Tootfinder

This https://arxiv.org/abs/2502.02939 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On grid homology for diagonal knots
We partially determine grid homology (combinatorial knot Floer homology) of diagonal knots, which are conjectured to be equivalent to positive braid knots, by exploiting nice grid diagrams. We compare diagonal knots to various classes of knots, such as positive braids, fibered positive knots, and $L$-space knots.

This https://arxiv.org/abs/2504.17644 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Bounded diagonal orbits in homogeneous spaces over function fields
This paper is about topological rigidity of diagonal group actions on the homogeneous $\SL_4\big(\F(\!(t^{-1})\!)\big)/\SL_4(\F[t])$ where $\F$ is a finite field of characteristic $3$. We show that there is a non-closed relatively compact orbit of the diagonal group.

On the weak and strong Lefschetz properties for initial ideals of determinantal ideals with respect to diagonal monomial orders
Hongmiao Yu
https://arxiv.org/abs/2506.05193

On the weak and strong Lefschetz properties for initial ideals of determinantal ideals with respect to diagonal monomial orders
We study the weak and strong Lefschetz properties for $R/\mathrm{in}(I_t)$, where $I_t$ is the ideal of a polynomial ring $R$ generated by the $t$-minors of an $m\times n$ matrix of indeterminates, and $\mathrm{in}(I_t)$ denotes the initial ideal of $I_t$ with respect to a diagonal monomial order. We show that when $I_t$ is generated by maximal minors (that is, $t=\mathrm{min}\{m,n\}$), the ring $R/\mathrm{in}(I_t)$ has the strong Lefschetz property for all $m$, $n$. In contrast, for $t<\mathrm…

There are days when autism feels overwhelming, and I find myself oversharing every thought and feeling that comes to mind.
But then, just as suddenly, my mood can shift. I’ll feel a surge of energy and want to shake things up.
That’s when I dive into my collection of anarchism memes and start posting my latest finds for everyone to enjoy!
We are here, unapologetically autistic and proud, and we refuse to be silenced!

This https://arxiv.org/abs/2503.19194 has been replaced.
initial toot: https://mastoxiv.page/@a…

Lorenz ratios of diagonal and Hall conductivities in a Dirac electron liquid
The magnetotransport properties of a two-dimensional electron liquid in graphene are analyzed in the hydrodynamic limit under isothermal conditions. It is shown that the Wiedemann-Franz law does not hold in this regime and that the Lorenz ratios constructed from the diagonal and Hall conductivities generally differ from each other. The breakdown of the Wiedemann-Franz law is most pronounced near charge neutrality, where the Lorenz ratio can exceed its nominal universal Sommerfeld value by an or…

This https://arxiv.org/abs/2401.04176 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Simple Diagonal State Designs with Reconfigurable Real-Time Circuits
Unitary designs are widely used in quantum computation, but in many practical settings it suffices to construct a diagonal state design generated with unitary gates diagonal in the computational basis. In this work, we introduce a simple and efficient diagonal state 3-design based on real-time evolutions under 2-local Hamiltonians. Our construction is inspired by the classical Girard-Hutchinson trace estimator in that it involves the stochastic preparation of many random-phase states. Though th…

Growth of block diagonal operators and symmetry-resolved Krylov complexity
Pawel Caputa, Giuseppe Di Giulio, Tran Quang Loc
https://arxiv.org/abs/2507.02033

Growth of block diagonal operators and symmetry-resolved Krylov complexity
This work addresses how the growth of invariant operators is influenced by their underlying symmetry structure. For this purpose, we introduce the symmetry-resolved Krylov complexity, which captures the time evolution of each block into which an operator, invariant under a given symmetry, can be decomposed. We find that, at early times, the complexity of the full operator is equal to the average of the symmetry-resolved contributions. At later times, however, the interplay among different charg…

Sparse Gaussian Processes: Structured Approximations and Power-EP Revisited
Thang D. Bui, Michalis K. Titsias
https://arxiv.org/abs/2507.02377 https://

Sparse Gaussian Processes: Structured Approximations and Power-EP Revisited
Inducing-point-based sparse variational Gaussian processes have become the standard workhorse for scaling up GP models. Recent advances show that these methods can be improved by introducing a diagonal scaling matrix to the conditional posterior density given the inducing points. This paper first considers an extension that employs a block-diagonal structure for the scaling matrix, provably tightening the variational lower bound. We then revisit the unifying framework of sparse GPs based on Pow…

Die letztwöchige Ö1-Diagonal-Sendung zur Person Laurie Anderson ist noch etwa 20 Tage online abrufbar. #sound
https://oe1.orf.at/programm/20250621/7980…

O Superwoman - Diagonal zur Person Laurie Anderson | SA | 21 06 2025 | 17:05
Ihre ersten Performances hatte die US-amerikanische Multimedia-Künstlerin und Musikerin Laurie Anderson in den 1970er Jahren. Von Beginn an arbeitete die 1947 in Illinois geborene Performerin an de...

This https://arxiv.org/abs/2503.14315 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Equiripple MIMO Beampattern Synthesis using Chebyshev Approximation
This letter presents a method for synthesizing equiripple MIMO transmit beampatterns using Chebyshev approximation. The MIMO beampattern is represented as a non-negative real-valued trigonometric polynomial where the $\ell^{\text{th}}$ order polynomial coefficient is the sum of the $\ell^{\text{th}}$ order diagonal of the waveform correlation matrix. The optimal coefficients for a given equiripple beampattern design is then posed as a Chebyshev approximation problem which is efficiently solved …

On the finite generation of the cohomology of bosonizations
Nicol\'as Andruskiewitsch, David Jaklitsch, Van C. Nguyen, Amrei Oswald, Julia Plavnik, Anne V. Shepler, Xingting Wang
https://arxiv.org/abs/2506.05267

On the finite generation of the cohomology of bosonizations
We use deformation sequences of (Hopf) algebras, extending the results of Negron and Pevtsova, to show that bosonizations of some suitable braided Hopf algebras by some suitable finite-dimensional Hopf algebras have finitely generated cohomology. In fact, our results are shown in more generality for smash products. As applications, we prove the bosonizations of some Nichols algebras (such as Nichols algebras of diagonal type, the restricted Jordan plane, Nichols algebras of direct sums of Jorda…

This https://arxiv.org/abs/2109.10887 has been replaced.
link: https://scholar.google.com/scholar?q=a

