Tootfinder

This https://arxiv.org/abs/2401.14528 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Infinitely many solutions for doubly critical variable-order $p(x)$-Choquard-Kirchhoff type equations via the concentration compactness method
In this paper, we prove the existence of infinitely many solutions of a doubly critical Choquard-Kirchhoff type equation \begin{equation*} \begin{split} &M(\mathcal{E}[u])(-Δ)_{p(\cdot)}^{s(\cdot)}u+V(x)|u|^{p(x)-2}u-\varepsilon_W W(x)|u|^{q_W(x)-2}u \\ &\quad\quad=\int_{\mathbb{R}^N} \frac{|u(x)|^{r(x)} |u(y)|^{r(y)-2}u(y)}{|x-y|^{α(x,y)}}dy+ |u|^{q_c(x)-2}u\quad\text{in $\mathbb{R}^N$} \end{split} \end{equation*} with variable smoo…

Binary forms with the same value set I
\'Etienne Fouvry, Peter Koymans
https://arxiv.org/abs/2404.11231 https://arxiv.org/pdf/240…

Binary forms with the same value set I
Given a binary form $F \in \mathbb{Z}[X, Y]$, we define its value set to be $\{F(x, y) : (x, y) \in \mathbb{Z}^2\}$. Let $F, G \in \mathbb{Z}[X, Y]$ be two binary forms of degree $d \geq 3$ and with non-zero discriminant. In a series of three papers, we will give necessary and sufficient conditions on $F$ and $G$ to have the same value set. These conditions will be entirely in terms of the automorphism groups of the forms. In this paper, we will build the general theory that reduces the probl…

This https://arxiv.org/abs/2310.13788 has been replaced.
link: https://scholar.google.com/scholar?q=a

A New and Faster Representation for Counting Integer Points in Parametric Polyhedra
In this paper, we consider the counting function $E_P(y) = |P_{y} \cap Z^{n_x}|$ for a parametric polyhedron $P_{y} = \{x \in R^{n_x} \colon A x \leq b + B y\}$, where $y \in R^{n_y}$. We give a new representation of $E_P(y)$, called a \emph{piece-wise step-polynomial with periodic coefficients}, which is a generalization of piece-wise step-polynomials and integer/rational Ehrhart's quasi-polynomials. It gives the fastest way to calculate $E_P(y)$ in certain scenarios. The most import…

Measurements of All-Particle Energy Spectrum and Mean Logarithmic Mass of Cosmic Rays from 0.3 to 30 PeV with LHAASO-KM2A
The LHAASO Collaboration, Zhen Cao, F. Aharonian, Q. An, A. Axikegu, Y. X. Bai, Y. W. Bao, D. Bastieri, X. J. Bi, Y. J. Bi, J. T. Cai, Q. Cao, W. Y. Cao, Zhe Cao, J. Chang, J. F. Chang, A. M. Chen, E. S. Chen, Liang Chen, Lin Chen, Long Chen, M. J. Chen, M. L. Chen, Q. H. Chen, S. H. Chen, S. Z. Chen, T. L. Chen, Y. Chen, N. Cheng, Y. D. Cheng, M. Y. Cui, S. W. Cui,…

Measurements of All-Particle Energy Spectrum and Mean Logarithmic Mass of Cosmic Rays from 0.3 to 30 PeV with LHAASO-KM2A
We present the measurements of all-particle energy spectrum and mean logarithmic mass of cosmic rays in the energy range of 0.3-30 PeV using data collected from LHAASO-KM2A between September 2021 and December 2022, which is based on a nearly composition-independent energy reconstruction method, achieving unprecedented accuracy. Our analysis reveals the position of the knee at $3.67 \pm 0.05 \pm 0.15$ PeV. Below the knee, the spectral index is found to be -$2.7413 \pm 0.0004 \pm 0.0050$, while a…

Being a grownup means starting with "today I'd like to Y" and finishing with "fuck no, I need to X instead".
Every.
Single.
Time.

This https://arxiv.org/abs/2401.14528 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Infinitely many solutions for doubly critical variable-order $p(x)$-Choquard-Kirchhoff type equations via the concentration compactness method
In this paper, we prove the existence of infinitely many solutions of a doubly critical Choquard-Kirchhoff type equation \begin{equation*} \begin{split} &M(\mathcal{E}[u])(-Δ)_{p(\cdot)}^{s(\cdot)}u+V(x)|u|^{p(x)-2}u-\varepsilon_W W(x)|u|^{q_W(x)-2}u \\ &\quad\quad=\int_{\mathbb{R}^N} \frac{|u(x)|^{r(x)} |u(y)|^{r(y)-2}u(y)}{|x-y|^{α(x,y)}}dy+ |u|^{q_c(x)-2}u\quad\text{in $\mathbb{R}^N$} \end{split} \end{equation*} with variable smoo…

Generalized zero-divisor graph of $*$-rings
Anita Lande, Anil Khairnar
https://arxiv.org/abs/2403.10161 https://arxiv.org/pdf/2403.10…

Generalized zero-divisor graph of $*$-rings
Let $R$ be a ring with involution $*$ and $Z^*(R)$ denotes the set of all non-zero zero-divisors of $R$. We associate a simple (undirected) graph $Γ'(R)$ with vertex set $Z^*(R)$ and two distinct vertices $x$ and $y$ are adjacent in $Γ'(R)$ if and only if $x^ny^*=0$ or $y^nx^*=0$, for some positive integer $n$. We find the diameter and girth of $Γ'(R)$. The characterizations are obtained for $*$-rings having $Γ'(R)$ a connected graph, a complete graph, and a star graph. Further, we have s…

"What has happened is not that we have become disengaged with computers. What has happened is that most of us with a computer do not care about it as a computer. Owning a Commodore 64 is no longer a badge of membership in the hobbyist computer club. That does not mean that the hobbyists are not out there, just that you have got to look harder to find them."

Interstellar Nitrogen Isotope Ratios: Measurements on tracers of C$^{14}$N and C$^{15}$N
J. L. Chen, J. S. Zhang, C. Henkel, Y. T. Yan, H. Z. Yu, Y. X. Wang, Y. P. Zou, J. Y. Zhao, X. Y. Wang
https://arxiv.org/abs/2406.09683

Interstellar Nitrogen Isotope Ratios: Measurements on tracers of C$^{14}$N and C$^{15}$N
The nitrogen isotope ratio 14N/15N is a powerful tool to trace Galactic stellar nucleosynthesis and constraining Galactic chemical evolution. Previous observations have found lower 14N/15N ratios in the Galactic center and higher values in the Galactic disk. This is consistent with the inside-out formation scenario of our Milky Way. However, previous studies mostly utilized double isotope ratios also including 12C/13C, which introduces additional uncertainties. Here we therefore present observa…

First Search for Light Fermionic Dark Matter Absorption on Electrons Using Germanium Detector in CDEX-10 Experiment
J. X. Liu, L. T. Yang, Q. Yue, K. J. Kang, Y. J. Li, H. P. An, Greeshma C., J. P. Chang, Y. H. Chen, J. P. Cheng, W. H. Dai, Z. Deng, C. H. Fang, X. P. Geng, H. Gong, Q. J. Guo, T. Guo, X. Y. Guo, L. He, J. R. He, J. W. Hu, H. X. Huang, T. C. Huang, L. Jiang, S. Karmakar, H. B. Li, H. Y. Li, J. M. Li, J. Li, M. C. Li, Q. Y. Li, R. M. J. Li, X. Q. Li, Y. L. Li, Y. F. Liang…

First Search for Light Fermionic Dark Matter Absorption on Electrons Using Germanium Detector in CDEX-10 Experiment
We present the first results of the search for sub-MeV fermionic dark matter absorbed by electron targets of Germanium using the 205.4~kg$\cdot$day data collected by the CDEX-10 experiment, with the analysis threshold of 160~eVee. No significant dark matter (DM) signals over the background are observed. Results are presented as limits on the cross section of DM--electron interaction. We present new constraints of cross section in the DM range of 0.1--10 keV/$c^2$ for vector and axial-vector int…

This https://arxiv.org/abs/2403.12756 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hurwitz moduli varieties parameterizing pointed covers of an algebraic curve with a fixed monodromy group
Given a smooth, projective curve $Y$, a point $y_0 \in Y$, a positive integer $n$, and a transitive subgroup $G$ of the symmetric group $S_{d}$ we study smooth, proper families, parameterized by algebraic varieties, of pointed degree $d$ covers of $(Y,y_0)$, $(X,x_{0})\to (Y,y_0)$, branched in $n$ points of $Y\setminus y_{0}$, whose monodromy group equals $G$. We construct a Hurwitz space $H$, an algebraic variety whose points are in bijective correspondence with the equivalence classes of poin…

This https://arxiv.org/abs/2303.00712 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Cluster-size decay in supercritical long-range percolation
We study the cluster-size distribution of supercritical long-range percolation on $\mathbb{Z}^d$, where two vertices $x,y\in\mathbb{Z}^d$ are connected by an edge with probability $\mathrm{p}(\|x-y\|):=p\min(1,β\|x-y\|)^{-dα}$ for parameters $p\in(0, 1]$, $α>1$, and $β>0$. We show that when $α>1+1/d$, and either $β$ or $p$ is sufficiently large, the probability that the origin is in a finite cluster of size at least $k$ decays as $\exp\big(-Θ(k^{(d-1)/d})\big)$. This …

