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The purpose of this paper is twofold. First, we show that the results in a companion paper on product rigidity for maps $ f: \Omega_1 \times \Omega_2 \subset \mathbb R^n \times \mathbb R^n \to \mathbb R^n \times \mathbb R^n $ in the Sobolev space $ W^{1, p} $ are sharp with respect to $ p $. Specifically, we show that for all $ n \ge 2 $ and all $ p < 2 $ there exist maps $ f \in W^{1, p} $ such that the weak differential $ Df $ is invertible almost everywhere and preserves or reverses the product structure almost everywhere, but $ f $ is not of the form $ f(x, y) = (f_1(x), f_2(y)) $ or = $ f(x, y) = (f_2(y), f_1(x)) $. Secondly, we develop a general toolbox to study $ W^{1, p} $ solutions of differential inclusions $ Du \in K $ for unbounded sets $ K $. As an illustration we give short proofs of results by Astala et al. on optimal $ W^{1, p} $ regularity for solutions of elliptic equations with measurable coefficients and results by Colombo and Tione on irregular solutions of the $ p $-Laplace equation. [ABSTRACT FROM AUTHOR]

This paper is concerned with optimal control problems governed by constrained hereditary second- order differential inclusions (DFIs). We also focus on delay-neutral and assigned Hale type DFIs, which arise in many fields of applied science and play a vital role in the mathematical modeling of real-life phenomena. To the best of our knowledge, such problems for second-order hereditary DFIs have not been considered in the literature from the viewpoint of optimality conditions. In this way we formulate sufficient conditions of optimality for second-order convex and nonconvex neutral functional-DFIs in Euler-Lagrange and Hamiltonian forms and transversality conditions. The results obtained are applied to some linear problems. [ABSTRACT FROM AUTHOR]

Turkey, as the largest refugee-hosting country, provides insights into the externalization of European borders and the internalization of its own borders. Oscillating between open-door and strict-border policies, alongside the political inactiveness of public authorities and CSOs governing Syrian mobility, Turkey reveals crucial dynamics. Focusing on Syrian refugees' housing in a refugee hub of Izmir, this study unravels internal bordering and explores its rationales and the involvement of non-state actors. Syrian refugees encounter three internal bordering mechanisms affecting their housing inclusion: selective overpricing, ethnic filtering and arbitrary interrogations. These differential inclusion practices, led by market actors (landlords and realtors), ethnic networks, and street-level bureaucrats (mukhtars and municipal officers), are driven by the prevalence of anti-refugee sentiment in Turkey, where Syrians are perceived as unwanted or undeserving. The internal bordering mechanisms are rooted in ethnic, economic, cultural, and security-based rationales, influenced by the personal interests and socio-economic backgrounds of the involved actors. [ABSTRACT FROM AUTHOR]

One of the core concepts of contemporary control theory is the idea that a dynamical system can be controlled. Several abstract settings have been developed to describe the distributed control systems in a domain in which the control is acted through the boundary. In this manuscript, we investigate the boundary approximate controllability (ABC) of stochastic differential inclusion (SDI) with Hilfer fractional derivative (HFD) and nonlocal condition by implementing the principle of stochastic analysis, the fixed-point theorem, fractional calculus and multi-valued map. Moreover, an example is offered to define the primary results. [ABSTRACT FROM AUTHOR]

This paper is devoted to study the rotational periodic boundary value problem for a fractional‐order nonlinear differential equation. Applying topology‐degree theory and the Leray‐Schauder fixed‐point theorem, we prove the existence and uniqueness of solution for the fractional‐order differential system. Furthermore, the existence of solution for a nonlinear differential system with a multivalued perturbation term is investigated by using set‐valued theory and techniques of functional analysis. Two examples of applications are given at the end. [ABSTRACT FROM AUTHOR]

Ill tills tliesis we will prove, ill infinite dimensional spaces, an existence result concerning the existence of solutions for a semilinear differential inclusions with fractional order. Then we establish the existence of a continuous selection for the multifunction which represents tl'ie solution sets. We consider the case wlien tliere is a delay. Our technique depends on using an appropriate fixed point theorem and a known result ensues the existence of continuous selections. Tile obtained results extend a recent publislied result, concerning the existence of solutions for a semilinear differential inclusions with fractional order, from finite dimensional spaces to infinite dimensional spaces. Moreover, our technique allows to study the existence of continuous selections for some semilinear differential inclusions with fractional order in infinite dimensional spaces. [ABSTRACT FROM AUTHOR]

