Design of Compliant Straight-line Mechanisms Using Flexural Joints

Straight-line compliant mechanisms are important building blocks to design a linear-motion stage, which is very useful in precision applications. However, only a few configurations of straight-line compliant mechanisms are applicable. To construct more kinds of them, an approach to design large-displacement straight-line flexural mechanisms with rotational flexural joints is proposed, which is based on a viewpoint that the straight-line motion is regarded as a compromise of rigid and compliant parasitic motion of a rotational flexural joint. An analytical design method based on the Taylor series expansion is proposed to quickly obtain an approximate solution. To illustrate and verify the proposed method, two kinds of flexural joints, cross-axis hinge and leaf-type isosceles-trapezoidal flexural（LITF） pivot are used to reconstruct straight-line flexural mechanisms. Their performances are obtained by analytic and FEA method respectively. The comparisons of the results show the accuracy of the approach. Both examples show that the proposed approach can convert a large-deflection flexural joint into approximate straight-line mechanism with a high linearity that is higher than 5 000 within 5 man displacement. This can lead to a new way to design, analyze or optimize straight-line flexure mechanisms.

The Odd-Point Ternary Approximating Schemes

We present a general formula to generate the family of odd-point ternary approximating subdivision schemes with a shape parameter for describing curves. The influence of parameter to the limit curves and the sufficient conditions of the continuities from C0 to C5 of 3- and 5-point schemes are discussed. Our family of 3-point and 5-point ternary schemes has higher order of derivative continuity than the family of 3-point and 5-point schemes presented by [Jian-ao Lian, On a-ary subdivision for curve design: II. 3-point and 5-point interpolatory schemes, Applications and Applied Mathematics: An International Journal, 3(2), 2008, 176-187]. Moreover, a 3-point ternary cubic B-spline is special case of our family of 3-point ternary scheme. The visual quality of schemes with examples is also demonstrated.

The <i>m</i>-Point Quaternary Approximating Subdivision Schemes

In this article, the objective is to introduce an algorithm to produce the quaternary m-point (for any integer m>1) approximating subdivision schemes, which have smaller support and higher smoothness, comparing to binary and ternary schemes. The proposed algorithm has been derived from uniform B-spline basis function using the Cox-de Boor recursion formula. In order to determine the convergence and smoothness of the proposed schemes, the Laurent polynomial method has been used.

Unification and Application of 3-point Approximating Subdivision Schemes of Varying Arity

In this paper, we propose and analyze a subdivision scheme which unifies 3-point approximating subdivision schemes of any arity in its compact form and has less support, computational cost and error bounds.? The usefulness of the scheme is illustrated by considering different examples along with its comparison with the established subdivision schemes. Moreover, B-splines of degree 4and well known 3-point schemes [1, 2, 3, 4, 6, 11, 12, 14, 15] are special cases of our proposed scheme.

Reconstruction of B-spline surface by interpolating boundary curves and approximating inner points

In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given bound- ary curves and simultaneously approximates some given inner points. The main idea of our method is： first, we construct an initial surface which interpolates the four given boundary curves; then, while keeping the boundary control points of the initial surface un- changed, we reposition the inner control points of the surface with energy optimization method. Examples show that our algorithm is practicable and effective.

Approximating and learning by Lipschitz kernel on the sphere

This paper investigates some approximation properties and learning rates of Lipschitz kernel on the sphere. A perfect convergence rate on the shifts of Lipschitz kernel on the sphere, which is faster than O（n-1/2）, is obtained, where n is the number of parameters needed in the approximation. By means of the approximation, a learning rate of regularized least square algorithm with the Lipschitz kernel on the sphere is also deduced.

A UNIFIED THREE POINT APPROXIMATING SUBDIVISION SCHEME

In this paper, we propose a three point approximating subdivision scheme, with three shape parameters, that unifies three different existing three point approximating schemes. Some sufficient conditions for subdivision curve C0 to C3 continuity and convergence of the scheme for generating tensor product surfaces for certain ranges of parameters by using Laurent polynomial method are discussed. The systems of curve and surface design based on our scheme have been developed successfully in garment CAD especially for clothes modelling.

On Approximating Two Distributions from a Single Complex-Valued Function

We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function and its Fourier transform. We show that this problem always has a solution within a specified degree of accuracy, provided the distributions satisfy the necessary regularity conditions. We describe the algorithm and construction of and provide examples of approximating several pairs of distributions using the algorithm.

Study on Numerical Comparison Method of Four-bar Straight-line Guidance Mechanism

In order to solve four-bar straight-line guidance mechanism synthesis problem for the arbitrarily given straight-line’s"angle requirement"and"point-position requirement",a numerical comparison synthesis method for single and double straight-line guidance mechanism is presented,which is convenient to realize by computer program.The basic idea of this method is:to select a four-bar linkage whose relative bar length of crank is 1 as a basic four-bar linkage.Then the other three relative bars’length is changed,and a lot of basic four-bar linkage can be obtained.There are many single and double ball-points of each basic four-bar linkage.With the motion of a basic four-bar linkage,there is straight-line segment of each Ball-point’s path.The data of these basic four-bar linkages is saved to a database.When designing a four-bar straight-line guidance mechanism,the design data is compared with the data in database and a satisfactory four-bar linkage can be obtained.The method effectively solves the straight-line guidance mechanism synthesis problem.

