General Class Research Articles

Relative State Counting for Semiclassical Black Holes

It has been shown that entropy differences between certain states of perturbative quantum gravity can be computed without specifying an ultraviolet completion. This is analogous to the situation in classical statistical mechanics, where entropy differences are defined but absolute entropy is not. Unlike in classical statistical mechanics, however, the entropy differences computed in perturbative quantum gravity do not have a clear physical interpretation. Here we construct a family of perturbative black hole states for which the entropy difference can be interpreted as a relative counting of states. Conceptually, this Letter begins with the algebra of mass fluctuations around a fixed black hole background, and points out that while this is a type I algebra, it is not a factor and therefore has no canonical definition of entropy. As in previous work, coupling the mass fluctuations to quantum matter embeds the mass algebra within a type II factor, in which entropy differences (but not absolute entropies) are well defined. It is then shown that for microcanonical wave functions of mass fluctuation, the type II entropy difference equals the logarithm of the dimension of the extra Hilbert space that is needed to map one microcanonical window to another using gauge-invariant unitaries. The Letter closes with comments on type II entropy difference in a more general class of states, where the von Neumann entropy difference does not have a physical interpretation, but “one-shot” entropy differences do. Published by the American Physical Society 2024

Bridging the Gap: Examining Student Engagement in a Hybrid POGIL General Chemistry Class

Bridging the Gap: Examining Student Engagement in a Hybrid POGIL General Chemistry Class

Sojourns of locally self-similar Gaussian processes

The cumulative Parisian ruin probability over a finite time interval [ 0 , T ] for a Gaussian risk process R ( t ) = u + c ( t ) − X ( t ) , t ≥ 0 , is the probability that the total time the process R ( t ) spends below zero during this interval exceeds a threshold L ≥ 0 . In this contribution we derive exact asymptotic approximations of the cumulative Parisian ruin probability for a general class of Gaussian processes introduced in D ȩ bicki and Tabiś [Pickands-Piterbarg constants for self-similar Gaussian processes, Probab. Math. Statist. 40 (2020), pp. 297–315. MR 4206416] assuming that X is locally self-similar. We illustrate our findings with several examples. As a byproduct we show that Berman's constants can be defined alternatively by a self-similar Gaussian process which could be quite different to the fractional Brownian motion.

Perturbations of classical fields by gravitational shockwaves

Gravitational shockwaves are geometries where components of the transverse curvature have abrupt behaviour across null hypersurfaces, which are fronts of the waves. We develop a general approach to describe classical field theories on such geometries in a linearized approximation, by using free scalar fields as a model. Perturbations caused by shockwaves exist above the wave front and are solutions to a characteristic Cauchy problem with initial data on the wave front determined by a supertranslation of ingoing fields. A special attention is paid to perturbations of fields of point-like sources generated by plane-fronted gravitational shockwaves. One has three effects: conversion of non-stationary perturbations into an outgoing radiation, a spherical scalar shockwave which appears when the gravitational wave hits the source, and a plane scalar shockwave accompanying the initial gravitational wave. Our analysis is applicable to gravitational shockwaves of a general class including geometries sourced by null particles and null branes.

Contribution to the Statistical Mechanics of Static Triplet Correlations and Structures in Fluids with Quantum Spinless Behavior

The current developments in the theory of quantum static triplet correlations and their associated structures (real r-space and Fourier k-space) in monatomic fluids are reviewed. The main framework utilized is Feynman’s path integral formalism (PI), and the issues addressed cover quantum diffraction effects and zero-spin bosonic exchange. The structures are associated with the external weak fields that reveal their nature, and due attention is paid to the underlying pair-level structures. Without the pair, level one cannot fully grasp the triplet extensions in the hierarchical ladder of structures, as both the pair and the triplet structures are essential ingredients in the triplet response functions. Three general classes of PI structures do arise: centroid, total continuous linear response, and instantaneous. Use of functional differentiation techniques is widely made, and, as a bonus, this leads to the identification of an exact extension of the “classical isomorphism” when the centroid structures are considered. In this connection, the direct correlation functions, as borrowed from classical statistical mechanics, play a key role (either exact or approximate) in the corresponding quantum applications. Additionally, as an auxiliary framework, the traditional closure schemes for triplets are also discussed, owing to their potential usefulness for rationalizing PI triplet results. To illustrate some basic concepts, new numerical calculations (path integral Monte Carlo PIMC and closures) are reported. They are focused on the purely diffraction regime and deal with supercritical helium-3 and the quantum hard-sphere fluid.

