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In this paper, we employ the theory of differential subordination to establish a theorem that delineates certain sufficient conditions for starlikeness, convexity, close-to-convexity, and quasi-convexity in relation to functions with fixed initial coefficients. Furthermore, we introduce some results derived from these conditions. Building upon this framework, we derive an extension of Nunokawa's lemma for analytic functions with fixed initial coefficients. [ABSTRACT FROM AUTHOR]

This work examines subordination conclusions for a specific subclass of p-valent meromorphic functions on the punctured unit disc of the complex plane where the function has a pole of order p. A new linear operator is used to define the subclass that is being studied. Furthermore, we present several corollaries with intriguing specific situations of the results. [ABSTRACT FROM AUTHOR]

The primary emphasis of the present study is to introduce some novel characterizations of the interval-valued (I. V) right symmetric quantum derivative and antiderivative operators relying on generalized Hukuhara difference. To continue the study, we start with the concept of symmetric differentiability in the interval-valued sense and explore some important properties. Furthermore, through the utilization of the (I. V) symmetric derivative operator, we develop the right-sided (I. V) integral operator and explore its key properties. Also, we establish various (I. V) trapezium-like inequalities by considering the newly proposed operators and support line. Later on, we deliver another proof of the trapezium inequality through an analytical approach. Also, we present the numerical and visual analysis for the verification of our results. [ABSTRACT FROM AUTHOR]

The primary emphasis of the present study is to introduce some novel characterizations of the interval-valued $ (\mathcal{I}.\mathcal{V}) $ right symmetric quantum derivative and antiderivative operators relying on generalized Hukuhara difference. To continue the study, we start with the concept of symmetric differentiability in the interval-valued sense and explore some important properties. Furthermore, through the utilization of the $ (\mathcal{I}.\mathcal{V}) $ symmetric derivative operator, we develop the right-sided $ (\mathcal{I}.\mathcal{V}) $ integral operator and explore its key properties. Also, we establish various $ (\mathcal{I}.\mathcal{V}) $ trapezium-like inequalities by considering the newly proposed operators and support line. Later on, we deliver another proof of the trapezium inequality through an analytical approach. Also, we present the numerical and visual analysis for the verification of our results.

Effective methods for determining the boundary of the normal class are very useful for detecting anomalies in commercial or security applications—a problem known as anomaly detection. This contribution proposes a nonparametric frontier-based classification (NPFC) method for anomaly detection. By relaxing the commonly used convexity assumption in the literature, a nonconvex-NPFC method is constructed and the nonconvex nonparametric frontier turns out to provide a more conservative boundary enveloping the normal class. By reflecting on the monotonic relation between the characteristic variables and the membership, the proposed NPFC method is in a more general form since both input-like and output-like characteristic variables are incorporated. In addition, by allowing some of the training observations to be misclassified, the convex- and nonconvex-NPFC methods are extended from a hard nonparametric frontier to a soft one, which also provides a more conservative boundary enclosing the normal class. Both simulation studies and a real-life data set are used to evaluate and compare the proposed NPFC methods to some well-established methods in the literature. The results show that the proposed NPFC methods have competitive classification performance and have consistent advantages in detecting abnormal samples, especially the nonconvex-NPFC methods. [ABSTRACT FROM AUTHOR]

Let S denote the class of analytic and univalent (i.e., one-to-one) functions f (z) = z + ∑ n = 2 ∞ a n z n in the unit disk D = { z ∈ C : | z | < 1 } . For f ∈ S , In 1999, Ma proposed the generalized Zalcman conjecture that | a n a m - a n + m - 1 | ≤ (n - 1) (m - 1) , for n ≥ 2 , m ≥ 2 , with equality only for the Koebe function k (z) = z / (1 - z) 2 and its rotations. In the same paper, Ma (J Math Anal Appl 234:328–339, 1999) asked for what positive real values of λ does the following inequality hold? 0.1 | λ a n a m - a n + m - 1 | ≤ λ n m - n - m + 1 (n ≥ 2 , m ≥ 3). Clearly equality holds for the Koebe function k (z) = z / (1 - z) 2 and its rotations. In this paper, we prove the inequality (0.1) for λ = 3 , n = 2 , m = 3 . Further, we provide a geometric condition on extremal function maximizing (0.1) for λ = 2 , n = 2 , m = 3 . [ABSTRACT FROM AUTHOR]

