Framework Of Spaces Research Articles

Bipolar b-Metric Spaces in Graph Setting and Related Fixed Points

In this article, we develop a new notion that combines fixed-point theory and graph theory: graphical bipolar b-metric spaces. We demonstrate fixed-point solutions in the framework of graphical bipolar b-metric spaces, employing covariant and contravariant mapping contractions, which is a new addition to this end. This article also features illustrative examples drawn from various contexts to further demonstrate our findings. This is a significant study since it melds ideas from graph theory with those from generalized bipolar metric spaces, and considers that the symmetry of the edges of the underlying graphs connected with the enunciated metric spaces is essential in the graphical metric spaces.

Perfect control for nonminimum-phase unstable systems defined in the multivariable continuous-time state–space framework — An inverse-based approach

In this paper, a new perfect control law dedicated to nonminimum-phase unstable LTI MIMO systems governed in the continuous-time state–space domain is proposed. Two algorithms are investigated, one of which has turned out to be definitely accurate. Henceforth, the inverse model control-based formula can be applied to any right-invertible plants having more input than output variables. Last, not least, through the application of some generalized inverses, the perfect control procedure guarantees the structural stability behavior even for unstable systems. Thus, the notion of the nonminimum-phase property should be understood in terms of a possible achieveability covering the entire class of LTI MIMO continuous-time plants. Theoretical and practical simulation examples performed in the Matlab/Simulink environment confirm the feasibility of the newly introduced approach.

Generalizing the Wells-Riley Infection Probability: A Superstatistical Scheme for Indoor Infection Risk Estimation.

Recent evidence supports that air is the main transmission pathway of the recently identified SARS-CoV-2 coronavirus that causes COVID-19 disease. Estimating the infection risk associated with an indoor space remains an open problem due to insufficient data concerning COVID-19 outbreaks, as well as, methodological challenges arising from cases where environmental (i.e., out-of-host) and immunological (i.e., within-host) heterogeneities cannot be neglected. This work addresses these issues by introducing a generalization of the elementary Wells-Riley infection probability model. To this end, we adopted a superstatistical approach where the exposure rate parameter is gamma-distributed across subvolumes of the indoor space. This enabled us to construct a susceptible (S)-exposed (E)-infected (I) dynamics model where the Tsallis entropic index q quantifies the degree of departure from a well-mixed (i.e., homogeneous) indoor-air-environment state. A cumulative-dose mechanism is employed to describe infection activation in relation to a host's immunological profile. We corroborate that the six-foot rule cannot guarantee the biosafety of susceptible occupants, even for exposure times as short as 15 min. Overall, our work seeks to provide a minimal (in terms of the size of the parameter space) framework for more realistic indoor SEI dynamics explorations while highlighting their Tsallisian entropic origin and the crucial yet elusive role that the innate immune system can play in shaping them. This may be useful for scientists and decision makers interested in probing different indoor biosafety protocols more thoroughly and comprehensively, thus motivating the use of nonadditive entropies in the emerging field of indoor space epidemiology.

Affine Geometry and Relativity

We present the basic concepts of space and time, the Galilean and pseudo-Euclidean geometry. We use an elementary geometric framework of affine spaces and groups of affine transformations to illustrate the natural relationship between classical mechanics and theory of relativity, which is quite often hidden, despite its fundamental importance. We have emphasized a passage from the group of Galilean motions to the group of Poincaré transformations of a plane. In particular, a 1-parametric family of natural deformations of the Poincaré group is described. We also visualized the underlying groups of Galilean, Euclidean, and pseudo-Euclidean rotations within the special linear group.

Existence Results for Wardoski-Type Convex Contractions and the Theory of Iterated Function Systems

The purpose of this paper is to define the notion of extended convex ℱ contraction by imposing less conditions on the function ℱ satisfying certain contractive conditions. We prove the existence of fixed points for these types of mappings in the setting of b-metric spaces. In addition, some illustrative examples are provided to show the usability of the obtained results. Lastly, we use the obtained fixed-point results to find the fractals with respect to the iterated function systems in the framework of b-metric spaces. Furthermore, the variables involved in the b-metric space are symmetric, and symmetry plays an important role in solving the nonlinear problems defined in operator theory.

