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.

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.

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.

Comments on “General solutions of plane problem for power function curved cracks”

An error has been found in Ref. [1]. In the case of n = 2, authors of Ref. [1] suggested the following conformal mapping function：

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.

Study on Prediction Method of Structural Three-parameter Power Function P-S-N Curve

This paper applies weighted least square method to estimate the three-parameter power function equation of the fatigue life curve, and uses comprehensive fatigue life coefficient to correct the equation, and at the same time combines probability statistics method to bring out the prediction method of structure＇s three- parameter power function P-S-N curve, finally applies the prediction method to a ship＇s frame-type elevate, based on the fatigue test data of it＇s material-SA06 aluminium alloy, to obtain it＇s structure＇s three-parameter power function P-S-N curve. Compared with the conventional least square method, the presented method can give

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

为任何积极整数 n ，著名 Smarandache 力量功能 SP (n)被定义为最小的积极整数 m 以便 n|mm ，在 m 和 n 有一样的主要 divisors.The 的地方，这份报纸的主要目的正在使用基本方法学习包含 Smarandache 力量功能 SP (n)的一个方程的积极整数答案并且获得某有趣的 results.At 一样的时间，我们关于相关方程给一个开的问题。

Simulation on control of beam halo-chaos by power function in the hackle periodic-focusing channel

The K-V beam through a hackle periodic-focusing magnetic field is studied using the particle-core model. The beam halo-chaos is found, and a power function controller is proposed based on mechanism of halo formation and strategy of controlling halo-chaos. Multiparticle simulation was performed to control the halo by using the power function control method. The results show that the halo-chaos and its regeneration can be eliminated effectively. We also find that the radial particle density evolvement is of uniformity at the beam’s centre as long as appropriate parameters are chosen.

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.

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.

Asymptotic Expansion of Standardized χ^(p)(n) Distribution and Power Function of χ^(p)(n)-Test

Suppose that Y follows a χ^(p)-distribution with n degrees of freedom, and Z is the standardized form of Y. Let f(z,n,p) and F(z,n,p) denote the density function and the distribution function of Z, respectively. In this paper, we obtain the asymptotic expansion for f(z,n,p) and F(z,n,p). The validity of these results is illuminated by some numerical examples. We also investigate the power function of χ^(p)-test by the asymptotic expansion.

Quantifying the short-term dynamics of soil organic carbon decomposition using a power function model

Introduction:Soil heterotrophic respiration(Rh,an indicator of soil organic carbon decomposition)is an important carbon efflux of terrestrial ecosystems.However,the dynamics of soil Rh and its empirical relations with climatic factors have not been well understood.Methods:We incubated soils of three subtropical forests at five temperatures(10,17,24,31,and 38°C)and five moistures(20,40,60,80,and 100%water holding capacity(WHC))over 90 days.Rh was measured throughout the course of the incubation.Three types of models(log-linear,exponential,and power model)were fitted to the measurements and evaluated based on the coefficient of determination(r2)and Akaike Information Criterion(AIC)of the model.Further regression analysis was used to derive the empirical relations between model parameters and the two climatic factors.Results:Among the three models,the power function model(Rh=R1 t−k)performed the best in fitting the descending trend of soil Rh with incubation time(r2>0.69 for 26 of 30 models).Both R1 and k generally increased linearly with soil temperature but varied quadratically with soil moisture in the three forest soils.Conclusions:This study demonstrated that the power function model was much more accurate than the exponential decay model in describing the decomposition dynamics of soil organic carbon(SOC)in mineral soils of subtropical forests.The empirical relations and parameter values derived from this incubation study may be incorporated into process-based ecosystem models to simulate Rh responses to climate changes.

Low-power functionality of silicon-nanowire-assembled inverters on bendable plastics

In this paper, we demonstrate the low-power functionality of silicon nanowire （SiNW）-assembled inverters on bendable plastics. Our bendable inverters are capable of operating at supply voltages as low as 0.8 V with a switching （or standby） power consumption of -0.2 nW （or -6.6 pW）. The low-power inverting operation with a voltage gain of -18 is attributable to the near-ideal characteristics of the component transistors that have selectively thinned SiNW channels and exhibit low, symmetrical threshold voltages of 0.40 and -0.39 V and low subthreshold swing values of 81 and 65 mV/dec. Moreover, mechanical bendability reveals that the inverting operation has good, stable fatigue properties.

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.

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.

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.

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

光线的 Schrödinger 方程的分析解决方案被在这篇文章使用几个积极力量、反力量的潜在的函数的紧张的联合条件学习。而且，当光线的 Schrödinger 方程的潜力是 V (r)=α 1 r 8+α 2 r 3+α 3 r 2+β 3 r −1+β 2 r −3+β 1 r −4。一般来说，仅仅有一个近似答案，然而并非有几个潜力的重叠的 Schrödinger 方程的分析答案。然而，决定分析答案的存在的条件被发现了，分析答案和它的精力水平结构与在这篇论文上面被打手势的潜力为 Schrödinger 方程被获得。根据在一个量系统的波浪功能的单个值、有限、连续的标准，作者第一通过光线的并列 r → 解决 asymptotic 解决方案并且 r → 0；第二，他们使与附近的系列答案结合的 asymptotic 答案成为不规则的奇特的邻居；然后他们比较力量系列系数，由为光线的 Schrödinger 方程的在潜在的功能的系数之中的紧张的联合推出静止州的波浪功能和相应精力水平结构的一系列分析答案；并且最后，他们讨论答案并且做结论。

Polynomial Functions Composed of Terms with Non-Integer Powers

Polynomial functions containing terms with non-integer powers are studied to disclose possible approaches for obtaining their roots as well as employing them for curve-fitting purposes. Several special cases representing equations from different categories are investigated for their roots. Curve-fitting applications to physically meaningful data by the use of fractional functions are worked out in detail. Relevance of this rarely worked subject to solutions of fractional differential equations is pointed out and existing potential in related future work is emphasized.

The Separation of Powers from Functions and the Establishment of a New Structure of Management and Operation of State-owned Assets

The development of the socialist market economy demands the furtherintensification of the reform of the management operating system (MOS)of the state-owned assets, the strengthening of the efficiency in the man-agement of state-owned assets,and the improvement of the operating bene-