Large Class Research Articles

Existence of solutions for time fractional semilinear parabolic equations in Besov–Morrey spaces

AbstractWe consider the Cauchy problem for a time fractional semilinear heat equation "Equation missing"where $$0<\alpha <1,\, \gamma >1,\, N\in \mathbb {Z}_{\geqslant 1}$$ 0 < α < 1 , γ > 1 , N ∈ Z ⩾ 1 and $$\mu (x)$$ μ ( x ) belongs to inhomogeneous/homogeneous Besov–Morrey spaces. The fractional derivative $$^{C}\partial ^{\alpha }_{t}$$ C ∂ t α is interpreted in the Caputo sense. We present sufficient conditions for the existence of local/global-in-time solutions to problem (P). Our results cover all existing results in the literature and can be applied to a large class of initial data.

Eventually entanglement breaking divisible quantum dynamics

Abstract It is shown that a large class of quantum dynamical maps on complex matrix algebras governed by time-local Master Equations tend to become entanglement breaking in the course of time. Such situation seems to be generic for quantum evolution and in particular, completely positive dynamical semigroups with a unique faithful stationary state enjoy this property. Inspired by this observation, we propose a new concept of eventually entanglement breaking divisible (eEB-divisible) dynamics. A dynamical map is eEB-divisible if any propagator becomes entanglement breaking in finite time. It turns out that eEB-divisibility is quite general and holds for a large class of quantum evolutions.

Investigation of Differentiated Instruction Model ESP Based on Students’ Needs at Vocational High School in Palembang

This study investigates the application of differentiated instruction (DI) models in English for Specific Purposes (ESP) classrooms at vocational high schools in Palembang, focusing on students’ linguistic and vocational needs. Using a systematic literature review (SLR) following PRISMA guidelines, the research analysed 15 articles from Scopus, ERIC, Google Scholar, and Web of Science. The findings reveal that DI strategies are inconsistently applied, with teachers often facing challenges due to large class sizes, insufficient training, and resource limitations. However, when implemented effectively, DI has been shown to improve student engagement and learning outcomes. The study identifies best practices for enhancing DI in vocational ESP settings, emphasizing the need for curriculum alignment, task variety, and professional development to address the unique needs of vocational students. Recommendations include providing ongoing teacher training and better resources to optimize DI models in such contexts.

QUASI-ERGODICITY OF COMPACT STRONG FELLER SEMIGROUPS ON $L^2$

Abstract We study the quasi-ergodicity of compact strong Feller semigroups $U_t$ , $t> 0$ , on $L^2(M,\mu )$ ; we assume that M is a locally compact Polish space equipped with a locally finite Borel measue $\mu $ . The operators $U_t$ are ultracontractive and positivity preserving, but not necessarily self-adjoint or normal. We are mainly interested in those cases where the measure $\mu $ is infinite and the semigroup is not intrinsically ultracontractive. We relate quasi-ergodicity on $L^p(M,\mu )$ and uniqueness of the quasi-stationary measure with the finiteness of the heat content of the semigroup (for large values of t) and with the progressive uniform ground state domination property. The latter property is equivalent to a variant of quasi-ergodicity which progressively propagates in space as $t \uparrow \infty $ ; the propagation rate is determined by the decay of . We discuss several applications and illustrate our results with examples. This includes a complete description of quasi-ergodicity for a large class of semigroups corresponding to non-local Schrödinger operators with confining potentials.

Charge-neutral electronic excitations in quantum insulators.

Experiments on quantum materials have uncovered many interesting quantum phases ranging from superconductivity to a variety of topological quantum matter including the recently observed fractional quantum anomalous Hall insulators. The findings have come in parallel with the development of approaches to probe the rich excitations inherent in such systems. In contrast to observing electrically charged excitations, the detection of charge-neutral electronic excitations in condensed matter remains difficult, although they are essential to understanding a large class of strongly correlated phases. Low-energy neutral excitations are especially important in characterizing unconventional phases featuring electron fractionalization, such as quantum spin liquids, spin ices and insulators with neutral Fermi surfaces. In this Perspective, we discuss searches for neutral fermionic, bosonic or anyonic excitations in unconventional insulators, highlighting theoretical and experimental progress in probing excitonic insulators, new quantum spin liquid candidates and emergent correlated insulators based on two-dimensional layered crystals and moiré materials. We outline the promises and challenges in probing and using quantum insulators, and discuss exciting new opportunities for future advancements offered by ideas rooted in next-generation quantum materials, devices and experimental schemes.

