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The well-known Stokes’ problems are reexamined by applying the Adomian decomposition method (ADM) associated with other mathematical techniques in this paper. Both the finite-depth (bounded) and infinite-depth (unbounded) cases are analyzed. The present paper raises and deals with two major concerns. The first one is that, for Stokes’ problems, it lacks one boundary condition at the expansion point to fully determine all coefficients of the ADM solution in which an unknown function appears. This unknown function which is dependent on the transformed variable will be determined by the boundary condition at the far end. The second concern is that the derived solution begins to deviate from the exact solution as the spatial variable grows for the unbounded problems. This can be greatly improved by introducing the Padé approximant to satisfy the boundary condition at the far end. For the second problems, the derived ADM solution can be easily separated into the steady-state and the transient parts for a deeper comprehension of the flow. The present result shows an excellent agreement with the exact solution. The ADM is therefore verified to be a reliable mathematical method to analyze Stokes’ problems of finite and infinite depths.

In this paper, an extension of some existing results related to finite-time stability (FTS) and finite-time boundedness (FTB) into the conformable fractional derivative is presented. Illustrative example is presented at the end of the paper to show the effectiveness of the proposed result.

This paper presents a new solubility optimal system to improve the efficiency of supercritical fluid extraction (SFE). The major contribution is a nonlinear temperature-pressure decoupling model constructed with unequal-interval grey optimal models (UEIGOMs) and Peng-Robinson models (PRMs). The linear parts of temperature and pressure process can be constructed with UEIGOM, respectively. The nonlinear parts of temperature and pressure process can be described by PRMs, respectively. The whole nonlinear model cannot be input-output decoupled resulting from the singularity of decoupling matrix for PRM. This problem on input-output nondecoupling can be transformed to the problem on disturbance decoupling for a class of MIMO nonlinear systems. Therefore, the whole nonlinear coupling model can be disturbance decoupled. Furthermore, solubility optimal method is presented in the paper; it can calculate the optimal pressure according to the given temperature, namely, optimal working points, to maximize solubility for SFE process. The feasibility, effectiveness, and practicality of the proposed nonlinear temperature-pressure decoupling model constructed with UEIGOMs and PRMs are verified by SFE experiments in biphenyl. Experiments using the designed solubility optimal system are carried out to demonstrate the effectiveness in control scheme, simplicity in structure, and flexibility in implementation for the proposed solubility optimal system based on a new nonlinear temperature-pressure coupling model constructed with UEIGOMs and PRMs.

This paper aims to investigate the stationary probability density functions of the Duffing oscillator with time delay subjected to combined harmonic and white noise excitation by the method of stochastic averaging and equivalent linearization. By the transformation based on the fundamental matrix of the degenerate Duffing system, the paper shows that the displacement and the velocity with time delay in the Duffing oscillator can be computed approximately in non-time delay terms. Hence, the stochastic system with time delay is transformed into the corresponding stochastic non-time delay equation in Ito sense. The approximate stationary probability density function of the original system can be found by combining the stochastic averaging method, the equivalent linearization method, and the technique of auxiliary function. The response of Duffing oscillator is investigated. The analytical results are verified by numerical simulation results.

The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of two-dimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion results. This paper applies boundary element method to solve the temperature calculation of discrete points in forward problems. The factors of measuring error and the number of measuring points zero error which impact the measurement result are discussed and compared with L-MM method in inverse problems. Instance calculation and analysis prove that the method applied in this paper still has good effectiveness and accuracy even if measurement error exists and the boundary measurement points’ number is reduced. The comparison indicates that the influence of error on the inversion solution can be minimized effectively using this method.

Simple finite connected graphs G=V,E of p≥2 vertices are considered in this paper. A connected detour set of G is defined as a subset S⊆V such that the induced subgraph GS is connected and every vertex of G lies on a u−v detour for some u,v∈S. The connected detour number cdnG of a graph G is the minimum order of the connected detour sets of G. In this paper, we determined cdnG for three special classes of graphs G, namely, unicyclic graphs, bicyclic graphs, and cog-graphs for Cp, Kp, and Km,n.

