Monotonicity Properties Research Articles

Efficient Numerical Implementation of the Time-Fractional Stochastic Stokes–Darcy Model

This paper presents an efficient numerical method for the fractional-order generalization of the stochastic Stokes–Darcy model, which finds application in various engineering, biomedical and environmental problems involving interaction between free fluid flow and flows in porous media. Unlike the classical model, this model allows taking into account the hereditary properties of the process under uncertainty conditions. The proposed numerical method is based on the combined use of the sparse grid stochastic collocation method, finite element/finite difference discretization, a fast numerical algorithm for computing the Caputo fractional derivative, and a cost-effective ensemble strategy. The hydraulic conductivity tensor is assumed to be uncertain in this problem, which is modeled by the reduced Karhunen–Loève expansion. The stability and convergence of the deterministic numerical method have been rigorously proved and validated by numerical tests. Utilizing the ensemble strategy allowed us to solve the deterministic problem once for all samples of the hydraulic conductivity tensor, rather than solving it separately for each sample. The use of the algorithm for computing the fractional derivatives significantly reduced both computational cost and memory usage. This study also analyzes the influence of fractional derivatives on the fluid flow process within the fractional-order Stokes–Darcy model under uncertainty conditions.

General weighted extropy of minimum and maximum ranked set sampling with unequal samples

. In industrial, environmental, and ecological investigations, ranked set sampling is a sample method that enables the experimenter to use the whole range of population values. The ranked set sampling process can be modified in two extremely helpful ways: maximum ranked set sampling with unequal samples and minimum ranked set sampling with unequal samples. They permit an increase in set size without too many ranking errors being introduced. In this article, we are defining general weighted extropy (GWJ) of minimum and maximum ranked set samples when samples are of unequal size (minRSSU and maxRSSU, respectively). Stochastic comparison and monotone properties have been studied under different situations. Additionally, we compare the extropy of these two sampling data with that of ranked set sampling data and simple random sampling data. Bounds of GWJ of minRSSU and maxRSSU have been obtained. Finally, we investigate the weighted discrimination information between simple random sampling, ranked set sampling, and minimum and maximum ranked set sampling with unequal sample sizes. Some results for equality of GWJ of minRSSU and maxRSSU under symmetric assumption are also obtained.

On indication, strict monotonicity, and efficiency of projections in a general class of path-based data envelopment analysis models

Data envelopment analysis (DEA) theory formulates a number of desirable properties that DEA models should satisfy. Among these, indication, strict monotonicity, and strong efficiency of projections tend to be grouped together in the sense that, in individual models, typically, either all three are satisfied or all three fail at the same time. Specifically, in slacks-based graph models, the three properties are always met; in path-based models, such as radial models, directional distance function models, and the hyperbolic function model, the three properties, with some minor exceptions, typically all fail.Motivated by this observation, the article examines relationships among indication, strict monotonicity, and strong efficiency of projections in the class of path-based models over variable returns-to-scale technology sets. Under mild assumptions, it is shown that the property of strict monotonicity and strong efficiency of projections are equivalent, and that both properties imply indication. This paper also characterises a narrow class of technology sets and path directions for which the three properties hold in path-based models.

Pricing Decisions in Dual-Channel Supply Chains Considering the Offline Channel Preference and Service Level

With the rapid development of e-commerce, the online channels encroaching on the offline sales market are becoming more serious, which will definitely harm the offline market. Moreover, there exists a certain percentage of consumers (mostly elderly people) who are not able to purchase online because they lack digital skills. Therefore, understanding the impact of the purchase channel preference and service level on pricing decisions is vital for the dual-channel supply chain management. Focusing on the channel preference and service level, we first develop an optimal pricing model containing centralized and decentralized decision-making for an online and offline retailer by deploying the Stackelberg game. We first develop a Stackleberg game to capture such a dual-channel supply chain with the offline channel preference and service level. Secondly, under centralized decision-making, we derive the optimal retail prices and obtain the optimal total profit. Thirdly, under decentralized decision-making, we obtain the optimal retail prices and optimal total profit as well. Moreover, extensive monotonicity properties when system parameters change are obtained. Relying on the theoretical results, firstly, we show that the improvement of the offline service level would lead to higher pricing of the commodities for both online and offline channels. From our numerical results, when the service level is improved, the offline and online optimal pricing increases by 47.5% and 31.1%, respectively, which may contradict the conventional belief that the improvement of one channel would harm another one. Secondly, we demonstrate that the benefit of improving the offline service level has a diminishing marginal effect. The numerical results show that when the current service level is low, the effectives of improving the service level is roughly five times that when the service level is high. This indicates that the investment in improving the offline service level should not be unlimited. Thirdly, we show that the pricing decision under centralized decision-making should be adopted with the existence of both the offline channel preference and offline service.

