Size-dependent vibration and buckling of porous functionally graded microplates based on modified couple stress theory in thermal environments by considering a dual power-law distribution of scale effects

In this study,the thermodynamic behaviors of the intrinsic frequency and buckling temperature of rectangular plates of functionally graded materials(FGMs)are explored based on the modified couple stress theory(MCST)and the novel dual powerlaw scale distribution theory.The effects of linear,homogeneous,and non-homogeneous temperature fields on the frequency and buckling temperature of FGM microplates are evaluated in detail.The results show that the porosity greatly affects the mechanical properties of FGM plates,reducing their frequency and flexural temperature compared with non-porous plates.Different temperature profiles alter plate frequencies and buckling temperatures.The presence and pattern of scale effect parameters are also shown to be crucial for the mechanical response of FGM plates.The present research aims to provide precise guidelines for the micro-electro-mechanical system(MEMS)fabrication by elucidating the complex interplay between thermal,material,and structural factors that affect the performance of FGM plates in advanced applications.

Risk-Balanced Routing Strategy for Service Function Chains of Cyber-Physical Power System Considering Cross-Space Cascading Failure

Cyber-physical power system(CPPS)has significantly improved the operational efficiency of power systems.However,cross-space cascading failures may occur due to the coupling characteristics,which poses a great threat to the safety and reliability of CPPS,and there is an acute need to reduce the probability of these failures.Towards this end,this paper first proposes a cascading failure index to identify and quantify the importance of different information in the same class of communication services.On this basis,a joint improved risk-balanced service function chain routing strategy(SFC-RS)is proposed,which is modeled as a robust optimization problem and solved by column-and-constraint generation(C-CG)algorithm.Compared with the traditional shortest-path routing algorithm,the superiority of SFC-RS is verified in the IEEE 30-bus system.The results demonstrate that SFC-RS effectively mitigates the risk associated with information transmission in the network,enhances information transmission accessibility,and effectively limits communication disruption from becoming the cause of cross-space cascading failures.

Evaluation of Generalized Error Function via Fast-Converging Power Series

A generalized form of the error function, Gp(x)=pΓ(1/p)∫0xe−tpdt, which is directly associated with the gamma function, is evaluated for arbitrary real values of p>1and 0x≤+∞by employing a fast-converging power series expansion developed in resolving the so-called Grandi’s paradox. Comparisons with accurate tabulated values for well-known cases such as the error function are presented using the expansions truncated at various orders.

Low-Power CMOS IC for Function Electrical Stimulation of Nerves

A low-power IC for function electrical stimulation （FES） of nerves is designed for an implantable system and fabricated in CSMC＇s 0.6μm CMOS technology. The IC can be used for stimulating animals＇ spinal nerve bundles and other nerves connected with a cuff type electrode. It consists of a pre-amplifier,a main amplifier,and an output stage. According to the neural signal spectrum,the bandwidth of the FES signal generator circuit is defined from 1Hz to 400kHz. The gain of the circuit is about 66dB with an output impedance of 900. The 1C can function under a single supply voltage of 3-5V. A rail-to-rail output stage helps to use the coupled power efficiently. The measured time domain performance shows that the bandwidth and the gain of the IC agree with the design. The power consumption is lower than 6mW.

A power function model for simulating creep mechanical properties of salt rock

In this paper,a new micro-creep model of salt rock is proposed based on a linear parallel bonded model(LPBM)using the two-dimensional particle flow code(PFC2D).The power function weakening form is assumed to describe the variation of the parallel bonded diameter(PBD)over time.By comparing with the parallel-bonded stress corrosion(PSC)model,a smaller stress fluctuation and smoother creep strain−time curves can be obtained by this power function model at the same stress level.The validity and adaptability of the model to simulate creep deformation of salt rock are verified through comparing the laboratory creep test curves and the Burgers model fitting result.The numerical results reveal that this model can be capable of capturing the creep deformation and damage behavior from the laboratory observations.

The invariant of the stiffness filter function with the weight filter function of the power function form

Based on the independent, continuous and map- ping （ICM） method and homogenization method, a research model is constructed to propose and deduce a theorem and corollary from the invariant between the weight filter func- tion and the corresponding stiffness filter function of the form of power function. The efficiency in searching for op- timum solution will be raised via the choice of rational filter functions, so the above mentioned results are very important to the further study of structural topology optimization.