In this paper, we investigate the distributed approximate subgradient-type method for minimizing a sum of differentiable and non-differentiable convex functions subject to nondifferentiable convex functional constraints in a Euclidean space. We establish the convergence of the sequence generated by our method to an optimal solution of the problem under consideration. Moreover, we derive a convergence rate of order $ \mathcal{O}(N^{1-a}) $ for the objective function values, where $ a\in (0.5, 1) $. Finally, we provide a numerical example illustrating the effectiveness of the proposed method.

In mathematical analysis theory of inequalities has considerable influence due to its massive utility in various fields of physical sciences. These are investigated via multiple approaches to acquire more precise and rectified forms of already celebrated consequences. Integral inequalities are investigated to compute the error bounds for quadrature schemes. Among all of them, one is Hermite-Hadamard inequality, which has mighty efficacy. Numerous generalizations have been proposed in the literature based on different novel and innovative procedures. In recent years, Bullen inequality has been very commonly studied inequality. The main objective of our progressive study is to establish a new set of Bullen-type inequalities concerning the Jensen-Mecer inequality. For the completion of the current investigation, we derive a new general Bullen-Mecer equality, which is beneficial to achieve our primary consequences. Furthermore, Considering the Bullen-Mecer equation, we employ the convexity property together with famous Hölder's type and Young's inequalities, bounding, and Lipschitz characteristics of functions to conclude new variants of generalized upper bounds of Bullen inequality. Also, we deliver some applications of outcomes to means, special functions, error bounds, and iterative methods to solve non-linear problems. Lastly, we verify our findings through various simulations. The advantage of the current study is that several results concerning Bullen's inequality can be retrieved from our proposed results and various new results can be achieved by choosing the values for γ and δ. By utilizing the similar technique that we have adopted new iterative schemes can be established from integral inequalities.

Background/Objectives: Anterior spinal fusion for primary thoracolumbar or lumbar (TL/L) adolescent idiopathic scoliosis, AIS, has advantages over posterior fusion, particularly in saving motion segments below the fusion construct. Traditionally, the approach is anterolaterally from the convexity. In adult degenerative scoliosis, the lateral or anterolateral approach may be performed from the traditional or from the concave approach which is less invasive and gives comparable outcomes. The purpose of the present pilot study was to assess the feasibility of the less invasive concave approach for younger AIS patients and compare it to the traditional convex approach over a 5-year follow-up period. Methods: The two cohorts were assessed by comparing pre- to postoperative radiographs, and clinical outcomes for pain, function, self-perception of appearance, and opinion of surgical success were prospectively obtained. Results: Radiographs found that primary TL/L scoliosis significantly improved from 53° to 18° (65%) for both the concave and convex cohorts. Sagittal alignments remained stable and there was no difference between cohorts. Coronal balance improved in both cohorts and sagittal balance was stable for both. Clinically, VAS back pain improved significantly for both cohorts initially and remained improved in the concave group. Leg pain, pain drawing, ODI disability, and VAS appearance scores improved and there was no difference between cohorts. The self-rating of success of the procedure was 100% at early and late follow-up periods. There were no neurological/surgical complications. Conclusions: The concave approach for anterior fusion for TL/L AIS is feasible with comparable radiographic and clinical outcomes to the traditional approach. [ABSTRACT FROM AUTHOR]

For decades, educational inequalities in mortality have widened and mortality among the least educated has stalled, even as overall mortality has improved, and an increasing proportion of young people have completed secondary and tertiary education. While researchers recognize that these trends are in part related to changing selection into education groups, there has been no unifying framework for understanding why the trends may be related. This article provides a unifying framework by introducing a concept called the “convex inequality regime,” a diminishing returns relationship between relative education and mortality. In populations where convex inequality regimes prevail, even without any changes in the institutions governing inequality or any changes in overall mortality conditions, education transitions result in an increase in mortality for the less educated and an increase in mortality inequality between education groups. The model also shows that lifespan variation increases for lower education groups because convex inequality regimes tend to increase relative mortality more rapidly at younger ages during an education transition. Even after an education transition is complete, inequality between education groups will continue to increase for decades due to the momentum of inequality, a cohort replacement phenomenon where younger more unequal cohorts replace older more equal cohorts. [ABSTRACT FROM AUTHOR]