Asymptotic error in the eigenfunction expansion for the Green's function of a Sturm-Liouville problem
We study the asymptotic error arising when approximating the Green's function of a Sturm-Liouville problem through a truncation of its eigenfunction expansion, both for the Green's function of a regular Sturm-Liouville problem and for the Green's function associated with the Hermite polynomials, the associated Laguerre polynomials, and the Jacobi polynomials, respectively. We prove that the asymptotic error obtained on the diagonal can be expressed in terms of the coefficients of the related se…

On 102-avoiding inversion sequences
JiSun Huh, Sangwook Kim, Seunghyun Seo, Heesung Shin
https://arxiv.org/abs/2506.02985 https://arx…

On 102-avoiding inversion sequences
In this article, we provide a bijection between the set of inversion sequences avoiding the pattern 102 and the set of 2-Schröder paths having neither peaks nor valleys and ending with a diagonal step. To achieve this, we introduce two intermediate objects, called UVD paths and labeled $F$-paths, and establish bijections among all four families. For each of these combinatorial objects, we define a natural statistic and enumerate the corresponding structures with respect to this statistic. In a…

Schöne #Feierabend-Beschäftigung; dem selbst hochgepumpten💪 Grundwasser beim versickern in die Baumscheibe zugucken 🤗
#Balkonien
#Baumgießen

This https://arxiv.org/abs/2503.00817 has been replaced.
initial toot: https://mastoxiv.page/@…

Uniaxial Ordering by Self-Assembly of Isotropic Octahedral Junctions
We demonstrate that isotropic octahedral (sixfold branched) junctions with three diagonal endpoint pairs of different colors almost inevitably form a macroscopic assembly of uniaxial order, exhibiting the perfect order of a single color. Monte Carlo simulations of the antiferromagnetic three-state Potts model on the tripartite reo net, consisting of corner-sharing regular octahedrons, confirm this counterintuitive prediction, while showcasing switching self-assembly upon an ordering phase trans…

Eigenvalue bounds for preconditioned symmetric multiple saddle-point matrices
L. Bergamaschi, A. Martinez, J. W. Pearson, A. Potschka
https://arxiv.org/abs/2506.02816

Eigenvalue bounds for preconditioned symmetric multiple saddle-point matrices
We develop eigenvalue bounds for symmetric, block tridiagonal multiple saddle-point linear systems, preconditioned with block diagonal matrices. We extend known results for $3 \times 3$ block systems [Bradley and Greif, IMA J.\ Numer. Anal. 43 (2023)] and for $4 \times 4$ systems [Pearson and Potschka, IMA J. Numer. Anal. 44 (2024)] to an arbitrary number of blocks. Moreover, our results generalize the bounds in [Sogn and Zulehner, IMA J. Numer. Anal. 39 (2018)], developed for an arbitrary numb…

Observations on robust diffusive stability and common Lyapunov functions
Blake McGrane-Corrigan, Rafael de Andrade Moral, Oliver Mason
https://arxiv.org/abs/2506.04863

Observations on robust diffusive stability and common Lyapunov functions
We consider the problem of robust diffusive stability (RDS) for a pair of Schur-stable nonnegative matrices. Specifically, we show that the existence of a common diagonal Lyapunov function is sufficient for RDS and highlight how this condition differs from recently published results based on linear copositive Lyapunov functions. We also present two results on RDS for extended Leslie matrices arising in population dynamics.

Computing finite Weyl groupoids
Iv\'an Angiono, Leandro Vendramin
https://arxiv.org/abs/2505.24555 https://arxiv.org/pdf/2505.245…

Computing finite Weyl groupoids
We present algorithms to compute generalized root systems of Nichols algebras of diagonal type and of contragredient Lie superalgebras. As a consequence, we obtain an algorithm to compute the Lyndon words in the Kharchenko PBW basis associated to each positive root, along with their corresponding hyperwords. This data is essential for obtaining a minimal presentation of Nichols algebras of diagonal type with a finite root system.

Local laws and spectral properties of deformed sparse random matrices
Ji Oon Lee, Inyoung Yeo
https://arxiv.org/abs/2507.02298 https://

Local laws and spectral properties of deformed sparse random matrices
We consider deformed sparse random matrices of the form $H= W+ λV$, where $W$ is a real symmetric sparse random matrix, $V$ is a random or deterministic, real, diagonal matrix whose entries are independent of $W$, and $λ= O(1) $ is a coupling constant. Under mild assumptions on the matrix entries of $W$ and $V$, we prove local laws for $H$ that compares the empirical spectral measure of it with a refined version of the deformed semicircle law. By applying the local laws, we also prove several…

On Graded Quasi-Cartan Pairs and Twisted Steinberg Algebras
Lisa Orloff Clark, Lynnel D. Naingue, Jocelyn P. Vilela
https://arxiv.org/abs/2505.24180 https:…

On Graded Quasi-Cartan Pairs and Twisted Steinberg Algebras
We generalise recent results about quasi-Cartan, Cartan and diagonal subalgebras by introducing graded versions. We show that there is a correspondence between graded algebraic quasi-Cartan/ Cartan/ diagonal pairs and certain graded twisted Steinberg algebras and that the associated graded discrete twist is unique. Our results include all discrete group algebras, and so are more general than the ungraded version.

This https://arxiv.org/abs/2407.18398 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Low-weight codewords in cyclic codes
We introduce a formula for determining the number of codewords of weight 2 in cyclic codes and provide results related to the count of codewords with weight 3. Additionally, we establish a recursive relationship for binary cyclic codes that connects their weight distribution to the number of solutions of associated systems of polynomial equations. This relationship allows for the computation of weight distributions from known solutions of systems of diagonal equations and vice versa, offering a…

This https://arxiv.org/abs/2501.17432 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Diagonal superexchange in a simple square CuO$_2$ lattice
Many microscopic models with the interaction between the next-nearest neighbours as a key parameter for cuprate physics have inspired us to study the diagonal superexchange interaction in a CuO$_2$ layer. Our investigation shows that models with extended hopping provide a correct representation of magnetic interactions only in a hypothetical square CuO$_2$ layer, where the diagonal superexchange interaction with the next-nearest neighbors always has the AFM nature. The conclusions are based on …

Luna won’t worry about that deflection. Great diagonal ball out to Arfsten from Tillman. That will get his head back on right. #USMNT