Dualizations of Approximations, ℵ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\aleph _1$$\\end{document}-Projectivity, and Vopěnka’s Principles

The approximation classes of modules that arise as components of cotorsion pairs are tied up by Salce’s duality. Here we consider general approximation classes of modules and investigate possibilities of dualization in dependence on closure properties of these classes. While some proofs are easily dualized, other dualizations require large cardinal principles, and some fail in ZFC, with counterexamples provided by classes of ℵ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\aleph _1$$\\end{document}-projective modules over non-perfect rings. For example, we show that the statement “each covering class of modules closed under homomorphic images is of the form Gen(M)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathrm{Gen\\,}}(M)$$\\end{document} for a module M” is equivalent to Vopěnka’s Principle.

Asymptotic Theory for a General Class of Short-Range Interaction Functionals

Asymptotic Theory for a General Class of Short-Range Interaction Functionals

A Study on Students’ Affective Attitudes and Learning Experiences in PBL Activities Utilizing an AI App in General English Classes

A Study on Students’ Affective Attitudes and Learning Experiences in PBL Activities Utilizing an AI App in General English Classes

A New Integral Transform and Applications: HK-Transform

In this paper, we propose a new integral transform called the Transform and employ it to analytically solve the Volterra integral equations (VIE.) of the first kind. To achieve this First we derive the transform of basic algebraic and transcendental mathematical functions. The fundamental characteristics of the transform, which can be used to solve a variety of functional equations, including, we then discuss the fundamental properties, such as ordinary differential equations and integral equations, then we discover the exact solution for general first class V.I.E. To illustrate the applicability of the transform, numerical problems are examined and handled carefully step-by-step. The results show that the proposed Transform new integral transform produces accurate solutions for first-kind VIE. without requiring time-consuming computations.

Can the Charlson comorbidity index help to guide DOAC dosing in patients with atrial fibrillation and improve the efficacy and safety of treatment? A subanalysis of the MAS study

BackgroundFrailty influences the effectiveness and safety of anticoagulant therapy in patients with atrial fibrillation (AF). The age-weighted Charlson comorbidity index may offer a valuable tool to assess the risk of adverse events in AF patients treated with direct oral anticoagulants (DOACs). This sub-analysis of MAS trial data aimed to assess whether using the Charlson index, instead of the standard criteria, would have led to different dosing and improved adverse event occurrence during treatment. MethodsThe MAS study looked for a relationship between DOAC levels assessed at baseline and adverse events during follow-up. The study is described in detail elsewhere. ResultsAmong the 1,657 patients studied, 832 (50.2 %) had a relatively low Charlson index (up to 6, general median class), of whom 132 (15.9 %) were treated with reduced doses. Conversely, among the 825 patients with a high Charlson index (≥7), 257 (31.1 %) received standard doses. A weak but statistically significant positive correlation (r = 0.1413, p < 0.0001 by ANOVA) was observed between increasing Charlson classes and DOAC levels standardized to allow comparability among drug results. However, no significant differences were found in the incidence or number of adverse events during follow-up, or in other parameters, between patients with low and high Charlson's scores. ConclusionsUtilizing the Charlson index would have led to notable differences in DOAC dosing compared to standard criteria. However, we found no evidence that its use would have improved the prediction of adverse events in AF patients enrolled in the MAS study.

Axion production via trapped misalignment from Peccei-Quinn symmetry breaking

The Peccei-Quinn (PQ) symmetry does not need to be exact, and even a tiny source of PQ breaking not aligned with the QCD anomaly might have significant phenomenological implications. In this study, we examine the effects of a general class of PQ-breaking operators on the axion cosmological production via misalignment, focussing on both temperature-dependent and independent PQ-breaking potentials. In particular, we show that a variant of the trapped misalignment mechanism can delay the onset of axion oscillation, leading to an axion dark matter window with ma ≫ 10−5 eV. This scenario is testable through various experimental approaches, including standard axion haloscopes and helioscopes, as well as searches for electric dipole moments and axion-mediated forces.

