Monotonicity Properties Research Articles

Monotonicity and positivity of several functions involving ratios and products of polygamma functions

Let ψ(x) denote the digamma function, that is, the logarithmic derivative of the classical Euler gamma function Γ(x). In the paper, the authors discover the monotonic properties of the functions ψ(n)(x)xψ(n+1)(x)andψ(n)(x)ψ(n)(1x) for n≥0 on (0,∞). With the aid of these monotonic properties, the authors confirm the positivity of the function ψ(x)+xψ′(x)−ψ(x)ψ(1x) on (0,∞). The authors also pose five open problems, generalizing the latter two of the three functions mentioned above and their related conclusions.

Oscillation Solutions for Nonlinear Second-Order Neutral Differential Equations

This research investigates the oscillation criteria of nonlinear second-order neutral differential equations with multiple delays, focusing on their noncanonical forms. By leveraging an innovative iterative technique, new relationships are established to enhance the monotonic properties of positive solutions. These advancements lead to the derivation of novel oscillation criteria that significantly extend and refine the existing body of knowledge in this domain. The proposed criteria address gaps in the literature, providing a robust framework for analyzing such differential equations. To demonstrate their practical implications, three illustrative examples are presented, showcasing the applicability and effectiveness of the results in solving real-world problems involving delay differential equations.

Hereditary properties of lower semicontinuous metric projection and solar properties of sets

Hereditary properties of lower semicontinuous metric projection and solar properties of sets

Non-decreasing martingale couplings

For many examples of couples (μ, ν) of probability measures on the real line in the convex order, we observe numerically that the Hobson and Neuberger martingale coupling, which maximizes for ρ = 1 the integral of |y − x|ρ with respect to any martingale coupling between μ and ν, is still very close to maximize this integral for ρ ∈ (0, 2) and minimize it for ρ > 2. We investigate theoretically when it is an optimizer for ρ ≠ 1 and exhibit rather restrictive sufficient conditions. We also exhibit couples (μ, ν) such that it is not an optimizer. The support of the Hobson and Neuberger coupling is known to satisfy some monotonicity property which we call non-decreasing. We check that the non-decreasing property is preserved for maximizers when ρ ∈ (0, 1]. In general, there exist distinct non-decreasing martingale couplings, and we find some decomposition of ν which is in one-to-one correspondence with martingale couplings non-decreasing in a generalized sense.

Hopf bifurcation analysis in cai system with fractional order

This work focuses on examining the dynamic behavior of a fractional-order hyperchaotic Cai system, a complex mathematical model with potential applications in various fields. The investigation begins by using the Routh-Hurwitz criteria, specifically adapted for fractional-order systems, to evaluate the local asymptotic stability of the equilibrium point. Additionally, the necessary conditions for the occurrence of Hopf bifurcation are derived, highlighting the system's transition from stable equilibrium to oscillatory dynamics. To further illustrate the system's complex behavior, phase portraits and chaotic attractors are generated for various parameter values. These visual representations, supported by detailed numerical simulations, provide a comprehensive depiction of the system's behavior under different conditions. The findings offer valuable insights into the stability and chaotic nature of the fractional-order hyperchaotic Cai system, enriching the understanding of its potential applications in modeling and control of complex systems. Through this analysis, the study contributes to the growing field of fractional-order dynamical systems, emphasizing their ability to describe and analyze phenomena with memory and hereditary properties.

Inheritance of real estate under conditions of cohabitation

Purpose. The purpose of the article is to explore the peculiarities of inheritance of real estate under conditions of joint residence, find out the legal consequences of the indissoluble marriage of the testator with a third person for the circle of heirs and determine their shares in the inheritance. The research methodology consists in the analysis of the provisions of the current legislation, the practice of their application and scientific doctrines. The research results revealed that joint residence can significantly affect the circle of heirs and their shares in the inheritance. In particular, the study showed that in the case of the indissoluble marriage of the testator with a third person, this person may have the right to a share in the inheritance, even if it has not been officially recognized heir. This can lead to difficulties in the section of the hereditary property between other heirs. Originality. The scientific novelty lies in a comprehensive analysis of the legal consequences of cohabitation on the inheritance of real estate under the conditions of the indissoluble marriage of the testator, which allows us to better understand the problems of the legal status of such heirs. Practical significance – providing recommendations on taking into account the issues of joint residence in the inheritance of real estate. It is necessary to pay attention to the relationship of formal legal requirements and principles of justice in determining the circle of heirs and the volume of their shares in the inheritance. The study of judicial practice in such hereditary disputes will reveal problematic aspects in the application of current legislation and formulate reasonable proposals for its improvement. The results of the study can be used to improve regulatory regulation in the field of inheritance in order to achieve a balance between compliance with formal requirements and ensuring fairness.

