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The Randić index (R) and the geometric-arithmetic index (GA) are found to be useful tools in QSPR and QSAR studies. In the Journal of Inequalities and Applications 180, 1-7, Lokesha, Shwetha Shetty, Ranjini, Cangul, and Cevik gave "New bounds for Randić and GA indices." In the paper, we first point out that Theorems 1, 2, and 4 are incorrect and in this short note we present the correct inequalities for Randić and GA indices. In the same paper, we provide the equality cases for Theorems 3, 5, and 6. [ABSTRACT FROM AUTHOR]

We consider a quantum system of large size N and its subsystem of size L, assuming that N is much larger than L, which can also be sufficiently large, i.e., 1 ≪ L ≲ N . A widely accepted mathematical version of this inequality is the asymptotic regime of successive limits: first the macroscopic limit N → ∞ , then an asymptotic analysis of the entanglement entropy as L → ∞ . In this paper, we consider another version of the above inequality: the regime of asymptotically proportional L and N, i.e., the simultaneous limits L → ∞ , N → ∞ , L / N → λ > 0 . Specifically, we consider a system of free fermions that is in its ground state, and such that its one-body Hamiltonian is a large random matrix, which is often used to model long-range hopping. By using random matrix theory, we show that in this case, the entanglement entropy obeys the volume law known for systems with short-range hopping but described either by a mixed state or a pure strongly excited state of the Hamiltonian. We also give streamlined proof of Page's formula for the entanglement entropy of black hole radiation for a wide class of typical ground states, thereby proving the universality and the typicality of the formula. [ABSTRACT FROM AUTHOR]

In this correspondence, we establish mean convergence theorems for the maximum of normed double sums of Banach space valued random elements. Most of the results pertain to random elements which are M-dependent. We expand and improve a number of particular cases in the literature on mean convergence of random elements in Banach spaces. One of the main contributions of the paper is to simplify and improve a recent result of Li, Presnell, and Rosalsky [Journal of Mathematical Inequalities, 16, 117–126 (2022)]. A new maximal inequality for double sums of M-dependent random elements is proved which may be of independent interest. The sharpness of the results is illustrated by four examples. [ABSTRACT FROM AUTHOR]

We consider a non-preemptive single machine scheduling problem for a non-negative penalty function f, where an optimal schedule satisfies the left-shifted property, i.e. in any optimal sequence all executions happen without idle time with a starting time t 0 ≥ 0 . For this problem, every job j has a priority weight w j and a processing time p j , and the goal is to find an order on the given jobs that minimizes ∑ w j f (C j) , where C j is the completion time of job j. This paper explores local dominance properties, which provide a powerful theoretical tool to better describe the structure of optimal solutions by identifying rules that at least one optimal solution must satisfy. We propose a novel approach, which allows to prove that the number of sequences that respect the local dominance property among three jobs is only two, not three, reducing the search space from n! to n ! / 3 ⌈ n / 3 ⌉ schedules. In addition, we define some non-trivial cases for the problem with a strictly convex penalty function that admits an optimal schedule, where the jobs are ordered in non-increasing weight. Finally, we provide some insights into three future research directions based on our results (i) to reduce the number of steps required by an exact exponential algorithm to solve the problem, (ii) to incorporate the dominance properties as valid inequalities in a mathematical formulation to speed up implicit enumeration methods, and (iii) to show the computational complexity of the problem of minimizing the sum of weighted mean squared deviation of the completion times with respect to a common due date for jobs with arbitrary weights, whose status is still open. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new convexity notion for inter-valued functions, known as Geometrically–Arithmetically Cr-h-convex functions (abbreviated as GA-Cr-h-CFs) and explore its properties. The family of GA-Cr-h-CFs simultaneously covers the family of GA-CFs, GA-h-CFs and GA-Cr-CFs. On the other hand, we demonstrate its equivalence with convex functions (CFs), h-CFs, Cr-CFs and Cr-h-CFs via exponential function. We also investigate necessary and sufficient conditions for GA-Cr-h-CFs via two corresponding real-valued GA-h-CFs. Due to significance and applications of mathematical inequalities, we apply our findings and propose several inequalities such as Jensen–Mercer inequality (JMI), Hermite–Hadamard inequality (HHI) and weighted Hermite–Hadamard-type inequalities (wHHIs) for GA-Cr-h-CFs. Through our results, we re-capture many known results and inequalities for subclasses of GA-Cr-h-CFs studied in the recent literature. [ABSTRACT FROM AUTHOR]