Long-time behavior of solutions to the general class of coupled nonlocal nonlinear wave equations

Long-time behavior of solutions to the general class of coupled nonlocal nonlinear wave equations

Principal eigenvectors in hypergraph Turán problems

For a general class of hypergraph Turán problems with uniformity $r$, we investigate the principal eigenvector for the $p$-spectral radius (in the sense of Keevash-Lenz-Mubayi and Nikiforov) for the extremal graphs, showing in a strong sense that these eigenvectors have close to equal weight on each vertex (equivalently, showing that the principal ratio is close to $1$). We investigate the sharpness of our result; it is likely sharp for the Turán tetrahedron problem. In the course of this latter discussion, we establish a lower bound on the $p$-spectral radius of an arbitrary $r$-graph in terms of the degrees of the graph. This builds on earlier work of Cardoso-Trevisan, Li-Zhou-Bu, Cioabă-Gregory, and Zhang. The case $1 &lt; p &lt; r$ of our results leads to some subtleties connected to Nikiforov's notion of $k$-tightness, arising from the Perron-Frobenius theory for the $p$-spectral radius. We raise a conjecture about these issues and provide some preliminary evidence for our conjecture.

Enabling 2D Electron Gas with High Room-Temperature Electron Mobility Exceeding 100cm2 Vs-1 at a Perovskite Oxide Interface.

In perovskite oxide heterostructures, bulk functional properties coexist with emergent physical phenomena at epitaxial interfaces. Notably, charge transfer at the interface between two insulating oxide layers can lead to the formation of a 2D electron gas (2DEG) with possible applications in, e.g., high-electron-mobility transistors and ferroelectric field-effect transistors. So far, the realization of oxide 2DEGs is, however, largely limited to the interface between the single-crystal substrate and epitaxial film, preventing their deliberate placement inside a larger device architecture. Additionally, the substrate-limited quality of perovskite oxide interfaces hampers room-temperature (RT) 2DEG performance due to notoriously low electron mobility. In this work, the controlled creation of an interfacial 2DEG at the epitaxial interface between perovskite oxides BaSnO3 and LaInO3 is demonstrated with enhanced RT electron mobility values up to 119 cm2 Vs-1-the highest RT value reported so far for a perovskite oxide 2DEG. Using a combination of state-of-the-art deposition modes during oxide molecular beam epitaxy, this approach opens up another degree of freedom in optimization and in situ control of the interface between two epitaxial oxide layers away from the substrate interface. Thus this approach is expected to apply to the general class of perovskite oxide 2DEG systems and to enable their improved compatibility with novel device concepts and integration across materialsplatforms.

Tail index estimation for tail adversarial stable time series with an application to high‐dimensional tail clustering

For stationary time series with regularly varying marginal distributions, an important problem is to estimate the associated tail index which characterizes the power‐law behavior of the tail distribution. For this, various results have been developed for independent data and certain types of dependent data. In this article, we consider the problem of tail index estimation under a recently proposed notion of serial tail dependence called the tail adversarial stability. Using the technique of adversarial innovation coupling and a martingale approximation scheme, we establish the consistency and central limit theorem of the tail index estimator for a general class of tail dependent time series. Based on the asymptotic normal distribution from the obtained central limit theorem, we further consider an application to cluster a large number of regularly varying time series based on their tail indices by using a robust mixture algorithm. The results are illustrated using numerical examples including Monte Carlo simulations and a real data analysis.

Study of a class of triangular starvation driven cross-diffusion systems

AbstractWe study the existence, regularity and uniqueness for a general class of triangular reaction-cross-diffusion systems coming from the study of starvation driven behavior for two species in competition. This study involves an equivalent system in non-divergence form, for which existence can be obtained thanks to Schauder’s fixed point theorem.

On decision problems concerning contextual insertions and deletions

The notions of stability, anti-stability, and error-correctability of a language that is modified by making contextual insertions in the words of the language were introduced in a previous paper by Bottoni et al. in 2011, where it was shown that these properties are decidable for regular languages. The authors proposed investigating the decidability of these properties for other classes of languages. Here, we derive necessary and sufficient conditions for a class of languages to have decidable stable, anti-stable, and error-correctable properties, and use these conditions to exhibit general classes of languages (strictly greater than the regular languages) for which the properties are decidable, and also simple classes (the first such classes) for which the properties are undecidable. We obtain identical results for the case when contextual deletions (instead of insertions) are made in the words of the language, and also with mixes of insertions and deletions. Our constructions also demonstrate that certain general problems involving nondeterministic generalized sequential machines (GSMs) applied to languages accepted by deterministic machine models are decidable, which is surprising as the deterministic language families do not need to be closed under GSM mappings.