Stochastic inflation as an open quantum system
Yue-Zhou Li
https://arxiv.org/abs/2507.02070 https://arxiv.org/pdf/2507.02070

Stochastic inflation as an open quantum system
We reinterpret Starobinsky's stochastic inflation as an open quantum system, where short-wavelength modes act as the environment for long-wavelength modes. Using the Schwinger-Keldysh formalism, we systematically trace out the environment and derive an effective theory for the reduced density matrix, including deviations from exact de Sitter. The resulting master equation is a Lindblad equation, which reduces to a Fokker-Planck equation for the diagonal elements up to higher orders in the slow-…

Bernstein-Markov measures and Toeplitz theory
Siarhei Finski
https://arxiv.org/abs/2506.01610 https://arxiv.org/pdf/2506.01610…

Bernstein-Markov measures and Toeplitz theory
We prove that Toeplitz operators associated with a Bernstein-Markov measure on a compact complex manifold endowed with a big line bundle form an algebra under composition. As an application, we derive a Szegő-type spectral equidistribution result for this class of operators. A key component of our approach is the off-diagonal asymptotic analysis of the Bergman kernel, also known as the Christoffel-Darboux kernel.

Eigenstate Thermalization Hypothesis (ETH) for off-diagonal matrix elements in integrable spin chains
Federico Rottoli, Vincenzo Alba
https://arxiv.org/abs/2505.23602

Eigenstate Thermalization Hypothesis (ETH) for off-diagonal matrix elements in integrable spin chains
We investigate off-diagonal matrix elements of local operators in integrable spin chains, focusing on the isotropic spin-$1/2$ Heisenberg chain ($XXX$ chain). We employ state-of-the-art Algebraic Bethe Ansatz results, which allow us to efficiently compute matrix elements of operators with support up to two sites between generic energy eigenstates. We consider both matrix elements between eigenstates that are in the same thermodynamic macrostate, as well as eigenstates that belong to different m…

Replaced article(s) found for quant-ph. https://arxiv.org/list/quant-ph/new
[2/3]:
- Estimating Bell Diagonal States with Separable Measurements
Noah Kaufmann, Maria Quadeer, David Elkouss

Quantum Hall Effect and Chern Phases in the 1/5-Depleted Square Lattice
Sara Aghtouman, Godfrey Gumbs, Mir Vahid Hosseini
https://arxiv.org/abs/2507.00932 …

Quantum Hall Effect and Chern Phases in the 1/5-Depleted Square Lattice
We investigate the fractional energy spectrum and quantum Hall response of a two-dimensional 1/5-depleted square lattice subjected to a perpendicular magnetic field. Using a tight-binding model that includes both nearest-neighbor (t_1) and next-nearest-neighbor (t_2) hopping, we compute the Hofstadter butterfly and extract quantized Hall conductivities via Chern number calculations. In the absence of diagonal hopping (t_2 =0), the spectrum exhibits exact particle-hole and flux-inversion symmetr…

Beyond diagonal approximations: improved covariance modeling for pulsar timing array data analysis
Marco Crisostomi, Rutger van Haasteren, Patrick M. Meyers, Michele Vallisneri
https://arxiv.org/abs/2506.13866

Beyond diagonal approximations: improved covariance modeling for pulsar timing array data analysis
Pulsar Timing Array (PTA) searches for nHz gravitational-wave backgrounds (GWBs) typically model time-correlated noise by assuming a diagonal covariance in Fourier space, neglecting inter-frequency correlations introduced by the finite observation window. We show that this diagonal approximation can lead to biased estimates of spectral parameters, especially for the common red process that represents the GWB. To address these limitations, we present a method that (i) computes the time-domain au…

Numerical Techniques for the Maximum Likelihood Toeplitz Covariance Matrix Estimation: Part I. Symmetric Toeplitz Matrices
Yuri Abramovich, Victor Abramovich, Tanit Pongsiri
https://arxiv.org/abs/2507.01230

Numerical Techniques for the Maximum Likelihood Toeplitz Covariance Matrix Estimation: Part I. Symmetric Toeplitz Matrices
In several applications, one must estimate a real-valued (symmetric) Toeplitz covariance matrix, typically shifted by the conjugated diagonal matrices of phase progression and phase "calibration" errors. Unlike the Hermitian Toeplitz covariance matrices, these symmetric matrices have a unique potential capability of being estimated regardless of these beam-steering phase progression and/or phase "calibration" errors. This unique capability is the primary motivation of this paper.

A General Test for Independent and Identically Distributed Hypothesis
Tongyu Li, Jonas Mueller, Fang Yao
https://arxiv.org/abs/2506.22361 https://

A General Test for Independent and Identically Distributed Hypothesis
We propose a simple and intuitive test for arguably the most prevailing hypothesis in statistics that data are independent and identically distributed (IID), based on a newly introduced off-diagonal sequential U-process. This IID test is fully nonparametric and applicable to random objects in general spaces, while requiring no specific alternatives such as structural breaks or serial dependence, which allows for detecting general types of violations of the IID assumption. An easy-to-implement j…

An Optimal Least-Square Solver For Scaled Partial-Isometric Linear Systems
Suvendu Kar, Murugesan Venkatapathi
https://arxiv.org/abs/2507.01434 https://

An Optimal Least-Square Solver For Scaled Partial-Isometric Linear Systems
We present an $O(mn)$ direct least-squares solver for $m \times n$ linear systems with a scaled partial isometry. The proposed algorithm is also useful when the system is block diagonal and each block is a scaled partial isometry with distinct scaling factors. We also include numerical experiments as a demonstration.

Decoupling Periodic Systems: An Algebraic Approach
Vladim\'ir Ku\v{c}era
https://arxiv.org/abs/2505.23616 https://arxiv.org/pdf/2…

Decoupling Periodic Systems: An Algebraic Approach
This paper addresses the problem of row-by-row (or diagonal) decoupling of discrete-time linear multi-input multi-output systems with periodic time-varying coefficients using periodic state feedback. Previous solutions have tackled row-by-row decoupling using dynamic compensation for square systems and block-decoupling through regular state feedback for nonsquare systems with more outputs than inputs. While it appears likely that a row-by-row state feedback solution for square systems can be de…

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 …

C*-diagonals with Cantor spectrum in Cuntz algebras
Samuel Evington, Philipp Sibbel
https://arxiv.org/abs/2506.22163 https://arxiv.or…

C*-diagonals with Cantor spectrum in Cuntz algebras
We prove that there exists a C*-diagonal with Cantor spectrum in the Cuntz algebra $\mathcal{O}_k$ for $2 \le k < \infty$. Our method generalises to an uncountable family of UCT Kirchberg algebras with distinct K-theory. Moreover, we construct principal étale groupoid models for these Cuntz algebras and UCT Kirchberg algebras.

