Tootfinder

Multiplicity free induction for the pairs $(\mathrm{GL}_{2}\times\mathrm{GL}_{2},\mathrm{diag}(\mathrm{GL}_{2}))$ and $(\mathrm{SL}_{3},\mathrm{GL}_{2})$ over finite fields
Elias Depuydt, Maarten van Pruijssen
https://arxiv.org/abs/2507.10790

Multiplicity free induction for the pairs $(\mathrm{GL}_{2}\times\mathrm{GL}_{2},\mathrm{diag}(\mathrm{GL}_{2}))$ and $(\mathrm{SL}_{3},\mathrm{GL}_{2})$ over finite fields
We classify the irredible representations of $\mathrm{GL}_{2}(q)$ for which the induction to the product group $\mathrm{GL}_{2}(q)\times\mathrm{GL}_{2}(q)$, under the diagonal embedding, decomposes multiplicity free. It turns out that only the irreducible representations of dimensions $1$ and $q-1$ have this property. We show that for $\mathrm{GL}_{2}(q)$ embedded into $\mathrm{SL}_{3}(q)$ via $g\mapsto\mathrm{diag}(g,\det g^{-1})$ none of the irreducible representations of $\mathrm{GL}_{2}(q)$…

Three more proofs of two congruences for Merca's partition function
Fabrizio Zanello
https://arxiv.org/abs/2509.09833 https://arxiv.org/pdf/2509.09833

Three more proofs of two congruences for Merca's partition function
In this note, we provide three new, very short proofs of two interesting congruences for Merca's partition function $a(n)$, which enumerates integer partitions where the odd parts have multiplicity at most 2. These modulo 2 congruences were first shown elementarily by Sellers. We then frame $a(n)$ into the much broader context of eta-quotients, and suggest how to comprehensively describe its parity behavior. In particular, extensive computations suggest that $a(n)$ is odd precisely 25\% of the …

Multiplicity dependence of $\Xi_c^ $ and $\Xi_c^0$ production in pp collisions at $\sqrt{s} = 13$ TeV
ALICE Collaboration
https://arxiv.org/abs/2508.09955 https://

Multiplicity dependence of $Ξ_c^+$ and $Ξ_c^0$ production in pp collisions at $\sqrt{s} = 13$ TeV
The first measurement at midrapidity ($|y| < 0.5$) of the production yield of the strange-charm baryons $Ξ_c^+$ and $Ξ_c^0$ as a function of charged-particle multiplicity in proton-proton collisions at $\sqrt{s} = 13$ TeV with the ALICE experiment at the LHC is reported. The $Ξ_c^+$ baryon is reconstructed via the $Ξ_c^+ \rightarrow Ξ^-π^+π^+$ decay channel in the range $4 < p_{\rm T} < 12$ GeV/$c$, while the $Ξ_c^0$ baryon is reconstructed via both the $Ξ_c^0 \rightarrow Ξ^…

Two-particle cumulant distribution: a probe of "true" elliptic flow
Satya Ranjan Nayak, Akash Das, B. K. Singh
https://arxiv.org/abs/2507.11026 h…

Two-particle cumulant distribution: a probe of "true" elliptic flow
In this work, we have shown the two-particle correlations of charged hadrons in d-Au collisions at 200 GeV. These correlations were studied at different multiplicities and pseudorapidity intervals. The two-particle correlations arise due to Color Reconnections, resonance decays, jet correlations, and "jet-like" correlations of low-energy partons in softer interactions. These correlations are inversely proportional to multiplicity but remain unaffected (slowly increase) for larger pseudorapidity…

"A 6 or a 9?": Ensemble Learning Through the Multiplicity of Performant Models and Explanations
Gianlucca Zuin, Adriano Veloso
https://arxiv.org/abs/2509.09073 https:/…

"A 6 or a 9?": Ensemble Learning Through the Multiplicity of Performant Models and Explanations
Creating models from past observations and ensuring their effectiveness on new data is the essence of machine learning. However, selecting models that generalize well remains a challenging task. Related to this topic, the Rashomon Effect refers to cases where multiple models perform similarly well for a given learning problem. This often occurs in real-world scenarios, like the manufacturing process or medical diagnosis, where diverse patterns in data lead to multiple high-performing solutions.…

Persistence probabilities for fractionally integrated fractional Brownian noise
G. Molchan
https://arxiv.org/abs/2509.10265 https://arxiv.org/pdf/2509.1026…

Persistence probabilities for fractionally integrated fractional Brownian noise
The main object the study is fractionally integrated fractional Brownian noise, I(t/a,H) where a>0 is the multiplicity(not necessarily an integer) of integration, and H is the Hurst parameter . The subject of the analysis is the persistence exponent e(a,H) that determines the power-law asymptotic of probability that the process will not exceed a fixit positive level in a growing time interval (0,T). In the important cases (a=1,H) and (a=2,H=1/2) these exponents are well known. To understand the…

Dependent Multiplicities in Dependent Linear Type Theory
Maximilian Dor\'e
https://arxiv.org/abs/2507.08759 https://arxiv.org/pdf…

Dependent Multiplicities in Dependent Linear Type Theory
We present a novel dependent linear type theory in which the multiplicity of some variable - i.e., the number of times the variable can be used in a program - can depend on other variables. This allows us to give precise resource annotations to many higher-order functions that cannot be adequately typed in any other system. Inspired by the Dialectica translation, our typing discipline is obtained by embedding linear logic into dependent type theory and specifying how the embedded logic interact…

Index theory for non-compact quantum graphs
Daniele Garrisi, Alessandro Portaluri, Li Wu
https://arxiv.org/abs/2509.09749 https://arxiv.org/pdf/2509.09749

Index theory for non-compact quantum graphs
We develop an index theory for variational problems on noncompact quantum graphs. The main results are a spectral flow formula, relating the net change of eigenvalues to the Maslov index of boundary data, and a Morse index theorem, equating the negative directions of the Lagrangian action with the total multiplicity of conjugate instants along the edges. These results extend classical tools in global analysis and symplectic geometry to graph based models, with applications to nonlinear wave e…

Multiplicity dependence of the entropy and heat capacity for pp collisions at LHC energies
C. E. Mungu\'ia L\'opez, D. Rosales Herrera, J. R. Alvarado Garc\'ia, A. Fern\'andez T\'ellez, J. E. Ram\'irez
https://arxiv.org/abs/2508.05058

Multiplicity dependence of the entropy and heat capacity for pp collisions at LHC energies
We investigate the multiplicity dependence of the transverse momentum spectrum of the charged particle production in pp collisions at LHC energies. To this end, we consider the experimental data sets classified with different multiplicity estimators, defined by the ALICE Collaboration, that are analyzed within the framework of nonextensive particle production. We compute the variance, kurtosis, Shannon entropy, and heat capacity of the $p_T$ spectrum to study the hardening process as a function…

Joint reductions and mixed Buchsbaum-Rim multiplicities of modules and a joint-reduction-number-zero theorem
Daniel Katz, Vijay Kodiyalam, J. K. Verma
https://arxiv.org/abs/2508.07437

Joint reductions and mixed Buchsbaum-Rim multiplicities of modules and a joint-reduction-number-zero theorem
We offer new definitions of joint reductions and mixed Buchsbaum-Rim multiplicity for certain collections of modules over a Noetherian local ring and illustrate their application to give two different proofs of a joint-reduction-number-zero theorem for integrally closed modules over two-dimensional regular local rings. We also relate the mixed Buchsbaum-Rim multiplicity of modules to the Euler-Poincaré characteristic of a natural Koszul complex and relate it to the mixed Buchsbaum-Rim multipli…

Strong Gelfand Pairs of the Dihedral and Dicyclic Groups
Joseph E. Marrow
https://arxiv.org/abs/2508.10756 https://arxiv.org/pdf/2508.10756

Strong Gelfand Pairs of the Dihedral and Dicyclic Groups
A strong Gelfand pair $(G, H)$ is a finite group $G$ and a subgroup $H$ where every irreducible character of $H$ induces to a multiplicity-free character of $G$. We determine the strong Gelfand pairs of the dihedral groups $D_{2n}$ and the dicyclic groups $Dic_{4n}$ for all $n$.

QCD-inspired description of multiplicity distributions in jets
Yu. L. Dokshitzer, B. R. Webber
https://arxiv.org/abs/2507.07691 https://

QCD-inspired description of multiplicity distributions in jets
We suggest a universal QCD-motivated expression for the Polyakov-KNO multiplicity distributions of hadrons in jets and compare it with data from $e^+e^-$ annihilation experiments. The moments and overall shape of the distributions in full events and quark and gluon jets, over a range of energies, are described with reasonable quantitative precision. In particular, the scaling violation predicted by QCD is seen clearly in the moments and high-multiplicity fluctuations.

