General Class Research Articles

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 $1 < p < r$ 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.

Observing Quantum Measurement Collapse as a Learnability Phase Transition

During a quantum measurement, superpositions of states with different observable properties probabilistically collapse into one with a sharp value of the measured observable. In macroscopic quantum systems, this collapse arises via a continuous measurement-induced phase transition (MIPT) at a critical value of the strength of interaction with the measurement apparatus. MIPTs lie outside established paradigms for equilibrium or nonequilibrium critical phenomena and delineate distinct, stable dynamical and computational phases of matter. Quantum computers enable programmable simulation of the interaction of a measurement apparatus with a dynamical quantum system, to explore MIPT phenomena over a range of system sizes while retaining quantum coherence. Yet, existing experimental protocols rely on fundamentally nonscalable postselection techniques or direct classical simulation of quantum circuits. Here, we report the scalable observation of finite-size scaling evidence for an observable-sharpening MIPT in monitored quantum circuits in a chain of Yb+171 ions in Quantinuum’s H1-1 trapped-ion quantum processor. By leveraging an equivalent description as a statistical physics problem, we implement scalable classical algorithms to infer the value of the measured observable from a single experimental shot. This technique enables a truly scalable protocol to observe observable-sharpening MIPTs in generic classes of circuits that cannot be directly classically simulated and also provides enhanced means to detect and suppress errors in the quantum simulation. Published by the American Physical Society 2024

A φ-Contractivity Fixed Point Theory and Associated φ-Invariant Self-Similar Sets

In this paper, we apply a generalized variant of the concept of fixed point theory due to contraction mappings on metric spaces to construct a general class of iterated function systems relative to the so-called φ-contraction mappings on a metric space. In particular, we give a general framework to the Hutchinson method of constructing self-similar sets as fixed points of suitable mappings issued from the φ-contractions on the metric space. The results may open a new axis in the generalization of self-similar sets and associated self-similar functions. Moreover, our results may be extended to general metric spaces with suitable assumptions. The theoretical results are applied for the computation of the fractal dimension of a concrete example of the new self-similar sets.

On the Oscillatory Behavior of Solutions of Second-Order Damped Differential Equations with Several Sub-Linear Neutral Terms

The oscillation and asymptotic behavior of solutions of a general class of damped second-order differential equations with several sub-linear neutral terms is considered. New sufficient conditions are established to fulfill a part of the gap in the oscillation theory for the case of sub-linear neutral equations. Our main results improve and generalize some of those recently published in the literature. Several examples are given to support our results.

Characterization of AI-enhanced magnetophoretic transistors operating in a tri-axial magnetic field for on-chip bioparticle sorting.

We demonstrate two general classes of magnetophoretic transistors, called the "trap" and the "repel-and-collect" transistors, capable of switching single magnetically labeled cells and magnetic particles between different paths in a microfluidic chamber. Compared with prior work on magnetophoretic transistors operating in a two-dimensional in-plane rotating field, the use of a tri-axial magnetic field has the fundamental advantages of preventing particle cluster formation and better syncing of single particles with the general operating clock. We use finite element methods to investigate the energy distribution on the chip surface and to predict the particle behavior at various device geometries. We then fabricate the proposed transistors and compare the experimental results with the simulation predictions. We found that with gate electrical currents of ~ 40mA for a transistor with proper geometry, complete switching of magnetic particles with diameters in the range of 8-15μm is achieved. We show that the device is reliable and works well at different magnetic field strengths (50-100 Oe) and frequencies (0.05-0.5Hz). We also employed an image processing code with a trained convolutional neural network to automate the proposed transistors for identifying and sorting particles with various sizes and magnetic susceptibilities with accuracies higher than 98%. The proposed transistors can be used in designing novel magnetophoretic circuits for important applications in biomedical microdevices and single-cell biology.

Preschool Teachers' Attitudes about Inclusive Education and Its Influencing Factors in China.

The purpose of this study is to describe the current status of preschool teachers' attitudes about inclusive education and discuss the factors that influence these attitudes. A total of 449 preschool teachers who have students with disabilities or special educational needs in their classrooms and 638 teachers without students with disabilities or special educational needs in their classrooms volunteered to complete the online survey. The survey included two components: a Basic Information Questionnaire and the Early Childhood Inclusive Education Attitude Questionnaire (ECIEAQ). Data were analyzed using descriptive statistics, t-tests, and ANOVA. Scores in the two dimensions of Positivity and Promotion were higher than those in the two dimensions of Resistance and Passivity, indicating an overall positive attitude about inclusive education. Attitudes about inclusive education significantly differed by gender, preschool location, inclusive education training opportunities, and receipt of a special education financial allowance. Inclusive class teachers who are female, aged over 30, teach classes with a child-to-teacher ratio of more than 14, and who work in urban areas show higher levels of Promotion or Resistance than general class teachers. Overall, preschool teachers hold a positive attitude about inclusive education. Training opportunities and a special education financial allowance should be provided to foster positive attitudes. Certain groups of inclusive class teachers may need more support and resources to implement inclusive education.

