Tootfinder

On the universal Casimir spectrum
R. L. Mkrtchyan
https://arxiv.org/abs/2509.13707 https://arxiv.org/pdf/2509.13707…

On the universal Casimir spectrum
We conjecture the connection between $su$ and $so$ members of universal, in Vogel's sense, multiplets. The key element is the notion of the {\it vertical componentwise sum} $\oplus_v$ of Young diagrams. Representations in the decomposition of the power of the adjoint representation of $su(N)$ algebra can be parameterized by a couple of $N$-independent Young diagrams $λ$ and $τ$, with equal area. We assume that the $so(N)$ member of the universal (Casimir) multiplet of a given $su(N)$ repres…

Smooth Trade-off for Tensor PCA via Sharp Bounds for Kikuchi Matrices
Pravesh K. Kothari, Jeff Xu
https://arxiv.org/abs/2510.03061 https://arxiv.org/pdf/25…

Smooth Trade-off for Tensor PCA via Sharp Bounds for Kikuchi Matrices
In this work, we revisit algorithms for Tensor PCA: given an order-$r$ tensor of the form $T = G+λ\cdot v^{\otimes r}$ where $G$ is a random symmetric Gaussian tensor with unit variance entries and $v$ is an unknown boolean vector in $\{\pm 1\}^n$, what's the minimum $λ$ at which one can distinguish $T$ from a random Gaussian tensor and more generally, recover $v$? As a result of a long line of work, we know that for any $\ell \in \N$, there is a $n^{O(\ell)}$ time algorithm that succeeds whe…

Explicit construction of infinite families of strongly regular digraphs with parameters $((v (2^{n 1}-4)t)2^{n-1}, k (2^n-2)t, t, \lambda, t)$
Viktor A. Byzov, Igor A. Pushkarev
https://arxiv.org/abs/2509.25425

Explicit construction of infinite families of strongly regular digraphs with parameters $((v+(2^{n+1}-4)t)2^{n-1}, k+(2^n-2)t, t, λ, t)$
An explicit construction of infinite sequences of strongly regular digraphs with parameter sets $((v+(2^{n+1}-4)t)2^{n-1}, k+(2^n-2)t, t, λ, t)$ is described. A computer program was used to find the initial digraphs. The remaining terms of the sequence are obtained by the constructed recurrence. Using the described approach, 11 families of strongly regular digraphs were found. In particular, these families contain digraphs $\text{dsrg}(72, 18, 5, 3, 5)$, $\text{dsrg}(76, 19, 5, 4, 5)$, $\text{…

On primitivity and reduction for half-flag-transitive block designs
Xiaoqin Zhan
https://arxiv.org/abs/2509.21781 https://arxiv.org/pdf/2509.21781

On primitivity and reduction for half-flag-transitive block designs
Let $\mathcal{D} = (\mathcal{P}, \mathcal{B})$ be a $2$-$(v, k, λ)$ design, and let $G$ be a half-flag-transitive automorphism group of ${\cal D}$. In this article, we first establish three sufficient conditions for $G$ to be point-primitive: (i) $λ\geq (r, 2λ)^2$, (ii) $r > 4λ(k-2)$, (iii) $(v-1,2k-2)\le2$. Next, we prove that for $λ\geq (r, 2λ)^2$, the group $G$ is either of affine type, almost simple type, or product type. Finally, we analyze the case where $G$ is of almost simple type…

Unified Dark Matter and Dark Energy in a model of Non-Canonical Scalar-Tensor Theory
Nihal Jalal Pullisseri, Sanil Unnikrishnan
https://arxiv.org/abs/2510.07103 https://

Unified Dark Matter and Dark Energy in a model of Non-Canonical Scalar-Tensor Theory
We consider a model of non-canonical scalar-tensor theory in which the kinetic term in the Brans-Dicke action is replaced by a non-canonical scalar field Lagrangian $\mathcal{L}(X, ϕ)= λX^αϕ^β- V(ϕ)$ where $X = (1/2) \partial_μ ϕ\partial^μ ϕ$ and $α$, $β$ and $λ$ are parameters of the model. This can be considered as a simple non-canonical generalization of the Brans-Dicke theory with a potential term which corresponds to a special case of this model with the values of the paramete…

