Showing papers on "Regular polygon published in 2022"

Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation

Abstract: The concepts of convex and non-convex functions play a key role in the study of optimization. So, with the help of these ideas, some inequalities can also be established. Moreover, the principles of convexity and symmetry are inextricably linked. In the last two years, convexity and symmetry have emerged as a new field due to considerable association. In this paper, we study a new version of interval-valued functions (I-V·Fs), known as left and right χ-pre-invex interval-valued functions (LR-χ-pre-invex I-V·Fs). For this class of non-convex I-V·Fs, we derive numerous new dynamic inequalities interval Riemann–Liouville fractional integral operators. The applications of these repercussions are taken into account in a unique way. In addition, instructive instances are provided to aid our conclusions. Meanwhile, we’ll discuss a few specific examples that may be extrapolated from our primary findings.

Reachable Set Estimation of Delayed Markovian Jump Neural Networks Based on an Improved Reciprocally Convex Inequality

Abstract: This brief investigates the reachable set estimation problem of the delayed Markovian jump neural networks (NNs) with bounded disturbances. First, an improved reciprocally convex inequality is proposed, which contains some existing ones as its special cases. Second, an augmented Lyapunov-Krasovskii functional (LKF) tailored for delayed Markovian jump NNs is proposed. Thirdly, based on the proposed reciprocally convex inequality and the augmented LKF, an accurate ellipsoidal description of the reachable set for delayed Markovian jump NNs is obtained. Finally, simulation results are given to illustrate the effectiveness of the proposed method.

Convex Analysis and Beyond

Abstract: The book presents a unified theory of convex functions, sets, and set-valued mappings/multifunctions in locally convex topological vector spaces.

Throughput Guarantees for Multi-Cell Wireless Powered Communication Networks With Non-Orthogonal Multiple Access

Abstract: The emerging non-orthogonal multiple access (NOMA) technology can effectively improve the throughput performance of Internet of Things (IoT) devices. Besides throughput maximization, ensuring throughput fairness is a practical design issue when implementing NOMA in wireless powered communication networks (WPCN). To this end, we investigate the joint transmission time and power allocation problem for NOMA communication, aiming to improve the sum-throughput while guaranteeing different wireless devices’ (WDs’) throughput in multi-cell WPCN. In particular, we first analyze the feasibility of the problem by deriving the necessary and sufficient conditions for the existence of feasible solutions and propose an efficient algorithm to obtain the set of feasible values of transmission time allocation. We then propose an efficient algorithm for the transmission time allocation to improve the sum-throughput. During each search iteration, we adopt the successive convex approximation (SCA) approach to transform the non-convex power allocation problem into a sequence of convex problems and obtain the locally optimal transmit power under a fixed transmission time. Numerical simulations show that the proposed algorithm can improve the sum-throughput while guaranteeing each WD’s throughput.

On the fractional double integral inclusion relations having exponential kernels via interval-valued co-ordinated convex mappings

Abstract: In the present study, over a rectangle from the plane R2, we define and develop the conceptions of the interval-valued fractional double integrals having exponential kernels, from which we exploit Hermite–Hadamard, Fejér–Hermite–Hadamard, as well as Pachpatte type inclusion relations regarding the interval-valued co-ordinated convex mappings. These inclusion relations can be viewed as certain substantial generalizations of the previously reported findings. To identify the correctness of the inclusion relations constructed in this work, we also provide three examples regarding the interval-valued co-ordinated convex mappings.

Convex-periodic, kink-periodic, peakon-soliton and kink bidirectional wave-solutions to new established two-mode generalization of Cahn-Allen equation

Abstract: In this paper, the evolutionary Cahn–Allen equation is upgraded into the generalized two-mode version via Korsunsky’s sense. The new established model is characterized in terms of the wave propagation form represented by the movement of two simultaneous waves of symmetric type. The Kudryashov-expansion method is used to extract some solitary wave solutions to the suggested model. Moreover, from mathematical point of view, some physical properties are explored to the two-mode Cahn–Allen equation via examining, graphically, the effect of the phase velocity and the dispersion parameters acting on the propagations of the obtained bidirectional wave-solutions. Finally, very interesting types of solutions are obtained to the new model by implementing a modified versions of the rational sine–cosine and sinh–cosh methods.