Optimal premium pricing in a competitive stochastic insurance market with incomplete information: A Bayesian game-theoretic approach

This paper examines a stochastic one-period insurance market with incomplete information. The aggregate amount of claims follows a compound Poisson distribution. Insurers are assumed to be exponential utility maximizers, with their degree of risk aversion forming their private information. A premium strategy is defined as a mapping between risk-aversion types and premium rates. The optimal premium strategies are denoted by the pure-strategy Bayesian Nash equilibrium, whose existence and uniqueness are demonstrated under specific conditions on the insurer-specific demand functions. Boundary and monotonicity properties for equilibrium premium strategies are derived.

Fast hybrid method for solving variational inequalities beyond monotonicity in real Banach spaces

In this work, we introduce a new inertial hybrid algorithm that combines the subgradient extragradient, Halpern, and S-iteration methods. We provide an approximate solution to variational inequality and common fixed point problem of relatively non-expansive mappings in real Banach spaces, where our cost operator is Lipschitz continuous and quasimonotone, and our step size is self-adaptive, non-monotone, and non-reliant on any line-search principle. We provide two strong convergence results with (and without) recourse to the monotonicity property, and further conduct several relevant numerical experiments to reveal the efficiency of our method over others in the literature.

Subsumption, correctness and relative correctness: Implications for software testing

Context. Several Research areas emerged and have been proceeding independently when in fact they have much in common. These include: mutant subsumption and mutant set minimization; relative correctness and the semantic definition of faults; differentiator sets and their application to test diversity; generate-and–validate methods of program repair; test suite coverage metrics.Objective. Highlight their analogies, commonalities and overlaps; explore their potential for synergy and shared research goals; unify several disparate concepts around a minimal set of artifacts.Method. Introduce and analyze a minimal set of concepts that enable us to model these disparate research efforts, and explore how these models may enable us to share insights between different research directions, and advance their respective goals.Results. Capturing absolute (total and partial) correctness and relative (total and partial) correctness with a single concept: detector sets. Using the same concept to quantify the effectiveness of test suites, and prove that the proposed measure satisfies appealing monotonicity properties. Using the measure of test suite effectiveness to model mutant set minimization as an optimization problem, characterized by an objective function and a constraint.Generalizing the concept of mutant subsumption using the concept of differentiator sets. Identifying analogies between detector sets and differentiator sets, and inferring relationships between subsumption and relative correctness.Conclusion. This paper does not aim to answer any pressing research question as much as it aims to raise research questions that use the insights gained from one research venue to gain a fresh perspective on a related research issue.

Order relations of the Wasserstein mean and the spectral geometric mean

On the space of positive definite matrices, several operator means are popular and have been studied extensively. In this paper, we investigate the near order and the Löwner order relations on the curves defined by the Wasserstein mean and the spectral geometric mean. We show that the near order $\preceq $ is stronger than the eigenvalue entrywise order and that $A\natural_t B \preceq A\diamond_t B$ for $t\in [0,1]$. We prove the monotonicity properties of the curves originated from the Wasserstein mean and the spectral geometric mean in terms of the near order. The Löwner order properties of the Wasserstein mean and the spectral geometric mean are also explored.

Convergence of lattice Boltzmann methods with overrelaxation for a nonlinear conservation law

We approximate a nonlinear multidimensional conservation law by Lattice Boltzmann Methods (LBM), based on underlying BGK type systems with finite number of velocities discretized by a transport-collision scheme. The collision part involves a relaxation parameter ω which value greatly influences the stability and accuracy of the method, as noted by many authors. In this article we clarify the relationship between ω and the parameters of the kinetic model and we highlight some new monotonicity properties which allow us to extend the previously obtained stability and convergence results. Numerical experiments are performed.

A strongly convergent algorithm for solving split equality problems beyond monotonicity

In this paper, we focus on some split inverse problems, namely the split equality variational inequalities and common fixed point problems, and combine various operator theory techniques to establish minimum-norm strong convergence for our proposed method. We present two strong convergent results with (and without) reference to the monotonicity property of the cost operators. Our convergence analyses assume very mild conditions and thus generalize and extend recent related results in the literature. Furthermore, several numerical examples illustrate the practical potentials and advantages of our proposed algorithm.

