Concave Convex Research Articles

Solving strongly convex-concave composite saddle-point problems with low dimension of one group of variable

Algorithmic methods are developed that guarantee efficient complexity estimates for strongly convex-concave saddle-point problems in the case when one group of variables has a high dimension, while another has a rather low dimension (up to 100). These methods are based on reducing problems of this type to the minimization (maximization) problem for a convex (concave) functional with respect to one of the variables such that an approximate value of the gradient at an arbitrary point can be obtained with the required accuracy using an auxiliary optimization subproblem with respect to the other variable. It is proposed to use the ellipsoid method and Vaidya's method for low-dimensional problems and accelerated gradient methods with inexact information about the gradient or subgradient for high-dimensional problems. In the case when one group of variables, ranging over a hypercube, has a very low dimension (up to five), another proposed approach to strongly convex-concave saddle-point problems is rather efficient. This approach is based on a new version of a multidimensional analogue of Nesterov's method on a square (the multidimensional dichotomy method) with the possibility to use inexact values of the gradient of the objective functional. Bibliography: 28 titles.

Quantile-based entropy function in past lifetime for order statistics and its properties

In this paper, we introduce a quantile version of past entropy for order statistics and study some of its properties. It is shown that this measure uniquely determine the quantile function. Two nonparametric classes of distributions are also defined based on the proposed measure. The closure of these classes under increasing convex (concave) transformations and weighted variables are discussed. Moreover, a new stochastic order based on this measure is defined and some features of it are investigated. We give desirable conditions for a function of a random variable to have more quantile past entropy for order statistics than original random variable.

Dissipativity-Based Robust Control with H∞-Optimal Performance

A controller is designed to minimize the closed-loop H∞-norm and satisfy an open-loop dissipativity constraint. The H∞-norm optimizes performance of a nominal LTI plant approximation, while the dissipativity constraint ensures stability of the true plant, which is composed of potentially nonlinear and uncertain subsystems robustly characterized by input-output properties. A local minimum to the NP-hard problem is found using the convex concave procedure, and an initialization is proposed that guarantees feasibility for a wide array of special cases. A numerical experiment compares the proposed design to the H∞-optimal controller for a network of nonlinear and LTI systems.

Life cycle assessment-driven collaborative optimization model of power dry cutting for face-hobbing hypoid gear production

Efficient, high-precision, energy-saving, green manufacturing and low-cost design is an increasingly important target to life cycle assessment (LCA) for high-performance hypoid gear production. With development of numerical controlled (NC) technology of hypoid generator, power dry cutting is enabling ever-higher levels of production efficiency and sustainability. It also has the potential to dramatically influence sustainable development of hypoid gear product. Sufficient guidance, in this respect, is lacking in the scholarly or practitioner literature. In this work, focusing on LCA for hypoid gear production, we further examine power dry cutting in terms of application and sustainability implications. We introduce collaborative optimization considering geometric accuracy and loaded contact performances into the power dry cutting. Here, LCA-driven power dry cutting collaborative optimization model is proposed for face-hobbing hypoid gear production. At first, complex machine kinematics between cutting tool and work blank are developed for power dry cutting simulation. Then, tooth flank mathematical modeling is performed to output discretization points in a closed-form of the whole tooth flank including concave flank and convex flank. Moreover, in order to improve LCA, an accurate model of material removal collaborative optimization considering both geometric accuracy and loaded contact pattern is established for face-hobbing hypoid gears. Where, time-varying material removal path planning is developed. Then, sensitivity analysis strategy and genetic algorithm (GA) are proposed for the proposed model solution, respectively. Finally, numerical instances can demonstrate that the proposed model can get a very important access to power dry cutting having high LCA for face-hobbing hypoid gear production.

Tooth profile design of a novel helical gear mechanism with improved geometry for a parallel shaft transmission

Abstract. Based on the space curve meshing equation, a novel helical gear mechanism with improved geometry is presented. First, equations of the theoretical contact curves were derived based on the space curve meshing theory. Then, tooth surfaces with a concave–convex meshing form were constructed, depending on the contact curves. The tooth profiles were improved as the theoretical contact curves were corrected by predestining the designed transmission errors. The effect of the center distance error on the transmission errors was studied, and the effects of gear modifications on transmission errors and maximum contact stresses were also investigated. The results show that the transmission error curves of the improved gear drive become much smoother. Maximum contact stresses of the improved gear drive are decreased synchronously.

