基于Sum of Squares分解技术的电力系统鲁棒综合控制方法

针对具有不确定干扰的汽轮发电机励磁与汽阀综合控制系统,建立鲁棒综合控制模型。运用基于Sum of Squares(SOS)分解技术的鲁棒控制方法(SOSRCA),设计电力系统鲁棒综合控制方法。该方法充分考虑了综合系统中存在的不确定参数及干扰,使发电机组具有较好的鲁棒性能。控制方法的求解过程是算法化、程序化的,避免了繁琐的递归设计和参数估计过程。最后,在三机电力系统仿真中,对基于SOSRCA所得出的鲁棒综合控制律进行仿真分析与讨论,验证其有效性及优越性。

Robust Control Synthesis of Polynomial Nonlinear Systems Using Sum of Squares Technique

在这篇论文，广场(求救) 加技术被用来与多项式向量领域为不明确的仿射的非线性的系统的一个类分析柔韧的州的反馈合成问题。没有或与保证费用或 Hperformance 目的，足够的条件被给获得答案到上述控制问题。而且，如此的可解决的条件能以能被 SOS 技术直接处理的州的依赖线性矩阵不平等(LMI ) 作为求救编程问题被提出。而且，一个想法被提供由介绍一些额外的多项式描述多项式或甚至合理的矩阵的逆。一个数字例子被举说明途径的有效性。

Sums of Squares of Fibonacci Numbers with Prime Indices

In this paper we present some identities for the sums of squares of Fibonacci and Lucas numbers with consecutive primes, using maximal prime gap G(x)~log2x, as indices.

Sums of Squares of Polygonal Numbers

Polygonal numbers and sums of squares of primes are distinct fields of number theory. Here we consider sums of squares of consecutive (of order and rank) polygonal numbers. We try to express sums of squares of polygonal numbers of consecutive orders in matrix form. We also try to find the solution of a Diophantine equation in terms of polygonal numbers.

Application of Bayesian regularized BP neural network model for analysis of aquatic ecological data—A case study of chlorophyll-a prediction in Nanzui water area of Dongting Lake

Bayesian regularized BP neural network（BRBPNN） technique was applied in the chlorophyll-α prediction of Nanzui water area in Dongting Lake. Through BP network interpolation method, the input and output samples of the network were obtained. After the selection of input variables using stepwise/multiple linear regression method in SPSS i1.0 software, the BRBPNN model was established between chlorophyll-α and environmental parameters, biological parameters. The achieved optimal network structure was 3-11-1 with the correlation coefficients and the mean square errors for the training set and the test set as 0.999 and 0.000？8426, 0.981 and 0.0216 respectively. The sum of square weights between each input neuron and the hidden layer of optimal BRBPNN models of different structures indicated that the effect of individual input parameter on chlorophyll- α declined in the order of alga amount 〉 secchi disc depth（SD） 〉 electrical conductivity （EC）. Additionally, it also demonstrated that the contributions of these three factors were the maximal for the change of chlorophyll-α concentration, total phosphorus（TP） and total nitrogen（TN） were the minimal. All the results showed that BRBPNN model was capable of automated regularization parameter selection and thus it may ensure the excellent generation ability and robustness. Thus, this study laid the foundation for the application of BRBPNN model in the analysis of aquatic ecological data（chlorophyll-α prediction） and the explanation about the effective eutrophication treatment measures for Nanzui water area in Dongting Lake.

Some Implications of the Gessel Identity

We generalize the congruences of Friedmann-Tamarkine (1909), Lehmer (1938), and Ernvall-Metsänkyla (1991) on the sums of powers of integers weighted by powers of the Fermat quotients to the next Fermat quotient power, namely to the third power of the Fermat quotient. Using this result and the Gessel identity (2005) combined with our past work (2021), we are able to relate residues of some truncated convolutions of Bernoulli numbers with some Ernvall-Metsänkyla residues to residues of some full convolutions of the same kind. We also establish some congruences concerning other related weighted sums of powers of integers when these sums are weighted by some analogs of the Teichmüller characters.

Shift, the Law of the Invention of Zero

After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first of all by developing the any base calculation of these powers, then by calculating triangles following the example of the “arithmetical” triangle of Pascal and showing how the formula of the binomial of Newton is driving the construction. The author also develops the consequences of the axiom of linear algebra for the decimal writing of numbers and the result that this provides for the calculation of infinite sums of the inverse of integers to successive powers. Then the implications of these new forms of calculation on calculator technologies, with in particular the storage of triangles which calculate powers in any base and the use of a multiplication table in a very large canonical base are discussed.

A Constructive Method of Pandiagonal Magic Squares

By means of this approach, a constructive method of pandiagonal magic squares is proposed. Pandiagonalmagic squares of order mn can be generated via two ones which are orders m and n, respectively.