Preserving properties of some Szasz-Mirakyan type operators

For a family of Szasz-Mirakyan type operators we prove that they preserve convex-type functions and that a monotonicity property verified by Cheney and Sharma in the case Szasz-Mirakyan operators holds for the variation study here. We also verify that several modulus of continuity are preserved.

Neuro-Optimal Event-Triggered Impulsive Control for Stochastic Systems via ADP.

This article presents a novel neural-network-based optimal event-triggered impulsive control method. First, a novel general-event-based impulsive transition matrix (GITM) is constructed to represent the probability distribution evolving characteristics regarding all system states across the impulsive actions, rather than the prefixed timing sequence. On the foundation of this GITM, the event-triggered impulsive adaptive dynamic programming (ETIADP) algorithm and its high-efficiency version (HEIADP) are developed to deal with the optimization problems for stochastic systems with event-triggered impulsive controls. It is shown that the obtained controller design scheme can reduce the computational and communication burden caused by updating the controller periodically. By analyzing the admissibility, monotonicity, and optimality properties of ETIADP and HEIADP, we further establish the approximation error bound of the neural networks to address the connection between the ideal and neural-network-based realizations of the present methods. It is proven that the iterative value functions of both the ETIADP and HEIADP algorithms fall in a small neighborhood of the optimum as the iteration index increases to infinity. By adopting a novel task synchronization mechanism, the proposed HEIADP algorithm fully utilizes the computing resources of multiprocessor systems (MPSs), while significantly reducing the memory requirement compared to traditional ADP approaches. Finally, we carry out a numerical study to show that the proposed methods can fulfill the desired goals.

New Monotonic Properties for Solutions of Odd-Order Advanced Nonlinear Differential Equations

The present paper studies the asymptotic and oscillatory properties of solutions of odd-order differential equations with advanced arguments and in a noncanonical case. By providing new and effective relationships between the corresponding function and the solution, we present strict and new criteria for testing whether the studied equation exhibits oscillatory behavior or converges to zero. Our results contribute uniquely to oscillation theory by presenting some theorems that improve and expand upon the results found in the existing literature. We also provide an example to corroborate the validity of our proposed criteria.

Multirate time-integration based on dynamic ODE partitioning through adaptively refined meshes for compressible fluid dynamics

In this paper, we apply the Paired-Explicit Runge-Kutta (P-ERK) schemes by Vermeire et al. [1,2] to dynamically partitioned systems arising from adaptive mesh refinement. The P-ERK schemes enable multirate time-integration with no changes in the spatial discretization methodology, making them readily implementable in existing codes that employ a method-of-lines approach.We show that speedup compared to a range of state of the art Runge-Kutta methods can be realized, despite additional overhead due to the dynamic re-assignment of flagging variables and restricting nonlinear stability properties. The effectiveness of the approach is demonstrated for a range of simulation setups for viscous and inviscid convection-dominated compressible flows for which we provide a reproducibility repository.In addition, we perform a thorough investigation of the nonlinear stability properties of the Paired-Explicit Runge-Kutta schemes regarding limitations due to the violation of monotonicity properties of the underlying spatial discretization. Furthermore, we present a novel approach for estimating the relevant eigenvalues of large Jacobians required for the optimization of stability polynomials.

Characterizing interfacial behavior of structurally cemented granular material using a large three-dimensional contact surface testing machine and a mesoscale bond model in DEM

Structuralized cementing technology takes full advantage of non-pressure controlled grouting technology to fill pores in coarse aggregates using self-compacting material with no need for vibration or mixing. By cementing the aggregates in a structured manner, structurally cemented material has properties between those of a discrete granular material and a continuous medium. The interface between different component structures exerts an important effect on the physical properties of the whole material. In this paper, the monotonic and cyclic mechanical properties of the contact interface properties of a structurally cemented material under different normal stresses are studied by performing experiments and numerical simulations. Through the study, the deformation displacement time history and volume change with the shear process are provided, the deformation process of the sample near the contact interface during the shear process is discussed, and the shear mechanics law with the strength mechanism under the simple shear condition is summarized.

A Partial Information Decomposition for Multivariate Gaussian Systems Based on Information Geometry.