This https://arxiv.org/abs/2404.03241 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A logarithm law for nonautonomous systems fastly converging to equilibrium and mean field coupled systems
We prove that if a nonautonomous system has in a certain sense a fast convergence to equilibrium (faster than any power law behavior) then the time $τ_{r}(x,y)$ needed for a typical point $x$ to enter for the first time in a ball $B(y,r)$ centered in $y$, with small radius \ $r $ scales as the local dimension of the equilibrium measure \ $μ$ at $y$, i.e. $$ \underset{r\rightarrow 0}{\lim }\frac{\log τ_{r}(x,y)}{-\log r}% =d_{μ}(y).$$ We then apply the general result to concrete systems of…

On the two-dimensional Brillouin flow
Ryan A. Revolinsky, Christopher J. Swenson, Nicholas M. Jordan, Y. Y. Lau, Ronald M. Gilgenbach
https://arxiv.org/abs/2404.11047

On the two-dimensional Brillouin flow
The Brillouin flow is a rectilinear, sheared electron fluid flow in a crossed electric field (E) and magnetic field (B), in the E x B direction with zero flow velocity and zero electric field at the surface with which the flow is in contact. It is broadly considered as the equilibrium electron flow in high power crossed-field devices including the magnetron and magnetically insulated transmission line oscillators. This paper provides an examination of Brillouin flow in two dimensions, in a cyli…

This https://arxiv.org/abs/2307.09737 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Probing for chiral $Z^\prime$ gauge boson through scattering measurement experiments
Motivated by the observation of tiny neutrino mass can not be explained within the framework of Standard Model (SM), we consider extra gauge extended scenarios in which tiny neutrino masses are generated through seesaw mechanism. These scenarios are equipped with beyond the standard model (BSM) neutral gauge boson called $Z^\prime$ in the general $U(1)_X$ symmetry which is a linear combination of $U(1)_Y$ and $U(1)_{B-L}$. In this case, left and right handed fermions interact differently with t…

This https://arxiv.org/abs/2403.09245 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Conditional plasticity of the unit ball of the $\ell_\infty$-sum of finitely many strictly convex Banach spaces
We prove that for any $\ell_\infty$-sum $Z = \bigoplus_{i \in [n]} X_i$ of finitely many strictly convex Banach spaces $(X_i)_{i \in [n]}$, an extremeness preserving 1-Lipschitz bijection $f\colon B_Z \to B_Z$ is an isometry, by constraining the componentwise behavior of the inverse $g=f^{-1}$ with a theorem admitting a graph-theoretic interpretation. We also show that if $X, Y$ are Banach spaces, then a bijective 1-Lipschitz non-isometry of type $B_X \to B_Y$ can be used to construct a bijecti…

This https://arxiv.org/abs/2310.08871 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An $L_{q}(L_{p})$-regularity theory for parabolic equations with integro-differential operators having low intensity kernels
In this article, we present the existence, uniqueness, and regularity of solutions to parabolic equations with non-local operators $$ \partial_{t}u(t,x) = \mathcal{L}^{a}u(t,x) + f(t,x), \quad t>0 $$ in $L_{q}(L_{p})$ spaces. Our spatial operator $\mathcal{L}^{a}$ is an integro-differential operator of the form $$ \int_{\mathbb{R}^{d}} \left( u(x+y)-u(x) -\nabla u(x) \cdot y \mathrm{1}_{|y|\leq 1} \right) a(t,y) j_{d}(|y|)dy. $$ Here, $a(t,y)$ is a merely bounded measurable …

Rotation and flipping invariant self-organizing maps with astronomical images: A cookbook and application to the VLA Sky Survey QuickLook images
A. N. Vantyghem, T. J. Galvin, B. Sebastian, C. P. O'Dea, Y. A. Gordon, M. Boyce, L. Rudnick, K. Polsterer, Heinz Andernach, M. Dionyssiou, P. Venkataraman, R. Norris, S. A. Baum, X. R. Wang, M. Huynh
ht…

Rotation and flipping invariant self-organizing maps with astronomical images: A cookbook and application to the VLA Sky Survey QuickLook images
Modern wide field radio surveys typically detect millions of objects. Techniques based on machine learning are proving to be useful for classifying large numbers of objects. The self-organizing map (SOM) is an unsupervised machine learning algorithm that projects a many-dimensional dataset onto a two- or three-dimensional lattice of neurons. This dimensionality reduction allows the user to visualize common features of the data better and develop algorithms for classifying objects that are not o…

Binary quadratic forms with the same value set
\'Etienne Fouvry, Peter Koymans
https://arxiv.org/abs/2404.09575 https://arxiv.org…

Binary quadratic forms with the same value set
Given a binary quadratic form $F \in \mathbb{Z}[X, Y]$, we define its value set $F(\mathbb{Z}^2)$ to be $\{F(x, y) : (x, y) \in \mathbb{Z}^2\}$. If $F$ and $G$ are two binary quadratic forms with integer coefficients, we give necessary and sufficient conditions on $F$ and $G$ for $F(\mathbb{Z}^2) = G(\mathbb{Z}^2)$.

Strong coalitions in graphs
Hamidreza Golmohammadi, Saeid Alikhani, Nima Ghanbari, I. I. Takhonov, A. Abaturov
https://arxiv.org/abs/2404.11575 https://

Strong coalitions in graphs
For a graph $G=(V,E)$, a set $D\subset V(G)$ is a strong dominating set of $G$, if for every vertex $x\in V (G)\setminus D$ there is a vertex $y\in D$ with $xy \in E(G)$ and $deg(x)\leq deg(y)$. A strong coalition consists of two disjoint sets of vertices $V_{1}$ and $V_{2}$, neither of which is a strong dominating set but whose union $V_{1}\cup V_{2}$, is a strong dominating set. A vertex partition $Ω=\{V_1, V_2,..., V_k \}$ of vertices in $G$ is a strong coalition partition, if every set $V_…

This https://arxiv.org/abs/2302.13218 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Schrödinger equation with finitely many $δ$-interactions: closed form, integral and series representations for solutions
A closed form solution for the one-dimensional Schrödinger equation with a finite number of $δ$-interactions \[ \mathbf{L}_{q,\mathfrak{I}_{N}}y:=-y^{\prime\prime}+\left( q(x)+\sum _{k=1}^{N}α_{k}δ(x-x_{k})\right) y=λy,\quad0

This https://arxiv.org/abs/2310.08871 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An $L_{q}(L_{p})$-regularity theory for parabolic equations with integro-differential operators having low intensity kernels
In this article, we present the existence, uniqueness, and regularity of solutions to parabolic equations with non-local operators $$ \partial_{t}u(t,x) = \mathcal{L}^{a}u(t,x) + f(t,x), \quad t>0 $$ in $L_{q}(L_{p})$ spaces. Our spatial operator $\mathcal{L}^{a}$ is an integro-differential operator of the form $$ \int_{\mathbb{R}^{d}} \left( u(x+y)-u(x) -\nabla u(x) \cdot y \mathrm{1}_{|y|\leq 1} \right) a(t,y) j_{d}(|y|)dy. $$ Here, $a(t,y)$ is a merely bounded measurable …

The galaxy group merger origin of the Cloverleaf odd radio circle system
E. Bulbul, X. Zhang, M. Kluge, M. Brueggen, B. Koribalski, A. Liu, E. Artis, Y. E. Bahar, F. Balzer, C. Garrel, V. Ghirardini, N. Malavasi, A. Merloni, K. Nandra, M. E. Ramos-Ceja, J. S. Sanders, S. Zelmer
https://arxiv.org/abs/2403.09808

The galaxy group merger origin of the Cloverleaf odd radio circle system
Odd radio circles (ORC) are a newly discovered class of extended faint radio sources of unknown origin. We report the first detection of diffuse X-ray gas at the location of a low-redshift ORC (z=0.046), known as Cloverleaf ORC. This observation was performed with the XMM-Newton X-ray telescope. The physical extent of the diffuse X-ray emission corresponds to approximately a 230 kpc by 160 kpc region, lying perpendicular to the radio emission detected by ASKAP. The X-ray spectrum shows characte…

Still true and a real problem for wikipedia:
https://mastodon.social/@jwz/112597373045800130

A unique Cartan subalgebra result for Bernoulli actions of weakly amenable groups
Changying Ding
https://arxiv.org/abs/2404.08182 https://

A unique Cartan subalgebra result for Bernoulli actions of weakly amenable groups
We show that if $Γ\curvearrowright (X^Γ,μ^Γ)$ is a Bernoulli action of an i.c.c. nonamenable group $Γ$ which is weakly amenable with Cowling-Haagerup constant $1$, and $Λ\curvearrowright(Y,ν)$ is a free ergodic p.m.p. algebraic action of a group $Λ$, then the isomorphism $L^\infty(X^Γ)\rtimesΓ\cong L^\infty(Y)\rtimesΛ$ implies that $L^\infty(X^Γ)$ and $L^\infty(Y)$ are unitarily conjugate. This is obtained by showing a new rigidity result of non properly proximal groups and combinin…

