Tootfinder

The Hebrew word for giving, natan (נתנ), is a palindrome, which reveals a deep truth about the reciprocal dynamic of giving: When one gives, they also receive in return.
In a recent study, researchers discovered that those who spent more of their income on others rather than themselves enjoyed significantly greater and longer lasting happiness. In fact, as little as a five-dollar gift was enough to produce measurable increases in one’s happiness. Overall, the self-reported happiness of…

Converse Barrier Certificates for Finite-time Safety Verification of Continuous-time Perturbed Deterministic Systems
Yonghan Li, Chenyu Wu, Taoran Wu, Shijie Wang, Bai Xue
https://arxiv.org/abs/2402.17167

Converse Barrier Certificates for Finite-time Safety Verification of Continuous-time Perturbed Deterministic Systems
In this paper, we investigate the problem of verifying the finite-time safety of continuous-time perturbed deterministic systems represented by ordinary differential equations in the presence of measurable disturbances. Given a finite time horizon, if the system is safe, it, starting from a compact initial set, will remain within an open and bounded safe region throughout the specified time horizon, regardless of the disturbances. The main contribution of this work is to uncover that there exis…

This https://arxiv.org/abs/2304.12316 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Constraining the onset density for the QCD phase transition with the neutrino signal from core-collapse supernovae
The occurrence of a first-order hadron-quark matter phase transition at high baryon densities is investigated in astrophysical simulations of core-collapse supernovae, to decipher yet incompletely understood properties of the dense matter equation of state (EOS) using neutrinos from such cosmic events. It is found that the emission of a nonstandard second neutrino burst, dominated by electron antineutrinos, is not only a measurable signal for the appearance of deconfined quark matter but also r…

Convexity of near-optimal orthogonal-pair-free sets on the unit sphere
Apurva Mudgal
https://arxiv.org/abs/2403.18404 https://arxiv.o…

Convexity of near-optimal orthogonal-pair-free sets on the unit sphere
A subset $S$ of the unit sphere $\mathbb{S}^2$ is called orthogonal-pair-free if and only if there do not exist two distinct points $u, v \in S$ at distance $\fracπ{2}$ from each other. Witsenhausen \cite{witsenhausen} asked the following question: {\it What is the least upper bound $α_3$ on the Lesbegue measure of any measurable orthogonal-pair-free subset of $\mathbb{S}^2$?} We prove the following result in this paper: Let $\mathcal{A}$ be the collection of all orthogonal-pair-free sets $S$…

Long Covid stats & me
Considering whether I would still say my own activities were limited "a lot"... I think it depends on what you're looking at.
The main specific thing I notice still not being able to do is particular bike rides, because the mileage I'm capable of dropped precipitously & is coming back very slowly.
But that very measurable limitation is probably indicative of stamina overall. So in that sense, yeah, "a lot", even though I can do most things to _some_ extent again now.

Critical Slowing Down in a Real Physical System
Mathias Marconi, Karin Alfaro-Bittner, Lucas Sarrazin, Massimo Giudici, Jorge R. Tredicce
https://arxiv.org/abs/2403.17973

Critical Slowing Down in a Real Physical System
The behavior of a dynamical system can exhibit abrupt changes when it crosses a tipping point. To prevent catastrophic events, it is useful to analyze indicators of the incoming bifurcation, as the divergence of the relaxation time of the system when approaching the critical point. However, this phenomenon, called critical slowing down (CSD), is hardly measurable in real physical systems. In this paper we provide experimental evidence of CSD in a laser system crossing the emission threshold and…

Fundamental solutions to Kolmogorov-Fokker-Planck equations with rough coefficients: existence, uniqueness, upper estimates
Pascal Auscher (LMO), Cyril Imbert (DMA), Lukas Niebel
https://arxiv.org/abs/2403.17468

Fundamental solutions to Kolmogorov-Fokker-Planck equations with rough coefficients: existence, uniqueness, upper estimates
We show the existence and uniqueness of fundamental solution operators to Kolmo\-gorov-Fokker-Planck equations with rough (measurable) coefficients and local or integral diffusion on finite and infinite time strips. In the local case, that is to say when the diffusion operator is of differential type, we prove $Ł^2$ decay using Davies' method and the conservation property. We also prove that the existence of a generalized fundamental solution with the expected pointwise Gaussian upper bound is…

Renormalization of the primordial inflationary power spectra
Silvia Pla, Ben A. Stefanek
https://arxiv.org/abs/2402.14910 https://arx…

Renormalization of the primordial inflationary power spectra
It has been suggested that the effects of renormalization significantly reduce the amplitude of the inflationary spectra at scales measurable in the cosmic microwave background. Via a gauge-invariant analysis, we compute the renormalized scalar and tensor power spectra and follow their evolution in an inflating universe that undergoes a transition to an FRW phase with a growing horizon. For perturbations originating from Minkowski vacuum fluctuations, we show that the standard prediction for th…

Ascent and Descent of Weighted Composition Operators on Lorentz spaces
Gopal Datt, Daljeet Singh Bajaj
https://arxiv.org/abs/2404.16491 https://

Ascent and Descent of Weighted Composition Operators on Lorentz spaces
The aim of this article is to detect the ascent and descent of weighted composition operators on Lorentz spaces. We investigate the conditions on the measurable transformation $T$ and the complex-valued measurable function $u$ defined on measure space $(X, \mathcal{A}, μ)$ that cause the weighted composition operators on Lorentz space $L(p, q)$, $1 < p \leq \infty, 1 \leq q \leq \infty$ to have finite or infinite ascent (descent). We also give a number of examples in support of our findings.

This https://arxiv.org/abs/2304.07214 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Cofinal types of ultrafilters over measurable cardinals
We develop the theory of cofinal types of ultrafilters over measurable cardinals and establish its connections to Galvin's property. We generalize fundamental results from the countable to the uncountable, but often in surprisingly strengthened forms, and present models with varying structures of the cofinal types of ultrafilters over measurable cardinals.

Weak convergence of probability measures on hyperspaces with the upper Fell-topology
Dietmar Ferger
https://arxiv.org/abs/2403.18798 https://

Weak convergence of probability measures on hyperspaces with the upper Fell-topology
Let E be a locally compact second countable Hausdorff space and F the pertaining family of all closed sets. We endow F respectively with the Fell-topology, the upper Fell topology or the upper Vietoris-topology and investigate weak convergence of probability measures on the corresponding hyperspaces with a focus on the upper Fell topology. The results can be transferred to distributional convergence of random closed sets in E with applications to the asymptotic behavior of measurable selection.

did you know: maximum-sized USB HS BULK packets where the payload is all-ones are about 16% longer to transmit than the ones where the payload is all-zeroes or random?
this is easily measurable using the #GlasgowInterfaceExplorer with a slightly modified benchmark applet:
I: g.applet.internal.benchmark: mode sink-zeroes: 42.84 MiB/s (342.70 Mb/s)
I: g.applet.int…