Information Protection Based on Extraction of Square Roots of Gaussian Integers

A cryptosystem based on computation of square roots of complex integers modulo composite n is described in this paper. This paper provides an algorithm extracting a square root of Gaussian integer. Various properties of square roots and a method for finding Gaussian generators are demonstrated. The generators can be instrumental in constructing other cryptosystems. It is shown how to significantly reduce average complexity of decryption per each block of ciphertext.

Asymptotic sum rate of MMSE receivers in multi-user distributed antenna systems

In this paper, the asymptotic sum rate of a multi-user distributed antenna system （DAS） is analyzed. To mitigate inter-user interference, minimum mean squared error （MMSE） receivers are utilized to cooperatively process received signals in the uplink. It shows that inter-user interference is efficiently mitigated and the uplink sum rate of a multi-user DAS is greatly improved by adopting MMSE receivers. For very large number of users and remote antennas, the asymptotic uplink sum rate of MMSE receivers is derived by using virtue of the random matrix theory, which can be The approximation is verified to be quite accurate by Monte Carlo simply calculated in an iterative way simulations.

On the Product of Integro Differential Equations and Their Solutions in Direct Sum Spaces

In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum spaces LZ（Ip）, p = 1,2 N of functions defined on each of the separate intervals with the case of one singular end-points and under suitable conditions on the function F that all solutions of the product quasi-integro differential equations are bounded and LZw -bounded on [0,b）.

A computational model of the human glucose-insulin regulatory system

Objective：A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced.The proposed method for the estimation of parameters for a system of ordinary differential equations（ODEs）that represent the time course of plasma glucose and insulin concentrations during glucose tolerance test（GTT）in physiological studies is presented.The aim of this study was to explore how to interpret those laboratory glucose and insulin data as well as enhance the Ackerman mathematical model.Methods：Parameters estimation for a system of ODEs was performed by minimizing the sum of squared residuals（SSR）function,which quantifies the difference between theoretical model predictions and GTT＇s experimental observations.Our proposed perturbation search and multiple-shooting methods were applied during the estimating process.Results：Based on the Ackerman＇s published data,we estimated the key parameters by applying R-based iterative computer programs.As a result,the theoretically simulated curves perfectly matched the experimental data points.Our model showed that the estimated parameters,computed frequency and period values,were proven a good indicator of diabetes.Conclusion：The present paper introduces a computational algorithm to biomedical problems,particularly to endocrinology and metabolism fields,which involves two coupled differential equations with four parameters describing the glucose-insulin regulatory system that Ackerman proposed earlier.The enhanced approach may provide clinicians in endocrinology and metabolism field insight into the transition nature of human metabolic mechanism from normal to impaired glucose tolerance.

Choice of estimation of unknown parameter under contaminated error model

The ε -contaminated normal distribution, ψ(Δ ) = (1 - ε )ψ0(Δ ) +εψ1 (Δ ), was considered as error model occurring in practice (ψ = probability function, Δ = observation error). The variances of the L1 (Least Absolute Sum) estimation and the L2 (Least Squares) estimation were compared with each other based on their asymptotic distribution. The revised L2 estimation was then derived. The conditions that the L1 estimation is superior to the L2 estimation and that the revised L2 estimation is superior to L1 estimation were discussed.

On Decompositions of Real Polynomials Using Mathematical Programming Methods

We present a procedure that gives us an SOS (sum of squares) decomposition of a given real polynomial in variables, if there exists such decomposition. For the case of real polynomials in non-commutative variables we extend this procedure to obtain a sum of hermitian squares SOHS) decomposition whenever there exists any. This extended procedure is the main scientific contribution of the paper.

ON THE UNIFORM STRONG APPROXIMATION OF MARCINKIEWICZ TYPE FOR MULTIVARIABLE CONTINUOUS FUNCTIONS

The rate of uniform strong approzimation of Marcinkiewicz type for multivariable continuous functions is obtained in this paper as follows：‖1/k＋1 ^k∑j=0 ｜Sj（f）-f｜^q‖≤C/k＋1^k∑j=0 Ej^q（f）,where Sj（f） denotes the square partial Fourier sum off and Ej（f） denotes the square best approximation of f by trigonometric polynomials of degree（j,j,…,j）,j=0,1,2.…

Computer program of nonlinear, curved regression for ‘probacent’-probability equation in biomedicine