Let G be a connected graph. A set S ⊆ V (G) is convex 2-dominating if S is both convex and 2-dominating. The minimum cardinality among all convex 2-dominating sets in G, denoted by γ2con(G), is called the convex 2-domination number of G. In this paper, we initiate the study of convex 2- domination in graphs. We show that any two positive integers a and b with 6 ≤ a ≤ b are, respectively, realizable as the convex domination number and convex 2-domination number of some connected graph. Furthermore, we characterize the convex 2-dominating sets in the join, corona, lexicographic product, and Cartesian product of two graphs and determine the corresponding convex 2-domination number of each of these graphs. [ABSTRACT FROM AUTHOR]

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Funding: This work was supported by the U.S. Department of Energy (DOE) Advanced Grid Modeling project, Coordinated Planning and Operation of Water and Power Infrastructures for Increased Resilience and Reliability. Incorporation of the PolyhedralRelaxations Julia package was supported by Los Alamos National Laboratory's Directed Research and Development program under the project Fast, Linear Programming-Based Algorithms with Solution Quality Guarantees for Nonlinear Optimal Control Problems [Grant 20220006ER]. All work at Los Alamos National Laboratory was conducted under the auspices of the National Nuclear Security Administration of the U.S. DOE, Contract No. 89233218CNA000001. This work was also authored in part by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the U.S. DOE, Contract No. DE-AC36-08GO28308. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0233) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0233). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

Let H be the class of harmonic functions f = h + g ¯ in the unit disk D : = { z ∈ C : | z | < 1 } , where h and g are analytic in D . In 2020, N. Ghosh and V. Allu introduced the class P H 0 (M) of normalized harmonic mappings defined by P H 0 (M) = { f = h + g ¯ ∈ H : Re (z h ′ ′ (z)) > - M + | z g ′ ′ (z) | with M > 0 , g ′ (0) = 0 , z ∈ D } . In this paper, we investigate various geometric properties such as starlikeness, convexity, convex combination and convolution for functions in the class P H 0 (M) . Furthermore, we determine the sharp Bohr–Rogosinski radius, improved Bohr radius and refined Bohr radius for the class P H 0 (M) . [ABSTRACT FROM AUTHOR]

The main purpose of this paper, is to introduce a new subclass of analytic functions involving Polylogarithm functions and obtain coefficient inequalities, distortion properties, extreme points, radii of starlikeness and convexity, Hadamard product, and convolution and integral operators for the class. [ABSTRACT FROM AUTHOR]

In mathematical analysis theory of inequalities has considerable influence due to its massive utility in various fields of physical sciences. These are investigated via multiple approaches to acquire more precise and rectified forms of already celebrated consequences. Integral inequalities are investigated to compute the error bounds for quadrature schemes. Among all of them, one is Hermite-Hadamard inequality, which has mighty efficacy. Numerous generalizations have been proposed in the literature based on different novel and innovative procedures. In recent years, Bullen inequality has been very commonly studied inequality. The main objective of our progressive study is to establish a new set of Bullen-type inequalities concerning the Jensen-Mecer inequality. For the completion of the current investigation, we derive a new general Bullen-Mecer equality, which is beneficial to achieve our primary consequences. Furthermore, Considering the Bullen-Mecer equation, we employ the convexity property together with famous Hölder's type and Young's inequalities, bounding, and Lipschitz characteristics of functions to conclude new variants of generalized upper bounds of Bullen inequality. Also, we deliver some applications of outcomes to means, special functions, error bounds, and iterative methods to solve non-linear problems. Lastly, we verify our findings through various simulations. The advantage of the current study is that several results concerning Bullen's inequality can be retrieved from our proposed results and various new results can be achieved by choosing the values for γ and δ. By utilizing the similar technique that we have adopted new iterative schemes can be established from integral inequalities. [ABSTRACT FROM AUTHOR]