Sehgal-Guseman-Type Fixed Point Theorems in Rectangular b -Metric Spaces and Solvability of Nonlinear Integral Equation

Firstly, the concept of a new triangular α -orbital admissible condition is introduced, and two fixed point theorems for Sehgal-Guseman-type mappings are investigated in the framework of rectangular b -metric spaces. Secondly, some examples are presented to illustrate the availability of our results. At the same time, we furnished the existence and uniqueness of solution of an integral equation.

Anisotropic Prodi–Serrin regularity criteria for the 3D Navier–Stokes equations involving the gradient of one velocity component

In this paper, we prove some optimal regularity criteria for the 3D incompressible Navier–Stokes equations involving the gradient of one velocity component in the framework of anisotropic Lebesgue spaces satisfying Prodi–Serrin condition. These results cover the previous ones established by Wolf (2015) and O (2023).

Circular designs for total effects under interference models

This paper studies circular designs for interference models, where a treatment assigned to a plot also affects its neighboring plots within a block. For the purpose of estimating total effects, the circular neighbor balanced design was shown to be universally optimal among designs which do not allow treatments to be neighbors of themselves. Our study shows that self-neighboring block sequences are actually the main ingredient for an optimal design. Here, we adopt the approximate design framework and study optimal designs in the whole design space. Our approach is flexible enough to accommodate all possible design parameters, that is the block size and the number of blocks and treatments. This approach can be broken down into two main steps: the identification of the minimal supporting set of block sequences and the optimality condition built on it. The former is critical for reducing the computational time from almost infinity to seconds. Meanwhile, the task of finding the minimal set is normally achieved through numerical methods, which can only handle small block sizes. Our approach is of a hybrid nature in order to deal with all design sizes. When block size is not large, we provide explicit expressions of the minimal set instead of relying on numerical methods. For larger block sizes when a typical numerical method would fail, we theoretically derived a reasonable size intermediate set of sequences, from which the minimal set can be quickly derived through a customized algorithm. Taking it further, the optimality conditions allow us to obtain both symmetric and asymmetric designs. Lastly, we also investigate the trade-off issue between circular and noncircular designs, and provide guidelines on the choices.

A new class of regularity criteria for the MHD and Navier–Stokes equations

In Skalak (0000) we studied a new class of the regularity criteria for the Navier–Stokes equations based on a remarkable idea that controlling the derivatives of some fundamental quantities like the pressure and the velocity along the streamlines yields the regularity of the weak solutions. We show in the present paper that the results from Skalak (0000) are extendable to the MHD equations and in the framework of the Besov spaces. For example, controlling the directional derivative of the magnetic Bernoulli pressure P along w+/|w+|, where w+=u+b and u and b denote the velocity field and the magnetic field, respectively, yields the regularity. We compare our results with the similar criteria from the literature.

Does regionalism increase industrial policy space? An analytical framework applied to the East African textiles and apparel sector

We introduce a multidimensional and multilevel framework for industrial policy space as the set of legally permitted, economically viable and politico-institutionally feasible policy options for industrial development, given constraints at the national, regional and global levels. This is applied to the East African Community (EAC) textiles and apparel (T&A) sector, using data from policy documents and semi-structured interviews. The EAC customs union nominally transfers trade policy sovereignty to the regional level, but we present evidence showing how the duty remission scheme allows governments to provide targeted trade policy rents to domestic T&A firms, maintaining national legal policy space. This comes at a cost, because firms benefiting from national duty remission rents may not sell their goods duty free in other EAC countries, so the expanded economic policy space offered by regional integration is curtailed. In the political-institutional sphere, the EAC allowed a new policy option to emerge at the regional level – import substitution of used clothes – but global-level policy space constraints prevented implementation when US authorities threatened to remove trade preferences underpinning thousands of jobs. Regional integration policies should take into account tensions between different dimensions and levels of industrial policy space to maximise prospects for sustainable development.

Diametrically Relatively Nonexpansive Mappings and a Characterization of Proximal Normal Structure

We consider a new type of cyclic (noncyclic) mappings, called diametrically relatively nonexpansive maps which contains properly the class of cyclic (noncyclic) relatively nonexpansive mappings. For such mappings we obtain existence results of best proximity points (pairs) in the framework of Busemann convex spaces and generalize the recent conclusions in this direction. We also present a characterization of proximal normal structure in term of best proximity points (pairs) for diametrically relatively nonexpansive mappings.