On the basis of experimental observations on animals, applications to clinical data on patients and theoretical statistical reasoning, the author developed a com-puter-assisted general mathematical model of the ‘probacent’-probability equation, Equation (1) and death rate (mortality probability) equation, Equation (2) derivable from Equation (1) that may be applica-ble as a general approximation method to make use-ful predictions of probable outcomes in a variety of biomedical phenomena [1-4]. Equations (1) and (2) contain a constant, γ and c, respectively. In the pre-vious studies, the author used the least maximum- difference principle to determine these constants that were expected to best fit reported data, minimizing the deviation. In this study, the author uses the method of computer-assisted least sum of squares to determine the constants, γ and c in constructing the ‘probacent’-related formulas best fitting the NCHS- reported data on survival probabilities and death rates in the US total adult population for 2001. The results of this study reveal that the method of com-puter-assisted mathematical analysis with the least sum of squares seems to be simple, more accurate, convenient and preferable than the previously used least maximum-difference principle, and better fit-ting the NCHS-reported data on survival probabili-ties and death rates in the US total adult population. The computer program of curved regression for the ‘probacent’-probability and death rate equations may be helpful in research in biomedicine.

Choice of an Advanced Rheological Model for Modeling the Viscoelastic Behavior of Hot Mixtures Asphalt (HMA) from Sénégal (West Africa)

The main purpose of this article is to choose among advanced rheological models used in the French rational design, one that best represents the viscoelastic behavior of asphalt mixtures mixed with aggregates of Senegal. The model chosen will be the basis for the development of computational tools for stress and strain for Senegal. However, the calibration of these models needs complex modulus test results. In opposition to mechanical models the complex modulus can directly characterize the viscoelastic behavior of bituminous materials. Here determination is performed in the laboratory by using several types of tests divided into two groups: homogeneous tests and non-homogeneous tests. The choice of model will be carried out by statistical analysis through the least squares method. To this end, a study was carried out to “Laboratory of Pavement and Bituminous Materials” (LCMB) with asphalt concrete mixed with aggregate from Senegal named basalt of Diack and quartzite of Bakel. In this study, the test used to measure the complex modulus is the Canadian test method LC 26-700 (Determination of the complex modulus by tension-compression). There mainly exist two viewing complex modulus planes for laboratory test results: the Cole and Cole plane and the Black space. The uniqueness of the data points in these two areas means that studied asphalt concretes are thermorheologically simple and that the principle of time-temperature superposition can be applied. This means that the master curve may be drawn and that the same modulus value can be obtained for different pairs (frequency-temperature). These master curves are fitted during the calibration process by the advanced rheological models. One of the most used software in the French rational design for the visualization of complex modulus test results and calibration of rheological models developed tools is named Visco-analysis. In this study, its use in interpreting the complex modulus test results and calibration models shows that, the studied asphalt concretes are thermorheologically simple, because they present good uniqueness of their Black and Cole and Cole and Black diagrams. They allow a good application of the principle of time temperature superposition. The statistical analysis of calibration models by the least squares method has shown that the three studied models are suitable for modeling the linear viscoelastic behavior of asphalt mixtures formulated with the basalt of Diack and the quartzite of Bakel. Indeed their calibration has very similar precision values of “Sum of Squared Deviation” (SSD) about 0.185. However, the lower precision value (0.169) is obtained with the 2S2P1D model.

On the Distribution of Square-full Numbers

Let Q(x) be the number of square-full numbers not exceeding x, x is a suffciently large positive number. Assuming the Riemann hypothesis to be tenable, an asymptotic formula of Q(x) with a new error is obtained.

Selection of Design Parameters for Generalized Sphere Decoding Algorithms

Various efficient generalized sphere decoding (GSD) algorithms have been proposed to approach optimal ML performance for underdetermined linear systems, by transforming the original problem into the full-column-rank one so that standard SD can be fully applied. However, their design parameters are heuristically set based on observation or the possibility of an ill-conditioned transformed matrix can affect their searching efficiency. This paper presents a better transformation to alleviate the ill-conditioned structure and provides a systematic approach to select design parameters for various GSD algorithms in order to high efficiency. Simulation results on the searching performance confirm that the proposed techniques can provide significant improvement.

Global Avalanche Characteristics of Boolean Functions by Concatenation

In order to measure the correlation propeties of two Boolean functions,the global avalanche characteristics of Boolean functions constructed by concatenation are discussed,i.e.,f_1‖f_2and f_1‖f_2‖f_3‖f_4.Firstly,for the function f = f_1‖f_2,the cross-correlation function of f_1,f_2 in the special condition are studied.In this case,f,f_1,f_2 must be in desired form.By computing their sum-of-squares indicators,the crosscorrelation function between f_1,f_2 is obtained.Secondly,for the function g = f_1‖f_2‖f_3‖f_4,by analyzing the relation among their auto-correlation functions,their sum-of-squares indicators are investigated.Based on them,the sum-of-squares indicators of functions obtained by Canteaut et al.are investigated.The results show that the correlation property of g is good when the correlation properties of Boolean functions f_1,f_2,f_3,f_4 are good.