There is much interest in the topic of partial information decomposition, both in developing new algorithms and in developing applications. An algorithm, based on standard results from information geometry, was recently proposed by Niu and Quinn (2019). They considered the case of three scalar random variables from an exponential family, including both discrete distributions and a trivariate Gaussian distribution. The purpose of this article is to extend their work to the general case of multivariate Gaussian systems having vector inputs and a vector output. By making use of standard results from information geometry, explicit expressions are derived for the components of the partial information decomposition for this system. These expressions depend on a real-valued parameter which is determined by performing a simple constrained convex optimisation. Furthermore, it is proved that the theoretical properties of non-negativity, self-redundancy, symmetry and monotonicity, which were proposed by Williams and Beer (2010), are valid for the decomposition Iig derived herein. Application of these results to real and simulated data show that the Iig algorithm does produce the results expected when clear expectations are available, although in some scenarios, it can overestimate the level of the synergy and shared information components of the decomposition, and correspondingly underestimate the levels of unique information. Comparisons of the Iig and Idep (Kay and Ince, 2018) methods show that they can both produce very similar results, but interesting differences are provided. The same may be said about comparisons between the Iig and Immi (Barrett, 2015) methods.

Kneser-type oscillation theorems for second-order functional differential equations with unbounded neutral coefficients

Abstract In this paper, we initiate the study of asymptotic and oscillatory properties of solutions to second-order functional differential equations with noncanonical operators and unbounded neutral coefficients, using a recent method of iteratively improved monotonicity properties of nonoscillatory solutions. Our results rely on ideas that essentially improve standard techniques for the investigation of differential equations with unbounded neutral terms with delay or advanced argument. The core of the method is presented in a form that suggests further generalizations for higher-order differential equations with unbounded neutral coefficients.

Point-set games and functions with the hereditary small oscillation property

Given a metric space X, we consider certain families of functions f:X→R having the hereditary oscillation property HSOP and the hereditary continuous restriction property HCRP on large sets. When X is Polish, among them there are families of Baire measurable functions, μ‾-measurable functions (for a finite nonatomic Borel measure μ on X) and Marczewski measurable functions. We obtain their characterizations using a class of equivalent point-set games. In similar aspects, we study cliquish functions, SZ-functions and countably continuous functions.

Super Bassian and nearly generalized Bassian Abelian groups

In connection to two recent publications of ours in Arch. Math. Basel (2021) and Acta Math. Hungar. (2022), respectively, and in regard to the results obtained in Arch. Math. Basel (2012), we have the motivation to study the near property of both Bassian and generalized Bassian groups. Concretely, we prove that if an arbitrary reduced group has the property that all of its proper subgroups are generalized Bassian, then it is also generalized Bassian itself, that is, if [Formula: see text] is an arbitrary nearly generalized Bassian group, then either [Formula: see text] is a quasi-cyclic group or [Formula: see text] is generalized Bassian of finite torsion-free rank. Moreover, we show that there is a complete description of the so-called super Bassian groups that are those groups whose epimorphic images are all Basian, and give their full characterization. Also, we establish that the hereditary property of Bassian groups gives nothing new as it coincides with the ordinary Bassian property.

Financing a capital-constrained supply chain: Equity or debt

Many retailers are small and medium enterprises (SMEs) with limited access to capital to finance their operations. Here, we consider a supply chain consisting of a capital-constrained retailer and a manufacturer and examine the effect of equity and debt financing schemes on their operational decisions. Using a game theoretical approach, for the risk-neutral scenario, we take expected profit maximization as the participants’ objective to examine the equilibria of their operational and financing decisions. We also examine the condition under which the manufacturer and retailer adopt equity or debt financing to earn additional profits. We find that when the retailer is highly capital-constrained, she benefits from either financing scheme, but the manufacturer prefers to offer equity financing over debt financing. Otherwise, if the retailer is less constrained, debt financing is preferable. We also extend our analysis to risk-averse participants using the conditional value-at-risk (CVaR) criterion. We show that the decreasing monotone property of the order quantity in the wholesale price, known in the risk-neutral setting, no longer holds. Indeed, the relationship depends on the participants’ risk aversion level; if the manufacturer is highly risk-averse, it chooses to provide equity financing to enhance its CVaR performance; otherwise, it offers debt financing. Our findings provide implications for decision-makers in choosing the optimal financing options and making the associated operations and financing decisions when considering risk attitudes.