A 2006 conjecture of Antunes and Freitas is addressed connecting the scaling-invariant polygonal isoperimetric and principal frequency deficits for triangles. This yields a quantitative polygonal Faber–Krahn inequality for triangles with an explicit constant. Furthermore, a problem mentioned in the 1951 book "Isoperimetric Inequalities In Mathematical Physics" by Pólya and Szegö is addressed: a formula is given for the principal frequency of a triangle. Moreover, a space of polygons is constructed for the classical Pólya and Szegö problem: in 1947, Pólya proved that if n = 3, 4 the regular polygon Pn minimizes the principal frequency of an n-gon with given area α > 0 and suggested that the same holds when n ≥ 5. In 1951, Pólya and Szegö discussed the possibility of counterexamples. This paper constructs explicit (2n − 4)–dimensional polygonal manifolds M (n , α) and proves the existence of a computable N ≥ 5 such that for all n ≥ N, the admissible n-gons are given via M (n , α) and there exists an explicit set A n (α) ⊂ M (n , α) such that Pn has the smallest principal frequency among n-gons in A n (α). Inter-alia when n ≥ 3, a formula is proved for the principal frequency of a convex P ∈ M (n , α) in terms of an equilateral n-gon with the same area; and, the set of equilateral polygons is proved to be an (n − 3)–dimensional submanifold of the (2n − 4)–dimensional manifold M (n , α) near Pn. The techniques involve a partial symmetrization, tensor calculus, the spectral theory of circulant matrices, and W2,p/BMO estimates. Last, an application is given in the context of electron bubbles. [ABSTRACT FROM AUTHOR]

s t r i n g U t i l s. c o n v e r t A b s t r a c t M a t h H t m l (formulaUtilTools.convertMathHtml( s t r i n g U t i l s. c o n v e r t M m l (!article.abstractinfoEn)),'en') Compared to the standard variational inequalities, inverse variational inequalities are more suitable for pricing American options with indefinite payoff. This paper investigated the initial-boundary value problem of inverse variational inequalities constituted by a class of non-divergence type parabolic operators. We established the existence and Hölder continuity of weak solutions. Since the comparison principle in the case of standard variational inequalities is no longer applicable, we constructed an integral inequality using differential inequalities to determine the global upper bound of the solution. By combining it with the continuous method, we obtained the existence of weak solutions. Additionally, by employing truncation factors, we obtained the lower bound of weak solutions in the cylindrical subdomain, thereby obtaining the Hölder continuity. [ABSTRACT FROM AUTHOR]

This paper is concerned with non-fragile output-feedback control for time-delay neural networks with persistent dwell time (PDT) switching in a continuous-time setting. The main purpose is to design an output-feedback controller subject to gain fluctuations, guaranteeing both asymptotic stability and L 2 -gain of the closed-loop control system. To achieve reduced conservatism, the controller is formulated to depend not only on the system mode but also on a time scheduler constructed based on the PDT switching rule and minimum time span. A criterion for the asymptotic stability and L 2 -gain analysis is established through the application of the Gronwall–Bellman inequality and mathematical induction. Then, a numerically tractable design approach for the desired controller is proposed, utilizing a four-section piecewise time-dependent Lyapunov–Krasovskii functional and several nonlinearity decoupling techniques. For comparative purposes, a simple case, independent of the time scheduler, is also investigated, and the corresponding controller design approach is presented. Finally, a simulation example is given to illustrate the effectiveness and superiority of the proposed system mode and time scheduler dual-dependent controller design approach. [ABSTRACT FROM AUTHOR]

