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• Double bias fields are introduced into fidelity term to approximate image intensity inhomogeneity. • The proposed energy function is strictly convex, and allows flexible initialization. • A TV (total variation) regularization term is introduced to keep convex level-set function smooth. • The proposed method is robust against to noise and intensity inhomogeneity. The existing active contour models (ACMs) based on bias field (BF) correction mostly rely on a single BF assumption and lack in-depth discussion on the convexity of the energy functional, often leading to the problem of local minima. To address this issue, this paper introduces a dual BF and proposes a convex level-set (LS) method based on multiplicative-additive (MA) model to achieve global minima. Firstly, a MA model is adopted as the fidelity term, and a kernel function is introduced to adjust the size of the intensity inhomogeneous neighborhood, enhancing the adaptability to intensity inhomogeneity. Then, the convex LS function is embedded in the variational framework to ensure convexity of each variable in the energy functional. This transformation turns the segmentation problem into a convex optimization problem. By introducing the total variation regularization term to smooth the LS function, the model's resistance to noise is effectively enhanced. Finally, by minimizing the proposed energy functional, image segmentation and BF correction are successfully achieved. Experimental results validate the global minima property of our model, while also demonstrating good flexibility in the initial contour. The proposed model achieves superior segmentation results compared to other classical ACMs on various types of images. [ABSTRACT FROM AUTHOR]

In this paper, a novel non-convex fractional-order image denoising model is proposed to suppress the staircase effect produced by the TV model while maintaining a neat contour. The model combines ℓ q (0 < q < 1) quasi-norm and fractional-order regularization, and employs a diffusion coefficient with a faster convergence rate to preserve more image edges and details. Additionally, an adaptive regularization parameter is designed to adjust the denoising performance of the algorithm. To obtain the optimal approximate solution of the model, an enhanced primal-dual algorithm is adopted and the complexity and convergence of the algorithm are theoretically analyzed. Finally, the effectiveness of the proposed method is demonstrated through numerical experiments. • A new non-convex FOTV model is proposed. • A new diffusion coefficient is introduced to retain more edge details of the image. • The existing primal-dual algorithm is improved, and the convergence of this algorithm is analyzed. • An adaptive regularization parameter is designed. [ABSTRACT FROM AUTHOR]

This paper is devoted to the stability analysis of a class of discrete-time switched systems under newly designed switching regularities. The utilized switching is extended from the primitive mode-dependent persistent dwell-time switching. By integrating the existing admissible edge-dependent average dwell-time switching into the mode-dependent persistent dwell-time regime, a novel admissible edge-dependent average persistent dwell-time strategy involving the notion of admissible transition edges is proposed. The integrated admissible edge-dependent average dwell-time switching has been confirmed to be superior to mode-dependent average dwell-time switching. This superiority makes the proposed switching more general than the relaxed mode-dependent persistent dwell-time switching in the literature. Even if the embedded admissible edge-dependent average dwell-time restrictions degrade to admissible edge-dependent dwell-time ones under special parameter settings, the resulting admissible edge-dependent persistent dwell-time switching retains the advantage of admissible transition edges to generalize the original mode-dependent persistent dwell-time switching. Meanwhile, to remove the switching information reliance in the existing multiple convex Lyapunov functions, an improved multiple convex Lyapunov function method is devised. The designed Lyapunov function can be used to implement broader feasible ranges and tighter lower bounds of admissible edge-dependent average persistent dwell-time (or admissible edge-dependent persistent dwell-time). Finally, the validity and efficiency of the presented approaches are illustrated by a three-phase inverter and a numerical example. • Admissible edge-dependent average persistent dwell-time switching is proposed. • Admissible edge-dependent persistent dwell-time switching is proposed. • A more widely applicable multiple convex Lyapunov function is raised. [ABSTRACT FROM AUTHOR]

• We propose a nonconvex prior for image smoothing. • The proposed algorithm of the nonconvex model has a convergence guarantee. • The performance of the prior outperforms the state-of-the-art. • The proposed method is flexible, convergent and has promising results. Image smoothing is a fundamental task in computer vision and graphics. This paper presents a new image smoothing method based on a truncated generalized Huber prior. The proposed model is neither convex nor concave and is hard to optimize. We first transform the prior into a concave one, then utilize the technique of half-quadratic minimization to get an equivalent convex surrogate function. Thus the numerical algorithm is obtained by solving a weighted least square problem and iteratively updating the weights. The convergence of the algorithm is theoretically guaranteed. The proposed method is flexible and powerful in preserving edge/structure and eliminating undesired information. The effectiveness of the proposed method is demonstrated by several applications, including scale space filtering, texture removal, and clip-art JPEG artifacts removal. [ABSTRACT FROM AUTHOR]