High multiplicity and global structure of coexistence states in a predator-prey model with saturation
Kousuke Kuto, Juli\'an L\'opez-G\'omez, Eduardo Mu\~noz-Hern\'andez
https://arxiv.org/abs/2508.05714

High multiplicity and global structure of coexistence states in a predator-prey model with saturation
This paper establishes that, under the appropriate range of values of the parameters involved in the formulation of the model, a diffusive predator-prey system with saturation can have an arbitrarily large number of coexistence states for sufficiently large saturation rates. Moreover, it ascertains the global structure of the set of coexistence states in the limiting system as the saturation rate blows-up.

MONOS: Multiplicity Of Northern O-type Spectroscopic systems. III. New orbits and Gaia TESS analysis for 10 SB2E systems
G. Holgado, J. Ma\'iz Apell\'aniz, R. C. Gamen
https://arxiv.org/abs/2508.04272

MONOS: Multiplicity Of Northern O-type Spectroscopic systems. III. New orbits and Gaia TESS analysis for 10 SB2E systems
The MONOS project (Multiplicity Of Northern O-type Spectroscopic systems) aims to characterize O-type spectroscopic binaries in the northern hemisphere (dec > -20 deg) using high-resolution spectroscopy and multi-epoch photometry. This study uses Gaia DR3 epoch photometry and TESS light curves to detect periodic variability and refine orbital solutions. We analyze ten O-type binaries with quality Gaia and TESS data and available high-resolution spectra, complemented by Hipparcos or MUDEHaR phot…

On the multiplicity of 1 as a Laplacian eigenvalue of a graph
Fenglei Tian, Dein Wong
https://arxiv.org/abs/2507.06184 https://arxiv.…

On the multiplicity of 1 as a Laplacian eigenvalue of a graph
Let $G$ be a graph with $p(G)$ pendant vertices and $q(G)$ quasi-pendant vertices. Denote by $m_{L(G)}(λ)$ the multiplicity of $λ$ as a Laplacian eigenvalue of $G$. Let $\overline{G}$ be the reduced graph of $G$, which can be obtained from $G$ by deleting some pendant vertices such that $p(\overline{G})=q(\overline{G})$. We first prove that $m_{L(G)}(1)=p(G)-q(G)+m_{L(\overline{G})}(1)$. Since deleting pendant path $P_3$ does not change the multiplicity of Laplacian eigenvalue 1 of a graph, w…

Existence and multiplicity of normalized solutions to a large class of elliptic equations on bounded domains with general boundary conditions
Claudianor O. Alves, Zhentao He, Chao Ji
https://arxiv.org/abs/2507.04624

Existence and multiplicity of normalized solutions to a large class of elliptic equations on bounded domains with general boundary conditions
In this paper, by adapting the perturbation method, we study the existence and multiplicity of normalized solutions for the following nonlinear Schrödinger equation $$ \left\{ \begin{array}{ll} -Δu = λu + f(u)\quad & \text{in } Ω, \mathcal{B}_{α,ζ,γ}u = 0 & \text{on } \partial Ω, \int_Ω |u|^2\,dx = μ, \end{array} \right. \leqno{(P)^μ_{α,ζ,γ}} $$ where $Ω\subset \mathbb{R}^N$ ($N \geq 1$) is a smooth bounded domain, $μ>0$ is prescribed, $λ\in \mat…

Replaced article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[3/5]:
- Systemizing Multiplicity: The Curious Case of Arbitrariness in Machine Learning
Prakhar Ganesh, Afaf Taik, Golnoosh Farnadi

A high stellar multiplicity rate amongst TESS planet candidates in the Neptunian desert using Gaia DR3 astrometry
Fintan Eeles-Nolle, David J. Armstrong
https://arxiv.org/abs/2506.22399

A high stellar multiplicity rate amongst TESS planet candidates in the Neptunian desert using Gaia DR3 astrometry
We aim to discover whether the stellar multiplicity rate may provide information on the origin of recently discovered planets in the Neptunian Desert. Using Gaia DR3 astrometry, we search for common proper motion companions to 1779 known exoplanet hosts and 2927 exoplanet candidate hosts from the TESS mission, both within 650 pc. We find overall stellar multiplicity rates of $16.6\pm0.9\%$ and $19.8\pm0.6\%$ for confirmed and candidate exoplanets, respectively. We find stellar multiplicity rate…

Metric version of the Zariski Multiplicity Conjecture is true for multiplicity two
A. Fernandes, Z. Jelonek, J. E. Sampaio
https://arxiv.org/abs/2509.03447 https://

Metric version of the Zariski Multiplicity Conjecture is true for multiplicity two
We prove that if two algebraic $(n-1)$-dimensional cones $P, R\subset\mathbb C^n$ are ambient homeomorphic, then their bases $B_P$ and $B_R$ have the same Euler characteristic. As an application, we show our main result: if $(X,0),(Y,0)\subset (\C^n,0)$ are germs of analytic hypersurfaces, which are ambient bi-Lipschitz equivalent and $m_0(X)=2$, then also $m_0(Y)=2.$. As another application, we also obtain a complete positive answer to the Metric Arnold-Vassiliev Problem, which says that if tw…

Tables of practical invariants for distinguishing multiplicity-free fusion categories up to rank 7
Gert Vercleyen
https://arxiv.org/abs/2507.00652 https://…

Tables of practical invariants for distinguishing multiplicity-free fusion categories up to rank 7
This paper discusses to what extent the census of multiplicity-free fusion categories up to rank 7, proposed by the software package Anyonica and the anyonwiki website, can be regarded as a proper classification. The questions of correctness and completeness are briefly discussed, and the question of inequivalence of the provided categories is resolved under the assumption that all proposed data is correct. This is done by providing tables of small sets of invariants for these categories, for w…

Is Repeated Bayesian Interim Analysis Consequence-Free?
Suyu Liu, Beibei Guo, Laura Thompson, Lei Nie, Ying Yuan
https://arxiv.org/abs/2508.07403 https://a…

Is Repeated Bayesian Interim Analysis Consequence-Free?
Interim analyses are commonly used in clinical trials to enable early stopping for efficacy, futility, or safety. While their impact on frequentist operating characteristics is well studied and broadly understood, the effect of repeated Bayesian interim analyses - when conducted without appropriate multiplicity adjustment - remains an area of active debate. In this article, we provide both theoretical justification and numerical evidence illustrating how such analyses affect key inferential pro…

Operator identities of multiplicity 3 for associative algebras
Murray R. Bremner
https://arxiv.org/abs/2507.23703 https://arxiv.org/pdf/2507.23703

Operator identities of multiplicity 3 for associative algebras
We consider algebraic identities for linear operators on associative algebras in which each term has degree 2 (the number of variables) and multiplicity 3 (the number of occurrences of the operator). We apply the methods of earlier work by the author and Elgendy which classified operator identities of degree 2, multiplicities 1 and 2. We begin with the general operator identity of multiplicity 3 which has 10 terms and indeterminate coefficients. We use the operadic concept of partial compositio…

Numerical Approximation and Bifurcation Results for an Elliptic Problem with Superlinear Subcritical Nonlinearity on the Boundary
Shalmali Bandyopadhyay, Thomas Lewis, Dustin Nichols
https://arxiv.org/abs/2509.08990

Numerical Approximation and Bifurcation Results for an Elliptic Problem with Superlinear Subcritical Nonlinearity on the Boundary
We develop numerical algorithms to approximate positive solutions of elliptic boundary value problems with superlinear subcritical nonlinearity on the boundary of the form $-Δu + u = 0$ in $Ω$ with $\frac{\partial u}{\partial η} = λf(u)$ on $\partialΩ$ as well as an extension to a corresponding system of equations. While existence, uniqueness, nonexistence, and multiplicity results for such problems are well-established, their numerical treatment presents computational challenges due to th…

Transverse slices and Zariski's multiplicity conjecture for quasihomogeneous surfaces
Otoniel Nogueira da Silva, Manoel Messias da Silva J\'unior
https://arxiv.org/abs/2509.01634

Transverse slices and Zariski's multiplicity conjecture for quasihomogeneous surfaces
In this work, we study finitely determined, quasihomogeneous, corank 1 map germs $f$ from $(\mathbb{C}^2,0)$ to $(\mathbb{C}^3,0)$. We introduce the notion of the $μ_{\boldsymbol{m},\boldsymbol{k}}$-minimal transverse slice of $f.$ Since this slice is a plane curve, we provide its (topological) normal form. In the irreducible case, under certain conditions, we prove that the number of characteristic exponents of the curve is upper semicontinuous. Furthermore, we show that every topologically t…

Multiplicity of young isolated #PlanetaryMassObjects in Taurus and Upper Scorpius: https://arxiv.org/abs/2506.14380 -> "Despite the limitations of small-number statistics and variations in spatial resolution and sensitivity, our results, combined with previous high-spatial-resolution surveys, suggest a notable difference in the multiplicity properties of objects below 25 M_Jupiter between Upper Sco and Taurus."