Introduction: Clear cell sarcoma (CCS) of the soft tissue is a type of tumor that primarily affects the deep soft tissues of the extremities and trunk. We report a case of CCS of soft tissue arising in the first metacarpal of the hand, focusing on the imaging features of CCS combined with the clinicopathological and immunological results. Case Presentation: In this case, computed tomography images showed a soft tissue mass at the first metacarpal, with heterogeneous density, unclear boundaries, and bone destruction. On magnetic resonance imaging (MRI), the mass showed slightly higher signal intensity on T1-weighted images and mixed hyperintensity on T2-weighted images, with inhomogeneous enhancements. On both T1-weighted and T2-weighted sequences, there were some hypointense strips. No significant enhancements were found in these hypointense strips. Conclusion: We suggest that hypointense strips on MRI should lead to the inclusion of CCS in differential diagnoses. [ABSTRACT FROM AUTHOR]

Background Methods Results Conclusion Childhood neurodegenerative diseases often pose a challenge to clinicians to diagnose because of the degree of genetic heterogeneity and variable presentations. Here, we present a child with progressive neurodegeneration consisting of spasticity, dystonia, and ataxia in which postmortem pathological analysis led to the diagnosis of interferon regulatory factor 2 binding protein like (IRF2BPL)‐related disorder.Detailed postmortem gross and histological examination was conducted, and findings consistent with dentatorubral‐pallidoluysian atrophy (DRPLA) and included polyglutamine (polyQ) inclusions. Follow up testing for the CAG repeat expansion at ATN1 was non‐diagnostic.Subsequent exome sequencing reanalysis of the research exome identified a pathogenic de novo IRF2BPL variant. The IRF2BPL c.562C>T, p.(Arg188Ter) variant, distal to the polyQ repeat tract, results in variable mRNA levels depending on the cell type examined with decreased mRNA in the brain, as well as destabilization of the protein product and corresponding downstream molecular abnormalities in patient derived cells.We provide the first detailed pathological description for IRF2BPL‐related disorder, termed NEDAMSS (neurodevelopmental disorder with regression, abnormal movements, loss of speech and seizures; Mendelian Inheritance in Man, 618088) and evidence for the inclusion of this condition in the differential diagnosis of spastic‐ataxic neurodegenerative conditions, reminiscent of DRPLA. Although the individuals with NEDAMSS do not carry an expansion, the polyQ repeat tract may play a role in the pathological inclusions that would represent a novel disease mechanism for polyQ repeats. © 2024 International Parkinson and Movement Disorder Society. [ABSTRACT FROM AUTHOR]

We study a singularly perturbed control system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are dense in the set of solutions of a certain differential inclusion and discuss an implication of this result for optimal control. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several new types of partial fractional derivatives in the continuous setting and the discrete setting. We analyze some classes of the abstract fractional differential equations and the abstract fractional difference equations depending on several variables, providing a great number of structural results, useful remarks and illustrative examples. Concerning some specific applications, we would like to mention here our investigation of the fractional partial differential inclusions with Riemann–Liouville and Caputo derivatives. We also establish the complex characterization theorem for the multidimensional vector-valued Laplace transform and provide certain applications. [ABSTRACT FROM AUTHOR]

This paper concerns control BVPs, driven by ODEs x ′ t = u t , using controls u 0 ·   & u 1 · in L 1 a , b , R 2 . We ask these two controls to satisfy a very simple restriction: at points where their first coordinates coincide, also their second coordinates must coincide; which allows one to write (u 1 − u 0) · = v · 1 , f · for some f · . Given a relaxed non bang-bang solution x ¯ · ∈ W 1 , 1 a , b , R 2 , a question relevant to applications was first posed three decades ago by A. Cellina: does there exist a bang-bang solution x ^ · having lower first-coordinate x ^ 1 · ≤ x ¯ 1 · ? Being the answer always yes in dimension d = 1 , hence without f · , as proved by Amar and Cellina, for d = 2 the problem is to find out which functions f · "are good", namely "allow such 1-lower bang-bang solution x ^ · to exist". The aim of this paper is to characterize "goodness of f · " geometrically, under "good data". We do it so well that a simple computational app in a smartphone allows one to easily determine whether an explicitly given f · is good. For example: non-monotonic functions tend to be good; while, on the contrary, strictly monotonic functions are never good. [ABSTRACT FROM AUTHOR]

This paper addresses the approximate controllability results for Hilfer fractional stochastic differential inclusions of order 1 < q < 2 . Stochastic analysis, cosine families, fixed point theory, and fractional calculus provide the foundation of the main results. First, we explored the prospects of finding mild solutions for the Hilfer fractional stochastic differential equation. Subsequently, we determined that the specified system is approximately controllable. Finally, an example displays the theoretical application of the results. [ABSTRACT FROM AUTHOR]

