ESTIMATION OF THE NUMBER OF CORRELATED SOURCES WITH COMMON FREQUENCIES BASED ON POWER SPECTRAL DENSITY

Blind source separation and estimation of the number of sources usually demand that the number of sensors should be greater than or equal to that of the sources, which, however, is very difficult to satisfy for the complex systems. A new estimating method based on power spectral density （PSD） is presented. When the relation between the number of sensors and that of sources is unknown, the PSD matrix is first obtained by the ratio of PSD of the observation signals, and then the bound of the number of correlated sources with common frequencies can be estimated by comparing every column vector of PSD matrix. The effectiveness of the proposed method is verified by theoretical analysis and experiments, and the influence of noise on the estimation of number of source is simulated.

POWER VECTORS,COMBINATORIAL VECTOR NUMBERS AND ITS THEORY OF FUNCTIONS

This paper syggests the power vector and the vector power series. The vector power series is a 'Combinatorial Vector Number' which is composed of a real number and a certain vector. Combinatorial rector variable and its functions have an important meaning. They have the fundamental operations of arithemetic too. From the theoretical analysis of functions for a combinatorial vector variable we would would know its function has the derivatives. the necessary and sufficient conditions. These conditions make up the charaders of 'Hyperbolic equation' and its integralions.

On the Expression of Composite Natural Numbers as Tensorial Products of Prime Natural Powers Vectors

This study describes how one can construct sets of composite natural numbers as tensorial products of the vectors created with the natural powers of prime numbers.

The Formula of General Term of the Sum of Equal Powers of Natural Numbers

The formula of general term of the sum of equal powers of natural numbers.

The Powers Sums, Bernoulli Numbers, Bernoulli Polynomials Rethinked

Utilizing translation operators we get the powers sums on arithmetic progressions and the Bernoulli polynomials of order munder the form of differential operators acting on monomials. It follows that (d/dn-d/dz) applied on a power sum has a meaning and is exactly equal to the Bernoulli polynomial of the same order. From this new property we get the formula giving powers sums in term of sums of successive derivatives of Bernoulli polynomial multiplied withprimitives of the same order of n. Then by changing the two arguments z,n into Z=z(z-1), λ where λ designed the 1st order power sums and proving that Bernoulli polynomials of odd order vanish for arguments equal to 0, 1/2, 1, we obtain easily the Faulhaber formula for powers sums in term of polynomials in λ having coefficients depending on Z. These coefficients are found to be derivatives of odd powers sums on integers expressed in Z. By the way we obtain the link between Faulhaber formulae for powers sums on integers and on arithmetic progressions. To complete the work we propose tables for calculating in easiest manners possibly the Bernoulli numbers, the Bernoulli polynomials, the powers sums and the Faulhaber formula for powers sums.

Fuzzy Risk Assessment Model of Power Transformer Based on Borda Number Theory

The power transformer is the key equipment of transforming voltage and exchanging power in the power system.It's safe and reliable operation directly influences the safe level of the power system.To study the risk assessment of power transformer which is very significant to improve the reliability of the power system,a fuzzy comprehensive risk assessment model of power transformer based on Borda number theory is proposed in this paper.At first,the fault types and risk factors of the power transformer are analyzed.Secondly,the basic framework of the fuzzy comprehensive evaluation is applied to quantify the risk factors.And then,Borda number theory is employed to analyze influence degree and occurrence probability of power transformer.At last,the various risk factors impact index and fuzzy comprehensive evaluation index of power transformer can be easily obtained.Applying this model,the relative importance degree of the risk factors can be horizontally compared according to the numerical index,the engineering staff can directly get the parameters of the transformer risk level and get a good description of the visual expression through using 5 score and similar visual language.

Selection of Coherent and Concise Formulae on Bernoulli Polynomials-Numbers-Series and Power Sums-Faulhaber Problems

Utilizing the translation operator to represent Bernoulli polynomials and power sums as polynomials of Sheffer-type, we obtain concisely almost all their known properties as so as many new ones, especially new recursion relations for calculating Bernoulli polynomials and numbers, new formulae for obtaining power sums of entire and complex numbers. Then by the change of arguments from z into Z = z(z-1) and n into λ which is the 1st order power sum we obtain the Faulhaber formula for powers sums in term of polynomials in λ having coefficients depending on Z. Practically we give tables for calculating in easiest possible manners, the Bernoulli numbers, polynomials, the general powers sums.

A Novel Power Optimization Method by Minimum Comparator Number Algorithm for Pipeline ADCs

The effects of stage numbers on power dissipation of pipeline analog-to-digital converter （ADC） are studied and a novel design method aiming for power optimization is presented. In this method, a minimum comparator number algorithm （MCNA） is first introduced, and then the optimum distribution of resolutions through pipeline ADC stages is deduced by MCNA. Based on the optimum stage-resolution distribution, an optimization method is established, which examines the precise function between ADC power and stage resolutions with a parameter of power ratio （Rp）. For 10-bit pipeline ADC with scaling down technology, the simulation results by using MATLAB CAD tools show that an eight-stage topology with 1-bit RSD correction achieves the power optimization indicated by the power reduction ratio.

