Tootfinder

Sectional Curvature, Isotropic Curvature, and Yau's Pinching Problem
Xiaolong Li
https://arxiv.org/abs/2508.21661 https://arxiv.org/pdf/2508.21661

Sectional Curvature, Isotropic Curvature, and Yau's Pinching Problem
We prove that if a closed Riemannian manifold $(M^n,g)$ has finite fundamental group and satisfies the curvature condition \begin{equation*} R_{1313} +R_{1414} +R_{2323} + R_{2424} > \tfrac{1}{2}\left(R_{1212} + R_{3434}\right) \end{equation*} for all orthonormal four-frame $\{e_1, e_2, e_3, e_4\} \subset T_pM$, then $M$ is homeomorphic to a spherical space form. This generalizes the famous sphere theorem under the stronger condition of $\frac{1}{4}$-pinched sectional curvature. As an applica…

Med-R$^3$: Enhancing Medical Retrieval-Augmented Reasoning of LLMs via Progressive Reinforcement Learning
Keer Lu, Zheng Liang, Youquan Li, Jiejun Tan, Da Pan, Shusen Zhang, Guosheng Dong, Huang Leng
https://arxiv.org/abs/2507.23541

Med-R$^3$: Enhancing Medical Retrieval-Augmented Reasoning of LLMs via Progressive Reinforcement Learning
In medical scenarios, effectively retrieving external knowledge and leveraging it for rigorous logical reasoning is of significant importance. Despite their potential, existing work has predominantly focused on enhancing either retrieval or reasoning capabilities of the models in isolation, with little attention given to their joint optimization, which leads to limited coordination between the two processes. Additionally, current methods rely heavily on supervised fine-tuning (SFT), which can c…

On jet schemes of determinantal varieties
Yifan Chen, Huaiqing Zuo
https://arxiv.org/abs/2506.22898 https://arxiv.org/pdf/2506.22898

On jet schemes of determinantal varieties
Determinantal varieties are important objects of study in algebraic geometry. In this paper, we will investigate them using the jet scheme approach. We have found a new connection for the Hilbert series between a determinantal variety and its jet schemes. We denote the $k$-th order jet scheme of the determinantal variety defined by $r$-minors in an $m \times n$ matrix as $\mathscr{L}^{m,n}_{r,k}$. For the special case where $m$, $n$, and $r$ are equal, and $m$ and $r$ are 3 while $k$ is 1, we e…

5-regular graphs and the 3-dimensional rigidity matroid
Rebecca Monks, Anthony Nixon
https://arxiv.org/abs/2506.22214 https://arxiv.o…

5-regular graphs and the 3-dimensional rigidity matroid
A bar-joint framework $(G,p)$ in Euclidean $d$-space is rigid if the only edge-length-preserving continuous motions arise from isometries of $\mathbb{R}^d$. In the generic case, rigidity is determined by the generic $d$-dimensional rigidity matroid of $G$. The combinatorial nature of this matroid is well understood when $d=1,2$ but open when $d\geq 3$. Jackson and Jordán 2005 characterised independence in this matroid for connected graphs with minimum degree at most $d+1$ and maximum degree at…

Constraining the Stellar-to-Halo Mass Relation with Galaxy Clustering and Weak Lensing from DES Year 3 Data
G. Zacharegkas, C. Chang, J. Prat, W. Hartley, S. Mucesh, A. Alarcon, O. Alves, A. Amon, K. Bechtol, M. R. Becker, G. Bernstein, J. Blazek, A. Campos, A. Carnero Rosell, M. Carrasco Kind, R. Cawthon, R. Chen, A. Choi, J. Cordero, C. Davis, J. Derose, H. Diehl, S. Dodelson, C. Doux, A. Drlica-Wagner, K. Eckert, T. F. Eifler, J. Elvin-Poole, S. Everett, X. Fang, A. Ferte, M. Gatti,…

Constraining the Stellar-to-Halo Mass Relation with Galaxy Clustering and Weak Lensing from DES Year 3 Data
We develop a framework to study the relation between the stellar mass of a galaxy and the total mass of its host dark matter halo using galaxy clustering and galaxy-galaxy lensing measurements. We model a wide range of scales, roughly from $\sim 100 \; {\rm kpc}$ to $\sim 100 \; {\rm Mpc}$, using a theoretical framework based on the Halo Occupation Distribution and data from Year 3 of the Dark Energy Survey (DES) dataset. The new advances of this work include: 1) the generation and validation o…

🇺🇦 #NowPlaying on KEXP's #Early
David Bowie:
🎵 Rebel Rebel
#DavidBowie
https://reworklab.bandcamp.com/track/rebel-rebel-remix-david-bowie-3
https://open.spotify.com/track/3bdEtobvgxJNoV8kiNGObK

NewsReX: A More Efficient Approach to News Recommendation with Keras 3 and JAX
Igor L. R. Azevedo, Toyotaro Suzumura, Yuichiro Yasui
https://arxiv.org/abs/2508.21572 https://

NewsReX: A More Efficient Approach to News Recommendation with Keras 3 and JAX
Reproducing and comparing results in news recommendation research has become increasingly difficult. This is due to a fragmented ecosystem of diverse codebases, varied configurations, and mainly due to resource-intensive models. We introduce NewsReX, an open-source library designed to streamline this process. Our key contribution is a modern implementation built on Keras 3 and JAX, which provides an increase in computational efficiency. Experiments show that NewsReX is faster than current imple…

Four-dimensional spectrum generating algebra for the superstring
Renann Lipinski Jusinskas, Aravindhan Srinivasan
https://arxiv.org/abs/2507.22973 https://…

Four-dimensional spectrum generating algebra for the superstring
We derive the spectrum generating algebra for the hybrid string with manifest $\mathcal{N}=1$ super Poincaré symmetry in $\mathbb{R}^{3,1}\times\mathbb{R}^{6}$. Our DDF operators establish a one-to-one correspondence with the conventional superstring spectrum, while making its four-dimensional structure manifest. We also discuss part of the antifield spectrum, and introduce a simple realization of the supersymmetry charges involving the $\mathbb{R}^{6}$ directions. As an application, we algebr…

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…

Cosmology from Planck CMB Lensing and DESI DR1 Quasar Tomography
R. de Belsunce, A. Krolewski, S. Chiarenza, E. Chaussidon, S. Ferraro, B. Hadzhiyska, C. Ravoux, N. Sailer, G. Farren, A. Tamone, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, T. Claybaugh, A. Cuceu, A. de la Macorra, J. Della Costa, Biprateep Dey, P. Doel, A. Font-Ribera, J. E. Forero-Romero, E. Gazta\~naga, S. Gontcho A Gontcho, G. Gutierrez, J. Guy, H. K. Herrera-Alcantar, K. Honscheid, M. Ishak, R. Joyce, S. Juneau, R.…

Cosmology from Planck CMB Lensing and DESI DR1 Quasar Tomography
We present a measurement of the amplitude of matter fluctuations over the redshift range 0.8 <= z <= 3.5 from the cross correlation of over 1.2 million spectroscopic quasars selected by the Dark Energy Spectroscopic Instrument (DESI) across 7,200 deg$^2$ (approx 170 quasars/deg$^2$) and Planck PR4 (NPIPE) cosmic microwave background (CMB) lensing maps. We perform a tomographic measurement in three bins centered at effective redshifts z=1.44, 2.27 and 2.75, which have ample overlap with the CMB …

Terahertz spin-orbit torque as a drive of spin dynamics in insulating antiferromagnet Cr$_{2}$O$_{3}$
R. M. Dubrovin, Z. V. Gareeva, A. V. Kimel, A. K. Zvezdin
https://arxiv.org/abs/2507.23367

Terahertz spin-orbit torque as a drive of spin dynamics in insulating antiferromagnet Cr$_{2}$O$_{3}$
Contrary to conventional wisdom that spin dynamics induced by current are exclusive to metallic magnets, we theoretically predict that such phenomena can also be realized in magnetic insulators, specifically in the magnetoelectric antiferromagnet $\mathrm{Cr}_{2}\mathrm{O}_{3}$. We reveal that the displacement current driven by the THz electric field is able to generate a N{é}el spin-orbit torque in this insulating system. By introducing an alternative electric dipole order parameter arising f…

Pulsatile Flows for Simplified Smart Fluids with Variable Power-Law: Analysis and Numerics
Luigi C. Berselli, Alex Kaltenbach
https://arxiv.org/abs/2507.22449 https://

Pulsatile Flows for Simplified Smart Fluids with Variable Power-Law: Analysis and Numerics
We study the fully-developed, time-periodic motion of a shear-dependent non-Newtonian fluid with variable exponent rheology through an infinite pipe $Ω:= \mathbb{R}\times Σ\subseteq \mathbb{R}^d$, $d\in \{2,3\}$, of arbitrary cross-section $Σ\subseteq \mathbb{R}^{d-1}$. The focus is on a generalized $p(\cdot)$-fluid model, where the power-law index is position-dependent (with respect to $Σ$), $\textit{i.e.}$, a function $p\colon Σ\to (1,+\infty)$. We prove the existence of time-periodic so…

Scale-resolved turbulent Prandtl number for Rayleigh-B\'{e}nard convection at $\boldsymbol{Pr =10^{-3}}$
Shashwat Bhattacharya, Dmitry Krasnov, Ambrish Pandey, Toshiyuki Gotoh, J\"org Schumacher
https://arxiv.org/abs/2506.22110

Scale-resolved turbulent Prandtl number for Rayleigh-Bénard convection at $\boldsymbol{Pr =10^{-3}}$
We present a framework to calculate the scale-resolved turbulent Prandtl number $Pr_t$ for the well-mixed and highly inertial bulk of a turbulent Rayleigh-Bénard mesoscale convection layer at a molecular Prandtl number $Pr=10^{-3}$. It builds on Kolmogorov's refined similarity hypothesis of homogeneous isotropic fluid and passive scalar turbulence, based on log-normally distributed amplitudes of kinetic energy and scalar dissipation rates that are coarse-grained over variable scales $r$ in the…

Тъжното е, че и аз не бих посмял да го взема на сляпо, но тук поне знаете, че обявата е моя:
Десктоп компютър i5 13400F GTX 1650 DDGR6 DDR4 3200 CL-16 • OLX.bg
https://www.olx.bg/d/ad/desktop-kompyutar-i5-13400f-gtx-1650…

OLX.bg - безплатни обяви
650 лв.: Частите на компютъра: CPU: Intel Core i5 13400F CPU COOLER: DeepCool AK400 (R-AK400-BKNNMN-G-1) GPU: ZOTAC GAMING GeForce GTX 1650 GDDR6 MB: Gigabyte H610M H DDR4 (rev. 1.1/1.3) RAM: 2x16GB DDR4 320...