Robotic manipulation and locomotion often entail nearly-simultaneous collisions—such as heel and toe strikes during a foot step—with outcomes that are extremely sensitive to the order in which impacts occur. Robotic simulators and state estimation commonly lack the fidelity and accuracy to predict this ordering, and instead pick one with a heuristic. This discrepancy degrades performance when model-based controllers and policies learned in simulation are placed on a real robot. We reconcile this issue with a set-valued rigid-body model which generates a broad set of outcomes to simultaneous frictional impacts with any impact ordering. We first extend Routh's impact model to multiple impacts by reformulating it as a differential inclusion (DI), and show that any solution will resolve all impacts in finite time. By considering time as a state, we embed this model into another DI which captures the continuous-time evolution of rigid-body dynamics, and guarantee existence of solutions. We finally cast simulation of simultaneous impacts as a linear complementarity problem (LCP), and develop an algorithm for tight approximation of the post-impact velocity set with probabilistic guarantees. We demonstrate our approach on several examples drawn from manipulation and legged locomotion, and compare the predictions to other models of rigid and compliant collisions. [ABSTRACT FROM AUTHOR]

In real Hilbert spaces, given a single-valued Lipschitz continuous and monotone operator, we study generalized split feasibility problem (GSFP) over solution set of monotone variational inclusion problem. An inertia iterative method is proposed to solve this problem, by showing that the sequence generated by the iteration converges strongly to solution of GSFP. As against previous methods, our step size is chosen to be simple and not depending on norm of associated bounded linear map as well as Lipschitz constant of the single-valued operator. The obtained result was applied to study split linear inverse problem, precisely, the LASSO problem. Lastly, with the aid of numerical examples, we exhibited efficiency of our algorithm and its dominance over other existing schemes. [ABSTRACT FROM AUTHOR]

We consider first-order methods with constant step size for minimizing locally Lipschitz coercive functions that are tame in an o-minimal structure on the real field. We prove that if the method is approximated by subgradient trajectories, then the iterates eventually remain in a neighborhood of a connected component of the set of critical points. Under suitable method-dependent regularity assumptions, this result applies to the subgradient method with momentum, the stochastic subgradient method with random reshuffling and momentum, and the random-permutations cyclic coordinate descent method. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the optimisation of parabolic type differential inclusions (DFIs) given by polyhedral set-valued mappings. For this, an auxiliary problem with a polyhedral parabolic discrete inclusion is defined. With the help of locally adjoint mappings and comparison of matrix-coefficients of discrete and discrete-approximate problems, necessary and sufficient optimality conditions for polyhedral-parabolic discrete-approximate inclusions are skilfully constructed. Thus, using the discretisation method and the features of the polyhedral nature of the problem, we prove sufficient optimality conditions for a polyhedral parabolic DFI. At the end of the paper, the numerical results are presented. [ABSTRACT FROM AUTHOR]

Abstract One of the core concepts of contemporary control theory is the idea that a dynamical system can be controlled. Several abstract settings have been developed to describe the distributed control systems in a domain in which the control is acted through the boundary. In this manuscript, we investigate the boundary approximate controllability (ABC) of stochastic differential inclusion (SDI) with Hilfer fractional derivative (HFD) and nonlocal condition by implementing the principle of stochastic analysis, the fixed-point theorem, fractional calculus and multi-valued map. Moreover, an example is offered to define the primary results.

We use essential limits inferior and superior of the nonlinear part of a discontinuous ODE to introduce some novel transversality conditions which imply that Filippov solutions are Carathéodory solutions. We also prove some uniqueness criteria based on different Lipschitz conditions on different parts of the domain separated from one another by boundaries which satisfy certain transversality conditions.

We examine the problem of reducing the control set in a dynamical system so that the solution set and the attainable sets remain essentially unchanged. We cite some classical results to exhibit the problem and promote a set-valued approach. A necessary condition is formulated by using a concept of set-valued derivative, which can be regarded as an extension of the classical Relaxation theorem. [ABSTRACT FROM AUTHOR]