Power and Cross-Spectra for the Turbulent Atmospheric Motion and Transports in the Domain of Wave Number Frequency Space: Theoretical Aspects

The study of large-scale atmospheric turbulence and transport processes is of vital importance in the general circulation of the atmosphere. The governing equations of the power and cross-spectra for the atmospheric motion and transports in the domain of wave number frequency space have been derived. The contributions of the nonlinear interactions of the atmospheric waves in velocity and temperature fields to the conversion of kinetic and potential energies and to the meridional transports of angular momentum and sensible heat in the atmosphere have been discussed.

Laminar natural convection characteristics in an enclosure with heated hexagonal block for non-Newtonian power law fluids

This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or uniform heat flux(UHF) thermal conditions. Governing equations(mass, momentum and energy) are solved by using finite volume method(FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number(10~3≤ Gr ≤ 10~6), Prandtl number(1 ≤ Pr ≤ 100) and power law index(0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection(j_(nH)). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design 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.

Linguistic Single-Valued Neutrosophic Power Aggregation Operators and Their Applications to Group Decision-Making Problems

Linguistic single-valued neutrosophic set(LSVNS)is a more reliable tool,which is designed to handle the uncertainties of the situations involving the qualitative data.In the present manuscript,we introduce some power aggregation operators(AOs)for the LSVNSs,whose purpose is to diminish the influence of inevitable arguments about the decision-making process.For it,first we develop some averaging power operators,namely,linguistic single-valued neutrosophic(LSVN)power averaging,weighted average,ordered weighted average,and hybrid averaging AOs along with their desirable properties.Further,we extend it to the geometric power AOs for LSVNSs.Based on the proposed work;an approach to solve the group decision-making problems is given along with the numerical example.Finally,a comparative study and the validity tests are present to discuss the reliability of the proposed operators.

Stability of GM(1,1) power model on vector transformation

The morbidity problem of the GM（1,1） power model in parameter identification is discussed by using multiple and rotation transformation of vectors. Firstly we consider the morbidity problem of the special matrix and prove that the condition number of the coefficient matrix is determined by the ratio of lengths and the included angle of the column vector, which could be adjusted by multiple and rotation transformation to turn the matrix to a well-conditioned one. Then partition the corresponding matrix of the GM（1,1） power model in accordance with the column vector and regulate the matrix to a well-conditioned one by multiple and rotation transformation of vectors, which completely solve the instability problem of the GM（1,1） power model. Numerical results show that vector transformation is a new method in studying the stability problem of the GM（1,1） power model.

Ant Colony Optimization Approach Based Genetic Algorithms for Multiobjective Optimal Power Flow Problem under Fuzziness

In this paper, a new optimization system based genetic algorithm is presented. Our approach integrates the merits of both ant colony optimization and genetic algorithm and it has two characteristic features. Firstly, since there is instabilities in the global market, implications of global financial crisis and the rapid fluctuations of prices, a fuzzy representation of the optimal power flow problem has been defined, where the input data involve many parameters whose possible values may be assigned by the expert. Secondly, by enhancing ant colony optimization through genetic algorithm, a strong robustness and more effectively algorithm was created. Also, stable Pareto set of solutions has been detected, where in a practical sense only Pareto optimal solutions that are stable are of interest since there are always uncertainties associated with efficiency data. The results on the standard IEEE systems demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto optimal nondominated solutions of the multiobjective OPF.

Mechanisms for non-ideal flow in low-power arc-heated supersonic nozzles

The flow in a low-powered arc gas heater com- bined with a supersonic nozzle of throat diameter less than 1 mm is quite complicated and difficult to describe in quan- titative detail. Experiments on arc-heated supersonic jet thrusters of monatomic gases argon and helium have been carried out and their performance measured. The flow charac- teristics are analyzed with the help of numerical simulation. Results show that the viscous effect is the most important factor causing the large difference between ideal and real performance. A large outer section of the exit flow is slow- moving. This is especially pronounced in helium, where 70 % of the exit area of the nozzle might be in subsonic flow. Fric- tion forces can be much larger than the net thrust, reaching several times higher in helium, resulting in very low efficien- cies. Other factors causing the differences between ideal and real flow include： complex flow in the throat region, electric arc extending to the nozzle expansion section, heat transfer to the inlet gas and from the hot plasma, and environmen- tal pressure in the vacuum chamber. It is recognized that the ordinary concepts of supersonic nozzle flow must be greatly modified when dealing with such complicated situations. The general concepts presented in this paper could be helpful in guiding the design and operation of this equipment.