This is the third full build iteration of my miniature #QRP unun supporting both EFHW and "random wire" antennas. At this point, it is still fiddly to build, but I'd expect an experienced #HamRadio DIY / homebrew enthusiast to find the build not terribly difficult.
There's nothing…

Higher path groupoids and the holonomy of formal power series connections
Matthew Cellot
https://arxiv.org/abs/2506.23880 https://arx…

Higher path groupoids and the holonomy of formal power series connections
Building on ideas of Kohno, we develop a framework for the construction of higher holonomy functors via the transport of formal power series connections. Using these techniques, we obtain functors from the path groupoid, the path 2-groupoid, and the path 3-groupoid of a manifold. As an application, we construct a Gray functor from the path 3-groupoid of the configuration space of $m$ points in $\mathbb{R}^n$ for $n\geqslant 4$.

One-Loop Calculations in Effective Field Theories with GoSam-3.0
Jens Braun, Benjamin Campillo Aveleira, Gudrun Heinrich, Marius H\"ofer, Stephen P. Jones, Matthias Kerner, Jannis Lang, Vitaly Magerya
https://arxiv.org/abs/2507.23549

One-Loop Calculations in Effective Field Theories with GoSam-3.0
We present a major update of the one-loop generator GoSam, containing performance improvements as well as new features, in particular functionalities that facilitate calculations beyond the Standard Model in Effective Field Theory frameworks.

Twisted embeddings of tori have small extrinsic systole
Sahana Vasudevan
https://arxiv.org/abs/2507.23766 https://arxiv.org/pdf/2507.23766

Twisted embeddings of tori have small extrinsic systole
We prove a type of systolic inequality for embeddings of $T^2$ in $\mathbb{R}^3$. In particular, a highly twisted $T^2$ embedded in $\mathbb{R}^3$ must contain a non-contractible loop of small $\mathbb{R}^3$-diameter.

High brightness multi-MeV photon source driven by a petawatt-scale laser wakefield accelerator
E. Gerstmayr, B. Kettle, M. J. V. Streeter, L. Tudor, O. J. Finlay, L. E. Bradley, R. Fitzgarrald, T. Foster, P. Gellersen, A. E. Gunn, O. Lawrence, P. P. Rajeev, B. K. Russell, D. R. Symes, C. D. Murphy, A. G. R. Thomas, C. P. Ridgers, G. Sarri, S. P. D. Mangles

High brightness multi-MeV photon source driven by a petawatt-scale laser wakefield accelerator
We present an experimental demonstration of a bright multi-MeV gamma source driven by a petawatt laser. The source generates on average $(1.2\pm0.6)\times10^9$ photons above 1 MeV per pulse, exceeding those of previous all-optical sources by a hundred times, and reached a peak spectral brightness of $(3.9 \pm 1.5)\times 10^{22}$ photons/mm$^2$/mrad$^2$/s/0.1%BW at $ε_γ\approx11$ MeV. The source was produced by inverse Compton scattering of a laser wakefield accelerated GeV electron beam and i…

Magnetic dilution in the triangular lattice antiferromagnet NaYb$_{1-x}$Lu$_{x}$O$_2$
Steven J. Gomez Alvarado, Brenden R. Ortiz, Soren Bear, Benito A. Gonzalez, Andrea N. Capa Salinas, Adam Berlie, Michael J. Graf, Stephen D. Wilson
https://arxiv.org/abs/2506.22613

Magnetic dilution in the triangular lattice antiferromagnet NaYb$_{1-x}$Lu$_{x}$O$_2$
The delafossite-like compound NaYbO$_2$ hosts a triangular lattice of Yb$^{3+}$ moments and is a promising candidate for realizing a quantum spin liquid state. Here we leverage the substitution of nonmagnetic Lu$^{3+}$ onto the Yb$^{3+}$ sites to track the evolution of the quantum disordered ground state with increasing magnetic disorder in NaYb$_{1-x}$Lu$_x$O$_2$. Low temperature $μ$SR measurements preclude conventional spin freezing and magnetic inhomogeneity, and instead resolve resilient, …

Local Wellposedness and Global Weak Solutions of the Pauli-Darwin/Poisswell Equations
Pierre Germain, Norbert J. Mauser, Jakob M\"oller
https://arxiv.org/abs/2506.22333

Local Wellposedness and Global Weak Solutions of the Pauli-Darwin/Poisswell Equations
We construct local (in time) strong solutions in $H^s(\mathbb{R}^3)$, $s>3/2$ and global weak solutions with finite energy for the Pauli-Darwin equation and the Pauli-Poisswell equation. These are the first rigorous results on these two models, which couple a 2-spinor with an electromagnetic field. The proofs rely on energy estimates for the strong solutions and compactness with an appropriate regularization for the weak solutions.

The cycloid as brachistochrone: A one-page proof, from first principles, without calculus
Gavin R. Putland
https://arxiv.org/abs/2507.22548 https://arxiv.o…

The cycloid as brachistochrone: A one-page proof, from first principles, without calculus
Johann Bernoulli's optical solution of the brachistochrone problem is rebuilt on underlying (non-optical) principles. An "optical interpretation" is given afterwards.

Diffusion in the Inverted Triangular Soft Lorentz Gas
Esko Toivonen, Aleksi Majaniemi, Rainer Klages, Esa R\"as\"anen
https://arxiv.org/abs/2506.23792

Diffusion in the Inverted Triangular Soft Lorentz Gas
We investigate diffusion in a two-dimensional inverted soft Lorentz gas, where attractive Fermi-type potential wells are arranged in a triangular lattice. This configuration contrasts with earlier studies of soft Lorentz gases involving repulsive scatterers. By systematically varying the gap width and softness of the potential, we explore a rich landscape of diffusive behaviors. We present numerical simulations of the mean squared displacement and compute diffusion coefficients, identifying ton…

The Internet has ruined headlines.
It used to be that headlines had names. Now they carefully DO NOT on purpose, because using a generic role description is more likely to get a click-through to see who it is. The problem has bled into ledes as well, which are no longer synopses of stories but rather secondary teasers. You may be a few paragraphs into a story before you can get the information that every Journo 101 teacher would have demanded be in the first 3 lines.

Omega Estimate for the Lattice Point Discrepancy of a Body of Revolution Using The Resonance Method
Nilmoni Karak
https://arxiv.org/abs/2506.22590 https://…

Omega Estimate for the Lattice Point Discrepancy of a Body of Revolution Using The Resonance Method
Using a recent method developed by Mahatab, we obtain an improved $Ω$-bound for the error term arising in lattice counting problem of bodies of revolution in $\mathbb R^3$ around a coordinate axis and having smooth boundary with bounded nonzero curvature. This strengthens an earlier result by Kühleitner and Nowak.

High-Precision Quantum Dynamics of He$_2$ b $^3\Pi_\mathrm{g}$-c $^3\Sigma_\mathrm{g}^ $ including Non-adiabatic, Relativistic and QED Corrections and Couplings
Bal\'azs R\'acsai, P\'eter Jeszenszki, \'Ad\'am Marg\'ocsy, Edit M\'atyus
https://arxiv.org/abs/2506.23879

High-Precision Quantum Dynamics of He$_2$ b $^3Π_\mathrm{g}$-c $^3Σ_\mathrm{g}^+$ including Non-adiabatic, Relativistic and QED Corrections and Couplings
Relativistic, quantum electrodynamics, as well as non-adiabatic corrections and couplings, are computed for the b $^3Π_\mathrm{g}$ and c $^3Σ_\mathrm{g}^+$ electronic states of the helium dimer. The underlying Born-Oppenheimer potential energy curves are converged to 1 ppm ($1:10^6$) relative precision using a variational explicitly correlated Gaussian approach. % The quantum nuclear motion is computed over the b $^3Π_\mathrm{g}$-c $^3Σ_\mathrm{g}^+$ (and B $^1Π_\mathrm{g}$-C $^1Σ_\mathrm…

At its core, #CCSignals is an attempt by Creative Commons, a Silicon Valley-based organisation, to legitimise the AI grifts of its donors – Google, Microsoft, and Meta (Zuckerberg).
Creative Commons was always a thinly-veiled attempt at enabling Big Tech data farmers to get more data (that’s why the whole “open data” realm is so well funded/popular – open as in “open for business” not fre…

Separating covering numbers and separating uniformity numbers of Hausdorff measures need large continuum
Tatsuya Goto
https://arxiv.org/abs/2506.22592 http…

Separating covering numbers and separating uniformity numbers of Hausdorff measures need large continuum
We show that if $\mathfrak{c} = \aleph_2$ then all covering numbers of Hausdorff measures $\operatorname{cov}(\mathcal{N}^s(\mathbb{R}^d))$ ($0 < s < d, d \in ω$) are equal and all uniformity numbers $\operatorname{non}(\mathcal{N}^s(\mathbb{R}^d))$ ($0 < s < d, d \in ω$) are equal. This is a partial answer to Problem 5.3 and 5.4 of [4].