Measurements of low energy nuclear recoil quenching factors for Na and I recoils in the NaI(Tl) scintillator
S. H. Lee, H. W. Joo, H. J. Kim, K. W. Kim, S. K. Kim, Y. D. Kim, Y. J. Ko, H. S. Lee, J. Y. Lee, H. S. Park, Y. S. Yoon
https://arxiv.org/abs/2402.15122

Measurements of low energy nuclear recoil quenching factors for Na and I recoils in the NaI(Tl) scintillator
Elastic scattering off nuclei in target detectors, involving interactions with dark matter and coherent elastic neutrino nuclear recoil (CE$ν$NS), results in the deposition of low energy within the nuclei, dissipating rapidly through a combination of heat and ionization. The primary energy loss mechanism for nuclear recoil is heat, leading to consistently smaller measurable scintillation signals compared to electron recoils of the same energy. The nuclear recoil quenching factor (QF), represen…

This https://arxiv.org/abs/2311.05611 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Landau Damping in an Electron Gas
Material science methods aim at developing efficient computational schemes for describing complex many-body effects and how they are revealed in experimentally measurable properties. Bethe-Salpeter equation in the self-consistent Hartree-Fock basis is often used for this purpose, and in this paper we employ the real-frequency diagrammatic Monte Carlo framework for solving the ladder-type Bethe-Salpeter equation for the 3-point vertex function (and, ultimately, for the system's polarization) to …

Weak solutions to Kolmogorov-Fokker-Planck equations: Regularity, existence and uniqueness
Pascal Auscher (LMO), Cyril Imbert (DMA), Lukas Niebel
https://arxiv.org/abs/2403.17464 …

Weak solutions to Kolmogorov-Fokker-Planck equations: Regularity, existence and uniqueness
In this article, we establish embeddings à la Lions and transfer of regularity à la Bouchut for a large scale of kinetic spaces. We use them to identify a notion of weak solutions to Kolmogorov-Fokker-Planck equations with (local or integral) diffusion and rough (measurable) coefficients under minimal requirements. We prove their existence and uniqueness for a large class of source terms, first in full space for the time, position and velocity variables and then for the kinetic Cauchy problem…

This https://arxiv.org/abs/2212.02371 has been replaced.
link: https://scholar.google.com/scholar?q=a

Integration in Cones
Measurable cones, with linear and measurable functions as morphisms, are a model of intuitionistic linear logic and of call-by-name probabilistic PCF which accommodates ``continuous data types'' such as the real line. So far however, they lacked a major feature to make them a model of more general probabilistic programming languages (notably call-by-value and call-by-push-value languages): a theory of integration for functions whose codomain is a cone, which is the key ingredient for interpreti…

This https://arxiv.org/abs/2312.15496 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

A Simple Bias Reduction for Chatterjee's Correlation
Chatterjee's rank correlation coefficient $ξ_n$ is an empirical index for detecting functional dependencies between two variables $X$ and $Y$. It is an estimator for a theoretical quantity $ξ$ that is zero for independence and one if $Y$ is a measurable function of $X$. Based on an equivalent characterization of sorted numbers, we derive an upper bound for $ξ_n$ and suggest a simple normalization aimed at reducing its bias for small sample size $n$. In Monte Carlo simulations of various case…

Decoupling parameter variation from noise: Biquadratic Lyapunov forms in data-driven LPV control
Chris Verhoek, Jaap Eising, Florian D\"orfler, Roland T\'oth
https://arxiv.org/abs/2403.16565

Decoupling parameter variation from noise: Biquadratic Lyapunov forms in data-driven LPV control
A promising step from linear towards nonlinear data-driven control is via the design of controllers for linear parameter-varying (LPV) systems, which are linear systems whose parameters are varying along a measurable scheduling signal. However, the interplay between uncertainty arising from corrupted data and the parameter-varying nature of these systems impacts the stability analysis, and limits the generalization of well-understood data-driven methods for linear time-invariant systems. In thi…

This https://arxiv.org/abs/2304.03800 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nuc…

Towards $\it{ab}$-$\it{initio}$ nuclear theory calculations of $δ_\mathrm{C}$
We propose a new theory framework to study the isospin-symmetry breaking correction $δ_\text{C}$ in superallowed nuclear beta decays, crucial for the precise determination of $|V_{ud}|$. Based on a general assumptions of the isovector dominance in ISB interactions, we construct a set of functions $F_{T_z}$ which involve nuclear matrix elements of isovector monopole operators and the nuclear Green's function. Via the functions $F_{T_z}$, a connection of $δ_\text{C}$ to measurable ele…

This https://arxiv.org/abs/2303.05137 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the Existence of Balancing Allocations and Factor Point Processes
In this article, we show that every stationary random measure on $\mathbb R^d$ that is essentially free (i.e., has no symmetries a.s.) admits a point process as a factor (i.e., as a measurable and translation-equivariant function of the measure). As a result, we improve the results of Last and Thorisson (2022) on the existence of a factor balancing allocation between ergodic pairs of stationary random measures $Φ$ and $Ψ$ with equal intensities. In particular, we prove that such an allocation…

This https://arxiv.org/abs/2306.17294 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Alternating cochains on Furstenberg boundaries and measurable cohomology
Nicolas Monod showed that the evaluation map $$H^*_m(G\curvearrowright G/P)\longrightarrow H^*_m(G)$$ between the measurable cohomology of the action of a connected semisimple Lie group $G$ on its Furstenberg boundary $G/P$ and the measurable cohomology of $G$ is surjective with a non-trivial kernel in all degrees below a constant depending on $G$ and less than or equal to the rank of $G$ plus $2$. When we were looking for explicit representatives of classes in this kernel, we were astonished t…

A self-improving property of Riesz potentials in BMO
You-Wei Benson Chen
https://arxiv.org/abs/2404.16707 https://arxiv.org/pdf/2404.…

A self-improving property of Riesz potentials in BMO
In this paper we prove that for non-negative measurable functions $f$, \begin{align*} I_αf \in BMO(\mathbb{R}^n) \text{ if and only if } I_αf \in BMO^β(\mathbb{R}^n) \text{ for } β\in (n-α,n]. \end{align*} Here $I_α$ denotes the Riesz potential of order $α$ and $BMO^β$ represents the space of functions of bounded $β$-dimensional mean oscillation.

This https://arxiv.org/abs/2401.01979 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Low level definability above large cardinals
We study some connections between definability in generalized descriptive set theory and large cardinals, particularly measurable cardinals and limits thereof, working in ZFC. We show that if $κ$ is a limit of measurable cardinals then there is no $Σ_1(H_κ\cup\mathrm{OR})$ wellorder of a subset of $P(κ)$ of length $\geqκ^+$; this answers a question of Lücke and Müller. However, in $M_1$, the minimal proper class mouse with a Woodin cardinal, for every uncountable cardinal $κ$ which is n…

Forward completeness implies bounded reachable sets for time-delay systems on the state space of essentially bounded measurable functions
Lucas BrivadisL2S, Antoine ChailletIUF, L2S, Andrii Mironchenko, Fabian Wirth
https://arxiv.org/abs/2403.06543

Forward completeness implies bounded reachable sets for time-delay systems on the state space of essentially bounded measurable functions
We consider time-delay systems with a finite number of delays in the state space $L^\infty\times\R^n$. In this framework, we show that forward completeness implies the bounded reachability sets property, while this implication was recently shown by J.L. Mancilla-Aguilar and H. Haimovich to fail in the state space of continuous functions. As a consequence, we show that global asymptotic stability is always uniform in the state space $L^\infty\times\R^n$.