Constraints on Ultra Heavy Dark Matter Properties from Dwarf Spheroidal Galaxies with LHAASO Observations
Zhen Cao, F. Aharonian, Q. An, Axikegu, Y. X. Bai, Y. W. Bao, D. Bastieri, X. J. Bi, Y. J. Bi, J. T. Cai, Q. Cao, W. Y. Cao, Zhe Cao, J. Chang, J. F. Chang, A. M. Chen, E. S. Chen, Liang Chen, Lin Chen, Long Chen, M. J. Chen, M. L. Chen, Q. H. Chen, S. H. Chen, S. Z. Chen, T. L. Chen, Y. Chen, N. Cheng, Y. D. Cheng, M. Y. Cui, S. W. Cui, X. H. Cui, Y. D. Cui, B. Z. Dai, H. L. Dai,…

Constraints on Ultra Heavy Dark Matter Properties from Dwarf Spheroidal Galaxies with LHAASO Observations
In this work we try to search for signals generated by ultra-heavy dark matter at the Large High Altitude Air Shower Observatory (LHAASO) data. We look for possible gamma-ray by dark matter annihilation or decay from 16 dwarf spheroidal galaxies in the field of view of LHAASO. Dwarf spheroidal galaxies are among the most promising targets for indirect detection of dark matter which have low fluxes of astrophysical $γ$-ray background while large amount of dark matter. By analyzing more than 700…

Compact subspaces of the space of separately continuous functions with the cross-uniform topology
Oleksandr Maslyuchenko, Vadym Myronyk, Roman Ivasiuk
https://arxiv.org/abs/2406.05705

Compact subspaces of the space of separately continuous functions with the cross-uniform topology
We consider two natural topologies on the space $S(X\times Y,Z)$ of all separately continuous functions defined on the product of two topological spaces $X$ and $Y$ and ranged into a topological or metric space $X$. These topologies are the cross-open topology and the cross-uniform topology. We show that these topologies coincides if $X$ and $Y$ are pseudocompacts and $Z$ is a metric space. We prove that a compact space $K$ embeds into $S(X\times Y,Z)$ for infinite compacts $X$, $Y$ and a metri…

Planar random motions in a vortex
Enzo Orsingher, Manfred Marvin Marchione
https://arxiv.org/abs/2404.11521 https://arxiv.org/pdf/240…

Planar random motions in a vortex
We study a planar random motion $\big(X(t),Y(t)\big)$ with orthogonal directions which can turn clockwise, counterclockwise and reverse its direction each with a different probability. The support of the process is given by a time-varying square and the singular distributions on the boundary and the diagonals of the square are obtained. In the interior of the support, we study the hydrodynamic limit of the distribution. We then investigate the time $T(t)$ spent by the process moving vertically …

This https://arxiv.org/abs/2404.07180 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Good bounds for sets lacking skew corners
A skew corner is a triple of points in $\mathbb{Z} \times \mathbb{Z}$ of the form $(x,y), (x, y + a)$ and $(x + a, y')$. Pratt posed the following question: how large can a set $A \subseteq [n] \times [n]$ be, provided it contains no non-trivial skew corner (i.e. one for which $a\not=0$)? We prove that $|A| \leq \exp(- c\log^c n) n^2$, for an absolute constant $c > 0$, which, along with a construction of Beker, essentially resolves Pratt's question. Our argument is represents a two-…

Search for solar axions by Primakoff effect with the full dataset of the CDEX-1B Experiment
L. T. Yang, S. K. Liu, Q. Yue, K. J. Kang, Y. J. Li, H. P. An, Greeshma C., J. P. Chang, Y. H. Chen, J. P. Cheng, W. H. Dai, Z. Deng, C. H. Fang, X. P. Geng, H. Gong, Q. J. Guo, T. Guo, X. Y. Guo, L. He, J. R. He, J. W. Hu, H. X. Huang, T. C. Huang, L. Jiang, S. Karmakar, H. B. Li, H. Y. Li, J. M. Li, J. Li, M. C. Li, Q. Y. Li, R. M. J. Li, X. Q. Li, Y. L. Li, Y. F. Liang, B. Liao, F. K. Lin, S.…

This https://arxiv.org/abs/2309.16580 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Superadditivity of anticanonical Iitaka dimension for contractions with F-split fibres
Given a fibration $f: X \to Y$ with general fibre $X_y$, over a field of positive characteristic, we establish the Iitaka-type inequality $κ(X,-K_X) \leq κ(X_y,-K_{X_y})+κ(Y,-K_Y)$ whenever $X_y$ has good F-singularities.

it's odd to say the least

Enrich your ggplots with extra panels along the x and y axis: #ggplot #dataviz

GitHub - jtlandis/ggside: ggplot2 extension allowing for plotting various geometries as side panels using the ggplot2 API
ggplot2 extension allowing for plotting various geometries as side panels using the ggplot2 API - jtlandis/ggside

This https://arxiv.org/abs/2403.15758 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An endpoint estimate for the maximal Calderón commutator with rough kernel
In this paper, the authors consider the endpoint estimates for the maximal Calderón commutator defined by $$T_{Ω,\,a}^*f(x)=\sup_{ε>0}\Big|\int_{|x-y|>ε}\frac{Ω(x-y)}{|x-y|^{d+1}} \big(a(x)-a(y)\big)f(y)dy\Big|,$$ where $Ω$ is homogeneous of degree zero, integrable on $S^{d-1}$ and has vanishing moment of order one, $a$ be a function on $\mathbb{R}^d$ such that $\nabla a\in L^{\infty}(\mathbb{R}^d)$. The authors prove that if $Ω\in L\log L(S^{d-1})$, then $T…

This https://arxiv.org/abs/2209.04838 has been replaced.
link: https://scholar.google.com/scholar?q=a

Localization with Single or Antipodal Distance Measurements
Given a polygonal workspace $W$, a depth sensor placed at point $p=(x,y)$ inside $W$ and oriented in direction $θ$ measures the distance $d=h(x,y,θ)$ between $p$ and the closest point on the boundary of $W$ along a ray emanating from $p$ in direction $θ$. We study the following problem: For a polygon $W$ with $n$ vertices, possibly with holes, preprocess it such that given a query real value $d> 0$, one can efficiently compute the preimage $h^{-1}(d) \subset W\times \mathbb{S}^1$, namely det…

Lecture on the combinatorial algebraic method for computing algebraic integrals
Bertrand Eynard
https://arxiv.org/abs/2405.20941 https://

Lecture on the combinatorial algebraic method for computing algebraic integrals
Consider an algebraic equation $P(x,y)=0$ where $P\in \mathbb C[x,y] $ (or $\mathbb F[x,y]$ with $\mathbb F\subset \mathbb C$ a subfield) is a bivariate polynomial, it defines a plane algebraic curve. We provide an efficient method for computing integrals of the type $ \int_γR(x,y)dx $ where $R(x,y)\in \mathbb C(x,y) $ is any rational fraction, and $y$ is solution of $P(x,y)=0$, and $γ$ any Jordan arc open or closed on the plane algebraic curve. The method uses only algebraic and combinatoria…

This https://arxiv.org/abs/2202.09894 has been replaced.
link: https://scholar.google.com/scholar?q=a

Third-order affine-invariant (systems of) PDEs in two independent variables as vanishing of the Fubini-Pick invariant
If one imposes that a $3^{\mathrm{rd}}$ order PDE $\mathcal{E}:=\{F(x,y,u,u_x,\dots,u_{xyy},u_{yyy})=0\}$ in two independent variables $x,y$ and one unknown function $u$ be invariant with respect to the group of affine transformation $\mathrm{Aff}(3)$ of $\mathbb{R}^3=\{(x,y,u)\}$, then it turns out that there is (up to a nowhere zero factor) only one choice of $F$. In this paper we study more in depth the geometry behind the occurrence of such a PDE: after proving the relationship of $F$ with …

This https://arxiv.org/abs/2404.07380 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Strong bounds for skew corner-free sets
Motivated by applications to matrix multiplication algorithms, Pratt asked (ITCS'24) how large a subset of $[n] \times [n]$ could be without containing a skew-corner: three points $(x,y), (x,y+h),(x+h,y')$ with $h \ne 0$. We prove any skew corner-free set has size at most $\exp(-Ω(\log^{1/12} n))\cdot n^2$, nearly matching the best known lower bound of $\exp(-O(\sqrt{\log n}))\cdot n^2$ by Beker (arXiv'24). Our techniques generalize those of Kelley and Meka's recent breakthrough on three-term …

This https://arxiv.org/abs/2303.03084 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

On Regression in Extreme Regions
The statistical learning problem consists in building a predictive function $\hat{f}$ based on independent copies of $(X,Y)$ so that $Y$ is approximated by $\hat{f}(X)$ with minimum (squared) error. Motivated by various applications, special attention is paid here to the case of extreme (i.e. very large) observations $X$. Because of their rarity, the contributions of such observations to the (empirical) error is negligible, and the predictive performance of empirical risk minimizers can be cons…

This https://arxiv.org/abs/2403.17955 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An effective estimate for the sum of two cubes problem
Let $f(x, y) \in \mathbb{Z}[x, y]$ be a cubic form with non-zero discriminant, and for each integer $m \in \mathbb{Z}$, let, $N_{f}(m)=\#\left\{(x, y) \in \mathbb{Z}^{2}: f(x, y)=m\right\} $. In 1983, Silverman proved that $N_{f}(m)>Ω\left((\log |m|)^{3 / 5}\right)$ when $f(x, y)=x^{3}+y^{3}$. In this paper, we obtain an explicit bound for $N_f(m)$, namely, showing that $N_{f}(m)>4.2\times 10^{-6}(\log |m|)^{11/13}$ (holds for infinitely many integers m), when $f(x, y)=x^{3…