Magnetic levitation by rotation described by a new type of Levitron
A. Doff, R. M. Szmoski
https://arxiv.org/abs/2506.23268 https://a…

Magnetic levitation by rotation described by a new type of Levitron
Recently, the authors[1][2] have highlighted a novel magnetic levitation phenomenon utilizing two magnetically equivalent permanent neodymium magnets. We propose that this system represents an analog of a scaled-up version of a Levitron[3][4]. The main distinction between these systems lies in the fact that the radius $m_/μ_f$ now is a function of the lateral displacement $δ_R$, and the adjustment required for magnetic trapping is not determined by the rotation speed of the float. Using an ef…

Rager:
https://github.com/w3c/wcag/issues/4460
Part of my frustration with this 1.2.5 discussion (no gaps means auto-pass a lack of AD) was the earlier assertion that videos always have gaps (ha ha, no:

1.2.3 / 1.2.5 Audio description - No pause · Issue #4460 · w3c/wcag
If a video has no pause in dialogue to provide audio descriptions, is the video considered to meet SC 1.2.3 / 1.2.5 Audio description? Even if the content author want to provide audio descriptions ...

Interplay of magnetic ordering and charge transport in a distorted ScAl$_3$C$_3$-type GdZn$_3$As$_3$
Zhiyu Zhou, Xiyu Chen, Jia-Yi Lu, Junchao Zhang, Xiong Luo, Guang-Han Cao, Shuai Dong, Zhi-Cheng Wang
https://arxiv.org/abs/2506.20454

Interplay of magnetic ordering and charge transport in a distorted ScAl$_3$C$_3$-type GdZn$_3$As$_3$
We present the synthesis and characterization of GdZn$_3$As$_3$, a previously unreported variant of the $RM_3X_3$ family ($R$ = lanthanides; $M$ = Zn, Cd; $X$ = P, As), prepared in both single-crystal and polycrystalline forms. Unlike other $RM_3X_3$ compounds that crystallize in undistorted hexagonal structures, GdZn$_3$As$_3$ adopts a distorted ScAl$_3$C$_3$-type orthorhombic structure with $Cmcm$ space group. Magnetic measurements demonstrate that GdZn$_3$As$_3$ undergoes a ferromagnetic tra…

Replaced article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[3/5]:
- Low-Confidence Gold: Refining Low-Confidence Samples for Efficient Instruction Tuning
Hongyi Cai, Jie Li, Mohammad Mahdinur Rahman, Wenzhen Dong

Universal Effective Charges in the $sd$ and $fp$ Shells
T. H. Ogunbeku, J. M. Allmond, T. J. Gray, W. -J. Ong, B. A. Brown, A. Gargano, R. Grzywacz, J. D. Holt, A. O. Macchiavelli, T. Miyagi, S. Neupane, B. C. Rasco, H. Schatz, B. M. Sherrill, O. B. Tarasov, H. Arora, A. D. Ayangeakaa, H. C. Berg, J. M. Berkman, D. L. Bleuel, K. Bosmpotinis, M. P. Carpenter, G. Cerizza, A. Chester, J. M. Christie, I. Cox, H. L. Crawford, B. P. Crider, J. Davis, A. A. Doetsch, J. G. Duarte, A. Estrade, …

Universal Effective Charges in the $sd$ and $fp$ Shells
The 247-keV state in $^{54}$Sc, populated in the $β$ decay of $^{54}$Ca, is reported here as a nanosecond isomer with a half-life of 26.0(22) ns. The state is interpreted as the $1^+$ member of the $πf_{7/2}\otimesνf_{5/2}$ spin-coupled multiplet, which decays to the $3^+,πf_{7/2} \otimes νp_{1/2}$ ground state. The new half-life corresponds to a pure $E2$ transition with a strength of 1.93(16) W.u., providing the most precise, unambiguous $B(E2)$ value in the neutron-rich $fp$ region to d…

Unique Surgery Descriptions along Knots
Marc Kegel, Misha Schmalian
https://arxiv.org/abs/2508.18521 https://arxiv.org/pdf/2508.18521

Unique Surgery Descriptions along Knots
We prove that for any non-trivial knot K, infinitely many r-surgeries K(r) along K have a unique surgery description along a knot. Moreover, we show that for any hyperbolic L-space knot K and infinitely many integer slopes n, the manifold K(n) has a unique surgery description. Here we say a 3-manifold M has a unique surgery description along a knot in S^3 if there is a unique pair (K,r) of a knot K and a slope r such that M is orientation-preservingly diffeomorphic to K(r). This generalises the…

Die Unterzeichner im Wortlaut lt Kurier:
"1. René Amry, ehem. Botschafter im Libanon
2. Dorothea Auer, Botschafterin in Zypern und Libyen i.R.
3. Moritz Ehrmann, ehem. Leiter des Austrian Center for Peace Schlaining
4. Johannes Eigner, Botschafter in Serbien und Russland i.R.
5. Benita Ferrero-Waldner, EU Kommissarin für Außenbeziehungen und Außenministerin i.R.
6. Irene Giner-Reichl, Botschafterin in China und Brasilien i.R.
7. Barbara Grosse, Botschafterin in Libyen
8. Heidemaria Gürer, Botschafterin u.a. in Türkiye und den Niederlanden i.R.
9. Thomas Hajnoczi, Botschafter und Vertreter bei der UNO in Genf i.R.
10. Ulrike Hartmann, Botschafterin und Sonderbeauftragte für den Westbalkan
11. Valentin Inzko, Botschafter und Hoher Repräsentant für Bosnien und Herzegowina i.R.
12. Peter Jankowitsch, Außenminister und Botschafter u.a. bei der UNO in New York i.R.
13. Gerald Kriechbaum, Botschafter in den Vereinigten Arabischen Emiraten i.R.
14. Rudolf Lennkh, Botschafter u.a. in Mexiko und beim Europarat i.R.
15. Eva Nowotny, Botschafterin in den USA, Frankreich und Großbritannien i.R.
16. Thomas Nowotny, Generalkonsul in New York und Konsulent bei der OECD i.R.
17. Wolfgang Petritsch, Botschafter und Hoher Repräsentant für Bosnien und Herzegowina i.R.
18. Christian Prosl, Botschafter in den USA und in Deutschland i.R.
19. Susanne Schmid, Leiterin des Büros für Konsularbeglaubigungen
20. Hans-Dietmar Schweisgut, Botschafter in China, Japan und bei der EU i.R.
21. Christian Strohal, Botschafter u.a. bei der UNO in Genf und Leiter des OSZE-Menschenrechtsbüros i.R.
22. Robert Thum, Regierungsrat und Amtsdirektor i.R.
23. Roberto Thym, stv. Abteilungsleiter des Unternehmensservice
24. Wolfgang Waldner, Staatssekretär und Botschafter in den USA i.R.
25. Isabella Wlcek, Fachoberinspektorin i.R.
26. Marieke Zimburg, Botschafterin in Jordanien"
https://kurier.at/politik/ausland/diplomaten-sanktionen-israel-nahost-gaza/403078151

LowKeyEMG: Electromyographic typing with a reduced keyset
Johannes Y. Lee, Derek Xiao, Shreyas Kaasyap, Nima R. Hadidi, John L. Zhou, Jacob Cunningham, Rakshith R. Gore, Deniz O. Eren, Jonathan C. Kao
https://arxiv.org/abs/2507.19736

LowKeyEMG: Electromyographic typing with a reduced keyset
We introduce LowKeyEMG, a real-time human-computer interface that enables efficient text entry using only 7 gesture classes decoded from surface electromyography (sEMG). Prior work has attempted full-alphabet decoding from sEMG, but decoding large character sets remains unreliable, especially for individuals with motor impairments. Instead, LowKeyEMG reduces the English alphabet to 4 gesture keys, with 3 more for space and system interaction, to reliably translate simple one-handed gestures int…

Weekend #Plankton Factoid 🦠🦐
More news about the potential collapse of an ocean current, the Atlantic Meridional Overturning Circulation (AMOC) which transfers heat from the tropics to northern Atlantic, giving Europe a much milder climate, controls plankton productivity, and importantly also generates deep ocean circulation by sinking cold dense water. Winter

Differentiation of Site-Specific Symmetry Breaking Orders in Y$_{1-x}$Pr$_x$Ba$_2$Cu$_3$O$_{6 y}$
L. Martinelli, S. R\"udiger, I. Bialo, J. Oppliger, F. Igoa Saldana, M. v. Zimmermann, E. Weschke, R. Arpaia, J. Chang
https://arxiv.org/abs/2507.20640

Differentiation of Site-Specific Symmetry Breaking Orders in Y$_{1-x}$Pr$_x$Ba$_2$Cu$_3$O$_{6+y}$
Solid matter is classified through symmetry of ordering phenomena. Experimentally, this approach is straightforward, except when distinct orderings occur with identical or almost identical symmetry breaking. Here we show that the cuprate system Y$_{1-x}$Pr$_x$Ba$_2$Cu$_3$O$_{6+y}$ hosts two distinct orderings with almost identical translational symmetry breaking. Only when applying site-sensitive resonant elastic x-ray scattering (REXS), charge ordering can be conclusively differentiated from a…