Relative position of seismic source and sensors has great influence on locating accuracy, particularly in far field conditions, and the accuracy will decrease seriously due to limited calculation precision and prior velocity error. In order to improve the locating accuracy of far field sources by isometric placed sensors in a straight line, a new locating method with nonprior velocity is proposed. After exhaustive research, this paper states that the hyperbola which is used for locating will be very close to its asymptote when seismic source locates in far field of sensors; therefore, the locating problem with prior velocity is equivalent to solving linear equations and the problem with nonprior velocity is equivalent to a nonlinear optimization problem with respect to the unknown velocity. And then, this paper proposed a new locating method based on a one-variable objective function with respect to the unknown velocity. Numerical experiments show that the proposed method has faster convergence speed, higher accuracy, and better stability.

In recent studies, papers related to the multiplicative based numerical methods demonstrate applicability and efficiency of these methods. Numerical root-finding methods are essential for nonlinear equations and have a wide range of applications in science and engineering. Therefore, the idea of root-finding methods based on multiplicative and Volterra calculi is self-evident. Newton-Raphson, Halley, Broyden, and perturbed root-finding methods are used in numerical analysis for approximating the roots of nonlinear equations. In this paper, Newton-Raphson methods and consequently perturbed root-finding methods are developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed root-finding methods is exposed by examples, and the results are compared with some ordinary methods. One of the striking results of the proposed method is that the rate of convergence for many problems are considerably larger than the original methods.

In order to improve the performance of the membrane element with vertex rigid rotational freedom, a new method to establish the local Cartesian coordinate system and calculate the derivatives of the shape functions with respect to the local coordinates is introduced in this paper. The membrane elements with vertex rigid rotational freedom such as GQ12 and GQ12M based on this new method can achieve higher precision results than traditional methods. The numerical results demonstrate that the elements GQ12 and GQ12M with this new method can provide better membrane elements for flat shell elements. Furthermore, this new method presented in this paper offers a new approach for other membrane elements used in flat shell element to improve the computing accuracy.

First of all, we establish a three-dimension open Kaldorian business cycle model under the condition of the fixed exchange rate. Secondly, with regard to the model, we discuss the existence of equilibrium point and the stability of the system near it with a time delay in currency supply as the bifurcating parameters of the system. Thirdly, we discuss the existence of Hopf bifurcation and investigate the stability of periodic solution generated by the Hopf bifurcation; then the direction of the Hopf bifurcation is given. Finally, a numerical simulation is given to confirm the theoretical results. This paper plays an important role in theoretical researching on the model of business cycle, and it is crucial for decision-maker to formulate the macroeconomic policies with the conclusions of this paper.

With new three-segment piecewise-linearity in the classic Chua’s system, two new types of 2-scroll and 3-scroll Chua’s attractors are found in this paper. By changing the outer segment slope of the three-segment piecewise-linearity as positive, the new 2-scroll Chua’s attractor has emerged from one zero index-1 saddle-focus and two symmetric stable nonzero node-foci. In particular, by newly introducing a piecewise-linear control function, an improved Chua’s system only with one zero index-2 saddle-focus and two stable nonzero node-foci is constructed, from which a 3-scroll Chua’s attractor is converged. Some remarks for Chua’s nonlinearities and the generating chaotic attractors are discussed, and the stabilities at the three equilibrium points are then analyzed, upon which the emerging mechanisms of the novel 2-scroll and 3-scroll Chua’s attractors are explored in depth. Furthermore, an analog electronic circuit built with operational amplifier and analog multiplier is designed and hardware circuit experiments are measured to verify the numerical simulations. These novel 2-scroll and 3-scroll Chua’s attractors reported in this paper are completely different from the classic Chua’s attractors, which will enrich the dynamics of the classic Chua’s system.

In this paper, we study the existence and multiplicity of nontrivial solutions for a class of biharmonic elliptic equation with Sobolev critical exponent in a bounded domain. By using the idea of the previous paper, we generalize the results and prove the existence and multiplicity of nontrivial solutions of the biharmonic elliptic equations.