Local grand variable exponent Lebesgue spaces

We introduce local grand variable exponent Lebesgue spaces, where the variable exponent Lebesgue space is “aggrandized” only at a given closed set F of measure zero. It is shown that, for different aggrandizers with positive Matuszewska–Orlicz indices, the corresponding local grand variable exponent Lebesgue spaces coincide. We show that the maximal operator, singular operators, and maximal singular operators are bounded in such spaces. Lastly, an application to a Dirichlet problem for the Poisson equation, where F may be chosen as the boundary of the domain, is provided within the framework of such local grand spaces.

A strongly convergent algorithm for solving multiple set split equality equilibrium and fixed point problems in Banach spaces

AbstractIn this article, using an Halpern extragradient method, we study a new iterative scheme for finding a common element of the set of solutions of multiple set split equality equilibrium problems consisting of pseudomonotone bifunctions and the set of fixed points for two finite families of Bregman quasi-nonexpansive mappings in the framework of p-uniformly convex Banach spaces, which are also uniformly smooth. For this purpose, we design an algorithm so that it does not depend on prior estimates of the Lipschitz-type constants for the pseudomonotone bifunctions. Furthermore, we present an application of our study for finding a common element of the set of solutions of multiple set split equality variational inequality problems and fixed point sets for two finite families of Bregman quasi-nonexpansive mappings. Finally, we conclude with two numerical experiments to support our proposed algorithm.

Gravitational inversion for arbitrary surface mass distribution—application to earth's time-variable gravity with topography

SUMMARY The aim of this paper is gravitational inversion, that is, the determination of the mass density distribution of a central body when given the observed external gravitational field that is produced by the mass itself. This inversion for a 3-D mass distribution is known to be grossly non-unique; whereas that for a 2-D mass distribution on a spherical surface is known to be unique. The latter justifies the surface ‘mascon’, or equivalent-water-thickness, solutions when not considering any interior mass transports for the Earth's time-variable gravity as observed by the GRACE satellite. In this paper, using the gravitational multipole formalism cast in the framework of linear Hilbert space with the notion of inner product, we do two things further: (i) we prove mathematically that the 2-D gravitational inversion on an arbitrary surface is unique; and (ii) we derive the algorithm that leads to the unique exact 2-D mass distribution solution, up to a truncated finite spherical harmonic degree. This pertains directly to reaching refined GRACE mascon solutions that account for the actual Earth surface shape including the ellipsoidal figure and the topography. In the process, we also (re)formulate the exact equations, for spherical or arbitrary shape, unifying the formulae that have appeared in the GRACE-relevant literature.

A self-adaptive inertial extragradient method for a class of split pseudomonotone variational inequality problems

Abstract In this article, we study a class of pseudomonotone split variational inequality problems (VIPs) with non-Lipschitz operator. We propose a new inertial extragradient method with self-adaptive step sizes for finding the solution to the aforementioned problem in the framework of Hilbert spaces. Moreover, we prove a strong convergence result for the proposed algorithm without prior knowledge of the operator norm and under mild conditions on the control parameters. The main advantages of our algorithm are: the strong convergence result obtained without prior knowledge of the operator norm and without the Lipschitz continuity condition often assumed by authors; the minimized number of projections per iteration compared to related results in the literature; the inertial technique employed, which speeds up the rate of convergence; and unlike several of the existing results in the literature on VIPs with non-Lipschitz operators, our method does not require any linesearch technique for its implementation. Finally, we present several numerical examples to illustrate the usefulness and applicability of our algorithm.

Iterative Schemes Involving Several Mutual Contractions

In this paper, we introduce the new concept of mutual Reich contraction that involves a pair of operators acting on a distance space. We chose the framework of strong b-metric spaces (generalizing the standard metric spaces) in order to add a more extended underlying structure. We provide sufficient conditions for two mutually Reich contractive maps in order to have a common fixed point. The result is extended to a family of operators of any cardinality. The dynamics of iterative discrete systems involving this type of self-maps is studied. In the case of normed spaces, we establish some relations between mutual Reich contractivity and classical contractivity for linear operators. Then, we introduce the new concept of mutual functional contractivity that generalizes the concept of classical Banach contraction, and perform a similar study to the Reich case. We also establish some relations between mutual functional contractions and Banach contractivity in the framework of quasinormed spaces and linear mappings. Lastly, we apply the obtained results to convolutional operators that had been defined by the first author acting on Bochner spaces of integrable Banach-valued curves.