Functionals with extrema at reproducing kernels

Abstract: Abstract We show that certain monotone functionals on the Hardy spaces and convex functionals on the Bergman spaces are maximized at the normalized reproducing kernels among the functions of norm 1, thus proving the contractivity conjecture of Pavlović and of Brevig, Ortega-Cerdà, Seip and Zhao and the Wehrl-type entropy conjecture for the SU (1, 1) group of Lieb and Solovej, respectively.

Integrated Waveform Design for MIMO Radar and Communication via Spatio-Spectral Modulation

Abstract: This paper considers the integrated waveform design to simultaneously achieve a desired radar beampattern and multi-users communication for a dual-function Multiple-Input Multiple-Output (MIMO) system. To this end, a spatio-spectral modulation strategy via shaping the spatial waveform Energy Spectral Density (ESD) in directions of communication is proposed for the communication function, while beampattern Integrated Sidelobe Level (ISL) is minimized to enhance radar detectability. Meanwhile, Peak-to-Average Ratio (PAR) and power restrictions to comply with the current hardware technique and the mainlobe width constraint to cohere the beampattern main energy on the spatial region of interest are forced, respectively. Exploiting an equivalent reformulation of the original non-convex optimization problem, a Sequential Block Enhancement (SBE) framework that alternately updates each waveform in each emitting antenna is developed to monotonically decrease ISL. Each block involves the Dinkelbach’s procedure, sequential convex approximation and Alternating Direction Method of Multipliers (ADMM) to obtain single waveform, while the analytic proof with the converged block being a Karush-Kuhn-Tucker (KKT) point is provided. Finally, numerical results highlight the effectiveness of both the proposed dual function scheme and the waveform synthesis technique in comparison with some counterparts.

Joint Communication and Trajectory Optimization for Multi-UAV Enabled Mobile Internet of Vehicles

Abstract: Due to its flexibility and high maneuverability, Unmanned Aerial Vehicle (UAV) is able to quickly provide wireless connections to the ground vehicles in mobile environment. In this paper, a multi-UAV enabled mobile Internet of Vehicles (IoV) model is proposed, where the UAVs track to serve the mobile vehicles and send downlink information to the vehicles during the flight time. Considering the constraints of anti-collision and communication interference between the UAVs, the system throughput is maximized by jointly optimizing vehicle communication scheduling, UAV power allocation and UAV trajectory. The formulated non-convex optimization problem is separated into three subproblems, including communication scheduling optimization, power allocation optimization and UAV trajectory optimization, which can be solved by successive convex approximation (SCA). A joint iterative optimization algorithm of the three subproblems is put forward to get the optimal solution. Then, a fairness optimization problem is proposed to guarantee the fair communications for each vehicle. The numerical results reveal the excellent performance of the multi-UAV enabled mobile IoV by joint communication and trajectory optimization.

Existence and multiplicity of solutions to concave–convex-type double-phase problems with variable exponent

Abstract: This paper is devoted to the study of the L ∞ -bound of solutions to the double-phase nonlinear problem with variable exponent by the case of a combined effect of concave–convex nonlinearities. The main tools are the De Giorgi iteration method and a truncated energy technique. Applying this and a variant of Ekeland’s variational principle, we give the existence of at least two distinct nontrivial solutions belonging to L ∞ -space when the condition on a nonlinear convex term does not assume the Ambrosetti–Rabinowitz condition in general. In addition, our problem admits a sequence of small energy solutions whose converge to zero in L ∞ space. To achieve this result, we apply the modified functional method and global variational formulation as the main tools.

A Cost-Effective Solution for Non-Convex Economic Load Dispatch Problems in Power Systems Using Slime Mould Algorithm

Abstract: Slime Mould Algorithm (SMA) is a newly designed meat-heuristic search that mimics the nature of slime mould during the oscillation phase. This is demonstrated in a unique mathematical formulation that utilizes adjustable weights to influence the sequence of both negative and positive propagation waves to develop a method to link food supply with intensive exploration capacity and exploitation affinity. The study shows the usage of the SM algorithm to solve a non-convex and cost-effective Load Dispatch Problem (ELD) in an electric power system. The effectiveness of SMA is investigated for single area economic load dispatch on large-, medium-, and small-scale power systems, with 3-, 5-, 6-, 10-, 13-, 15-, 20-, 38-, and 40-unit test systems, and the results are substantiated by finding the difference between other well-known meta-heuristic algorithms. The SMA is more efficient than other standard, heuristic, and meta-heuristic search strategies in granting extremely ambitious outputs according to the comparison records.