A Novel Diamond-like Carbon based photocathode for PICOSEC Micromegas detector
X. Wang, Y. Zhou, R. Aleksan, Y. Angelis, J. Bortfeldt, F. Brunbauer, M. Brunoldi, E. Chatzianagnostou, J. Datta, K. Degmelt, G. Fanourakis, D. Fiorina, K. J. Floethner, M. Gallinaro, F. Garcia, I. Giomataris, K. Gnanvo, F. J. Iguaz, D. Janssens, A. Kallitsopoulou, M. Kovacic, B. Kross, P. Legou, M. Lisowska, J. Liu, J. Liu, I. Maniatis, J. McKisson, Y. Meng, H. Muller, E. Oliveri, G. Orlandini, A. Pandey, T…

A Novel Diamond-like Carbon based photocathode for PICOSEC Micromegas detector
The PICOSEC Micromegas (MM) is a Cherenkov photodetector based on the MM detector operating in a two-stage amplification mode. Prototypes equipped with a cesium iodide (CsI) photocathode have shown promising time resolutions as low as 24 picoseconds (ps) for Minimum Ionizing Particles. However, due to the high hygroscopicity and susceptibility to ion bombardment of the CsI photocathode, alternative photocathode materials such as pure aluminum, pure chromium, as well as Diamond-like Carbon (DLC)…

The Injective category number on continuous maps
Cesar A. Ipanaque Zapata, Roland Rabanal
https://arxiv.org/abs/2405.04317 https://ar…

The Injective category number on continuous maps
We present the notion of injective category number of a map $f\colon X\to Y$ with basic results about this numerical invariant. For instance, we explore the injective category number under pullbacks and compositions. In the case that $f$ is the quotient map $q:X\to X/τ$, where $X$ is a normal space and $τ:X\to X$ is a fixed-point free involution, we show that the injective category of $q$ is equal to the index of $(X,τ)$ plus $2$.

I just wrote a C function with two uninitialized variables whose values are defined by non-trivial logic that follows. Justified, yet I feel like I committed a crime. But that's how rare uninitialized variables should be in code.
Did my best to assure future readers of the code:
//x, y guaranteed to have intentional values before use
X x;
Y y;
PS: I'm aware of lambdas, structured bindings, std::pair 🙏🏽

A Graph-Theoretical Approach to Ring Analysis: An Exploration of Dominant Metric Dimension in Compressed Zero Divisor Graphs and Its Interplay with Ring Structures
Nasir Ali, Hafiz Muhammad Afzal Siddiqui, Muhammad Imran Qureshi
https://arxiv.org/abs/2405.04934

A Graph-Theoretical Approach to Ring Analysis: An Exploration of Dominant Metric Dimension in Compressed Zero Divisor Graphs and Its Interplay with Ring Structures
The paper systematically classifies rings based on the dominant metric dimensions (Ddim) of their associated CZDG, establishing consequential bounds for the Ddim of these compressed zero-divisor graphs. The authors investigate the interplay between the ring-theoretic properties of a ring ( R ) and associated CZDG. An undirected graph consisting of vertex set ( Z(R_E)\{[0]}\ =\ R_E\{[0],[1]}), where ( R_E=\{[x]:\ x\in R\} ) and ([x]=\{y\in R:\ \text{ann}(x)=\text{ann}(y)\} ) is called a compress…

This https://arxiv.org/abs/2404.13661 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Equational theory of ordinals with addition and left multiplication by $ω$
We show that the equational theory of the structure $\langle ω^ω: (x,y)\mapsto x+y, x\mapsto ωx \rangle $ is finitely axiomatizable and give a simple axiom schema when the domain is the set of transfinite ordinals. We give an algorithm that given a pair of terms $(E,F)$ decides in linear time with respect of their common length whether or not $E=F$ is a consequence of the axioms.

This https://arxiv.org/abs/2404.08470 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Gamma positivity of variations of $(α,t)$-Eulerian polynomials
In 1977 Carlitz and Scoville introduced the cycle $(α,t)$-Eulerian polynomials $A^{\mathrm{cyc}}_n(x,y, t\,|\,α)$ by enumerating permutations with respect to the number of excedances, drops, fixed points and cycles. In this paper, we introduce a nine-variable generalization of the Eulerian polynomials $A_n(u_1,u_2,u_3,u_4, f, g, t\,|\,α, β)$ in terms of descent based statistics of permutations and prove a connection formula between these two kinds of generalized Eulerian polynomia…

So if someone asks, or you're about to ask "Are you okay with X or Y?"
figure out if the question means
"do you think X is gross?"
or "do you think X is harmful?"
is the question about the emotional or about the rational?

This https://arxiv.org/abs/2308.14033 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the Impact of an IRS on the Out-of-Band Performance in Sub-6 GHz & mmWave Frequencies
Intelligent reflecting surfaces (IRSs) were introduced to enhance the performance of wireless communication systems. However, from a service provider's viewpoint, a concern with the use of an IRS is its effect on out-of-band (OOB) quality of service. Specifically, if two operators, say X and Y, provide services in a given geographical area using non-overlapping frequency bands, and if operator X uses an IRS to enhance the spectral efficiency (SE) of its users (UEs), does it degrade the performa…

Non-Isomorphic Groups with Isomorphic Power and Commuting Graphs
Surbhi, Geetha Venkataraman
https://arxiv.org/abs/2406.00710 https://

Non-Isomorphic Groups with Isomorphic Power and Commuting Graphs
The power graph of a group $G$ is a graph with vertex set $G$, in which two vertices are adjacent if one is some power of the other. In the commuting graph, with $G$ as the vertex set, two vertices are joined by an edge if they commute in $G$. The enhanced power graph of a group $G$ is a graph with vertex set $G$ and an edge joining two vertices $x$ and $y$ if $\langle x,y\rangle$ is cyclic. In this paper, we answer a question posed by P. J. Cameron, namely, if there exist groups $G$ and $H$ su…

This https://arxiv.org/abs/2403.12756 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hurwitz moduli varieties parameterizing pointed covers of an algebraic curve with a fixed monodromy group
Given a smooth, projective curve $Y$, a point $y_0 \in Y$, a positive integer $n$, and a transitive subgroup $G$ of the symmetric group $S_{d}$ we study smooth, proper families, parameterized by algebraic varieties, of pointed degree $d$ covers of $(Y,y_0)$, $(X,x_{0})\to (Y,y_0)$, branched in $n$ points of $Y\setminus y_{0}$, whose monodromy group equals $G$. We construct a Hurwitz space $H$, an algebraic variety whose points are in bijective correspondence with the equivalence classes of poin…

Growth and characterization of the La$_{3}$Ni$_{2}$O$_{7-\delta}$ thin films: dominant contribution of the $d_{x^{2}-y^{2}}$ orbital at ambient pressure
Yuecong Liu, Mengjun Ou, Haifeng Chu, Huan Yang, Qing Li, Yingjie Zhang, Hai-Hu Wen
https://arxiv.org/abs/2406.08789

Growth and characterization of the La$_{3}$Ni$_{2}$O$_{7-δ}$ thin films: dominant contribution of the $d_{x^{2}-y^{2}}$ orbital at ambient pressure
By using the pulsed-laser-ablation technique, we have successfully grown the La$_{3}$Ni$_{2}$O$_{7-δ}$ thin films with $c$-axis orientation perpendicular to the film surface. X-ray diffraction shows that the (00l) peaks can be well indexed to the La$_{3}$Ni$_{2}$O$_{7-δ}$ phase. Resistive measurements show that the samples can be tuned from weak insulating to metallic behavior through adjusting the growth conditions. Surprisingly, all curves of $ρ-T$ in the temperature region of 2$\sim$300~K…

Distribution spaces associated with elliptic operators
Iryna Chepurukhina, Aleksandr Murach
https://arxiv.org/abs/2406.08150 https://…

Distribution spaces associated with elliptic operators
We study complex distribution spaces given over a bounded Lipschitz domain $Ω$ and associated with an elliptic differential operator $A$ with $C^{\infty}$-coefficients on $\overlineΩ$. If $X$ and $Y$ are quasi-Banach distribution spaces over $Ω$, then the space $X(A,Y)$ under study consists of all distributions $u\in X$ such that $Au\in Y$ and is endowed with the graph quasi-norm. Assuming $X$ to be an arbitrary Besov space or Triebel--Lizorkin space over $Ω$, we find sufficient conditions …

Some extensions of the Brouwer fixed point theorem
Jiehua Mai, Enhui Shi, Kesong Yan, Fanping Zeng
https://arxiv.org/abs/2404.05248 https://

Some extensions of the Brouwer fixed point theorem
We study the existence of fixed points for continuous maps $f$ from an $n$-ball $X$ in $\mathbb R^n$ to $\mathbb R^n$ with $n\geq 1$. We show that $f$ has a fixed point if, for some absolute retract $Y\subset\partial X$, $f(Y)\subset X$ and $\partial X-Y$ is an $(f, X)$-blockading set. For $n\geq 2$, let $D$ be an $n$-ball in $X$ and $Y$ be an $(n-1)$-ball in $\partial X$. Relying on the result just mentioned, we show the existence of a fixed point of $f$, if $D$ and $Y$ are well placed and beh…

On the Problem of Separating Variables in Multivariate Polynomial Ideals
Manfred Buchacher, Manuel Kauers
https://arxiv.org/abs/2405.19223 https://<…

On the Problem of Separating Variables in Multivariate Polynomial Ideals
For a given ideal I in K[x_1,...,x_n,y_1,...,y_m] in a polynomial ring with n+m variables, we want to find all elements that can be written as f-g for some f in K[x_1,...,x_n] and some g in K[y_1,...,y_m], i.e., all elements of I that contain no term involving at the same time one of the x_1,...,x_n and one of the y_1,...,y_m. For principal ideals and for ideals of dimension zero, we give a algorithms that compute all these polynomials in a finite number of steps.