Analysis of Stability and Large Deflection Buckle of Rolled Strip by Third Power B-Spline Function Method

A new method——the third power B-spline function method is developed to analyse the stability and the buckle of rolled strip under residual stress.The large deflection theory of thin plate is used to calculate the buckle of rolled strip and criterion of critical buckle is given.The computed results tally with those of experiment well,which provides theoretical basis and method for developing the mathematical model of flatness control.

Modeling Distortion Signals of Power Grid Based on Wiener-G Functionals

The uniform mathematical model of distortion signals in power grid has been setup with the theory of Wiener-G Functional. Firstly,the Matlab simulation models were established. Secondly,the Wiener kernel of power load was found based on the Gaussian white noise as input. And then the uniform mathematical model of the power grid signal was established according to the homogeneous of the same order of Wiener functional series. Finally,taking three typical distortion sources which are semiconductor rectifier,electric locomotive and electric arc furnace in power grid as examples,we have validated the model through the Matlab simulation and analyzed the simulation errors. The results show that the uniform mathematical model of distortion signals in power grid can approximation the actual model by growing the items of the series under the condition of the enough storage space and computing speed.

The Analytic Solution of Schrdinger Equation with Potential Function Superposed by Six Terms with Positive-power and Inverse-power Potentials

The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrodinger equation is V（r） =α1r^8 ＋α2r^3 ＋ α3r^2 ＋β3r^-1 ＋β2r^-3 ＋β1r6-4. Generally speaking, there is only an approximate solution, but not analytic solution for SchrSdinger equation with several potentials＇ superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrodinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → ∞ and r →0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial SchrSdinger equation; and lastly, they discuss the solutions and make conclusions.

Multi-group pin power reconstruction method based on colorset form functions

A multi-group pin power reconstruction method that fully exploits nodal information obtained from global coarse mesh solution has been developed.It expands the intra-nodal flux distributions into nonseparable semi-analytic basis functions,and a colorset based form function generating method is proposed,which can accurately model the spectral interaction occurring at assembly interface.To demonstrate its accuracy and applicability to realistic problems, the new method is tested against two benchmark problems,including a mixed-oxide fuel problem.The results show that the new method is comparable in accuracy to fine-mesh methods.

General solutions of plane problem for power function curved cracks

A new exact and universal conformal mapping is proposed. Using Muskhelishvili＇s complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natural number, and the general solutions of the stress intensity factors （SIFs） for mode I and mode II at the crack tip are obtained under the remotely uniform tensile loads. The present results can be reduced to the well-known solutions when the power of the function takes different natural numbers. Numerical examples are conducted to reveal the effects of the coefficient, the power, and the projected length along the x-axis of the power function curved crack on the SIFs for mode I and mode II.

Investigations into Some Simple Expressions of the Gamma Function in Wind Power Theoretical Estimate by the Weibull Distribution

The Weibull distribution is a probability density function (PDF) which is widely used in the study of meteorological data. The statistical analysis of the wind speed v by using the Weibull distribution leads to the estimate of the mean wind speed , the variance of v around and the mean power density in the wind. The gamma function Γ is involved in those calculations, particularly Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k). The paper reports the use of the Weibull PDF f(v) to estimate the gamma function. The study was performed by looking for the wind speeds related to the maximum values of f(v), v2 f(v) and v3 f(v). As a result, some approximate relationships were obtained for Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k), that use some fitting polynomial functions. Very good agreements were found between the exact and the estimated values of Γ (1+n/k) that can be used for the estimation of the mean wind speed , the variance σ2 of the wind speed v;around the mean speed and the average wind power density.

Modulating properties by light ion irradiation:From novel functional materials to semiconductor power devices

In this review,the application of light ion irradiation is discussed for tailoring novel functional materials and for improving the performance in SiC or Si based electrical power devices.The deep traps and electronic disorder produced by light ion irradiation can modify the electrical,magnetic,and optical properties of films(e.g.,dilute ferromagnetic semiconductors and topological materials).Additionally,benefiting from the high reproducibility,precise manipulation of functional depth and density of defects,as well as the flexible patternability,the helium or proton ion irradiation has been successfully employed in improving the dynamic performance of SiC and Si based PiN diode power devices by reducing their majority carrier lifetime,although the static performance is sacrificed due to deep level traps.Such a trade-off has been regarded as the key point to compromise the static and dynamic performances of power devices.As a result,herein the light ion irradiation is highlighted in both exploring new physics and optimizing the performance in functional materials and electrical devices.

