Related papers: Some Extensions of Witt's Theorem
We prove a general extension theorem for holomorphic line bundles on reduced complex spaces, equipped with singular hermitian metrics, whose curvature currents can be extended as positive, closed currents. The result has applications to…
In this note, we show that there is some counterexample for isoperimetric inequality if the condition $(\phi')^2-\phi"\phi\leq 1$ does not hold in warped product space.
We prove a conjecture that arose in the context of a subspace enumeration problem over finite fields. We prove, more generally, a bibasic, double-sum identity, which extends a $q$-analogue of the (terminating) binomial theorem.
Extra dimensions with boundaries are often used in the literature, to provide phenomenological models that mimic the standard model. In this context, we explore possible modifications to Newton's law due to the existence of an…
It is proposed that to the usual probability theory, three definitions and a new theorem are added, the resulting theory allows one to displace the central role usually given to the notion of conditional probability. When a mapping $\phi$…
A flag of codes $C_0 \subsetneq C_1 \subsetneq \cdots \subsetneq C_s \subseteq {\mathbb F}_q^n$ is said to satisfy the {\it isometry-dual property} if there exists ${\bf x}\in (\mathbb{F}_q^*)^n$ such that the code $C_i$ is {\bf…
We show that any quantum irreducible flag manifold satisfies an analogue of the Einstein condition, expressing proportionality between the Ricci tensor and the metric, at least in a small open interval around the classical value of the…
Given a conformal QFT local net of von Neumann algebras B_2 on the two-dimensional Minkowski spacetime with irreducible subnet A\otimes\A, where A is a completely rational net on the left/right light-ray, we show how to consistently add a…
Given a finite set $E$, a subset $D\sub E$ (viewed as a function $E\to \F_2$) is orthogonal to a given subspace $\FF$ of the $\F_2$-vector space of functions $E\to \F_2$ as soon as $D$ is orthogonal to every $\sub$-minimal element of $\FF$.…
The purpose of this paper is to study Virasoro extensions of the q-deformed Witt Hom-Lie superalgebra. Moreover, we provide the cohomology and deformations of the Ramond Hom-superalgebra and special Ramond Hom-superalgebra.
The aim of this paper is twofold. The first is to give a quantitative version of Schmidt's subspace theorem for arbitrary families of higher degree polynomials. The second is to give a generalization of the subspace theorem for arbitrary…
T-duality of gauge theories on a noncommutative $T^d$ can be extended to include fields with twisted boundary conditions. The resulting T-dual theories contain novel nonlocal fields. These fields represent dipoles of constant magnitude.…
For any non-degenerate, quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a corresponding cohomological field theory associated to the singularity. This theory is analogous to…
The problem of bi-equivariant extension of continuous maps of binary $G$-spaces is considered. The concept of a structural map of distributive binary $G$-spaces is introduced, and a theorem on the bi-equivariant extension of structural maps…
Let $F$ be a field of characteristic $2$, $\pi$ be an $n$-fold bilinear Pfister form over $F$ and $\varphi$ an arbitrary quadratic form over $F$. In this note, we investigate Witt index, defect, total isotropy index and higher isotropy…
The aim of the article is an extension of the Monodromy Conjecture of Denef and Loeser in dimension two, incorporating zeta functions with differential forms and targeting all monodromy eigenvalues, and also considering singular ambient…
We establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a Schubert polynomial by either an elementary…
We extend the concept of the law of a finite graph to graphings, which are, in general, infinite graphs whose vertices are equipped with the structure of a probability space. By doing this, we obtain a vast array of new unimodular measures.…
The Whitney extension theorem is a classical result in analysis giving a necessary and sufficient condition for a function defined on a closed set to be extendable to the whole space with a given class of regularity. It has been adapted to…
We extend harmonic map techniques to the setting of more general differential equations in conformal geometry. We obtain an extension of Siu's rigidity to Kahler-Weyl geometry and apply the latter to Vaisman's conjecture. Other applications…