Interval-value Pythagorean Fuzzy Prioritized Aggregation Operators for Selecting an Eco-Friendly Transportation Mode Selection

When selecting an environmentally friendly mode of transportation, many factors must be taken into account, such as capacity, delivery time, cost-effectiveness, and environmental impact. This is a difficult decision-making problem since it calls for the simultaneous evaluation and prioritization of several criteria. A thorough and methodical approach is required to make an informed decision that satisfies particular transportation needs while adhering to sustainability goals. The process entails balancing various trade-offs to determine the most environmentally friendly mode of transportation. When solving multi-attribute group decision-making (MAGDM) problems, prioritization is essential. Prioritization in fuzzy systems has been implemented through a variety of techniques and approaches. This paper tackles the MAGDM problem within the Pythagorean fuzzy (PyF) framework, taking into account the different requirements for experts and characteristics. We present new Aczel Alsina aggregation operators (AOs), whose efficient handling of uncertainties makes a major contribution to fuzzy mathematics. We suggest several PyF AOs, such as the PyF-prioritized Aczel Alsina geometric (PyFPAAG) and PyF-prioritized Aczel Alsina averaging (PyFPAAA), which are based on the Aczel Alsina t-norm and t-conorm. We show these AOs satisfy the aggregation criteria by examining their monotonicity, boundedness, and idempotency properties. The prioritization weights are derived from expert knowledge, enabling the suggested operators to capture the prioritization phenomenon among the aggregated arguments. Using a MAGDM technique, the proposed AOs are used to evaluate eco-friendly transportation modes. Their significance is confirmed by contrasting them with other well-known AOs.

On Qi’s Normalized Remainder of Maclaurin Power Series Expansion of Logarithm of Secant Function

In the study, the authors introduce Qi’s normalized remainder of the Maclaurin power series expansion of the function lnsecx=−lncosx; in view of a monotonicity rule for the ratio of two Maclaurin power series and by virtue of the logarithmic convexity of the function (2x−1)ζ(x) on (1,∞), they prove the logarithmic convexity of Qi’s normalized remainder; with the aid of a monotonicity rule for the ratio of two Maclaurin power series, the authors present the monotonic property of the ratio between two Qi’s normalized remainders.

Kasner eons in Lovelock black holes

In the vicinity of spacelike singularities, general relativity predicts that the metric behaves, at each point, as a Kasner space which undergoes a series of “Kasner epochs” and “eras” characterized by certain transition rules. The period during which this process takes place defines a “Kasner eon,” which comes to an end when higher-curvature or quantum effects become relevant. When higher-curvature densities are included in the action, spacetime can undergo transitions into additional Kasner eons. During each eon, the metric behaves locally as a Kasner solution to the higher-curvature density controlling the dynamics. In this paper we identify the presence of Kasner eons in the interior of static and spherically symmetric Lovelock gravity black holes. We determine the conditions under which eons occur and study the Kasner metrics which characterize them, as well as the transitions between them. We show that the null energy condition implies a monotonicity property for the effective Kasner exponent at the end of the Einsteinian eon. We also characterize the Kasner solutions of more general higher-curvature theories of gravity. In particular, we observe that the Einstein gravity condition that the sum of the Kasner exponents adds up to 1, ∑i=1D−1pi=1, admits a universal generalization in the form of a family of Kasner metrics satisfying ∑i=1D−1pi=2n−1 which exists for any order-n higher-curvature density and in general dimensions. Published by the American Physical Society 2024

Mean value inequalities for the Riemann zeta function

We study monotonicity properties of the functions x ↦ ζ ( x ) + ζ ( 1 / x ) and x ↦ 1 ζ ( x ) + 1 ζ ( 1 / x ) and apply our results to obtain sharp bounds for the arithmetic, geometric and harmonic means of ζ ( x ) and ζ ( 1 / x ) .

Anisotropic flows of Forchheimer-type in porous media and their steady states

We study the anisotropic Forchheimer-typed flows for compressible fluids in porous media. The first half of the paper is devoted to understanding the nonlinear structure of the anisotropic momentum equations. Unlike the isotropic flows, the important monotonicity properties are not automatically satisfied in this case. Therefore, various sufficient conditions for them are derived and applied to the experimental data. In the second half of the paper, we prove the existence and uniqueness of the steady state flows subject to a nonhomogeneous Dirichlet boundary condition. It is also established that these steady states, in appropriate functional spaces, have local Hölder continuous dependence on the forcing function and the boundary data.