Abstract The present investigation aims to examine the geometric properties of the normalized form of the combination of generalized Lommel–Wright function J λ , μ ν , m ( z ) : = Γ m ( λ + 1 ) Γ ( λ + μ + 1 ) 2 2 λ + μ z 1 − ( ν / 2 ) − λ J λ , μ ν , m ( z ) $\mathfrak{J}_{\lambda ,\mu}^{\nu ,m}(z):=\Gamma ^{m}(\lambda +1) \Gamma (\lambda +\mu +1)2^{2\lambda +\mu}z^{1-(\nu /2)-\lambda} \mathcal{J}_{\lambda ,\mu }^{\nu ,m}(\sqrt{z})$ , where the function J λ , μ ν , m $\mathcal{J}_{\lambda ,\mu}^{\nu ,m}$ satisfies the differential equation J λ , μ ν , m ( z ) : = ( 1 − 2 λ − ν ) J λ , μ ν , m ( z ) + z ( J λ , μ ν , m ( z ) ) ′ $\mathcal{J}_{\lambda ,\mu}^{\nu ,m}(z):=(1-2\lambda -\nu )J_{ \lambda ,\mu}^{\nu ,m}(z)+z (J_{\lambda ,\mu }^{\nu ,m}(z) )^{\prime}$ with J ν , λ μ , m ( z ) = ( z 2 ) 2 λ + ν ∑ k = 0 ∞ ( − 1 ) k Γ m ( k + λ + 1 ) Γ ( k μ + ν + λ + 1 ) ( z 2 ) 2 k $$ J_{\nu ,\lambda}^{\mu ,m}(z)= \biggl(\frac{z}{2} \biggr)^{2\lambda + \nu} \sum_{k=0}^{\infty} \frac{(-1)^{k}}{\Gamma ^{m} (k+\lambda +1 )\Gamma (k\mu +\nu +\lambda +1 )} \biggl(\frac{z}{ 2} \biggr)^{2k} $$ for λ ∈ C ∖ Z − $\lambda \in \mathbb{C}\setminus \mathbb{Z}^{-}$ , Z − : = { − 1 , − 2 , − 3 , … } $\mathbb{Z}^{-}:= \{ -1,-2,-3,\ldots \}$ , m ∈ N $m\in \mathbb{N}$ , ν ∈ C $\nu \in \mathbb{C}$ , and μ ∈ N 0 : = N ∪ { 0 } $\mu \in \mathbb{N}_{0}:=\mathbb{N}\cup \{0\}$ . In particular, we employ a new procedure using mathematical induction, as well as an estimate for the upper and lower bounds for the gamma function inspired by Li and Chen (J. Inequal. Pure Appl. Math. 8(1):28, 2007), to evaluate the starlikeness and convexity of order α, 0 ≤ α < 1 $0\leq \alpha

We consider the volume preserving flow of smooth, closed and convex hypersurfaces in the hyperbolic space \mathbb {H}^{n+1} (n\geq 2) with the speed given by arbitrary positive power \alpha of the Gauss curvature. We prove that if the initial hypersurface is convex, then the smooth solution of the flow remains convex and exists for all positive time t\in [0,\infty). Moreover, we apply a result of Kohlmann which characterises the geodesic ball using the hyperbolic curvature measures and an argument of Alexandrov reflection to prove that the flow converges to a geodesic sphere exponentially in the smooth topology. This can be viewed as the first result for non-local type volume preserving curvature flows for hypersurfaces in the hyperbolic space with only convexity required on the initial data. [ABSTRACT FROM AUTHOR]

If a subset of vertices of a graph, designed in such a way that the remaining vertices have unique identification (usually called representations) with respect to the selected subset, then this subset is named as a metric basis (or resolving set). The minimum count of the elements of this subset is called as metric dimension. This concept opens the gate for different new parameters, like faulttolerant metric dimension, in which the failure of any member of the designed subset is tolerated and the remaining subset fulfills the requirements of the resolving set. In the pattern of the resolving sets, a concept was introduced where the representations of edges must be unique instead of vertices. This concept was called the edge metric dimension, and this as well as the previously mentioned concepts belong to the idea of resolvability parameters in graph theory. In this paper, we find all the above resolving parametric sets of a convex polytope F♃ and compare their cardinalities. [ABSTRACT FROM AUTHOR]