Inequalities for 1/(1-cos(x)) and its derivatives
Horst Alzer, Henrik L. Pedersen
https://arxiv.org/abs/2406.08932 https://arxiv.org/…

Inequalities for 1/(1-cos(x)) and its derivatives
We prove that the function $g(x)= 1 / \bigl( 1 - \cos(x) \bigr)$ is completely monotonic on $(0,π]$ and absolutely monotonic on $[π, 2π)$, and we determine the best possible bounds $λ_n$ and $μ_n$ such that the inequalities $$ λ_n \leq g^{(n)}(x)+g^{(n)}(y)-g^{(n)}(x+y) \quad (n \geq 0 \,\,\, \mbox{even}) $$ and $$ μ_n \leq g^{(n)}(x+y)-g^{(n)}(x)-g^{(n)}(y) \quad (n \geq 1 \,\,\, \mbox{odd}) $$ hold for all $x,y\in (0,π)$ with $x+y\leq π$.

LHAASO-KM2A detector simulation using Geant4
Zhen Cao, F. Aharonian, Q. An, Axikegu, Y. X. Bai, Y. W. Bao, D. Bastieri, X. J. Bi, Y. J. Bi, J. T. Cai, Q. Cao, W. Y. Cao, Zhe Cao, J. Chang, J. F. Chang, A. M. Chen, E. S. Chen, Liang Chen, Lin Chen, Long Chen, M. J. Chen, M. L. Chen, Q. H. Chen, S. H. Chen, S. Z. Chen, T. L. Chen, Y. Chen, N. Cheng, Y. D. Cheng, M. Y. Cui, S. W. Cui, X. H. Cui, Y. D. Cui, B. Z. Dai, H. L. Dai, Z. G. Dai, Danzengluobu, X. Q. Dong, K. K. Duan, J. H. Fan,…

LHAASO-KM2A detector simulation using Geant4
KM2A is one of the main sub-arrays of LHAASO, working on gamma ray astronomy and cosmic ray physics at energies above 10 TeV. Detector simulation is the important foundation for estimating detector performance and data analysis. It is a big challenge to simulate the KM2A detector in the framework of Geant4 due to the need to track numerous photons from a large number of detector units (>6000) with large altitude difference (30 m) and huge coverage (1.3 km^2). In this paper, the design of the KM…

Role of nonlocal heat transport on the laser ablative Rayleigh-Taylor instability
Z. H. Chen, X. H. Yang, G. B. Zhang, Y. Y. Ma, R. Yan, H. Xu, Z. M. Sheng, F. Q. Shao, J. Zhang
https://arxiv.org/abs/2404.08216

Role of nonlocal heat transport on the laser ablative Rayleigh-Taylor instability
Ablative Rayleigh-Taylor instability (ARTI) and nonlocal heat transport are the critical problems in laser-driven inertial confinement fusion, while their coupling with each other is not completely understood yet. Here the ARTI in the presence of nonlocal heat transport is studied self-consistently for the first time theoretically and by using radiation hydrodynamic simulations. It is found that the nonlocal heat flux generated by the hot electron transport tends to attenuate the growth of inst…

Distribution spaces associated with elliptic operators
Iryna Chepurukhina, Aleksandr Murach
https://arxiv.org/abs/2406.08150 https://…

Distribution spaces associated with elliptic operators
We study complex distribution spaces given over a bounded Lipschitz domain $Ω$ and associated with an elliptic differential operator $A$ with $C^{\infty}$-coefficients on $\overlineΩ$. If $X$ and $Y$ are quasi-Banach distribution spaces over $Ω$, then the space $X(A,Y)$ under study consists of all distributions $u\in X$ such that $Au\in Y$ and is endowed with the graph quasi-norm. Assuming $X$ to be an arbitrary Besov space or Triebel--Lizorkin space over $Ω$, we find sufficient conditions …

Non-trivial Integer Solutions of $x^r y^r=Dz^p$
Yasemin Kara, Diana Mocanu, Ekin \"Ozman
https://arxiv.org/abs/2404.07319 https://

Non-trivial Integer Solutions of $x^r+y^r=Dz^p$
In this paper, we use the modular method together with some standard conjectures to prove that infinitely many equations of the type $x^r+y^r=Dz^p$ do not have any non-trivial primitive integer solutions, where $r>5$ is a fixed prime, whenever $p$ is large enough.

This https://arxiv.org/abs/2205.06020 has been replaced.
link: https://scholar.google.com/scholar?q=a

Hurwitz moduli varieties parameterizing Galois covers of an algebraic curve
Given a smooth, projective curve $Y$, a finite group $G$ and a positive integer $n$ we study smooth, proper families $X\to Y\times S\to S$ of Galois covers of $Y$ with Galois group isomorphic to $G$ branched in $n$ points, parameterized by algebraic varieties $S$. When $G$ is with trivial center we prove that the Hurwitz space $H^G_n(Y)$ is a fine moduli variety for this moduli problem and construct explicitly the universal family. For arbitrary $G$ we prove that $H^G_n(Y)$ is a coarse moduli v…

A Graph-Theoretical Approach to Ring Analysis: An Exploration of Dominant Metric Dimension in Compressed Zero Divisor Graphs and Its Interplay with Ring Structures
Nasir Ali, Hafiz Muhammad Afzal Siddiqui, Muhammad Imran Qureshi
https://arxiv.org/abs/2405.04934

A Graph-Theoretical Approach to Ring Analysis: An Exploration of Dominant Metric Dimension in Compressed Zero Divisor Graphs and Its Interplay with Ring Structures
The paper systematically classifies rings based on the dominant metric dimensions (Ddim) of their associated CZDG, establishing consequential bounds for the Ddim of these compressed zero-divisor graphs. The authors investigate the interplay between the ring-theoretic properties of a ring ( R ) and associated CZDG. An undirected graph consisting of vertex set ( Z(R_E)\{[0]}\ =\ R_E\{[0],[1]}), where ( R_E=\{[x]:\ x\in R\} ) and ([x]=\{y\in R:\ \text{ann}(x)=\text{ann}(y)\} ) is called a compress…

Spatial resolution improvements with finer-pitch GEMs
K. J. Fl\"othner (CERN, Helmholtz-Institut f\"ur Strahlen- und Kernphysik, University of Bonn), L. Scharenberg (CERN), A. Brask (Aarhus University, CERN), F. Brunbauer (CERN), F. Garcia (Helsinki Institute of Physics), D. Janssens (CERN), B. Ketzer (Helmholtz-Institut f\"ur Strahlen- und Kernphysik, University of Bonn), M. Lisowska (CERN, Universit\'e Paris-Saclay), H. Muller (CERN, Physikalisches Institut, Univer…

Spatial resolution improvements with finer-pitch GEMs
Gas Electron Multipliers (GEMs) are used in many particle physics experiments, employing their 'standard' configuration with amplification holes of 140 um pitch in a hexagonal pattern. However, the collection of the charge cloud from the primary ionisation electrons from the drift region of the detector into the GEM holes affects the position information from the initial interacting particle. In this paper, the results from studies with a triple-GEM detector with an X-Y-strip readout anode are …

This https://arxiv.org/abs/2310.13750 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Optimal weighted Fourier restriction estimates for the sphere in 2D
We prove optimal Fourier restriction estimates for the unit sphere in two-dimensional Euclidean space. Our results yield weighted versions of the 2D Restriction Conjecture involving the weight functions $(1+|x|)^α(1+|y|)^β$ and $(1+|x|+|y|)^γ$ with $α,β,γ\geq 0$.

