On power series statistical convergence and new uniform integrability of double sequences

In the present paper,we mostly focus on P_(p)^(2)-statistical convergence.We will look into the uniform integrability via the power series method and its characterizations for double sequences.Also,the notions of P_(p)^(2)-statistically Cauchy sequence,P_(p)^(2)-statistical boundedness and core for double sequences will be described in addition to these findings.

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.

Dynamic analysis of a rotating tapered cantilever Timoshenko beam based on the power series method

The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, flapwise, and edgewise directions and three cross-sectional angles of torsion, flapwise bending, and edgewise bending, are obtained by the Euler angle descriptions. The power series method is then used to inves- tigate the natural frequencies and the corresponding complex mode functions. It is found that all the natural frequencies are increased by the centrifugal stiffening except the twist frequency, which is slightly decreased. The tapering ratio increases the first transverse, torsional, and axial frequencies, while decreases the second transverse frequency. Because of the pre-twist, all the directions are gyroscopically coupled with the phase differences among the six degrees.

VECTOR-VALUED RANDOM POWER SERIES ON THE UNIT BALL OF C～n

In this article, the authors study the vector-valued random power series on the unit ball of C^n and get vector-valued Salem-Zygmund theorem for them by using martingale technique. Further, the relationships between vector-valued random power series and several function spaces are also studied.

Simulation Study on Series Capacitor Compensation to Improve the Voltage Quality of Rural Power Distribution Network

In order to improve the voltage quality of rural power distribution network, the series capacitor in distribution lines is proposed. The principle of series capacitor compensation technology to improve the quality of rural power distribution lines voltage is analyzed. The real rural power distribution network simulation model is established by Power System Power System Analysis Software Package (PSASP). Simulation analysis the effect of series capacitor compensation technology to improve the voltage quality of rural power distribution network, The simulation results show that the series capacitor compensation can effectively improve the voltage quality and reduce network losses and improve the transmission capacity of rural power distribution network.

THE NATURAL BOUNDARY OF SOME RANDOM POWER SERIES

Suppose that {X(n)(omega)} are independent random complex variable sequence, E(X(n)) = 0 and [GRAPHICS] (V(X(n) = sigma(n)2). If reversed capital E-epsilon > 0 such that for all P (H) > 1-epsilon, we have [GRAPHICS] Then the circle {\Z\ = rho} is almost surely a natural boundary of the random series [GRAPHICS]

The Degenerate Form of the Adomian Polynomials in the Power Series Method for Nonlinear Ordinary Differential Equations

In this paper, we propose a new variation of the Adomian polynomials, which we call the degenerate Adomian polynomials, for the power series solutions of nonlinear ordinary differential equations with nonseparable nonlinearities. We establish efficient algorithms for the degenerate Adomian polynomials. Next we compare the results by the Adomian decomposition method using the classic Adomian polynomials with the results by the Rach-Adomian-Meyers modified decomposition method incorporating the degenerate Adomian polynomials, which itself has been shown to be a confluence of the Adomian decomposition method and the power series method. Convergence acceleration techniques including the diagonal Pade approximants are considered, and new numeric algorithms for the multistage decomposition are deduced using the degenerate Adomian polynomials. Our new technique provides a significant advantage for automated calculations when computing the power series form of the solution for nonlinear ordinary differential equations. Several expository examples are investigated to demonstrate its reliability and efficiency.

An Exact Analysis of the Fundamental and First Higher Order Mode in Graded Index Fibers with Direct Power Series Method

An exact and fast analytic method based on power series is established to predict the modal field distributions, Petermann-2 spot size, the normalized propagation constant corresponding to fundamental and first higher order mode in graded index fibers with any arbitrary power law profile. The variation of normalized cut-off frequencies of some LPlm modes in graded index fibers with different profile exponents are also shown here and an empirical relation between them is determined.

Solution of Duffing-Harmonic Oscillator by the Power Series Method

This paper provides a power series solution to the Duffing-harmonic oscillator and compares the frequencies with those obtained by the harmonic balance method.To capture the periodic motion of the oscillator,the power series expansion is used upon transforming the time variable into an“oscillating time”which reduces the governing equation to a form well-conditioned for a power series solution.A recurrence equation for the series coefficients is established in terms of the“oscillating time”frequency which is then determined by employing Rayleigh’s energy principle.The response of the oscillator is compared with a numerical solution and good agreement is demonstrated.

Nonlinear Free Vibration of a Cantilever Beam Using the Power Series Method

An analytical approach based on the power series method is used to analyze the free vibration of a cantilever beam with geometric and inertia nonlinearities.The time variable is transformed into a“harmonically oscillating time”variable which transforms the governing equation into a form well-conditioned for a power series analysis.Rayleigh’s energy principle is also used to determine the vibration frequency.Convergence of the power series solution is demonstrated and excellent agreement is seen for the vibration response with a numerical solution.

A General Analytic Approximation Technique for the Modified Bessel Functions with Fractional Order Iv (x), Applied to I1/6(x) and I1/7(x)

A general technique to obtain simple analytic approximations for the first kind of modified Bessel functions. The general procedure is shown, and the parameter determination is explained through the applications to this particular case I1/6(x)and I1/7(x). In this way, it shows how to apply the technique to any particular orderν, in order to obtain an approximation valid for any positive value of the variable x. In the present method power series and asymptotic expansion are simultaneously used. The technique is an extension of the multipoint quasirational approximation method, MPQA. The main idea is to look for a bridge function between the power and asymptotic expansion of the I1/6(x), and similar procedure for I1/7(x). To perform this, rational functions are combined with hyperbolic ones and fractional powers. The number of parameters to be determined for each case is four. The maximum relative errors are 0.0049 for ν=1/6, and 0.0047 for ν=7. However, these relative errors decrease outside of the small region of the variables, wherein the maximum relative errors are reached. There is a clear advantage of this procedure compared with any other ones.