Global regularity and incompressible limit of 2D compressible Navier-Stokes equations with large bulk viscosity
Shengquan Liu, Jianwen Zhang
https://arxiv.org/abs/2506.22235

Global regularity and incompressible limit of 2D compressible Navier-Stokes equations with large bulk viscosity
In this paper, we study the global regularity of large solutions with vacuum to the two-dimensional compressible Navier-Stokes equations on $\mathbb{T}^{2}=\mathbb{R}^{2}/\mathbb{Z}^{2}$, when the volume (bulk) viscosity coefficient $ν$ is sufficiently large. It firstly fixes a flaw in [10, Proposition 3.3], which concerns the $ν$-independent global $t$-weighted estimates of the solutions. Amending the proof requires non-trivially mathematical analysis. As a by-product, the incompressible lim…

Spectroscopic Analysis of Pictor II: a very low metallicity ultra-faint dwarf galaxy bound to the Large Magellanic Cloud
A. B. Pace (University of Virginia), T. S. Li, A. P. Ji, J. D. Simon, W. Cerny, A. M. Senkevich, A. Drlica-Wagner, K. Bechtol, C. Y. Tan, A. Chiti, D. Erkal, C. E. Mart\'inez-V\'azquez, P. S. Ferguson, R. G. Kron, K R. Atzberger, A. Chaturvedi, J. A. Frieman, N. Kallivayalil, G. Limberg, G. E. Medina, V. M. Placco, A. H. Riley, D. J. Sand, G. S. Stringfellow,…

Spectroscopic Analysis of Pictor II: a very low metallicity ultra-faint dwarf galaxy bound to the Large Magellanic Cloud
We present Magellan/IMACS and Magellan/MIKE spectroscopy of the ultra-faint dwarf (UFD) galaxy Pictor~II (Pic~II) that is located only 12 kpc from the Large Magellanic Cloud (LMC). From the IMACS spectroscopy, we identify 13 member stars and measure a mean heliocentric velocity of $326.9\pm1.1~{\rm km~s^{-1}}$, a velocity dispersion of $3.5_{-0.9}^{+1.1}~{\rm km~s^{-1}}$, a mean metallicity of $\overline{\rm [Fe/H]}=-2.99\pm0.06$, and an upper limit on the metallicity dispersion of $σ_{\rm [Fe…

VLT observations of interstellar comet 3I/ATLAS II. From quiescence to glow: Dramatic rise of Ni I emission and incipient CN outgassing at large heliocentric distances
Rohan Rahatgaonkar, Juan Pablo Carvajal, Thomas H. Puzia, Baltasar Luco, Emmanuel Jehin, Damien Hutsem\'ekers, Cyrielle Opitom, Jean Manfroid, Micha\"el Marsset, Bin Yang, Laura Buchanan, Wesley C. Fraser, John Forbes, Michele Bannister, Dennis Bodewits, Bryce T. Bolin, Matthew Belyakov, Matthew M. Knight, Colin…

VLT observations of interstellar comet 3I/ATLAS II. From quiescence to glow: Dramatic rise of Ni I emission and incipient CN outgassing at large heliocentric distances
We report VLT spectroscopy of the interstellar comet 3I/ATLAS (C/2025 N1) from $r_{\rm h}\!\simeq\!4.4$ to $2.85$ au using X-shooter (300-550 nm, $R\!\simeq\!3000$) and UVES (optical, $R\!\simeq\!35k-80k$). The coma is dust-dominated with a fairly constant red optical continuum slope ($\sim$21-22\%/1000Å). At $r_{\rm h}\!\simeq\!3.17$ au we derive $3σ$ limits of $Q({\rm OH})<7.76\times10^{23}\ {\rm s^{-1}}$, but find no indications for [O I], C$_2$, C$_3$ or NH$_2$. We report detection of CN …

On a minimal free resolution of the residue field over a local ring of codepth 3 of class T
Van C. Nguyen, Oana Veliche
https://arxiv.org/abs/2506.21505 ht…

On a minimal free resolution of the residue field over a local ring of codepth 3 of class T
Let $R$ be any local ring with residue field $k$, and $A$ the homology of the Koszul complex on a minimal set of generators of the maximal ideal of $R$. In this paper, we show that a minimal free resolution of $k$ over $R$ can be obtained from a graded minimal free resolution of $k$ over $A$. More precisely, this is done by the iterated mapping cone construction, introduced by the authors in a previous work, using specific choices of ingredients. As applications, using this general perspective,…

Amorphous Solid Model of Vectorial Hopfield Neural Networks
F. Gallavotti, A. Zaccone
https://arxiv.org/abs/2507.22787 https://arxiv.org/pdf/2507.22787

Amorphous Solid Model of Vectorial Hopfield Neural Networks
We present a vectorial extension of the Hopfield associative memory model inspired by the theory of amorphous solids, where binary neural states are replaced by unit vectors $\mathbf{s}_i \in \mathbb{R}^3$ on the sphere $S^2$. The generalized Hebbian learning rule creates a block-structured weight matrix through outer products of stored pattern vectors, analogous to the Hessian matrix structure in amorphous solids. We demonstrate that this model exhibits quantifiable structural properties chara…

SVOM GRB 250314A at z $\simeq$ 7.3: an exploding star in the era of reionization
B. Cordier, J. Y. Wei, N. R. Tanvir, S. D. Vergani, D. B. Malesani, J. P. U. Fynbo, A. de Ugarte Postigo, A. Saccardi, F. Daigne, J. -L. Atteia, O. Godet, D. Gotz, Y. L. Qiu, S. Schanne, L. P. Xin, B. Zhang, S. N. Zhang, A. J. Nayana, L. Piro, B. Schneider, A. J. Levan, A. L. Thakur, Z. P. Zhu, G. Corcoran, N. A. Rakotondrainibe, V. D'Elia, D. Turpin, J. F. Agui Fernandez, M. A. Aloy, J. An, M. Bai, S.…

SVOM GRB 250314A at z $\simeq$ 7.3: an exploding star in the era of reionization
Most long Gamma-ray bursts originate from a rare type of massive stellar explosion. Their afterglows, while rapidly fading, can be initially extremely luminous at optical/near-infrared wavelengths, making them detectable at large cosmological distances. Here we report the detection and observations of GRB 250314A by the SVOM satellite and the subsequent follow-up campaign with the near-infrared afterglow discovery and the spectroscopic measurements of its redshift z $\simeq$ 7.3 . This burst ha…

A Common Origin of Asymmetric Self-interacting Dark Matter and Dirac Leptogenesis
Manoranjan Dutta, Nimmala Narendra
https://arxiv.org/abs/2506.22388 https…

A Common Origin of Asymmetric Self-interacting Dark Matter and Dirac Leptogenesis
Assuming dark matter to be asymmetric as well as self-interacting and neutrinos to be Dirac fermions, we propose a framework to address the observed baryon imbalance of the universe. We add three right-handed neutrinos $ν_{R_i},\,{i=1,2,3}$, one singlet fermion $χ$, a doublet fermion $ψ$, and heavy scalar doublets $η_i,\,{i=1,2}$ to the Standard Model. Both $χ$ and $ψ$ are fermions with non-zero charge under an extended $U(1)_{B-L} \times U(1)_D$ symmetry. Additionally, a $\mathcal{Z}_2$ …

Web 3.0 Requires Data Integrity
New integrity-focused standards are necessary to enable the trusted AI services of tomorrow.
🔐 https://cacm.acm.org/opinion/web-3-0-requires-data-integrity/

Infinitely many counterexamples to a conjecture of Lov\'asz
Aida Abiad, Frederik Garbe, Xavier Povill, Christoph Spiegel
https://arxiv.org/abs/2506.21286

Infinitely many counterexamples to a conjecture of Lovász
Motivated by the well-known conjecture of Ryser which relates maximum matchings to minimum vertex covers in $r$-partite $r$-uniform hypergraphs, Lovász formulated a stronger conjecture. It states that one can always reduce the matching number by removing $r-1$ vertices. This conjecture was very recently disproven for $r=3$ by Clow, Haxell, and Mohar using the line graph of a $3$-regular graph of order $102$. Building on this, we describe a simple infinite family of counterexamples based on gen…

H\"older continuous dissipative solutions of ideal MHD with nonzero helicity
Alberto Enciso, Javier Pe\~nafiel-Tom\'as, Daniel Peralta-Salas
https://arxiv.org/abs/2507.23749

Hölder continuous dissipative solutions of ideal MHD with nonzero helicity
We prove the existence of weak solutions to the 3D ideal MHD equations, of class $C^α$ with $α=10^{-8}$, for which the total energy and the cross helicity (i.e., the so-called Elsässer energies) are not conserved. The solutions do not possess any symmetry properties and the magnetic helicity, which is necessarily conserved for Hölder continuous solutions, is nonzero. The construction, which works both on the torus $\mathbb{T}^3$ and on $\mathbb{R}^3$ with compact spatial support, is based o…

Self-shrinkers with any number of ends in $\mathbb{R}^{3}$ by stacking $\mathbb{R}^{2}$
Guanhua Shao, Jiahua Zou
https://arxiv.org/abs/2507.18825 https://a…

Self-shrinkers with any number of ends in $\mathbb{R}^{3}$ by stacking $\mathbb{R}^{2}$
For each half-integer $J$ and large enough integer $m$ we construct by PDE gluing methods a self-shrinker $\breve{M}[J,m]$ with $2J+1$ ends and genus $2J(m-1)$. $\breve{M}[J,m]$ resembles the stacking of $2J+1$ levels of the plane $\mathbb{R}^2$ in $\mathbb{R}^3$ that have been connected by $2Jm$ catenoidal bridges with $m$ bridges connecting each pair of adjacent levels. It observes the symmetry of an $m$-gonal prism (when $J$ is a half integer) or an $m$-gonal antiprism (when $J$ is an intege…