In this paper, the complete f-moment convergence for weighted sums of sequences of extended negatively dependent random variables is investigated. As a result, we not only extend and generalize some results on complete convergence obtained by Wu and Zhai (Journal of Mathematical Inequalities, 13(1): 251-260, 2019), but also get some results on the complete consistency for the estimator of nonparametric regression models and provide some simulations to assess the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the cavity–magnon steering and qubit–qubit steering of a hybrid quantum system consisting of a single-mode magnon, a two-qubit state, and a single-mode cavity field in the presence of their damping rates. The temporal wave vector of the system is obtained for the initial maximally entangled two-qubit state and initial vacuum state of the magnon and cavity modes. Additionally, the mathematical inequalities for obtaining the cavity–magnon steering and qubit–qubit steering are introduced. The findings reveal that steering between the magnon and cavity is asymmetric, while steering between the two qubits is symmetric in our system. Increasing the atom–field coupling improves steering from magnon to field, while reducing steering between the two qubits. Moreover, increasing magnon–field coupling enhances and elevates the lower bounds of qubit–qubit steering. Further, adding the damping rates causes deterioration of the cavity–magnon steering and qubit–qubit steering. However, the steering persistence is slightly greater when damping originates from the cavity field rather than the magnon modes based on the coupling parameters. [ABSTRACT FROM AUTHOR]

The Jensen, Jensen–Mercer, and Hermite–Hadamard inequalities have been key in advancing convex inequalities for scalars and operators, with several applications in fields like mathematical physics, operator theory and mathematical inequalities. This paper presents a new argument leading to interesting refinements of these celebrated inequalities. Applications that include entropy and operator inequalities will be presented. [ABSTRACT FROM AUTHOR]

This paper investigates the cavity–magnon steering and qubit–qubit steering of a hybrid quantum system consisting of a single-mode magnon, a two-qubit state, and a single-mode cavity field in the presence of their damping rates. The temporal wave vector of the system is obtained for the initial maximally entangled two-qubit state and initial vacuum state of the magnon and cavity modes. Additionally, the mathematical inequalities for obtaining the cavity–magnon steering and qubit–qubit steering are introduced. The findings reveal that steering between the magnon and cavity is asymmetric, while steering between the two qubits is symmetric in our system. Increasing the atom–field coupling improves steering from magnon to field, while reducing steering between the two qubits. Moreover, increasing magnon–field coupling enhances and elevates the lower bounds of qubit–qubit steering. Further, adding the damping rates causes deterioration of the cavity–magnon steering and qubit–qubit steering. However, the steering persistence is slightly greater when damping originates from the cavity field rather than the magnon modes based on the coupling parameters. [ABSTRACT FROM AUTHOR]

In the recent era of research developments, mathematical inequalities and their applications perform a very consequential role in different aspects, and they provide an engaging area for research activities. In this paper, we propose a new approach for the improvement of the classical majorization inequality and its weighted versions in a discrete sense. The proposed improvements give several estimates for the majorization differences. Some earlier improvements of the Jensen and Slater inequalities are deduced as direct consequences of the obtained results. We also discuss the conditions under which the main results give better estimates for the majorization differences. Applications of the acquired results are also presented in information theory. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new kind of conformable stochastic impulsive differential systems (CSIDS) involving discrete distribution of Bernoulli. For random discontinuous trajectories, we modify the tracking error of piecewise continuous variables by a zero-order holder. First, the improved P-type and PDα-type learning laws of the random iterative learning control (ILC) scheme are designed through global and local averaging operators. Next, we establish sufficient conditions for convergence of the tracking error in the expectation sense and prove the main results by using the impulsive Gronwall inequality and mathematical analysis tools. Finally, the theoretical results are verified by two numerical examples, and the tracking performance is compared for different conformable order of α. [ABSTRACT FROM AUTHOR]