The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

The nonlinearity inmany problems occurs because of the complexity of the given physical phenomena.The present paper investigates the non-linear fractional partial differential equations’solutions using the Caputo operator with Laplace residual power seriesmethod.It is found that the present technique has a direct and simple implementation to solve the targeted problems.The comparison of the obtained solutions has been done with actual solutions to the problems.The fractional-order solutions are presented and considered to be the focal point of this research article.The results of the proposed technique are highly accurate and provide useful information about the actual dynamics of each problem.Because of the simple implementation,the present technique can be extended to solve other important fractional order problems.

The Fractional Investigation of Fornberg-Whitham Equation Using an Efficient Technique

In the last few decades,it has become increasingly clear that fractional calculus always plays a very significant role in various branches of applied sciences.For this reason,fractional partial differential equations(FPDEs)are of more importance to model the different physical processes in nature more accurately.Therefore,the analytical or numerical solutions to these problems are taken into serious consideration and several techniques or algorithms have been developed for their solution.In the current work,the idea of fractional calculus has been used,and fractional FornbergWhithamequation(FFWE)is represented in its fractional view analysis.Awell-knownmethod which is residual power series method(RPSM),is then implemented to solve FFWE.TheRPSMresults are discussed through graphs and tables which conform to the higher accuracy of the proposed technique.The solutions at different fractional orders are obtained and shown to be convergent toward an integer-order solution.Because the RPSM procedure is simple and straightforward,it can be extended to solve other FPDEs and their systems.

Important Issues and Results When Considering the Stochastic Representation of Wind Power Plants in a Generation Optimization Model: An Application to the Large Brazilian Interconnected Power System

Wind power has an increasing share of the Brazilian energy market and may represent 11.6% of total capacity by 2024. For large hydro-thermal systems having high-storage capacity, a complementarity between hydro and wind production could have important effects. The current optimization models are applied to dispatch power plants to meet the market demand and optimize the generation dispatches considering only hydroelectric and thermal power plants. The remaining sources, including wind power, small-hydroelectric plants and biomass plants, are excluded from the optimization model and are included deterministically. This work introduces a general methodology to represent the stochastic behavior of wind production aimed at the planning and operation of large interconnected power systems. In fact, considering the generation of the wind power source stochastically could show the complementarity between the hydro and wind power production, reducing the energy price in the spot market with the reduction of thermal power dispatches. In addition to that, with a reduction in wind power and a simultaneous dry-season occurrence, this model, is able to show the need of thermal power plants dispatches as well as the reduction of the risk of energy shortages.

THE VALUE DISTRIBUTION OF RANDOM ANALYTIC DIRICHLET SERIES OF NEUTRAL GROWTH(I)

This paper deals with the value distribution of random Dirichlet series whose coefficients are a martingale difference sequence, and which is of neutral growth.

Readjustment of the Paper [J.Kaur and S.S.Bhatia,Integrability and L^1-Convergence of Double Cosine Trigonometric Series,Anal.Theory Appl.,27(1)(2011),pp.32–39.]

In this paper, we show that new modified double cosine trigonometric sums introduced in [1] are inappropriate, the class of double sequences Jintroduced there is unusable for such sums and consequently the results obtained in it are completely incorrect. We here introduce appropriate modified double cosine trigonometric sums making the class Jusable considering a particular double cosine trigonometric series.

The Combination of Two Control Strategies for Series Hybrid Electric Vehicles

With most countries paying attention to the environment protection, hybrid electric vehicles have become a focus of automobile research and development due to the characteristics of energy saving and low emission. Power follower control strategy(PFCS) and DC-link voltage control strategy are two sorts of control strategies for series hybrid electric vehicles(HEVs). Combining those two control strategies is a new idea for control strategy of series hybrid electric vehicles. By tuning essential parameters which are the defined constants under DClink voltage control and under PFCS, the points of minimum mass of equivalent fuel consumption(EFC) corresponding to a series of variables are marked for worldwide harmonized light vehicles test procedure(WLTP). The fuel economy of series HEVs with the combination control schemes performs better compared with individual control scheme. The results show the effects of the combination control schemes for series HEVs driving in an urban environment.

REFLEXIVITY OF POWERS OF THE MULTIPLICATION OPERATOR ON SPECIAL FUNCTION SPACES

In this paper we present sufficient conditions for reflexivity of any powers of the multiplication operator acting on Banach spaces of formal Laurent series.

ON THE COMMUTATIVITY OF MULTIPLE SERIES AND BASIC SEQUENCE

Let X be a Banach space and be a sequence in X. The author shows that is a basic sequence if and only if converges for every j≥1 and holds for every choice of scalar variables {αnj} such that converges for each n≥ 1 and any choice of scalar variables {rn} such that converges. Moreover, some applications about the result are given.

Domain of Euler Mean in the Space of Absolutely p-Summable Double Sequences with 0

In this study, as the domain of four dimensional Euler mean E(r,s) of orders r,sin the space L_p for 0 < p < 1, we examine the double sequence space ε_p^(r,s) and some properties of four dimensional Euler mean. We determine the α-and β(bp)-duals of the space εp r,s, and characterize the classes(ε_p^(r,s):M_u),(ε_p^(r,s):C_(bp)) and(ε_p^(r,s):L_q) of four dimensional matrix transformations, where 1 ≤q < ∞. Finally, we shortly emphasize on the Euler spaces of single and double sequences, and note some further suggestions.