This https://arxiv.org/abs/2401.00433 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Quantized collision invariants on the sphere
We show that a measurable function $g:\mathbb{S}^{d-1}\to\mathbb{R}$, with $d\geq 3$, satisfies the functional relation \begin{equation*} g(ω)+g(ω_*)=g(ω')+g(ω_*'), \end{equation*} for all admissible $ω,ω_*,ω',ω_*'\in\mathbb{S}^{d-1}$ in the sense that \begin{equation*} ω+ω_*=ω'+ω_*', \end{equation*} if and only if it can be written as \begin{equation*} g(ω)=A+B\cdotω, \end{equation*} for some constants $A\in \mathbb{R}$ and $B\in\mathbb{R}^d$. Such functions form a family of qu…

Representations of currents taking values in $PGL(2, Q_q)$
Maria Gabriella Kuhn
https://arxiv.org/abs/2403.12956 https://arxiv.org/pd…

Representations of currents taking values in $PGL(2, Q_q)$
Let $G=PGL(2,Q_q)$. In this paper we shall investigate the group of measurable currents taking values in $G$. The key observation is that $G$ is acting by automorphisms on a homogeneous tree, which will play the role of the upper half plane in the case of $PSL(2,R)$.

Neutrino-Dark Sector Equilibration and Primordial Element Abundances
Cara Giovanetti, Martin Schmaltz, Neal Weiner
https://arxiv.org/abs/2402.10264 https:/…

Neutrino-Dark Sector Equilibration and Primordial Element Abundances
After neutrinos decouple from the photon bath, they can populate a thermal dark sector. If this occurs at a temperature above ~100 keV, this can have measurable impacts on light element abundances. We calculate light element abundances in this scenario, studying the impact from rapid cooling of the Standard Model neutrinos, and from an increase in the number of relativistic degrees of freedom $N_{\rm{eff}}$, which can occur in the presence of a mass threshold. We incorporate these changes in th…

This https://arxiv.org/abs/2109.05458 has been replaced.
link: https://scholar.google.com/scholar?q=a

Games characterizing certain families of functions
We obtain several game characterizations of Baire 1 functions between Polish spaces X, Y which extends the recent result of V. Kiss. Then we propose similar characterizations for equi-Bare 1 families of functions. Also, using related ideas, we give game characterizations of Baire measurable and Lebesgue measurable functions.

Rapid Optical Flare in the Extreme TeV Blazar 1ES 0229 200 on Intraday Timescale with TESS
Shubham Kishore, Alok C. Gupta, Paul J. Wiita, S. N. Tiwari
https://arxiv.org/abs/2404.13638

Rapid Optical Flare in the Extreme TeV Blazar 1ES 0229+200 on Intraday Timescale with TESS
The extreme TeV blazar 1ES 0229+200 is a high-frequency-peaked BL Lacertae object. It has not shown intraday variability in extensive optical and X-ray observations. Nor has it shown any significant variability on any measurable timescale in the 1-100 GeV energy range over a 14-year span, but variations in the source flux around its average are present in the energy range above 200 GeV. We searched for intraday optical variability in 1ES 0229+200 as part of an ongoing project to search for vari…

This https://arxiv.org/abs/2308.10500 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Quantum statistical mechanics from a Bohmian perspective
We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The continuity equation for any closed or open system suggests a natural Bohmian interpretation in terms of microscopic particle trajectories, that make the same measurable predictions as standard quantum theory. The microscopic trajectories are not directly observa…

Automated Unit Test Improvement using Large Language Models at Meta
Nadia Alshahwan, Jubin Chheda, Anastasia Finegenova, Beliz Gokkaya, Mark Harman, Inna Harper, Alexandru Marginean, Shubho Sengupta, Eddy Wang
https://arxiv.org/abs/2402.09171

Automated Unit Test Improvement using Large Language Models at Meta
This paper describes Meta's TestGen-LLM tool, which uses LLMs to automatically improve existing human-written tests. TestGen-LLM verifies that its generated test classes successfully clear a set of filters that assure measurable improvement over the original test suite, thereby eliminating problems due to LLM hallucination. We describe the deployment of TestGen-LLM at Meta test-a-thons for the Instagram and Facebook platforms. In an evaluation on Reels and Stories products for Instagram, 75% of…

Long #covid may cause cognitive decline of about six IQ points, study finds - The Washington Post
https://www.washingtonpost.com/wellness/20

Long covid may cause cognitive decline of about six IQ points, study finds
Covid may cause measurable, long-term effects on cognition and memory, a new study published Thursday in the New England Journal of Medicine suggests.

This https://arxiv.org/abs/2401.01979 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Low level definability above large cardinals
We study some connections between definability in generalized descriptive set theory and large cardinals, particularly measurable cardinals and limits thereof, working in ZFC. We show that if $κ$ is a limit of measurable cardinals then there is no $Σ_1(H_κ\cup\mathrm{OR})$ wellorder of a subset of $P(κ)$ of length $\geqκ^+$; this answers a question of Lücke and Müller. However, in $M_1$, the minimal proper class mouse with a Woodin cardinal, for every uncountable cardinal $κ$ which is n…

On the existence of Newton series and the asymptotics of finite differences
Glenn Bruda
https://arxiv.org/abs/2404.04288 https://arxi…

On the existence of Newton series and the asymptotics of finite differences
Suppose a complex function $f$ has a Lebesgue measurable inverse Laplace transform. We show that the $n$th order forward and backward differences of $f$ at $z_0\in\mathbb{C}$ tend to zero as $n\to\infty$ whenever $z_0$ lies in the region of absolute convergence of $f$. Under the same hypothesis, we show that the Newton series of $f$ centered at $z_0$ exists and converges in the half-plane $\Re(z)>\Re(z_0)$. Assuming instead that $f$ has a Lebesgue measurable inverse Fourier transform, we show t…

This https://arxiv.org/abs/2307.04698 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Khintchine-type double recurrence in abelian groups
We prove a Khintchine-type recurrence theorem for pairs of endomorphisms of a countable discrete abelian group. As a special case of the main result, if $Γ$ is a countable discrete abelian group, $φ, ψ\in End(Γ)$, and $ψ- φ$ is an injective endomorphism with finite index image, then for any ergodic measure-preserving $Γ$-system $\left( X, \mathcal{X}, μ, (T_g)_{g \in Γ} \right)$, any measurable set $A \in \mathcal{X}$, and any $\varepsilon > 0$, the set of $g \in Γ$ for which $$μ\lef…

This https://arxiv.org/abs/2308.06156 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Quantification of propagation modes in an astronomical instrument from its radiation pattern
In modern radio astronomy, one of the key technologies is to widen the frequency coverage of an instrument. The effects of higher-order modes on an instrument associated with wider bandwidths have been reported, which may degrade observation precision. It is important to quantify the higher-order propagation modes, though their power is too small to measure directly. Instead of the direct measurement of modes, we make an attempt to deduce them based on measurable radiation patterns. Assuming a …