This paper proposes an indicator for discriminating difference among subjects for several data of objects with respect to variables based on similarity (or dissimilarity) of objects. If we observe several data related to different subjects, consisting of the same objects and variables over the subjects, obtaining difference among the subjects is sometimes important for understanding the data difference depending on the subjects' individuality on the data. Therefore, this paper proposes an indicator whose score shows the individuality for each subject. The indicator is defined by using an idea of the objective function of convex clustering. Based on the basic methodology of the indicator, two kinds of indicator are proposed; one is an indicator used for each result of multidimensional scaling, and another is utilized for each result of fuzzy clustering, corresponding to each subject. Numerical examples show the better performance of the proposed indicators, which show the individuality of subjects. [ABSTRACT FROM AUTHOR]

Uncertainty propagation analysis is a key issue for the safety and optimal design of spacecraft structures. This paper proposes an interval reduced basis method (IRBM) for predicting static response of spacecraft structures with unknown-but-bounded uncertainties. Meanwhile, an integrated framework on the basis of IRBM is established by coupling the current finite element codes, which lays the foundation for development of an easy-to-use interval finite element software. In this paper, the novel idea is to approximate the static response using a linear combination of interval basis vectors with undetermined coefficients. The reduced order equations for computing the undetermined coefficients are derived based on Galerkin scheme. For the second-order approximation in IRBM, the static response is easily converted into a family of quadratic programming problems subject to box constraints. The difference of convex functions algorithm is employed to solve these quadratic programming problems. The proposed method can improve the accuracy of the traditional first-order approximation and perform the efficient computation of the second-order approximation of the structural response. Two numerical examples are presented to show the good performance of the proposed method. And an engineering example is performed for its application. [ABSTRACT FROM AUTHOR]

In recent years, a class of soft (deformable) robots has attracted the attention of researchers due to their continuum features being advantageous over rigid robots for dexterous and safe compliant motions. These distinct advantages are obtained from the elastomer hyperelastic material properties because continuum robots are manufactured and actuated through embedded pneumatic energy fields. In this way, the continuum deformation raises novel problems in modeling and control due to its highly nonlinear behavior. That is, the deformable shape of its components varies continuously, unlike rigid robots, suggesting that the controller should compensate for its varying continuum model. Motivated by the deformable soft robot subject to parametric uncertainties and unmodeled dynamics, this paper proposes an adaptive, instead of constant, tuning of feedback gains of a model-free controller. The tuning mechanism is based on a knowledge-based scheme using a discrete wavelet neural network (DWN) by an efficient input–output identification updating its parameters and weights online, with a gradient descent algorithm driven by the identification error. At the same time, the control feedback gains are self-tuned, minimizing a convex cost function of tracking errors. Dynamic simulations show the performance of the proposed approach considering the parameters of a real soft robot mimicking a gelatin-like behavior. Finally, some discussions on the proposed scheme's computational cost, feasibility, and viability are briefly addressed. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of spacecraft six degree of freedom (6-DOF) pose tracking control with collision avoidance and field of view (FOV) pyramid-type constraints during the autonomous proximity maneuver. The constraints are modeled as pyramid envelopes, which can better represent some real cases with less conservativeness comparing with commonly used cone-shaped model. A novel modeling method is proposed to describe the pyramid-type constraints in the dual-quaternion frame. Based on the specific geometric property of the pyramid constraints, a new convex artificial potential function (APF) with only one global minimum is designed, which incorporates the pose constraints into the control design procedure. Then, an integrated APF based control law is presented to simultaneously control the rotational and translational motion of the spacecraft without violating the pyramid constraints. The stability of the closed-loop system is demonstrated through the Lyapunov theory, and numerical simulation results are carried out to show the effectiveness of the proposed control law. • The motion constraint is described as pyramid envelope with less system conservative. • A novel method is used to build the pyramid envelope model in dual quaternion frame. • A new convex potential function with clear meaning and simple form is designed. • An artificial potential function based feedback 6-DOF control law is designed. • Numerical simulations verify the effectiveness of the proposed control law. [ABSTRACT FROM AUTHOR]