Least Energy Solutions for Cooperative and Competitive Schr\"odinger Systems with Neumann Boundary Conditions
Simone Mauro, Delia Schiera, Hugo Tavares
https://arxiv.org/abs/2509.18835

Least Energy Solutions for Cooperative and Competitive Schrödinger Systems with Neumann Boundary Conditions
We study the following gradient elliptic system with Neumann boundary conditions \begin{equation*} -Δu + λ_1 u = u^3 + βuv^2, \ -Δv + λ_2 v = v^3 + βu^2 v \ \text{in } Ω,\qquad \frac{\partial u}{\partial ν} = \frac{\partial v}{\partial ν} = 0 \ \text{on } \partial Ω, \end{equation*} where $Ω\subset \mathbb{R}^N $ is a bounded $ C^2$ domain with $ N \leq 4 $, and $ ν$ denotes the outward unit normal on the boundary. We investigate the existence of non-constant least energy solutions …

Multi-Channel Silicon-Organic Hybrid PICs for 200G/{\lambda} and 400G/{\lambda} PAM4 Transmission
Lewis E. Johnson, Ari Novack, Scott R. Hammond, Meisam Bahadori, Kevin M. O'Malley, Delwin L. Elder, Matthew Streshinsky, Brad Booth
https://arxiv.org/abs/2509.24825

Multi-Channel Silicon-Organic Hybrid PICs for 200G/λ and 400G/λ PAM4 Transmission
We demonstrate open-eye 224G PAM4 transmission in a 1.6T-DR8 PIC implementing low-Vπ silicon-organic hybrid modulators (VπL < 0.5 V-mm) with >80 3 dB GHz bandwidth and a variant capable of 400G/λ (> 110 GHz) for 3.2T-DR8. Both PIC variants use commercial crosslinkable organic electro- optic materials.

Estimates of the first Dirichlet eigenvalue of graphs
Huiqiu Lin, Lianping Liu, Zhe You, Da Zhao
https://arxiv.org/abs/2510.04557 https://arxiv.org/pdf/251…

Estimates of the first Dirichlet eigenvalue of graphs
Inspired by the Li--Yau eigenvalue-diameter estimates, we investigate lower bounds for the first Dirichlet eigenvalue in terms of the diameter (or inscribed radius) of a graph. Let $G = (V, E)$ be a graph with boundary $B$. Assume that the interior $Ω= V \setminus B$ is connected. Let $r$ be the inscribed radius of $(G, B)$ and $d$ be the maximum degree of $G$. We prove that $$λ_1(G, B) \geq \frac{d - 1}{r d^r},$$ which can be viewed as an analogue of the Lin--Yau bound and the Meng--Lin boun…

On the Semicontinuity of Functionals on Function Spaces
Fernanda M. Ba\^eta, Monika Ludwig
https://arxiv.org/abs/2509.17426 https://arxiv.org/pdf/2509.1742…

On the Semicontinuity of Functionals on Function Spaces
Results on the upper and lower semicontinuity of functionals defined on spaces of convex and more general functions are established. In particular, the following result is obtained. Let $ϕ(v; \cdot)$ be the density of the absolutely continuous part of a Radon measure $Φ(v; \cdot)$ associated to a function $v\colon X\rightarrow \mathbb{R}$ defined on the measure space $(X,λ)$. For concave $ζ\colon [0, \infty)\rightarrow[0,\infty)$ with $\lim_{t\to 0} ζ(t)=0$ and $\lim_{t\to\infty}ζ(t)/t= 0…

