Compactness Criterion Research Articles

Nonlocal H-convergence for topologically nontrivial domains

The notion of nonlocal H-convergence is extended to domains with nontrivial topology, that is, domains with non-vanishing harmonic Dirichlet and/or Neumann fields. If the space of harmonic Dirichlet (or Neumann) fields is infinite-dimensional, there is an abundance of choice of pairwise incomparable topologies generalising the one for topologically trivial Ω. It will be demonstrated that if the domain satisfies the Maxwell compactness property the corresponding natural version of the corresponding (generalised) nonlocal H-convergence topology has no such ambiguity. Moreover, on multiplication operators the nonlocal H-topology coincides with the one induced by (local) H-convergence introduced by Murat and Tartar. The topology is used to obtain nonlocal homogenisation results including convergence of the associated energy for electrostatics. The derived techniques prove useful to deduce a new compactness criterion relevant for nonlinear static Maxwell problems.

Performance assessment of sustainable asphalt concrete using steel slag, with an artificial neural network prediction of asphalt concrete behavior

This research evaluated the possibility of using Moroccan steelworks slag as a substitute for natural aggregates in asphalt mixtures, using chemical and mechanical analyses to demonstrate its compatibility with this application. Two granular mixtures, M1 and M2, were developed, incorporating respectively 15% and 25% natural sand (0/1.25) with slag aggregates to obtain granular mixtures complying with local standards. These mixtures were then tested with three different asphalt contents (4.7%, 5.2%, and 5.7%). Mechanical tests, including a gyratory compactor, Marshall stability, and Duriez strength, were carried out. In particular, the M1:5.2 and M2:5.2 mixtures met compaction criteria and showed remarkable Marshall Stability values, reaching 23.49 kN and 21.81 kN respectively. In comparison, the control mixtures only achieved a maximum stability of 11 kN. Thermal properties were also assessed, showing that the maximum thermal conductivity was achieved at an asphalt content of 5.2%. The slag-based mixtures, M1 and M2, showed higher thermal conductivity than the control mix M0, with maximum values of 0.74W/mK for M1 and 0.86W/mK for M2, compared with 0.56W/mK for M0. The overall results show that the M1 and M2 mixtures had improved thermal and mechanical properties compared with the M0 control mix. Artificial neural network (ANN) modelling was carried out using Marshall Test data. It showed excellent performance in predicting the stability and flow properties of asphalt mixtures. These results suggest that incorporating steelmaking slag into asphalt concrete mixtures was an effective strategy for simultaneously improving their thermal and mechanical properties.

Relative weak compactness in infinite-dimensional Fefferman-Meyer duality

Let E be a Banach space such that E′ has the Radon-Nikodým property. The aim of this work is to connect relative weak compactness in the E-valued martingale Hardy space H1(μ,E) to a convex compactness criterion in a weaker topology, such as the topology of uniform convergence on compacts in measure. These results represent a dynamic version of the deep result of Diestel, Ruess, and Schachermayer on relative weak compactness in L1(μ,E). In the reflexive case, we obtain a Kadec-Pełczyński dichotomy for H1(μ,E)-bounded sequences, which decomposes a subsequence into a relatively weakly compact part, a pointwise weakly convexly convergent part, and a null part converging to zero uniformly on compacts in measure. As a corollary, we investigate a parameterized version of the vector-valued Komlós theorem without the assumption of H1(μ,E)-boundedness.

Energy efficient cluster-based routing protocol for WSN using multi-strategy fusion snake optimizer and minimum spanning tree

In recent years, the widespread adoption of wireless sensor networks (WSN) has resulted in the growing integration of the internet of things (IoT). However, WSN encounters limitations related to energy and sensor node lifespan, making the development of an efficient routing protocol a critical concern. Cluster technology offers a promising solution to this challenge. This study introduces a novel cluster routing protocol for WSN. The system selects cluster heads and relay nodes utilizing the multi-strategy fusion snake optimizer (MSSO) and employs the minimum spanning tree algorithm for inter-cluster routing planning, thereby extending the system’s lifecycle and conserving network energy. In pursuit of an optimal clustering scheme, the paper also introduces tactics involving dynamic parameter updating, adaptive alpha mutation, and bi-directional search optimization within MSSO. These techniques significantly increase the algorithm convergence speed and expand the available search space. Furthermore, a novel efficient clustering routing model for WSN is presented. The model generates different objective functions for selecting cluster heads and relay nodes, considering factors such as location, energy, base station distance, intra-cluster compactness, inter-cluster separation, and other relevant criteria. When selecting cluster heads, the fuzzy c-means (FCM) algorithm is integrated into MSSO to improve the optimization performance of the algorithm. When planning inter-cluster routing, the next hop node is selected for the relay node based on distance, residual energy, and direction.The experimental results demonstrate that the proposed protocol reduces energy consumption by at least 26.64% compared to other cluster routing protocols including LEACH, ESO, EEWC, GWO, and EECHS-ISSADE. Additionally, it increases the network lifetime of WSN by at least 25.84%, extends the stable period by at least 52.43%, and boosts the network throughput by at least 40.99%.