In this paper, a kind of BAM neural networks with leakage delays in the negative feedback terms and time-varying delays in activation functions was considered. By constructing a suitable Lyapunov function and using inequality techniques, some sufficient conditions to ensure the existence and exponential stability of antiperiodic solutions of these neural networks were derived. These conditions extend some results recently appearing in recent papers. Lastly, an example is given to show the feasibility of these conditions.

The purpose of this paper is to present some existence and uniqueness results for common fixed point theorems for θ-ϕ contraction mappings with two metrics endowed with a directed graph. In addition, by using our main results, we obtain some results about coupled coincidence points endowed with a directed graph. Our results generalize those presented in previous papers.

This paper studies the stabilization problem for a class of unified chaotic systems subject to uncertainties and input nonlinearity. Based on the sliding mode control theory, we present a new method for the sliding mode controller design and the control law algorithm for such systems. In order to achieve the goal of stabilization unified chaotic systems, the presented controller can make the movement starting from any point in the state space reach the sliding mode in limited time and asymptotically reach the origin along the switching surface. Compared with the existing literature, the controller designed in this paper has many advantages, such as small chattering, good stability, and less conservative. The analysis of the motion equation and the simulation results all demonstrate that the method is effective.

The periodic nonuniform sampling plays an important role in digital signal processing and other engineering fields. In this paper, we introduce the Gaussian regularization method to accelerate the convergence rate of periodic nonuniform sampling series. We prove that the truncation error of the Gaussian regularized periodic nonuniform sampling series decays exponentially. Numerical experiments are presented to demonstrate our result.

In this paper, some fixed-point theorems are established for strongly subadditive maps on CΩ,ϒ (where CΩ,ϒ denotes the space of ϒ-valued continuous functions on a compact Hausdorff space Ω and ϒ is a unital Banach algebra). Finally, the result is applied to prove the existence and uniqueness of a solution for a system of nonlinear integrodifferential equations.

In this paper, we propose an efficient compact finite difference method for a class of time-fractional subdiffusion equations with spatially variable coefficients. Based on the L2-1σ approximation formula of the time-fractional derivative and a fourth-order compact finite difference approximation to the spatial derivative, an efficient compact finite difference method is developed. The local truncation error and the solvability of the developed method are discussed in detail. The unconditional stability of the resulting scheme and also its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method. Numerical examples are provided to demonstrate the accuracy and the theoretical results.

In this paper, we propose a numerical method for solving the time fractional Richards’ equation. We first approximate the time fractional derivative of the mentioned equations by a scheme of order O(τ2−α), 0

For a quaternion matrix A, we denote by Aϕ the matrix obtained by applying ϕ entrywise to the transposed matrix AT, where ϕ is a nonstandard involution of quaternions. A is said to be ϕ-Hermitian or ϕ-skew-Hermitian if A=Aϕ or A=−Aϕ, respectively. In this paper, we give a complete characterization of the nonstandard involutions ϕ of quaternions and their conjugacy properties; then we establish a new real representation of a quaternion matrix. Based on this, we derive some necessary and sufficient conditions for the existence of a ϕ-Hermitian solution or ϕ-skew-Hermitian solution to the quaternion matrix equation AX=B. Moreover, we give solutions of the quaternion equation when it is solvable.

In this paper, we introduce two new classes of acceptability indexes, named quasi-concave acceptability indexes and coherent acceptability indexes, for portfolio vectors. We establish the one-to-one correspondence between quasi-concave (coherent, resp.) acceptability indexes and convex (coherent, resp.) risk measures for portfolio vectors. We derive the representation results for coherent and convex risk measures. Finally, based on these results, we derive the representation results for quasi-concave acceptability indexes and coherent acceptability indexes for portfolio vectors. These new acceptability indexes can be considered as a kind of multivariate extension of univariate coherent and quasi-concave acceptability indexes introduced by Cherny and Madan (2009) and Rosazza Gianin and Sgarra (2013), respectively.