The Legend of Vox Machina Staffel 4 kommt nächstes Jahr und eine finale Staffel 5 bereits bestellt
(Spoiler für Staffel 3, 4 und 5 im letzten Absatz bei EnWorld)
https://www.enworld.org/threads/critical-roles-the-legen…

Floer homotopy theory for monotone Lagrangians
Ciprian Mircea Bonciocat
https://arxiv.org/abs/2506.17431 https://arxiv.org/pdf/2506.1…

Floer homotopy theory for monotone Lagrangians
We circumvent one of the roadblocks in associating Floer homotopy types to monotone Lagrangians, namely the curvature phenomena occurring in high dimensions. Given $N \ge 3$ and $R$ a connective $\mathbb E_1$-ring spectrum, there is a notion of an $N$-truncated, $R$-oriented flow category, to which we associate a module prospectrum over the Postnikov truncation $τ_{\le N - 3}R$. This endows ordinary Floer cohomology with an action of the Steenrod algebra over $τ_{\le N-3}R$, and also induces …

On the Prym map of degree 4 cyclic covers of genus 2 curves
Anatoli Shatsila
https://arxiv.org/abs/2508.20838 https://arxiv.org/pdf/2508.20838

On the Prym map of degree 4 cyclic covers of genus 2 curves
In this paper, we study the Prym map associated to degree 4 étale cyclic covers of genus 2 curves. We show that its non-empty fibers, apart from two exceptional fibers, are isomorphic to the intersection of an elliptic normal curve in $\mathbb{P}^3$ with an affine space $\mathbb{A}^3 \subset \mathbb{P}^3$. Moreover, we obtain a new description of the space of degree 4 étale cyclic covers of genus 2 curves $\mathcal{R}_2^4$ and find equations of elliptic and hyperelliptic curves arising from s…

Assouad type spectra for some self-affine sponges
Qiang Huo
https://arxiv.org/abs/2507.22698 https://arxiv.org/pdf/2507.22698

Assouad type spectra for some self-affine sponges
In this paper we compute the Assouad and lower spectra of Bedford--McMullen sponges in $\mathbb{R}^3$ explicitly. According to the formulae established, we discover that the spectra are not determined by the ratio set, and the box, lower and Assouad dimensions of the sponge anymore, which is unlike the situation in a planar carpet. As a by-product, we construct two Bedford--McMullen sponges on the same grid, both of which have non-uniform fibres. Particularly, they share the same box, lower and…

Finite groups with nearly half as many cyclic subgroups as elements
Vaibhav Chhajer, Sumana Hatui, Palash Sharma
https://arxiv.org/abs/2506.21163 https://

Finite groups with nearly half as many cyclic subgroups as elements
Suppose $C(G)$ denotes the set of all cyclic subgroups of a finite group $G$, and $\mathcal{O}_{2}(G)$ denotes the number of elements of order $2$ in $G$. In [Marius T., Finite groups with a certain number of cyclic subgroups. The American Mathematical Monthly 122.3 (2015): 275-276], an open problem was asked to classify the groups $G$ with $|C(G)|=|G|-r$, where $2 \leq r \leq |G|-1$. In this article, first we show that there are infinitely many groups $G$ with $&#…

Packers vs. Seahawks odds, predictions: No. 1 expert gives free 2025 NFL preseason picks for Saturday Aug. 23

https://www.cbssports.com/nfl/news/packers-seahawks-pre…

Imaging a moving point source in R^3 from the time of arrival at sparse observation points
Guanqiu Ma, Haonan Zhang, Hongxia Guo
https://arxiv.org/abs/2507.20204 https://…

Imaging a moving point source in R^3 from the time of arrival at sparse observation points
In this paper, we introduce a novel numerical method for reconstructing the trajectory within three-dimensional space, where both the emission moment and spatial location of the point source are unknown. Our approach relies solely on measuring the time of arrival at five or seven properly chosen observation points. By utilizing the distinctive geometric configuration of these five or seven observation points, we establish the uniqueness of the trajectory and emission moment of the point source …

The existence and upper bound for stable photon spheres in static spherically symmetric black holes
Yong Song, Jiaqi Fu, Yiting Cen
https://arxiv.org/abs/2508.19823 https://

The existence and upper bound for stable photon spheres in static spherically symmetric black holes
In this work, we establish the existence conditions and a universal upper bound on the radius of stable photon spheres (SPS) outside the event horizons of static, spherically symmetric, asymptotically flat black holes surrounded by matter fields. We prove that stable photon spheres exist if the external matter satisfies specific conditions. Furthermore, under the additional assumption of a monotonically decreasing mass-radius ratio $m(r)/r^3$ outside the horizon, we derive a strict upper bound …

Hyperfine interaction of electrons confined in CsPbI$_3$ nanocrystals with nuclear spin fluctuations
Sergey R. Meliakov, Evgeny A. Zhukov, Vasilii V. Belykh, Kirill V. Kavokin, Mikhail O. Nestoklon, Elena V. Kolobkova, Maria S. Kuznetsova, Manfred Bayer, Dmitri R. Yakovlev
https://arxiv.org/abs/2508.17881

Hyperfine interaction of electrons confined in CsPbI$_3$ nanocrystals with nuclear spin fluctuations
The coherent spin dynamics of electrons are investigated for CsPbI$_3$ perovskite nanocrystals in a glass matrix using time-resolved Faraday ellipticity. In nanocrystals with a diameter of about 11 nm, the Larmor precession frequency has a linear dependence on magnetic field corresponding to the electron Landé $g$-factor of 2.07. We find a finite Larmor precession frequency at zero magnetic field, corresponding to the electron spin splitting of $0.8$ $μ$eV. This splitting is explained by the …

On string theory on (deformed) $AdS_3\times \mathbb{T}^3$
Soumangsu Chakraborty, Amit Giveon
https://arxiv.org/abs/2507.15929 https://

On string theory on (deformed) $AdS_3\times \mathbb{T}^3$
We revisit the fermionic string theory on $AdS_3\times \mathcal{N}$ with $k=1$, and its single-trace $T\bar T$ deformation, with a focus on the $(2,2)$ superstring on (deformed) $AdS_3\times \mathbb{T}^3$. In a certain limit, it is dual to the symmetric product of the ($T\bar T$-deformed) SCFT$_2$ on $\mathbb{R}\times \mathbb{T}^3$. We present the winding-one delta-function normalizable worldsheet operators which, in the $k=1$ decoupling limit, correspond to those of $\mathbb{R}\times \mathbb{T…

Spectral trends across the rings and inner moons of Uranus and Neptune from JWST NIRCam images
M. M. Hedman, I. de Pater, R. Cartwright, M. El Moutamid, R. DeColibus, M. Showlater, M. S. Tiscareno, N. Rowe-Gurney, M. T. Roman, L. Fletcher, H. B. Hammel
https://arxiv.org/abs/2506.18650

Spectral trends across the rings and inner moons of Uranus and Neptune from JWST NIRCam images
JWST NIRCam images provide low-resolution spectra of the rings and inner moons orbiting Uranus and Neptune. These data reveal systematic variations in spectral parameters like the strength of the strong OH absorption band around 3 microns and the spectral slopes at continuum wavelengths. Neptune's rings show an extremely weak 3-micron band, which is likely due to the small particle sizes in these dusty rings. Neptune's small inner moons also have weaker 3-micron bands and redder continua than U…

Uniform Tur\'an density beyond 3-graphs
Ander Lamaison
https://arxiv.org/abs/2508.20696 https://arxiv.org/pdf/2508.20696…

Uniform Turán density beyond 3-graphs
In the 1980s, Erdős and Sós first introduced an extremal problem on hypergraphs with density constraints. Given an $r$-uniform hypergraph $F$ (or $r$-graph for short), its uniform Turán density $π_u(F)$ is the smallest value of $d$ in which every hypergraph $H$ in which every linear-sized subhypergraph of $H$ has edge density at least $d$ contains $F$ as a subgraph. The first non-zero value of $π_u(F)$ was not found until 30 years later. Progress in studying the set of values of the unif…

Chandra X-ray Observatory study of the X-ray emission of PKS 0023-26 and comparison with recent ALMA results
A. Siemiginowska, R. Morganti, G. Fabbiano, E. O'Sullivan, T. Oosterloo, C. Tadhunter, D. Burke
https://arxiv.org/abs/2507.23100

Chandra X-ray Observatory study of the X-ray emission of PKS 0023-26 and comparison with recent ALMA results
We present a deep high-resolution Chandra X-ray Observatory image data of a powerful compact radio source PKS 0023-26 associated with a quasar at redshift 0.322. The earlier studies of the optical environment suggested that the source could be located in a galaxy cluster or a group. However, we report a non-detection of hot gas on large scales (out to $\sim 60$ kpc radius) and place an upper limit on the X-ray luminosity of $<3\times10^{42}$ erg s$^{-1}$, consistent only with the presence of a …

Low-lying zeros of Hilbert modular $L$-functions weighted by powers of central $L$-values
Zhining Wei, Liyang Yang, Shifan Zhao
https://arxiv.org/abs/2508.18469 https://

Low-lying zeros of Hilbert modular $L$-functions weighted by powers of central $L$-values
Let $\mathcal{F}(\textbf{k},\mathfrak{q})$ be the set of primitive Hilbert modular forms of weight $\textbf{k}$ and prime level $\mathfrak{q}$, with trivial central character. We study the one-level density of low-lying zeros of $L(s,π)$ weighted by powers of central $L$-values $L(1/2,π)^r$, where $π$ runs through $\mathcal{F}(\textbf{k},\mathfrak{q})$. For $r=1,2,3$, we show that the resulting distributions $W_r$ match with predictions from Random Matrix Theory. For general $r \geq 1$, we a…