In this paper, we present generalized Jensen-Mercer inequality for a generalized h -convex function on fractal sets. We proved Hermite-Hadamard-Mercer local fractional integral inequalities via integral operators pertaining Mittag-Leffler kernel. Also, we drive two new local fractional integral identities for differentiable functions. By employing these integral identities, we derive some new Hermite-Mercer type inequalities for generalized h -convex function in local fractional calculus settings. Finally, we give some examples to emphasize the applications of derived results. These results will be a significant addition to Jensen-type inequalities in the literature. [ABSTRACT FROM AUTHOR]

Abstract This paper suggests a novel continuous-time gradient descent algorithm of a constrained convex unknown function with a stochastic noise in the observed data. The penalty function approach is employed to introduce the restrictions of the system and to provide a successful optimization process. The solution is restricted to a static scheme dealing with the class of strongly convex functions subject to a set of constraints. To estimate the stochastic gradient we employ a modified version of the synchronous detection method. All the parameters of the proposed approach are decreasing in time to both compensate noise effect in the observations and to provide the mean-square convergence of the suggested approach. We present two different numerical examples to validate the contributions of the paper. [ABSTRACT FROM AUTHOR]

This paper is devoted to numerical analysis of a new class of elliptic variational–hemivariational inequalities in the study of a family of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modeled by a nonmonotone multivalued subdifferential relation allowing slip dependence. The problem involves a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set for the locking constraints and a nonconvex locally Lipschitz friction potential. Solution existence and uniqueness result on the inequality can be found in Migórski and Ogorzaly (2017). In this paper, we introduce and analyze a finite element method to solve the variational–hemivariational inequality. We derive a Céa type inequality that serves as a starting point of error estimation. Numerical results are reported, showing the performance of the numerical method. [ABSTRACT FROM AUTHOR]

This paper concerns three classes of real-valued functions on intervals, operator monotone functions, operator convex functions, and strongly operator convex functions. Strongly operator convex functions were previously treated in [3] and [4], where operator algebraic semicontinuity theory or operator theory were substantially used. In this paper we provide an alternate treatment that uses only operator inequalities (or even just matrix inequalities). We show also that if t 0 is a point in the domain of a continuous function f , then f is operator monotone if and only if ( f ( t ) − f ( t 0 ) / ( t − t 0 ) is strongly operator convex. Using this and previously known results, we provide some methods for constructing new functions in one of the three classes from old ones. We also include some discussion of completely monotone functions in this context and some results on the operator convexity or strong operator convexity of φ ∘ f when f is operator convex or strongly operator convex. [ABSTRACT FROM AUTHOR]

In this paper we consider the optimal mass transport problem for relativistic cost functions, introduced in [12] as a generalization of the relativistic heat cost. A typical example of such a cost function is c t ( x , y ) = h ( y − x t ) , h being a strictly convex function when the variable lies on a given ball, and infinite otherwise. It has been already proved that, for every t larger than some critical time T > 0 , existence and uniqueness of optimal maps hold; nonetheless, the existence of a Kantorovich potential is known only under quite restrictive assumptions. Moreover, the total cost corresponding to time t has been only proved to be a decreasing right-continuous function of t . In this paper, we extend the existence of Kantorovich potentials to a much broader setting, and we show that the total cost is a continuous function. To obtain both results the two main crucial steps are a refined “chain lemma” and the result that, for t > T , the points moving at maximal distance are negligible for the optimal plan. [ABSTRACT FROM AUTHOR]

In this paper, we establish a novel identity by leveraging fractional integral operators of Riemann-type. Subsequently, we employ this identity to investigate Bullen's fractional integral inequalities within the framework of classical convex functions. The validity of these innovative inequalities is verified through the visualization of 2D and 3D graphs. Furthermore, we obtain certain well-known results as special cases to our main findings and express them as remarks. Lastly, we derive differences in mean estimates, which serve as valuable tools for representing complex information, facilitating decision-making and aiding analysis in various fields. [ABSTRACT FROM AUTHOR]

This paper addresses the global optimal consensus problem with time-varying objective functions and state-coupled inequality constraints. By integrating the predefined-time consensus and prediction-correction schemes, a distributed optimization protocol is proposed for the cooperative interception scenarios involving the unmanned aerial vehicle (UAV) swarm. Specifically, the δ -exact penalty method is utilized to eliminate the coupled constraints. A prediction-correction term with the penalty function is then established to track the trajectory of the time-varying optimal solution. Additionally, an edge-based predefined-time consensus term is introduced to facilitate the state consensus among UAVs. Under the undirected and connected topology, the proposed protocol ensures the predefined-time state consensus and asymptotically minimizes the sum of individual convex objective functions. Furthermore, the protocol is extended to other scenarios involving switching topology, directed detail-balanced topology, and external disturbances. Numerical simulations illustrate that the UAV swarm can form the predesigned interception formation with a predefined-time frame and effectively track the target swarm. [ABSTRACT FROM AUTHOR]