Functional Differential Equations with an Advanced Neutral Term: New Monotonic Properties of Recursive Nature to Optimize Oscillation Criteria

The goal of this study is to derive new conditions that improve the testing of the oscillatory and asymptotic features of fourth-order differential equations with an advanced neutral term. By using Riccati techniques and comparison with lower-order equations, we establish new criteria that verify the absence of positive solutions and, consequently, the oscillation of all solutions to the investigated equation. Using our results to analyze a few specific instances of the examined equation, we can ultimately clarify the significance of the new inequalities. Our results are an extension of previous results that considered equations with a neutral delay term and also an improvement of previous results that considered only equations with an advanced neutral term.

AB-Couped fixed point theorems results in partially ordered S-metric spaces

The concepts presented in this paper pertain to the development and examination of AB-coupled fixed point results for mapping in partially ordered S-metric spaces that possess the strong mixed monotone property. The existence and uniqueness of AB-coupled fixed points are also demonstrated. We generalize the main theorems of Gnana Bhaskar and Lakshmikantham (2006) in [15] and Virendra Singh Chouhan and Richa Sharma (2015) [4].

A network epidemic model: From the mathematical analysis to machine learning experiments

We consider a generic Susceptible–Infected–Recovered–Hospitalized–Deceased model for the spread of infectious diseases over contact networks. Precisely, the deceased compartment tracks the cumulative number of deaths that are not offset by births. After properly reducing the model to a nonlinear susceptible–infected–recovered (SIR) model on a graph, we systematically investigate its invariant sets, its stability, convergence, monotonicity and equilibrium properties. Given the significant influence of network structure on infection dynamics, the basic reproduction number is insufficient for predicting disease evolution. We introduce more suitable threshold conditions for the model. However, due to the inherent high dimensionality of networks, modelling transmission through them necessitates numerical methods. This work provides numerical demonstrations of epidemic spread, validating the derived threshold conditions. Additionally, we highlight the limitations of social distancing measures in the presence of stable equilibria with a persistent infected population using especially machine learning tools.

Optimizing speed of a green truckload pickup and delivery routing problem with outsourcing: Heuristic and exact approaches

Optimizing fuel consumption cost alongside truck speed decisions is crucial for transportation enterprises when making outsourcing decisions. However, existing research on truck fuel consumption optimization is not state-of-the-art, leading to suboptimal outsourcing outcomes. This study addresses a green truckload pickup and delivery problem with outsourcing, focusing on speed optimization and fuel consumption cost. We model the problem as a multi-attribute directed graph and propose an arc-based mixed-integer programming model and a set-partitioning binary programming model. We then analyze the monotonic properties of arc cost, simplify the set-partitioning model, and develop a mixed-integer programming-based heuristic, a branch-and-price algorithm, and a column-generation-based heuristic. To tackle the challenge of speed decisions in fuel consumption optimization, we design specific extension and dominance rules within a labeling algorithm. All algorithms are tested on several sets of instances. Numerical experiments demonstrate the effectiveness of the proposed models and algorithms.

Series expansion, higher-order monotonicity properties and inequalities for the modulus of the GrÖtzsch ring

Abstract For $r\in(0,1)$ , let $\mu \left( r\right) $ be the modulus of the plane Grötzsch ring $\mathbb{B}^2\setminus[0,r]$ , where $\mathbb{B}^2$ is the unit disk. In this paper, we prove that \begin{equation*} \mu \left( r\right) =\ln \frac{4}{r}-\sum_{n=1}^{\infty }\frac{\theta _{n}}{ 2n}r^{2n}, \end{equation*} with $\theta _{n}\in \left( 0,1\right)$ . Employing this series expansion, we obtain several absolutely monotonic and (logarithmically) completely monotonic functions involving $\mu \left( r\right) $ , which yields some new results and extend certain known ones. Moreover, we give an affirmative answer to the conjecture proposed by Alzer and Richards in H. Alzer and K. Richards, On the modulus of the Grötzsch ring, J. Math. Anal. Appl. 432(1): (2015), 134–141, DOI 10.1016/j.jmaa.2015.06.057. As applications, several new sharp bounds and functional inequalities for $\mu \left( r\right) $ are established.