Thermal transmission is very significant in the industrial and engineering sectors. This research aims to investigate the MHD stagnation point movement of methanol and water-driven Cu −Al2O3 hybrid nanofluid flow via an exponentially extending cylinder. An inclined magnetic field’s control, suction or injection and viscous dissipation impacts are used and considered in the flow paradigm, as no prior research has been performed on it. This motivated the authors to perform a computational analysis of the distinct base fluid (water and methanol)-driven hybrid nanofluid flow with the aforementioned impacts, which gives distinctiveness to the flow model. The basic partial differential equation flow mechanism has been streamlined to nondimensional ordinary differential equations by the inclusion of distinct dimensionless factors, which are simulated employing the BVP4c methodology. The impacts of dimensionless variables, namely the Eckert factor, suction/injection term, Biot factor, velocity ratio term and magnetic factor, on the flow speed, thermal distribution, rate of shearing stress and thermal transmission are delineated in figures and demonstrated with tables. The major findings specify that methanol-based hybrid nanofluid (Cu −Al2O3/methanol) has a significantly higher thermal transmission rate when compared with the water-based hybrid nanofluid (Cu −Al2O3/water). Furthermore, it has been shown that the methanol-based hybrid nanofluid has an absolute friction drag that is up to 26.5% larger than that of nanofluid. The thermal gradient reduces with the enhancement of Ec and M. Moreover, the fluid temperature upsurges as Ec and Bi elevate. These outcomes significantly advance fluid dynamics and nanofluid research, offering opportunities for improved thermal transmission in numerous industrial and engineering sectors. A noteworthy validation with previously published work has also been performed. [ABSTRACT FROM AUTHOR]

The main innovation of this article is to establish the existence and approximate controllability of Hilfer fractional differential inclusions of order 1<μ<2$$ 1<\mu <2 $$ using Clarke's subdifferential type in Hilbert spaces. By applying the fixed‐point theorem for multivalued maps, fractional calculus, generalized Clarke's subdifferential, and cosine families, we derive a novel existence result for the mild solutions of the Hilfer fractional differential inclusion system. Furthermore, we develop and demonstrate a new set of sufficient conditions for the approximate controllability of Hilfer fractional differential systems. These criteria are based on the assumption that the associated linear part of the system is approximately controllable. Finally, an example is provided to show the theoretical findings. [ABSTRACT FROM AUTHOR]

Fibromyalgia (FM) is a chronic non-inflammatory disorder mainly characterized by widespread musculoskeletal pain, fatigue, sleep disturbances, and a constellation of other symptoms. For this reason, delineating a clear distinction between pure FM and FM-like picture attributable to other common diseases can be extremely challenging. Physicians must identify the most significant confounders in individual patients and implement an appropriate diagnostic workflow, carefully choosing a minimal (but sufficient) set of tests to be used for identifying the most plausible diseases in the specific case. This article discusses prevalent non-rheumatological conditions commonly observed in the general population that can manifest with clinical features similar to primary FM. Given their frequent inclusion in the differential diagnosis of FM patients, the focus will be on elucidating the distinctive clinical characteristics of each condition. Additionally, the most cost-effective and efficient diagnostic methodologies for accurately discerning these conditions will be examined. [ABSTRACT FROM AUTHOR]

In this paper, we present new methods for solving the problem of the asymptotic behavior of trajectories of control systems governed by functional differential inclusions with nonconvex-valued right-hand sides. The main tool for solving this problem is the method of nonsmooth integral guiding potentials. [ABSTRACT FROM AUTHOR]

The results in this paper are related to the existence of solutions to hybrid and non-hybrid discrete fractional three-point boundary value inclusion problems for the elastic beam equation. The development of our results is attributed to the use of the Caputo and difference operators. The existence results for the non-hybrid discrete fractional inclusion problem are established by using fixed point theory for multi-valued upper semi-continuous maps, and the case of the hybrid discrete fractional inclusion problem is treated by Dhage's fixed point theory. Additionally, we present two examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this work, we introduce a new definition for the fractional differential operator that generalizes several well-known fractional differential operators. In fact, we introduce the notion of the p -proportional ω -weighted κ -Hilfer derivative includes an exponential function, D a , λ σ , ρ , p , κ , ω , and then we consider a non-instantaneous impulse differential inclusion containing D a , λ σ , ρ , p , κ , ω with order σ ∈ (1 , 2) and of kind ρ ∈ [ 0 , 1 ] in Banach spaces. We deduce the relevant relationship between any solution to the studied problem and the integral equation that corresponds to it, and then, by using an appropriate fixed-point theorem for multi-valued functions, we give two results for the existence of these solutions. In the first result, we show the compactness of the solution set. Next, we introduce the concept of the (p , ω , κ) -generalized Ulam-Hyeres stability of solutions, and, using the properties of the multi-valued weakly Picard operator, we present a result regarding the (p , ω , κ) -generalized Ulam-Rassias stability of the objective problem. Since many fractional differential operators are particular cases of the operator D a , λ σ , ρ , p , κ , ω , our work generalizes a number of recent findings. In addition, there are no past works on this kind of fractional differential inclusion, so this work is original and enjoyable. In the last section, we present examples to support our findings. [ABSTRACT FROM AUTHOR]