The Straight-Line Depreciation Method Used by Selected Companies and Educational Institutions in the Philippines

The straight-line method in computing for depreciation expense is the prevailing method used in the Philippines. This paper aims to determine the rationale behind the use of this method. The objective of the study is to determine the length of time within which the depreciation method is used, reasons in using the method, the rate of depreciation used by the companies, and the effects of the depreciation expense on their operating expenses. It also determines if the companies＇ decisions to use the straight-line method are influenced by the factors mentioned by Reynolds （196 I）----expected amount of services over the life of assets, the amount and timing of operating costs, the decline in the physical efficiency of the assets, and the rate of return--and if they considered capital investments and tax reduction in using this method. The study shows that companies and educational institutions use the straight-line method of computing depreciation expenses, because it is easy to use in computing the depreciation expenses, in comparing with previous years＇ computations, and in keeping track of the expenses. It is also convenient for tax administration and financial reporting. The rate of depreciation used varies, because the companies and educational institutions use their past experiences in determining the life of fixed assets. The percentage of depreciation to the operating expenses also varies. The companies and educational institutions adhered to the factors mentioned by Reynolds （1961） in choosing the straight-line method of depreciation. The companies did not consider reduction of tax in using the straight-line method.

The 4-Point α-Ary Approximating Subdivision Scheme

A general formula for 4-point α-Ary approximating subdivision scheme for curve designing is introduced for any arity α≥2. The new scheme is extension of B-spline of degree 6. Laurent polynomial method is used to investigate the continuity of the scheme. The variety of effects can be achieved in correspondence for different values of parameter. The applications of the proposed scheme are illustrated in comparison with the established subdivision schemes.

A novel method for simulating nuclear explosion with chemical explosion to form an approximate plane wave: Field test and numerical simulation

A nuclear explosion in the rock mass medium can produce strong shock waves,seismic shocks,and other destructive effects,which can cause extreme damage to the underground protection infrastructures.With the increase in nuclear explosion power,underground protection engineering enabled by explosion-proof impact theory and technology ushered in a new challenge.This paper proposes to simulate nuclear explosion tests with on-site chemical explosion tests in the form of multi-hole explosions.First,the mechanism of using multi-hole simultaneous blasting to simulate a nuclear explosion to generate approximate plane waves was analyzed.The plane pressure curve at the vault of the underground protective tunnel under the action of the multi-hole simultaneous blasting was then obtained using the impact test in the rock mass at the site.According to the peak pressure at the vault plane,it was divided into three regions:the stress superposition region,the superposition region after surface reflection,and the approximate plane stress wave zone.A numerical simulation approach was developed using PFC and FLAC to study the peak particle velocity in the surrounding rock of the underground protective cave under the action of multi-hole blasting.The time-history curves of pressure and peak pressure partition obtained by the on-site multi-hole simultaneous blasting test and numerical simulation were compared and analyzed,to verify the correctness and rationality of the formation of an approximate plane wave in the simulated nuclear explosion.This comparison and analysis also provided a theoretical foundation and some research ideas for the ensuing study on the impact of a nuclear explosion.

A constructive method for approximating trigonometric functions and their integrals

This paper presents an interpolation-based method(IBM)for approximating some trigonometric functions or their integrals as well.It provides two-sided bounds for each function,which also achieves much better approximation effects than those of prevailing methods.In principle,the IBM can be applied for bounding more bounded smooth functions and their integrals as well,and its applications include approximating the integral of sin(x)/x function and improving the famous square root inequalities.

A Regularization Method for Approximating the Inverse Laplace Transform

A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Fourier transformation are easily applied. We finally obtain a regularized approximation to the inverse Laplace transform as finite sum

A Ternary 4-Point Approximating Subdivision Scheme

In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new insertion control points on a finer grid are computed by weighted sums of already existing control points. In the limit of the recursive process, data is defined on a dense set of point, The objective is to find an improved subdivision approximating algorithm which has a smaller support and a higher approximating order. The author chooses a ternary scheme because the best way to get a smaller support is to pass from the binary to ternary or complex algorithm and uses polynomial reproducing propriety to get higher approximation order. Using the cardinal Lagrange polynomials the author has proposed a 4-point approximating ternary subdivision algorithm and found that a higher regularity of limit function does not guarantee a higher approximating order. The proposed 4-point ternary approximation subdivision family algorithms with the mask a have the limit function in C2 and have approximation order 4. Also the author has demonstrated that in this class there is no algorithm whose limit function is in C3. It can be seen that this stationary ternary 4-point approximating symmetrical subdivision algorithm has a lower computational cost than the 6-point binary approximation subdivision algorithm for a greater range of points.