This https://arxiv.org/abs/2312.00015 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the $\ell_0$ Isoperimetric Coefficient of Measurable Sets
In this paper we prove that the $\ell_0$ isoperimetric coefficient for any axis-aligned cubes, $ψ_{\mathcal{C}}$, is $Θ(n^{-1/2})$ and that the isoperimetric coefficient for any measurable body $K$, $ψ_K$, is of order $O(n^{-1/2})$. As a corollary we deduce that axis-aligned cubes essentially "maximize" the $\ell_0$ isoperimetric coefficient: There exists a positive constant $q > 0$ such that $ψ_K \leq q \cdot ψ_{\mathcal{C}}$, whenever $\mathcal{C}$ is an axis-aligned cube and $K$ is any …

This https://arxiv.org/abs/2303.09452 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Learning-Based Modeling of Human-Autonomous Vehicle Interaction for Improved Safety in Mixed-Vehicle Platooning Control
The rising presence of autonomous vehicles (AVs) on public roads necessitates the development of advanced control strategies that account for the unpredictable nature of human-driven vehicles (HVs). This study introduces a learning-based method for modeling HV behavior, combining a traditional first-principles approach with a Gaussian process (GP) learning component. This hybrid model enhances the accuracy of velocity predictions and provides measurable uncertainty estimates. We leverage this m…

Signature of systemic rotation in 21 Galactic Globular Clusters from APOGEE-2
Ilaria Petralia, Dante Minniti, Jos\'e G. Fern\'andez-Trincado, Richard R. Lane, Ricardo P. Schiavon
https://arxiv.org/abs/2404.10902

Signature of systemic rotation in 21 Galactic Globular Clusters from APOGEE-2
Context. Traditionally, Globular Clusters (GCs) have been assumed to be quasi-relaxed non-rotating systems, characterized by spherical symmetry and orbital isotropy. However, in recent years, a growing set of observational evidence is unveiling an unexpected dynamical complexity in Galactic GCs. Indeed, kinematic studies show that a measurable amount of internal rotation is present in many present-day GCs. Aims. The objective of this work is to analyse the APOGEE-2 Value-Added Catalogs (VACs) D…

This https://arxiv.org/abs/2401.14062 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Minimal doubling for small subsets in compact Lie groups
We prove a sharp bound for the minimal doubling of a small measurable subset of a compact connected Lie group. Namely, let $G$ be a compact connected Lie group of dimension $d_G$, we show that for for all measurable subsets $A$, we have $$μ_G(A^2) \geq \left(2^{d_G-d_H} - Cμ_G(A)^{\frac{2}{d_G-d_H}}\right)μ_G(A)$$ where $d_H$ is the maximal dimension of a proper closed subgroup $H$ and $C > 0$ is a dimensional constant. This settles a conjecture of Breuillard and Green, and recovers and impr…

This https://arxiv.org/abs/2312.15367 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Global Sobolev regularity for nonvariational operators built with homogeneous Hörmander vector fields
We consider a class of nonvariational degenerate elliptic operators of the kind \[ Lu=\sum_{i,j=1}^{m}a_{ij}\left( x\right) X_{i}X_{j}u \] where $\left\{ a_{ij}\left( x\right) \right\} _{i,j=1}^{m}$ is a symmetric uniformly positive matrix of bounded measurable functions defined in the whole $\mathbb{R}^{n}$ ($n>m$), possibly discontinuos but satisfying a $VMO$ assumption, and $X_{1},...,X_{m}$ are real smooth vector fields satisfying Hörmander rank condition in the whole $\mathbb{R}^{n}$ and …

This https://arxiv.org/abs/2308.15764 has been replaced.
initial toot: https://mastoxiv.page/@…

Stochastic Thermodynamics of Brownian motion in Temperature Gradient
We study stochastic thermodynamics of a Brownian particle which is subjected to a temperature gradient and is confined by an external potential. We first formulate an over-damped Ito-Langevin theory in terms of local temperature, friction coefficient, and steady state distribution, all of which are experimentally measurable. We then study the associated stochastic thermodynamics theory. We analyze the excess entropy production (EP) both at trajectory level and at ensemble level, and derive the …

This https://arxiv.org/abs/2311.02678 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Borsik's properties of topological spaces and their applications
Let X be an uncountable Polish space. Lubica Hola showed recently that there are 2^continuum many quasi-continuous real valued functions defined on the uncountable Polish space that are not Borel measurable. Inspired by Hola's result, we are extending it in two directions. First, we prove that the same conclusion holds when X is an uncountable Polish space and Y is any Hausdorff space with |Y|>1 then the family of all non-Borel measurable quasi-continuous functions has cardinality at …

#NutritionScience
1/5
The intricate world of phytochemicals holds many treasures, and among them are catechins, the compelling constituents of green tea. These polyphenolic compounds have garnered attention in scientific circles for their significant health benefits, measurable in rigorous peer-reviewed studies.

This https://arxiv.org/abs/2211.13199 has been replaced.
link: https://scholar.google.com/scholar?q=a

Aharonov-Bohm effect in phase space
The Aharonov-Bohm effect is a genuine quantum effect typically characterized by a measurable phase shift in the wave function for a charged particle that encircles an electromagnetic field located in a region inaccessible to the mentioned particle. However, this definition is not possible in the majority of the phase space descriptions since they are based on quasiprobability distributions. In this work, we characterize for the first time the Aharonov-Bohm effect within two different formalisms…

This https://arxiv.org/abs/1905.04480 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Real-Valued Bochner integral and the Modern Real-Valued Measurable function on $\mathbb{R}$
The like-Lebesgue integral of real-valued measurable functions (abbreviated as \textit{RVM-MI})is the most complete and appropriate integration Theory. Integrals are also defined in abstract spaces since Pettis (1938). In particular, Bochner integrals received much interest with very recent researches. It is very commode to use the \textit{RVM-MI} in constructing Bochner integral in Banach or in locally convex spaces. In this simple not, we prove that the Bochner integral and the \textit{RVM-MI…

Optimal Portfolio Choice with Cross-Impact Propagators
Eduardo Abi Jaber, Eyal Neuman, Sturmius Tuschmann
https://arxiv.org/abs/2403.10273 https://<…

Optimal Portfolio Choice with Cross-Impact Propagators
We consider a class of optimal portfolio choice problems in continuous time where the agent's transactions create both transient cross-impact driven by a matrix-valued Volterra propagator, as well as temporary price impact. We formulate this problem as the maximization of a revenue-risk functional, where the agent also exploits available information on a progressively measurable price predicting signal. We solve the maximization problem explicitly in terms of operator resolvents, by reducing th…

Accretion, greybody factor, quasinormal modes, power spectrum, sparsity of Hawking radiation, and weak gravitational lensing of a minimum measurable length inspired Schwarzchild black hole
Himangshu Barman, Ahmad Al-Badawi, Sohan Kumar Jha, Anisur Rahaman
https://arXiv.org/abs/2401.14833…

