Monotonicity Properties Research Articles

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 ) .

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].

Monotonicity properties for Bernoulli percolation on layered graphs— A Markov chain approach

A layered graph G× is the Cartesian product of a graph G=(V,E) with the linear graph Z, e.g. Z× is the 2D square lattice Z2. For Bernoulli percolation with parameter p∈[0,1] on G× one intuitively would expect that Pp((o,0)↔(v,n))≥Pp((o,0)↔(v,n+1)) for all o,v∈V and n≥0. This is reminiscent of the better known bunkbed conjecture. Here we introduce an approach to the above monotonicity conjecture that makes use of a Markov chain building the percolation pattern layer by layer. In case of finite G we thus can show that for some N≥0 the above holds for all n≥No,v∈V and p∈[0,1]. One might hope that this Markov chain approach could be useful for other problems concerning Bernoulli percolation on layered graphs.

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.

A Look at Generalized Trigonometric Functions as Functions of Their Two Parameters and Further New Properties

Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect to parameters have not been thoroughly studied. In this paper, we make an attempt to fill this gap. Our results are not complete; for some functions, we manage to establish (log)-convexity/concavity in parameters, while for others, we only managed the prove monotonicity, in which case we present necessary and sufficient conditions for convexity/concavity. In the course of the investigation, we found two hypergeometric representations for the generalized cosine and hyperbolic cosine functions which appear to be new. In the last section of the paper, we present four explicit integral evaluations of combinations of generalized trigonometric/hyperbolic functions in terms of hypergeometric functions.

Distributional Properties of Generalized Diversity Index Based on two-key Species Abundance Models

In the area of ecological research, the study of species diversity of a community or population seems to have been fully developed. However, the problem of how the distributions and expectations of the sample diversity indices are affected by population diversity has received little attention. This paper is concerned with methods of moments of improved generalized diversity index, N(α,β) due to Shamia's (2013) proposal which includes special cases. This improved index is a further generalization due to Good as described by Backowski et al., (1997). In this article, the first four central moments of N(α,β) are derived for both general species relative abundance models: the Broken-Stick model and Sequential-Breakage model within a range of (α,β) considered. This allows the determination of the skewness and kurtosis of N(α,β) and thus gives information about the behaviour of the distribution of the improved index. The results are applied for comparing the diversities of the communities based on the samples n>s, and they yielded certain desirable monotonicity properties for large samples. It can be also shown that such indices are asymptotically normally distributed.

Rényi second laws for black holes

Hawking’s black hole area theorem provides a geometric realization of the second law of thermodynamics and constrains gravitational processes. In this work we explore a one-parameter extension of this constraint formulated in terms of the monotonicity properties of Rényi entropies. We focus on black hole mergers in asymptotically AdS space and determine new restrictions which these Rényi second laws impose on the final state. We evaluate the entropic inequalities starting from the thermodynamic ensembles description of black hole geometries, and find that for many situations they set more stringent bounds than those imposed by the area increase theorem.

Second-order strongly nonlinear impulsive coupled systems

This paper presents sufficient conditions for the solvability of a second-order coupled system, composed of two differential equations involving different laplacians applied to fully discontinuous nonlinearities, two-point boundary conditions, and generalized impulsive effects. Applying the lower and upper solutions technique and Schauder’s fixed point theorem, it is obtained an existence and localization theorem, based on local monotone properties on the nonlinearities and the impulsive functions.

Around strongly operator convex functions

We establish the subadditivity of strongly operator convex functions on (0,∞) and (−∞,0). By utilizing the properties of strongly operator convex functions, we derive the subadditivity property of operator monotone functions on (−∞,0). We introduce new operator inequalities involving strongly operator convex functions and weighted operator means. In addition, we explore the relationship between strongly operator convex and Kwong functions on (0,∞). Moreover, we study strongly operator convex functions on (a,∞) with −∞<a and on the left half-line (−∞,b) with b<∞. We demonstrate that any nonconstant strongly operator convex function on (a,∞) is strictly operator decreasing, and any nonconstant strongly operator convex function on (−∞,b) is strictly operator monotone. Consequently, for a strongly operator convex function g on (a,∞) or (−∞,b), we provide lower bounds for |g(A)−g(B)| whenever A−B>0.

The last-success stopping problem with random observation times

AbstractSuppose N independent Bernoulli trials with success probabilities $$p_1, p_2,\ldots $$ p 1 , p 2 , … are observed sequentially at times of a mixed binomial process. The task is to maximise, by using a nonanticipating stopping strategy, the probability of stopping at the last success. The case $$p_k=1/k$$ p k = 1 / k has been studied by many authors as a version of the familiar best choice problem, where both N and the observation times are random. We consider a more general profile $$p_k=\theta /(\theta +k-1)$$ p k = θ / ( θ + k - 1 ) and assume that the prior distribution of N is negative binomial with shape parameter $$\nu $$ ν , so the arrivals occur at times of a mixed Poisson process. The setting with two parameters offers a high flexibility in understanding the nature of the optimal strategy, which we show is intrinsically related to monotonicity properties of the Gaussian hypergeometric function. Using this connection, we find that the myopic stopping strategy is optimal if and only if $$\nu \ge \theta $$ ν ≥ θ . Furthermore, we derive formulas to assess the winning probability and discuss limit forms of the problem for large N.

A dissection of the monotonicity property of binary operations from a dominance point of view

In this paper, we expound weaker forms of increasingness of binary operations on a lattice by reducing the number of variables involved in the classical formulation of the increasingness property as seen from the viewpoint of dominance between binary operations. We investigate the relationships among these weaker forms. Furthermore, we demonstrate the role of these weaker forms in characterizing the meet and join operations of a lattice and a chain in particular. Finally, we provide ample generic examples.

Application of impact-based and laser-based surface severe plastic deformation methods on additively manufactured 316L: Microstructure, tensile and fatigue behaviors

Applying post-processing methods can play a crucial role in addressing defects inherent in the as-built state of additively manufactured materials. This study comprehensively examined the effects of various post-processing techniques, including surface severe plastic deformation (SSPD) methods such as severe shot peening (SSP), ultrasonic shot peening (USP), ultrasonic nanocrystal surface modification (UNSM), and laser shock peening (LSP), combined with stress relieving (SR) on the tensile properties and fatigue behavior of laser powder bed fusion (LB-PBF) stainless steel AISI 316L specimens. Experimental characterization was carried out, focusing on microstructure, porosity, surface texture, hardness, residual stresses, monotonic tensile properties, and rotating bending fatigue behavior. The results demonstrated an excellent combination of enhanced strength and ductility after applying SR and SSPD treatments. Additionally, the post-processing methods significantly improved fatigue behavior by increasing strength, closing subsurface pores, surface layer nanocrystallization and hardening, inducing compressive residual stresses, and modifying the surface texture. Notably, in the high-cycle fatigue regime at the lowest stress amplitude, the SR + UNSM treated specimens exhibited the greatest improvement in fatigue life, followed by SR + USP, SR + SSP, SR + LSP, and SR, when compared to the as-built state.