine variety X is simple if and only if X is a smooth variety. Given proof is self-contained and does not…
We study a class of Lorentz violating quantum field theories that contain higher space derivatives, but no higher time derivatives, and become renormalizable in the large N expansion. The fixed points of their renormalization-group flows…
We prove that there are continuum-many axiomatic extensions of the full Lambek calculus with exchange that have the deductive interpolation property. Further, we extend this result to both classical and intuitionistic linear logic as well…
We show, in Zermelo-Fraenkel set theory without the Axiom of Choice, that the existence of a discontinuous homomorphism of the additive group of real numbers induces a selector for the Vitali equivalence relation $\mathbb{R}/\mathbb{Q}$.…
This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations with completely monotone kernels, such as linear…
In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory $\mathcal{T}_0$ with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which…
For analytic operator functions, we prove accumulation of branches of complex eigenvalues to the essential spectrum. Moreover, we show minimality and completeness of the corresponding system of eigenvectors and associated vectors. These…
Let $\mathcal{A}$ be a real line arrangement and $\mathcal{D}(\mathcal{A})$ the module of $\mathcal{A}$-derivations view as the set of polynomial vector fields which possess $\mathcal{A}$ as an invariant set. We first characterize…
In order to understand the parameter space of monic and centered complex polynomial vector fields of degree d in the complex plane, decomposed by the combinatorial classes of the vector fields, it is interesting to know the number of loci…
In this paper, we survey constructions of and nonexistence results on combinatorial/geometric structures which arise from unions of cyclotomic classes of finite fields. In particular, we survey both classical and recent results on…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…