Entropy and multiplicity of hadrons in the high energy limit within dipole cascade models
Krzysztof Kutak, S\'andor L\"ok\"os
https://arxiv.org/abs/2509.07898 http…

Entropy and multiplicity of hadrons in the high energy limit within dipole cascade models
We investigate and compare QCD dipole cascade models, the 1D Mueller dipole model, its high energy limit and its generalization that follows from studies of 1D systems with conformal symmetry. To address the ambiguity stemming from different definitions of the rapidity ranges in experimental measurements, we propose the entropy as the function of the logarithm of the average multiplicity, $S(\ln\langle n \rangle)$, as a universal observable. From the solutions of the models, we calculate both t…

Optimal Risk Sharing Without Preference Convexity: An Aggregate Convexity Approach
Vasily Melnikov
https://arxiv.org/abs/2509.08832 https://arxiv.org/pdf/2…

Optimal Risk Sharing Without Preference Convexity: An Aggregate Convexity Approach
We consider the optimal risk sharing problem with a continuum of agents, modeled via a non-atomic measure space. Individual preferences are not assumed to be convex. We show the multiplicity of agents induces the value function to be convex, allowing for the application of convex duality techniques to risk sharing without preference convexity. The proof in the finite-dimensional case is based on aggregate convexity principles emanating from Lyapunov convexity, while the infinite-dimensional cas…

First direct access to the $\rho^0$p interaction via correlation studies at the LHC
ALICE Collaboration
https://arxiv.org/abs/2508.09867 https://arxiv.org/…

First direct access to the $ρ^0$p interaction via correlation studies at the LHC
Direct measurements of the $ρ^0$p interaction have remained so far elusive, with most insights derived indirectly from photoproduction or low-energy partial wave analyses. This letter presents the first direct observation of the $ρ^0$p interaction, obtained through two-particle correlations measured in high-multiplicity, ultrarelativistic proton-proton collisions at $\sqrt{s} = 13$ TeV by the ALICE Collaboration at the LHC. Two-particle correlation data, analyzed within chiral effective field…

Measure $0$ of the singular set for $2$-valued stationary hypercurrents
Jonas Hirsch, Luca Spolaor
https://arxiv.org/abs/2509.05544 https://arxiv.org/pdf/2…

Measure $0$ of the singular set for $2$-valued stationary hypercurrents
We prove that the singular set of a multiplicity $2$ integral hypercurrent that is stationary in the sense of varifolds has a singular set of measure zero.

Exploring a Gamified Personality Assessment Method through Interaction with Multi-Personality LLM Agents
Baiqiao Zhang, Xiangxian Li, Chao Zhou, Xinyu Gai, Zhifeng Liao, Juan Liu, Xue Yang, Niqi Liu, Xiaojuan Ma, Yong-jin Liu, Yulong Bian
https://arxiv.org/abs/2507.04005

Exploring a Gamified Personality Assessment Method through Interaction with Multi-Personality LLM Agents
The execution of effective and imperceptible personality assessments is receiving increasing attention in psychology and human-computer interaction fields. This study explores an interactive approach for personality assessment, focusing on the multiplicity of personality representation. We propose a framework of gamified personality assessment through multi-personality representations (Multi-PR GPA). The framework leverages Large Language Models to empower virtual agents with diverse personalit…

Solving Skolem problem for negative indexed $k-$generalized Pell numbers
Monalisa Mohapatra, Pritam Kumar Bhoi, Gopal Krishna Panda
https://arxiv.org/abs/2509.04503 https://

Solving Skolem problem for negative indexed $k-$generalized Pell numbers
In this paper, we address the Skolem problem for the $k-$Generalized Pell numbers ($P_n^{(k)}$) extended to negative indices. We focus on identifying and bounding the indices $n<0$ for which $P_n^{(k)}=0.$ In particular, we establish that the zero multiplicity is $ χ_k = 1 + (k(k-2)/4),$ if $k$ is even and $1 + ((k - 1)^2/4)$, if $k$ is odd for all $k \in [4, 500].$

Modular analogs of character formulas and multiplicities of induced representations
Patrick Allen, Preston Wake, Robin Zhang
https://arxiv.org/abs/2508.06657 https://

Modular analogs of character formulas and multiplicities of induced representations
Let $G$ be a finite group, $k$ a characteristic-$p$ field, and $π$ be a simple $k[G]$-module. We show that if $π$ is in a $p$-nilpotent block with cyclic defect group, then $π$ appears with multiplicity at most one in the socle and cosocle of induced $k[G]$-modules that are multiplicity-free in characteristic zero and satisfy some additional hypotheses. We show that this applies, in particular, to certain Deligne--Lusztig modules $π$. As an application, we prove that well-known character fo…

Key Physical Parameters Influencing Fragmentation and Multiplicity in Dense Cores of Orion A
Jo-Shui Kao, Hsi-Wei Yen, Shih-Ping Lai
https://arxiv.org/abs/2507.22470 https://

Key Physical Parameters Influencing Fragmentation and Multiplicity in Dense Cores of Orion A
When dense cores in molecular clouds or filamentary structures collapse and form protostars, they may undergo fragmentation and form binary or multiple systems. In this paper, we investigated the key mechanisms influencing fragmentation by comparing the physical conditions of fragmented and unfragmented dense cores (~0.1 pc) in Orion A. Utilizing archival submillimeter continuum data from the James Clerk Maxwell Telescope (JCMT) and the Atacama Large Millimeter/Submillimeter Array survey of Cla…

Multiplicity of singular solutions for semilinear elliptic equations with superlinear source terms
Yohei Fujishima, Norisuke Ioku
https://arxiv.org/abs/2507.20450 https://

Multiplicity of singular solutions for semilinear elliptic equations with superlinear source terms
This paper investigates the multiplicity of singular solutions for the nonlinear elliptic equation $-Δu =f(u)$ near the origin. Applying the classification of nonlinear functions and the transformation, which were developed by the authors, we generalize the multiplicity results known for the concrete model nonlinearity $f(u)=u^p$ with $\frac{N}{N-2}

Counting finite $O$-sequences of a given multiplicity
Francesca Cioffi, Margherita Guida
https://arxiv.org/abs/2507.23438 https://arxiv.org/pdf/2507.23438

Counting finite $O$-sequences of a given multiplicity
We study the number $O_d$ of finite $O$-sequences of a given multiplicity $d$, with particular attention to the computation of $O_d$. We show that the sequence $(O_d)_d$ is sub-Fibonacci, and that if the sequence $(O_d / O_{d-1})_d$ converges, its limit is bounded above by the golden ratio. This analysis also produces an elementary method for computing $O_d$. In addition, we derive an iterative formula for $O_d$ by exploiting a decomposition of lex-segment ideals introduced by S. Linusson in a …

Linear groups of alternating type containing non-scalar elements with all but one eigenvalues of multiplicity 1
Alexandre Zalesski
https://arxiv.org/abs/2509.05770 https://

Linear groups of alternating type containing non-scalar elements with all but one eigenvalues of multiplicity 1
We determine the irreducible representations of alternating and symmetric groups and their universal central extensions that contain a non-scalar element with all but one eigenvalues of multiplicity 1. The ground field is algebraically closed of arbitrary characteristic.