This https://arxiv.org/abs/2505.07739 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Torsion modules and differential operators in infinitely many variables
This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with respect to the diagonal ideal in the tensor square of the ring. Various notions of torsion modules for an infinitely generated ideal in a commutative ring lead to various notions of differential operators. We discuss differential operators of transfinite orders…

Off-diagonal deformations of regular Schwarzschild black holes and general relativistic G. Perelman thermodynamics
Sergiu I. Vacaru, El\c{s}en Veli Veliev
https://arxiv.org/abs/2505.18208

Off-diagonal deformations of regular Schwarzschild black holes and general relativistic G. Perelman thermodynamics
We construct new classes of solutions describing generic off-diagonal deformations of regular Schwarzschild black holes (BHs) in general relativity (GR). Examples of such (primary) diagonal metrics reducing the Einstein equations to integrable systems of nonlinear ordinary differential equations were studied in a recent work by R. Casadio, A. Kamenshchik and J. Ovalle in Phys. Rev. D 111 (2025) 064036. We develop and apply our anholonomic frame and connection deformations method, which allows u…

The multilinear fractional bounded mean oscillation operator theory I: sparse domination, sparse $T1$ theorem, off-diagonal extrapolation, quantitative weighted estimate -- for generalized commutators
Xi Cen, Zichen Song
https://arxiv.org/abs/2506.23486

The multilinear fractional bounded mean oscillation operator theory I: sparse domination, sparse $T1$ theorem, off-diagonal extrapolation, quantitative weighted estimate -- for generalized commutators
This paper introduces and studies a class of multilinear fractional bounded mean oscillation operators (denoted {\rm $m$-FBMOOs}) defined on ball-basis measure spaces $(X, μ, \mathcal{B})$. These operators serve as a generalization of canonical classes, such as the multilinear fractional maximal operators, the multilinear fractional Ahlfors-Beurling operators, the multilinear pseudo-differential operators with multi-parameter Hörmander symbol, and some multilinear operators admitting $\mathbb…

Constraining parameters of spinor field dark energy: An alternative to $\Lambda$CDM model under the spherically symmetric FLRW space-time
Bijan Saha, Mahendra Goray
https://arxiv.org/abs/2506.16323

Constraining parameters of spinor field dark energy: An alternative to $Λ$CDM model under the spherically symmetric FLRW space-time
This study constrains the cosmological parameters within the scope of a spherically symmetric FLRW cosmological model, the role of a nonlinear spinor field in the universe's evolution. To test this approach, we incorporate the recent Cosmic chronometers, Supernova, and Sloan Digital Sky Survey data. It is found that if spherical coordinates give the FLRW model, the energy-momentum tensor (EMT) of the spinor field possesses nontrivial non-diagonal components. These non-diagonal components of EMT…

A note on instantaneous gelation for coagulation kernels vanishing on the diagonal
Iulia Cristian (LJLL), Barbara Niethammer, Juan J. L. Vel\'azquez
https://arxiv.org/abs/2506.11573

A note on instantaneous gelation for coagulation kernels vanishing on the diagonal
We prove that instantaneous gelation (i.e., instantaneous loss of mass) occurs for coagulation equations with sum-type kernels of homogeneity greater than one which vanish on the diagonal. Our proof includes solutions that are Radon measures if we exclude the case of initial data that are a single Dirac delta.

Join our #Luanti server they said. A few days have passed and I built this. Now what?
Contemplating my life choices.

@… @… honestly, that’s not a bad idea. 😝
@… suggested putting a sticker over the “PAR” that ma…

This https://arxiv.org/abs/2505.18468 has been replaced.
initial toot: https://mastoxiv.page/@a…

Generalized many-body exciton g-factors: magnetic hybridization and non-monotonic Rydberg series in monolayer WSe\textsubscript{2}
Magneto-optics of low dimensional semiconductors, such as monolayer transition metal dichalcogenides, offers a vast playground for exploring complex quantum phenomena. However, current \textit{ab initio} approaches fail to capture important experimental observations related to brightening of excitonic levels and their g-factor dependence. Here, we develop a robust and general first principles framework for many-body exciton g-factors by incorporating off-diagonal terms for the spin and orbital …

Hybrid High-Order formulations with turbulence modelling capabilities for incompressible flow problems
Lorenzo Botti, Daniele Antonio Di Pietro, Francesco Carlo Massa
https://arxiv.org/abs/2505.22480

Hybrid High-Order formulations with turbulence modelling capabilities for incompressible flow problems
We propose a Hybrid High-Order (HHO) formulation of the incompressible Navier--Stokes equations, that is well suited to be employed for the simulation of turbulent flows. The spatial discretization relies on hybrid velocity and pressure spaces and the temporal discretization is based on Explicit Singly Diagonal Implicit Runge-Kutta (ESDIRK) methods. The formulation possesses some attractive features that can be fruitfully exploited when high-fidelity computations are required, namely: pressure-…

This https://arxiv.org/abs/2504.13809 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Fast Direct Solver for Boundary Integral Equations Using Quadrature By Expansion
We construct and analyze a hierarchical direct solver for linear systems arising from the discretization of boundary integral equations using the Quadrature by Expansion (QBX) method. Our scheme builds on the existing theory of Hierarchical Semi-Separable (HSS) matrix operators that contain low-rank off-diagonal submatrices. We use proxy-based approximations of the far-field interactions and the Interpolative Decomposition (ID) to construct compressed HSS operators that are used as fast direct …

Complete Boundary Phase Diagram of the Spin-$\frac{1}{2}$ XXZ Chain with Boundary Fields in the Anti-Ferromagnetic Gapped Regime
Parameshwar R. Pasnoori, Yicheng Tang, Junhyun Lee, J. H. Pixley, Patrick Azaria, Natan Andrei
https://arxiv.org/abs/2507.00386