Accretion, greybody factor, quasinormal modes, power spectrum, sparsity of Hawking radiation, and weak gravitational lensing of a minimum measurable length inspired Schwarzchild black hole
In this manuscript, we delve into an analytic and numerical probe of shadow with different accretion models, quasinormal modes, Hawking radiation, and gravitational lensing to study observational impacts of quantum effect introduced throughh linear-quadratic GUP(LQG). Our investigation reveals that the shadows of LQG modified black holes are smaller and brighter than Schwarzschild black holes. To examine the impact of the quantum correction on the quasinormal mode, linear-quadratic GUP modified…

Towards the boundary of the fine curve graph
Jonathan Bowden, Sebastian Hensel, Richard Webb
https://arxiv.org/abs/2402.18948 https://

Towards the boundary of the fine curve graph
The fine curve graph was introduced as a geometric tool to study the homeomorphisms of surfaces. In this paper we study the Gromov boundary of this space and the local topology near points associated with minimal measurable foliations. We then give several applications including finding explicit elements with positive stable commutator length, and proving a Tits alternative for subgroups of $\textrm{Homeo}(S)$ containing a pseudo-Anosov map, generalizing a result of Hurtado-Xue.

MiTU-Net: A fine-tuned U-Net with SegFormer backbone for segmenting pubic symphysis-fetal head
Fangyijie Wang, Guenole Silvestre, Kathleen Curran
https://arXiv.org/abs/2401.15513 …

MiTU-Net: A fine-tuned U-Net with SegFormer backbone for segmenting pubic symphysis-fetal head
Ultrasound measurements have been examined as potential tools for predicting the likelihood of successful vaginal delivery. The angle of progression (AoP) is a measurable parameter that can be obtained during the initial stage of labor. The AoP is defined as the angle between a straight line along the longitudinal axis of the pubic symphysis (PS) and a line from the inferior edge of the PS to the leading edge of the fetal head (FH). However, the process of measuring AoP on ultrasound images is …

This https://arxiv.org/abs/2307.00788 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Positive mass gap of quantum Yang-Mills Fields
We construct a 4-dimensional quantum field theory on a Hilbert space, dependent on a simple Lie Algebra of a compact Lie group, that satisfies Wightman's axioms. This Hilbert space can be written as a countable sum of non-separable Hilbert spaces, each indexed by a non-trivial, inequivalent irreducible representation of the Lie Algebra. In each component Hilbert space, a state is given by a triple, a space-like rectangular surface $S$ in $\mathbb{R}^4$, a measurable section of the Lie Algebra…

On the eigenvalue distribution of spatio-spectral limiting operators in higher dimensions, II
Kevin Hughes, Arie Israel, Azita Mayeli
https://arxiv.org/abs/2403.13092

On the eigenvalue distribution of spatio-spectral limiting operators in higher dimensions, II
Let $F$, $S$ be bounded measurable sets in $\mathbb{R}^d$. Let $P_F : L^2(\mathbb{R}^d) \rightarrow L^2(\mathbb{R}^d) $ be the orthogonal projection on the subspace of functions with compact support on $F$, and let $B_S : L^2(\mathbb{R}^d) \rightarrow L^2(\mathbb{R}^d)$ be the orthogonal projection on the subspace of functions with Fourier transforms having compact support on $S$. In this paper, we derive improved distributional estimates on the eigenvalue sequence $1 \geq λ_1(F,S) \geq λ_2(F…

This https://arxiv.org/abs/2303.17963 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent States
As control engineering methods are applied to increasingly complex systems, data-driven approaches for system identification appear as a promising alternative to physics-based modeling. While the Bayesian approaches prevalent for safety-critical applications usually rely on the availability of state measurements, the states of a complex system are often not directly measurable. It may then be necessary to jointly estimate the dynamics and the latent state, making the quantification of uncertain…

A variational principle for entropy of a random dynamical system
Yuan Lian
https://arxiv.org/abs/2403.07488 https://arxiv.org/pdf/240…

A variational principle for entropy of a random dynamical system
In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable fiber entropy of a random dynamical system.

On the differentiation of integrals in measure spaces along filters: II
Fausto Di Biase, Steven G. Krantz
https://arxiv.org/abs/2404.13157 https://<…

On the differentiation of integrals in measure spaces along filters: II
Let $X$ be a complete measure space of finite measure. The Lebesgue transform of an integrable function $f$ on $X$ encodes the collection of all the mean-values of $f$ on all measurable subsets of $X$ of positive measure. In the problem of the differentiation of integrals, one seeks to recapture $f$ from its Lebesgue transform. In previous work we showed that, in all known results, $f$ may be recaputed from its Lebesgue transform by means of a limiting process associated to an appropriate famil…

This https://arxiv.org/abs/2307.13367 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

The minimum measurable eccentricity from gravitational waves of LISA massive black hole binaries
We explore the eccentricity measurement threshold of LISA for gravitational waves radiated by massive black hole binaries (MBHBs) with redshifted BH masses $M_z$ in the range $10^{4.5}$-$10^{7.5}~{\rm M}_\odot$ at redshift $z=1$. The eccentricity can be an important tracer of the environment where MBHBs evolve to reach the merger phase. To consider LISA's motion and apply the time delay interferometry, we employ the lisabeta software and produce year-long eccentric waveforms using the inspiral-…

Introenumerability, autoreducibility, and randomness
Ang Li
https://arxiv.org/abs/2402.08247 https://arxiv.org/pdf/2402.08247<…

Introenumerability, autoreducibility, and randomness
We define $Ψ$-autoreducible sets given an autoreduction procedure $Ψ$. Then, we show that for any $Ψ$, a measurable class of $Ψ$-autoreducible sets has measure zero. Using this, we show that classes of cototal, uniformly introenumerable, introenumerable, and hyper-cototal enumeration degrees all have measure zero. By analyzing the arithmetical complexity of the classes of cototal sets and cototal enumeration degrees, we show that weakly 2-random sets cannot be cototal and weakly 3-random se…

This https://arxiv.org/abs/2302.08565 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Variance Sum Rule for Entropy Production
Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule for displacement and force variances that permits us to measure the entropy production rate $σ$ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optica…

This https://arxiv.org/abs/2310.02026 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Harnack inequality to the homogeneous nonlinear degenerate parabolic equations
In this paper, the Harnack inequality result are established for a new class of the homogeneous nonlinear degenerate parabolic equations \begin{align*} div A(t,x,u,\nabla_x u)-\partial_t \vert u\vert^{p-2}u=0 \end{align*} on a bounded domain $ D \subset R^{n+1}. $ Let $A(t,x,ξ,η)$ be measurable function on $R\times R^n\times R\times R^n\to R^n$ that satisfies the Caratheodory conditions for $ \, \text{arbitrary } \, (t,x)\in D$ and $(ξ,η)\in R^{1}\times R^n.$ The following growth conditions…

This https://arxiv.org/abs/2210.16446 has been replaced.
link: https://scholar.google.com/scholar?q=a

