The Series of Reciprocals of Non-central Binomial Coefficients

Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients. As the result of splitting items, some identities of series of numbers values of reciprocals of binomial coefficients are given. The method of splitting terms offered in this paper is a new combinatorial analysis way and elementary method to create new series.

Zero-inflated non-central negative binomial distribution

In this article, the zero-inflated non-central negative binomial(ZINNB) distribution is introduced. Some of its basic properties are obtained. In addition, we use the maximum likelihood estimation method to estimate the parameters of the ZINNB distribution, and illustrate its application by fitting the actual data sets.

Determine the Eigen Function of Schrodinger Equation with Non-Central Potential by Using NU Method

So far, Schrodinger equation with central potential has been solved in different methods but solving this equation with non-central potentials is less dealt with. Solving such equations are way more difficult and complicated and a certain and limited number of non-central potentials can be solved. In this paper, we introduce one of the solvable kinds of such potentials and we will use NU method for solving Schrodinger equation and then by using this method we have calculated particular figures of its energy and function.

An Extension of the Non-central Wishart Distribution with Integer Shape Vector

This research paper deals with an extension of the non-central Wishart introduced in 1944 by Anderson and Girshick,that is the non-central Riesz distribution when the scale parameter is derived from a discrete vector.It is related to the matrix of normal samples with monotonous missing data.We characterize this distribution by means of its Laplace transform and we give an algorithm for generating it.Then we investigate,based on the method of the moment,the estimation of the parameters of the proposed model.The performance of the proposed estimators is evaluated by a numerical study.

Implementing an Optimal Energy Management System for a Set of Microgrids Using the Harmony Search Algorithm

A microgrid(MG)refers to a set of loads,generation resources and energy storage systems acting as a controllable load or a generator to supply power and heating to a local area.The MG-generated power management is a central topic for MG design and operation.The existence of dispersed generation(DG)resources has faced MG management with new issues.Depending on the level of exchanges between an MG and the main grid,the MG operation states can be divided into independent or grid-connected ones.Energy management in MGs aims to supply power at the lowest cost for optimal load response.This study examines MG energy management in two operational modes of islanded and grid-connected,and proposes a structure with two control layers(primary and secondary)for energy management.At the principal level of control,the energy management system is determined individually for all MG by taking into consideration the probability constraints and RES uncertainty by the Weibull the probability density function(PDF),generation resources’power as well as the generation surplus and deficit of each MG.Then,the information of the power surplus and deficit of each MG must be sent to the central energy management system.To confirm the proposed structure,a case system with two MGs and a condensive load is simulated by using a multi-time harmony search algorithm.Several scenarios are applied to evaluate the performance of this algorithm.The findings clearly show the effectiveness of the proposed system in the energy management of several MGs,leading to the optimal performance of the resources per MG.Moreover,the proposed control scheme properly controls the MG and grid’s performance in their interactions and offers a high level of robustness,stable behavior under different conditions and high quality of power supply.

Analysis of the Probability Model of Wind Load on the Offshore Wind Turbine

According to the actual measurement data, probability models of horizontal wind load were obtained based on wind velocity statistic and power spectral density function of fluctuating wind velocity through stochastic sampling and using spectrum analysis method. Through the comparison of two models, probability models of horizontal wind load based on probability models of fluctuating wind velocity were obtained by revising the mean and variance of fluctuating wind velocity. Results show that the variance takes lower value when the power spectral density function of fluctuating wind velocity is used to obtain the probability model of horizontal wind load. The quadratic term of fluctuating wind velocity takes a small contribution value in total wind load with almost no contribution to the model of horizontal wind load. It is convenient for practical engineering to obtain the models of horizontal wind load by using probability models of fluctuating wind velocity.