Complete Sampling of the $uv$ Plane with Realistic Radio Arrays: Introducing the RULES Algorithm, with Application to 21 cm Foreground Wedge Removal
Vincent MacKay, Zhilei Xu, Ruby Byrne, Jacqueline Hewitt
https://arxiv.org/abs/2509.15296

Complete Sampling of the $uv$ Plane with Realistic Radio Arrays: Introducing the RULES Algorithm, with Application to 21 cm Foreground Wedge Removal
We introduce the Radio-array $uv$ Layout Engineering Strategy (RULES), an algorithm for designing radio arrays that achieve complete coverage of the $uv$ plane, defined as, at minimum, regular sampling at half the observing wavelength ($λ$) along the $u$ and $v$ axes within a specified range of baseline lengths. Using RULES, we generate $uv$-complete layouts that cover the range $10λ\leq|(u,v)|\leq 100λ$ with fewer than 1000 antennas of diameter $5λ$, comparable to current and pla…

Optimizers of the Finite-Rank Hardy-Lieb-Thirring Inequality for Hardy-Schr\"odinger Operator
Bin Chen, Yujin Guo, Shuang Wu
https://arxiv.org/abs/2509.17307 https://

Optimizers of the Finite-Rank Hardy-Lieb-Thirring Inequality for Hardy-Schrödinger Operator
We study the following finite-rank Hardy-Lieb-Thirring inequality of Hardy-Schrödinger operator: \begin{equation*} \sum_{i=1}^N\left|λ_i\Big(-Δ-\frac{c}{|x|^2}-V\Big)\right|^s\leq C_{s,d}^{(N)}\int_{\mathbb R^d}V_+^{s+\frac d2}dx, \end{equation*} where $N\in\mathbb N^+$, $d\geq3$, $00$ is the best constant of Hardy's inequality, and $V\in L^{s+\frac d2}(\mathbb R^d)$ holds for $s>0$. Here $λ_i\big(-Δ-{c}{|x|^{-2}}-V\big)$…

Next highest weight and other lower $SU(3)$ irreducible representations with proxy-$SU(4)$ symmetry for nuclei with $32 \le \mbox{Z,N} \le 46$
V. K. B. Kota
https://arxiv.org/abs/2510.00800

Next highest weight and other lower $SU(3)$ irreducible representations with proxy-$SU(4)$ symmetry for nuclei with $32 \le \mbox{Z,N} \le 46$
In the applications of proxy-SU(3) model in the context of determining $(β,γ)$ values for nuclei across the periodic table, for understanding the preponderance of triaxial shapes in nuclei with $Z \ge 30$, it is seen that one needs not only the highest weight (hw) or leading $SU(3)$ irreducible representation (irrep) $(λ_H, μ_H)$ but also the lower $SU(3)$ irreps $(λ,μ)$ such that $2λ+ μ=2λ_H + μ_H-3r$ with $r=0,1$ and $2$ [Bonatsos et al., Symmetry {\bf 16}, 1625 (2024)]. These give …

Spectral extremal problems for the $(p,Q)$-spectral radius of hypergraphs
Jian Zheng, Honghai Li, Li Su
https://arxiv.org/abs/2510.02776 https://arxiv.org/…

Spectral extremal problems for the $(p,Q)$-spectral radius of hypergraphs
Let $Q$ be an $s$-vertex $r$-uniform hypergraph, and let $H$ be an $n$-vertex $r$-uniform hypergraph. Denote by $\mathcal{N}(Q,H)$ the number of isomorphic copies of $Q$ in $H$. For a hereditary family $\mathcal{P}$ of $r$-uniform hypergraphs, define $$π(Q,\mathcal{P}):=\lim\limits_{n\to \infty}\binom{n}{s}^{-1}\max\{\mathcal{N}(Q,H): H\in \mathcal{P}~~\mbox{and}~~|V(H)|=n\}.$$ For $p\geq1$, the $(p,Q)$-spectral radius of $H$ is defined as $$λ^{(p)}(Q,H):=\max_{\|\mathbf{x}\
…