Evolutionary Safe Padé Approximation Scheme for Dynamical Study of Nonlinear Cervical Human Papilloma Virus Infection Model

This study proposes a structure-preserving evolutionary framework to find a semi-analytical approximate solution for a nonlinear cervical cancer epidemic(CCE)model.The underlying CCE model lacks a closed-form exact solution.Numerical solutions obtained through traditional finite difference schemes do not ensure the preservation of the model’s necessary properties,such as positivity,boundedness,and feasibility.Therefore,the development of structure-preserving semi-analytical approaches is always necessary.This research introduces an intelligently supervised computational paradigm to solve the underlying CCE model’s physical properties by formulating an equivalent unconstrained optimization problem.Singularity-free safe Padérational functions approximate the mathematical shape of state variables,while the model’s physical requirements are treated as problem constraints.The primary model of the governing differential equations is imposed to minimize the error between approximate solutions.An evolutionary algorithm,the Genetic Algorithm with Multi-Parent Crossover(GA-MPC),executes the optimization task.The resulting method is the Evolutionary Safe PadéApproximation(ESPA)scheme.The proof of unconditional convergence of the ESPA scheme on the CCE model is supported by numerical simulations.The performance of the ESPA scheme on the CCE model is thoroughly investigated by considering various orders of non-singular Padéapproximants.

Approximately Bi-Similar Symbolic Model for Discretetime Interconnected Switched System

Dear Editor,This letter concerns the development of approximately bi-similar symbolic models for a discrete-time interconnected switched system(DT-ISS).The DT-ISS under consideration is formed by connecting multiple switched systems known as component switched systems(CSSs).Although the problem of constructing approximately bi-similar symbolic models for DT-ISS has been addressed in some literature,the previous works have relied on the assumption that all the subsystems of CSSs are incrementally input-state stable.

Determining Hubbard U of VO_(2) by the quasi-harmonic approximation

Vanadium dioxide VO_(2) is a strongly correlated material that undergoes a metal-to-insulator transition around 340 K.In order to describe the electron correlation effects in VO_(2), the DFT+U method is commonly employed in calculations.However, the choice of the Hubbard U parameter has been a subject of debate and its value has been reported over a wide range. In this paper, taking focus on the phase transition behavior of VO_(2), the Hubbard U parameter for vanadium oxide is determined by using the quasi-harmonic approximation(QHA). First-principles calculations demonstrate that the phase transition temperature can be modulated by varying the U values. The phase transition temperature can be well reproduced by the calculations using the Perdew–Burke–Ernzerhof functional combined with the U parameter of 1.5eV. Additionally,the calculated band structure, insulating or metallic properties, and phonon dispersion with this U value are in line with experimental observations. By employing the QHA to determine the Hubbard U parameter, this study provides valuable insights into the phase transition behavior of VO_(2). The findings highlight the importance of electron correlation effects in accurately describing the properties of this material. The agreement between the calculated results and experimental observations further validates the chosen U value and supports the use of the DFT+U method in studying VO_(2).

Saddlepoint Approximation Method in Reliability Analysis:A Review

The escalating need for reliability analysis(RA)and reliability-based design optimization(RBDO)within engineering challenges has prompted the advancement of saddlepoint approximationmethods(SAM)tailored for such problems.This article offers a detailed overview of the general SAM and summarizes the method characteristics first.Subsequently,recent enhancements in the SAM theoretical framework are assessed.Notably,the mean value first-order saddlepoint approximation(MVFOSA)bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation(MVSOSA);the latter serves as an auxiliary approach to the former.Their distinction is rooted in the varying expansion orders of the performance function as implemented through the Taylor method.Both the saddlepoint approximation and third-moment(SATM)and saddlepoint approximation and fourth-moment(SAFM)strategies model the cumulant generating function(CGF)by leveraging the initial random moments of the function.Although their optimal application domains diverge,each method consistently ensures superior relative precision,enhanced efficiency,and sustained stability.Every method elucidated is exemplified through pertinent RA or RBDO scenarios.By juxtaposing them against alternative strategies,the efficacy of these methods becomes evident.The outcomes proffered are subsequently employed as a foundation for contemplating prospective theoretical and practical research endeavors concerning SAMs.The main purpose and value of this article is to review the SAM and reliability-related issues,which can provide some reference and inspiration for future research scholars in this field.

Gamma Approximation Based Multi-Antenna Covert Communication Detection

Covert communication technology makes wireless communication more secure,but it also provides more opportunities for illegal users to transmit harmful information.In order to detect the illegal covert communication of the lawbreakers in real time for subsequent processing,this paper proposes a Gamma approximation-based detection method for multi-antenna covert communication systems.Specifically,the Gamma approximation property is used to calculate the miss detection rate and false alarm rate of the monitor firstly.Then the optimization problem to minimize the sum of the missed detection rate and the false alarm rate is proposed.The optimal detection threshold and the minimum error detection probability are solved according to the properties of the Lambert W function.Finally,simulation results are given to demonstrate the effectiveness of the proposed method.