Bas-relief modeling from RGB monocular images with regional division characteristics

Traditional Bas-relief modeling methods are often limited to inefficient and difficult to be altered after the product is formed. This paper presents a novel method for bas-relief modeling from RGB monocular images with regional division characteristics. The problem discussed in this paper involves edge detection, region division, height value recovery and three-dimensional reconstruction of image. In our framework, we can automatically obtain the pixel height of each area in the image and can adjust the concave–convex relationship of each image area to obtain a bas-relief modeling which can be printed directly in 3D. The edge detection algorithm used Gaussian difference pyramid to combine the luminance information and chrominance information of digital image; the regions of the RGB monocular image are divided by the improved connected-component labeling algorithm;and the 3D pixel point cloud of each region is calculated by the shape-from-shading algorithm. Different from previous work, our method can fully obtain the image height field data and completely restored the depth information,which makes it possible to use any RGB monocular image for bas-relief modeling. Experiments with groups of images show that our method can effectively generate bas-relief modeling.

Existence of Solutions to Fractional Elliptic Equation with the Hardy Potential and Concave–Convex Nonlinearities

Existence of Solutions to Fractional Elliptic Equation with the Hardy Potential and Concave–Convex Nonlinearities

Energy-Efficient Power Allocation for Multiuser Distributed MISO Systems With Beamforming and Imperfect CSI

In this article, we study the energy-efficient power allocation (PA) for multiuser distributed multiple-input-single-output (D-MISO) system with beamforming (BF) and imperfect channel state information (CSI). Given a target bit error rate, the system energy efficiency (EE) with imperfect CSI is deduced. Subject to the power budget constraints, a constrained optimization problem is first formulated to maximize EE of single-user D-MISO. The optimal BF is shown to be aligned with the channel direction that renders the joint optimization problem to be a PA problem. A near-optimal PA scheme is proposed to tackle this problem by using the concave–convex procedure method and fractional programming (FP) and block coordinate descent (BCD) method, and it can provide nearly optimal performance close to that of optimal exhaustive search scheme with less complexity. On this basis, a suboptimal PA scheme based on the FP and BCD method is developed to further decrease the complexity and maintain similar performance to near-optimal scheme, and it is suitable for the system with more distributed antennas. With these results, two PA schemes are, respectively, proposed for multiuser D-MISO with imperfect CSI to maximize EE. The first scheme can obtain better performance with relatively higher complexity, and the second scheme can gain the performance close to the first scheme with lower complexity, and only smaller performance loss is found. Interestingly, these two schemes have the same optimal performance for perfect CSI, and include the existing ones under perfect CSI as special cases. Simulation results verify the effectiveness of the developed schemes.

Modeling the Behavior of an Aggregate Skeleton during Static Creep of an Asphalt Mixture Based on a Three-Dimensional Mesoscale Random Model

The aggregate skeleton and its evolution under external loads are crucial to evaluate the mechanical properties of the asphalt mixture. This study developed a method to identify the three-dimensionally (3D) aggregate skeleton based on geometry information. The proposed method can identify the evolution process of the aggregate skeleton during loading in the finite element method (FEM). Random models based on the Gilbert–Johnson–Keerthi (GJK) algorithm are used to study the influence of the concave–convex degree of the gradation curve and the magnitude of the creep load on the aggregate skeleton during the creep process. The results indicate that the aggregate skeleton undergoes three stages during creep: aggregate redistribution, skeleton formation, and skeleton failure after reaching the ultimate load, while the increase of load causes the aggregate skeleton to lose its bearing capacity faster. More coarse aggregate raises the strength of the aggregate skeleton, but it is more likely to break down quickly once it reaches the strength. More fine aggregate enhances the stability of the aggregate skeleton. The proposed identification method can serve as a general tool to investigate the evolution process of the internal aggregate structure of the asphalt mixture.

Scattering by a low-velocity charge with applied magnetic fields in a Laguerre–Gaussian beam

A method to analyze the scattering characteristics of a Laguerre–Gaussian (LG) vortex beam by a low-velocity charge in a steady applied magnetic field is investigated in this paper. Based on the plane wave angular spectrum representation and the electromagnetic radiation theory of a moving charge, the expressions of the scattered field and scattered power per unit solid angle are presented. Considering a low-velocity electron, the distribution of the scattered power per unit solid angle is numerically simulated. The effects of electron motion parameters, beam parameters, and applied magnetic field are discussed in detail. The results show that the longitudinal motion of the electron, which is parallel to the direction of the applied magnetic field, makes the distribution of the scattered power no longer maintain radial consistency but has a concave–convex distribution. Due to the periodicity of the circular motion of the electron in the applied magnetic field, the scattering power distribution pattern consists of many annular lobes. The spectral characteristics of the backscattered field are analyzed by fast Fourier transform. It is confirmed that the scattered field satisfies the rotational and the linear Doppler effects, and the accuracy of the formula provided in this paper is verified. This work lays a foundation for further study of the scattering characteristics of plasma on vortex electromagnetic waves and helps to promote the in-depth development of vortex beams in the field of plasma diagnosis.