In this study, we explore the existence and uniqueness of solutions for a boundary value problem defined by coupled sequential fractional differential inclusions. This investigation is augmented by the introduction of a novel set of generalized Riemann–Liouville boundary conditions. Utilizing Carathéodory functions and Lipschitz mappings, we establish existence results for these nonlocal boundary conditions. Utilizing fixed-point theorems designed for multi-valued maps, we obtain significant existence results for the problem, considering both convex and non-convex values. The derived results are clearly demonstrated with an illustrative example. Numerical examples are provided to validate the theoretical conclusions, contributing to a deeper understanding of fractional-order boundary value problems. [ABSTRACT FROM AUTHOR]

• Combine extrinsic GFDM with absorbing boundary condition for simulating acoustic wave propagation on surfaces. • Accuracy simulation of wave propagation on surfaces with periodic holes or inclusions. • Give convergence analysis for increasing node density and decreasing frequency. • Reveal significant impact of periodic structures. • Investigate effects of filling fraction & surface curvature on transmission. This paper introduces a localized meshless method to analyze time-harmonic acoustic wave propagation on curved surfaces with periodic holes/inclusions. In particular, the generalized finite difference method is used as a localized meshless technique to discretize the surface gradient and Laplace-Beltrami operators defined extrinsically in the governing equations. An absorbing boundary condition is introduced to reduce reflections from boundaries and accurately simulate wave propagation on unclosed surfaces with periodic inclusions. Several benchmark examples demonstrate the efficiency and accuracy of the proposed method in simulating acoustic wave propagation on surfaces with diverse geometries, including complex shapes and periodic holes or inclusions. [ABSTRACT FROM AUTHOR]

Tick-borne rickettsioses are considered among the oldest known vector-borne zoonotic diseases. Among the rickettsiae, Rickettsia africae is the most reported and important in Africa, as it is the aetiological agent of African tick bite fever (ATBF). Studies describing the prevalence of R. africae in southern Africa are fragmented, as they are limited to small geographical areas and focused on Amblyomma hebraeum and Amblyomma variegatum as vectors. Amblyomma spp. ticks were collected in Angola, Mozambique, South Africa, Zambia and Zimbabwe during the sampling period from March 2020 to September 2022. Rickettsia africae was detected using the ompA gene, while characterisation was conducted using omp, ompA, ompB and gltA genes. In total, 7734 Amblyomma spp. ticks were collected and were morphologically and molecularly identified as Amblyomma eburneum, A. hebraeum, Amblyomma pomposum and A. variegatum. Low levels of variability were observed in the phylogenetic analysis of the R. africae concatenated genes. The prevalence of R. africae ranged from 11.7% in South Africa to 35.7% in Zambia. This is one of the largest studies on R. africae prevalence in southern Africa and highlights the need for the inclusion of ATBF as a differential diagnosis when inhabitants and travellers present with flu-like symptoms in the documented countries. [ABSTRACT FROM AUTHOR]

In the present article, we have introduced the notions of γ-admissibility for the pair of q-ROF set-valued maps and admissible hybrid q-ROF Z -contraction. Notions introduced in the article generalizes the existing concepts in fuzzy literature. Common fixed point result for a pair of γ-admissible q-ROF mappings in b-metric spaces utilizing the introduced contraction is presented. A nontrivial example to support the obtained results is also included. As an application, we have discussed the existence of solution of system of non-linear n-th order differential inclusions with non-local and integral boundary conditions. [ABSTRACT FROM AUTHOR]

In the region between two closely located stiff inclusions, the stress, which is the gradient of a solution to the Lamé system with partially infinite coefficients, may become arbitrarily large as the distance between interfacial boundaries of inclusions tends to zero. The primary aim of this paper is to give a sharp description in terms of the asymptotic behavior of the stress concentration, as the distance between interfacial boundaries of inclusions goes to zero. For that purpose, we capture all the blow‐up factor matrices, whose elements comprise of some certain integrals of the solutions in the case when two inclusions are touching. Then, we are able to establish the asymptotic formulas of the stress concentration in the presence of two close‐to‐touching m$$ m $$‐convex inclusions in all dimensions. Furthermore, an example of curvilinear squares with rounded‐off angles is also presented for future application in numerical computations and simulations. [ABSTRACT FROM AUTHOR]