Multiplicity distributions in QCD jets and jet topics
Xiang-Pan Duan, Lin Chen, Guo-Liang Ma, Carlos A. Salgado, Bin Wu
https://arxiv.org/abs/2509.06158 https://

Multiplicity distributions in QCD jets and jet topics
We evaluate the Koba--Nielsen--Olesen (KNO) scaling functions for quark- and gluon-initiated jets by incorporating energy conservation into the Double Logarithmic Approximation (DLA). The resulting modified DLA (MDLA) expressions differ substantially from the DLA predictions and qualitatively align with the recently proposed QCD-inspired expressions, albeit with some quantitative differences. By fixing the two parameters in the MDLA expressions, we show that the inclusive charged-particle multi…

Lithium Abundances of Main-Sequence Stars in the Old Open Cluster NGC 188: Probes of Stellar Evolution Beyond the Solar Age
Qinghui Sun, Constantine P. Deliyannis, Bruce A. Twarog, Barbara J. Anthony-Twarog
https://arxiv.org/abs/2509.02931

Lithium Abundances of Main-Sequence Stars in the Old Open Cluster NGC 188: Probes of Stellar Evolution Beyond the Solar Age
We present lithium abundances for 119 main-sequence stars in the 6.3 Gyr open cluster NGC 188, using high-resolution, high signal-to-noise ratio spectra from WIYN/Hydra. We observe the stars over multiple nights and measure radial velocities for each night, which we combine with Gaia proper motions to identify multiplicity and cluster membership. We identify 95 single members, 14 binary members, 9 members with uncertain multiplicity, and 1 single likely member. We determine effective temperatur…

ODE Methods for Computing One-Dimensional Self-Motion Manifolds
Dominic Guri, George Kantor
https://arxiv.org/abs/2507.21957 https://arxiv.org/pdf/2507.219…

ODE Methods for Computing One-Dimensional Self-Motion Manifolds
Redundant manipulators are well understood to offer infinite joint configurations for achieving a desired end-effector pose. The multiplicity of inverse kinematics (IK) solutions allows for the simultaneous solving of auxiliary tasks like avoiding joint limits or obstacles. However, the most widely used IK solvers are numerical gradient-based iterative methods that inherently return a locally optimal solution. In this work, we explore the computation of self-motion manifolds (SMMs), which repre…

The spectrum of the Steklov-Helmholtz operator
Nilima Nigam, Kshitij Patil, Weiran Sun
https://arxiv.org/abs/2509.07249 https://arxiv.org/pdf/2509.07249

The spectrum of the Steklov-Helmholtz operator
We present a wavenumber-robust strategy for computing Steklov eigenpairs of the Helmholtz operator $-Δ-μ^2$. As the wavenumber $μ\rightarrow μ_D$ from below (where $μ_D^2 $ is a Dirichlet- Laplace eigenvalue of multiplicity $\ell$), the lowest $\ell$ Steklov-Helmholtz eigenvalues diverge to $-\infty$. Computationally, the Steklov-Helmholtz eigenvalue problem becomes severely ill-conditioned when $μ\approx μ_D$. We first reformulate the problem in terms of a suitably-defined Dirichlet-t…

Unital Specker $\ell$-groups and boolean multispaces
Marco Abbadini, Daniele Mundici
https://arxiv.org/abs/2508.21500 https://arxiv.org/pdf/2508.21500

Unital Specker $\ell$-groups and boolean multispaces
As a topological generalization of the notion of multiset, a boolean multispace is a boolean space $X$ with a continuous function $u\colon X\to \mathbb Z_{>0}$, where $\mathbb Z_{>0}=\{1,2,\dots\}$ has the discrete topology. In this paper the category of boolean multispaces and continuous multiplicity-decreasing morphisms with respect to the divisibility order is shown to be dually equivalent to the category of unital Specker $\ell$-groups and unital $\ell$-homomorphisms. This result extends St…

1D Vlasov Simulations of QED Cascades Over Pulsar Polar Caps
Dingyi Ye, Alexander Y. Chen
https://arxiv.org/abs/2507.15804 https://ar…

1D Vlasov Simulations of QED Cascades Over Pulsar Polar Caps
Recent developments in the study of pulsar radio emission revealed that the microphysics of quantum electrodynamic (QED) pair cascades at pulsar polar caps may be responsible for generating the observed coherent radio waves. However, modeling the pair cascades in the polar cap region poses significant challenges, particularly under conditions of high plasma multiplicity. Traditional Particle-in-Cell (PIC) methods often face rapidly increasing computational costs as the multiplicity grows expone…

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes
Spencer Becker-Kahn, Paul Minter, Neshan Wickramasekera
https://arxiv.org/abs/2507.13148

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes
We study stationary integral $n$-varifolds $V$ in the unit ball $B_1(0)\subset\mathbb{R}^{n+k}$. Allard's regularity theorem establishes the existence of $ε= ε(n,k)\in (0,1)$ for which if $V$ is $ε$-close (as varifolds) to the plane $P_0 = \{0\}^k\times\mathbb{R}^n$ with multiplicity 1 then, in $B_{1/2}(0)$, $V$ is represented by a single $C^{1,α}$ minimal graph. However, when instead $P_0$ occurs with multiplicity $Q\in \{2,3,\dotsc\}$, simple examples show that this conclusion, now as a m…

A Perturbative Multiplicity Theorem for the Borsuk-Ulam Setting
Karim Mansour
https://arxiv.org/abs/2507.11556 https://arxiv.org/pdf/2507.11556

A Perturbative Multiplicity Theorem for the Borsuk-Ulam Setting
We prove a generalization of the classical Borsuk--Ulam Theorem under small perturbations (shaking) of the sphere. We show that for a generic perturbation of a continuous map $f : S^2 \to \mathbb{R}^2$, the number of points $x \in S^2$ such that $f_ε(x) = f_ε(-x)$ becomes finite and odd, and may exceed the classical lower bound of one antipodal coincidence. In particular, we show the existence of maps with 3, 5, or 7 such points, and explain the unbounded nature of this multiplicity under hig…

Existence and multiplicity of normalized solutions for the quasi-linear Schr\"{o}dinger equations with mixed nonlinearities
Qihan He, Hao Wang
https://arxiv.org/abs/2507.00375

Existence and multiplicity of normalized solutions for the quasi-linear Schrödinger equations with mixed nonlinearities
In this paper, we study the existence and multiplicity of the normalized solutions to the following quasi-linear problem \begin{equation*} -Δu-Δ(|u|^2)u+λu=|u|^{p-2}u+τ|u|^{q-2}u, \text{ in }\mathbb{R}^N,~ 1\leq N\leq4, \end{equation*} with prescribed mass $$\int_{\mathbb{R}^N}|u|^2dx=a ,$$ where $λ\in\mathbb{R}$ appears as a Lagrange multiplier and the parameters $a,τ$ are all positive constants. We are concerned about the mass-mixed case $2

System size and event shape dependence of particle-identified balance functions in proton-proton collisions at $\sqrt{s}=13$ TeV
Subash Chandra Behera, Arvind Khuntia
https://arxiv.org/abs/2508.21030

System size and event shape dependence of particle-identified balance functions in proton-proton collisions at $\sqrt{s}=13$ TeV
We investigate charge balance functions for identified hadron pairs (pions, kaons, and protons) in proton-proton (pp) collisions at $\sqrt{s}=13$~TeV, using transverse spherocity to classify event topology and charged particle multiplicity to select system size. Simulations with PYTHIA8 and EPOS-LHC reveal that balance function widths in rapidity and azimuthal angle depend on multiplicity and event shape. In PYTHIA8, widths decrease monotonically with multiplicity, consistent with local charge …

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems
Fleur Hendriks, Ond\v{r}ej Roko\v{s}, Martin Do\v{s}k\'a\v{r}, Marc G. D. Geers, Vlado Menkovski
https://arxiv.org/abs/2509.03340

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems
Bifurcation phenomena in nonlinear dynamical systems often lead to multiple coexisting stable solutions, particularly in the presence of symmetry breaking. Deterministic machine learning models struggle to capture this multiplicity, averaging over solutions and failing to represent lower-symmetry outcomes. In this work, we propose a generative framework based on flow matching to model the full probability distribution over bifurcation outcomes. Our method enables direct sampling of multiple val…

Hilbert-Kunz multiplicity of quadrics via Ehrhart theory
Igor Pak, Boris Shapiro, Ilya Smirnov, Ken-ichi Yoshida
https://arxiv.org/abs/2508.17915 https://a…

Hilbert-Kunz multiplicity of quadrics via Ehrhart theory
We show that the Hilbert-Kunz multiplicity of the d-dimensional non-degenerate quadric hypersurface of characteristic p > 2 is a rational function of p composed from the Ehrhart polynomials of integer polytopes. In consequence, we explain and recover a result of Gessel and Monsky and prove that the Hilbert-Kunz multiplicity of quadrics of fixed characteristic is a decreasing function of dimension.