Generalized version of Jensen and Hermite-Hadamard inequalities for interval-valued $ (h_1, h_2) $-Godunova-Levin functions

Abstract: Interval analysis distinguishes between inclusion relation and order relation. Under the inclusion relation, convexity and nonconvexity contribute to different kinds of inequalities. The construction and refinement of classical inequalities have received a great deal of attention for many classes of convex as well as nonconvex functions. Convex theory, however, is commonly known to rely on Godunova-Levin functions because their properties enable us to determine inequality terms more precisely than those obtained from convex functions. The purpose of this study was to introduce a ($ \subseteq $) relation to established Jensen-type and Hermite-Hadamard inequalities using $ (h_1, h_2) $-Godunova-Levin interval-valued functions. To strengthen the validity of our results, we provide several examples and obtain some new and previously unknown results.

Stability Analysis for Delayed Neural Networks via a Generalized Reciprocally Convex Inequality

Abstract: This article deals with the stability of neural networks (NNs) with time-varying delay. First, a generalized reciprocally convex inequality (RCI) is presented, providing a tight bound for reciprocally convex combinations. This inequality includes some existing ones as special case. Second, in order to cater for the use of the generalized RCI, a novel Lyapunov-Krasovskii functional (LKF) is constructed, which includes a generalized delay-product term. Third, based on the generalized RCI and the novel LKF, several stability criteria for the delayed NNs under study are put forward. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the proposed stability criteria.

Approximate convex decomposition for 3D meshes with collision-aware concavity and tree search

Abstract: Approximate convex decomposition aims to decompose a 3D shape into a set of almost convex components, whose convex hulls can then be used to represent the input shape. It thus enables efficient geometry processing algorithms specifically designed for convex shapes and has been widely used in game engines, physics simulations, and animation. While prior works can capture the global structure of input shapes, they may fail to preserve fine-grained details (e.g., filling a toaster's slots), which are critical for retaining the functionality of objects in interactive environments. In this paper, we propose a novel method that addresses the limitations of existing approaches from three perspectives: (a) We introduce a novel collision-aware concavity metric that examines the distance between a shape and its convex hull from both the boundary and the interior. The proposed concavity preserves collision conditions and is more robust to detect various approximation errors. (b) We decompose shapes by directly cutting meshes with 3D planes. It ensures generated convex hulls are intersection-free and avoids voxelization errors. (c) Instead of using a one-step greedy strategy, we propose employing a multi-step tree search to determine the cutting planes, which leads to a globally better solution and avoids unnecessary cuttings. Through extensive evaluation on a large-scale articulated object dataset, we show that our method generates decompositions closer to the original shape with fewer components. It thus supports delicate and efficient object interaction in downstream applications.

The Fuglede conjecture for convex domains is true in all dimensions

Abstract: A set $\Omega \subset \mathbb{R}^d$ is said to be spectral if the space $L^2(\Omega)$ has an orthogonal basis of exponential functions. A conjecture due to Fuglede (1974) stated that $\Omega$ is a spectral set if and only if it can tile the space by translations. While this conjecture was disproved for general sets, it has long been known that for a convex body $\Omega \subset \mathbb{R}^d$ the "tiling implies spectral" part of the conjecture is in fact true. To the contrary, the "spectral implies tiling" direction of the conjecture for convex bodies was proved only in $\mathbb{R}^2$, and also in $\mathbb{R}^3$ under the a priori assumption that $\Omega$ is a convex polytope. In higher dimensions, this direction of the conjecture remained completely open (even in the case when $\Omega$ is a polytope) and could not be treated using the previously developed techniques. In this paper we fully settle Fuglede's conjecture for convex bodies affirmatively in all dimensions, i.e. we prove that if a convex body $\Omega \subset \mathbb{R}^d$ is a spectral set then $\Omega$ is a convex polytope which can tile the space by translations. To prove this we introduce a new technique, involving a construction from crystallographic diffraction theory, which allows us to establish a geometric "weak tiling" condition necessary for a set $\Omega \subset \mathbb{R}^d$ to be spectral.