Ranking Independent Variables in Linear Models

In this article, the true model of sizep is considered. The importance of the independent variables will be studied. The model by dropping independent variable one at a time is called a reduced model, and the size of the model is p-1. The non-centrality quantity is employed to measure the strength of influence on the true model for the independent variable dropped. The larger influence is defined to be more important in the true model. In this article, the goal is ranking the importance of the independent variables to study the structure of the models. It is important in the practical application. The confidence interval approach is used to rank the degrees of the influence of the independent variables in linear models and achieve the goal. An illustrative example is given, and the modeling procedure is studied to check the assumptions step by step in this example to make sure the assumptions satisfied in the true model. As a result, the proposed method can be used efficiently.

Asymptotic distributions of non-central studentized statistics

Let X 1, ..., X n be independent and identically distributed random variables and W n = W n (X 1, ..., X n ) be an estimator of parameter ?. Denote T n = (W n ? ? 0)/s n , where s n 2 is a variance estimator of W n . In this paper a general result on the limiting distributions of the non-central studentized statistic T n is given. Especially, when s n 2 is the jacknife estimate of variance, it is shown that the limit could be normal, a weighted χ 2 distribution, a stable distribution, or a mixture of normal and stable distribution. Applications to the power of the studentized U- and L- tests are also discussed.

Non-Central Zone 3D Sound Field Reproduction for Multichannel System

The 22.2 multichannel system and its simplified system with 10-channel and 8-channel have been proposed, which brings people 3 D listening experience. But these systems could only accurately reproduce sound field at a central listening point which is called sweetspot. In order to solve this problem, this paper proposes a non-central zone sound field reproduction method PVMDZ（particle velocity matching between different zones） based on the physical property of sound. The proposed method matches the physical property of sound of non-central zone in reconstructed sound field with that of central zone in original sound field, so the reproduced non-central zone would produce the same listening experience as the central zone of the original system does. By experiments, we compare the performances of the proposed method with the traditional one, and the result proves that the sound field error of proposed method is reduced.

THE LIMITING DISTRIBUTIONS OF SOME SUBCLASSES OF THE GENERALIZED NON-CENTRAL t-DISTRIBUTION

A general theorem on the limiting distribution of the generalized t-distribution is obtained,many applications of this theorem to some subclasses of elliptically contoured distributions in cluding multivariate normal and multivariate t distributions are discussed.Further,their limiting distributions by density function are derived.

Echocardiographic and clinical outcomes of central versus non-central percutaneous edge-toedge repair of degenerative mitral regurgitation

ABSTRACT Objectives We aimed to assess the clinical and echocardiographic results of MitraClip implantation in non-central de- generative mitralregurgitation （dMR） compared to central dMR. Background It is unknown if the use of the MitraClip therapy in non-central dMR is as safe and effective as in central dMR.

Spatial distributions of magnetic field in the RHIC and LHC energy regions

Relativistic heavy-ion collisions can produce extremely strong magnetic fields in the collision regions. The spatial variation features of the magnetic fields are analyzed in detail for non-central Pb Pb collisions at LHC at √SNN= 900, 2760 and 7000 GeV and Au-Au collisions at RHIC at √SNN=62.4, 130 and 200 GeV. The dependencies of magnetic field on proper time, collision energies and impact parameters are investigated in this paper. It is shown that an enormous and highly inhomogeneous spatial distribution magnetic field can indeed be created in off-centre relativistic heavy-ion collisions in RHIC and LHC energy regions. The enormous magnetic field is produced just after the collision, and the magnitude of magnetic field of the LHC energy region is larger than that of the RHIC energy region at small proper time. It is found that the magnetic field in the LHC energy region decreases more quickly with the increase of proper time than that of the RHIC energy region.

Exact Solutions of the Morse-like Potential,Step-Up and Step-Down Operators via Laplace Transform Approach

We intend to realize the step-up and step-down operators of the potential V (x) = V1 e 2βx+V2 e βx. It is found that these operators satisfy the commutation relations for the SU(2) group. We find the eigenfunctions and the eigenvalues of the potential by using the Laplace transform approach to study the Lie algebra satisfied the ladder operators of the potential under consideration. Our results are similar to the ones obtained for the Morse potential (β→β).