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.

ICU患者置入Power PICC导管特殊异位原因分析

目的:探讨ICU患者置入Power PICC导管后头端反折向上至同侧和对侧锁骨下静脉、头臂静脉等特殊异位的相关因素。方法:回顾性分析2021年9月至2022年9月某三甲医院ICU 520例PICC置管患者,通过胸部X线确定PICC导管头端反折向上至对侧和同侧锁骨下静脉、头臂静脉的患者,分析其特殊异位发生因素。结果:胸部X线结果显示25例患者PICC管头端反折向上异位至对侧和同侧锁骨下静脉、头臂静脉或颈内静脉,异位发生率4.8%,不同静脉置管反折异位发生率相比差异无统计学意义,P>0.05。结论:ICU患者PICC置入发生导管头端反折向上至同侧和对侧锁骨下静脉、头臂静脉等特殊异位的发生因素较多,包括同时留置CVC或血透管、正在滴注或泵入多种药物、PICC管头端异位的隐匿性、导管材质、自身疾病及机械通气等危险因素。

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.

SELF-DUAL PERMUTATION CODES OVER FORMAL POWER SERIES RINGS AND FINITE PRINCIPAL IDEAL RINGS

In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power series rings. These results allow for obtaining some conditions for non-existence of self-dual permutation codes over formal power series rings. Finally, we describe self-dual permutation codes over finite principal ideal rings by examining permutation codes over their component chain rings.

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]

On Skew Power-serieswise nil-Armendariz Rings

For a ring endomorphism α, in this paper we introduce the notion of s-power- serieswise nil-Armendariz rings, which are a generalization of α-power-serieswise Armendariz rings. A number of properties of this generalization are established, and the extensions of α- power-serieswise nil-Armendariz rings are investigated. Which generalizes the corresponding results of nil-Armendariz rings and power-serieswise nil-Armendariz rings.

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.

Principal Quasi-Baerness of Rings of Generalized Power Series

Let R be a ring such that all left semicentral idempotents are central and （S, ≤） a strictly totally ordered monoid satisfying that 0 ≤s for all s ∈S. It is shown that [[R^S≤]], the ring of generalized power series with coefficients in R and exponents in S, is right p.q.Baer if and only if R is right p.q.Baer and any S-indexed subset of I（R） has a generalized join in I（R）, where I（R） is the set of all idempotents of R.

PS-modules over Rings of Generalized Power Series

Let R be a commutative ring and (S, ≤) a strictly totally ordered monoid which satisfies the condition that 0 ≤ s for every s ∈ S. In this paper we show that if RM is a PS-module, then the module [[MS≤]] of generalized power series over M is a PS [[RS,≤]]-module.

Wind power time series simulation model based on typical daily output processes and Markov algorithm

The simulation of wind power time series is a key process in renewable power allocation planning,operation mode calculation,and safety assessment.Traditional single-point modeling methods discretely generate wind power at each moment;however,they ignore the daily output characteristics and are unable to consider both modeling accuracy and efficiency.To resolve this problem,a wind power time series simulation model based on typical daily output processes and Markov algorithm is proposed.First,a typical daily output process classification method based on time series similarity and modified K-means clustering algorithm is presented.Second,considering the typical daily output processes as status variables,a wind power time series simulation model based on Markov algorithm is constructed.Finally,a case is analyzed based on the measured data of a wind farm in China.The proposed model is then compared with traditional methods to verify its effectiveness and applicability.The comparison results indicate that the statistical characteristics,probability distributions,and autocorrelation characteristics of the wind power time series generated by the proposed model are better than those of the traditional methods.Moreover,modeling efficiency considerably improves.

Analysis on the capacity degradation mechanism of a series lithium-ion power battery pack based on inconsistency of capacity

The lithium-ion battery has been widely used as an energy source. Charge rate, discharge rate, and operating tem- perature are very important factors for the capacity degradations of power batteries and battery packs. Firstly, in this paper we make use of an accelerated life test and a statistical analysis method to establish the capacity accelerated degradation model under three constant stress parameters according to the degradation data, which are charge rate, discharge rate, and operating temperature, and then we propose a capacity degradation model according to the current residual capacity of a Li-ion cell under dynamic stress parameters. Secondly, we analyze the charge and discharge process of a series power battery pack and interpret the correlation between the capacity degradations of the battery pack and its charge/discharge rate. According to this cycling condition, we establish a capacity degradation model of a series power battery pack under inconsistent capacity of cells, and analyze the degradation mechanism with capacity variance and operating temperature difference. The comparative analysis of test results shows that the inconsistent operating temperatures of cells in the series power battery pack are the main cause of its degradation; when the difference between inconsistent temperatures is narrowed by 5 ℃, the cycle life can be improved by more than 50%. Therefore, it effectively improves the cycle life of the series battery pack to reasonably assemble the batteries according to their capacities and to narrow the differences in operating temperature among cells.