Residual extropy in ranked set sampling: Properties, comparative analysis, and estimation

Ranked set sampling (RSS) has gained significant significance in numerous practical domains, such as environmental and ecological studies, and statistical genetics. This article focuses on investigating the concept of extropy as a measure of residual uncertainty in RSS. It is devoted to discussing various monotone properties and characterization results associated with the residual extropy of RSS. Additionally, a comparative analysis is conducted between the residual extropy of RSS and its counterpart in simple random sampling. Optimal minima and maxima values for the residual extropy of RSS are determined. To further contribute to the field, a consistent estimator for the residual extropy of RSS is proposed. The effectiveness of this estimator is demonstrated through three illustrative examples, highlighting its performance in practical scenarios.

Path Algebra-Driven Classification Solution to Realize User-Centric Performance-Oriented Virtual Network Embeddings

The intense diversity of the Next-Generation Networking environments like 6G and the forthcoming deployment of immersive applications with varied user-specific requirements transform the efficient allocation of resources into a real challenge. Traditional solutions like the shortest path algorithm and mono-constraint methodologies are inadequate to handle customized user-defined performance parameters and effectively classify physical resources according to these intricate demands. This research offers a new evaluation mechanism to successfully replace the aforementioned traditional path ranking and path selection techniques. Specifically, the proposed framework is integrated with optimization-oriented metrics, each indicating a unique aspect of performance for evaluating candidate network paths. The deployed metrics are then algebraically synthesized to provide a distinctive multidimensional description of the examined substrate resources. These primary and composite metrics adhere to the fundamental monotonicity and isotonicity properties of a Path Algebra; hence, the validity and optimality of the proposed evaluation mechanism is guaranteed by design. To tackle the complexity created by the variety of human-centric customization, a novel methodology that analyzes and determines the weighted influence of the synthesized metrics depending on the characteristics of the served user-centric application is also introduced. The chosen suitable weights address performance-oriented mission-critical tailored objectives for adaptive optimizations. Its innovative algebraic design allows it to successfully describe and rank candidate paths in a versatile way, whether in legacy or modern architectures. The experimental data of the first scenario show that 62.5% and 50% of highlighted path evaluations proposed by the shortest path and unidimensional constraint strategies, respectively, suffer from moderate performance-oriented values compared to the proposed framework. Likewise, the results of the second examined scenario reveal that the proposed composite metric yields more suitable path rankings by 50% in contrast to its traditional counterparts, rendering the contested evaluation mechanisms obsolete.

Treatment of cancer patients by generalizing a Fermatean normal vague set with aggregation operators

Multi-attribute decision-making problems can be solved using a Fermatean vague set. Fermatean vague sets are extension of vague sets. We initiated generalized Fermatean vague weighted averaging, generalized Fermatean vague weighted geometric, power generalized Fermatean vague weighted averaging and power generalized Fermatean vague weighted geometric. The algebraic structures such as associative, distributive, idempotent, bounded, commutativity and monotonicity properties are satisfied by generalized Fermatean vague numbers. We discussed some mathematical properties of these sets, as well as the Hamming distance and Euclidean distance. An algorithm that uses aggregation operators to solves multi-attribute decision-making problems. The fields of computer science and medicine are essential for medical diagnosis research. Choosing cancer treatment is a complex process. Patients and health care professionals must communicate effectively to make the right decision about their cancer treatment. There are a number of factors that influence patients treatment decisions. As far as cancer patients are concerned, there are five types of cancer patients. Many different treatments are currently available and they are often combined as part of an overall treatment plan involving various treatment options. Patients with which cancer can be treated in various ways, such as cystoscopy, biopsy, blood tests and CT scan of the urogram. We intended to choose the best treatment based on our comparisons and options. Thus, it is evident that natural number q has a significant influence on the models. Additionally, flowchart based multi-criteria decision-making is offered and applied to a numerical example to show the efficiency of the recommended approach. The results are evaluated for different values of the parameter. Moreover, a comparative analysis has been performed to illustrate the superior outcomes of the suggested approach in comparison with existing methodologies.

Joint optimization of condition-based production and maintenance with mutual production-deterioration dependencies

Production control and maintenance scheduling are the two major cost-effective methodologies in the manufacturing systems. The existing literature considers these processes in isolation or with unidirectional dependencies. To fill this gap, we propose an integrated control model of maintenance and production process considering the mutual influence between production and deterioration in a single-machine system. By leveraging condition monitoring data, we enhance decision-making effectiveness and develop a comprehensive framework based on an infinite-horizon Markov decision process. We establish and prove the monotonic structural properties of total profit and maintenance actions relative to machine state, and develop an improved value iteration algorithm to reduce the computational space. Numerical experiments demonstrate the performance of our model in maximizing profits compared to traditional condition-based maintenance and condition-based production approaches. Sensitivity analysis further highlights key parameters influencing optimal policies, providing valuable insights for practical applications.