Unlabeled Compressed Sensing from Multiple Measurement Vectors
Mohamed Akrout, Amine Mezghani, Faouzi Bellili
https://arxiv.org/abs/2406.08290 https://

Unlabeled Compressed Sensing from Multiple Measurement Vectors
This paper introduces an algorithmic solution to a broader class of unlabeled sensing problems with multiple measurement vectors (MMV). The goal is to recover an unknown structured signal matrix, $\mathbf{X}$, from its noisy linear observation matrix, $\mathbf{Y}$, whose rows are further randomly shuffled by an unknown permutation matrix $\mathbf{U}$. A new Bayes-optimal unlabeled compressed sensing (UCS) recovery algorithm is developed from the bilinear approximate message passing (Bi-VAMP) fr…

On the independence number of sparser random Cayley graphs
Marcelo Campos, Gabriel Dahia, Jo\~ao Pedro Marciano
https://arxiv.org/abs/2406.09361 https://…

On the independence number of sparser random Cayley graphs
The Cayley sum graph $Γ_A$ of a set $A \subseteq \mathbb{Z}_n$ is defined to have vertex set $\mathbb{Z}_n$ and an edge between two distinct vertices $x, y \in \mathbb{Z}_n$ if $x + y \in A$. Green and Morris proved that if the set $A$ is a $p$-random subset of $\mathbb{Z}_n$ with $p = 1/2$, then the independence number of $Γ_A$ is asymptotically equal to $α(G(n, 1/2))$ with high probability. Our main theorem is the first extension of their result to $p = o(1)$: we show that, with high proba…

Minimal amenable subshift with full mean dimension
Zhengyu Yin, Zubiao Xiao
https://arxiv.org/abs/2406.08280 https://arxiv.org/pdf/24…

Minimal amenable subshift with full mean dimension
Let $G$ be an infinite countable amenable group and $P$ a polyhedron with topological dimension $dim(P)<\infty$. We construct a minimal subshift $(X,G)$ such that its mean topological dimension is equal to $dim(P)$. This result answers the question of D. Dou in \cite{DD}, moreover, it is also an extension of the work of L. Jin and Y. Qiao \cite{JQ} for $\mathbb{Z}$-action.

Non-trivial Integer Solutions of $x^r y^r=Dz^p$
Yasemin Kara, Diana Mocanu, Ekin \"Ozman
https://arxiv.org/abs/2404.07319 https://

Non-trivial Integer Solutions of $x^r+y^r=Dz^p$
In this paper, we use the modular method together with some standard conjectures to prove that infinitely many equations of the type $x^r+y^r=Dz^p$ do not have any non-trivial primitive integer solutions, where $r>5$ is a fixed prime, whenever $p$ is large enough.

This https://arxiv.org/abs/2205.06020 has been replaced.
link: https://scholar.google.com/scholar?q=a

Hurwitz moduli varieties parameterizing Galois covers of an algebraic curve
Given a smooth, projective curve $Y$, a finite group $G$ and a positive integer $n$ we study smooth, proper families $X\to Y\times S\to S$ of Galois covers of $Y$ with Galois group isomorphic to $G$ branched in $n$ points, parameterized by algebraic varieties $S$. When $G$ is with trivial center we prove that the Hurwitz space $H^G_n(Y)$ is a fine moduli variety for this moduli problem and construct explicitly the universal family. For arbitrary $G$ we prove that $H^G_n(Y)$ is a coarse moduli v…

This https://arxiv.org/abs/2310.13750 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Optimal weighted Fourier restriction estimates for the sphere in 2D
We prove optimal Fourier restriction estimates for the unit sphere in two-dimensional Euclidean space. Our results yield weighted versions of the 2D Restriction Conjecture involving the weight functions $(1+|x|)^α(1+|y|)^β$ and $(1+|x|+|y|)^γ$ with $α,β,γ\geq 0$.

On the independence number of sparser random Cayley graphs
Marcelo Campos, Gabriel Dahia, Jo\~ao Pedro Marciano
https://arxiv.org/abs/2406.09361 https://…

On the independence number of sparser random Cayley graphs
The Cayley sum graph $Γ_A$ of a set $A \subseteq \mathbb{Z}_n$ is defined to have vertex set $\mathbb{Z}_n$ and an edge between two distinct vertices $x, y \in \mathbb{Z}_n$ if $x + y \in A$. Green and Morris proved that if the set $A$ is a $p$-random subset of $\mathbb{Z}_n$ with $p = 1/2$, then the independence number of $Γ_A$ is asymptotically equal to $α(G(n, 1/2))$ with high probability. Our main theorem is the first extension of their result to $p = o(1)$: we show that, with high proba…

Discovery of a shock-compressed magnetic field in the north-western rim of the young supernova remnant RX J1713.7-3946 with X-ray polarimetry
Riccardo Ferrazzoli, Dmitry Prokhorov, Niccol\`o Bucciantini, Patrick Slane, Jacco Vink, Martina Cardillo, Yi-Jung Yang, Stefano Silvestri, Ping Zhou, Enrico Costa, Nicola Omodei, C. -Y. Ng, Paolo Soffitta, Martin C. Weisskopf, Luca Baldini, Alessandro Di Marco, Victor Doroshenko, Jeremy Heyl, Philip Kaaret, Dawoon E. Kim, Fr\'ed\'eric Ma…

Measurement of Electron Antineutrino Oscillation Amplitude and Frequency via Neutron Capture on Hydrogen at Daya Bay
Daya Bay collaboration, F. P. An, W. D. Bai, A. B. Balantekin, M. Bishai, S. Blyth, G. F. Cao, J. Cao, J. F. Chang, Y. Chang, H. S. Chen, H. Y. Chen, S. M. Chen, Y. Chen, Y. X. Chen, Z. Y. Chen, J. Cheng, J. Cheng, Y. -C. Cheng, Z. K. Cheng, J. J. Cherwinka, M. C. Chu, J. P. Cummings, O. Dalager, F. S. Deng, X. Y. Ding, Y. Y. Ding, M. V. Diwan, T. Dohnal, D. Dolzhikov, J…

Measurement of Electron Antineutrino Oscillation Amplitude and Frequency via Neutron Capture on Hydrogen at Daya Bay
This Letter reports the first measurement of the oscillation amplitude and frequency of reactor antineutrinos at Daya Bay via neutron capture on hydrogen using 1958 days of data. With over 3.6 million signal candidates, an optimized candidate selection, improved treatment of backgrounds and efficiencies, refined energy calibration, and an energy response model for the capture-on-hydrogen sensitive region, the relative $\overlineν_{e}$ rates and energy spectra variation among the near and far d…

Pointwise two-point function estimates and a non-pertubative proof of mean-field critical behaviour for long-range percolation
Tom Hutchcroft
https://arxiv.org/abs/2404.07276

Pointwise two-point function estimates and a non-pertubative proof of mean-field critical behaviour for long-range percolation
In long-range percolation on $\mathbb{Z}^d$, we connect each pair of distinct points $x$ and $y$ by an edge independently at random with probability $1-\exp(-β\|x-y\|^{-d-α})$, where $α>0$ is fixed and $β\geq 0$ is a parameter. In a previous paper, we proved that if $0<α

This https://arxiv.org/abs/2403.17955 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An Effective Lower Bound on the Integer Cube Sum
Let $f(x, y) \in \mathbb{Z}[x, y]$ be a cubic form with non-zero discriminant, and for each integer $m \in \mathbb{Z}$, let, $N_{f}(m)=\#\left\{(x, y) \in \mathbb{Z}^{2}: f(x, y)=m\right\} $. In 1983, Silverman proved that $N_{f}(m)>Ω\left((\log |m|)^{3 / 5}\right)$ when $f(x, y)=x^{3}+y^{3}$. In this paper, we obtain an explicit bound for $N_f(m)$, namely, showing that $N_{f}(m)>13\times 10^{-6}(\log |m|)^{11/13}$ (holds for infinitely many integers m), when $f(x, y)=x^{3}…

This https://arxiv.org/abs/2301.00206 has been replaced.
link: https://scholar.google.com/scholar?q=a

Melnikov's persistence for completely degenerate Hamiltonian systems with high co-dimension
In this paper, we study the Melnikov's persistence about lower-dimensional invariant tori for completely degenerate Hamiltonian systems with the following Hamiltonian \begin{equation*} H(x,y,u,v)=h(y)+g(u,v)+\varepsilon P(x,y,u,v),~~~(x,y,u,v)\in \mathbb{T}^n\times{G}\times \mathbb{R}^d\times \mathbb{R}^d, \end{equation*} where $n\geq2$ and $d\geq1$ are positive integers, $g=o(|u|^2+|v|^2)$ admits complete degeneracy and certain transversality, and $\varepsilon P$ is the sma…

Existence results for problems involving non local operator with an asymmetric weight and with a critical nonlinearity
Sana Benhafsia (LAMA), Rejeb Hadiji (LAMA)
https://arxiv.org/abs/2404.07531

Existence results for problems involving non local operator with an asymmetric weight and with a critical nonlinearity
Recently, a great attention has been focused on the study of fractional and non-local operators of elliptic type, both for the pure mathematical research and in view of concrete real-world applications. We consider the following non local problem on $\mathbb{H}_0^s(Ω) \subset L^{q_s}(Ω)$, with $q_s :=\frac{2n}{n-2s}$, $s\in ]0, 1[$ and $n\geq 3$ \begin{equation}\int_{\mathbb{R}^n}p(x) \bigg(\int_{\mathbb{R}^n}\frac{|u(x)-u(y)|^2}{|x-y|^{n+2s}}dy\bigg)dx-λ\int_Ω|u(x)…

Well-covered Unit Graphs of Finite Rings
Shahin Rahimi, Ashkan Nikseresht
https://arxiv.org/abs/2404.07189 https://arxiv.org/pdf/2404…

Well-covered Unit Graphs of Finite Rings
Let $R$ be a finite ring with identity. The unit graph (unitary Cayley graph) of $R$ is the graph with vertex set $R$, where two distinct vertices $x$ and $y$ are adjacent exactly whenever $x+y$ is a unit in $R$ ($x-y$ is a unit in $R$). Here, we study independent sets of unit graphs of matrix rings over finite fields and use them to characterize all finite rings for which the unit graph is well-covered or Cohen-Macaulay. Moreover, we show that the unit graph of $R$ is well-covered if and only …