Simple PI-PD tuning rules based on the centroid of the stability region for controlling unstable and integrating processes.

Abstract: Designing the parameters of a PI-PD controller is very challenging. Consequently, the centroid of the convex stability boundary locus approach was employed to overcome this challenge. Unfortunately, this approach requires deriving several equations for constructing the stability regions of the PI-PD controller. Also, it computes the centroid of the stability region based on visual observations without using any analytical methods. Therefore, it is time-consuming, and the accuracy of its computations is questionable. This paper suggests simple tuning rules for computing the gains of PI-PD controllers based on the centroid of the stability region to handle the limitations of the centroid of the convex stability boundary locus approach. A robustness analysis has also been conducted to gauge the performance of the proposed tuning rules. Moreover, several simulation examples and a real-time application have been considered for evaluating the effectiveness and the feasibility of the suggested approach.

Safety of Dynamical Systems With Multiple Non-Convex Unsafe Sets Using Control Barrier Functions

Abstract: This letter presents an approach to deal with safety of dynamical systems in presence of multiple non-convex unsafe sets. While optimal control and model predictive control strategies can be employed in these scenarios, they suffer from high computational complexity in case of general nonlinear systems. Leveraging control barrier functions, on the other hand, results in computationally efficient control algorithms. Nevertheless, when safety guarantees have to be enforced alongside stability objectives, undesired asymptotically stable equilibrium points have been shown to arise. We propose a computationally efficient optimization-based approach which allows us to ensure safety of dynamical systems without introducing undesired equilibria even in presence of multiple non-convex unsafe sets. The developed control algorithm is showcased in simulation and in a real robot navigation application.

Self-Sustainable Reconfigurable Intelligent Surface Aided Simultaneous Terahertz Information and Power Transfer (STIPT)

Abstract: This paper proposes a new simultaneous terahertz (THz) information and power transfer (STIPT) system, which utilizes a reconfigurable intelligent surface (RIS) for both the data and power transmission. We aim to maximize the information users’ (IUs’) sum data rate while guaranteeing the power harvesting requirements of energy users (EUs) and RIS. To solve the formulated non-convex problem, the block coordinate descent (BCD) based algorithm is adopted to alternately optimize the transmit precoding of IUs, RIS’s reflecting coefficients, and the position of RIS. Additionally, the penalty constrained convex approximation (PCCA) algorithm is proposed to optimize the deployment of the RIS, where the introduced penalties ensure that the solution is always feasible. The simulation results show that the proposed solution outperforms the benchmark schemes, and the proposed BCD algorithm can greatly improve the performance of the STIPT system.

Some integral inequalities for generalized left and right log convex interval-valued functions based upon the pseudo-order relation

Abstract: Abstract It is a well-known fact that inclusion and pseudo-order relations are two different concepts which are defined on the interval spaces, and we can define different types of convexities with the help of both relations. By means of pseudo-order relation, the present article deals with the new notions of convex functions which are known as left and right log- s s -convex interval-valued functions (IVFs) in the second sense. The main motivation of this study is to present new inequalities for left and right log- s s -convex-IVFs. Therefore, we establish some new Jensen-type, Hermite-Hadamard (HH)-type, and Hermite-Hadamard-Fejér (HH-Fejér)-type inequalities for this kind of IVF, which generalize some known results. To strengthen our main results, we provide nontrivial examples of left and right log- s s -convex IVFs.