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.

Power spectral density analysis for nonlinear systems based on Volterra series

A consequence of nonlinearities is a multi-harmonic response via a monoharmonic excitation.A similar phenomenon also exists in random vibration.The power spectral density(PSD)analysis of random vibration for nonlinear systems is studied in this paper.The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function(GFRF).For a class of nonlinear systems,the growing exponential method is used to determine the first 3 rd-order GFRFs.The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input.The relationship between the peak of PSD and the parameters of the nonlinear system is discussed.By using the proposed method,the nonlinear characteristics of multi-band output via single-band input can be well predicted.The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD.This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.

Research on Reduction of Solar Power Curtailment with Grid Connected Energy Storage System Based on Time-Series Production Simulation

Due to the variable output of renewable energy (RE) generation, difficulties of dispatching RE for power system operators could not be avoided. One of possible solutions is the energy storage technology, especially the battery storage system. The large-scale energy storage system is available to support power system reliable flexibility for load following and system frequency regulation. In this paper, the bottlenecks of large-scale solar power generation dispatching and operation in Qinghai grid are discussed, and a new PV-energy storage coordinated dispatching method is proposed for reduction of PV curtailment in Qinghai. Moreover, the validation based on the time-series production simulation is provided using real data from Qinghai. The results indicate that the proposed method can effectively decrease the curtailment of solar power and future vision of large-scale solar power coordinated operation with energy storage system is also presented.

Grey series time-delay predicting model in state estimation for power distribution networks

A new combined model is proposed to obtain predictive data value applied in state estimation for radial power distribution networks. The time delay part of the model is calculated by a recursive least squares algorithm of system identification, which can gradually forget past information. The grey series part of the model uses an equal dimension new information model (EDNIM) and it applies 3 points smoothing method to preprocess the original data and modify remnant difference by GM(1,1). Through the optimization of the coefficient of the model, we are able to minimize the error variance of predictive data. A case study shows that the proposed method achieved high calculation precision and speed and it can be used to obtain the predictive value in real time state estimation of power distribution networks.

Dynamic stiffness for thin-walled structures by power series

The dynamic stiffness method is introduced to analyze thin-walled structures including thin-walled straight beams and spatial twisted helix beam. A dynamic stiffness matrix is formed by using frequency dependent shape functions which are exact solutions of the governing differential equations. With the obtained thin-walled beam dynamic stiffness matrices, the thin-walled frame dynamic stiffness matrix can also be formulated by satisfying the required displacements compatibility and forces equilib-rium, a method which is similar to the finite element method (FEM). Then the thin-walled structure natural frequencies can be found by equating the determinant of the system dynamic stiffness matrix to zero. By this way, just one element and several elements can exactly predict many modes of a thin-walled beam and a spatial thin-walled frame, respectively. Several cases are studied and the results are compared with the existing solutions of other methods. The natural frequencies and buckling loads of these thin-walled structures are computed.

Note on Barenblatt power series solution to Boussinesq equation

To the serf-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a power series solution. However, he listed only the first three coefficients and did not give the recurrent formula among the coefficients. A formal proof of convergence of the series did not appear in his works. In this paper, the recurrent formula for the coefficients is obtained by using the method of power series expansion, and the convergence of the series is proven. The results can be easily understood and used by engineers in the catchment hydrology and baseflow studies as well as to solve agricultural drainage problems.

Application of Power Series on Vibration Analyses

Power series is extensively used for engineering studies. To raise the synthesis efficiency and computation accuracy of vibration mode synthesis (MS), the choosing of power series as the component mode-function is studied in this paper, and emphasis is laid on its effect upon the system computation accuracy when using the mode synthesis method for a high speed compound rotating elastic system.