Replaced article(s) found for stat.ML. https://arxiv.org/list/stat.ML/new
[2/2]:
- Reconsidering Fairness Through Unawareness From the Perspective of Model Multiplicity
Benedikt H\"oltgen, Nuria Oliver

Cosmic Threads: Interlinking the Stellar Initial Mass Function from Star-Birth to Galaxies
Tereza Jerabkova, Donatella Romano, Pavel Kroupa, Philippe Andr\'e, Martyna Chru\'sli\'nska, Fabio Fontanot, Andrew Hopkins, Vikrant Jadhav, Natalia Lah\'en, Yueh-Ning Lee, Alessio Mucciarelli, Stefania Salvadori, Long Wang, Zhiqiang Yan, Morten Andersen, Anna Durrant, Fabien Louvet, Mariya Lyubenova, Francesca Matteucci, Piyush Sharda, Glenn van de Ven, Alexandre Vazdekis

Cosmic Threads: Interlinking the Stellar Initial Mass Function from Star-Birth to Galaxies
The stellar initial mass function (sIMF) describes the distribution of stellar masses formed in a single star formation event in a molecular cloud clump. It is fundamental to astrophysics and cosmology, shaping our understanding of unresolved stellar populations, galactic chemical enrichment and habitable zones, and black hole growth. This White Paper reviews studies on the core mass function, stellar multiplicity, and dynamical processes affecting sIMF determinations, as well as the link betwe…

Multiplicity dependence of f$_0$(980) production in pp collisions at $\sqrt{s} = 13$ TeV
ALICE Collaboration
https://arxiv.org/abs/2507.19347 https://arxiv…

Multiplicity dependence of f$_0$(980) production in pp collisions at $\sqrt{s} = 13$ TeV
The dependence of f$_0$(980) production on the final-state charged-particle multiplicity is reported for proton-proton (pp) collisions at the centre-of-mass energy, $\sqrt{s}= 13$ TeV. The production of f$_0$(980) is measured with the ALICE detector via the f$_0(980) \rightarrow π^{+}π^{-}$ decay channel in a midrapidity region of $|y| < 0.5$. The evolution of the integrated yields and mean transverse momentum of f$_{0}$(980) as a function of charged-particle multiplicity measured i…

Trees with extremal Laplacian eigenvalue multiplicity
Vinayak Gupta, Gargi Lather, R. Balaji
https://arxiv.org/abs/2507.15472 https://

Trees with extremal Laplacian eigenvalue multiplicity
Let $T$ be a tree. Suppose $λ$ is an eigenvalue of the Laplacian matrix of $T$ with multiplicity $m_{T}(λ)$. It is known that $m_{T}(λ) \leq p(T)-1$, where $p(T)$ is the number of pendant vertices of $T$. In this paper, we characterize all trees $T$ for which there exists an eigenvalue $λ$ such that $m_{T}(λ)=p(T)-1$. We show that such trees are precisely either paths, or there exists an integer $q$ such that if $α$ and $β$ are two distinct pendant vertices, then the distance $d(α,β)$ …

Cannonball Polygons with Multiplicities
Anji Dong, Katerina Saettone, Kendra Song, Alexandru Zaharescu
https://arxiv.org/abs/2507.18057 https://arxiv.org/p…

Cannonball Polygons with Multiplicities
We generalize the Cannonball Problem by introducing integer-valued and non-increasing arithmetic functions $w$. We associate these functions $w$ with certain polygons, which we call cannonball polygons. Through this correspondence, we show that for any $Z\in\mathbb{N}$, there exists a cannonball polygon with multiplicity 8 and largest side of length $Z$. Moreover, for any multiplicity $s$ greater than 8, we provide an asymptotic formula for the number of distinct classes of cannonball polygons …

CFP: DEADLINE EXTENDED: EMoDiR Panels "The Devil and Dissent: Early Modern Perspectives," RSA 72nd Annual Meeting, San Francisco (February 19-21, 2026)
https://ift.tt/fXawzIA
Pirino on Suzuki, 'Humanitarian Internationalism Under Empire: The Global Evolution of the Japanese…
via Input 4 …

The Small Separation A-Star Companion Population: Tentative Signatures of Enhanced Multiplicity with Primary Mass
Matthew De Furio, Tyler Gardner, John D. Monnier, Michael R. Meyer, Kaitlin M. Kratter, Cyprien Lanthermann, Narsireddy Anugu, Stefan Kraus, Benjamin R. Setterholm
https://arxiv.org/abs/2507.17705…

The Small Separation A-Star Companion Population: Tentative Signatures of Enhanced Multiplicity with Primary Mass
We present updated results from our near-infrared long-baseline interferometry (LBI) survey to constrain the multiplicity properties of intermediate-mass A-type stars within 80 pc. Previous adaptive optics surveys of A-type stars are incomplete at separations $<$ 20au. Therefore, a LBI survey allows us to explore separations previously unexplored. Our sample consists of 54 A-type primaries with estimated masses between 1.44-2.93 M$_{\odot}$ and ages 10-790 Myr, which we observed with the MIRC-X…

Tropical regions of near mass-shell pentabox
A. V. Belitsky, V. A. Smirnov
https://arxiv.org/abs/2508.14298 https://arxiv.org/pdf/2508.14298

Tropical regions of near mass-shell pentabox
Coulomb branch amplitudes of maximally supersymmetric Yang-Mills theory display infrared properties different from their conformal counterparts. While the four-leg amplitude is known to very high perturbative orders, amplitudes of higher multiplicity fall into an uncharted territory starting already from two loops. The reason for this is that they are not easily amenable to traditional techniques like canonical differential equations due to the uncontrolled swelling of solutions to integration-…

Replaced article(s) found for math.AP. https://arxiv.org/list/math.AP/new
[1/1]:
- Existence and Multiplicity of Solutions for a Cooperative Elliptic System Using Morse Theory
Leandro Rec\^ova, Adolfo Rumbos

MINDS. Young binary systems with JWST/MIRI: Variable water-rich primaries and extended emission
Nicolas T. Kurtovic, Sierra L. Grant, Milou Temmink, Andrew D. Sellek, Ewine F. van Dishoeck, Thomas Henning, Inga Kamp, Valentin Christiaens, Andrea Banzatti, Danny Gasman, Till Kaeufer, Lucas M. Stapper, Riccardo Franceschi, Manuel G\"udel, Pierre-Olivier Lagage, Marissa Vlasblom, Giulia Perotti, Kamber Schwarz, Alice Somigliana

MINDS. Young binary systems with JWST/MIRI: Variable water-rich primaries and extended emission
As part of the JWST GTO program MINDS, we analyze the mid-infrared emission of three Class II binary systems: VW Cha, WX Cha, and RW Aur, to investigate the impact of stellar multiplicity on the chemistry and physics of their inner disk. We analyze the 1D spectrum from JWST/MIRI-MRS for primary and secondary disks separately, extracted by combining forward modeling with a theoretical PSF and aperture photometry. We modeled the molecular lines with 0D slab models. We interpret the results by com…

Multiplicity dependence of K$^*(892)^{\pm}$ production in pp collisions at $\sqrt{s}$ = 13 TeV
ALICE Collaboration
https://arxiv.org/abs/2507.19332 https://

Multiplicity dependence of K$^*(892)^{\pm}$ production in pp collisions at $\sqrt{s}$ = 13 TeV
The first results of K$^*$(892)$^{\pm}$ production at midrapidity ($|y| < 0.5$) in pp collisions at $\sqrt{s} = 13$ TeV as a function of the event multiplicity are presented. The K$^*$(892)$^{\pm}$ has been reconstructed via its hadronic decay channel K$^*$(892)$^{\pm} \rightarrow π^{\pm} + K_{\rm S}^0$ using the ALICE detector at the LHC. For each multiplicity class the differential transverse momentum ($p_{\rm T}$) spectrum, the mean transverse momentum $\langle p_{\rm T} \rangle$,…

Resonances for the one dimensional Schr\"odinger operator with the matrix-valued complex square-well potential
Yuri Latushkin, Alin Pogan
https://arxiv.org/abs/2509.00235 h…

Resonances for the one dimensional Schrödinger operator with the matrix-valued complex square-well potential
We study the resonances of (generally, non-selfadjoint) Schrödinger operators with matrix-valued square-well potentials. We compute explicitly the Jost function and derive complex transcendental equations for the resonances. We prove several results concerning the distribution of resonances in the complex plane. We compute the multiplicity of resonances and prove a version of the Weyl Law for the number of resonances.

Hilbert-Kunz multiplicity and $F$-signature can disagree
Seungsu Lee, Suchitra Pande, Austyn Simpson
https://arxiv.org/abs/2508.19985 https://arxiv.org/pdf…

Hilbert-Kunz multiplicity and $F$-signature can disagree
We compute the $F$-signature function of the ample cone of any nontrivial ruled surface over $\mathbb{P}^1_k$ where $k$ is an algebraically closed field of prime characteristic. As an application, we construct a Noetherian $F$-finite strongly $F$-regular ring $R$ of prime characteristic admitting two maximal ideals $\mathfrak{n}_1,\mathfrak{n}_2\in \mathrm{Spec} R$ at which the Hilbert-Kunz multiplicity and $F$-signature measure different singularities; that is, $\operatorname{e}_{\operatorname…

FASTColor -- Full-color Amplitude Surrogate Toolkit for QCD
Javier Mari\~no Villadamigo, Rikkert Frederix, Tilman Plehn, Timea Vitos, Ramon Winterhalder
https://arxiv.org/abs/2509.07068

FASTColor -- Full-color Amplitude Surrogate Toolkit for QCD
High-multiplicity events remain a bottleneck for LHC simulations due to their computational cost. We present a ML-surrogate approach to accelerate matrix element reweighting from leading-color (LC) to full-color (FC) accuracy, building on recent advancements in LC event generation. Comparing a variety of modern network architectures for representative QCD processes, we achieve speed-up of around a factor two over the current LC-to-FC baseline. We also show how transformers learn and exploit und…

Enumeration of geometric Weierstrass points of metric graphs
Diego A. Robayo Bargans
https://arxiv.org/abs/2506.22130 https://arxiv.o…

Enumeration of geometric Weierstrass points of metric graphs
A classical result states that on a smooth algebraic curve of genus $g$ the number of Weierstrass points, counted with multiplicity, is $g^3-g$. In this paper, we introduce the notion of geometric Weierstrass points of metric graphs and show that a generic metric graph of genus $g$ has $g^3-g$ geometric Weierstrass points counted with multiplicity. Our methods also provide a new proof of the existence of Weierstrass points on metric graphs of genus bigger than or equal to $2$.