Combined heat and power economic dispatch (CHPED) can enhance energy efficiency compared with conventional economic dispatch (ED). From the optimization standpoint, the CHPED problem usually involves the nonlinear products of heat and power generation variables, nonconvex objective functions, and nonconvex feasible operating range. Thus, its solution method should be able to cope with the problematic nonconvex problem since finding a poor solution for the CHPED implies reducing the maximum achievable efficiency. This paper presents an effective method utilizing several mathematical transformations to cope with the nonlinear, nonconvex terms. The method transforms the nonconvex regions and nonlinear functions into convex polyhedrons and segments. Then, the method formulates the polyhedrons and segments with integer variables, logical constraints, and combinatorial restrictions. Thus, we derive a mixed integer model, which optimization software can better solve. Simulation results illustrate the effectiveness of the method presented and its advantages compared with existing CHPED solution techniques in the literature. [Display omitted] • Transforming nonconvex feasible operating ranges in CHP units into some polyhedrons. • Converting nonconvex cost functions into linear segments. • Presenting a robust solution method for the optimal operation of a CHP. [ABSTRACT FROM AUTHOR]

Bounding hulls such as convex hull, α -shape, χ -hull, concave hull, crust, etc. offer a wide variety of useful applications. In this paper, we explore another bounding hull, namely α -concave hull, as a generalization of convex hull. The parameter α determines the smoothness level of the constructed hull on a set of points. We show that it is NP-hard to compute α -concave hull on a set of points for any 0 < α < π . This leads us to a generalization of Fekete work (when α = π ). We also introduce α − M A C P as an NP-hard problem similar to the problem of computing α -concave hull and present an approximation algorithm for α − M A C P . The paper ends by implementing the proposed algorithm and comparing the experimental results against those of convex hull and α -shape models. [ABSTRACT FROM AUTHOR]

In this paper, we derive the time-fractional Cahn–Hilliard equation from continuum mixture theory with a modification of Fick's law of diffusion. This model describes the process of phase separation with nonlocal memory effects. We analyze the existence, uniqueness, and regularity of weak solutions of the time-fractional Cahn–Hilliard equation. In this regard, we consider degenerating mobility functions and free energies of Landau, Flory–Huggins and double-obstacle type. We apply the Faedo–Galerkin method to the system, derive energy estimates, and use compactness theorems to pass to the limit in the discrete form. In order to compensate for the missing chain rule of fractional derivatives, we prove a fractional chain inequality for semiconvex functions. The work concludes with numerical simulations and a sensitivity analysis showing the influence of the fractional power. Here, we consider a convolution quadrature scheme for the time-fractional component, and use a mixed finite element method for the space discretization. [ABSTRACT FROM AUTHOR]

Convex optimization is explored in this paper to maximize the security against power analysis attacks while minimizing the power and performance overheads for a cryptographic circuit employs a random dynamic voltage and frequency scaling (RDVFS) technique. To realize this optimization goal, firstly, non-convex functions are used for modeling all the critical parameters related to the RDVFS technique to create a non-convex objective function. Subsequently, the non-convex objective function is appropriately converted into a convex objective function in order to grab the global optimum value. By transforming the acquired convex objective function into the Lagrange dual function and using Karush–Kuhn–Tucker (KKT) conditions to solve this optimization problem, the best RDVFS strategy can be uncovered. As shown in the result, after employing convex optimization for a cryptographic circuit with a RDVFS technique, the corresponding figure-of-merit (FOM) is enhanced by 43.4%. Moreover, in comparison with the conventional machine learning technique, the proposed convex optimization technique improves the overall FOM related with RDVFS technique by 17.6% while reducing 85.3% computational time. • Random dynamic voltage and frequency scaling (RDVFS) is beneficial for improving the robustness of cryptographic circuits. • RDVFS technique undermines the performance and power saving of cryptographic circuits. • Convex optimization can be utilized for improving the security of RDVFS technique without increasing the overall overhead significantly. • Convex optimization methodology has a better efficiency for optimizing RDVFS technique as compared to the training methodology related with MLP neural networks. [ABSTRACT FROM AUTHOR]