This paper introduces several refinements of the classical Selberg inequality, which is considered a significant result in the study of the spectral theory of symmetric spaces, a central topic in the field of symmetry studies. By utilizing the contraction property of the Selberg operator, we derive improved versions of the classical Selberg inequality. Additionally, we demonstrate the interdependence among well-known inequalities such as Cauchy–Schwarz, Bessel, and the Selberg inequality, revealing that these inequalities can be deduced from one another. This study showcases the enhancements made to the classical Selberg inequality and establishes the interconnectedness of various mathematical inequalities. [ABSTRACT FROM AUTHOR]

In this paper, some open two-point Newton-Cotes type integral inequalities for functions whose first derivatives are convex via Riemann-Liouville fractional integrals are established. Our finding generalize some already known results. In order to illustrate the efficiency of our main results, some applications are given. [ABSTRACT FROM AUTHOR]

This paper aims to obtain the bounds of a class of integral operators containing Mittag–Leffler functions in their kernels. A recently defined unified Mittag–Leffler function plays a vital role in connecting the results of this paper with the well-known bounds of fractional integral operators published in the recent past. The symmetry of a function about a line is a fascinating property that plays an important role in mathematical inequalities. A variant of the Hermite–Hadamard inequality is established using the closely symmetric property for (α , m) -convex functions. [ABSTRACT FROM AUTHOR]

Fractional integral operators are useful tools for generalizing classical integral inequalities. Convex functions play very important role in the theory of mathematical inequalities. This paper aims to investigate the Hadamard type inequalities for a generalized class of functions namely strongly (α , h − m) -p-convex functions by using Riemann–Liouville fractional integrals. The results established in this paper give refinements of various well-known inequalities which have been published in the recent past. [ABSTRACT FROM AUTHOR]

Motivated by recent investigations relating the sharpness of the Jensen inequality, this paper concerns with the sharpness of the converse of the Jensen inequality. For this reason, the Jensen inequality has become one of the most discussed developmental inequalities in the current literature on mathematical inequalities. In this Special Issue, we present new results related to classical inequalities, such as the Jensen inequality, Jensen-Steffensen inequality, Jessen inequality, Grüss inequality, Chebyshev inequality, etc. [Extracted from the article]

This paper further investigates the problem of stability for a general linear system with time-varying delays. Firstly an improved type of Lyapunov–Krasovskii functional is introduced with integral and nonintegral terms and time-correlation terms. Referring a few existing papers, some valid inequalities mathematical analysis techniques are used in this paper in order to reduce the conservatism of the system. Finally, two examples are presented to demonstrate the advantages of the proposed tactics in this paper. [ABSTRACT FROM AUTHOR]

Many researchers have been attracted to the study of convex analysis theory due to both facts, theoretical significance, and the applications in optimization, economics, and other fields, which has led to numerous improvements and extensions of the subject over the years. An essential part of the theory of mathematical inequalities is the convex function and its extensions. In the recent past, the study of Jensen–Mercer inequality and Hermite–Hadamard–Mercer type inequalities has remained a topic of interest in mathematical inequalities. In this paper, we study several inequalities for GA-h-convex functions and its subclasses, including GA-convex functions, GA-s-convex functions, GA-Q-convex functions, and GA-P-convex functions. We prove the Jensen–Mercer inequality for GA-h-convex functions and give weighted Hermite–Hadamard inequalities by applying the newly established Jensen–Mercer inequality. We also establish inequalities of Hermite–Hadamard–Mercer type. Thus, we give new insights and variants of Jensen–Mercer and related inequalities for GA-h-convex functions. Furthermore, we apply our main results along with Hadamard fractional integrals to prove weighted Hermite–Hadamard–Mercer inequalities for GA-h-convex functions and its subclasses. As special cases of the proven results, we capture several well-known results from the relevant literature. [ABSTRACT FROM AUTHOR]