Convex Optimization for Parameter Synthesis in MDPs

Probabilistic model-checking aims to prove whether a Markov decision process (MDP) satisfies a temporal logic specification. The underlying methods rely on an often unrealistic assumption that the MDP is precisely known. Consequently, parametric MDPs (pMDPs) extend MDPs with transition probabilities that are functions over unspecified parameters. The parameter synthesis problem is to compute an instantiation of these unspecified parameters such that the resulting MDP satisfies the temporal logic specification. We formulate the parameter synthesis problem as a quadratically constrained quadratic program, which is nonconvex and is NP-hard to solve in general. We develop two approaches that iteratively obtain locally optimal solutions. The first approach exploits the so-called convex–concave procedure (CCP), and the second approach utilizes a sequential convex programming (SCP) method. The techniques improve the runtime and scalability by multiple orders of magnitude compared to black-box CCP and SCP by merging ideas from convex optimization and probabilistic model-checking. We demonstrate the approaches on a satellite collision avoidance problem with hundreds of thousands of states and tens of thousands of parameters and their scalability on a wide range of commonly used benchmarks.

Existence and nonexistence of positive solutions of some elliptic problems with variable exponents

In this paper, we study the existence and the nonexistence of some positive solutions for nonlinear equations involving variable exponent Laplace operator and concave–convex second term: under Robin boundary condition in a regular open‐bounded domain of . The ‐Laplacian is given by where and . Our proofs are based on the subsupersolutions method mixed with variational arguments.

Analysis of sagittal spinal alignment at the adolescent age: for furniture design

Knowledge of the parameters of the human spine is essential in designing ergonomic furniture. The purpose of this study was to evaluate spinal alignment in adolescents of various ages. The lengths, curvatures, and concave–convex spacings of the spine were investigated in 268 participants aged 9–18 years. Ten ages were classified, and the rate of increase of parameters was calculated for each age and age group. The results showed that spinal parameters, except for cervical lordosis, increased with age. Adolescents were classified as 9–10, 11–12, 13–15, and 16–18 years old. A rapid increment of lengths and concave–convex spacings occurred at ages 13–15, while that of curvatures occurred at ages 16–18. Spinal parameters differed significantly among the age groups (p < 0.05). Concave–convex spacings reflected differences in the spine more clearly than the other parameters. This study suggests the necessity of designing spine-related furniture based on spinal parameters, thus providing adaptive support for the adolescent spine, particularly the lumbar spine. Practitioner summary: This study examined spinal lengths, curvatures, and concave–convex spacings in adolescents aged 9–8 years and then divided them into four age groups. Concave–convex spacings effectively reflected spinal differences between age groups, particularly the lumbar spine. These results can inform the ergonomic design of spine-related furniture. HIGHLIGHTS Spinal parameters increased progressively between 9 and 18 years. Regression analysis showed good linear correlations between TK, LL, SK, TS, and LS with age. Age classification of adolescents was Group I (9–10 years), Group II (11–12 years), Group III (13–15 years), and Group IV (16–18 years). The rapid increment of lengths and concave–convex spacings were in Group III while that of curvatures were in Group IV. Concave–convex spacings were vital parameters to evaluate the global balance of the spine. The lumbar spine is an essential segment for characterizing spinal alignment.