• Two typical failure processes are analyzed in the context of maintenance. • A convex function is proposed to describe the condition-based inspection. • Dependences between two failure processes are modeled in the threshold of preventive maintenance. • Different objects are considered to obtain the optimal maintenance parameters. This paper explores how the dependence between competing failure processes affects the condition-based preventive maintenance policy. The exposed failures caused by degradation and random shock are explicitly modeled respectively through two stochastic processes, i.e. Gamma process and compound Poisson process. Condition-based inspections are scheduled by introducing a convex function describing the relationship between degradation level and inspection interval. The preventive maintenance policy is planned to improve the operation efficiency which is adversely affected by the existing failures. The effect of failure dependence on the condition-based maintenance is analyzed through the preventive maintenance threshold of which initial value is fixed and is weaken by the following arrived shocks then. Imperfect maintenance effect is also considered to describe the irreversible aging process. Monte Carlo simulation technique and genetic algorithm are both employed to obtain the optimal parameters which determine the frequencies of inspection and maintenance. An illustrate example of a gearbox in the wind power industry is studied to demonstrate how the proposed maintenance policy balances the conflicting objectives in engineering practice. [ABSTRACT FROM AUTHOR]

• Compensated convex transforms of functions on convex bounded domains. • Numerical scheme with linear complexity to compute the Moreau envelope. • Convergence proof of the numerical scheme. • Estimate of the iterations needed for computing the exact discrete Moreau envelope. • Application to image processing and shape interrogation. Compensated convex transforms have been introduced for extended real valued functions defined over R n. In their application to image processing, interpolation and shape interrogation, where one deals with functions defined over a bounded domain, the implicit assumption was made that the function coincides with its transform at the boundary of the data domain. In this paper, we introduce local compensated convex transforms for functions defined in bounded open convex subsets Ω of R n by making specific extensions of the function to the whole space, and establish their relations to globally defined compensated convex transforms via the mixed critical Moreau envelopes. We find that the compensated convex transforms of such extensions coincide with the local compensated convex transforms in the closure of Ω. We also propose a numerical scheme for computing Moreau envelopes, establishing convergence of the scheme with the rate of convergence depending on the regularity of the original function. We give an estimate of the number of iterations needed for computing the discrete Moreau envelope. We then apply the local compensated convex transforms to image processing and shape interrogation. Our results are compared with those obtained by using schemes based on computing the convex envelope from the original definition of compensated convex transforms. [ABSTRACT FROM AUTHOR]

Recently, introducing nonconvex loss functions in support vector machine (SVM) to improve the robustness against varies noises has been drawing much attention. In this paper, we first construct a new robust capped asymmetric elastic net (CaEN) loss function. Second, we describe a novel robust Huberized kernel-based (HK) loss function and theoretically demonstrate several important properties, such as smoothness, boundness and the trade-off between the standard least squares and the truncated least squares. Finally, we apply the CaEN loss and the HK loss into elastic net nonparallel hyperplane SVM (ENNHSVM) to develop a fused robust geometric nonparallel SVM (FRGNHSVM). The proposed FRGNHSVM not only inherits the advantages of ENNHSVM but also improves the robustness of classification problems. An efficient Pegasos-based DC (difference of convex functions) algorithm is implemented to solve the FRGNHSVM optimization problem. In comparison with four famous SVMs, including Lagrangian SVM, twin SVM, pinball SVM and C-loss twin SVM, experimental results on simulations and twelve UCI datasets show that the proposed FRGNHSVM can often improve more than 5% average prediction accuracy. Moreover, the performance of the high prediction accuracy of FRGHNSVM is more significant along with the ratio of label noise increasing, indicating its superiority in dealing with label-contaminated datasets. • A novel FRGNHSVM is proposed for robust binary learning problems. • FRGNHSVM is stable for re-sampling and robust to outliers. • The designed Pegasos-based DC algorithm is scalable and applicable to large data. • Experimental results demonstrate the effectiveness of FRGNHSVM. [ABSTRACT FROM AUTHOR]

In the paper a theorem of Piccard's type is proved and, consequently, the continuity of D -measurable polynomial functions of n -th order as well as D -measurable n -convex functions is shown. The paper refers to the papers [6] and [9] . [ABSTRACT FROM AUTHOR]