Inertial algorithm for solving split inclusion problem in Banach spaces

The purpose of this paper is to propose an algorithm for finding a common element of the set of fixed points of relatively nonexpansive mapping and the set of solutions of split inclusion problem with a way of selecting the stepsize without prior knowledge of the operator norm in the framework of Banach spaces. Then, the main result is used to the common fixed point problems of a family of relatively nonexpansive mappings and split equilibrium problem. Finally, a numerical example is provided to illustrate the main result.

An inertial viscosity algorithm for solving monotone variational inclusion and common fixed point problems of strict pseudocontractions

In this paper, we study the problem of finding the solution of monotone variational inclusion problem (MVIP) with constraint of common fixed point problem (CFPP) of strict pseudocontractions. We propose a new viscosity method, which combines the inertial technique with self-adaptive step size strategy for approximating the solution of the problem in the framework of Hilbert spaces. Unlike several of the existing results in the literature, our proposed method does not require the co-coerciveness and Lipschitz continuity assumptions of the associated single-valued operator. Also, our method does not involve any linesearch technique which could be time-consuming, rather we employ a self-adaptive step size technique that generates a nonmonotonic sequence of step sizes. Moreover, we prove strong convergence result for our algorithm under some mild conditions and apply our result to study other optimization problems. We present several numerical experiments to demonstrate the computational advantage of our proposed method over the existing methods in the literature. Our result complements several of the existing results in the current literature in this direction.

An Electromagnetic Information Theory Based Model for Efficient Characterization of MIMO Systems in Complex Space

It is the pursuit of a multiple-input-multiple-output (MIMO) system to approach and even break the limit of channel capacity. However, it is always a big challenge to efficiently characterize the MIMO systems in complex space and get better propagation performance than the conventional MIMO systems considering only free space, which is important for guiding the power and phase allocation of antenna units. In this manuscript, an Electromagnetic-Information-Theory (EMIT) based model is developed for efficient characterization of MIMO systems in complex space. The group-T-matrix-based multiple scattering fast algorithm, the mode-decomposition-based characterization method, and their joint theoretical framework in complex space are discussed. Firstly, key informatics parameters in free electromagnetic space based on a dyadic Green's function are derived. Next, a novel group-T-matrix-based multiple scattering fast algorithm is developed to describe a representative inhomogeneous electromagnetic space. All the analytical results are validated by simulations. In addition, the complete form of the EMIT-based model is proposed to derive the informatics parameters frequently used in electromagnetic propagation, through integrating the mode analysis method with the dyadic Green's function matrix. Finally, as a proof-or-concept, microwave anechoic chamber measurements of a cylindrical array is performed, demonstrating the effectiveness of the EMIT-based model. Meanwhile, a case of image transmission with limited power is presented to illustrate how to use this EMIT-based model to guide the power and phase allocation of antenna units for real MIMO applications.

Orthogonal Time Frequency Space and Predictive Beamforming-Enabled URLLC in Vehicular Networks

To fulfill the requirements of future intelligent transportation system in 6G era, ultra-reliable and low-latency vehicular communications is of great importance. In high-mobility scenarios, the conventional orthogonal frequency division multiplexing (OFDM) modulation may fail to work due to high Doppler spreads. Moreover, the dynamic network topology imposes challenges on aligning the beams in multiple antenna systems. In this context, this article introduces a new orthogonal time frequency space (OTFS) and sensing-assisted predictive beamforming framework for supporting reliable and low-latency vehicular communications. In particular, we will first overview the OTFS modulation scheme, which performs data transmission in the delay-Doppler (DD) domain and discuss its superiority in improving communication reliability in vehicular networks. Then the sensing-assisted predictive beamforming scheme will be introduced, which does not rely on dedicated pilots for beam pairing, leading to very low overhead and latency. Benefiting from the DD channel representation, we briefly discuss the potential of channel prediction. Lastly, the challenges and future research directions are summarized.