Let D be the unit disk in the complex plane C and denote T=∂D. Write Hom+T,∂Ω for the class of all sense-preserving homeomorphism of T onto the boundary of a C2 convex Jordan domain Ω. In this paper, five equivalent conditions for the solutions of triharmonic equations ∂z∂z¯3ω=ff∈CD¯ with Dirichlet boundary value conditions ωzz¯zz¯T=γ2∈CT,ωzz¯T=γ1∈CT and ωT=γ0∈Hom+T,∂Ω to be Lipschitz continuous are presented.

In this paper, we introduce an iterative method for approximating a common solution of monotone inclusion problem and fixed point of Bregman nonspreading mappings in a reflexive Banach space. Using the Bregman distance function, we study the composition of the resolvent of a maximal monotone operator and the antiresolvent of a Bregman inverse strongly monotone operator and introduce a Halpern-type iteration for approximating a common zero of a maximal monotone operator and a Bregman inverse strongly monotone operator which is also a fixed point of a Bregman nonspreading mapping. We further state and prove a strong convergence result using the iterative algorithm introduced. This result extends many works on finding a common solution of the monotone inclusion problem and fixed-point problem for nonlinear mappings in a real Hilbert space to a reflexive Banach space.

The Jacobi–Davidson iteration method is efficient for computing several eigenpairs of Hermitian matrices. Although the involved correction equation in the Jacobi–Davidson method has many developed variants, the behaviors of them are not clear for us. In this paper, we aim to explore, theoretically, the convergence property of the Jacobi–Davidson method influenced by different types of correction equations. As a by-product, we derive the optimal expansion vector, which imposed a shift-and-invert transform on a vector located in the prescribed subspace, to expand the current subspace.

In this paper, we enrich and develop power-type Aczél-Vasić-Pečarić’s inequalities. First of all, we give some new versions of theorems and corollaries about Aczél-Vasić-Pečarić’s inequalities by quoting some lemmas. Moreover, in combination with Hölder’s inequality, we give some applications of the new version of Aczél-Vasić-Pečarić’s inequality and give its proof process.

In this paper, we consider a stochastic SIQR epidemic model with saturated incidence rate. By constructing a proper Lyapunov function, we obtain the existence and uniqueness of positive solution for this SIQR model. Furthermore, we study the dynamical properties of this stochastic SIQR model; that is, (i) we establish the sufficient condition for the existence of ergodic stationary distribution of the model; (ii) we obtain the extinction of the disease under some conditions. At last, numerical simulations are introduced to illustrate our theoretical results.

In this paper, we consider the dual wavelet frames in both continuum setting, i.e., on manifolds, and discrete setting, i.e., on graphs. Firstly, we give sufficient conditions for the existence of dual wavelet frames on manifolds by their corresponding masks. Then, we present the formula of the decomposition and reconstruction for the dual wavelet frame transforms on graphs. Finally, we give a numerical example to illustrate the validity of the dual wavelet frame transformation applied to the graph data.

On the conditions that the spacecraft engine is in finite thrust mode and the maneuver time is given, it takes a long time to compute the minimum duration transfer trajectories of space-to-ground vehicles, which is mainly because the initial values of the adjoint variables involved in the optimization model have no definite physical meanings and the model is sensitive to them. In order to develop space-to-ground transfer trajectory programmes in real time in an uncertain environment for the decision makers, we propose a fast method for computing the minimum duration transfer trajectories of space-to-ground vehicles with the given position of the landing point and the arbitrary maneuver point. First, the optimization model based on the hybrid method is established to compute the minimum duration transfer trajectory. Then, the region composed of maneuverable points is gridded and the initial values of the adjoint variables and the values of partial state variables of the minimum duration transfer trajectories at all gridded points are computed and saved to a database. Finally, the predicted values of the initial values of the adjoint variables and the values of partial state variables at any maneuver point within the region composed of maneuverable points are computed by using a binary cubic interpolation method. Finally, the minimum duration transfer trajectory is obtained by the hybrid method which takes the neighborhood of the predicted values as the search ranges of the initial values of the adjoint variables and the values of partial state variables. Simulation results demonstrate that the proposed method, which requires only 2.93% of the computational time of the hybrid method, can improve substantially the computational time of the minimum duration transfer trajectory of a space-to-ground vehicle under the guarantee of ensuring accuracy. The methodology of converting the time domain into the space domain is well applied in this paper.