\'Etude statistique du facteur premier m\'edian, 4: somme des inverses
Jonathan Rotg\'e
https://arxiv.org/abs/2507.02739 https://

Étude statistique du facteur premier médian, 4: somme des inverses
We consider the sum of the reciprocals of the middle prime factor of an integer, defined according to multiplicity or not. We obtain an asymptotic expansion in the first case and an asymptotic formula involving an implicit parameter in the second. Both these results improve on previous estimates available in the literature.

Benchmarks and applications of the nuclear deexcitation event generator \textsc{NucDeEx}
Seisho Abe
https://arxiv.org/abs/2508.04040 https://arxiv.org/pdf/…

Benchmarks and applications of the nuclear deexcitation event generator \textsc{NucDeEx}
Neutron multiplicity is a key observable in recent neutrino experiments that can enhance the sensitivity of various neutrino physics searches. Nuclear deexcitation plays a significant role in neutron emissions associated with neutrino-nucleus interactions; therefore, precise prediction of this process is eessential. To address this need, a general-purpose nuclear deexcitation event generator \textsc{NucDeEx} was developed and released as an open-source package. The treatment of low-lying discre…

Lipschitz geometry of the image of finite mappings
Juan Jos\'e Nu\~no Ballesteros, Vin\'icius de Oliveira Prado, Guillermo Pe\~nafort Sanchis, Jos\'e Edson Sampaio
https://arxiv.org/abs/2507.21405

Lipschitz geometry of the image of finite mappings
This paper is devoted to the study of the LNE property in complex analytic hypersurface parametrized germs, that is, the sets that are images of finite analytic map germs from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{n+1},0)$. We prove that if the multiplicity of $f$ is equal to his generic degree, then the image of $f$ is LNE at 0 if and only if it is a smooth germ. We also show that every finite corank 1 map is sattisfies the previous hypothesis. Moreover, we show that for an injective map germ $f…

Multiplicity of young isolated planetary mass objects in Taurus and Upper Scorpius
H. Bouy, G. Duch\^ene, G. Strampelli, J. Aguilar, J. Olivares, D. Barrado, S. N. Raymond, N. Hu\'elamo, M. Tamura, E. Bertin, W. Brandner, J. -C. Cuillandre, P. A. B. Galli, N. Miret-Roig
https://arxiv.org/abs/2506.14380

Multiplicity of young isolated planetary mass objects in Taurus and Upper Scorpius
Free-floating planetary mass objects-worlds that roam interstellar space untethered to a parent star-challenge conventional notions of planetary formation and migration, but also of star and brown dwarf formation. We focus on the multiplicity among free-floating planets. By virtue of their low binding energy (compared to other objects formed in these environments), these low-mass substellar binaries represent a most sensitive probe of the mechanisms at play during the star formation process. We…

Normalized solutions for fractional Choquard equation with critical growth on bounded domain
Divya Goel, Asmita Rai
https://arxiv.org/abs/2509.07618 https://

Normalized solutions for fractional Choquard equation with critical growth on bounded domain
In this work, we establish the multiplicity of positive solutions for the following critical fractional Choquard equation with a perturbation on the star-shaped bounded domain $$ \left\{ \begin{array}{lr} (-Δ)^s u = λu +α|u|^{p-2}u+ \left( \int\limits_Ω \frac{|u(y)|^{2^{*}_{μ,s}}}{|x-y|^ μ}\, dy\right) |u|^{2^{*}_{μ,s}-2}u\; \text{in} \; Ω,\\ u>0\; \text{in}\; Ω,\; \\ u = 0\; \text{in} \; \mathbb{R}^{N}\backslashΩ, \\ \int_Ω|u|^2 dx…

Balanced Steinhaus triangles
Jonathan Chappelon
https://arxiv.org/abs/2508.05159 https://arxiv.org/pdf/2508.05159…

Balanced Steinhaus triangles
A Steinhaus triangle modulo $m$ is a finite down-pointing triangle of elements in the finite cyclic group $\mathbb{Z}/m\mathbb{Z}$ satisfying the same local rule as the standard Pascal triangle modulo $m$. A Steinhaus triangle modulo $m$ is said to be balanced if it contains all the elements of $\mathbb{Z}/m\mathbb{Z}$ with the same multiplicity. In this paper, the existence of infinitely many balanced Steinhaus triangles modulo $m$, for any positive integer $m$, is shown. This is achieved by c…

The multinomial dimer model
Richard Kenyon, Catherine Wolfram
https://arxiv.org/abs/2506.12171 https://arxiv.org/pdf/2506.12171

The multinomial dimer model
An $N$-dimer cover of a graph is a collection of edges (with multiplicity) such that each vertex is contained in exactly $N$ edges in the collection. The multinomial dimer model is a natural probability measure on $N$-dimer covers. We study the behavior of these measures on periodic bipartite graphs in ${\mathbb R}^d$, in the scaling limit as the multiplicity $N$ and then the size of the graph go to infinity. In this iterated limit, we prove a large deviation principle, where the rate functio…

Replaced article(s) found for math.AC. https://arxiv.org/list/math.AC/new
[1/1]:
- Perfectoid signature, perfectoid Hilbert-Kunz multiplicity, and an application to local fundament...
Hanlin Cai, Seungsu Lee, Linquan Ma, Karl Schwede, Kevin Tucker

Replaced article(s) found for nucl-ex. https://arxiv.org/list/nucl-ex/new
[1/1]:
- Multiplicity dependence of charm baryon and charm meson production in pPb collisions at $\sqrt{s_...
CMS Collaboration

How cross section fluctuations affect multiplicity and geometry in pA collisions
Chiara Le Roux
https://arxiv.org/abs/2507.21843 https://arxiv.org/pdf/2507…

How cross section fluctuations affect multiplicity and geometry in pA collisions
In this paper, a new Monte Carlo Glauber model is developed for pA collisions. It uses the hadronic cross sections calculated within the KMR model as implemented in the SHRiMPS minimum bias module of the SHERPA event generator. These cross sections are obtained as functions of impact parameter and, therefore, are ready for use in a Glauber model without additional assumptions regarding their impact parameter dependence. We compare the results obtained with those from a Black Disk model and from…

Bifurcation and stability of stationary shear flows of Ericksen-Leslie model for nematic liquid crystals
Weishi Liu, Majed Sofiani
https://arxiv.org/abs/2508.19125 https://

Bifurcation and stability of stationary shear flows of Ericksen-Leslie model for nematic liquid crystals
In this work, focusing on a critical case for shear flows of nematic liquid crystals, we investigate multiplicity and stability of stationary solutions via the parabolic Ericksen-Leslie system. We establish a one-to-one correspondence between the set of the stationary solutions with the set of solutions of an algebraic equation. The existence of multiple stationary solutions is established through countably many saddle-node bifurcations at critical shear speeds for the algebraic equation. We th…

Multiple solutions to a class of $p$-Laplacian Schr\"{o}dinger equations
Lin Zhang
https://arxiv.org/abs/2509.05556 https://arxiv.org/pdf/2509.05556…

Multiple solutions to a class of $p$-Laplacian Schrödinger equations
In this paper, we will prove the existence of infinitely many solutions to the following equation by utilizing the variational perturbation method \begin{equation*} -div(A(x,u)|\nabla u|^{p-2}\nabla u)+\frac{1}{p}A_{t}(x,u)|\nabla u|^{p}+V(x)|u|^{p-2}u=g(x, u), ~~ x\in\mathbb{R}^{N}, \end{equation*} where $2

Unboundedness of fixed point multiplicities on a K3 surface
Kenji Hashimoto, Yuta Takada
https://arxiv.org/abs/2508.18814 https://arxiv.org/pdf/2508.18814

Unboundedness of fixed point multiplicities on a K3 surface
We exhibit automorphisms of a certain K3 surface in $\mathbb{P}^1\times \mathbb{P}^1 \times \mathbb{P}^1$ with an isolated fixed point at which the induced action on the stalk of the structure sheaf is arbitrarily close to the identity. This implies that the multiplicities of these automorphisms at the fixed point can be arbitrarily large. As another application, we show that the intersection multiplicity of two isomorphic curves at a point can be arbitrarily large on this K3 surface.