Measurable Imbeddings, Free Products, and Graph Products
We study Measurable Imbeddability between groups, which is an order-like generalization of Measure Equivalence that allows the imbedded group to have an infinite measure fundamental domain. We prove if $Λ_1$ measurably imbeds into $Γ_1$, and $Λ_2$ measurably imbeds into $Γ_2$ under an additional assumption that lets the corresponding fundamental domains to be arranged in a special way, then $Λ_1 * Λ_2$ measurably imbeds into $Γ_1 * Γ_2$. Building upon the techniques we used, we show tha…

UKF-Based Sensor Fusion for Joint-Torque Sensorless Humanoid Robots
Ines Sorrentino, Giulio Romualdi, Daniele Pucci
https://arxiv.org/abs/2402.18380 https:…

UKF-Based Sensor Fusion for Joint-Torque Sensorless Humanoid Robots
This paper proposes a novel sensor fusion based on Unscented Kalman Filtering for the online estimation of joint-torques of humanoid robots without joint-torque sensors. At the feature level, the proposed approach considers multimodal measurements (e.g. currents, accelerations, etc.) and non-directly measurable effects, such as external contacts, thus leading to joint torques readily usable in control architectures for human-robot interaction. The proposed sensor fusion can also integrate distr…

This https://arxiv.org/abs/2312.13535 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Bounded pluriharmonic functions and holomorphic functions on Teichmüller space
In this paper, we discuss the boundary behavior of bounded pluriharmonic functions on the Teichmüller space. We will show a version of the Fatou theorem that every bounded pluriharmonic function admits the radial limits along the Teichmüller geodesic rays, and a version of the F. and M. Riesz theorem that the radial limit of a non-constant bounded holomorphic function is not constant on any non-null measurable set on the Bers boundary in terms of the pluriharmonic measure. As a corollary, we …

This https://arxiv.org/abs/2404.04176 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Gravitational lensing by a Lorentz-violating black hole
In this work, we study the gravitational lensing by a Lorentz-violating (LV) black hole inspired by the recent contribution [1]. Explicitly, we concentrate on a specific application: we perform the computation of gravitational lensing effects under the strong field limit. In particular, we analytically derive the deflection angle so that the lens equation can also be addressed. This methodological approach yields physically measurable outcomes, including the determination of relativistic image …

Quantitative uniqueness estimates for stochastic parabolic equations on the whole Euclidean space
Yuanhang Liu, Donghui Yang, Xingwu Zeng, Can Zhang
https://arxiv.org/abs/2402.12703

Quantitative uniqueness estimates for stochastic parabolic equations on the whole Euclidean space
In this paper, a quantitative estimate of unique continuation for the stochastic heat equation with bounded potentials on the whole Euclidean space is established. This paper generalizes the earlier results in [29] and [17] from a bounded domain to an unbounded one. The proof is based on the locally parabolic-type frequency function method. An observability estimate from measurable sets in time for the same equation is also derived.

This https://arxiv.org/abs/2401.00433 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Quantized collision invariants on the sphere
We show that a measurable function $g:\mathbb{S}^{d-1}\to\mathbb{R}$, with $d\geq 3$, satisfies the functional relation \begin{equation*} g(ω)+g(ω_*)=g(ω')+g(ω_*'), \end{equation*} for all admissible $ω,ω_*,ω',ω_*'\in\mathbb{S}^{d-1}$ in the sense that \begin{equation*} ω+ω_*=ω'+ω_*', \end{equation*} if and only if it can be written as \begin{equation*} g(ω)=A+B\cdotω, \end{equation*} for some constants $A\in \mathbb{R}$ and $B\in\mathbb{R}^d$. Such functions form a family of qu…

This https://arxiv.org/abs/2304.06998 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Evolution of structure functions in momentum space
We formulate the momentum-space Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for structure functions measurable in deeply inelastic scattering. We construct a six-dimensional basis of structure functions that allows for a full three flavor structure and thereby provides a way to calculate perturbative predictions for physical cross sections directly without unobservable parton distribution functions (PDFs) and without the associated scheme dependence. We derive the DGL…

Abstract Hardy inequalities: The case p=1
Alejandro Santacruz Hidalgo
https://arxiv.org/abs/2402.13335 https://arxiv.org/pdf/2402.133…

Abstract Hardy inequalities: The case p=1
Boundedness of an abstract formulation of Hardy operators between Lebesgue spaces over general measure spaces is studied and, when the domain is L^1, shown to be equivalent to the existence of a Hardy inequality on the half line with general Borel measures. This is done by extending the greatest decreasing minorant construction to general measure spaces depending on a totally ordered collection of measurable sets, called an ordered core. A functional description of the greatest decreasing minor…

This https://arxiv.org/abs/2401.14062 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Minimal doubling for small subsets in compact Lie groups
We prove a sharp bound for the minimal doubling of a small measurable subset of a compact connected Lie group. Namely, let $G$ be a compact connected Lie group of dimension $d_G$, we show that for every $ε> 0$ and for all measurable subsets $A$ of small enough Haar measure, we have $$ μ_G(A^2) > \left(2^{d_G - d_H}-ε\right)μ_G(A)$$ where $d_H$ is the maximal dimension of a proper closed subgroup $H$. This settles a conjecture of Breuillard and Green and recovers - with completely differ…

This https://arxiv.org/abs/2307.08683 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Quantum Covariance Scalar Products and Efficient Estimation of Max-Ent Projections
The maximum-entropy principle (Max-Ent) is a valuable and extensively used tool in statistical mechanics and quantum information theory. It provides a method for inferring the state of a system by utilizing a reduced set of parameters associated with measurable quantities. However, the computational cost of employing Max-Ent projections in simulations of quantum many-body systems is a significant drawback, primarily due to the computational cost of evaluating these projections. In this work, a …

This https://arxiv.org/abs/2402.15122 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepe…

Measurements of low energy nuclear recoil quenching factors for Na and I recoils in the NaI(Tl) scintillator
Elastic scattering off nuclei in target detectors, involving interactions with dark matter and coherent elastic neutrino nuclear recoil (CE$ν$NS), results in the deposition of low energy within the nuclei, dissipating rapidly through a combination of heat and ionization. The primary energy loss mechanism for nuclear recoil is heat, leading to consistently smaller measurable scintillation signals compared to electron recoils of the same energy. The nuclear recoil quenching factor (QF), represen…

This https://arxiv.org/abs/2311.04075 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

General relativistic dynamical tides in binary inspirals, without modes
A neutron star in an inspiraling binary system is tidally deformed by its companion, and the effect leaves a measurable imprint on the emitted gravitational waves. While the tidal interaction falls within the regime of static tides during the early stages of inspiral, a regime of dynamical tides takes over in the later stages. The description of dynamical tides found in the literature makes integral use of a spectral representation of the tidal deformation, in which it is expressed as a sum ove…

This https://arxiv.org/abs/2306.09553 has been replaced.
initial toot: https://mastoxiv.page/@…

On data and dimension in chemistry I -- irreversibility, concealment and emergent conservation laws
Chemical systems are interpreted through the species they contain and the reactions they may undergo, i.e., their chemical reaction network (CRN). In spite of their central importance to chemistry, the structure of CRNs continues to be challenging to deduce from data. Although there exist structural laws relating species, reactions, conserved quantities and cycles, there has been limited attention to their measurable consequences. One such is the dimension of the chemical data: the number of in…

Some remarks on K-closedness of the couples of real Hardy spaces
Ioann Vasilyev
https://arxiv.org/abs/2402.12581 https://arxiv.org/pd…

Some remarks on K-closedness of the couples of real Hardy spaces
In this paper K closedness is proved in the case of the couple of real Hardy spaces in the corresponding couple of Lebesgue spaces. This means roughly that any measurable decomposition of an analytic function gives rise to an "analytic" decomposition with summands of roughly the same size. The proof uses Bourgain's method, the atomic decomposition for Hardy spaces and the subharmonic property of the gradient of a system of conjugate harmonic functions.