This paper deals with p-maxian problem on cycles with an upper bound on the distances of all facilities. We consider the case of p = 2 and show that, in the worst case, the optimal solution contains at least one vertex of the underlying cycle, which helps to develop an efficient algorithm to solve the constrained 2-maxian problem. Based on this property, we develop a linear time algorithm for the constrained 2-maxian problem on a cycle. We also discuss the relations between the constrained and unconstrained 2-maxian problems on which the underlying graphs are cycles. [ABSTRACT FROM AUTHOR]

The present investigation aims to examine the geometric properties of the normalized form of the combination of generalized Lommel–Wright function J λ , μ ν , m (z) : = Γ m (λ + 1) Γ (λ + μ + 1) 2 2 λ + μ z 1 − (ν / 2) − λ J λ , μ ν , m (z) , where the function J λ , μ ν , m satisfies the differential equation J λ , μ ν , m (z) : = (1 − 2 λ − ν) J λ , μ ν , m (z) + z (J λ , μ ν , m (z)) ′ with J ν , λ μ , m (z) = (z 2) 2 λ + ν ∑ k = 0 ∞ (− 1) k Γ m (k + λ + 1) Γ (k μ + ν + λ + 1) (z 2) 2 k for λ ∈ C ∖ Z − , Z − : = { − 1 , − 2 , − 3 , ... } , m ∈ N , ν ∈ C , and μ ∈ N 0 : = N ∪ { 0 } . In particular, we employ a new procedure using mathematical induction, as well as an estimate for the upper and lower bounds for the gamma function inspired by Li and Chen (J. Inequal. Pure Appl. Math. 8(1):28, 2007), to evaluate the starlikeness and convexity of order α, 0 ≤ α < 1 . Ultimately, we discuss the starlikeness and convexity of order zero for J λ , μ ν , m , and it turns out that they are useful to extend the range of validity for the parameter λ to λ ≥ 0 where the main concept of the proofs comes from some technical manipulations given by Mocanu (Libertas Math. 13:27–40, 1993). Our results improve, complement, and generalize some well-known (nonsharp) estimates. [ABSTRACT FROM AUTHOR]

We prove a number of results involving categories enriched over CMet, the category of complete metric spaces with possibly infinite distances. The category CPMet of path complete metric spaces is locally N1-presentable, closed monoidal, and coreflective in CMet. We also prove that the category CCMet of convex complete metric spaces is not closed monoidal and characterize the isometry-N0-generated objects in CMET, CPMET and CCMET, answering questions by Di Liberti and Rosický. Other results include the automatic completeness of a colimit of a diagram of bi-Lipschitz morphisms between complete metric spaces and a characterization of those pairs (metric space, unital C*-algebra) that have a tensor product in the CMet-enriched category of unital C*-algebras. [ABSTRACT FROM AUTHOR]

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The purpose of the present paper is to introduce subclasses of p - valent functions defined by linear operator. Inclusion relationships for functions in these subclasses are discussed. [ABSTRACT FROM AUTHOR]

Seminal works of Hardy and Littlewood on the growth of analytic functions contain the comparison of the integral means M p (r , f) , M p (r , f ′) , M q (r , f) . For a complex-valued harmonic function f in the unit disk, using the notation | ∇ f | = (| f z | 2 + | f z ¯ | 2) 1 / 2 we explore the relation between M p (r , f) and M p (r , ∇ f) . We show that if | ∇ f | grows sufficiently slowly, then f is continuous on the closed unit disk and the boundary function satisfies a Lipschitz condition. We also prove that for 1 ≤ p < q ≤ ∞ , it is possible to give an estimate on the growth of M q (r , f) whenever the growth of M p (r , f) is known. We notably obtain Baernstein type inequalities for the major geometric subclasses of univalent harmonic mappings such as convex, starlike, close-to-convex, and convex in one direction functions. Some of these results are sharp. A growth estimate and a coefficient bound for the whole class of univalent harmonic mappings are given as well. [ABSTRACT FROM AUTHOR]

