相关论文: Norm principles for forms of higher degree permitt…
The scalar field theory with higher derivatives is considered in the first order formalism. The field equation of the forth order describes scalar particles possessing two mass states. The first order relativistic wave equation in the…
Notions of finite type play an important role in several complex variables. The most standard notion is D'Angelo type, which measures the order of contact of holomorphic curves with the boundary of a domain in ${\mathbb C}^n$. For the $\bar…
Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work we extend this…
We use a generalization of a construction by Ziegler to show that for any field $F$ and any countable collection of countable subsets $A_i \subseteq F, i \in \calI \subset \Z_{>0}$ there exist infinitely many fields $K$ of arbitrary…
Let k be a global field of characteristic not 2. The classical Hasse-Minkowski theorem states that if two quadratic forms become isomorphic over all the completions of k, then they are isomorphic over k as well. It is natural to ask whether…
The basis for the field theory are properties of the closed exterior differential forms (skew-symmetric differential forms defined on manifolds with the closed metric forms), which reflect properties of the conservation laws for physical…
This paper has been withdrawn. This paper focuses on the admissibility condition for fractional-order singular system with order $\alpha \in (0,1)$. The definitions of regularity, impulse-free and admissibility are given first, then a…
Schwinger's formalism in quantum field theory can be easily implemented in the case of scalar theories in $D$ dimension with exponential interactions, such as $\mu^D\exp(\alpha\phi)$. In particular, we use the relation $$…
We give an upper bound for the norm of the determinant of additively indecomposable, totally positive definite quadratic forms defined over the ring of integers of totally real number fields. We apply these results to find lower and upper…
A finite group $G$ is said to be admissible over a field $F$ if there exists a division algebra $D$ central over $F$ with a maximal subfield $L$ such that $L/F$ is Galois with group $G$. In this paper we give a complete characterization of…
We consider a "superposition operator" obtained through the continuous superposition of operators of mixed fractional order, modulated by a signed Borel finite measure defined over the set $[0, 1]$. The relevance of this operator is rooted…
In this article, the standard correspondence between the ideal class group of a quadratic number field and the equivalence classes of binary quadratic forms of given discriminant is generalized to any base number field of narrow class…
We define the notion of a sheaf over a complex of groups. As an application, we give a criterion for the developability of a complex of groups. When the developability is witnessed by a morphism to $\mathrm{GL}(V)$ for some $V$, our…
In this paper we prove two new abstract compactness criteria in normed spaces. To this end we first introduce the notion of an equinormed set using a suitable family of semi-norms on the given normed space satisfying some natural…
We obtain lower bounds for the maximum dimension of a simple FG-module, where G is a finite group and F is an algebraically closed field of characteristic p. The bounds are described in terms of properties of p-subgroups of G. When p is 2…
We consider a weak version of the Rost Nilpotence Principle. For characteristic zero fields k, we show that if it holds for all smooth projective schemes over k, then the Rost Nilpotence Principle does also. We also correct the proof of a…
In two companion papers it was shown how to separate out from a scattering function in quantum electrodynamics a distinguished part that meets the correspondence-principle and pole-factorization requirements. The integrals that define the…
Recently, the $k$-normal element over finite fields is defined and characterized by Huczynska et al.. In this paper, the characterization of $k$-normal elements, by using to give a generalization of Schwartz's theorem, which allows us to…
We prove a differential analog of a theorem of Chevalley on extending homomorphisms for rings with commuting derivations, generalizing a theorem of Kac. As a corollary, we establish that, under suitable hypotheses, the image of a…
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.