This https://arxiv.org/abs/2401.14062 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Minimal doubling for small subsets in compact Lie groups
We prove a sharp bound for the minimal doubling of a small measurable subset of a compact connected Lie group. Namely, let $G$ be a compact connected Lie group of dimension $d_G$, we show that for every $ε> 0$ and for all measurable subsets $A$ of small enough Haar measure, we have $$ μ_G(A^2) > \left(2^{d_G - d_H}-ε\right)μ_G(A)$$ where $d_H$ is the maximal dimension of a proper closed subgroup $H$. This settles a conjecture of Breuillard and Green and recovers - with completely differ…

Dirichlet problems associated to abstract nonlocal space-time differential operators
Joshua Willems
https://arxiv.org/abs/2404.11289 https://

Dirichlet problems associated to abstract nonlocal space-time differential operators
Let the abstract fractional space--time operator $(\partial_t + A)^s$ be given, where $s \in (0,\infty)$ and $-A \colon \mathsf{D}(A) \subseteq X \to X$ is a linear operator generating a uniformly bounded strongly measurable semigroup $(S(t))_{t\ge0}$ on a complex Banach space $X$. We consider the corresponding Dirichlet problem of finding a function $u \colon \mathbb{R} \to X$ such that $(\partial_t + A)^s u(t) = 0$ on $(t_0, \infty)$ and $u(t) = g(t)$ on $(-\infty, t_0]$, for given $t_0 \in \…

This https://arxiv.org/abs/2304.06998 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Evolution of structure functions in momentum space
We formulate the momentum-space Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for structure functions measurable in deeply inelastic scattering. We construct a six-dimensional basis of structure functions that allows for a full three flavor structure and thereby provides a way to calculate perturbative predictions for physical cross sections directly without unobservable parton distribution functions (PDFs) and without the associated scheme dependence. We derive the DGL…

Gravitational lensing by a Lorentz-violating black hole
A. A. Ara\'ujo Filho, J. R. Nascimento, A. Yu. Petrov, P. J. Porf\'irio
https://arxiv.org/abs/2404.04176

Gravitational lensing by a Lorentz-violating black hole
In this work, we study the gravitational lensing by a Lorentz-violating (LV) black hole inspired by the recent contribution [1]. Explicitly, we concentrate on a specific application: we perform the computation of gravitational lensing effects under the strong field limit. In particular, we analytically derive the deflection angle so that the lens equation can also be addressed. This methodological approach yields physically measurable outcomes, including the determination of relativistic image …

This https://arxiv.org/abs/2302.07507 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A regularity theory for an initial value problem with a time-measurable pseudo-differential operator in a weighted $L_p$-space
In this study, we investigate the existence, uniqueness, and maximal regularity estimates of solutions to homogeneous initial value problems involving time-measurable pseudo-differential operators within the framework of weighted mixed norm Lebesgue spaces. The class of temporal weights in our regularity estimates contains Muckenhoupt's class, and the initial data is in weighted Besov spaces with variable order.

Vector-Valued Holomorphic Functions and Abstract Fubini-Type Theorems
Bernhard H. Haak (IMB), Markus Haase
https://arxiv.org/abs/2403.11712 https://…

Vector-Valued Holomorphic Functions and Abstract Fubini-Type Theorems
Let $f = f(z,t)$ be a function holomorphic in $z \in O \subseteq {\mathbb C}^d$ for fixed $t\in Ω$ and measurable in $t$ for fixed $z$ and such that$z \mapsto f(z,\cdot)$ is bounded with values in$E := L_{p}(Ω)$, $1\le p \le \infty$. It is proved (among other things) that \[ \langle t\mapsto φ( f(\cdot,t) ), μ\rangle= φ(z \mapsto \langle f(z, \cdot) , μ\rangle )\] whenever $μ\in E'$ and $φ$ is a linear functional on $H^\infty(O)$ that is sequentially continuous with respect to bounded p…

This https://arxiv.org/abs/2309.16893 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nuc…

Data-driven reevaluation of $ft$-values in superallowed $β$ decays
We present a comprehensive re-evaluation of the $ft$ values in superallowed nuclear $β$ decays crucial for the precise determination of $V_{ud}$ and low-energy tests of the electroweak Standard Model. It consists of the first, fully data-driven analysis of the nuclear $β$ decay form factor, that utilizes isospin relations to connect the nuclear charged weak distribution to the measurable charge distributions. This prescription supersedes previous shell-model estimations, and allows for a rigo…

This https://arxiv.org/abs/2401.00433 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Quantized collision invariants on the sphere
We show that a measurable function $g:\mathbb{S}^{d-1}\to\mathbb{R}$, with $d\geq 3$, satisfies the functional relation \begin{equation*} g(ω)+g(ω_*)=g(ω')+g(ω_*'), \end{equation*} for all admissible $ω,ω_*,ω',ω_*'\in\mathbb{S}^{d-1}$ in the sense that \begin{equation*} ω+ω_*=ω'+ω_*', \end{equation*} if and only if it can be written as \begin{equation*} g(ω)=A+B\cdotω, \end{equation*} for some constants $A\in \mathbb{R}$ and $B\in\mathbb{R}^d$. Such functions form a family of qu…

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 …

Geometric logarithmic-Hardy and Hardy-Poincar\'e inequalities on stratified groups
Marianna Chatzakou
https://arxiv.org/abs/2402.10279 https://<…

Geometric logarithmic-Hardy and Hardy-Poincaré inequalities on stratified groups
We develop a unified strategy to obtain the geometric logarithmic Hardy inequality on any open set M of a stratified group, provided the validity of the Hardy inequality in this setting, where the so-called "weight" is regarded to be any measurable non-negative function on M . Provided the legitimacy of the latter for some open set and for some weight, we also show an inequality that is an extension of the "generalised Poincaré inequality" introduced by Beckner with the addition of a weight, a…

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 …

This https://arxiv.org/abs/2306.09553 has been replaced.
initial toot: https://mastoxiv.page/@…

On data and dimension in chemistry I -- irreversibility, concealment and emergent conservation laws
Chemical systems are interpreted through the species they contain and the reactions they may undergo, i.e., their chemical reaction network (CRN). In spite of their central importance to chemistry, the structure of CRNs continues to be challenging to deduce from data. Although there exist structural laws relating species, reactions, conserved quantities and cycles, there has been limited attention to their measurable consequences. One such is the dimension of the chemical data: the number of in…