Complete Boundary Phase Diagram of the Spin-$\frac{1}{2}$ XXZ Chain with Boundary Fields in the Anti-Ferromagnetic Gapped Regime
We consider the spin $\frac{1}{2}$ XXZ chain with diagonal boundary fields and solve it exactly using Bethe ansatz in the gapped anti-ferromagnetic regime and obtain the complete phase boundary diagram. Depending on the values of the boundary fields, the system exhibits several phases which can be categorized based on the ground state exhibited by the system and also based on the number of bound states localized at the boundaries. We show that the Hilbert space is comprised of a certain number …

Snowflake by Louise Nealon is a fun book with odd characters. Here is what I thought: #review

Torsional modulation of atmospheric neutrino oscillation
Riya Barick, Amitabha Lahiri
https://arxiv.org/abs/2506.19354 https://arxiv.…

Torsional modulation of atmospheric neutrino oscillation
Fermions act as sources of spacetime torsion. However, this torsion is non-dynamical and can be eliminated using its equations of motion. The resulting theory features an effective four-fermion interaction in a torsion-free background. Generically this interaction is non-universal and violates parity. When neutrinos propagate through matter, they experience the effect of this geometrical interaction, which is similar to the MSW effect, but diagonal in the mass basis. Since this quartic interact…

Efficient Training for Optical Computing
Manon P. Bart, Nick Sparks, Ryan T. Glasser
https://arxiv.org/abs/2506.20833 https://arxiv.o…

Efficient Training for Optical Computing
Diffractive optical information processors have demonstrated significant promise in delivering high-speed, parallel, and energy efficient inference for scaling machine learning tasks. Training, however, remains a major computational bottleneck, compounded by large datasets and many simulations required for state-of-the-art classification models. The underlying linear transformations in such systems are inherently constrained to compositions of circulant and diagonal matrix factors, representing…

Replaced article(s) found for eess.SP. https://arxiv.org/list/eess.SP/new
[1/1]:
- Modern Base Station Architecture: Enabling Passive Beamforming with Beyond Diagonal RISs
Mahmoud Raeisi, Hui Chen, Henk Wymeersch, Ertugrul Basar

Off-diagonal estimates of the Bergman kernel associated to Siegel varieties
Anilatmaja Aryasomayajula, Harinarayanan G
https://arxiv.org/abs/2506.17583 htt…

Off-diagonal estimates of the Bergman kernel associated to Siegel varieties
For $g\geq 2$, let $Γ\subset\mathrm{Sp}(2g,\mathbb{R})$ be a discrete subgroup, which is either a cocompact subgroup or an arithmetic subgroup without torsion elements, and let $\mathbb{H}_{g}$ denote the Siegel upper half space of genus $g$. Let $X_Γ:=Γ\backslash\mathbb{H}_{g}$ denote the quotient space, which is a complex manifold of dimension $g(g+1)/2$. Let $Ω_{X_Γ}$ denote the cotangent bundle, and let $\ell:=\mathrm{det}(Ω_{X_Γ})$ denote the determinant line bundle of $Ω_{X_Γ}$. …

Faster Low-Rank Approximation and Kernel Ridge Regression via the Block-Nystr\"om Method
Sachin Garg, Micha{\l} Derezi\'nski
https://arxiv.org/abs/2506.17556

Faster Low-Rank Approximation and Kernel Ridge Regression via the Block-Nyström Method
The Nyström method is a popular low-rank approximation technique for large matrices that arise in kernel methods and convex optimization. Yet, when the data exhibits heavy-tailed spectral decay, the effective dimension of the problem often becomes so large that even the Nyström method may be outside of our computational budget. To address this, we propose Block-Nyström, an algorithm that injects a block-diagonal structure into the Nyström method, thereby significantly reducing its computati…

Angular Momentum Fluctuations in the Phonon Vacuum of Symmetric Crystals
Rule Yi, Violet Williams, Benedetta Flebus
https://arxiv.org/abs/2506.21801 https:…

Angular Momentum Fluctuations in the Phonon Vacuum of Symmetric Crystals
Although time-reversal and inversion symmetry constrain the angular momentum of each phonon mode to vanish, we show that the vacuum state of crystals with such symmetries can nevertheless exhibit finite angular momentum fluctuations. These fluctuations arise from quantum coherence between nondegenerate, orthogonally polarized modes and are encoded in the off-diagonal components of the angular momentum operator. Their origin lies in the noncommutativity between the phonon Hamiltonian and angular…

Computing matrix $\varphi$-functions arising in exponential integrators
Awad H. Al-Mohy, Xiaobo Liu
https://arxiv.org/abs/2506.01193 https://

Computing matrix $φ$-functions arising in exponential integrators
A new scaling and recovering algorithm is proposed for simultaneously computing the matrix $φ$-functions that arise in exponential integrator methods for the numerical solution of certain first-order systems of ordinary differential equations (ODEs). The algorithm initially scales the input matrix down by a nonnegative integer power of two, then computes the $[m/m]$ diagonal Padé approximant to $φ_p$, where $p$ is the largest index of interest. The remaining $[m+p{-}j/m]$ Padé approximants …

Rovibrational computations for He$_2^ $ X$^ \ \Sigma_\mathrm{u}^ $ including non-adiabatic, relativistic and QED corrections
Edit M\'atyus, \'Ad\'am Marg\'ocsy
https://arxiv.org/abs/2506.19120

Rovibrational computations for He$_2^+$ X$^+\ Σ_\mathrm{u}^+$ including non-adiabatic, relativistic and QED corrections
We report the potential energy curve, the diagonal Born-Oppenheimer, non-adiabatic mass, relativistic, and leading-order QED corrections for the ground electronic state of the helium dimer cation; the higher-order QED and finite-nuclear size effects are also estimated. The computations are carried out with an improved error control and over a much broader configuration range compared to earlier work [D. Ferenc, V. I. Korobov, and E. Mátyus, Phys. Rev. Lett. 125, 213001 (2020)]. As a result, al…

S-wave flavor-singlet meson mixing in QCD with light and charm quarks
Juan Andr\'es Urrea-Ni\~no, Jacob Finkenrath, Roman H\"ollwieser, Francesco Knechtli, Tomasz Korzec, Michael Peardon
https://arxiv.org/abs/2506.22132