This https://arxiv.org/abs/2210.11225 has been replaced.
link: https://scholar.google.com/scholar?q=a

Dirichlet Heat kernel estimates for a large class of anisotropic Markov processes
Let $Z=(Z^{1}, \ldots, Z^{d})$ be the d-dimensional Lévy {process} where {$Z^i$'s} are independent 1-dimensional Lévy {processes} with identical jumping kernel $ ν^1(r) =r^{-1}ϕ(r)^{-1}$. Here $ϕ$ is {an} increasing function with weakly scaling condition of order $\underline α, \overline α\in (0, 2)$. We consider a symmetric function $J(x,y)$ comparable to \begin{align*} \begin{cases} ν^1(|x^i - y^i|)\qquad&\text{ if $x^i \ne y^i$ for some $i$ and $x^j = y^j$ for all $j \ne …

On the weighted contraharmonic means
Ali Zamani
https://arxiv.org/abs/2406.08986 https://arxiv.org/pdf/2406.08986

On the weighted contraharmonic means
Let $\mathscr{A}$ be a unital $C^*$-algebra with unit $e$ and let $ν\in(0, 1)$. We introduce the concept of the $ν$-weighted contraharmonic of two positive definite elements $a$ and $b$ of $\mathscr{A}$ by \begin{align*} {C}_ν(a, b):= (1-ν)ν^{-1}b + ν(1-ν)^{-1}a - \left((1-ν)a^{-1}+νb^{-1}\right)^{-1}. \end{align*} We show that \begin{align*} {C}_ν(a, b)= \displaystyle{\max_{x+y=e}}\left\{(1-ν)^{-1}\left(νa - x^*ax\right) + ν^{-1}\left((1-ν)b - y^*by\right)\right\}, \end{align*} a…

This https://arxiv.org/abs/2211.02908 has been replaced.
link: https://scholar.google.com/scholar?q=a

Paucity phenomena for polynomial products
Let $P(x)\in \mathbb{Z}[x]$ be a polynomial with at least two distinct complex roots. We prove that the number of solutions $(x_1, \dots, x_k, y_1, \dots, y_k)\in [N]^{2k}$ to the equation \[ \prod_{1\le i \le k} P(x_i) = \prod_{1\le j \le k} P(y_j)\neq 0 \] (for any $k\ge 1$) is asymptotically $k!N^{k}$ as $N\to +\infty$. This solves a question first proposed and studied by Najnudel. The result can also be interpreted as saying that all even moments of random partial sums $\frac{1}{\sqrt{N}}…

Recovery of the X-ray polarization of Swift J1727.8$-$1613 after the soft to hard spectral transition
J. Podgorn\'y, J. Svoboda, M. Dov\v{c}iak, A. Veledina, J. Poutanen, P. Kaaret, S. Bianchi, A. Ingram, F. Capitanio, S. R. Datta, E. Egron, H. Krawczynski, G. Matt, F. Muleri, P. -O. Petrucci, T. D. Russell, J. F. Steiner, N. Bollemeijer, M. Brigitte, R. Emami, J. A. Garc\'ia, K. Hu, M. N. Iacolina, V. Kravtsov, L. Marra, G. Mastroserio, T. Mu\~noz-Darias, E. Nathan, M. Negro, …

Recovery of the X-ray polarization of Swift J1727.8$-$1613 after the soft to hard spectral transition
We report on the detection of X-ray polarization in the black-hole X-ray binary Swift J1727.8$-$1613 during its dim hard spectral state by the Imaging X-ray Polarimetry Explorer (IXPE). This is the first detection of the X-ray polarization at the transition from the soft to the hard state in an X-ray binary. We find a 2$-$8 keV averaged polarization degree of (3.3 ${\pm}$ 0.4) % and the corresponding polarization angle of 3° ${\pm}$ 4°, which matches with the polarization detected during the …

Probing Dark Matter Particles from Evaporating Primordial Black Holes via Electron Scattering in the CDEX-10 Experiment
Z. H. Zhang, L. T. Yang, Q. Yue, K. J. Kang, Y. J. Li, H. P. An, Greeshma C., J. P. Chang, Y. H. Chen, J. P. Cheng, W. H. Dai, Z. Deng, C. H. Fang, X. P. Geng, H. Gong, Q. J. Guo, T. Guo, X. Y. Guo, L. He, S. M. He, J. W. Hu, H. X. Huang, T. C. Huang, L. Jiang, S. Karmakar, H. B. Li, H. Y. Li, J. M. Li, J. Li, Q. Y. Li, R. M. J. Li, X. Q. Li, Y. L. Li, Y. F. Liang, B.…

Probing Dark Matter Particles from Evaporating Primordial Black Holes via Electron Scattering in the CDEX-10 Experiment
Dark matter (DM) is a major constituent of the Universe. However, no definite evidence of DM particles (denoted as ``$χ$") has been found in DM direct detection (DD) experiments to date. There is a novel concept that detecting $χ$ from evaporating primordial black holes (PBHs). We search for $χ$ emitted from PBHs by investigating their interaction with target electrons. The examined PBH masses range from 1$\times$10$^{15}$ to 7$\times$10$^{16}$ g under the current limits of PBH abundance $f_…

Nearby cycles at infinity as a triangulated functor
Khoa Bang Pham
https://arxiv.org/abs/2404.07910 https://arxiv.org/pdf/2404.07910<…

Nearby cycles at infinity as a triangulated functor
Let $k$ be a field and $g \colon Y \longrightarrow X$, $f \colon X \longrightarrow \mathbb{A}_k^1$ be morphisms of quasi-projective $k$-varieties. In his thesis, Ayoub developed the theory of motivic nearby cycles functors $Ψ_{f},Ψ_{f \circ g}$. They are equipped with several base change morphisms such as $μ_g \colon g_{σ!}Ψ_{f \circ g} \longrightarrow Ψ_f g_{η!}$, $ν_g\colon Ψ_{f \circ g}g_η^! \longrightarrow g_σ^!Ψ_f$, which are isomorphisms if $g$ is projective and smooth, respec…

Good bounds for sets lacking skew corners
Luka Mili\'cevi\'c
https://arxiv.org/abs/2404.07180 https://arxiv.org/pdf/2404.0718…

Good bounds for sets lacking skew corners
A skew corner is a triple of points in $\mathbb{Z} \times \mathbb{Z}$ of the form $(x,y), (x, y + a)$ and $(x + a, y')$. Pratt posed the following question: how large can a set $A \subseteq [n] \times [n]$ be, provided it contains no non-trivial skew corner (i.e. one for which $a\not=0$)? We prove that $|A| \leq \exp(- c\log^c n) n^2$, for an absolute constant $c > 0$, which, along with a construction of Beker, essentially resolves Pratt's question. Our argument is represents a two-…

A logarithm law for nonautonomous systems fastly converging to equilibrium and mean field coupled systems
Stefano Galatolo, Davide Faranda
https://arxiv.org/abs/2404.03241

A logarithm law for nonautonomous systems fastly converging to equilibrium and mean field coupled systems
We prove that if a nonautonomous system has in a certain sense a fast convergence to equilibrium (faster than any power law behavior) then the time $τ_{r}(x,y)$ needed for a typical point $x$ to enter for the first time in a ball $B(y,r)$ centered in $y$, with small radius \ $r $ scales as the local dimension of the equilibrium measure \ $μ$ at $y$, i.e. $$ \underset{r\rightarrow 0}{\lim }\frac{\log τ_{r}(x,y)}{-\log r}% =d_{μ}(y).$$ We then apply the general result to concrete systems of…

On the weighted contraharmonic means
Ali Zamani
https://arxiv.org/abs/2406.08986 https://arxiv.org/pdf/2406.08986

On the weighted contraharmonic means
Let $\mathscr{A}$ be a unital $C^*$-algebra with unit $e$ and let $ν\in(0, 1)$. We introduce the concept of the $ν$-weighted contraharmonic of two positive definite elements $a$ and $b$ of $\mathscr{A}$ by \begin{align*} {C}_ν(a, b):= (1-ν)ν^{-1}b + ν(1-ν)^{-1}a - \left((1-ν)a^{-1}+νb^{-1}\right)^{-1}. \end{align*} We show that \begin{align*} {C}_ν(a, b)= \displaystyle{\max_{x+y=e}}\left\{(1-ν)^{-1}\left(νa - x^*ax\right) + ν^{-1}\left((1-ν)b - y^*by\right)\right\}, \end{align*} a…

An Effective Lower Bound on the Integer Cube Sum
Saunak Bhattacharjee
https://arxiv.org/abs/2403.17955 https://arxiv.org/pdf/2403.179…

An Effective Lower Bound on the Integer Cube Sum
Let $f(x, y) \in \mathbb{Z}[x, y]$ be a cubic form with non-zero discriminant, and for each integer $m \in \mathbb{Z}$, let, $N_{f}(m)=\#\left\{(x, y) \in \mathbb{Z}^{2}: f(x, y)=m\right\} $. In 1983, Silverman proved that $N_{f}(m)>Ω\left((\log |m|)^{3 / 5}\right)$ when $f(x, y)=x^{3}+y^{3}$. In this paper, we obtain an explicit bound for $N_f(m)$, namely, showing that $N_{f}(m)>13\times 10^{-6}(\log |m|)^{11/13}$ (holds for infinitely many integers m), when $f(x, y)=x^{3}…

