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arXiv Preprints
Chevalley formulae for the motivic Chern classes of Schubert cells and for the stable envelopes
We prove a Chevalley formula to multiply the motivic Chern classes of Schubert cells in a generalized flag manifold $G/P$ by the class of any line bundle $\mathcal{L}_λ$. Our formula is given in terms of the $λ$-chains of Lenart and Postnikov. Its ...
math:math:AGmath:math:COmath:math:RT
arXiv Preprints
Coherent Quantum Speed Limits
We establish a comprehensive theoretical framework for coherent quantum speed limits (QSLs), deriving fundamental bounds on the rate of quantum evolution that explicitly isolate the contribution of quantum coherence. By applying Hölder's inequa...
physics:quant-phphysics:cond-mat:quant-gas
arXiv Preprints
Harnack inequalities for equations of type prescribed scalar curvature
We give Harnack inequalities for solutions of equations of type prescribed scalar curvature in dimensions n $\ge$ 4.
math:math:AP
arXiv Preprints
Limits on the Primordial Black Holes Dark Matter with future MeV detectors
Primordial black holes (PBHs) are a compelling candidate for Dark Matter (DM). There remain significant parameter spaces to be explored despite current astrophysical observations have set strong limits. Utilizing advanced MeV observation instruments,...
physics:astro-ph:HE
arXiv Preprints
On the Frobenius fields of abelian varieties over number fields
Let $A$ be a non-CM simple abelian variety over a number field $K$. For a place $v$ of $K$ such that $A$ has good reduction at $v$, let $F(A,v)$ denote the Frobenius field generated by the corresponding Frobenius eigenvalues. Assuming $A$ has connect...
math:math:NT
arXiv Preprints
Lower bounds on fibered Yang-Mills functionals: generic nefness and semistability of direct images
The main goal of this paper is to generalize a part of the relationship between mean curvature and Harder-Narasimhan filtrations of holomorphic vector bundles to arbitrary polarized fibrations. More precisely, for a polarized family of complex projec...
math:math:DGmath:math:AGmath:math:CV
arXiv Preprints
MLFEF: Machine Learning Fusion Model with Empirical Formula to Explore the Momentum in Competitive Sports
Tennis is so popular that coaches and players are curious about factors other than skill, such as momentum. This article will try to define and quantify momentum, providing a basis for real-time analysis of tennis matches. Based on the tennis Grand S...
cs:cs:LG
arXiv Preprints
The $\bar\partial$-problem on $Z(q)$-domains
Given a complex manifold containing a relatively compact $Z(q)$ domain, we give sufficient geometric conditions on the domain so that its $L^2$-cohomology in degree $(p,q)$ (known to be finite dimensional) vanishes. The condition consists of the exis...
math:math:CV
arXiv Preprints
Cabello's nonlocality argument for multisetting high-dimensional systems and its experimental test
Recent advancements have expanded Hardy's nonlocality arguments into multisetting and multidimensional systems to enhance quantum correlations. In comparison with Hardy's nonlocal argument, Cabello's nonlocal argument (CNA) emerges as ...
physics:quant-ph
arXiv Preprints
Exact upper bounds for the minimum sizes of strong and weak separating path systems of cliques
We prove an upper bound of $n+9$ for the strong separation number of the complete graph $K_n$, and an upper bound of $n+1$ for its weak separation number. This improves on the previous best known bound of $(1+o(1))n$ for both cases.
math:math:CO
arXiv Preprints
Systematic errors in searches for nanohertz gravitational waves
A number of pulsar timing arrays have recently reported preliminary evidence for the existence of a nanohertz frequency gravitational-wave background. These analyses rely on detailed noise analyses, which are inherently complex due to the many astrop...
physics:astro-ph:HE
arXiv Preprints
Arena: Efficiently Training Large Models via Dynamic Scheduling and Adaptive Parallelism Co-Design
Efficiently training large-scale models (LMs) in GPU clusters involves two separate avenues: inter-job dynamic scheduling and intra-job adaptive parallelism (AP). However, existing dynamic schedulers struggle with large-model scheduling due to the mi...
cs:cs:DCcs:cs:LG
arXiv Preprints
New and old Saito-Kurokawa lifts classically via $L^2$ norms and bounds on their supnorms: level aspect
In the first half of the paper, we lay down a classical approach to the study of Saito-Kurokawa (SK) lifts of (Hecke congruence) square-free level, including the allied new-oldform theory. Our treatment of this relies on a novel idea of computing ran...
math:math:NT
arXiv Preprints
Mekler's Construction and Murphy's Law for 2-Nilpotent Groups
Mekler's construction is a powerful technique for building purely algebraic structures from combinatorial ones. Its power lies in the fact that it allows various model-theoretic tameness properties of the combinatorial structure to transfer to t...
math:math:LOmath:math:COmath:math:GR
arXiv Preprints
Quantifying Noise of Dynamic Vision Sensor
Dynamic visual sensors (DVS) are characterized by a large amount of background activity (BA) noise, which it is mixed with the original (cleaned) sensor signal. The dynamic nature of the signal and the absence in practical application of the ground t...
cs:cs:CV
arXiv Preprints
Raman resonances mediated by excitonic polarons in BiVO$_4$
Excitonic polarons are quasiparticles formed by a Coulomb-bound electron-hole pair with strong coupling to lattice vibrations. Despite high fundamental interest in excitonic polarons, the experimental investigation of these particles remains challeng...
physics:cond-mat:mtrl-sci
arXiv Preprints
All meromorphic solutions of Fermat-type functional equations
In this paper, by making use of properties of elliptic functions, we describe meromorphic solutions of Fermat-type functional equations $f(z)^{n}+f(L(z))^{m}=1$ over the complex plane $\mathbb{C}$, where $L(z)$ is a nonconstant entire function, $m$ a...
math:math:CV
arXiv Preprints
Bifurcations for Lagrangian systems and geodesics II
This is the second part of a two--part series investigating bifurcation phenomena in autonomous Lagrangian systems and geodesic flows on Finsler and Riemannian manifolds. Building upon the abstract bifurcation theorems established in earlier work and...
math:math:DSmath:math:CAmath:math:DGmath:math:FA
arXiv Preprints
RIS-aided Wireless Communication with Movable Elements Geometry Impact on Performance
Reconfigurable Intelligent Surfaces (RIS) are known as a promising technology to improve the performance of wireless communication networks, and have been extensively studied. Movable Antennas (MA) are a novel technology that fully exploits the anten...
eess:eess:SYcs:cs:SY
arXiv Preprints
On the Decidability of Monadic Theories of Arithmetic Predicates
We investigate the decidability of the monadic second-order (MSO) theory of the structure $\langle \mathbb{N};<,P_1, \ldots,P_d \rangle$, for various unary predicates $P_1,\ldots,P_d \subseteq \mathbb{N}$. We focus in particular on 'arithmeti...
cs:cs:LO