Related papers: Steenbrink vanishing extended
Supersymmetry is one of the most plausible and theoretically motivated frameworks for extending the Standard Model. However, any supersymmetry in Nature must be a broken symmetry. Dynamical supersymmetry breaking (DSB) is an attractive idea…
A cohomological vanishing property is proved for finitely supported ideals in an arbitrary d-dimensional regular local ring. (Such vanishing implies some refined Briancon-Skoda-type results, not otherwise known in mixed characteristic.) It…
We establish the singularity with respect to Lebesgue measure as a function of time of the conditional probability that the sum of two one-dimensional Brownian motions will exit from the unit interval before time $t$, given the trajectory…
Non-equilibrium systems in steady states are commonly described by generalized statistical mechanical theories such as non-extensive statistics and superstatistics. Superstatistics assumes that the inverse temperature $\beta = 1/(k_B T)$…
We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any…
For regular local ring, the ``second vanishing theorem'' or ``SVT'' of local cohomology has been proved in several cases. In this paper, we explore the result similar to that of the SVT to Stanley-Reisner ring with an interpretation from…
Initially developed to capture technical innovation and later adapted to identify scientific breakthroughs, the Disruption Index (D-index) offers the first quantitative framework for analyzing transformative research. Despite its promise,…
We develop the `duality approach', that has been extensively studied for classical models of transport, for quantum systems in contact with a thermal `Lindbladian' bath. The method provides (a) a mapping of the original model to a simpler…
The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with…
We prove a general vanishing theorem for the cohomology of products of symmetric and skew-symmetric powers of an ample vector bundle on a smooth complex projective variety. Special cases include an extension of classical theorems of…
This is a mostly expository paper, intended to explain a very natural relationship between two a priori distinct notions appearing in the literature: Generic Vanishing in the context of vanishing theorems and birational geometry, and…
The deleting items and disturbing mesh theorems of Riemann Integral are extended to multiple integral,line integral and surface integral respectively by constructing various of incomplete Riemann sum and non-Riemann sum sequences which…
A natural unit interval order is a naturally labelled partially ordered set that avoids patterns ${\bf 3} + {\bf 1}$ and $\bf 2 + 2$. To each natural unit interval order one can associate a symmetric function. The Stanley-Stembridge…
This is a sequel to "Kodaira-Saito vanishing via Higgs bundles in positive characteristic" (arXiv:1611.09880). However, unlike the previous paper, all the arguments here are in characteristic zero. The main result is a Kodaira vanishing…
We give a diagrammatic summary of the connections between various theorems and conjectures about the vanishing of the Euler characteristic.
We examine the various indices defined on pairs of almost commuting unitary matrices that can detect pairs that are far from commuting pairs. We do this in two symmetry classes, that of general unitary matrices and that of self-dual…
In this article, we give a condition on the vanishing of finitely many homogeneous components which must imply the asymptotic vanishing for multigraded modules. We apply our result to multi-Rees algebras of ideals. As a consequence, we…
In this article we introduce a dual of the uniform boundedness principle which does not require completeness and gives an indirect means for testing the boundedness of a set. The dual principle, although known to the analyst and despite its…
A new index for internal evaluation of clustering is introduced. The index is defined as a mixture of two sub-indices. The first sub-index $ I_a $ is called the Ambiguous Index; the second sub-index $ I_s $ is called the Similarity Index.…
The paper attempts to develop a suitable accessibility index for networks where each link has a value such that a smaller number is preferred like distance, cost, or travel time. A measure called distance sum is characterized by three…