Recent papers investigated the maximum infection time t P 3 ( G ) of the P 3 -convexity (also called maximum time of 2-neighbor bootstrap percolation) and the maximum infection time t m o ( G ) of the monophonic convexity. In 2014, it was proved that, for bipartite graphs, deciding whether t P 3 ( G ) ≥ k is polynomial time solvable for k ≤ 4 , but is NP-complete for k ≥ 5 [23] . In 2015, it was proved that deciding whether t m o ( G ) ≥ 2 is NP-complete even for bipartite graphs [12] . In this paper, we investigate the maximum infection time t g d ( G ) of the geodesic convexity. We prove that deciding whether t g d ( G ) ≥ k is polynomial time solvable for k = 1 , but is NP-complete for k ≥ 2 even for bipartite graphs. We also present an O ( n 3 m ) -time algorithm to determine t g d ( G ) and t m o ( G ) in distance-hereditary graphs. For this, we characterize all minimal hull sets of a general graph in the monophonic convexity. Moreover, we improve the complexity of the fastest known algorithm for finding a minimum hull set of a general graph in the monophonic convexity. [ABSTRACT FROM AUTHOR]

In this paper, we report on some recent results obtained in our joint paper Papageorgiou and Rădulescu (2015). We consider a Robin problem driven by a nonhomogeneous differential operator and with a reaction that exhibits competing effects of concave (that is, sublinear) and convex (that is, superlinear) nonlinearities. Without employing the Ambrosetti–Rabinowitz condition, we establish a bifurcation property of the positive solutions near the origin. The approach relies on variational methods and elliptic estimates. [ABSTRACT FROM AUTHOR]

The classical Bourbaki–Alaoglu theorem asserts that the polar U ∘ of a neighborhood of 0 in a locally convex topological vector space V is a weak ⁎ compact subset of the dual space V ⁎ . G. Plotkin has proved an analogous theorem in the framework of continuous d-cones, a kind of asymmetric version of topological vector spaces in Domain Theory. In this paper we extend Plotkin's results. We consider topological spaces X with a finitary continuous algebraic structure in the sense of universal algebra instead of a cone structure. Linear functionals are replaced by continuous algebra homomorphisms into a test algebra R replacing the reals. Our main result, Theorem 5.8 , concerns the compactness of the space C ⁎ of continuous homomorphisms from X to R under appropriate hypotheses. We exhibit conditions under which C ⁎ is not only a space but also an algebra, as in the classical situation. This leads us to the notion of entropicity in the sense of universal algebra. The background for our investigation is Domain Theory and its use in denotational semantics (see [8] ). Thus our spaces are strongly non-Hausdorff. This paper can be seen as a contribution to asymmetric topology and analysis. [ABSTRACT FROM AUTHOR]

In this paper, we theoretically analyze principal properties of coordinate-wise minimization and we answer a few open questions related to it. In particular, we show that for minimizing any differentiable convex function on a given convex polyhedron, there exists a finite set of directions determined only by the polyhedron such that any local minimum with respect to these directions is a global minimum. We prove that the set of directions has a 'nice' structure for polyhedra defined by a k -regular matrix, which is a generalization of total unimodularity. We proceed to show that for some simple polyhedra, the number of these directions is polynomial, which subsumes already existing algorithms. We prove that the main result can not be extended for the case when the polyhedron is not known in advance or if the optimization is performed over a general convex set. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give some conditions for univalence of analytic functions in the unit disc | z | < 1. We consider starlike functions such that z f ′ (z) ∕ f (z) lies in a vertical strip. In the second part we present some conditions on z f ′ ′ (z) ∕ f ′ (z) for f to be univalent. [ABSTRACT FROM AUTHOR]

In this paper, for a given Eaton triple (V , G , D) , we present a characterization of G -increasing real functions by using the maximality property of their directional derivatives. It generalizes Schur-Ostrowski's condition related to Schur-convexity of a function. It is also useful in establishing theorems of von Neumann-Davis type regarding the form of group-invariant real functions with certain kinds of convexity. We introduce and investigate weak Eaton triples and their chains. We show a method for constructing new Eaton triples. We apply it to define generalized arrangement-increasing (AI) functions. We prove that the mentioned derivatives of G -increasing maps are generalized AI functions. [ABSTRACT FROM AUTHOR]