S-wave flavor-singlet meson mixing in QCD with light and charm quarks
We investigate the mixing between flavor-singlet light meson and charmonium operators in the S-wave channels, i.e. pseudo-scalar and vector channel, at two different pion masses. We measure statistically significant non-zero correlations between operators with different quark content corresponding to off-diagonal entries of a flavor-singlet mixing correlation matrix. By solving a GEVP we extract the low-lying energy spectrum and compare it with the one obtained by the different types of operato…

Single-exponential bounds for diagonals of D-finite power series
Shaoshi Chen, Fr\'ed\'eric Chyzak, Pingchuan Ma, Chaochao Zhu
https://arxiv.org/abs/2506.22011

Single-exponential bounds for diagonals of D-finite power series
D-finite power series appear ubiquitously in combinatorics, number theory, and mathematical physics. They satisfy systems of linear partial differential equations whose solution spaces are finite-dimensional, which makes them enjoy a lot of nice properties. After attempts by others in the 1980s, Lipshitz was the first to prove that the class they form in the multivariate case is closed under the operation of diagonal. In particular, an earlier work by Gessel had addressed the D-finiteness of th…

Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Frames
Haiyang Yu, Yuchao Lin, Xuan Zhang, Xiaofeng Qian, Shuiwang Ji
https://arxiv.org/abs/2506.09398

Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Frames
We consider the task of predicting Hamiltonian matrices to accelerate electronic structure calculations, which plays an important role in physics, chemistry, and materials science. Motivated by the inherent relationship between the off-diagonal blocks of the Hamiltonian matrix and the SO(2) local frame, we propose a novel and efficient network, called QHNetV2, that achieves global SO(3) equivariance without the costly SO(3) Clebsch-Gordan tensor products. This is achieved by introducing a set o…

This https://arxiv.org/abs/2412.16740 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hilbert's tenth problem for systems of diagonal quadratic forms, and Büchi's problem
In this paper we complete Büchi's proof that there is no decision algorithm for the solubility in integers of arbitrary systems of diagonal quadratic form equations, by proving the assertion that whenever $x_1^2, \cdots, x_5^2$ are five squares such that the second differences satisfy \[x_{k+2}^2 - 2 x_{k+1}^2 + x_k^2 = 2\] for $k = 1,2,3$, then they must be consecutive. This answers a question of J.~Richard~Büchi.

This https://arxiv.org/abs/2112.12859 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Countable, Dense, Dedekind-Complete Subset of $\mathbb{R}$ Constructed by Extending $\mathbb{Q}$ via Simultaneous Marking of Closed Intervals with Rational Endpoints
This article explores the model-dependent nature of set cardinality, emphasizing that cardinality is not absolute but varies across different axiomatic frameworks. Although Cantor's diagonal argument shows the real numbers are non-denumerable within ZF (Zermelo-Fraenkel set theory), the precise cardinality of the continuum remains unsettled and depends critically on model assumptions. For instance, under Gödel's inner-model axiom V=Ultimate L, the Continuum Hypothesis (CH) holds, whereas Marti…

Elliptic constant cycle curves on Kummer surfaces
Jiexiang Huang
https://arxiv.org/abs/2506.06260 https://arxiv.org/pdf/2506.06260

Elliptic constant cycle curves on Kummer surfaces
The order of a constant cycle curve $C \subset X$ on a K3 surface, defined by Huybrechts, is a positive integer that measures the obstruction to decomposing the diagonal class $Δ_C$ in the Chow group $\mathrm{CH}^2(X \times C)$. In this paper, we compute the order of elliptic constant cycle curves that naturally arise on Kummer surfaces, by passing to the transcendental intermediate Jacobian $J_{\mathrm{tr}}^3(X \times C)$. As a consequence, every $n \in \mathbb{N}$ can be realized as the orde…

Contractive upper triangular matrices with prescribed diagonals and superdiagonals
Axel Renard
https://arxiv.org/abs/2506.15444 https://

Contractive upper triangular matrices with prescribed diagonals and superdiagonals
A characterization of the matrix representation of the compressed shift acting on a finite-dimensional model space endowed with the Takenaka-Malmquist-Walsh basis, among all upper triangular matrices, is proved. For a fixed dimension, this matrix is the unique matrix with spectral norm no greater than one and with a prescribed diagonal and superdiagonal. We also discuss an extension to the setting of infinite matrices.

Superconductivity and inhomogeneous charge-ordered state in the two-Dimensional Hubbard model -- Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model IV
Takashi Yanagisawa
https://arxiv.org/abs/2506.12736

Superconductivity and inhomogeneous charge-ordered state in the two-Dimensional Hubbard model -- Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model IV
We investigate the ground-state properties of the two-dimensional Hubbard model, based on the off-diagonal wave function variational Monte Carlo method. We use an optimized wave function that is improved from an initial one-body wave function by multiplying by multiple correlation operators that are given by the form of exp($-S$)-type where $S$ is a suitable operator. We examine the inhomogeneous ground state at near 1/8 doping in the strongly correlated region where the on-site Coulomb interac…

Complete Minimal Form Factors for Irrelevant Deformations of Integrable Quantum Field Theory
Fabio Sailis, Olalla A. Castro-Alvaredo, Stefano Negro
https://arxiv.org/abs/2506.20517

Complete Minimal Form Factors for Irrelevant Deformations of Integrable Quantum Field Theory
In this paper, we present a method to compute the minimal form factors of diagonal integrable field theories perturbed by generalized $T \bar{T}$ perturbations. Building on existing results by the same authors, these MFFs are constructed in such a way as not to allow for any free parameters, an issue that plagued previous solutions. The MFFs are derived from a generalization of the standard integral representation which has been used since the birth of the form factor bootstrap program. Their a…

Noncontextual Pauli Hamiltonians
Alexis Ralli, Tim Weaving, Peter J. Love
https://arxiv.org/abs/2506.19778 https://arxiv.org/pdf/2506…

Noncontextual Pauli Hamiltonians
Contextuality is a key feature of quantum mechanics, and identification of noncontextual subtheories of quantum mechanics is of both fundamental and practical importance. Recently, noncontextual Pauli Hamiltonians have been defined in the setting of variational quantum algorithms. In this work we rigorously establish a number of properties of noncontextual Pauli Hamiltonians. We prove that these Hamiltonians can be composed of more Pauli operators than diagonal Hamiltonians. This establishes th…