Distinguishing Siegel modular forms
Arvind Kumar, Ariel Weiss
https://arxiv.org/abs/2506.22264 https://arxiv.org/pdf/2506.22264

Distinguishing Siegel modular forms
Let $f$ and $f'$ be genus $2$ cuspidal Siegel paramodular newforms. We prove that if their Hecke eigenvalues $a_p$ and $a_p'$ satisfy a non-trivial polynomial relation $P(a_p, a_p') = 0$ for a set of primes $p$ of positive density, then $f$ and $f'$ are twists of each other by a Dirichlet character. In particular, if both forms have trivial nebentypus, then they differ by a quadratic twist. This result extends the strong multiplicity one theorem, which handles the case $P(x,y) = x - y$, to arbi…

Generalization and Power of Kocay's Lemma in Graph Reconstruction
Peter Stark
https://arxiv.org/abs/2509.02604 https://arxiv.org/pdf/2509.02604

Generalization and Power of Kocay's Lemma in Graph Reconstruction
This paper generalizes Kocay's lemma, with particular applications to graph reconstruction, as well as discussing and proving aspects around the power of these generalizations and Kocay's original lemma, with a result on the reconstruction of the multiplicity of a tree T as a subgraph of G.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations
Lidan Wang
https://arxiv.org/abs/2508.18840 https://arxiv.or…

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations
In this paper, we study the discrete fractional logarithmic Kirchhoff equation $$ \left(a+b \int_{\mathbb{Z}^d}|\nabla^s u|^{2} d μ\right) (-Δ)^s u+h(x) u=|u|^{p-2}u \log u^{2}, \quad x\in \mathbb{Z}^d, $$ where $a,\,b>0$ and $04$; then we verify the existence of ground state sign-changing solutions based on the method of Nehari manifold f…

Soft and semihard components of multiplicity distributions in the $k_T$ factorization approach
H. R. Martins-Fontes, F. S. Navarra
https://arxiv.org/abs/2506.17127

Soft and semihard components of multiplicity distributions in the $k_T$ factorization approach
Particle production in hadronic collisions can be studied in the low-momentum (soft) and high-momentum (hard) transfer regimes. While the latter can be well understood with in perturbative QCD the former contains non-perturbative effects which cannot be calculated from first principles. There is also an intermediate regime called semihard, in which the momentum transfer runs typically from $~1$ to $~10$ GeV. As the hadron-hadron collision energy increases, we expect to see a relative growth of …

Upper bound on the multiplicity of eigenvalues of the Sch\"odinger-Dirichlet operator in dimension two
Mourad Choulli
https://arxiv.org/abs/2506.14463

Upper bound on the multiplicity of eigenvalues of the Schödinger-Dirichlet operator in dimension two
We establish an upper bound on the multiplicity of eigenvalues of the Schödinger-Dirichlet operator in dimension two. We give a proof based on a generalized Morse Lemma due to Cheng \cite{Ch}.

Embedding a Praeger-Xu graph into a surface
Zhaochen Ding, Zheng Guo, Luyi Liu
https://arxiv.org/abs/2507.01716 https://arxiv.org/pdf…

Embedding a Praeger-Xu graph into a surface
Rotary maps (orientably regular maps) are highly symmetric graph embeddings on orientable surfaces. This paper classifies all rotary maps whose underlying graphs are Praeger-Xu graphs, denoted $\operatorname{C}(p,r,s)$, for any odd prime $p$ that does not divide $r$. Our main result establishes a one-to-one correspondence between the isomorphism classes of these maps and the multiplicity-free representations of the dihedral group $\operatorname{D}_{2r}$ over the finite field $\mathbb{F}_p$. Thi…

Replaced article(s) found for math.AC. https://arxiv.org/list/math.AC/new
[1/1]:
- Regularity and multiplicity of Veronese type algebras
Kuei-Nuan Lin, Yi-Huang Shen

Probing non-perturbative QCD aspects on particle production in pp collisions with forward-backward correlations using \texttt{PYTHIA8}
Rohit Agarwala, Kalyan Dey
https://arxiv.org/abs/2508.03124

Probing non-perturbative QCD aspects on particle production in pp collisions with forward-backward correlations using \texttt{PYTHIA8}
We employ PYTHIA8 simulations to study forward-backward (FB) correlations in pp collisions at LHC energies, probing non-perturbative QCD dynamics via color reconnection (CR) and QCD radiation (ISR/FSR). Using \texttt{PYTHIA8} (v8.311) under ALICE/ATLAS kinematics, we analyze: extensive: FB multiplicity ($b_{\rm corr}^{\rm mult}$) and summed $p_{\rm T}$ ($b_{\rm corr}^{\sum p_{\rm T}}$) correlations; intensive: FB mean $p_{\rm T}$ ($b_{\rm corr}^{\overline p_{\rm T}}$) correlations; and \textit{…

Permanental Analog of the Rank-Nullity Theorem for Symmetric Matrices
Priyanshu Kumar Pant, Surabhi Chakrabartty, Ranveer Singh
https://arxiv.org/abs/2507.01344

Permanental Analog of the Rank-Nullity Theorem for Symmetric Matrices
The rank-nullity theorem is a core result in the study of matrices. The rank of an $n \times n$ matrix is equal to the size of its largest square submatrix with a nonzero determinant; it can be computed in $O(n^{2.37})$ time. For symmetric matrices, the rank equals to the number of nonzero eigenvalues (that is, the nonzero roots of the characteristic polynomial), which implies that the nullity equals the multiplicity of zero eigenvalue. Similar to the rank, the permanental rank of a matrix is t…

Multiplicity results for mixed local-nonlocal variable exponent problem involving singular and superlinear term
Shammi Malhotra, Ambesh Kumar Pandey, K. Sreenadh
https://arxiv.org/abs/2506.19793

Multiplicity results for mixed local-nonlocal variable exponent problem involving singular and superlinear term
In this paper, we study a class of quasilinear elliptic equations involving both local and nonlocal operators with variable exponents. The problem exhibits singular nonlinearities along with a subcritical superlinear growth term and a parameter $λ$. We study the existence of multiple solutions with the help of variational methods by restricting the associated energy functional on appropriate subsets of the Nehari manifold. Using the topological index and the structure of the fibering maps, we …

The Corona-Australis star-forming region: New insights on its formation history from detailed stellar and disk analysis
Elisabetta Rigliaco, Raffaele Gratton, Valerio Nascimbeni
https://arxiv.org/abs/2508.19757

The Corona-Australis star-forming region: New insights on its formation history from detailed stellar and disk analysis
The star-forming complex of Corona Australis (CrA) is one of the closest and most isolated molecular clouds. It belongs to a chain of clusters that show age gradients with distance from the galactic plane. We aim to provide suggestions regarding its formation history by examining the stellar and disk populations, stellar multiplicity, and interstellar absorption. We made a census of stars and disks using Gaia DR3 and infrared data. Interstellar absorption in the direction of each star was deriv…

Entanglement entropy, Monte Carlo event generators, and soft gluons DIScovery
Martin Hentschinski, Hannes Jung, Krzysztof Kutak
https://arxiv.org/abs/2509.03400 https://

Entanglement entropy, Monte Carlo event generators, and soft gluons DIScovery
We study entropy production in Deep Inelastic Scattering using Monte Carlo simulations. We show that the dominant contribution to entropy is due to soft gluons. This contribution is usually neglected in standard Monte Carlo approaches, since it does not affect hadronic spectra. However, it is relevant for entropy and multiplicity distributions, as we demonstrate with explicit calculations. We further show that, as one lowers the cutoff - i.e. includes soft gluons - thereby making the Monte Carl…

Existence and regularity of weak solutions for mixed local and nonlocal semilinear elliptic equations
Fuwei Cheng, Xifeng Su, Jiwen Zhang
https://arxiv.org/abs/2508.01162 https:…

Existence and regularity of weak solutions for mixed local and nonlocal semilinear elliptic equations
We study the existence, multiplicity and regularity results of weak solutions for the Dirichlet problem of a semi-linear elliptic equation driven by the mixture of the usual Laplacian and fractional Laplacian \begin{equation*} \left\{% \begin{array}{ll} -Δu + (-Δ)^{s} u+ a(x)\ u =f(x,u) & \hbox{in $Ω$,} u=0 & \hbox{in $\mathbb{R}^n\backslashΩ$} \end{array}% \right. \end{equation*} where $s \in (0,1)$, $Ω\subset \mathbb{R}^{n}$ is a bounded domain, the coefficient $a$ is a…