The critical speed and hunting frequency are two basic research objects of vehicle system dynamics and have a significant influence on the dynamic performance. A lateral dynamic model with 17 degrees of freedom was established in this study to investigate the critical speed and hunting frequency of a high-speed railway vehicle. The nonlinearities of wheel/rail contact geometry, creep forces, and yaw damper were all considered. A heuristic nonlinear creep model was employed to estimate the contact force between the wheel and the rail. The Maxwell model, which covers the influence of the stiffness characteristic, is used to simulate the yaw damper. To reflect the blow-off of the yaw damper, the damping coefficient is described by stages. Based on the mathematical model, the combined effects of vehicle parameters on the critical speed in the straight line and hunting frequency of the wheelset were investigated innovatively. The novel phenomenon that the hunting frequency exhibits a sudden increase from a smaller value to a larger value when the blow-off of the yaw damper occurs was discovered during the calculations. The extents to which various parameters affect the critical speed and hunting frequency are clear on the basis of the numerical results. Moreover, all of the parameter values were divided into three sections to determine the sensitive range for the critical speed and hunting frequency. The results show that the first section of values plays the decisive role on both the critical speed and the hunting frequency for all parameters analyzed. The investigation in this paper enriches the study of hunting stability and gives some ideas to probably solve the abnormal vibrations during the actual operation.

Based on the robust chaos theorem of S-unimodal maps, this paper studies a kind of cubic polynomial discrete maps (CPDMs) and sets up a novel theorem. This theorem gives general conditions for the occurrence of robust chaos in the CPDMs. By using the theorem, we construct a CPDM. The parameter regions of chaotic robustness of the CPDM are larger than these of Logistic map. By using a fixed point arithmetic, we investigate the cycle lengths of the CPDM and a Logistic map. The results show that the maximum cycle lengths of 1000 chaotic sequences with length 3×107 generated by different initial value conditions exponentially increase with the resolutions. When the resolutions reach 10-7~10-13, the maximum cycle lengths of the cubic polynomial chaotic sequences are significantly greater than these of the Logistic map. When the resolution reaches 10-14, there is the situation without cycle for 1000 cubic polynomial chaotic sequences with length 3×107. By using the CPDM and Logistic map, we design four chaos-based pseudorandom number generators (CPRNGs): CPRNGI, CPRNGII, CPRNGIII, and CPRNGIV. The randomness of two 1000 key streams consisting of 20000 bits is tested, respectively, generated by the four CPRNGs. The result suggests that CPRNGIII based on the cubic polynomial chaotic generalized synchronic system has better performance.

In this paper, a second-order accurate (in time) energy stable Fourier spectral scheme for the fractional-in-space Cahn-Hilliard (CH) equation is considered. The time is discretized by the implicit backward differentiation formula (BDF), along with a linear stabilized term which represents a second-order Douglas-Dupont-type regularization. The semidiscrete schemes are shown to be energy stable and to be mass conservative. Then we further use Fourier-spectral methods to discretize the space. Some numerical examples are included to testify the effectiveness of our proposed method. In addition, it shows that the fractional order controls the thickness and the lifetime of the interface, which is typically diffusive in integer order case.

In this paper, we first introduce a class of tensors, called positive semidefinite plus tensors on a closed cone, and discuss its simple properties; and then, we focus on investigating properties of solution sets of two classes of tensor complementarity problems. We study the solvability of a generalized tensor complementarity problem with aD-strictly copositive tensor and a positive semidefinite plus tensor on a closed cone and show that the solution set of such a complementarity problem is bounded. Moreover, we prove that a related conic tensor complementarity problem is solvable if the involved tensor is positive semidefinite on a closed convex cone and is uniquely solvable if the involved tensor is strictly positive semidefinite on a closed convex cone. As an application, we also investigate a static traffic equilibrium problem which is reformulated as a concerned complementarity problem. A specific example is also given.