Nearby cycles at infinity as a triangulated functor
Khoa Bang Pham
https://arxiv.org/abs/2404.07910 https://arxiv.org/pdf/2404.07910<…

Nearby cycles at infinity as a triangulated functor
Let $k$ be a field and $g \colon Y \longrightarrow X$, $f \colon X \longrightarrow \mathbb{A}_k^1$ be morphisms of quasi-projective $k$-varieties. In his thesis, Ayoub developed the theory of motivic nearby cycles functors $Ψ_{f},Ψ_{f \circ g}$. They are equipped with several base change morphisms such as $μ_g \colon g_{σ!}Ψ_{f \circ g} \longrightarrow Ψ_f g_{η!}$, $ν_g\colon Ψ_{f \circ g}g_η^! \longrightarrow g_σ^!Ψ_f$, which are isomorphisms if $g$ is projective and smooth, respec…

On combinatorial structure and algebraic characterizations of distance-regular digraphs
Giusy Monzillo, Safet Peni\'c
https://arxiv.org/abs/2404.03910 …

On combinatorial structure and algebraic characterizations of distance-regular digraphs
Let $Γ=Γ(A)$ denote a simple strongly connected digraph with vertex set $X$, diameter $D$, and let $\{A_0,A:=A_1,A_2,\ldots,A_D\}$ denote the set of distance-$i$ matrices of $Γ$. Let $\{R_i\}_{i=0}^D$ denote a partition of $X\times X$, where $R_i=\{(x,y)\in X\times X\mid (A_i)_{xy}=1\}$ $(0\le i\le D)$. The digraph $Γ$ is distance-regular if and only if $(X,\{R_i\}_{i=0}^D)$ is a commutative association scheme. In this paper, we describe the combinatorial structure of $Γ$ in the sense of e…

Stability for a family of planar systems with nilpotent critical points
Ziwei Zhuang, Changjian Liu
https://arxiv.org/abs/2406.02226 https://

Stability for a family of planar systems with nilpotent critical points
Consider a family of planar polynomial systems $\dot x = y^{2l-1} - x^{2k+1}, \dot y =-x +m y^{2s+1},$ where $l,k,s\in\mathbb{N^*},$ $2\le l \le 2s$ and $m\in\mathbb{R}.$ We study the center-focus problem on its origin which is a monodromic nilpotent critical point. By directly calculating the generalized Lyapunov constants, we find that the origin is always a focus and we complete the classification of its stability. This includes the most difficult case: $s=kl$ and $m=(2k+1)!!/(2kl+1)!_{(2l)}…

On the solvability of systems of equations revisited
Thang Pham, Steven Senger, Nguyen Trung-Tuan, Nguyen Duc-Thang, Le Anh Vinh
https://arxiv.org/abs/2405.03086

On the solvability of systems of equations revisited
In this paper, we introduce a new and direct approach to study the solvability of systems of equations generated by bilinear forms. More precisely, let $B (\cdot, \cdot)$ be a non-degenerate bilinear form and $E$ be a set in $\mathbb{F}_q^2$. We prove that if $|E|\gg q^{5/3}$ then the number of triples $(B(x, y), B(y, z), B(z, x))$ with $x, y, z\in E$ is at least $cq^3$ for some positive constant $c$. This significantly improves a result due to the fifth listed author (2009).

On the solvability of systems of equations revisited
Thang Pham, Steven Senger, Nguyen Trung-Tuan, Nguyen Duc-Thang, Le Anh Vinh
https://arxiv.org/abs/2405.03086

On the solvability of systems of equations revisited
In this paper, we introduce a new and direct approach to study the solvability of systems of equations generated by bilinear forms. More precisely, let $B (\cdot, \cdot)$ be a non-degenerate bilinear form and $E$ be a set in $\mathbb{F}_q^2$. We prove that if $|E|\gg q^{5/3}$ then the number of triples $(B(x, y), B(y, z), B(z, x))$ with $x, y, z\in E$ is at least $cq^3$ for some positive constant $c$. This significantly improves a result due to the fifth listed author (2009).

Clusters, toric ranks, and 2-ranks of hyperelliptic curves in the wild case
Leonardo Fiore, Jeffrey Yelton
https://arxiv.org/abs/2403.19700 https://…

Clusters, toric ranks, and 2-ranks of hyperelliptic curves in the wild case
Given a Galois cover $Y \to X$ of smooth projective geometrically connected curves over a complete discrete valuation field $K$ with algebraically closed residue field, we define a semistable model of $Y$ over the ring of integers of a finite extension of $K$ which we call the \emph{relatively stable model} $\mathcal{Y}^{\mathrm{rst}}$ of $Y$, and we discuss its properties, eventually focusing on the case when $Y : y^2 = f(x)$ is a hyperelliptic curve viewed as a degree-$2$ cover of the project…

Codes with Hierarchical Locality on Artin-Schreier Surfaces
Jennifer Berg, Beth Malmskog, Mckenzie West
https://arxiv.org/abs/2405.19533 https://

Codes with Hierarchical Locality on Artin-Schreier Surfaces
In this article, we construct codes with hierarchical locality using natural geometric structures in Artin-Schreier surfaces of the form $y^p-y=f(x,z)$. Our main theorem describes the codes, their hierarchical structure and recovery algorithms, and gives parameters. We also develop a family of examples using codes defined over $\mathbb{F}_{p^2}$ on the surface $y^p-y=x^{p+1}z^2+x^2z^{p+1}$. We count the $\mathbb{F}_{p^2}$-rational points on the surface, a topic of more general number theoretic …

This https://arxiv.org/abs/2111.09777 has been replaced.
link: https://scholar.google.com/scholar?q=a

The $a$-numbers of non-hyperelliptic curves of genus 3 with cyclic automorphism group of order 6
In this paper, we study non-hyperelliptic curves of genus $3$ with cyclic automorphism group of order $6$. Over an algebraically closed field $K$ of characteristic $\neq 2,3$, such curves are written as plane quartics $C_r: x^3 z + y^4 + r y^2 z^2 + z^4 = 0$ with one parameter $r$. As the first main theorem, we show that $r\neq 0,\pm 2$ and give a necessary and sufficient condition with respect to $r$ and $r'$ such that $C_r \cong C_{r'}$. By describing the Hasse-Witt matrix of $C_r$ in terms o…

This https://arxiv.org/abs/2403.00407 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Configurations in the Euclidean space related to the 3D genome reconstruction problem from partially phased data
A motivation for studying the following problems comes from applications to Biology; see \cite{cifuentes20233d}. In the $3$-dimensional Euclidean space ${\bf{E}}^3$, fix six pairwise distinct points \begin{equation*} \label{eqA} \begin{array}{ccc} A=(a_1,a_2,a_3), & B=(b_1,b_2,b_3), & C=(c_1,c_2,c_3), \\ D=(d_1,d_2,d_3), & E=(e_1,e_2,e_3), & F=(f_1,f_2,f_3) \end{array} \end{equation*} together with two further points $X^*=(x_1^*,x_2^*,x_3^*)$ and $Y^*=(y_1^*,y_2^*,y_3^*)$ in $\mathbf{E}^3$. We …

On split families of Thue equations with linear recurrence sequences as factors
Tobias Hilgart
https://arxiv.org/abs/2406.01111 https://

On split families of Thue equations with linear recurrence sequences as factors
We consider a parametrised family of Thue equations, \[ (x-G_1(n)\, y) \cdots (x-G_d(n)\, y) - y^d = \pm 1, \] which was first considered by Thomas to have an explicit set of solutions for parameters $n$ larger than some effectively computable constant. In the case where the parameter functions are polynomials belonging to an explicitly described family, this is known to be true. We consider other parameter functions, namely linear recurrence sequences, for which it is not obvious that a si…

Zero-one Grothendieck Polynomials
Yiming Chen, Neil J. Y. Fan, Zelin Ye
https://arxiv.org/abs/2405.05483 https://arxiv.org/pdf/2405.0…

Zero-one Grothendieck Polynomials
Fink, Mészáros and St.Dizier showed that the Schubert polynomial $\mathfrak{S}_w(x)$ is zero-one if and only if $w$ avoids twelve permutation patterns. In this paper, we prove that the Grothendieck polynomial $\mathfrak{G}_w(x)$ is zero-one, i.e., with coefficients either 0 or $\pm$1, if and only if $w$ avoids six patterns. As applications, we show that zero-one homogeneous Grothendieck polynomials are Lorentzian, partially confirming three conjectures of Huh, Matherne, Mészáros and St.Dizi…

This https://arxiv.org/abs/2404.09575 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Binary quadratic forms with the same value set
Given a binary quadratic form $F \in \mathbb{Z}[X, Y]$, we define its value set $F(\mathbb{Z}^2)$ to be $\{F(x, y) : (x, y) \in \mathbb{Z}^2\}$. If $F$ and $G$ are two binary quadratic forms with integer coefficients, we give necessary and sufficient conditions on $F$ and $G$ for $F(\mathbb{Z}^2) = G(\mathbb{Z}^2)$.