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.

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.

Demonstration of a small‐scale power generator using supercritical CO_(2)

The supercritical CO_(2)(sCO_(2))power cycle could improve efficiencies for a wide range of thermal power plants.The sCO_(2)turbine generator plays an important role in the sCO_(2)power cycle by directly converting thermal energy into mechanical work and electric power.The operation of the generator encounters challenges,including high temperature,high pressure,high rotational speed,and other engineering problems,such as leakage.Experimental studies of sCO_(2)turbines are insufficient because of the significant difficulties in turbine manufacturing and system construction.Unlike most experimental investigations that primarily focus on 100 kW‐or MW‐scale power generation systems,we consider,for the first time,a small‐scale power generator using sCO_(2).A partial admission axial turbine was designed and manufactured with a rated rotational speed of 40,000 rpm,and a CO_(2)transcritical power cycle test loop was constructed to validate the performance of our manufactured generator.A resistant gas was proposed in the constructed turbine expander to solve the leakage issue.Both dynamic and steady performances were investigated.The results indicated that a peak electric power of 11.55 kW was achieved at 29,369 rpm.The maximum total efficiency of the turbo‐generator was 58.98%,which was affected by both the turbine rotational speed and pressure ratio,according to the proposed performance map.

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.

Principal Quasi-Baerness of Rings of Skew Generalized Power Series

Let R be a ring and （S, 〈） be a strictly totally ordered monoid satisfying that 0 〈 s for all s C S. It is shown that if A is a weakly rigid homomorphism, then the skew generalized power series ring [[RS,-〈, λ]] is right p.q.-Baer if and only if R is right p.q.-Baer and any S-indexed subset of S,（R） has a generalized join in S,（R）. Several known results follow as consequences of our results.

Nilpotent Elements and Nil-Reflexive Property of Generalized Power Series Rings

Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory.

Numerical Solutions of a Generalized Nth Order Boundary Value Problems Using Power Series Approximation Method

In this paper, a new approach called Power Series Approximation Method (PSAM) is developed for the numerical solution of a generalized linear and non-linear higher order Boundary Value Problems (BVPs). The proposed method is efficient and effective on the experimentation on some selected thirteen-order, twelve-order and ten-order boundary value problems as compared with the analytic solutions and other existing methods such as the Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) available in the literature. A convergence analysis of PSAM is also provided.

Optimization of the Gas Generator in Composite Power System with Tip-Jet Rotor

The key and bottleneck of research on the tip-jet rotor compound helicopter lies in the power system. Computational Fluid Dynamics (CFD) was used to numerically simulate the gas generator and rotor inner passage of the tip-jet rotor composite power system, studying the effects of intake mode, inner cavity structure, propellant components, and injection amount on the characteristics of the composite power system. The results show that when a single high-temperature exhaust gas enters, the gas generator outlet fluid is uneven and asymmetric;when two-way high-temperature exhaust gas enters, the outlet temperature of the gas generator with a tilted inlet is more uniform than that with a vertical inlet;adding an inner cavity improves the temperature and velocity distribution of the gas generator's internal flow field;increasing the energy of the propellant is beneficial for improving the available moment.

Increasing the Efficiency and Level of Environmental Safety of Pro-Environmental City Heat Supply Technologies by Low Power Nuclear Plants

In connection with the current prospect of decarbonization of coal energy through the use of small nuclear power plants (SNPPs) at existing TPPs as heat sources for heat supply to municipal heating networks, there is a technological need to improve heat supply schemes to increase their environmental friendliness and efficiency. The paper proves the feasibility of using the heat-feeding mode of ASHPs for urban heat supply by heating the network water with steam taken from the turbine. The ratio of electric and thermal power of a “nuclear” combined heat and power plant is given. The advantage of using a heat pump, which provides twice as much electrical power with the same heat output, is established. Taking into account that heat in these modes is supplied with different potential, the energy efficiency was used to compare these options. To increase the heat supply capacity, a scheme with the use of a high-pressure heater in the backpressure mode and with the heating of network water with hot steam was proposed. Heat supply from ASHPs is efficient and environmentally friendly even in the case of significant remoteness of heat consumers.

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.

A Numerical Convex Lens for the State-Discretized Modeling and Simulation of Megawatt Power Electronics Systems as Generalized Hybrid Systems

Modeling and simulation have emerged as an indispensable approach to create numerical experiment platforms and study engineering systems.However,the increasingly complicated systems that engineers face today dramatically challenge state-of-the-art modeling and simulation approaches.Such complicated systems,which are composed of not only continuous states but also discrete events,and which contain complex dynamics across multiple timescales,are defined as generalized hybrid systems(GHSs)in this paper.As a representative GHS,megawatt power electronics(MPE)systems have been largely integrated into the modern power grid,but MPE simulation remains a bottleneck due to its unacceptable time cost and poor convergence.To address this challenge,this paper proposes the numerical convex lens approach to achieve state-discretized modeling and simulation of GHSs.This approach transforms conventional time-discretized passive simulations designed for pure-continuous systems into state-discretized selective simulations designed for GHSs.When this approach was applied to a largescale MPE-based renewable energy system,a 1000-fold increase in simulation speed was achieved,in comparison with existing software.Furthermore,the proposed approach uniquely enables the switching transient simulation of a largescale megawatt system with high accuracy,compared with experimental results,and with no convergence concerns.The numerical convex lens approach leads to the highly efficient simulation of intricate GHSs across multiple timescales,and thus significantly extends engineers’capability to study systems with numerical experiments.

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.

The exponentiated generalized power Lindley distribution: Properties and applications

In this paper, we introduce a new extension of the power Lindley distribution, called the exponentiated generalized power Lindley distribution. Several mathematical properties of the new model such as the shapes of the density and hazard rate functions, the quantile function, moments, mean deviations, Bonferroni and Lorenz curves and order statistics are derived. Moreover, we discuss the parameter estimation of the new distribution using the maximum likelihood and diagonally weighted least squares methods. A simulation study is performed to evaluate the estimators. We use two real data sets to illustrate the applicability of the new model. Empirical findings show that the proposed model provides better fits than some other well-known extensions of Lindley distributions.

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.

Convergence Properties of Generalized Fourier Series on a Parallel Hexagon Domain

A new Rogosinski-type kernel function is constructed using kernel function of partial sums Sn（f; t） of generalized Fourier series on a parallel hexagon domain Ω associating with threedirection partition. We prove that an operator Wn（f; t） with the new kernel function converges uniformly to any continuous function f（t） ∈ Cn（Ω） （the space of all continuous functions with period Ω） on Ω. Moreover, the convergence order of the operator is presented for the smooth approached function.

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.

THE GENERALIZED LOWER ORDER OF DIRICHLET SERIES

In this paper,we study the generalized lower order of entire functions defined by Dirichlet series.By constructing the Newton polygon based on Knopp-Kojima’s formula,we obtain a relation between the coefficients of the Dirichlet series and its generalized lower order.

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.