T.Z. Mirkovic [14] obtained new inequalities of Wirtinger type by using some classical inequalities and special means for convex function. So in this paper, we obtain some inequalities of Wirtinger type for s-convex function, m-convex function, (α,m)-convex function, quasi-convex function and P-function. Also several special cases are discussed, which can be deduced from our main results. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of anti-invariant Riemannian submersions in complex space forms. [ABSTRACT FROM AUTHOR]

Different types of mathematical inequalities have been largely analyzed and employed. In this paper, we introduce improvements to some Ostrowski type inequalities and present their corresponding proofs. The presented proofs are based on applying the celebrated Hayashi inequality to certain functions. We provide examples that show these improvements. Illustrations of the obtained results are stated in a probability framework. [ABSTRACT FROM AUTHOR]

This paper introduced and studied for the first time the object of neutrosophic quasigroup Q(Q,.) over a quasigroup (Q,.). It was shown that the direct product of any two neutrosophic quasigroups is a neutrosophic quasigroup. Also, it was established that the holomorph of any neutrosophic quasigroup is a neutrosophic quasigroup. The soft set theory which Molodtsov innovated is a potent mathematical tool used for solving mathematical problems with uncertainties and things that are not clearly defined. We broaden soft set theory by introducing soft neutrosophic quasigroup (NF;A)Q(Q,.) over a neutrosophic quasigroup Q(Q,.). We introduced and established the order of a finite soft neutrosophic quasigroup with varied mathematical inequality expressions which exist between the order of a finite neutrosophic quasigroup and that of its soft neutrosophic quasigroup. [ABSTRACT FROM AUTHOR]

In this paper, we study the nonoscillatory behavior of three classes of fractional difference equations. The investigations are presented in three different folds. Unlike most existing nonoscillation results which have been established by employing Riccati transformation technique, we employ herein an easily verifiable approach based on the fractional Taylor's difference formula, some features of discrete fractional calculus and mathematical inequalities. The theoretical findings are demonstrated by examples. We end the paper by a concluding remark. [ABSTRACT FROM AUTHOR]

In this research paper, we consider a class of boundary value problems for a nonlinear Langevin equation involving two generalized Hilfer fractional derivatives supplemented with nonlocal integral and infinite-point boundary conditions. At first, we derive the equivalent solution to the proposed problem at hand by relying on the results and properties of the generalized fractional calculus. Next, we investigate and develop sufficient conditions for the existence and uniqueness of solutions by means of semigroups of operator approach and the Krasnoselskii fixed point theorems as well as Banach contraction principle. Moreover, by means of Gronwall's inequality lemma and mathematical techniques, we analyze Ulam-Hyers and Ulam-Hyers-Rassias stability results. Eventually, we construct an illustrative example in order to show the applicability of key results. [ABSTRACT FROM AUTHOR]

This paper introduced and studied for the first time the object of neutrosophic quasigroup Q(Q,·) over a quasigroup (Q, ·). It was shown that the direct product of any two neutrosophic quasigroups is a neutrosophic quasigroup. Also, it was established that the holomorph of any neutrosophic quasigroup is a neutrosophic quasigroup. The soft set theory which Molodtsov innovated is a potent mathematical tool used for solving mathematical problems with uncertainties and things that are not clearly defined. We broaden soft set theory by introducing soft neutrosophic quasigroup (NF, A)... over a neutrosophic quasigroup Q(Q,·). We introduced and established the order of a finite soft neutrosophic quasigroup with varied mathematical inequality expressions which exist between the order of a finite neutrosophic quasigroup and that of its soft neutrosophic quasigroup. [ABSTRACT FROM AUTHOR]