Gravitational lensing observables in stationary and axisymmetric solutions in general relativity
Matteo Luca Ruggiero, Davide Astesiano
https://arxiv.org/abs/2506.17192

Gravitational lensing observables in stationary and axisymmetric solutions in general relativity
We investigate light propagation in self-gravitating systems composed of an axially symmetric, stationary, rotating dust fluid. These configurations are intrinsically relativistic, sustained entirely by their rotation, since no compact or finite dust distribution can exist under the same symmetry conditions in Newtonian gravity. In such systems, rotational effects arise from off-diagonal components of the spacetime metric, which are not negligible compared to their Newtonian counterparts. We an…

Variational Inference with Mixtures of Isotropic Gaussians
Marguerite Petit-Talamon, Marc Lambert, Anna Korba
https://arxiv.org/abs/2506.13613 https://

Variational Inference with Mixtures of Isotropic Gaussians
Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL) divergence. In this paper, we focus on the following parametric family: mixtures of isotropic Gaussians (i.e., with diagonal covariance matrices proportional to the identity) and uniform weights. We develop a variational framework and provide efficient algori…

Exceptional point in a PT symmetric non-Hermitian terahertz plasmonic metasurface
Anshul Bhardwaj, Maidul Islam, Chandan Kumar, Anuraj Panwar, Gagan Kumar
https://arxiv.org/abs/2506.17906

Exceptional point in a PT symmetric non-Hermitian terahertz plasmonic metasurface
In this paper, we experimentally demonstrate a non-Hermitian open PT-symmetric terahertz metasurface comprising complementary plasmonic structures capable of exhibiting an exceptional point (EP). The metasurface consists of two resonators of different sizes, representing effective gain and loss elements, placed orthogonally in close proximity to realize a non-Hermitian configuration leading to a PT symmetry state. A diagonal displacement of one resonator within this strongly coupled near-field …

Rovibrational computations for the He$_2$ a $^3\Sigma_\mathrm{u}^ $ state including non-adiabatic, relativistic, and QED corrections
\'Ad\'am Marg\'ocsy, Bal\'azs R\'acsai, P\'eter Jeszenszki, Edit M\'atyus
https://arxiv.org/abs/2506.19116

Rovibrational computations for the He$_2$ a $^3Σ_\mathrm{u}^+$ state including non-adiabatic, relativistic, and QED corrections
A potential energy curve (PEC) accurate to a fraction of 1 ppm ($1:10^6$) is computed for the $^3Σ_\mathrm{u}^+$ state of He$_2$ endowed with relativistic and QED corrections. The nuclear Schrödinger equation is solved on this PEC with diagonal Born-Oppenheimer and non-adiabatic mass corrections to obtain highly accurate rotational-vibrational levels. The computed rovibrational intervals and fine-structure splittings, spanning over several orders of magnitude in energy, are found to be in rem…

This https://arxiv.org/abs/2503.03933 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Arithmetic properties of Cantor sets involving non-diagonal forms
We show conditions on $k$ such that any number $x$ in the interval $[0, k/2]$ can be represented in the form $x_1^{a_1} x_2^{a_2} + x_3^{a_3} x_4^{a_4} + \cdots + x_{k-1}^{a_{k-1}} x_k^{a_k}$, where the exponents $a_{2i-1}$ and $a_{2i}$ are positive integers satisfying $a_{2i-1} + a_{2i} = s$ for $i = 1, 2, \dots, k/2$, and each $x_i$ belongs to the generalized Cantor set. Moreover, we discuss different types of non-diagonal polynomials and clarify the optimal results in low-dimensional cases.

Replaced article(s) found for cond-mat.dis-nn. https://arxiv.org/list/cond-mat.dis-nn/new
[1/1]:
Localization with non-Hermitian off-diagonal disorder

Collective Oscillations of Bose-Einstein Condensates in a Synthetic Magnetic Field
Huaxin He, Fengtao Pang, Yongping Zhang, Chunlei Qu
https://arxiv.org/abs/2506.09341

Collective Oscillations of Bose-Einstein Condensates in a Synthetic Magnetic Field
We study the collective oscillations of spin-orbit-coupled Bose-Einstein condensates in the presence of position-dependent detuning. Specifically, we explore the quadrupole modes of the system using both numerical and analytical approaches based on the Gross-Pitaevskii equation and hydrodynamic theory. Due to spin-orbit coupling and the synthetic magnetic field, {the $xy$ scissors mode couples with a superposition of the three diagonal quadrupole modes ($x^2$, $y^2$, and $z^2$),} resulting in t…

Properties and applications of partial multiple weights for fractional integrals
Wang Dinghuai, Yin Huicheng
https://arxiv.org/abs/2505.21007 https://

Properties and applications of partial multiple weights for fractional integrals
In this paper, through the introduction of partial multiple weights, we firstly study the related Rubio de Francia extrapolation theorem within the framework of partial Muckenhoupt classes and further obtain the corresponding extrapolation theorem for two types of off-diagonal estimates. Secondly, we establish some weighted estimates for fractional integrals associated with partial Muckenhoupt weights. As applications, several basic inequalities (including the Fefferman-Phong inequality, the de…

Transcendental Brauer groups of cubic generalised Kummer surfaces
Giorgio Navone
https://arxiv.org/abs/2506.16372 https://arxiv.org/p…

Transcendental Brauer groups of cubic generalised Kummer surfaces
Given a cubic curve $C$ over a number field, we consider the K3 surface $Y_C$ constructed as the minimal desingularisation of the quotient of $C \times C$ by an automorphism of order 3. We relate the transcendental Brauer groups of $Y_C$ and $C \times C$, allowing us to explicitly compute the former group in the case of a diagonal cubic curve defined over $\mathbb{Q}$. We obtain conjectural insight on the existence of Galois cubic points over $\mathbb{Q}$ for everywhere locally soluble diagonal…

Motivic Steenrod operations at the characteristic via infinite ramification
Toni Annala, Elden Elmanto
https://arxiv.org/abs/2506.05585 https://

Motivic Steenrod operations at the characteristic via infinite ramification
We construct motivic power operations on the mod-$p$ motivic cohomology of $\Fb_p$-schemes using a motivic refinement of Nizioł's theorem. The key input is a purity theorem for motivic cohomology established by Levine. Our operations satisfy the expected properties (naturality, Adem relations, and the Cartan formula) for all bidegrees, generalizing previous results of Primozic which were only know along the ``Chow diagonal.'' We offer geometric applications of our construction: 1) an example o…