In order to control pests and eventually maintain the number of pests below the economic threshold, in this paper, based on the nonsmooth dynamical system, a two-stage-structured pest control Filippov model is proposed. We take the total number of juvenile and adult pest population as the control index to determine whether or not to implement chemical control strategies. The sliding-mode domain and conditions for the existence of regular and virtual equilibria, pseudoequilibrium, boundary equilibria, and tangent points are given. Further, the sufficient condition of the locally asymptotic stability of pseudoequilibrium is obtained. By numerical simulations, the local bifurcations of the equilibria are discussed. Our results show that the total number of pest populations can be successfully controlled below the economic threshold by taking suitable threshold policy.

The roughness and uncertainty are important parameters of surface morphology. The least square middle line method is often used to estimate the roughness and its uncertainty. However, the roughness and its uncertainty obtained by the least square middle line method are inaccurate. This paper proposes a method to calculate exactly the roughness and its uncertainty by piecewise fitting the smooth B-spline filter assessment middle lines. A B-spline smoothing filter is selected to determine the assessment middle line of roughness. The B-spline filter can not only give the accurate roughness, but also obtain the smooth assessment middle line. The model of roughness uncertainty is proposed by piecewise fitting B-spline filter middle lines as the quadratic curves. The S-shaped test part is used to verify the model of roughness uncertainty.

There are many accidents of slope failure due to rainfall at home and abroad, which have caused heavy casualties and property losses. Stability analysis and evaluation of slope have become a research hotspot. Aiming at the slope stability under different rainfall, this paper takes Yuebao Open-pit Mine slope as an example, has constructed a dynamic variable weight (VW) model of influencing factors on slope stability, and has analyzed the dynamic change and correlation of the slope indexes weights under different monthly maximum rainfall. On this basis, the dynamic evaluation model of slope stability has been established based on uncertainty measurement (UM), and the risk importance (RI) q which is proposed has quantitatively evaluated the risk degree of slope. The results show that under different monthly maximum rainfall the weight of each index is no longer a fixed value but a nonlinear and dynamic change law, and there is a strong correlation among the monthly maximum rainfall, internal friction angle, and cohesion. In addition, the q increases gradually with the increase of the monthly maximum rainfall, and the stability evaluation results are highly consistent with the HP1 slope, which have verified the reliability of the dynamic evaluation model. So, it can provide technical support for the safety production and management of open-pit slope and can also provide reference for related research.

The aim of this paper is to prove the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings defined on generalized metric spaces with a graph. Our results improve and extend several recent results of metric fixed point theory.

This paper proposes a generalized modified iterative scheme where the composed self-mapping driving can have distinct step-dependent composition order in both the auxiliary iterative equation and the main one integrated in Ishikawa’s scheme. The self-mapping which drives the iterative scheme is a perturbed 2-cyclic one on the union of two sequences of nonempty closed subsets Ann=0∞ and Bnn=0∞ of a uniformly convex Banach space. As a consequence of the perturbation, such a driving self-mapping can lose its cyclic contractive nature along the transients of the iterative process. These sequences can be, in general, distinct of the initial subsets due to either computational or unmodeled perturbations associated with the self-mapping calculations through the iterative process. It is assumed that the set-theoretic limits below of the sequences of sets Ann=0∞ and Bnn=0∞ exist. The existence of fixed best proximity points in the set-theoretic limits of the sequences to which the iterated sequences converge is investigated in the case that the cyclic disposal exists under the asymptotic removal of the perturbations or under its convergence of the driving self-mapping to a limit contractive cyclic structure.