In the humanitarian landscape, especially post-COVID-19, there has been a notable pivot towards inclusivity and participatory methodologies, emphasizing the pivotal role of refugee-led organizations (RLOs). In Lebanon, amidst persistent economic and political turmoil, RLOs serve as crucial support systems for Syrian and Palestinian refugees within an environment plagued by inconsistent refugee policies and heightened vulnerabilities. Academic discourse underscores the increasing significance of RLOs in humanitarian assistance, yet systemic hurdles such as power differentials and tokenistic inclusion have emerged, constraining their effectiveness and integration within the humanitarian sphere. This study critically examines the application of inclusivity within humanitarian operations, aligned with the principles outlined in the Agenda for Humanity, specifically scrutinizing how prevailing narratives and operational dynamics may marginalize RLOs in Lebanon, thereby impeding their efficacy. It endeavors to evaluate how RLOs can assert themselves as principal stakeholders in humanitarian endeavors, striving for a more equitable and pragmatic approach to power dynamics and strategic planning for refugee communities. Utilizing a qualitative and participatory methodology, this research engages with diverse RLOs in Lebanon, conducting interviews to realistically and practically frame their experiences, obstacles, and contributions within the humanitarian landscape across entrenched and often rigid hierarchies, power dynamics, and tokenism within Lebanon's broader humanitarian landscape. [ABSTRACT FROM AUTHOR]

We are considering differential-algebraic equations with embedded optimization criteria (DAEOs), in which the embedded optimization problem is solved by global optimization. This leads to differential inclusions for cases in which there are multiple global optimizers at the same time. Jump events from one global optimum to another result in nonsmooth DAEs and reduce the order of convergence of the numerical integrator to first-order. Implementation of event detection and location as introduced in this work preserves the higher-order convergence behaviour of the integrator. This allows the computation of discrete tangent and adjoint sensitivities for optimal control problems. [ABSTRACT FROM AUTHOR]

The pursuit of understanding fixed points and their applications has been significantly enhanced through the exploration of multi-valued mappings. This article introduces the concept of multi-valued mappings within C*-algebra-valued metric spaces. By utilizing the lower bound property, this study extends the Banach, Kannan, and Chatterjea theorems for multi-valued mappings in such spaces (for example see [14]). Moreover, the application aspect is enriched through the provision of an existence result for AB-Caputo partial hyperbolic type fractional differential inclusions. This result enhances the applicability of such inclusions, bridging the gap between theory and application. The paper concludes by offering few open problems that set the stage for future researchers in this field. The results presented here not only generalize numerous findings in the existing literature but also offer new insights into this area of research. [ABSTRACT FROM AUTHOR]

In this article, we construct sufficient conditions that secure the non-emptiness and compactness of the set of antiperiodic solutions of an impulsive fractional differential inclusion involving an ω-weighted ϱ–Hilfer fractional derivative, D 0 , t σ , v , ϱ , ω , of order σ ∈ (1 , 2) , in infinite-dimensional Banach spaces. First, we deduce the formula of antiperiodic solutions for the observed problem. Then, we give two theorems regarding the existence of these solutions. In the first, by using a fixed-point theorem for condensing multivalued functions, we show the non-emptiness and compactness of the set of antiperiodic solutions; and in the second, by applying a fixed-point theorem for contraction multivalued functions, we prove the non-emptiness of this set. Because many types of famous fractional differential operators are particular cases from the operator D 0 , t σ , v , ϱ , ω , our results generalize several recent results. Moreover, there are no previous studies on antiperiodic solutions for this type of fractional differential inclusion, so this work is novel and interesting. We provide two examples to illustrate and support our conclusions. [ABSTRACT FROM AUTHOR]

We consider the long-term dynamics of the vanishing stepsize subgradient method in the case when the objective function is neither smooth nor convex. We assume that this function is locally Lipschitz and path differentiable, i.e., admits a chain rule. Our study departs from other works in the sense that we focus on the behavior of the oscillations, and to do this we use closed measures, a concept that complements the technique of asymptotic pseudotrajectories developed in this setting by Benaïm--Hofbauer--Sorin. We recover known convergence results, establish new ones, and show a local principle of oscillation compensation for the velocities. Roughly speaking, the time average of gradients around one limit point vanishes. Various cases are discussed, providing new insight into the oscillation and the stabilization phenomena. [ABSTRACT FROM AUTHOR]

In this study, we investigate the effect of Clarke's subdifferential type on the optimal control results for fractional differential systems of order 1

West Nile Virus (WNV) is an arbovirus endemic to many countries and has caused over 56,000 cases, with 2776 deaths in the U.S. from 1999 to 2022. WNV occurs most often in the fall, typically affecting elderly populations in states like Nebraska and Arizona. Currently, supportive care is the only management for WNV. Our case is a female patient in her mid-70s in an intermountain state who presented in the fall with WNV meningoencephalitis and experienced a delay in care due to the unique clinical presentation. This demonstrates the importance of early inclusion of WNV in the differential for altered mental status, especially with WNV risk factors, and expedition of supportive care. Doing so could potentially reduce antibiotic duration and hospital costs. [ABSTRACT FROM AUTHOR]