In this paper, we aim to state well-known Ostrowski inequality via fractional Montgomery identity for the class of $\phi-\lambda-$ convex functions. This generalized class of convex function contains other well-known convex functions from literature, allowing us to derive Ostrowski-type inequalities as specific instances. Moreover, we present Ostrowski-type inequalities for which certain powers of absolute derivatives are $\phi-\lambda-$ convex using various techniques, including Hölder's inequality and the power mean inequality. Consequently, various established results would be captured as special cases. Moreover, we provide applications in terms of special means, allowing us to derive many numerical inequalities related to special means from Ostrowski-type inequalities.

This work examines subordination conclusions for a specific subclass of p-valent meromorphic functions on the punctured unit disc of the complex plane where the function has a pole of order p. A new linear operator is used to define the subclass that is being studied. Furthermore, we present several corollaries with intriguing specific situations of the results.

In this paper, we employ the theory of differential subordination to establish a theorem that delineates certain sufficient conditions for starlikeness, convexity, close-to-convexity, and quasi-convexity in relation to functions with fixed initial coefficients. Furthermore, we introduce some results derived from these conditions. Building upon this framework, we derive an extension of Nunokawa’s lemma for analytic functions with fixed initial coefficients.

Initialization plays an important role in the accuracy of endmember extraction algorithms (EEAs) in linear hyperspectral unmixing (LHU). Random initialization can lead to varying endmembers generated by EEAs. To address this challenge, an initialization strategy has been introduced, encompassing vertex component analysis (VCA), automatic target generation process (ATGP), among others. These techniques significantly contribute to enhancing the accuracy of EEAs. However, complex initialization is sometimes less preferable, prompting the unexplored question of whether there exists an EEA robust to initialization. This paper focuses on analyzing this issue within the context of minimum simplex volume-based (MV) methods, which have received considerable attention in the past two decades due to their robustness against the absence of pure pixels. MV methods typically formulate LHU as an optimization problem, most of which includes a non-convex volume term. Additionally, many MV methods use VCA as an initialization strategy. Firstly, this paper demonstrates that the variable splitting augmented Lagrangian approach (SISAL), as a representative non-convex MV method, heavily depends on initialization. To our knowledge, the impact of initialization for MV methods has not been thoroughly analyzed before. Furthermore, this paper proposes an initially robust MV method by introducing a new convex MV term. Numerical experiments conducted on simulated and real datasets demonstrate its outstanding performance in accuracy and robustness to initialization. Throughout the experiments the proposed method proves to be the most stable, which is crucial in real scene where the ground truth is unknown beforehand. [ABSTRACT FROM AUTHOR]

In this study, a novel family of analytical functions connected to convex functions in the open unit is introduced and investigated. Additionally, relationships between this class and other subclasses of analytic functions are deduced. Further, different results for the mentioned class and several new interesting properties are obtained. [ABSTRACT FROM AUTHOR]

Symmetric derivatives and integrals are extensively studied to overcome the limitations of classical derivatives and integral operators. In the current investigation, we explore the quantum symmetric derivatives on finite intervals. We introduced the idea of right quantum symmetric derivatives and integral operators and studied various properties of both operators as well. Using these concepts, we deliver new variants of Young's inequality, Hölder's inequality, Minkowski's inequality, Hermite–Hadamard's inequality, Ostrowski's inequality, and Gruss–Chebysev inequality. We report the Hermite–Hadamard's inequalities by taking into account the differentiability of convex mappings. These fundamental results are pivotal to studying the various other problems in the field of inequalities. The validation of results is also supported with some visuals. [ABSTRACT FROM AUTHOR]