Inspired by the work of Zhefei He and Mingjin Wang which was published in the Journal of Inequalities and Applications in 2015, this paper further generalizes some related results to the case of multidimensional random variables. The resulting inequality for covariance is then applied to different multidimensional statistical distributions (multiuniform, multinomial, and multinormal). Coordinate dependence of the inequality is also examined. The obtained formulas could be useful for making estimates in multivariate statistics.

The aim of this paper is to introduce the notion of admissible multivalued mappings and to set up fixed point results for such mappings fulfilling generalized locally Ćirić type rational-contractive conditions on a closed ball in complete dislocated b-metric space. Example and application have been given to demonstrate the novelty of our results. Our results combine, extend, and infer several comparable results in the existing literature.

Dynamic relaxation (DR) is a widely used numerical method to determine the static equilibrium of a dynamic system. However, it is difficult to apply conventional DR methods to nonlinear models because they require estimation of a stiffness matrix of the model. To resolve the forementioned problem, a new dynamic relaxation method using continuous kinetic damping (CKDR) was proposed in previous research. The CKDR method does not require any model parameters including the stiffness matrix, and it possesses absolute stability and a second-order convergence rate. However, the convergence rate is proportional to square of the step size, and this may result in a low convergence rate if the selected step size is excessively small. This problem leads to difficulties in the practical use of CKDR. Thus, an adaptive step-size method is proposed in this paper to control the convergence rate of CKDR. The proposed method estimates natural frequency of the model and determines adaptive step size. Static equilibrium simulations were performed for three different models to verify the method. The results revealed that the computational cost of CKDR with a variable step size was very efficient when compared to fixed step sizes and that the convergence rate was also controlled as intended. In addition, the lowest natural frequencies of models in static equilibrium were accurately estimated.

The reliability polynomial R(S,p) of a finite graph or hypergraph S=(V,E) gives the probability that the operational edges or hyperedges of S induce a connected spanning subgraph or subhypergraph, respectively, assuming that all (hyper)edges of S fail independently with an identical probability q=1-p. In this paper, we investigate the probability that the hyperedges of a hypergraph with randomly failing hyperedges induce a connected spanning subhypergraph. The computation of the reliability for (hyper)graphs is an NP-hard problem. We provide recurrence relations for the reliability of r-uniform complete hypergraphs with hyperedge failure. Consequently, we determine and calculate the number of connected spanning subhypergraphs with given size in the r-uniform complete hypergraphs.

This paper presents a parametric level set-based method (PLSM) for multimaterial topology optimization of heat conduction structures with volume constraints. A parametric level set-based optimization model of heat conduction structures is built with multimaterial level set (MM-LS) model, which describes the boundaries of different materials by the combination of all level set functions. The heat dissipation efficiency which means the quadratic temperature gradient is conducted as the objective function. The adjoint method is utilized to calculate the sensitivities of the objective function with respect to expansion coefficients of the compactly supported radial basis functions (CSRBFs). The optimal configuration is achieved by updating the expansion coefficients gradually with the method of moving asymptotes (MMA). Several numerical examples are discussed to demonstrate effectiveness of the proposed method for multimaterial topology optimization of heat conduction structures.

The two-component μ-Hunter-Saxton system is considered in the spatially periodic setting. Firstly, a wave-breaking criterion is derived by employing the localization analysis of the transport equation theory. Secondly, several sufficient conditions of the blow-up solutions are established by using the classic method. The results obtained in this paper are new and different from those in previous works.

In this paper, we introduce the concept of a rectangular metric-like space, along with its topology, and we prove some fixed point theorems for different contraction types. We also introduce the concept of modified metric-like spaces and we prove some topological and convergence properties under the symmetric convergence. Some examples are given to illustrate the new introduced metric type spaces.