JWST reveals a supernova following a gamma-ray burst at z $\simeq$ 7.3
A. J. Levan, B. Schneider, E. Le Floc'h, G. Brammer, N. R. Tanvir, D. B. Malesani, A. Martin-Carrillo, A. Rossi, A. Saccardi, A. Sneppen, S. D. Vergani, J. An, J. -L. Atteia, F. E. Bauer, V. Buat, S. Campana, A. Chrimes, B. Cordier, L. Cotter, F. Daigne, V. D'Elia, M. De Pasquale, A. de Ugarte Postigo, G. Corcoran, R. A. J. Eyles-Ferris, H. Fausey, A. S. Fruchter, O. Godet, B. P. Gompertz, D. Gotz, N. Habeeb…

JWST reveals a supernova following a gamma-ray burst at z $\simeq$ 7.3
The majority of energetic long-duration gamma-ray bursts (GRBs) are thought to arise from the collapse of massive stars, making them powerful tracers of star formation across cosmic time. Evidence for this origin comes from the presence of supernovae in the aftermath of the GRB event, whose properties in turn link back to those of the collapsing star. In principle, with GRBs we can study the properties of individual stars in the distant universe. Here, we present JWST/NIRCAM observations that d…

Cohen-Macaulay approximations and the $\text{SC}_r$-condition
Richard F. Bartels
https://arxiv.org/abs/2507.14424 https://arxiv.org/p…

Cohen-Macaulay approximations and the $\text{SC}_r$-condition
We study the relation between MCM approximations and FID hulls of modules over a Cohen-Macaulay local ring $R$ with canonical module, specifically when $R$ is generically Gorenstein. We then generalize a result of Kato, who proved that a Gorenstein complete local ring $R$ satisfies the $\text{SC}_{2}$-condition if and only if $R$ is a UFD. For $r \geq 3$, we prove a criterion for when an MCM $R$-module $M$ satisfies the $\text{SC}_{r}$-condition, assuming that its first syzygy $Ω_{R}^{1}(M)$ s…

Replaced article(s) found for nlin.CD. https://arxiv.org/list/nlin.CD/new
[1/1]:
- Orbital cluster-based network modelling
Antonio Colanera, Nan Deng, Matteo Chiatto, Luigi de Luca, Bernd R. Noack

Approximation of time-periodic flow past a translating body by flows in bounded domains
Thomas Eiter, Ana Leonor Silvestre
https://arxiv.org/abs/2507.23697 https://

Approximation of time-periodic flow past a translating body by flows in bounded domains
We consider a time-periodic incompressible three-dimensional Navier-Stokes flow past a translating rigid body. In the first part of the paper, we establish the existence and uniqueness of strong solutions in the exterior domain $Ω\subset {\mathbb R}^3$ that satisfy pointwise estimates for both the velocity and pressure. The fundamental solution of the time-periodic Oseen equations plays a central role in obtaining these estimates. The second part focuses on approximating this exterior flow wit…

Graphs With the Same Edge Count in Each Neighborhood
Nathan S. Sheffield, Zoe Xi
https://arxiv.org/abs/2507.14473 https://arxiv.org/p…

Graphs With the Same Edge Count in Each Neighborhood
In a recent paper, Caro, Lauri, Mifsud, Yuster, and Zarb ask which parameters $r$ and $c$ admit the existence of an $r$-regular graph such that the neighborhood of each vertex induces exactly $c$ edges. They show that every $r$ with $c$ satisfying $0\leq c\leq {r\choose 2}-5r^{3/2}$ is achievable, but no $r$ with $c$ satisfying ${r\choose 2}-\lfloor\frac{r}{3}\rfloor\leq c\leq {r\choose 2}-1$ is. We strengthen the bound in their nonexistence result from ${r\choose 2}-\lfloor\frac{r}{3}\rfloor$ …

Principled Personas: Defining and Measuring the Intended Effects of Persona Prompting on Task Performance
Pedro Henrique Luz de Araujo, Paul R\"ottger, Dirk Hovy, Benjamin Roth
https://arxiv.org/abs/2508.19764

Principled Personas: Defining and Measuring the Intended Effects of Persona Prompting on Task Performance
Expert persona prompting -- assigning roles such as expert in math to language models -- is widely used for task improvement. However, prior work shows mixed results on its effectiveness, and does not consider when and why personas should improve performance. We analyze the literature on persona prompting for task improvement and distill three desiderata: 1) performance advantage of expert personas, 2) robustness to irrelevant persona attributes, and 3) fidelity to persona attributes. We then e…

A Systematic Search for Big Dippers in ASAS-SN
B. JoHantgen, D. M. Rowan, R. For\'es-Toribio, C. S. Kochanek, K. Z. Stanek, B. J. Shappee, Subo Dong, J. L. Prieto, Todd A. Thompson
https://arxiv.org/abs/2507.19594

A Systematic Search for Big Dippers in ASAS-SN
Dipper stars are extrinsically variable stars with deep dimming events due to extended, often dusty, structures produced by a wide range of mechanisms such as collisions, protoplanetary evolution or stellar winds. ASAS-SN has discovered 12 dipper-like objects as part of its normal operations. Here we systematically search the $\sim 5.1$ million ASAS-SN targets with $13

A large color $R$-matrix for $\mathfrak{sl}_3$
Angus Gruen, Lara San Mart\'in Su\'arez
https://arxiv.org/abs/2508.15171 https://arxiv.org/pdf/2508.…

A large color $R$-matrix for $\mathfrak{sl}_3$
We construct the invariant $F_K^{\mathfrak{sl}_3}\in\mathbb{Z}[q,q^{-1}][[x,y]]$ for any positive braid knot $K$, whose existence was conjectured by Park, building on earlier work of Gukov--Manolescu. The main step in our work extends a result by the first author on the invariant associated to symmetric representations of $\mathfrak{sl}_3$ to all irreducible representations. We conclude with a conjectural framework for constructing $F_K^{\mathfrak{sl}_N}$ for arbitrary $N$.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$
Sisi Huang, Xiaohua Yao
https://arxiv.org/abs/2506.23119 http…

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$
It is known that the discrete Laplace operator $Δ$ on the lattice $\mathbb{Z}$ satisfies the following sharp time decay estimate: $$\big\|e^{itΔ}\big\|_{\ell^1\rightarrow\ell^{\infty}}\lesssim|t|^{-\frac{1}{3}},\quad t\neq0,$$ which is slower than the usual $ O(|t|^{-\frac{1}{2}})$ decay in the continuous case on $\mathbb{R}$. However, this paper shows that the discrete bi-Laplacian $Δ^2$ on $\mathbb{Z}$ actually exhibits the same sharp decay estimate $|t&#…

On the first Neumann eigenvalue for critical points of a weighted area functional with asymptotically flat ends
A. L. Mart\'inez-Trivi\~no
https://arxiv.org/abs/2507.20955 h…

On the first Neumann eigenvalue for critical points of a weighted area functional with asymptotically flat ends
In the following work, we obtain a lower bound for the first Neumann eingevalue of the drift Laplacian $Δ^φ$ for a family of properly embedded $[φ,\vec{e}_{3}]$-minimal surfaces in $\mathbb{R}^3$ with concave function $φ$ and asymptotically flat ends. As application, we obtain a control on the topology for that surfaces with finite total curvature. The strategy will consists in an integration of the Bouchner's formula by the works of A. Lichnerowicz and S. Brendle, R. Tsiamis and relate sai…

Crosslisted article(s) found for physics.class-ph. https://arxiv.org/list/physics.class-ph/new
[1/1]:
- Thermodynamics and stability of non-equilibrium steady states in open systems -- case study for c...
V\'it Pr\r{u}\v{s}a

Charge density wave in intermetallic oxides R$_5$Pb$_3$O (R = La and Ce)
Rafaela F. S. Penacchio, Siham Mohamed, Haley A. Harms, Lin-Lin Wang, Sergey L. Bud'ko, Paul. C Canfield, Tyler J. Slade
https://arxiv.org/abs/2507.15817

Charge density wave in intermetallic oxides R$_5$Pb$_3$O (R = La and Ce)
The R$_5$Pb$_3$O family was discovered decades ago, but has remained largely unexplored. Here, we report single crystal growth and basic characterization for the La and Ce members of this family. At room temperature, these compounds adopt a tetragonal structure (I4/mcm), where R and Pb atoms form linear chains along the c-axis. We identify a second-order structural phase transition at 260 K and 145 K for R = La and Ce, respectively. Single crystal X-ray diffraction reveals a lattice modulation …

A comparative study of finite element methods for a class of harmonic map heat flow problems
Nam Anh Nguyen, Arnold Reusken
https://arxiv.org/abs/2508.20590 https://

A comparative study of finite element methods for a class of harmonic map heat flow problems
In this paper, we review and systematically compare three finite element discretization methods for a harmonic map heat flow problem from the unit disk in $\mathbb{R}^2$ to the unit sphere in $\mathbb{R}^3$ in an unified framework. Numerical tests validate the convergence rates in a regime of smooth solutions and are used to compare the methods in terms of computational efficiency. For one of the methods a discrete inf-sup stability result is derived.