In this article, we introduce the Boyd-Wong type multivalued contractions and demonstrate that such mappings have a fixed point. Additionally, we look at the solvability of a few (k – ~)-Hilfer initial value fractional differential inclusions of order n − 1 < α < n (n ≥ 2). To demonstrate the usability of our result, an example is provided. [ABSTRACT FROM AUTHOR]

In this paper, the non-autonomous fractional evolution inclusions of Clarke subdifferential type in a separable reflexive Banach space are investigated. The mild solution of the non-autonomous fractional evolution inclusions of Clarke subdifferential type is defined by introducing the operators ψ (t , τ) and ϕ (t , τ) and V(t), which are generated by the operator - A (t) and probability density function. Combined the measure of non-compactness, some properties of the Clarke subdifferential with fixed point theorem of κ - condensing multi-valued maps, a new existence result of mild solution is established. Moreover, an existence result of optimal control pair for the Lagrange problem is also derived. The results obtained in this paper extend the study of fractional autonomous evolution equations to the non-autonomous fractional evolution inclusions. Finally, a fractional partial differential inclusion with control is provided to illustrate the applications of the obtained main results. [ABSTRACT FROM AUTHOR]

We study the three-dimensional problem of a spheroidal compressible liquid inclusion perfectly bonded to an infinite transversely isotropic elastic matrix subjected to a uniform axisymmetric stress field at infinity. The original boundary value problem is reduced to a set of three coupled linear algebraic equations. The internal uniform hydrostatic tension within the liquid inclusion and the elastic field of displacements and stresses in the matrix are then determined via the solution of this set of linear algebraic equations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate a class of nonconvex-constrained differential hemivariational inequalities consisting of nonlinear evolution equations and evolutionary hemivariational inequalities. The admissible set of constraints is closed and star-shaped with respect to a certain ball in a reflexive Banach space. We construct an auxiliary inclusion problem and obtain the existence results by applying a surjectivity theorem for multivalued pseudomonotone operators and the properties of Clarke subgradient operator. Moreover, the existence of a solution to the original problem is established by hemivariational inequality approach and a penalization method in which a small parameter does not have to tend to zero. Finally, an application of the main results is provided. [ABSTRACT FROM AUTHOR]

This paper focuses on a system of differential inclusions expressing hemivariational inequalities driven by competing operators constructed with p-Laplacians that involve two real parameters. The existence of a generalized solution is shown by means of an approximation process through approximate solutions in finite dimensional spaces. When the parameters are negative, the generalized solutions become weak solutions. The main novelty of this work is the solvability of systems of differential inclusions for which the ellipticity condition may fail. [ABSTRACT FROM AUTHOR]

The paper considers the possibility of changing the morphology of inclusions in diamonds based on the study of these inclusions and the inclusion–diamond boundary. Raman spectroscopy and transmission electron microscopy methods were used. According to the literature data, it is known that the octahedral form of mineral inclusions in diamond is induced, and does not correspond to the initial conditions of joint growth of diamond and inclusion, but the mechanism of this process is not considered. Solids differ in the value of surface Gibbs energy; the harder the material, the higher its melting point and the greater the value of surface Gibbs energy In the case of the diamond–inclusion pair, the surface energy of diamond far exceeds the surface energy of the inclusion. Diamond crystals have a surface energy value for an octahedron face of 5.3 J/m2, dodecahedron—6.5 J/m2, and cube—9.2 J/m2, i.e. it is anomalously high compared to the surface tension of silicate and other minerals. Therefore, the mineral inclusion in diamond tends to the form corresponding to the minimum of free energy in the "diamond–inclusion" pair, and when the energy of diamond dominates, the final shape will be determined by it, i.e. it will be an octahedron. The authors suggest the possibility of redistribution of diamond substance around the inclusion with simultaneous change of the inclusion morphology. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the finite‐time tracking problem for nonlinear impulsive differential inclusion systems with randomly varying trial lengths. First, we convert the set‐valued mapping in the differential inclusion systems to single‐valued mapping by a Steiner‐type selector. For the tracking problem of random discontinuous output trajectories, this paper defines a piecewise continuous variable by zero‐order holder to correct the tracking error of segmented continuity. Then, we introduce the average operator with forgetting factor to design three novel learning schemes, and establish convergence results by using the mathematical analysis tools such as impulsive Gronwall inequality and λ$$ \lambda $$‐norm. Finally, a numerical example verifies the validity of the theoretical results, and we compare the tracking performance of the output trajectories for different forgetting factors. [ABSTRACT FROM AUTHOR]