Quantum calculus has numerous applications in mathematics. This novel class of functions may be used to produce a variety of conclusions in convex analysis, special functions, quantum mechanics, related optimization theory, and mathematical inequalities. It can drive additional research in a variety of pure and applied fields. This article's main objective is to introduce and study a new class of preinvex functions, which is called higher-order generalized strongly n-polynomial preinvex function. We derive a new q 1 q 2 -integral identity for mixed partial q 1 q 2 -differentiable functions. Because of the nature of generalized convexity theory, there is a strong link between preinvexity and symmetry. Utilizing this as an auxiliary result, we derive some estimates of upper bound for functions whose mixed partial q 1 q 2 -differentiable functions are higher-order generalized strongly n-polynomial preinvex functions on co-ordinates. Our results are the generalizations of the results in earlier papers. Quantum inequalities of this type and the techniques used to solve them have applications in a wide range of fields where symmetry is important. [ABSTRACT FROM AUTHOR]

The sixth paper, "On Some New Ostrowski-Mercer-Type Inequalities for Differentiable Functions", by Sial et al. [[6]], establishes a new integral identity involving differentiable functions and uses it for some new Ostrowski-Mercer-type inequalities for differentiable convex functions. The importance of inequalities in Mathematics is beautifully summarized in a citation attributed to Respected Professor Andrey Nikolaevich Kolmogorov: HT

An extension in Montgomery identity with the help of Taylor's formula on time scales is provided in the paper, which is used to establish Ostrowski type inequality, midpoint inequality and trapezoid type inequality on time scales in generalized forms. The weighted version of obtained Montgomery identity and respective Ostrowski inequality are also addressed at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, a new distributed robust filtering problem is investigated for a class of discrete-time systems subject to parameter uncertainty over sensor networks under the event-based transmission mechanism, where the uncertainty in the target plant is norm-bounded. To save limited network resources, an event-based communication strategy is presented to arrange data scheduling, where the next triggering time of each node can be predicted, and thus continuous listening is avoided. By employing the robust regularized least-squares estimation approach, a local robust recursive algorithm is first developed by minimizing the given quadratic cost index. Then, a fully distributed information fusion scheme is implemented by exchanging information between adjacent nodes, where the local information spreads to the entire network after a finite-step iteration under the connected topology. Furthermore, by utilizing the matrix inequality technique and the mathematical induction approach, some sufficient conditions are derived to ensure the uniform boundedness of the weighting matrices. Finally, an illustrative example is given to validate the developed distributed robust filtering algorithm. [ABSTRACT FROM AUTHOR]

An H∞ observer‐based control problem of delayed Linear Parameter Varying (LPV) stochastic system is addressed in this paper. In the LPV stochastic system, stochastic behaviors and external disturbance in real environment are respectively described by stochastic difference function. Furthermore, the delay effects on state and control input are considered as time‐varying case for wide application. For the control problem, a lemma dealing with the delay terms is proposed to increase some slack variables. Based on the proposed lemma and the chosen Lyapunov‐Krasovskii function, some sufficient conditions are derived to relax the conservatism of stability criterion. Besides, disturbance effect on state and estimation error is constrained via H∞ performance for improving transient response. Through using the extended projection lemma, the derived conditions are formulated as strict Linear Matrix Inequality (LMI) problem. To avoid the potential oscillation, another lemma is proposed to separately assign the performance level during solving the conditions. All feasible solutions can be directly obtained by convex optimization algorithm without using extra calculation. Therefore, an observer‐based controller is established to guarantee the asymptotical stability and H∞ performance in the mean square. Finally, some numerical simulations are provided to demonstrate the effectiveness and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with iterative learning control for conformable impulsive differential equations. For nonlinear and linear problems varying with the initial state, we design standard P-type, D γ -type, and conformable P I γ D γ -type learning update laws. Next, we establish sufficient conditions for tracking error convergence and use impulsive Gronwall inequality and mathematical analysis tools to prove the main results. Finally, three numerical examples are given to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

For the speed control system of autonomous electric vehicle (AEV), challenge happens with how to determine an appropriate driving speed to satisfy the dynamic environment while resisting uncertainty and disturbance. Therefore, this paper proposes a robust optimal speed control approach based on hierarchical architecture for AEV through combining deep reinforcement learning (DRL) and robust control. In decision‐making layer, a deep maximum entropy proximal policy optimization (DMEPPO) algorithm is presented to obtain an optimal speed via dynamic environment information, heuristic target entropy and adaptive entropy constraint. In motion control layer, to track the learned optimal speed while resisting uncertainty and disturbance, a robust speed controller is designed by the linear matrix inequality (LMI). Finally, simulation experiment results show that the proposed robust optimal speed control scheme based on hierarchical architecture for AEV is feasible and effective. [ABSTRACT FROM AUTHOR]