Compactness Criterion for Families of Quantum Operations in the Strong Convergence Topology and Its Applications

Compactness Criterion for Families of Quantum Operations in the Strong Convergence Topology and Its Applications

Low windage dual‐band omnidirectional antenna for high‐speed aircraft communication application

AbstractThe letter presents a low‐windage omnidirectional antenna for high‐speed aircraft in the UHF and L bands. It combines a planar biconical antenna with a printed tape parasitic branch monopole antenna. Upgrading the traditional restricted‐length biconical antenna to a double‐layer planar design meets the compact, lightweight, and low windage requirements of airborne use. To enhance bandwidth and meet the lightweight, compact criteria of high‐speed aircraft, the planar‐printed monopole antenna integrates parasitic stubs and loop antenna concepts. Experimental results exhibit excellent isolation between antenna elements, with over 15 dB segregation and operational spectrum return loss of 27% and 18% at 10 dB. The voltage standing wave ratio is below 2, with less than 5 dB variation in the horizontal radiation pattern across frequency bands. The antenna, measuring 20 mm × 190 mm × 270 mm and weighing around 0.5 kg, holds great promise for high‐speed aircraft applications.

Diameter estimates under integral radial m-Bakry–Émery Ricci curvature bounds

By using some line integrals in terms of the radial [Formula: see text]-Bakry–Émery and radial [Formula: see text]-modified Bakry–Émery Ricci curvatures, we give various compactness criteria for complete Riemannian manifolds when [Formula: see text] is a positive constant, a negative constant, or infinity. Our results not only guarantee the compactness of complete Riemannian manifolds allowing the presence of negative amounts of the radial [Formula: see text]-Bakry–Émery and radial [Formula: see text]-modified Bakry–Émery Ricci curvatures, but also give new Myers-type theorems via [Formula: see text]-Bakry–Émery and [Formula: see text]-modified Bakry–Émery Ricci curvatures even the line integrals are reduced to pointwise positive lower bounds on the [Formula: see text]-Bakry–Émery and [Formula: see text]-modified Bakry–Émery Ricci curvatures. The key ingredients in proving our results are Riccati inequalities obtained from Bochner–Weitzenböck formulas via [Formula: see text]-Bakry–Émery and [Formula: see text]-modified Bakry–Émery Ricci curvatures.

NONLOCAL BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION ON THE HALF-LINE

This paper aims to investigate a class for nonlocal fractional boundary value problem on an infinite interval due to its importance in provide a powerful tool for mathematical modeling of complex phenomena in science. New existence results are acquired for the given problem by using the Krasnosel’skii’s fixed point theorem. Moreover, sufficient conditions are obtained as well as a modified compactness criterion that guarantees the existence of at least one solution. In addition, an illustrative example is given in the final part of the paper.

Solvability of a Hadamard Fractional Boundary Value Problem at Resonance on Infinite Domain

This paper investigates the existence of solutions for Hadamard fractional differential equations with integral boundary conditions at resonance on infinite domain. By constructing two suitable Banach spaces, establishing an appropriate compactness criterion, and defining appropriate projectors, we study an existence theorem upon the coincidence degree theory of Mawhin. An example is given to illustrate our main result.

A selection theorem for essentially regulated functions of several variables

Helly's selection theorem provides a criterion for compactness of sets of single-variable functions with bounded pointwise variation. Fraňková has given a proper extension of Helly's theorem to the setting of single-variable regulated functions. We show how a similar approach yields a natural notion of regulated functions of several variables, together with an extension of the standard compactness criterion for multi-variable functions of bounded variation.

Energy saving when using equipment for the disposal of low-potential waste heat

The article discusses the problem of energy saving in the context of comparing different types of heat exchangers for the utilization of high-potential waste heat. The advantages and disadvantages of various regenerative ventilation schemes are analyzed and the most efficient heat exchangers are proposed for use in various fields. These include various types of regenerative heat exchangers. The factors influencing reliability and creation of optimal operating modes with high energy savings are considered. Recommendations for the use of enthalpy heat exchangers with the required technical characteristics are given. Various types of nozzles are shown to ensure better efficiency. The advantages and disadvantages of regenerative heat exchangers with an intermediate carrier and techniques for reducing the cost of manufacturing such structures are considered. The areas of application of small-sized plate heat exchangers are given. The principle of operation of heat exchangers on heat pipes (HHP) and their technical characteristics are considered. A compactness criterion has been introduced, which allows comparing different types of heat exchangers. The instantaneous boiling apparatus for the utilization of low-potential internal (by-product) energy resources (IER) and possible applications are considered in detail. In all cases of using the considered schemes, the prospects for their development in industry are noted.