The hydrodynamic coefficients are important parameters for predicting the motion of the glider and upgrading the hull design. In this paper, based on the Reynolds number similarity theory, 6 degrees of freedom (DOFs) of the fluid force and torque of a 1:1 full-scale glider model are measured. The present measurements were carried out at (2 - 14m/s) by varying attack angles and sideslip angles (-9 - 9°), respectively. The measurements were used to study the variation of the hydrodynamics of the glider, and the measurements have also been used to validate results obtained from a CFD code that uses RNG k-ε. The hydrodynamic force coefficients obtained from CFD accord well with the measurements. However, the torque coefficients difference is fairly large. Dynamics simulation results show that CFD results can be used to design and study the motion characteristics of gliders. In order to simplify the design process of gliders, we fit the empirical formula based on the experimental data and obtain a drag coefficient equation with Reynolds number. The influence of two kinds of appendages of the Conductance-Temperature-Depth (CTD) unit and thruster unit on the glider drag were studied by a contrast test. The analysis results can provide reference for design and the motion investigate of gliders.

This paper is concerned with the vibration-driven system which can move due to the periodic motion of the internal mass and the dry friction; the system can be modeled as Filippov system and has the property of stick-slip motion. Different periodic solutions of stick-slip motion can be analyzed through sliding bifurcation, two-parameter numerical continuation for sliding bifurcation is carried out to get the different bifurcation curves, and the bifurcation curves divide the parameters plane into different regions which stand for different stick-slip motion of the periodic solution. Furthermore, continuations with additional condition v=0 are carried out for the directional control of the vibration-driven system in one period; the curves divide the parameter plane into different progressions.

Stochastic response of a plate on the generalized foundation driven by random excitation is solved in this paper. Governing differential equation is obtained by employing the Galerkin method. The generalized harmonic function technique is applied to the governing equation of motion. Using the stochastic averaging method (SAM), the system is approximated by the time homogeneous diffusive Markov process. Corresponding approximate stationary probability function is achieved by solving associated Fokker-Plank-Kolmogorov (FPK). An analytical solution is presented for the stationary probability of the amplitude and velocity. Validity of the stationary probability is verified by Monte-Carlo simulation. Parametric study is carried out to investigate effects of foundation parameters and excitation intensity on the stationary probability function. It is found that the fractional properties act similar to the foundation stiffness and damping and can be employed as a new control parameter for the support design.

Metaheuristics (MH) aptitude to move past local optimums makes them an attractive technique to approach complex computational problems, such as the Travelling Salesman Problem (TSP), but there is lack of information on the parameterization procedure and the appropriate parameters to improve MHs' performance. In this paper the parameterization procedure of Simulated Annealing (SA) and Discrete Artificial Bee Colony (DABC) is addressed, with a focus on the Neighborhood Structure (NS). Numerous NS have been proposed for specific problems, which seem to indicate that the NS is a special parameter, whose optimization is independent of other parameters. The performance of eight NS was examined with SA and DABC under two optimization constraints, regarding computational time variation, to determine if there is one appropriate NS for the TSP problem, independent of the rest of the parameters of the optimization procedure. The computational study carried out for comparing the evaluation of the NS, including a statistical analysis, demonstrated a nonproportional increase in the performance of DABC with some NS. For SA the improvement of the solutions appeared to be more uniform with an almost nonexistent variance in improvement., This work is supported by FEDER Funds through the "Programa Operacional Factores de Competitividade (COMPETE)" and by National Funds through FCT "Fundação para a Ciência e a Tecnologia" under the Projects FCOMP-01-0124-FEDER-PEst-OE/EEI/UI0760/2011, PEst-OE/EEI/UI0760/2014, and PEst2015-2020.

This paper presents fully discrete stabilized finite element methods for two-dimensional Bingham fluid flow based on the method of regularization. Motivated by the Brezzi-Pitkäranta stabilized finite element method, the equal-order piecewise linear finite element approximation is used for both the velocity and the pressure. Based on Euler semi-implicit scheme, a fully discrete scheme is introduced. It is shown that the proposed fully discrete stabilized finite element scheme results in the h1/2 error order for the velocity in the discrete norms corresponding to L2(0,T;H1(Ω)2)∩L∞(0,T;L2(Ω)2).

Let Fq be a finite field with q elements and n a positive integer. In this paper, we use matrix method to give all primitive idempotents of irreducible cyclic codes of length n, whose prime divisors divide q-1.