This paper is primarily dedicated to investigating the existence of solutions for an impulsive fractional neutral pantograph integro-differential system (IFNPIDS) through the utilization of the Caputo-Fabrizio (CF) operator. We introduce a novel solution for our addressing system and employ fixed-point techniques to establish innovative results. The paper concludes by presenting two numerical examples, illustrating the practical applicability of our theoretical findings. [ABSTRACT FROM AUTHOR]

This paper studies the methods used by Gulf Cooperation Council (GCC) nations for surveillance and control of the migrant population on their land, its main argument being—the Kafala system as practised in the GCC nations, for organising the guest workers, is more than just an arrangement handling migration but rather is a technology of migrant control in itself wherein citizens are tasked with overseeing and managing the presence and actions of foreigners within the national borders, a responsibility typically held by the state-resulting in partial privatisation of control over migration. For this, they have refurbished the age-old Kafala to craft it into a cutting-edge technology of migrant control and surveillance by linking every migrant to his citizen–sponsor, who, on behalf of the state, wields complete control on the mobility, social life and employment of the Makful (migrant). The paper, through the concepts of porous and indeterminate borders, tries to show how borders do not "exclude" but there is "differential inclusion" of the migrants, which is no less violent than exclusionary measures, wherein borders exist between the male migrant and the female, between the skilled migrant and the unskilled and between the migrant from South–East Asia and the expats from Organisation for Economic Co-operation and Development (OECD) countries—by the use of tactics such as ethnic stereotyping, structural violence, racial segregation, etc.; for example-different kinds of visas provided to them based on their skills, sponsors retaining workers' passport controlling their mobility, regulating their salary, their forced confinement and restrictions on their channels of communication thus, mapping them in a system of "structural dependence". The study seeks to question the sponsorship system within the broader context of surveillance techniques that regulate migrant populations. By juxtaposing it with conventional surveillance measures such as CCTV cameras and GPS-based controls, it contends that the sponsorship system operates as a form of control that is both coercive and extensive, effectively tethering individuals to their sponsors who wield authority over all facets of their lives. [ABSTRACT FROM AUTHOR]

This work primarily delves into three key areas: the presence of mild solutions, exploration of the topological and geometrical makeup of solution sets, and the continuous dependency of solutions on a second-order semilinear integro-differential inclusion. The Bohnenblust-Karlin fixedpoint method has been integrated with Grimmer's theory of resolvent operators. Ultimately, the study delves into a mild solution for a partial integro-differential inclusion to showcase the achieved outcomes. [ABSTRACT FROM AUTHOR]

Many scholars have lately explored fractional-order boundary value issues with a variety of conditions, including classical, nonlocal, multipoint, periodic/anti-periodic, fractional-order, and integral boundary conditions. In this manuscript, the existence and uniqueness of solutions to sequential fractional differential inclusions via a novel set of nonlocal boundary conditions were investigated. The existence results were presented under a new class of nonlocal boundary conditions, Carath'eodory functions, and Lipschitz mappings. Further, fixed-point techniques have been applied to study the existence of results under convex and non-convex multi-valued mappings. Ultimately, to support our findings, we analyzed an illustrative example. [ABSTRACT FROM AUTHOR]

Why use a viabilistic approach to model economy? Because it is urgent to re-assess the modeling of the business cycle that integrates dynamic money creation and that has at its core the notion of constraints. The purpose of this paper is thus to propose an evolutionary economic model using a mathematical framework derived from set-valued analysis, differential inclusions and viability theory. As this approach is dynamical, the model will not use two concepts on which neo-classical economics are built i.e., (1) the existence of static repeated equilibria, (2) the optimization by an economic agent of a utility function. Furthermore, we will not use any self-organization process or "invisible hand", as in our viabilist framework the economic viability will be maintained by explicit choices of the economic agents and of the lender of last resort over the budgetary and monetary rules to apply. Indeed, even simple constraints on the second-derivative of the means of payments already induce four-phased business cycles. Coupling these constraints over the creation of means of payment with economic evolutions of prices and commodities through a budgetary constraint allows for a single formalism, tackling jointly the question of the viability of economic and monetary evolutions. [ABSTRACT FROM AUTHOR]

We consider a Sturm-Liouville type system of differential inclusions with nonlocal integral boundary conditions and we obtain an existence result for this problem in the case when the set-valued maps have nonconvex values. [ABSTRACT FROM AUTHOR]