Caputo-Hadamard fractional boundary-value problems in $ {\mathfrak{L}}^\mathfrak{p} $-spaces

<abstract><p>The focal point of this investigation is the exploration of solutions for Caputo-Hadamard fractional differential equations with boundary conditions, and it follows the initial formulation of a model that is intended to address practical problems. The research emphasizes resolving the challenges associated with determining precise solutions across diverse scenarios. The application of the Burton-Kirk fixed-point theorem and the Kolmogorov compactness criterion in $ {\mathfrak{L}}^\mathfrak{p} $-spaces ensures the existence of the solution to our problem. Banach's theory is crucial for the establishment of solution uniqueness, and it is complemented by utilizing the Hölder inequality in integral analysis. Stability analyses from the Ulam-Hyers perspective provide key insights into the system's reliability. We have included practical examples, tables, and figures, thereby furnishing a comprehensive and multifaceted examination of the outcomes.</p></abstract>

The existence of solutions of Hadamard fractional differential equations with integral and discrete boundary conditions on infinite interval

<abstract><p>In this article, the properties of solutions of Hadamard fractional differential equations are investigated on an infinite interval. The equations are subject to integral and discrete boundary conditions. A new proper compactness criterion is introduced in a unique space. By applying the monotone iterative technique, we have obtained two positive solutions. And, an error estimate is also shown at the end. This study innovatively uses a monotonic iterative approach to study Hadamard fractional boundary-value problems containing multiple fractional derivative terms on infinite intervals, and it enriches some of the existing conclusions. Meanwhile, it is potentially of practical significance in the research field of computational fluid dynamics related to blood flow problems and in the direction of the development of viscoelastic fluids.</p></abstract>

Duality and stable compactness in Orlicz-type modules

Orlicz-type modules are module analogues of classical Orlicz spaces. We study duality and stable compactness in Orlicz-type modules. We characterize the conditional Köthe dual of an Orlicz-type module as the space of all σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document}-order continuous module homomorphisms. We find an order continuity criterion for stable compactness in Orlicz-type modules. As an application, we obtain a robust representation result for conditional risk measures on Orlicz spaces.

Fixed/preassigned-time output synchronization for T–S fuzzy complex networks via quantized control

This article is devoted to the analysis of fixed-time (FXT) and preassigned-time (PAT) output synchronization for T–S fuzzy complex networks (CNs). Firstly, to improve transmission efficiency of information, a kind of pure power-law control strategy with logarithmic quantization is designed and the power-law terms have only one free parameter. Then, by applying FXT stability theorem as well as inequality skills, some compact criteria are obtained to achieve FXT output synchronization of T–S fuzzy CNs, and the restriction on the output matrix with positive definite and diagonal form is removed. Furthermore, the PAT output synchronization of T–S fuzzy CNs is further explored by developing a quantized control scheme with power-law form. Three numerical examples in the end are given to attest the proposed control design and criteria.

Quasi-monotone convergence of plurisubharmonic functions

The complex Monge-Ampère operator has been defined for locally bounded plurisubharmonic functions by Bedford-Taylor in the 80's. This definition has been extended to compact complex manifolds, and to various classes of mildly unbounded quasi-plurisubharmonic functions by various authors. As this operator is not continuous for the L1-topology, several stronger topologies have been introduced over the last decades to remedy this, while maintaining efficient compactness criteria. The purpose of this note is to show that these stronger topologies are essentially equivalent to the natural quasi-monotone topology that we introduce and study here.

A comparative study for the spectral properties of Toeplitz and Hankel operators

In this introductory review, we study Hankel and Toeplitz operators considering them as acting on certain spaces of analytic functions, namely Hardy spaces and compare their spectral properties such as their compactness criteria. In contrast to Toeplitz operators, the symbol of a Hankel operator is not uniquely determined by the operator. We also connect Toeplitz operators with Fredholm operators and give some of the most beautiful properties of Toeplitz operators such as the essential spectrum of Toeplitz operator with continuous symbol and the index of Toeplitz operator introducing Fredholm operators firstly.

Direct approach-based synchronization of fully quaternion-valued neural networks with inertial term and time-varying delay

In this article, the global exponential and asymptotic synchronization for a type of quaternion-valued inertial delayed neural networks (QIDNNs) are explored by introducing a direct analysis approach. Above all, without reducing the order or decomposing the models of QIDNNs, a compact quaternion-valued control scheme is developed to ensure synchronization. In addition, two new Lyapunov functionals are constructed directly and several compact criteria represented by matrix inequalities are derived by means of the theory of quaternion and inequality technique. Furthermore, a quaternion-valued adaptive control law is proposed to automatically determine the control costs, and the synchronization is guaranteed by the aid of Barbalat Lemma. Lastly, the derived results are affirmed via a numerical example.

Existence and uniqueness of weak solutions to a truncated system for a class of time-fractional reaction–diffusion–advection systems

In this paper, we study the existence and uniqueness of the weak solutions for a truncated system of a class of time-fractional reaction–diffusion–advection systems with discontinuous diffusion. Our approaches are based upon the classical Galerkin’s method and some new compactness criteria for proving the existence of weak solutions to time-fractional PDEs.

Weighted $$L^{p}$$-boundedness and $$L^{p}$$-compactness criteria to commutators of operators with kernels satisfying Hörmander type estimates

Weighted $$L^{p}$$-boundedness and $$L^{p}$$-compactness criteria to commutators of operators with kernels satisfying Hörmander type estimates