On the homology of big mapping class groups

AbstractWe prove that the mapping class group of the one‐holed Cantor tree surface is acyclic. This in turn determines the homology of the mapping class group of the once‐punctured Cantor tree surface (i.e. the plane minus a Cantor set), in particular answering a recent question of Calegari and Chen. We in fact prove these results for a general class of infinite‐type surfaces called binary tree surfaces. To prove our results we use two main ingredients: one is a modification of an argument of Mather related to the notion of dissipated groups; the other is a general homological stability result for mapping class groups of infinite‐type surfaces.

Optimal impulse control problems with time delays: An illustrative example

For impulse control systems described by a measure driven differential equation, depending linearly on the measure, it is customary to interpret the state trajectory corresponding to an impulse control, specified by a measure, as the limit of state trajectories associated with some sequence of conventional controls approximating the measure. It is known that, when the measure is vector valued, it is possible that different choices of approximating sequences for the measure give rise to different limiting state trajectories. If the measure is scalar valued, however, there is a unique limiting trajectory. Now consider impulse control systems, in which the right side of the measure driven differential equation depends on both the current and delayed states. In recent work by the authors it has been shown that, for such impulse control systems with time delay, the state trajectory corresponding to a given measure may be non-unique, even when the measure is scalar valued. It was also shown that each limiting state trajectory can be identified with the unique state trajectory associated with some measure together with a family of ‘attached controls’. (The attached controls capture the nature of the measure approximation.) The authors also derived a maximum principle governing minimizers for a general class of impulse optimal control problems with time delay, in which the domain of the optimization problem comprises measures coupled with a family of ‘attached controls’. The purpose of this paper is both to illustrate, by means of an example, this newly discovered non-uniqueness phenomenon and to provide the first application of the new maximum principle, to investigate minimizers for scalar input impulse optimal control problems with time delay, in circumstances when limiting state trajectories associated with a given measure control are not unique. The example is an optimal control problem, for which the underlying control system is a forced harmonic oscillator, with scalar impulse control, in which the control gain is a nonlinear function of the current and delayed states.

Global stability of coexistence equilibria for [formula omitted]-species models of facultative mutualism

We further pursue an investigation on an abstract model characterizing the dynamics of a general class of n-species facultative mutualisms that was initiated in Georgescu et al. (2017), establishing biologically relevant sufficient conditions for the global asymptotic stability of the coexistence equilibria. These conditions are given in terms of per-species limits of growth-to-loss ratios computed at higher population densities, complemented by either monotonicity or sublinearity inequalities, and are observed to hold for n-species versions of mutualistic models in current use. The specific modeling details that require either of these conditions being satisfied are outlined and discussed. As mutualisms can enhance species diversification and facilitate stable coexistence via a plethora of mechanisms, it is then important to understand the stability of speciose mutualisms, our results being of potential interest to theoretical ecologists studying the coexistence of many interacting species and to conservationists aiming for rare species preservation.

Fractional Reverse Inequalities Involving Generic Interval-Valued Convex Functions and Applications

The relation between fractional calculus and convexity significantly impacts the development of the theory of integral inequalities. In this paper, we explore the reverse of Minkowski and Hölder’s inequality, unified Jensen’s inequality, and Hermite–Hadamard (H-H)-like inequalities using fractional calculus and a generic class of interval-valued convexity. We introduce the concept of I.V-(⋏,ℏ) generic class of convexity, which unifies several existing definitions of convexity. By utilizing Riemann–Liouville (R-L) fractional operators and I.V-(⋏,ℏ) convexity to derive new improvements of the H-H- and Fejer and Pachpatte-like inequalities. Our results are quite unified; by substituting the different values of parameters, we obtain a blend of new and existing inequalities. These results are fruitful for establishing bounds for I.V R-L integral operators. Furthermore, we discuss various implications of our findings, along with numerical examples and simulations to enhance the reliability of our results.

Generalized likelihood ratio method for stochastic models with uniform random numbers as inputs

We propose a new unbiased stochastic gradient estimator for a family of stochastic models driven by uniform random numbers as inputs. Dropping the requirement that the tails of the density of the input random variables decay smoothly, the estimator extends the applicability of the generalized likelihood ratio (GLR) method. We demonstrate the new estimator for several general classes of input random variates, including independent inverse transform random variates and dependent input random variables governed by an Archimedean copula. We show how the new estimator works in settings such as density estimation, and we illustrate applications to credit risk derivatives. Numerical experiments substantiate broad applicability and flexibility in dealing with discontinuities in the sample performance.

A note on the standard zero-free region for [formula omitted]-functions

In this short note, we establish a standard zero-free region for a general class of L-functions for which their logarithms have coefficients with nonnegative real parts, including the Rankin–Selberg L-functions for unitary cuspidal automorphic representations.