The median location problem concerns finding locations of one or several new facilities that minimize the overall weighted distances from the existing to the new facilities. We address the problem of locating one new facility with a radius r on networks. Furthermore, the radius r is flexible and the objective function is the conic combination of the traditional 1-median function and the value r. We call this problem an extensive 1-median problem with radius on networks. To solve the problem, we first induce the so-called finite dominating set, that contains all points on the underlying network and radius values which are candidate for the optimal solution of the problem. This helps to develop a combinatorial algorithm that solves the problem on a general network G = (V,E) in O(|E||V|³) time. We also consider the underlying problem with improved algorithm on trees. Based the convexity of the objective function with variable radius, we develop a linear time algorithm to find an extensive 1-median with radius on the underlying tree. [ABSTRACT FROM AUTHOR]

High-quality convex colloidal photonic crystals can be grown on the tip of an optical fiber by self-assembly using the hanging drop method. They are convex-shaped, produce the diffraction of reflecting light with high efficiency (blazing colors), and have a high curvature. The convex colloidal crystals are easily detachable and, as free-standing objects, they are mechanically robust, allowing their manipulation and use as convex reflective diffraction devices in imaging spectrometers. Currently, the same characteristics are obtained by using gratings-based structures. The optical fiber/colloidal crystal interface is disordered; thus, no light diffraction can be registered. The ordering at this interface was highly increased by forming a polystyrene spacer on the optical fiber tip, which served as a self-assembly substrate for silica colloid, as a mechanical bond between the fiber and the crystal, and as a filler reservoir for an inverse-opal synthesis. The silica opal-like grown on the optical fiber tip can be transformed into a high-quality polystyrene (blazing colors) inverse-opal by using the polystyrene spacer as a filler. We found that the colloidal crystal axisymmetric self-assembles onto the optical fiber tip only if a maximum volume of the colloid drop is settled on a flat end of the polystyrene spacer. [ABSTRACT FROM AUTHOR]

Due to its success in handling large optimization problems, the iterative alternating direction method of multipliers (ADMM) has garnered attention. In this article, we discuss the ADMM algorithm's history, theoretical characteristics, and applications. Moreover, we explore new ADMM improvements and their benefits over alternative optimization approaches. Furthermore, we discuss ADMM research gaps and future prospects. [ABSTRACT FROM AUTHOR]

In this article, we studied the geometric properties of generalized Wright-Bessel functions. For this purpose, we determined sufficient conditions for univalency, convexity, starlikeness and close-to-convexity of the generalized Wright-Bessel functions in the open unit disk. [ABSTRACT FROM AUTHOR]

Making use of Ruscheweyh derivative, we dene a new class of starlike functions of complex order subordinate to a conic domain impacted by Janowski functions. Coecient estimates and Fekete-Szego inequalities for the dened class are our main results. Some of our results generalize the related work of some authors. [ABSTRACT FROM AUTHOR]

Strongly Janowski functions are used to define certain classes of analytic functions which generalize the concepts of close-to-convexity and bounded boundary rotation. Coefficient results, a necessary condition, distortion bounds, Hankel determinant problem and several other interesting properties of these classes are studied. Some significant well known results are derived as special cases. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to analyze the Montgomery identities and Ostrowski like inequalities, within the framework of quantum calculus. The study utilizes qϖ3 and qϖ4 differentiable functions to establish two new Montgomery identities, which are essential for the development of our main results which are new quantum estimates of general Ostrowski type inequality. The study involves numerous techniques, including q-identities, Hölder-like inequalities, and the Jensen-Mercer inequality for convex mappings, to derive the main outcomes of the paper. Additionally, the study presents special cases, numerical validation, and graphical illustrations to support the main results.

The median location problem concerns finding locations of one or several new facilities that minimize the overall weighted distances from the existing to the new facilities. We address the problem of locating one new facility with a radius \(r\) on networks. Furthermore, the radius \(r\) is flexible and the objective function is the conic combination of the traditional 1-median function and the value \(r\). We call this problem an extensive 1-median problem with radius on networks. To solve the problem, we first induce the so-called finite dominating set, that contains all points on the underlying network and radius values which are candidate for the optimal solution of the problem. This helps to develop a combinatorial algorithm that solves the problem on a general network \(G=(V,E)\) in \(O(|E||V|^3)\) time. We also consider the underlying problem with improved algorithm on trees. Based the convexity of the objective function with variable radius, we develop a linear time algorithm to find an extensive 1-median with radius on the underlying tree.