Fano schemes of sub-maximal elementary symmetric functions
Alexandru Chirvasitu
https://arxiv.org/abs/2507.19163 https://arxiv.org/pdf/2507.19163

Fano schemes of sub-maximal elementary symmetric functions
Denote by $E_r$ the $r^{th}$ elementary symmetric polynomial in $\dim V$ variables for a vector space $V$ over an infinite field $\Bbbk$. We describe the rational points on the Fano scheme $F_{d-1}(Z(E_{\dim V-1}))$ of projective $(d-1)$-spaces contained in the zero locus of $E_{\dim V-1}$. Isolated points exist precisely for $\dim V=2d$, in which case they are in bijection with the $1\cdot 3\cdots (2d-1)$ pairings on a $2d$-element set. This, in particular, confirming a conjecture of Ambartsou…

Identifying Long Radio Transients with Accompanying X-Ray Emission as Disk-Jet Precessing Black Holes: The Case of ASKAP J1832-0911
Antonios Nathanail
https://arxiv.org/abs/2506.17389

Identifying Long Radio Transients with Accompanying X-Ray Emission as Disk-Jet Precessing Black Holes: The Case of ASKAP J1832-0911
Aims: In this work we investigate whether the 2 min bursts every 44 min from ASKAP J1832-0911 can be explained by Lense-Thirring precession of an intermediate-mass black hole (IMBH) accretion disk launching a Blandford-Znajek jet, as an alternative to magnetar or white-dwarf models. Methods: We derive the Lense-Thirring period $ P_{\rm LT}=\frac{πG M}{a c^3}r^3 $ and solve $P_{\rm LT}=44$ min for black-hole mass M and dimensionless radius $r=R/R_g$. We estimate the equipartition field B at r, …

Effective action of bosonic string theory at order $\alpha'^3$
Mehdi Ameri, Alireza Pahlavan, Mohammad R. Garousi
https://arxiv.org/abs/2506.19471 http…

Effective action of bosonic string theory at order $α'^3$
In this work, we derive the classical effective action of bosonic string theory at order $α'^{3}$ for the metric, Kalb-Ramond field, and dilaton by imposing a higher-derivative extension of the Buscher rules on the circular reduction of the minimal basis at this order, in the schemes where their corresponding actions at order $α'$ are the Meissner and the Metsaev-Tseytlin schemes. We find that T-duality fixes all coupling constants in terms of the known overall factor at order $α'$ and a sin…

Multiple sign-changing and semi-nodal normalized solutions for a Gross-Pitaevskii type system on bounded domain: the $L^2$-supercritical case
Tianhao Liu, Linjie Song, Qiaoran Wu, Wenming Zou
https://arxiv.org/abs/2506.22152

Multiple sign-changing and semi-nodal normalized solutions for a Gross-Pitaevskii type system on bounded domain: the $L^2$-supercritical case
In this paper we investigate the existence of multiple sign-changing and semi-nodal normalized solutions for an $m$-coupled elliptic system of the Gross-Pitaevskii type: \begin{equation} \left\{ \begin{aligned} &-Δu_j + λ_j u_j = \sum_{k=1 }^mβ_{kj} u_k^2 u_j, \quad u_j \in H_0^1(Ω), &\int_Ωu_j^2dx = c_j, \quad j = 1,2,\cdots,m. \end{aligned} \right. \end{equation} Here, $Ω\subset \mathbb{R}^N$ ($N = 3,4$) is a bounded domain. The constants $β_{kj} \neq 0$ and $c_j > 0$…

Non-Universal Flipped Trinification Models with Arbitrary $\beta$
Richard H. Benavides, Yithsbey Giraldo, Eduardo Rojas
https://arxiv.org/abs/2506.16693 ht…

Non-Universal Flipped Trinification Models with Arbitrary $β$
We explore the recently proposed gauge symmetry \( SU(3)_C \otimes SU(3)_L \otimes SU(3)_R \otimes U(1)_X \), which naturally embeds both the Left-Right symmetric model and the 3-3-1 model as subgroups. Within this unified framework, we propose four families of leptons and quarks. A detailed analysis of their contributions to gauge anomaly cancellation is carried out for a general value of the parameter $β$. From this analysis, eight non-universal anomaly-free three-family models and four no…

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions
Nasser Abdo Saeed Bulkhali, A. Vanitha, M. P. Chaudhary
https://arxiv.org/abs/2507.13645

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions
Generalized $m$-gonal numbers are those $p_m(x)= [ (m - 2)x^2 - (m - 4)x ]/2 $ where $x$ and $m$ are integers with $m \geq 3$. If any nonnegative integer can be written in the form $ap_r(h)+bp_s(l)+cp_t(m)+dp_u(n)$, where $a,b,c,d$ are positive integers, then we call $ap_r(h)+bp_s(l)+cp_t(m)+dp_u(n)$ a universal quaternary sum. In this paper, we determine the universality of many quaternary sums when $r,s,t,u \in \{3,4,5,8\}$, using the theory of Ramanujan's theta function identities

A note on the strength of a hypercube
Melissa A. Huggan, M. E. Messinger, Dylan Pearson
https://arxiv.org/abs/2507.21908 https://arxiv.org/pdf/2507.21908…

A note on the strength of a hypercube
As a generalization of super magic strength, the strength of a graph was introduced in [R. Ichishima, F.A. Muntaner-Batle, A. Oshima, Bounds for the strength of graphs, Austral. J. of Combin. 72(3) (2018) 492-508]. For a vertex ordering $f$ of graph $G$, the strength of $f$ is the maximum sum of the labels on any pair of adjacent vertices. The strength of $G$ is defined as the minimum strength of $f$, taken over all vertex orderings of $G$. The strength of the hypercube is unknown, but bounded.…

Replaced article(s) found for cs.CL. https://arxiv.org/list/cs.CL/new
[2/3]:
- Toward Structured Knowledge Reasoning: Contrastive Retrieval-Augmented Generation on Experience
Gu, Xian, Xie, Liu, Liu, Zhong, Gao, Tan, Hu, Li

On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type
Jefferson Baudin, Tatsuro Kawakami, Linus R\"osler
https://arxiv.org/abs/2506.21381

On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type
Given a Cohen-Macaulay scheme of klt type $X$ and a resolution $π\colon Y\to X$, we show that $R^1π_*ω_Y=0$. We deduce that if $\mathrm{dim}(X)=3$, then $X$ satisfies Grauert-Riemenschneider vanishing and therefore has rational singularities. We also obtain that in arbitrary dimension, if $X$ is of finite type over a perfect field of characteristic $p>0$, then $X$ has $\mathbb{Q}_p$-rational singularities.

Subgraph Entropy
Tawfiq Ahmed, Tarik Aougab, Matt Clay
https://arxiv.org/abs/2506.18838 https://arxiv.org/pdf/2506.18838

Subgraph Entropy
Given $r \geq 3$, we prove that there exists $λ>0$ depending only on $r$ so that if $G$ is a metric graph of rank $r$ with metric entropy $1$, then there exists a proper subgraph $H$ of $G$ with metric entropy at least $λ$. This answers a question of the second two authors together with Rieck. We interpret this as a graph theoretic version of the Bers Lemma from hyperbolic geometry, and explain some connections to the pressure metric on the Culler-Vogtmann Outer Space.

The MALATANG survey: Dense gas distribution on sub-kiloparsec scales across the disk of M82
Jian-Fa Wang, Yu Gao, Xue-Jian Jiang, Li Ji, Zhi-Yu Zhang, Jun-Zhi Wang, Jun-Feng Wang, R. Thomas Greve, Yan Jiang, Ashley Bemis, Elias Brinks, Aeree Chung, J. Malcolm Currie, Richard de Grijs, Taotao Fang, C. Luis Ho, Bumhyun Lee, Satoki Matsushita, Micha{\l} Micha{\l}owski, Soojong Pak, Panomporn Poojon, G. Mark Rawlings, Amelie Saintonge, Yi-Chen Sun, Jing Zhou

The MALATANG survey: Dense gas distribution on sub-kiloparsec scales across the disk of M82
We present observations of HCN J=4-3 and HCO^+ J=4-3 lines obtained with the James Clerk Maxwell Telescope as part of the MALATANG survey, combined with archival HCN J=1-0 and HCO^+ J=1-0 data from the Green Bank Telescope, to study the spatial distribution and excitation conditions of dense molecular gas in the disk of M82. We detect HCN J=4-3 and HCO^+ J=4-3 emission within the central region (< 500 pc) of the galaxy, while the J=1-0 emission lines exhibit a more extended spatial distribution…

Schr\"odinger-Bopp-Podolsky system with sublinear and critical nonlinearities: solutions at negative energy levels and asymptotic behaviour
Heydy M. Santos Damian, Gaetano Siciliano
https://arxiv.org/abs/2507.19444

Schrödinger-Bopp-Podolsky system with sublinear and critical nonlinearities: solutions at negative energy levels and asymptotic behaviour
We consider the following Schrödinger-Bopp-Podolsky system with critical and sublinear terms \begin{equation*} \begin{cases} - Δu+ u+Q(x)ϕu= \vert u\vert^4 u+ λK(x)\vert u \vert^{p-1}u&\mbox{ in }\ \mathbb{R}^3 \smallskip - Δϕ+ a^{2}Δ^{2} ϕ= 4πQ(x) u^{2}& \mbox{ in }\ \mathbb{R}^3. \end{cases} \end{equation*} Here $u,ϕ:\mathbb {R}^{3}\rightarrow \mathbb{R}$ are the unknowns, $Q$ and $K$ are given functions satisfying mild assumptions, $a\geq0, λ>0$ are parameters and $p\in (0,1)$…

The infrared jet of M87 observed with JWST
Jan R\"oder, Maciek Wielgus, Joseph B. Jensen, Gagandeep S. Anand, R. Brent Tully
https://arxiv.org/abs/2507.18716 https://