Kinetics and Mechanism of PPh3/Ni-Catalyzed, Zn-Mediated, Aryl Chloride Homocoupling: Antagonistic Effects of ZnCl2/Cl.

The Ni/PPh3-catalyzed homocoupling of aryl chlorides in DMF using Zn as the stochiometric reducing agent is one of a general class of Ni-catalyzed processes, where the mechanism has been a matter of long-standing debate. This study re-evaluates prior conclusions and insights. NMR spectroscopy is used to identify [(PPh3)2NiII(Ar)Cl] as a key intermediate and to explore the indirect roles of using Zn as the reductant. The [ZnCl2] coproduct is responsible for several features, including a sequential transmetalation pathway involving [ArZnCl]. [ZnCl2] also abstracts halide from [(PPh3)2NiCl2] to generate [NiIICl(DMF)5]+[ZnCl3(DMF)]-, and in doing so, affects the NiII + Ni0 ↔ 2 NiI speciation. [ZnCl2] thus acts as an accelerator and inhibitor, resulting in mildly sigmoidal reaction profiles. When the [ZnCl2] concentration becomes too high or the phosphine ligand concentration too low, catalysis stalls. Turnover is restored by the addition of further phosphine ligand, or chloride ion. In the presence of an exogenous chloride ion, turnover is rapid, again proceeding via [(PPh3)2NiII(Ar)Cl] but via dinuclear metathesis. The generation of [ZnCl3(DMF)]- results in mutually antagonistic effects between [ZnCl2] and [Cl]- such that turnover proceeds via one mechanism or the other, depending on which species is in excess. The intermediacy of [ArZnCl] suggests a solution to the long-standing anomaly that many other reductants were found to be much less effective than Zn in inducing turnover of Ni/PPh3 catalyzed aryl chloride homocoupling in DMF. The use of DMAc as a solvent in place of DMF inhibits stalling through the steric inhibition of mixed metalate generation.

Extended Special Linear group ESL2(F) and matrix equations in SL2(F), SL2(Z) and GL2(Fp)

The problem of roots existence for different classes of matrix such as simple and semisimple matrices from SL2(F), SL2(Z) and GL2(F) are solved. For this purpose, we first introduced the concept of an extended special linear group ESL2(F), which is generalisation of the matrix group SL2(F), where F is arbitrary perfect field. The group of unimodular matrices and extended symplectic group ESp2(R) are generalised by us, their structures are found. Our criterion oriented on a general class of matrix depending of the form of minimal and characteristic polynomials, moreover a proposed criterion holds in GL2(F), where F is an arbitrary field. The method of matrix factorisation is outlined. We show that ESL2(F) is a set of all square matrix roots from SL2(F) except of that established in our root existence criterion.

Access for Students with Extensive Support Needs to State-Adopted Grade-Level Standards and Curriculum in General Education Classes: A Content Analysis of the Literature

In this article, we provide a summary of a literature review conducted to determine how the published literature, including research articles, conceptual articles, and chapters, (a) describes access to the state-adopted grade-level standards in general education classes for students with extensive support needs (ESN) and (b) discusses recommended processes for determining meaningful access to the state-adopted grade-level standards in general education classes for students with ESN. We reviewed a total of 554 pieces of published literature considered for inclusion in our summary. Based on our inclusion and exclusion criteria, we included 32 articles and chapters in the final analysis. The review yielded important information related to six themes, including (a) the language used to describe students with ESN; (b) the varying understandings, or perceptions, of what access to the state-adopted grade-level standards means; (c) the recommended steps in the processes that teams might use to provide access to the state-adopted grade-level standards, and the alignment between standards and Individualized Education Program goals; (d) the short- and long-term outcomes of access to and inclusion in the general education curriculum; (e) who is involved; and (f) the ways in which progress monitoring and assessment were implemented. We conclude with our recommendations for future research.