The objective of this paper is to explore novel unified continuous and discrete versions of the Trapezium-Jensen-Mercer (TJM) inequality, incorporating the concept of convex mapping within the framework of $ {\mathfrak{q}} $-calculus, and utilizing majorized tuples as a tool. To accomplish this goal, we establish two fundamental lemmas that utilize the $ _{{\varsigma_{1}}}{\mathfrak{q}} $ and $ ^{{{\varsigma_{2}}}}{\mathfrak{q}} $ differentiability of mappings, which are critical in obtaining new left and right side estimations of the midpoint $ {\mathfrak{q}} $-TJM inequality in conjunction with convex mappings. Our findings are significant in a way that they unify and improve upon existing results. We provide evidence of the validity and comprehensibility of our outcomes by presenting various applications to means, numerical examples, and graphical illustrations.

Tube bundle recuperators are generally designed to operate with smooth tubes. Structured tubes can be used to increase the efficiency of recuperators. Compared to smooth tubes, the surface for heat transfer is increased and thus heat transfer is enhanced. This effect is accompanied by an increased pressure loss, which must be kept as low as possible. Four tube geometries with different honeycomb structures are examined. The results are compared with the performance of a smooth tube. The investigations were carried out both numerically and experimentally at different off-gas and combustion air velocities. The experimental results show that the highest heat transfer is achieved with the concave 6 mm structured tube. The greatest pressure loss also occurs here. The validation of the numerical model has shown issues in resolving the turbulence.

In this paper, the CQN_Chen function is used to characterize the plastic anisotropic evolution of 304 stainless steel (SS304). The uniaxial tensile tests along different loading directions are conducted to experimentally investigate the anisotropic hardening behavior for SS304. The experimental data indicates that the anisotropy of SS304 is weak. The convexity analysis is carried out by the geometry-inspired numerical convex analysis method for the CQN_Chen yield locus during plastic deformation. The Hill48, SY2009 and CQN functions are used as the comparison to evaluate the accuracy of the CQN_Chen function in characterizing plastic evolution. The predicted values are compared with the experimental data. The comparison demonstrates that the CQN_Chen function can accurately characterize anisotropic hardening behavior under uniaxial tension along distinct loading directions and equibiaxial tension. Simultaneously, the CQN_Chen model has the capacity to adjust the yield surface shape between uniaxial tension and equibiaxial tension. The CQN_Chen model is recommended to characterize plastic evolving behavior under uniaxial tension along different directions and equibiaxial tension. [ABSTRACT FROM AUTHOR]

This paper aims to introduce a measure of the non-univalency of a harmonic mapping. By using it, we find the best approximation of an analytic function by a univalent harmonic mapping. [ABSTRACT FROM AUTHOR]

The main idea of the current investigation is to explore some new aspects of Ostrowski's type integral inequalities implementing the generalized Jensen–Mercer inequality established for generalized s-convexity in fractal space. To proceed further with this task, we construct a new generalized integral equality for first-order local differentiable functions, which will serve as an auxiliary result to restore some new bounds for Ostrowski inequality. We establish our desired results by employing the equality, some renowned generalized integral inequalities like Hölder's, power mean, Yang-Hölder's, bounded characteristics of the functions and considering generalized s-convexity characteristics of functions. Also, in support of our main findings, we deliver specific applications to means, and numerical integration and graphical visualization are also presented here. [ABSTRACT FROM AUTHOR]

The objective of this paper is to explore novel unified continuous and discrete versions of the Trapezium-Jensen-Mercer (TJM) inequality, incorporating the concept of convex mapping within the framework of q-calculus, and utilizing majorized tuples as a tool. To accomplish this goal, we establish two fundamental lemmas that utilize the 1q and 2q differentiability of mappings, which are critical in obtaining new left and right side estimations of the midpoint q-TJM inequality in conjunction with convex mappings. Our findings are significant in a way that they unify and improve upon existing results. We provide evidence of the validity and comprehensibility of our outcomes by presenting various applications to means, numerical examples, and graphical illustrations. [ABSTRACT FROM AUTHOR]