Employing convex shape absorber for enhancing the performance of solar still desalination system

Abstract: • New convex absorber solar still has been tested and compared with conventional one. • Convex height, wick type, nanoparticles, and phase change material have considered. • Convex solar still showed about 54% superior productivity than conventional one. • Nano black paint increases the productivity of convex solar still by 18%. • Using nano phase change material enhanced the yield of convex solar still by 40%. This paper presents an experimental study for new solar still (SS) called convex SS. The convex SS has been tested at different convex heights, different wick materials, with Nano (Ag) black paint, and with Nano phase change material (paraffin wax + Ag). The results showed that, at 15 cm convex height and jute wick the convex SS showed 54% superior productivity than conventional SS. Besides, the data illustrated that, increasing the convex height increases the daily productivity of the convex SS till reaching the peak at 15 cm. Then, the yield started to decrease again at convex height larger than 15 cm. additionally; the jute wick showed higher performance with convex SS compared with cotton wick. The thermal efficiency of convex SS at 15 cm height showed about 41.2% and 40.8% for jute and cotton wicks, respectively. Furthermore, adding Ag nanoparticles to the black paint used to paint the convex surface increased the daily productivity to be 72% over conventional SS. As well, using thermal energy storage material (paraffin wax) mixed with Ag nanoparticles (2.5 wt.%) and Nano black paint enhanced the daily productivity of the convex SS to be 112% higher than conventional SS. So, it can be concluded that using Nano PCM enhanced the productivity of convex SS by about 40%. The economic analysis indicated that, the price per liter of fresh water is estimated to be 0.028 and 0.025 $/ l for conventional SS and convex SS, respectively.

New Riemann–Liouville Fractional-Order Inclusions for Convex Functions via Interval-Valued Settings Associated with Pseudo-Order Relations

Abstract: In this study, we focus on the newly introduced concept of LR-convex interval-valued functions to establish new variants of the Hermite–Hadamard (H-H) type and Pachpatte type inequalities for Riemann–Liouville fractional integrals. By presenting some numerical examples, we also verify the correctness of the results that we have derived in this paper. Because the results, which are related to the differintegral of the ϱ1+ϱ22 type, are novel in the context of the LR-convex interval-valued functions, we believe that this will be a useful contribution for motivating future research in this area.

An intermittent Onsager theorem

Abstract: For any regularity exponent $\beta<\frac 12$, we construct non-conservative weak solutions to the 3D incompressible Euler equations in the class $C^0_t (H^{\beta} \cap L^{\frac{1}{(1-2\beta)}})$. By interpolation, such solutions belong to $C^0_tB^{s}_{3,\infty}$ for $s$ approaching $\frac 13$ as $\beta$ approaches $\frac 12$. Hence this result provides a new proof of the flexible side of the $L^3$-based Onsager conjecture. Of equal importance is that the intermittent nature of our solutions matches that of turbulent flows, which are observed to possess an $L^2$-based regularity index exceeding $\frac 13$. Thus our result does not imply, and is not implied by, the work of Isett [A proof of Onsager's conjecture, Annals of Mathematics, 188(3):871, 2018], who gave a proof of the H\"older-based Onsager conjecture. Our proof builds on the authors' previous joint work with Buckmaster et al. (Intermittent convex integration for the 3D Euler equations: (AMS-217), Princeton University Press, 2023), in which an intermittent convex integration scheme is developed for the 3D incompressible Euler equations. We employ a scheme with higher-order Reynolds stresses, which are corrected via a combinatorial placement of intermittent pipe flows of optimal relative intermittency.

Fundamental barriers to high-dimensional regression with convex penalties

Abstract: In high-dimensional regression, we attempt to estimate a parameter vector β0∈Rp from n≲p observations {(yi,xi)}i≤n, where xi∈Rp is a vector of predictors and yi is a response variable. A well-established approach uses convex regularizers to promote specific structures (e.g., sparsity) of the estimate βˆ while allowing for practical algorithms. Theoretical analysis implies that convex penalization schemes have nearly optimal estimation properties in certain settings. However, in general the gaps between statistically optimal estimation (with unbounded computational resources) and convex methods are poorly understood. We show that when the statistican has very simple structural information about the distribution of the entries of β0, a large gap frequently exists between the best performance achieved by any convex regularizer satisfying a mild technical condition and either: (i) the optimal statistical error or (ii) the statistical error achieved by optimal approximate message passing algorithms. Remarkably, a gap occurs at high enough signal-to-noise ratio if and only if the distribution of the coordinates of β0 is not log-concave. These conclusions follow from an analysis of standard Gaussian designs. Our lower bounds are expected to be generally tight, and we prove tightness under certain conditions.