Inverse eigenvalue problem for discrete Schr\"odinger operators of a graph
Anzila Laikhuram, Jephian C. -H. Lin
https://arxiv.org/abs/2506.15430 https…

Inverse eigenvalue problem for discrete Schrödinger operators of a graph
A discrete Schrödinger operator of a graph $G$ is a real symmetric matrix whose $i,j$-entry, $i \neq j$, is negative if $\{i,j\}$ is an edge and zero if it is not an edge, while diagonal entries can be any real numbers. The discrete Schrödinger operators have been used to study vibration theory and the Colin de Verdière parameter. The inverse eigenvalue problem for discrete Schrödinger operators of a graph aims to characterize the possible spectra among discrete Schrödinger operators of a …

Ricci Curvature of Strong Product Graphs
Guiqiang Mou
https://arxiv.org/abs/2506.13269 https://arxiv.org/pdf/2506.13269

Ricci Curvature of Strong Product Graphs
We establish for the first time the explicit curvature formulas for the horizontal and vertical edges of the strong product of two regular graphs. We complement this result with showing that there does not exist a nice formula for the curvatures of diagonal edges, except for a special case in terms of curvatures of the factors. This gives the curvature formulas for all edges of the product of a complete graph and a regular graph. We also present an accessible and simpler proof of the curvature …

Emergent Viscous Hydrodynamics From a Single Quantum Particle
Zhi-Li Zhou, Mauricio Hippert, Nicki Mullins, Jorge Noronha
https://arxiv.org/abs/2506.06618 …

Emergent Viscous Hydrodynamics From a Single Quantum Particle
We investigate an explicit example of how spatial decoherence can lead to hydrodynamic behavior in the late-time, long-wavelength regime of open quantum systems. We focus on the case of a single non-relativistic quantum particle linearly coupled to a thermal bath of noninteracting harmonic oscillators at temperature $T$, a la Caldeira and Leggett. Taking advantage of decoherence in the position representation, we expand the reduced density matrix in powers of the off-diagonal spatial components…

Electron-magnon coupling at the interface of a "twin-twisted" antiferromagnet
Yue Sun, Fanhao Meng, Sijia Ke, Kun Xu, Hongrui Zhang, Aljoscha Soll, Zden\v{e}k Sofer, Arun Majumdar, Ramamoorthy Ramesh, Jeffrey B. Neaton, Jie Yao, Joseph Orenstein
https://arxiv.org/abs/2506.10080…

Electron-magnon coupling at the interface of a "twin-twisted" antiferromagnet
We identify a "twin-twist" angle in orthorhombic two-dimensional magnets that maximizes interlayer orbital overlap and enables strong interfacial coupling. Focusing on the van der Waals antiferromagnet CrSBr, we show that this twist angle, near 72 deg, aligns diagonal lattice vectors across the layers, enhancing the interlayer hopping that is spin-forbidden in pristine systems and orbital-forbidden in 90-deg-twisted samples. The enhanced hopping modifies the electronic structure and activates a…

Slimmer Geminals For Accurate F12 Electronic Structure Models
Samuel R. Powell, Edward F. Valeev
https://arxiv.org/abs/2506.10780 https://

Slimmer Geminals For Accurate F12 Electronic Structure Models
The Slater-type F12 geminal lengthscales originally tuned for the second-order Møller-Plesset F12 method are too large for higher-order F12 methods formulated using the SP (diagonal fixed-coefficient spin-adapted) F12 ansatz. The new geminal parameters reported herein reduce the basis set incompleteness errors (BSIE) of absolute coupled-cluster singles and doubles F12 correlation energies by a significant - and increasing with the cardinal number of the basis - margin. The effect of geminal re…

Kinetic magnetism in the crossover between the square and triangular lattice Fermi-Hubbard models
Darren Pereira, Erich J. Mueller
https://arxiv.org/abs/2506.15669

Kinetic magnetism in the crossover between the square and triangular lattice Fermi-Hubbard models
We calculate the spin correlations that result from the motion of a single dopant in the hard-core Fermi-Hubbard model, as the geometry evolves from a square to a triangular lattice. In particular, we consider the square lattice with an additional hopping along one diagonal, whose strength is continuously varied. We use a high-temperature expansion which expresses the partition function as a sum over closed paths taken by the dopant. We sample thousands of diagrams in the space of closed paths …

The Ramsey number of the 4-cycle versus a book graph
Chunyang Dou, Tianyu Li, Qizhong Lin, Xing Peng
https://arxiv.org/abs/2506.10477 https://

The Ramsey number of the 4-cycle versus a book graph
Given positive integers $n$ and $k$, the book graph $B_n^{(k)}$ consists of $n$ copies of $K_{k+1}$ sharing a common $K_k$. The book graph is a common generalization of a star and a clique, which can be seen by taking $k=1$ and $n=1$ respectively. In addition, the Ramsey number of a book graph is closely related to the diagonal Ramsey number. Thus the study of extremal problems related to the book graph is of substantial significance. In this paper, we aim to investigate the Ramsey number $r(C_…

Efficient multigrid solvers for mixed-degree local discontinuous Galerkin multiphase Stokes problems
Robert I. Saye
https://arxiv.org/abs/2506.09933 https:…

Efficient multigrid solvers for mixed-degree local discontinuous Galerkin multiphase Stokes problems
We design and investigate efficient multigrid solvers for multiphase Stokes problems discretised via mixed-degree local discontinuous Galerkin methods. Using the template of a standard multigrid V-cycle, we develop a smoother analogous to element-wise block Gauss-Seidel, except the diagonal block inverses are replaced with an approximation that balances the smoothing of the velocity and pressure variables, factoring in the unequal scaling of the various Stokes system operators, and optimised vi…

This https://arxiv.org/abs/2412.11528 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Water Cells in Compositions of 1s and 2s
Mansour and Shattuck introduced the notion of water cells for integer compositions in 2018. We focus on compositions with parts restricted to 1 and 2 and consider the array of counts for such compositions of $n$ with $k$ water cells, establishing generating functions for the columns and diagonal sums, recurrences within the array in the spirit of Pascal's lemma, and connections to other restricted compositions. Most of our proofs are combinatorial, but we also make connections to Riordan arrays.