In 1964, Levinson [4] proved integral inequalities concerning generalization of Hardy's inequalities. In this paper two results are given. First one is extension of the Levinson Integral inequalities via convexity and the second is for the Levinson Integral inequalities of Hardy, this inequalities are established for p < 1 and some related inequalities are also considered with a sharp constant. [ABSTRACT FROM AUTHOR]

Introductory mathematics courses, including precalculus and calculus, largely influence Black and Latin* students' persistence and sense of belonging in STEM. However, prior research on instruction in these courses for advancing more equitable outcomes is limited. This paper presents findings from a study of 18 Black and Latina/o students' perceptions of introductory mathematics instruction as a racialized and gendered experience at a large, public, and historically white research university. Sociological perspectives of logics and mechanisms of inequality guided an analysis of Black and Latina/o students' group interview responses on how instruction perpetuates racial and gendered oppression. Two logics were identified: (i) Instructors hold more mathematical authority than students in classrooms; and (ii) Calculus coursework is used to weed out students 'not cut out' for STEM. These logics, coupled with the influence of broader sociohistorical forces (e.g., cultural scripts of behavior, stereotypes), gave rise to mechanisms of inequality through seemingly neutral instructional practices that reinforce racial-gendered distribution of classroom participation and STEM persistence. Our findings inform implications for STEM higher education researchers and mathematics faculty to foster socially affirming STEM instruction, especially in introductory courses. [ABSTRACT FROM AUTHOR]

In the present paper, an interesting subclass of meromorphic univalent functions defined on a punctured unit disk E={z:|z|1>1} has been considered and studied. A sufficient condition for these functions to be univalent and sense preserving in the class has been obtained. Certain geometric properties of the functions of the subclass of meromorphic functions has been discussed, such as coefficient inequality, starlike-ness, convexity, growth and distortion, convex linear combination and extreme points of the functions of the class by fixing some Taylor coefficients. [ABSTRACT FROM AUTHOR]

In this paper, BDG-type inequality for G-stochastic calculus with respect to G-Lévy process is obtained, and solutions of the stochastic differential equations driven by the G-Lévy process under the non-Lipschitz condition are constructed. Furthermore, the mean square exponential stability and quasi-sure exponential stability of the solution using the G-Lyapunov function method is established. [ABSTRACT FROM AUTHOR]

Abstract Multivariable operator theory is used to provide Bohr inequalities for free holomorphic functions with operator coefficients on the regular polyball B n , n = (n 1 , ... , n k) ∈ N k , which is a noncommutative analogue of the scalar polyball (C n 1 ) 1 × ⋯ × (C n k ) 1. The Bohr radius K m h (B n) (resp. K h (B n)) associated with the multi-homogeneous (resp. homogeneous) power series expansions of the free holomorphic functions are the main objects of study in this paper. We extend a theorem of Bombieri and Bourgain for the disc D : = { z ∈ C : | z | < 1 } to the polyball, and obtain the estimations 1 3 k < K m h (B n) < 2 log ⁡ k k if k > 1 , extending Boas-Khavinson result for the scalar polydisc D k. With respect to the homogeneous power series expansion, we prove that K h (B n) = 1 / 3 , extending the classical result, and obtain analogues of Carathéodory, Fejér, and Egerváry-Szász inequalities for free holomorphic functions with operator coefficients and positive real parts on the polyball. These results are used to provide multivariable analogues of Landau's inequality and Bohr's inequality when the norm is replaced by the numerical radius of an operator. When specialized to the regular polydisc D k (which corresponds to the case n 1 = ⋯ = n k = 1), we obtain new results concerning Bohr, Landau, Fejér, and Harnack inequalities for operator-valued holomorphic functions and k -pluriharmonic functions on the scalar polydisc D k. The results of the paper can be used to obtain Bohr type inequalities for the noncommutative ball algebra A n , the Hardy algebra F n ∞ , and the C ⁎ -algebra C ⁎ (S) , generated by the universal model S of the polyball B n. [ABSTRACT FROM AUTHOR]