Optimization and Sizing of a Stand-Alone Photovoltaic System and Assessment of Random Load Fluctuation on Power Supply

This study presents an optimization technique and design for a stand-alone photovoltaic (PV) system to provide the required electricity for a single residential household in remote areas. From the basic solar components analysis, the irradiance on tilted surface is derived and compared to that on horizontal surface for Furu-Awa locality to infer the appropriate tilt angle (β) that maximizes the collection of solar energy. Seven optimum values of β applicable to the PV network were then derived depending of the period of the year and this simulation resulted that the panels are to be adjusted seven times a year. The optimization technique for load demand based on total apparent power of the household appliances produces an increase of 18% compared to the simple case of the PV components design using active power but leads to the optimum configuration that meets the real load demand of the household. Following the sizing of the station, reliability tests simulations were conducted for a one year corresponding period to infer the sensitivity of power supply to initial state of charge, to check the system autonomy and to evaluate the effect of random variation of the load on the smooth functioning of the PV system using a pseudo random number generator. This analysis shows that the minimum capacity of the battery for normal run of the Plan is 22.2% and that with random fluctuation of load, there will be periods of the year where the system experiences power failure depending on how important is the variation. The result of the study may imply a small increase in the cost of the entire plant but improves the stability and flexibility of such a station.

Optimal Number of Relays in Cooperative Communication in Wireless Sensor Networks

Wireless Sensor Networks (WSN) typically consist of resource constrained micro sensors that organize itself into multihop wireless network. Sensors collect data and send it directly, or through intermediate hops in cooperative communication system, to the collection point. These sensors are powered up by batteries, for which the replacement or recharging is very difficult. With finite energy, we can transmit a finite amount of information. Therefore, minimizing the power consumption for data transmission becomes a most important design consideration for wireless sensor networks. In this paper, we discuss the optimal power consumption in cooperative wireless sensor network that are placed on a grid. We study different cases for the optimal power consumption in such grids by varying the grid distance and number of nodes in the grid. We assume the cases of grids from 2 × 2 up to 5 × 5 in increasing complexity of calculations. The results show that the optimal path that consumes the least power is the path along the diagonal using of the grid when the source and the destination and the furthest two nodes in the grid. This path takes intermediate nodes (relays) along it based on some threshold distances. For example, in 5 × 5 cases;the first threshold between the direct distance and between using one relay in the middle is 31.6 m the second threshold distance is 63.3 m after which using three relays is the best in power consumption between the source and the destination.

Multiple Dispatching Reactive Power and Voltage Coordinated Control Method

This paper studies the reactive power and voltage coordinated control scheme. According to the characteristics of Hunan power grid, the coordinated schemes about Hunan power grid with Central China Power Grid, as well as Changsha power grid are proposed. At the same time, this paper builds a two-way interactive and multiple dispatching reactive power and voltage coordinated control mode, and can be successfully applied in Hunan power grid. The operation results show that this control scheme fulfills the ability of large power grids in optimal allocating of resources, effectively integrates the reactive power resources of the entire grid, achieves the purpose of reducing power grid loss, improving voltage quality, reducing the operating numbers of the reactive power equipment.

BERNOULLI CONVOLUTIONS ASSOCIATED WITH CERTAIN NON-PISOT NUMBERS

The Bernoulli convolution ν λ measure is shown to be absolutely continuous with L 2 density for almost all 12<λ<1,and singular if λ -1 is a Pisot number. It is an open question whether the Pisot type Bernoulli convolutions are the only singular ones. In this paper,we construct a family of non-Pisot type Bernoulli convolutions ν λ such that their density functions,if they exist,are not L 2. We also construct other Bernolulli convolutions whose density functions,if they exist,behave rather badly.

Experimental Evaluation of CT Number Changes in 320-Row CBCT Volume Scan for Proton Range Calculation

We investigated the longitudinal positional dependence of CT number in 320-row Cone Beam Computed Tomography (CBCT) volume scan (320-row volume scan) using a simple geometric phantom (SGP) and a chest simulation phantom (CSP) in order to evaluate its effect on proton range calculation. The SGP consisted of lung substitute material (LSM) and a cylindrical phantom (CP) made of high-density polyethylene. The CSP was an anthropomorphic phantom similar to the human chest. The two phantoms were scanned using 320-row volume scan in various longitudinal positions from the central beam axis. In experiments using the SGP, an image blur at the boundary of the two materials became gradually evident when the LSM was placed far away from the beam central axis. The image blur of the phantom was consistent with the gradation in CT number. The maximum difference in CT numbers between the 64-row helical scan and 320-row volume scan at the boundary of the two materials was consistent with approximately 50% of the relative proton stopping power. In contrast, the CT number profile in each longitudinal position was fairly consistent and longitudinal positional dependence rarely occurred in the CSP experiments. Pass lengths of CT beams through areas with widely different electron densities were shorter, and thus did not significantly impact CT numbers. Based on findings from the CSP experiments, we considered 320-row volume scan to be feasible for proton range calculation in clinical settings, although the relatively large longitudinal positional dependence of CT number should be accounted for when doing so.