In this paper, the notion of [ S ] -lineability (originally coined by Vladimir I. Gurariy) is introduced and developed in a general abstract setting. This new notion is, then, applied to specific situations, as for instance, classes of differentiable nowhere monotone functions as well as families of vectors having dense orbit with respect to an operator. Large convex structures are also shown to exist inside the family of topologically mixing continuous selfmaps of a real compact interval. [ABSTRACT FROM AUTHOR]

This paper presents the notion of a variation entropy. This concept is an entropy framework for the gradient of the solution of a conservation law instead of on the solution itself. It appears that all semi-norms are admissible variation entropies. This provides insight into the total variation diminishing property and justifies it from entropy principles. The framework allows to derive new local variation diminishing properties in the continuous form. This can facilitate the design of new numerical methods for problems that contain discontinuities. • The notion of variation entropy is presented. • This is an entropy concept based on the gradient of the solution. • It justifies the TVD property from an entropy perspective. • Variation entropies are convex homogeneous functions. • The variation entropy concept serves to facilitate the design of numerical methods which preclude spurious oscillations. [ABSTRACT FROM AUTHOR]

Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D. In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π) such that the function h + e i θ g is convex in D. In this article, we first disprove a more flexible conjecture: " Let f = h + g ‾ be a convex harmonic mapping in the disk D. Then there is a θ ∈ [ 0 , 2 π) such that the function h + e i θ g is starlike in D ". In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. [ABSTRACT FROM AUTHOR]

Summation inequalities method for quadratic functions plays a key role in the field of stability analysis, in which the information of time-varying delay and states can be introduced. Generally, the information of delay variation is introduced by the forward difference of Lyapunov–Krasovskii functional, which may lead to some underutilized delay information due to its internal constraints. This paper proposes a new summation inequality for quadratic functions by defining a set of convex functions, which simultaneously introduces the delay amplitude and variation in a summation inequality. A delay amplitude and variation-dependent stability criterion is obtained by using the summation inequality. A numerical example is given to substantiate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract: Aichholzer et al. [O. Aichholzer, C. Huemer, S. Kappes, B. Speckmann, C.D. Tóth, Decompositions, partitions, and coverings with convex polygons and pseudo-triangles, Graphs and Combinatorics 23 (2007) 481–507] introduced the notion of pseudo-convex partitioning of planar point sets and proved that the pseudo-convex partition number satisfies . In this paper we prove that , which improves the upper bound on to , thus answering a question posed by Aichholzer et al. in the same paper. [Copyright &y& Elsevier]

Abstract: In this paper, we study the error in the approximation of a convex function obtained via a one-parameter family of approximation schemes, which we refer to as barycentric approximation schemes. For a given finite set of pairwise distinct points in , the barycentric approximation of a convex function is of the form: where is a set of barycentric coordinates with respect to the point set . The main content of this paper is two-fold. The first goal is to derive sharp upper and lower bounds on all barycentric coordinates over the convex polytope . The second objective of the paper is to exploit the convexity assumption heavily and establish a number of upper and lower pointwise bounds on the approximation error for approximating arbitrary convex functions. These bounds depend solely on computable quantities related to the data values of the function, the largest and smallest barycentric coordinates. For convex twice continuously differentiable functions, we derive an optimal error estimate. We show that the Delaunay triangulation gives access to efficient algorithms for computing optimal barycentric approximation. Finally, numerical examples are used to show the success of the method. [Copyright &y& Elsevier]

This paper presents a theoretical framework termed the convex modular modelling (CMM) framework, which provides a convenient and expedient approach for constructing thermodynamically consistent constitutive models. This paper demonstrates how the CMM framework can be used to build increasingly complex constitutive models by mixing and matching re-usable components from a library of convex base functions in a systematic manner. It also describes the use of the modified LogSumExp (MLSE) function as a general and smooth approximation to the pointwise maximum function for any yield function (e.g. the Mohr-Coulomb/Tresca yield function). The MLSE function is then used to develop several new yield functions such as a convex and smooth approximation of the Matsuoka-Nakai yield function, a generalised polygonal yield function and a 'Reuleaux triangle'-shaped yield function. As CMM is simple to use, it potentially offers a more accessible path for constitutive modellers to take advantage of the hyperplasticity framework to develop robust constitutive models. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the breadth first search algorithm and the convex hull solution of large-scale 3D/2D point set were used to directly obtain the fragment characteristics and distributions of the debris cloud produced in a hypervelocity impact, which was simulated by the smooth particle hydrodynamics (SPH) method. The computational method of debris identification and characteristic parameters recognizing from numerical simulation data produced by SPH method was developed. The numerical simulation was compared with test which was carried out at the ballistic range of CARDC (China Aerodynamics Research & Development Center). The fragment number and mass distribution obtained by the numerical calculation agree with those obtained from the test. The method developed in this paper can acquire the fragment characteristics and distributions from hypervelocity impact numerical simulation results, and can be used for data processing and damage analysis in numerical simulation of hypervelocity impact. [Copyright &y& Elsevier]