Bloch classification surface for three-band systems

Abstract Topologically protected states can be found in physical systems, that show singularities in some energy contour diagram. These singularities can be characterized by winding numbers, defined on a classification surface, which maps physical state parameters. We have found a classification surface, which applies for three-band hamiltonian systems in the same way than standard Bloch surface does for two-band ones. This generalized Bloch surface is universal in the sense that it classifies a very large class of three-band systems, which we have exhaustively studied, finding specific classification surfaces, applying for each one.

Large coupling asymptotics for the Lyapunov exponents of some Schrödinger cocyles over strongly expanding circle endomorphisms

ABSTRACT We quantify the coupling asymptotics for the Lyapunov exponent of the Schrödinger cocycle over strongly expanding maps x ↦ bx ( mod 1 ) on T , for a large class of potential functions. We refine the previous lower bound results for these Lyapunov exponents, to get asymptotic results for all E ∈ R and for sufficiently expanding circle maps.

Importance sampling for option pricing with feedforward neural networks

AbstractWe study the problem of reducing the variance of Monte Carlo estimators through performing suitable changes of the sampling measure computed by feedforward neural networks. To this end, building on the concept of vector stochastic integration, we characterise the Cameron–Martin spaces of a large class of Gaussian measures induced by vector-valued continuous local martingales with deterministic covariation. We prove that feedforward neural networks enjoy, up to an isometry, the universal approximation property in these topological spaces. We then prove that sampling measures generated by feedforward neural networks can approximate the optimal sampling measure arbitrarily well. We conclude with a comprehensive numerical study pricing path-dependent European options for asset price models that incorporate factors such as changing business activity, knock-out barriers, dynamic correlations and high-dimensional baskets.

Hermite interpolation with retractions on manifolds

AbstractInterpolation of data on non-Euclidean spaces is an active research area fostered by its numerous applications. This work considers the Hermite interpolation problem: finding a sufficiently smooth manifold curve that interpolates a collection of data points on a Riemannian manifold while matching a prescribed derivative at each point. A novel procedure relying on the general concept of retractions is proposed to solve this problem on a large class of manifolds, including those for which computing the Riemannian exponential or logarithmic maps is not straightforward, such as the manifold of fixed-rank matrices. The well-posedness of the method is analyzed by introducing and showing the existence of retraction-convex sets, a generalization of geodesically convex sets. A classical result on the asymptotic interpolation error of Hermite interpolation is extended to the manifold setting. Finally numerical experiments on the manifold of fixed-rank matrices and the Stiefel manifold of matrices with orthonormal columns illustrate these results and the effectiveness of the method.

Communicative Language Teaching and Contextual Teaching and Learning: Challenges and Prospects in Chinese High-School English Education

This paper explores two widely employed language teaching methods in second and foreign language education: Communicative Language Teaching (CLT) and Contextual Teaching and Learning (CTL), and analyzes their applicability in Chinese high-school English curriculum. CLT primarily focuses on developing students' "communicative competence", which encompasses linguistic, sociolinguistic, textual, and strategic abilities. CTL, on the other hand, emphasizes connecting academic knowledge to students’ personal, social, and cultural contexts, helping them understand and apply what they learn in real-life situations. While the goals of both CLT and CTL align with the objectives of the Chinese high-school English curriculum, which aims to enhance students' ability to use language effectively in real-life contexts, there are significant challenges in implementing these approaches in practice. Major obstacles include an exam-oriented educational system, teacher-centered classroom models, large class sizes, and insufficient teacher training in both CLT and CTL methods. The paper concludes that although CLT and CTL have the potential to enhance students' language competence, their widespread and effective application in Chinese high-school English classrooms remains limited due to these barriers.

Obstacles in Instructing English at Village Elementary Schools in Bangladesh: A Study and Proposals

Elementary education serves as the foundation for students' future endeavors. Each year, many students in rural Bangladesh fail public examinations, and those who pass often do so by rote memorization, lacking proficiency in the four key language skills required for competence in English. Primary education was chosen for this study as it is a crucial stage where teachers bear full responsibility for student learning. The primary objective of this research was to identify the obstacles in teaching and learning English at the elementary level in rural areas of Bangladesh. Data were gathered using two sets of questionnaires administered to both students and teachers to assess the state of English language education in these primary schools. Additionally, teacher interviews and classroom observations, guided by an observation checklist, were conducted to gain a comprehensive understanding of the current teaching practices. The findings reveal that the majority of rural students struggle with English due to several factors, including a shortage of skilled and trained teachers, inadequate teacher training, inappropriate teaching methods and materials, limited contact hours, large class sizes, and insufficient pedagogical knowledge. This paper also includes several recommendations based on the research findings to address these challenges effectively.