The infrared jet of M87 observed with JWST
We present the first JWST+NIRCam images of the giant elliptical active galaxy M87 and its jet at 0.90, 1.50, 2.77 and 3.56 $μ$m. We analysed the large-scale jet structure, identifying prominent components, and determined the near-infrared spectral index. The data were calibrated using the standard JWST pipeline. We subtracted a constant background level and a smooth model of the galaxy surface brightness to isolate the jet. The total image fluxes measured in the NIRCam filters follow the infra…

The number of regular simplices in higher dimensions
Felix Christian Clemen, Adrian Dumitrescu, Dingyuan Liu
https://arxiv.org/abs/2507.19841 https://arxiv…

The number of regular simplices in higher dimensions
We study the extremal function $S^k_d(n)$, defined as the maximum number of regular $(k-1)$-simplices spanned by $n$ points in $\mathbb{R}^d$. For any fixed $d\geq2k\geq6$, we determine the asymptotic behavior of $S^k_d(n)$ up to a multiplicative constant in the lower-order term. In particular, when $k=3$, we determine the exact value of $S^3_d(n)$, for all even dimensions $d\geq6$ and sufficiently large $n$. This resolves a conjecture of Erdős in a stronger form. The proof leverages technique…

Quaternionic Analysis of Conformal Maps and the Willmore Functional
Ross Ogilvie, Martin Ulrich Schmidt
https://arxiv.org/abs/2506.17723 https://

Quaternionic Analysis of Conformal Maps and the Willmore Functional
Quaternionic analysis, which describes conformal maps from Riemann surfaces into $\mathbb{R}^3$ or $\mathbb{R}^4$, is extended to weakly conformal maps. As a consequence we present a new proof that on any compact Riemann surface $X$ the Willmore functional, the integral of the square of the mean curvature, attains a minimum on the space of smooth conformal maps from $X$ to $\mathbb{R}^3$ or $\mathbb{R}^4$. This was first proven by Kuwert and Schätzle under the assumption that the infimum of th…

ALMA survey of a massive node of the Cosmic Web at $z\sim 3$. II. A dynamically cold and massive disk galaxy in the proximity of a hyperluminous quasar
A. Pensabene, S. Cantalupo, W. Wang, C. Bacchini, F. Fraternali, M. Bischetti, C. Cicone, R. Decarli, G. Pezzulli, M. Galbiati, T. Lazeyras, N. Ledos, G. Quadri, A. Travascio
https://

ALMA survey of a massive node of the Cosmic Web at $z\sim 3$. II. A dynamically cold and massive disk galaxy in the proximity of a hyperluminous quasar
Advancing our understanding of the formation and evolution of early massive galaxies and black holes requires detailed studies of dense structures in the high-redshift Universe. In this work, we present high-angular resolution ($\simeq0.3''$) ALMA observations targeting the CO(4--3) line and the underlying 3-mm dust continuum toward the Cosmic Web node MQN01, a region identified through deep multiwavelength surveys as one of the densest concentrations of galaxies and AGN at cosmic noon. At the …

Hypergraphs without complete partite subgraphs
Dhruv Mubayi
https://arxiv.org/abs/2507.06390 https://arxiv.org/pdf/2507.06390

Hypergraphs without complete partite subgraphs
Fix integers $r \ge 2$ and $2\le s_1\le \cdots \le s_{r-1}\le s_r$ and set $S=\prod_{i=1}^{r-1}s_i$. Let $K=K(s_1, \ldots, s_{r-1}, s_r)$ denote the complete $r$-partite $r$-uniform hypergraph with parts of size $s_1, \ldots, s_{r-1}, s_r$. We prove that the maximum number of edges in an $r$-partite $r$-uniform hypergraph with parts $X_1, \ldots, X_r$ each of size $n$ with no copy of $K$ where the part of size $s_i$ is in $X_i$ for all $i$ is $n^{r-1/S-o(1)}$ provided $s_r> 3^{S+o(S)}$. In othe…

Stability with minuscule structure for chromatic thresholds
Jaehoon Kim, Hong Liu, Chong Shangguan, Guanghui Wang, Zhuo Wu, Yisai Xue
https://arxiv.org/abs/2506.14748

Stability with minuscule structure for chromatic thresholds
The chromatic threshold $δ_χ(H)$ of a graph $H$ is the infimum of $d>0$ such that the chromatic number of every $n$-vertex $H$-free graph with minimum degree at least $d n$ is bounded by a constant depending only on $H$ and $d$. Allen, B{ö}ttcher, Griffiths, Kohayakawa, and Morris determined the chromatic threshold for every $H$; in particular, they showed that if $χ(H)=r\ge 3$, then $δ_χ(H) \in\{\frac{r-3}{r-2},~\frac{2 r-5}{2 r-3},~\frac{r-2}{r-1}\}$. While the chromatic thresholds have…

Longest odd cycles in non-bipartite $C_{2k 1}$-free graphs
Rui Wang, Shipeng Wang
https://arxiv.org/abs/2508.16199 https://arxiv.org/pdf/2508.16199

Longest odd cycles in non-bipartite $C_{2k+1}$-free graphs
In strengthening a result of Andrásfai, Erdős and Sós in 1974, Häggkvist proved that if $G$ is an $n$-vertex $C_{2k+1}$-free graph with minimum degree $δ(G)>\frac{2n}{2k+3}$ and $n>\binom{k+2}{2}(2k+3)(3k+2)$, then $G$ contains no odd cycle of length greater than $\frac{k+1}{2}$. This result has many applications.In this paper, we consider a similar problem by replacing minimum degree condition with edge number condition. We prove that for integers $n,k,r$ with $k\geq 2,3\leq r\leq 2k$ and…

Axisymmetric self-similar solutions to the MHD equations without magnetic diffusion
Shaoheng Zhang
https://arxiv.org/abs/2506.20131 https://

Axisymmetric self-similar solutions to the MHD equations without magnetic diffusion
We study the axisymmetric self-similar solutions $(\mathbf{u},\mathbf{B})$ to the stationary MHD equations without magnetic diffusion, where $\mathbf{B}$ has only the swirl component. Our first result states that in $\mathbb{R}^3\setminus\{0\}$, $\mathbf{u}$ is a Landau solution and $\mathbf{B}=0$. Our second result proves the triviality of axisymmetric self-similar solutions in the half-space $\mathbb{R}^3_+$ with the no-slip boundary condition or the Navier slip boundary condition.

Minimal hypergraph non-jumps
Benedict Randall Shaw
https://arxiv.org/abs/2506.09620 https://arxiv.org/pdf/2506.09620

Minimal hypergraph non-jumps
An $r$-uniform hypergraph, or $r$-graph, has density $|E(G)|/|V(G)^{(r)}|$. We say $α$ is a jump for $r$-graphs if there is some constant $δ=δ(α)$ such that, for each $\varepsilon>0$ and $n\geq r$, any sufficiently large $r$-graph of density at least $\varepsilon$ has a subgraph of order $n$ and density at least $α+δ$. For $r=2$, all $α$ are jumps. For $r\geq 3$, Erdős showed all $[0,\frac{r!}{r^r})$ are jumps, and conjectured all $[0,1)$ are jumps. Since then, a var…

All Type-2 isomorphic circulant graphs of $C_{16}(R)$ and $C_{24}(S)$
Vilfred Kamalappan
https://arxiv.org/abs/2508.09384 https://arxiv.org/pdf/2508.09384

All Type-2 isomorphic circulant graphs of $C_{16}(R)$ and $C_{24}(S)$
Circulant graphs $C_n(R)$ and $C_n(S)$ are said to be \emph{Adam's isomorphic} or {\em Type-1 isomorphic} if there exist some $a\in \mathbb{Z}_n^*$ such that $S = a R$ under arithmetic reflexive modulo $n$ \cite{ad67}. In 1970, Elspas and Turner \cite{eltu} raised a question on the isomorphism of $C_{16}(1,2,7)$ and $C_{16}(2,3,5)$ and in 1996, Vilfred \cite{v96} gave its answer by defining Type-2 isomorphism of $C_n(R)$ w.r.t. $m$ $\ni$ $m$ = $\gcd(n, r) > 1$, $r\in R$ and $r,n\in\mathbb{N}$ a…

Non-bipartite graphs without theta subgraphs
Longfei Fang, Huiqiu Lin
https://arxiv.org/abs/2508.12855 https://arxiv.org/pdf/2508.12855

Non-bipartite graphs without theta subgraphs
Fix a color-critical graph $H$ with $χ(H)=r+1\geq 3$. Simonovits' chromatic critical edge theorem and Nikiforov's spectral chromatic critical edge theorem imply that $T_{n,r}$ is the extremal graph with the maximum size and the maximum spectral radius over all $H$-free graphs of order $n$, respectively. Since $T_{n,r}$ is $r$-partite, it is interesting to study the Turán number and the spectral Turán number of a color-critical graph $H$ in non-$r$-partite graphs. Denote by ${\rm EX}_{r+1}(n,…

A New Proof of Fine's Identity using Wildberger's Polynomial Formula
Dean Rubine
https://arxiv.org/abs/2508.12055 https://arxiv.org/pdf/2508.12055

A New Proof of Fine's Identity using Wildberger's Polynomial Formula
In 1959, N. J. Fine showed that the sum of the multinomial coefficients corresponding to the partitions of a natural number $n$ into $r$ parts is a binomial coefficient: $$ \sum_{\substack{k_1 + k_2 + k_3 + {}\ldots = r \\ k_1 + 2k_2 + 3k_3 + {}\ldots = n }} \binom{r}{k_1, k_2, k_3, \ldots } = \binom{n - 1}{r - 1} $$ Fine gives a rather pithy proof, though we're still stuck on the part that says, ``We begin with an important though obvious remark.'' In 2025, Wildberger and Rubine gave the serie…