Abstract: In this paper we investigate an interesting subclass of analytic univalent functions in the open unit disc on the complex plane. This class was introduced by Sokół [J. Sokół, On starlike functions connected with Fibonacci numbers, Folia Scient. Univ. Tech. Resoviensis 175 (1999) 111–116]. The class is strongly related to the class considered earlier by the authors of the present work in their paper [J. Dziok, R. K. Raina, J. Sokół, Certain results for a class of convex functions related to shell-like curve connected with Fibonacci Numbers, Comput. Math. Appl. 61 (2011) 2606–2613]. Apart from furnishing some genuine remarks, we present certain new results for the class of functions, and also mention some relevant cases for this function class. [Copyright &y& Elsevier]

The general sum-connectivity index of a graph G is χ α (G) = ∑ u v ∈ E (G) (d (u) + d (v)) α , where d (u) denotes the degree of vertex u ∈ V (G) , and α is a non-zero real number. Ali et al. (2019) proved that the unique graph obtained from the star S n by adding ν edge(s) between a fixed pendant vertex u and ν other pendant vertices, has the maximum χ α value in the collection of all n -vertex connected graphs having cyclomatic number ν with the constraints ν = 5 , n ≥ 7 , α > 1 or n ≥ 8 , 6 ≤ ν ≤ n − 2 , α ≥ 2 and conjectured that this result also holds for n ≥ 8 , 6 ≤ ν ≤ n − 2 and 1 < α < 2. In this paper, we provide a proof of this conjecture. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is to establish Hermite–Hadamard, Hermite–Hadamard–Fejér,Dragomir–Agarwal and Pachpatte type inequalities for new fractional integral operators with exponential kernel. These results allow us to obtain a new class of functional inequalities which generalizes known inequalities involving convex functions. Furthermore, the obtained results may act as a useful source of inspiration for future research in convex analysis and related optimization fields. [ABSTRACT FROM AUTHOR]

As a high-efficiency training method for single layer feedforward neural networks, extreme learning machine (ELM) has drawn much interest recently, but its robustness is not good due to the adoption of the square loss function. Hence, the convex loss function in ELM is replaced with a nonconvex loss function, i.e., the C-loss function, so a novel algorithm, called C-loss based ELM (CELM), is proposed in this paper. According to the experimental results on a toy example and two benchmark data sets, CELM performs better than the other algorithms with respect to the generalization performance. To be more important, when CELM is used to estimate power of small-scale turbojet engine, it also dominates the other algorithms, which makes the development of the potential control structure, viz., the direct power control, for the unmanned aerial vehicles more feasible. [ABSTRACT FROM AUTHOR]

Abstract This paper is devoted to the study of non-existence of certain type of convex functions on a Riemannian manifold with a pole. To this end, we have developed the notion of odd and even functions on a Riemannian manifold with a pole and proved the non-existence of non-trivial and non-negative differentiable odd convex function whose gradient is complete. Finally, we have deduced an inequality related with convex function. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a new total generalized variational(TGV) model for restoring images with multiplicative noise is proposed, which contains a nonconvex fidelity term and a TGV term. We use a difference of convex functions algorithm (DCA) to deal with the proposed model. For multiplicative noise removal, there exist many models and algorithms, most of which focus on convex approximation so that numerical algorithms with guaranteed convergence can be designed. Unlike these algorithms, we use the DCA algorithm to remove multiplicative noise. By numerical experiments, it is shown that the proposed approach leads to a better solution compared with the gradient projection algorithm for solving the classic multiplicative noise removal models. We prove that the sequence generated by the DCA algorithm converges to a stationary point, which satisfies the first order optimality condition. Finally, we demonstrate the performance of our whole scheme by numerical examples. A comparison with other methods is provided as well. Numerical results demonstrate that the proposed algorithm significantly outperforms some previous methods for multiplicative Gamma noise removal. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite–Hadamard's inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of real numbers, some error estimates for the formula midpoint are given. Finally, new inequalities for some special and q -special functions are also pointed out. [ABSTRACT FROM AUTHOR]