Raychaudhuri equation and the dynamics of cosmic evolution
Madhukrishna Chakraborty, Subenoy Chakraborty
https://arxiv.org/abs/2402.17800 https://

Raychaudhuri equation and the dynamics of cosmic evolution
The paper deals with the Raychaudhuri equation (RE) which is a non-linear ordinary differential equation in $Θ$, the expansion scalar corresponding to a geodesic flow. Focusing theorem which follows as a consequence of the RE has been restated in terms of the cosmic parameter $q$ (deceleration parameter) both for Einstein gravity and for modified gravity theories. Measurable quantities namely the luminosity distance and density parameter are shown to have an upper bound using the Raychaudhuri …

This https://arxiv.org/abs/2105.11810 has been replaced.
link: https://scholar.google.com/scholar?q=a

Algebraic structures in the family of non-Lebesgue measurable sets
In the additive topological group $(\mathbb{R},+)$ of real numbers, we construct families of sets for which elements are not measurable in the Lebesgue sense. The constructed families have algebraic structures of being semigroups (i.e., closed under finite unions of sets), and invariant under the action of the group $Φ(\mathbb{R})$ of all translations of $\mathbb{R}$ onto itself. Those semigroups are constructed by using Vitali selectors and Bernstein subsets on $\mathbb{R}$. In particular, we…

Raychaudhuri equation and the dynamics of cosmic evolution
Madhukrishna Chakraborty, Subenoy Chakraborty
https://arxiv.org/abs/2402.17800 https://

Raychaudhuri equation and the dynamics of cosmic evolution
The paper deals with the Raychaudhuri equation (RE) which is a non-linear ordinary differential equation in $Θ$, the expansion scalar corresponding to a geodesic flow. Focusing theorem which follows as a consequence of the RE has been restated in terms of the cosmic parameter $q$ (deceleration parameter) both for Einstein gravity and for modified gravity theories. Measurable quantities namely the luminosity distance and density parameter are shown to have an upper bound using the Raychaudhuri …

This https://arxiv.org/abs/2311.02825 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Entropy-cost type Propagation of Chaos for Mean Field Interacting Particle System
In this paper, the quantitative entropy-cost type propagation of chaos for mean field interacting particle system is obtained, where the interaction is bounded and the initial distribution of mean field interacting particles converges to that of corresponding McKean-Vlasov SDEs in Wasserstein distance. In the finite dimension case, the interaction is merely assumed to be bounded measurable and the noise can be multiplicative, while for the semi-linear SPDEs, the interaction is required to be bo…

This https://arxiv.org/abs/2209.10572 has been replaced.
link: https://scholar.google.com/scholar?q=a

Optimal domains for elliptic eigenvalue problems with rough coefficients
We prove the existence of an open set minimizing the first Dirichlet eigenvalue of an elliptic operator with bounded, measurable coefficients, over all open sets of a given measure. Our proof is based on a free boundary approach: we characterize the eigenfunction on the optimal set as the minimizer of a penalized functional, and derive openness of the optimal set as a consequence of a Hölder estimate for the eigenfunction. We also prove that the optimal eigenfunction grows at most linearly fro…

From equilibrium to non-equilibrium statistical mechanics of liquids
O. Joaquín-Jaime, R. Peredo-Ortiz, M. Medina-Noyola, L.F. Elizondo-Aguilera
https://arXiv.org/abs/2401.15220 <…

From equilibrium to non-equilibrium statistical mechanics of liquids
Relevant and fundamental concepts of the statistical mechanical theory of classical liquids are ordinarily introduced in the context of the description of thermodynamic equilibrium states. This makes explicit reference to probability distribution functions of \emph{equilibrium} statistical ensembles (canonical, microcanonical, ...) in the derivation of general and fundamental relations between inter-particle interactions and measurable macroscopic properties of a given system. This includes, fo…

This https://arxiv.org/abs/2001.11901 has been replaced.
link: https://scholar.google.com/scholar?q=a

Solvability for non-smooth Schrödinger equations with singular potentials and square integrable data
We develop a holomorphic functional calculus for first-order operators $DB$ to solve boundary value problems for Schrödinger equations $-\mathrm{div}\, A \nabla u + a V u = 0$ in the upper half-space $\mathbb{R}^{n+1}_+$ with $n\in\mathbb{N}$. This relies on quadratic estimates for $DB$, which are proved for coefficients $A,a,V$ that are independent of the transversal direction to the boundary, and comprised of a complex-elliptic pair $(A,a)$ that are bounded and measurable, and a singular pot…

This https://arxiv.org/abs/2403.17464 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Weak solutions to Kolmogorov-Fokker-Planck equations: Regularity, existence and uniqueness
In this article, we establish embeddings à la Lions and transfer of regularity à la Bouchut for a large scale of kinetic spaces. We use them to identify a notion of weak solutions to Kolmogorov-Fokker-Planck equations with (local or integral) diffusion and rough (measurable) coefficients under minimal requirements. We prove their existence and uniqueness for a large class of source terms, first in full space for the time, position and velocity variables and then for the kinetic Cauchy problem…

This https://arxiv.org/abs/1711.11021 has been replaced.
link: https://scholar.google.com/scholar?q=a

A characterization of a nonlinear integral triangle inequality
Let $(E,\|.\|)$ be a Banach space and let $(Ω,μ)$ be a Lebesgue measure space. We characterize, for all $p>0$, measurable functions $u:Ω\rightarrow \mathbb{R}$ for which \begin{equation*} \left\| \int_Ω f\,dμ\right\|^{p}\,\leq\,\int_Ω u \| f \|^{p}\,dμ.\tag{I} \end{equation*} We characterize $u$ for the reverse of (I) as well. The discrete counterpart of this problem is also solved.

Existence, uniqueness, and regularity of solutions to nonlinear and non-smooth parabolic obstacle problems
Durandard Th\'eo, Strulovici Bruno
https://arxiv.org/abs/2404.01498 …

Existence, uniqueness, and regularity of solutions to nonlinear and non-smooth parabolic obstacle problems
We establish the existence, uniqueness, and $W^{1,2,p}$-regularity of solutions to fully nonlinear parabolic obstacle problems when the obstacle is the pointwise supremum of arbitrary functions in $W^{1,2,p}$ and the operator is only assumed to be measurable in the state and time variables. The results hold for a large class of non-smooth obstacles, including all convex obstacles. Applied to stopping problems, they imply that the decision maker never stops at a convex kink of the stopping payof…

This https://arxiv.org/abs/2403.17468 has been replaced.
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Fundamental solutions to Kolmogorov-Fokker-Planck equations with rough coefficients: existence, uniqueness, upper estimates
We show the existence and uniqueness of fundamental solution operators to Kolmo\-gorov-Fokker-Planck equations with rough (measurable) coefficients and local or integral diffusion on finite and infinite time strips. In the local case, that is to say when the diffusion operator is of differential type, we prove $Ł^2$ decay using Davies' method and the conservation property. We also prove that the existence of a generalized fundamental solution with the expected pointwise Gaussian upper bound is…