Characterization of Power-Function Distribution through Expectation

For the characterization of the power function distribution, one needs any arbitrary non constant function only in place of independence of suitable function of order statistics, linear relation of conditional expectation, recurrence relations between expectations of function of order statistics, distributional properties of exponential distribution, record valves, lower record statistics, product of order statistics and Lorenz curve, etc. available in the literature. The goal of this research is not to give a different path-breaking approach for the characterization of power function distribution through the expectation of non constant function of random variable and provide a method to characterize the power function distribution as remark. Examples are given for the illustrative purpose.

Series Representation of Power Function

This paper presents the way to make expansion for the next form function: to the numerical series. The most widely used methods to solve this problem are Newtons Binomial Theorem and Fundamental Theorem of Calculus (that is, derivative and integral are inverse operators). The paper provides the other kind of solution, except above described theorems.

On the Solutions of an Equation Involving the Smarandache Power Function SP（n）

For any positive integer n, the famous Smarandache power function SP（n） is defined as the smallest positive integer m such that n｜m^m, where m and n have the same prime divisors. The main purpose of this paper is using the elementary methods to study the positive integer solutions of an equation involving the Smarandache power function SP（n） and obtain some interesting results. At the same time, we give an open problem about the related equation.

Control Charts for the Shape Parameter of Power Function Distribution under Different Classical Estimators

In practice,the control charts for monitoring of process mean are based on the normality assumption.But the performance of the control charts is seriously affected if the process of quality characteristics departs from normality.For such situations,we have modified the already existing control charts such as Shewhart control chart,exponentially weighted moving average(EWMA)control chart and hybrid exponentially weighted moving average(HEWMA)control chart by assuming that the distribution of underlying process follows Power function distribution(PFD).By considering the situation that the parameters of PFD are unknown,we estimate them by using three classical estimation methods,i.e.,percentile estimator(P.E),maximum likelihood estimator(MLE)and modified maximum likelihood estimator(MMLE).We construct Shewhart,EWMA and HEWMA control charts based on P.E,MLE and MMLE.We have compared all these control charts using Monte Carlo simulation studies and concluded that HEWMA control chart under MLE is more sensitive to detect an early shift in the shape parameter when the distribution of the underlying process follows power function distribution.

Computational Precision of the Power Function for Conditional Tests of Assumptions of the Rasch Model

Draxler and Zessin [1] derived the power function for a class of conditional tests of assumptions of a psychometric model known as the Rasch model and suggested an MCMC approach developed by Verhelst [2] for the numerical approximation of the power of the tests. In this contribution, the precision of the Verhelst approach is investigated and compared with an exact sampling procedure proposed by Miller and Harrison [3] for which the discrete probability distribution to be sampled from is exactly known. Results show no substantial differences between the two numerical procedures and quite accurate power computations. Regarding the question of computing time the Verhelst approach will have to be considered much more efficient.

Average Power Function of Noise and Its Applications in Seasonal Time Series Modeling and Forecasting

This paper presents a new method of detecting multi-periodicities in a seasonal time series. Conventional methods such as the average power spectrum or the autocorrelation function plot have been used in detecting multiple periodicities. However, there are numerous cases where those methods either fail, or lead to incorrectly detected periods. This, in turn in applications, produces improper models and results in larger forecasting errors. There is a strong need for a new approach to detecting multi-periodicities. This paper tends to fill this gap by proposing a new method which relies on a mathematical instrument, called the Average Power Function of Noise (APFN) of a time series. APFN has a prominent property that it has a strict local minimum at each period of the time series. This characteristic helps one in detecting periods in time series. Unlike the power spectrum method where it is assumed that the time series is composed of sinusoidal functions of different frequencies, in APFN it is assumed that the time series is periodic, the unique and a much weaker assumption. Therefore, this new instrument is expected to be more powerful in multi-periodicity detection than both the autocorrelation function plot and the average power spectrum. Properties of APFN and applications of the new method in periodicity detection and in forecasting are presented.

Taking into Account of Functional Constraints in Optimization of Modes of Power Systems by Genetic Algorithms

The development of the capabilities of computational tools has created up new possibilities for the effective use of a number of classical mathematical methods and algorithms for solving many important problems in the power engineering. In particular, a set of algorithms are developed to optimize the modes of electric power systems based on genetic algorithms. At the same time, the issues of taking into account functional constraints in solving such problems by genetic algorithms need to be improved. In accordance with it in this article the problems of taking into account of different constraints in optimization of modes of power systems using genetic algorithms are considered. The algorithm of optimization by genetic algorithm taking into account of functional constraints in forms of equality and inequality by penalty functions is proposed. The results of research of proposed algorithm’s efficiency in example of optimization of mode of power system with 8 buses, 4 thermal power plants and 3 transmission lines with controlled power flow are presented.