Invariants of toric double determinantal rings
Jennifer Biermann, Emanuela De Negri, Oleksandra Gasanova, Asl{\i} Musapa\c{s}ao\u{g}lu, Sudeshna Roy
https://arxiv.org/abs/2506.22730

Invariants of toric double determinantal rings
We study a class of double determinantal ideals denoted $I_{mn}^r$, which are generated by minors of size 2, and show that they are equal to the Hibi rings of certain finite distributive lattices. We compute the number of minimal generators of $I_{mn}^r$, as well as the multiplicity, regularity, a-invariant, Hilbert function, and $h$-polynomial of the ring $R/I_{mn}^r$, and we give a new proof of the dimension of $R/I_{mn}^r$. We also characterize when the ring $R/I_{mn}^r$ is Gorenstein, there…

Cross talk between experimental data and simple validation of shell closure in pre-actinides
Punit Dubey, Mahima Upadhyay, Mahesh Choudhary, Namrata Singh, Sriya Paul, Shweta Singh, N. Saneesh, Mohit Kumar, Rishabh Prajapati, K. S. Golda, Akhil Jhingan, P. Sugathan, Jhilam Sadhukhan, Raghav Aggarwal, Kiran, Ajay Kumar
https://arxiv.org/ab…

Cross talk between experimental data and simple validation of shell closure in pre-actinides
Two back-to-back experiments, 28Si + 178Hf and 28Si + 186W, were intentionally conducted to validate the role of shell closure in pre-actinides by studying neutron multiplicity in compound nucleus (CN) 206Rn and 214Ra. In the first experiment, Dubey et al. [Phys. Rev. C 112, L011602 (2025)], we established the influence of the neutron shell closure. In the present work, the CN 214Ra was deliberately selected to investigate the dependence of the total neutron multiplicity (Mtotal) on the proton …

Worldline Modeling of Ultra-Intense Lasers for N-photon Scattering Processes
Ivan Ahumada, Patrick Copinger, James P. Edwards, Karthik Rajeev
https://arxiv.org/abs/2508.00105 ht…

Worldline Modeling of Ultra-Intense Lasers for N-photon Scattering Processes
The modeling of present and future ultra-intense lasers demands techniques that go beyond the standard diagrammatic approach to non-perturbatively fully capture the effects of strong fields. We illustrate the first-quantized path integral representation for strong-field quantum electrodynamics as a means of accessing the laser being treated as a background field, which is treated without recourse to perturbation theory. We examine an all-multiplicity construction for $N-$photon scattering proce…

Multiplicity of dead core solutions in indefinite elliptic problems
Vladimir Bobkov, Humberto Ramos Quoirin
https://arxiv.org/abs/2507.14016 https://

Multiplicity of dead core solutions in indefinite elliptic problems
We investigate nonnegative solutions of indefinite elliptic problems which enjoy the dead core phenomenon. Our model is the subhomogeneous problem $$ -Δ_p u = (a^+(x) - μa^-(x))|u|^{q-2}u, \quad u \in W_0^{1,p}(Ω), $$ where $Ω$ is a bounded domain in $\mathbb{R}^N$, $1 0$. Thanks to a dead core formation property, we obtain multiple nonnegative dead core solutions of this problem for $μ$ large enough. This assertion, in combination with a uniqueness feature, yields…

Algebraic invariants of the special fiber ring of ladder determinantal modules
Alessandra Costantini, Louiza Fouli, Kriti Goel, Kuei-Nuan Lin, Haydee Lindo, Whitney Liske, Maral Mostafazadehfard
https://arxiv.org/abs/2507.22167

Algebraic invariants of the special fiber ring of ladder determinantal modules
We provide explicit formulas for key invariants of special fiber rings of ladder determinantal modules, that is, modules that are direct sums of ideals of maximal minors of a ladder matrix. Our results are given in terms of the combinatorial data of the associated ladder matrix. In particular, we compute its dimension, regularity, $a$-invariant, and multiplicity, which via \textsc{Sagbi} degeneration coincide with those of Hibi rings associated to a distributive lattice. Then, via Gröbner dege…

Polynomiality of the Bigraded Subdimension of Diagonal Harmonics
Xinxuan Wang
https://arxiv.org/abs/2506.16566 https://arxiv.org/pdf/…

Polynomiality of the Bigraded Subdimension of Diagonal Harmonics
A sequence of representations \(V_n\) of the symmetric group \(S_n\) is called representation (multiplicity) stable if, after some \(n\), the irreducible decomposition of \(V_n\) stabilizes. In particular, Church and Farb (2013) showed that for fixed \(a\) and \(b\), the space of diagonal harmonics \(DH_n^{a,b}\) exhibits this behavior, with its dimension eventually stabilizing to a polynomial in \(n\). Building on this result, we use the Schedules Formula by Haglund and Loehr (2005) to obtain …

On stable solutions to the Allen-Cahn equation with bounded energy density in $\mathbb{R}^4$
Enric Florit-Simon, Joaquim Serra
https://arxiv.org/abs/2509.02739 https://

On stable solutions to the Allen-Cahn equation with bounded energy density in $\mathbb{R}^4$
We show that stable solutions $u:\mathbb{R}^4\to (-1,1)$ to the Allen-Cahn equation with bounded energy density (or equivalently, with cubic energy growth) are one-dimensional. This is known to entail important geometric consequences, such as robust curvature estimates for stable phase transitions, and the multiplicity one and Morse index conjectures of Marques-Neves for Allen-Cahn approximations of minimal hypersurfaces in closed 4-manifolds.

Kaon-deuteron femtoscopy from unitarized chiral interactions
\`Angels Ramos, Juan M. Torres-Rincon, Alejandro de Fagoaga, Esteve Cabr\'e
https://arxiv.org/abs/2507.22593 htt…

Kaon-deuteron femtoscopy from unitarized chiral interactions
We have performed a theoretical study of the correlation functions of $K^- d$ and $K^+ d$ pairs and compared them with those provided by the ALICE Collaboration from Pb-Pb collisions, and also from high-multiplicity p-p collisions in the case of $K^+ d$. In addition to implementing the effect of the Coulomb force, the $K^- d$ and $K^+ d$ wave functions are derived from the corresponding strong scattering amplitudes that are built employing a unitarized chiral model for the elementary $K^- N$ an…

Caccioppoli-type inequalities for the Dunkl-$A$-Laplacian and their application to nonexistence result
Athulya P, Sandeep Kumar Verma
https://arxiv.org/abs/2509.00565 https://…

Caccioppoli-type inequalities for the Dunkl-$A$-Laplacian and their application to nonexistence result
For a suitable function $A:\mathbb{R}^n\to \mathbb{R}^n$, we introduce the $A$-Laplacian in the Dunkl framework as $Δ_{k,A}(u) =\text{div}_k(A(\nabla_ku))$, where $\nabla_k$ is the Dunkl-gradient operator associated with the multiplicity function $k$ and the root system $\mathcal{R}$. We derive the local and global Caccioppoli-type inequality for an element $u$ in the Dunkl-Orlicz-Sobolev space, satisfying the Dunkl-differential inequality $$ -Δ_{k, A}(u) \geq bΦ(u)χ_{\{u>0\}}. $$ Using the…

All-gluon amplitudes with off-shell recursion in multiplet bases
Oskar Bolinder, Rikkert Frederix, Malin Sjodahl
https://arxiv.org/abs/2507.22636 https://a…

All-gluon amplitudes with off-shell recursion in multiplet bases
The efficient computation of color-summed QCD amplitudes at high parton multiplicities remains a central challenge for precision collider predictions. Existing approaches using trace, color-flow, or adjoint bases suffer from non-orthogonality, which complicates the color algebra and scales poorly with multiplicity. In this work, we present an off-shell recursive framework for computing all-gluon tree-level amplitudes directly in orthogonal multiplet bases. Utilizing Wigner $6j$ coefficients, we…

Multiple solutions for Schr{\"o}dinger-Poisson-Slater equations with critical growth
Shibo Liu
https://arxiv.org/abs/2507.00295 https://

Multiple solutions for Schr{ö}dinger-Poisson-Slater equations with critical growth
We obtain multiple solutions for the zero mass Schr{ö}dinger-Poisson-Slater equation \[ - Δu + \left( \frac{1}{4 π| x |} \ast u^2 \right) u = λg (x) | u |^{p - 2} u + | u |^{6 - 2} u \text{, \ \ \ \ } u \in \mathcal{D}^{1, 2} (\mathbb{R}^3) \text{} \] for $λ\gg 1$, where $p \in (4, 6)$ and $g \in L^{6 / (6 - p)} (\mathbb{R}^3)$. The crucial (PS)$_c$ condition is verified using a simpler method. Similar multiplicity result is also obtained for related equation …