Identifiability analysis of the fixed-effects one-parameter logistic positive exponent model.

In addition to the usual slope and location parameters included in a regular two-parameter logistic model (2PL), the logistic positive exponent (LPE) model incorporates an item parameter that leads to asymmetric item characteristic curves, which have recently been shown to be useful in some contexts. Although this model has been used in some empirical studies, an identifiability analysis (i.e., checking the (un)identified status of a model and searching for identifiablity restrictions to make an unidentified model identified) has not yet been established. In this paper, we formalize the unidentified status of a large class of fixed-effects item response theory models that includes the LPE model and related versions of it. In addition, we conduct an identifiability analysis of a particular version of the LPE model that is based on the fixed-effects one-parameter logistic model (1PL), which we call the 1PL-LPE model. The main result indicates that the 1PL-LPE model is not identifiable. Ways to make the 1PL-LPE useful in practice and how different strategies for identifiability analyses may affect other versions of the model are also discussed.

A novel translationally invariant supersymmetric chain with inverse-square interactions: partition function, thermodynamics and criticality

Abstract We introduce a novel family of translationally invariant su ( m | n ) supersymmetric spin chains with long-range interaction not directly associated with a root system. We study the symmetries of this model, establishing in particular the existence of a boson–fermion duality characteristic of this type of system. Taking advantage of the relation of the new chains with an associated many-body supersymmetric spin dynamical model, we are able to compute their partition function in closed form for all values of m and n and for an arbitrary number of spins. When both m and n are even, we show that the partition function factorizes as the product of the partition functions of two supersymmetric Haldane–Shastry spin chains, which in turn leads to a simple expression for the thermodynamic free energy per spin in terms of the Perron eigenvalue of a suitable transfer matrix. We use this expression to study the thermodynamics of a large class of these chains, showing in particular that the specific heat presents a single Schottky peak at approximately the same temperature as a suitable k-level model. We also analyze the critical behavior of the new chains, and in particular, the ground-state degeneracy and the existence of low-energy excitations with a linear energy–momentum dispersion relation. In this way, we show that the only possible critical chains are those with m = 0 , 1 , 2 . In addition, using the explicit formula for the partition function we are able to establish the criticality of the su ( 0 | n ) and su ( 2 | n ) chains with even n, and to evaluate the central charge of their associated conformal field theory.

Self-similar spirals for the generalized surface quasi-geostrophic equations

We construct a large class of nontrivial (nonradial) self-similar solutions of the generalized surface quasi-geostrophic equations (gSQG). To the best of our knowledge, this is the first rigorous construction of any self-similar solution for these equations. The solutions are of spiral type, locally integrable, and may have mixed sign. Moreover, they bear some resemblance to the finite time singularity scenario numerically proposed by Scott–Dritschel [J. Fluid Mechanics 863, article no. R2 (2019)] in the SQG patch setting.

Cosmological collider non-Gaussianity from multiple scalars and R2 gravity

Cosmological collider signals of primordial non-Gaussianity arise at tree level when an extra scalar has Hubble mass during inflation. We critically review the formalism finding that a large class of inflationary theories, based on Planck-scale physics, predict a scalar bi-spectrum around the gravitational floor level. This mild signal arises for example in R2 gravity, in the regime where its gravitational scalar has Hubble-scale mass. Signals much above the gravitational floor arise in theories where scalars undergo multiple turns during inflation, thanks to sub-Planckian physics.

A closure theorem for $\Gamma$-convergence and $H$-convergence with applications to non-periodic homogenization

In this work we examine the stability of some classes of integrals, in particular with respect to homogenization. The prototypical case is the homogenization of quadratic energies with periodic coefficients perturbed by a term vanishing at infinity, which has recently been examined in the framework of elliptic PDEs. We use localization techniques and higher-integrability Meyers-type results to provide a closure theorem by \Gamma -convergence within a large class of integral functionals. From such a result we derive stability theorems in homogenization which comprise the case of perturbations with zero average on the whole space. The results are also extended to the stochastic case, and specialized to the G -convergence of operators corresponding to quadratic forms. A corresponding analysis is also carried out for non-symmetric operators using the localization properties of H -convergence. Finally, we treat the case of perforated domains with Neumann boundary condition, and their stability.

Polynomial approximation of discounted moments

AbstractWe introduce an approximation strategy for the discounted moments of a stochastic process that can approximate the true moments for a large class of problems. These moments appear in pricing formulas of financial products such as bonds and credit derivatives. The approximation relies on a high-order power series expansion of the infinitesimal generator and draws parallels with the theory of polynomial processes. We demonstrate applications to bond pricing and credit derivatives. In the special cases that allow an analytical solution, the approximation error decreases to around 10 to 100 times machine precision for higher orders. When no analytical solution exists, we numerically compare the approximation with existing numerical techniques.