In this paper, we establish two versions of the existence theorems of solutions set of generalized vector variational-like inequalities in fuzzy environment by using two different notions; the first one by using affineness and the second by using the notion of vector O-diagonally convexity. Moreover, an example is established in order to illustrate the main problem. The results of this paper can be viewed as a significant improvement and refinement of several other previously existing known results. [ABSTRACT FROM AUTHOR]

The problem of H∞ robust control based on event‐triggered sampling for a class of singular hybrid systems with Markovian jump is considered in this paper. The primary object of this paper here is to design the event‐triggered sampling controller for a class of uncertain singular Markovian systems, and two fundamental issues on mean square exponential admissibility and H∞ robust performance are fully addressed. By making use of a suitable Lyapunov functional, in combination with both infinitesimal operator and linear matrices inequalities(LMIs), the sufficient criteria are derived to guarantee the controlled singular hybrid system with Markovian jump is robustly exponentially mean‐square admissible and has a prescribed H∞ performance γ. Finally, a typical RLC circuit system is given to show the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the exponential stability, passivity, and $\boldsymbol {(\mathfrak {Q},\mathfrak {S},\mathfrak {R})}$ - $\boldsymbol {\gamma }$ -dissipativity of generalized neural networks (GNNs) including mixed time-varying delays in state vectors. Novel exponential stability, passivity, and $\boldsymbol {(\mathfrak {Q},\mathfrak {S},\mathfrak {R})}$ - $\boldsymbol {\gamma }$ -dissipativity criteria are developed in the form of linear matrix inequalities for continuous-time GNNs by constructing an appropriate Lyapunov-Krasovskii functional (LKF) and applying a new weighted integral inequality for handling integral terms in the time derivative of the established LKF for both single and double integrals. Some special cases are also discussed. The superiority of employing the method presented in this paper over some existing methods is verified by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we establish two versions of the existence theorems of solutions set of generalized vector variational-like inequalities in fuzzy environment by using two different notions; the first one by using affineness and the second by using the notion of vector O-diagonally convexity. Moreover, an example is established in order to illustrate the main problem. The results of this paper can be viewed as a significant improvement and refinement of several other previously existing known results. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the H ∞ state estimation problem for time-varying artificial neural networks with component-based distributed delays and stochastic protocol scheduling. A shared communication channel is adopted for data transmissions between the sensors and the estimator. For the purpose of avoiding data collisions, the stochastic protocol is used to schedule the transmission opportunities of sensors. A finite-horizon H ∞ index is introduced to reflect the performance specification of the estimation. The aim of this paper is to design a time-varying H ∞ estimator over a given finite-horizon such that the dynamics of the estimation error satisfy the given H ∞ performance requirement. Sufficient conditions are established for the existence of the desired estimator and the explicit expressions of the desired estimator parameters are then given in terms of the solutions to a set of recursive linear matrix inequalities. Finally, a numerical example is given to demonstrate the effectiveness of the developed state estimation scheme. [ABSTRACT FROM AUTHOR]

Cross-entropy for uncertain variables is used to measure the divergence between two uncertainty distributions. Logarithm cross-entropy and quadratic cross-entropy for uncertain variables fail to measure the degree of divergence associated with some uncertain variables; thus, this paper proposes a new definition of cross-entropy for uncertain variables as a supplement and discusses its properties. A formula of cross-entropy is derived via inverse uncertainty distributions. Moreover, this paper also defines the generalized cross-entropy of uncertain variables and investigates its properties. [ABSTRACT FROM AUTHOR]