Electric Flash Butt Rail Weld Failure Called “Concave–Convex”

Electric Flash Butt Rail Weld Failure Called “Concave–Convex”

Multiple Solutions for Discrete Schrödinger Equations with Concave–Convex Nonlinearities

Multiple Solutions for Discrete Schrödinger Equations with Concave–Convex Nonlinearities

Dynamic policy for idling time preservation

AbstractThis study aims to determine and evaluate dynamic idling policies where an agent can idle while some customers remain waiting. This type of policies can be employed in situations where the flow of urgent customers does not allow the agent to spend sufficient time on back‐office tasks. We model the system as a single‐agent exponential queue with abandonment. The objective is to minimize the system's congestion while ensuring a certain proportion of idling time for the agent. Using a Markov decision process approach, we prove that the optimal policy is a threshold policy according to which the agent should idle above (below) a certain threshold on the queue length if the congestion‐related performance measure is concave (convex) with respect to the number of customers present. We subsequently obtain the stationary probabilities, performance measures, and idling time duration, expressed using complex integrals. We show how these integrals can be numerically computed and provide simpler expressions for fast‐agent and heavy‐traffic asymptotic cases. In practice, the most common way to regulate congestion is to control access to the service by rejecting some customers upon arrival. Our analysis reveals that idling policies allow high levels of idling probability that such rejection policies cannot reach. Furthermore, the greatest benefit of implementing an optimal idling policy occurs when the objective occupation rate is close to 50% in highly congested situations.

Propagation characteristics of adjustable abnormal hollow beams in gradient negative refractive index material

In this paper, the propagation characteristics of adjustable abnormal hollow (AAH) beams in gradient negative refractive index material are investigated theoretically and numerically. We focus on analyzing and discussing the intensity pattern, beam width and axial intensity of AAH beam, and give the mathematical expressions of these physical quantities. The results show that the AAH beams can have many different evolution forms. In general, the intensity pattern of AAH beam changes periodically during the propagation, but solitons can be formed under special parameters. Through parameter control, the beam width of AAH beam can be widened or compressed in one or two transverse directions, or even constant in one transverse direction and periodically changed in the other transverse direction. The evolution of axial light intensity of AAH beam can also show different transmission types such as concave type, flat-top type and convex type.

Surface modification and tooth contact analysis of variable hyperbolic circular-arc-tooth-trace cylindrical gears

Abstract. To improve the bearing capacity and provide the mathematical model basis for vibration and noise reduction of the variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear, the tooth surface modification design method based on the parabolic forming blade and cutter inclination was proposed. The geometric design of inclined cutter was completed. The modified tooth surface equation was deduced, and the influence of modification parameters on tooth surface curvature characteristics was analysed further. The tooth contact analysis (TCA) was established, and the influence of modification parameters on the elliptical contact area was analysed. Research shows that the parabolic coefficient a and the parabolic vertex position u0 have effects on the main curvature of concave–convex tooth surface, both the tooth profile and the tooth line direction, but the cutter inclination angle only has influence on the curvature of the tooth line direction, and the influence is larger. The cutter inclination angle γ, parabola coefficient a, and parabolic vertex position u0 have certain influences on the elliptical contact area. The cutter inclination angle γ is the most important modification parameter to improve the bearing capacity, but the excessive cutter inclination angle will cause bridge contact, the value range cutter inclination γ can be determined based on the tooth line radius. The research results provide a technical basis for improving the bearing capacity of the VH-CATT cylindrical gear and optimising the design.

Performance of thermosolutal discharge for double diffusive mixed convection of hybrid nanofluid in a lid driven concave–convex chamber

Performance of thermosolutal discharge for double diffusive mixed convection of hybrid nanofluid in a lid driven concave–convex chamber

Experimental and finite element analysis on the sound absorption performance of wedge-like knitted composite

Limited by the single mechanism of sound absorption, most current sound-absorbing materials exhibit difficulties in balancing weight and acoustic performance. In this work, a flexible wedge-like knitted composite (WKC) realized by knitting and coating technology with multiple sound-absorbing mechanisms including porous sound absorption mechanism and wedge-like structure resonant mechanism is proposed. To study the influence mechanisms of coating and wedge structure on the sound absorption performance, experiment and finite element analysis were both conducted. By improving the porosity distribution through the addition of viscoelastic layer, the sound absorption coefficient (SAC) is enhanced by 239%, which is originated from the infiltrated silica gel into the fabric pores, increasing the complexity of the penetration path. The wedge structure plays a necessary role on enhancing the sound absorption coefficient under low frequency because the concave–convex surface of wedge generates stronger resonance of rear air cavity. The size effect of wedge shape is analyzed in terms of acoustic vibration angle and acoustic energy dissipation density. The increase of the acoustic vibration angle increases the reflection collision path and speed of sound vibration, which further enhances the energy dissipation. Therefore, the combination of viscoelastic coating layer and wedge structure effectively promote the sound absorption, especially at low frequency. This work provides guidance for the structural design and realization of innovative flexible sound absorbing materials, which is promising in application prospect of indoor curtain interiors, wall coverings and automotive interiors.