Existence and stability of almost finite energy weak solutions to the quantum Euler-Maxwell system

In this paper we prove the existence of global in time, finite energy weak solutions to the quantum magnetohydrodynamics (QMHD) system, for a large class of initial data that are slightly more regular than being of finite energy. No restriction is given on their size or the uniform positivity of the mass density. The QMHD system is a well-established model in superconductivity due to Feynman, and is intimately related to a nonlinear Maxwell-Schrödinger (NLMS) system via the Madelung transformations. The lack of global well-posedness (GWP) results for the NLMS system in the energy norm provides an obstruction to stability of its solutions, and consequently to the use of approximation arguments to make rigorous the Madelung approach. We implement here a new strategy, that derives weak solutions to QMHD starting from weak solutions to NLMS, by exploiting its Duhamel formulation. This derivation is rigorously justified by means of suitable dispersive/smoothing estimates for almost finite energy weak solutions to NLMS. The corresponding weak solutions to QMHD satisfy a generalized irrotationality condition, that allows for the presence of non-trivial vorticity (e.g., vortex filaments) concentrated in the vacuum region. This is in sharp contrast with the Euler-Maxwell system where the dispersion is not able to deal with the vorticity transport, therefore almost GWP (for regular solutions that are small perturbations of constant states) holds only in a lifespan, reciprocal of the size of the initial vorticity. Moreover, we also prove a stability property in the energy norm of the weak solutions constructed by our approach. This result follows from new local smoothing estimates for NLMS that are also of independent interest. As a byproduct, we also show the stability for the electromagnetic Lorentz force.

Higher-order interactions lead to ‘reluctant’ synchrony breaking

To model dynamical systems on networks with higher-order (non-pairwise) interactions, we recently introduced a new class of ordinary differential equations (ODEs) on hypernetworks. Here, we consider one-parameter synchrony breaking bifurcations in such ODEs. We call a synchrony breaking steady-state branch ‘reluctant’ if it is tangent to a synchrony space, but does not lie inside it. We prove that reluctant synchrony breaking is ubiquitous in hypernetwork systems, by constructing a large class of examples that support it. We also give an explicit formula for the order of tangency to the synchrony space of a reluctant steady-state branch.

Recent Advancements and SAR Studies of Synthetic Coumarins as MAO-B Inhibitors: An Updated Review.

The oxidative deamination of a wide range of endogenous and exogenous amines is catalyzed by a family of enzymes known as monoamine oxidases (MAOs), which are reliant on flavin-adenine dinucleotides. Numerous neurological conditions, such as Parkinson's disease (PD) and Alzheimer's disease (AD), are significantly correlated with changes in the amounts of biogenic amines in the brain caused by MAO. Hydrogen peroxide, reactive oxygen species, and ammonia, among other toxic consequences of this oxidative breakdown, can harm brain cells' mitochondria and cause oxidative damage. The prime objective of this review article was to highlight and conclude the recent advancements in structure-activity relationships of synthetic derivatives of coumarins for MAO-B inhibition, published in the last five years' research articles. The literature (between 2019 and 2023) was searched from platforms like Science Direct, Google Scholar, PubMed, etc. After going through the literature, we have found a number of coumarin derivatives being synthesized by researchers for the inhibition of MAO-B for the management of diseases associated with the enzyme such as Alzheimer's Disease and Parkinson's Disease. The effect of these coumarin derivatives on the enzyme depends on the substitutions associated with the structure. The structure-activity relationships of the synthetic coumarin derivatives that are popular nowadays have been described and summarized in the current study. The results revealed the updated review on SAR studies of synthetic coumarins as MAO-B inhibitors, specifically for Alzheimer's Disease and Parkinson's Disease. The patents reported on coumarin derivatives as MAO-B inhibitors were also highlighted. Recently, coumarins, a large class of chemicals with both natural and synthetic sources, have drawn a lot of attention because of the vast range of biological actions they have that are linked to neurological problems. Numerous studies have demonstrated that chemically produced and naturally occurring coumarin analogs both exhibited strong MAO-B inhibitory action. Coumarins bind to MAO-B reversibly thereby preventing the breakdown of neurotransmitters like dopamine leading to the inhibition of the enzyme A number of MAO-B blockers have been proven to be efficient therapies for treating neurological diseases like Alzheimer's Disease and Parkinson's Disease. To combat these illnesses, there is still an urgent need to find effective treatment compounds.