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A new Las Vegas algorithm is presented for the composition of two polynomials modulo a third one, over an arbitrary field. When the degrees of these polynomials are bounded by n, the algorithm uses O(n1.43) field operations, breaking through the 3/2 barrier in the exponent for the first time. The previous fastest algebraic algorithms, due to Brent and Kung in 1978, require O(n1.63) field operations in general, and n3/2+o(1) field operations in the special case of power series over a field of large enough characteristic. If cubic-time matrix multiplication is used, the new algorithm runs in n5/3+o(1) operations, while previous ones run in O(n2) operations. Our approach relies on the computation of a matrix of algebraic relations that is typically of small size. Randomization is used to reduce arbitrary input to this favorable situation. [ABSTRACT FROM AUTHOR]

Let $ \mathbf{A}_{\infty } $ A ∞ be an integer ring of a formal Laurent series field in one variable $ \frac {1}{t} $ 1 t over a finite field of order q, with a maximal ideal $ \mathbf{M}_{\infty } $ M ∞ . Then, we introduce beta-transformations $ U_{\beta } $ U β on $ \mathbf{A}_{\infty } $ A ∞ that are topologically isomorphic and measurably isomorphic to the well-known beta-transformation $ T_{\beta } $ T β on $ \mathbf{M}_{\infty } $ M ∞ . We prove various metrical properties of $ U_{\beta } $ U β such as (total) ergodicity and mixing of any order through explicit representations of both $ U_{\beta } $ U β and its nth iterate $ U_{\beta }^n $ U β n with respect to the shift operators. Furthermore, we examine dynamical connections between the measure-preserving property of 1-Lipschitz functions and the locally scaling property of $ (q^{-k}, q^k) $ (q − k , q k) -Lipschitz functions, in terms of the coefficients of van der Put and Carlitz–Wagner. [ABSTRACT FROM AUTHOR]

When k is a finite field, [J. Becker, J. Denef and L. Lipshitz, Further remarks on the elementary theory of formal power series rings, in Model Theory of Algebra and Arithmetic, Proceedings Karpacz, Poland, Lecture Notes in Mathematics, Vol. 834 (Springer, Berlin, 1979)] observed that the total residue map res : k ((t)) → k , which picks out the constant term of the Laurent series, is definable in the language of rings with a parameter for t. Driven by this observation, we study the theory VF res , ι of valued fields equipped with a linear form res : K → k which restricts to the residue map on the valuation ring. We prove that VF res , ι does not admit a model companion. In addition, we show that (k ((t)) , res) is undecidable whenever k is an infinite field. As a consequence, we get that (ℂ ((t)) , Res 0) is undecidable, where Res 0 : f ↦ Res 0 (f) maps f to its complex residue at 0. [ABSTRACT FROM AUTHOR]

This paper centers around one of several generalizations of primary ideals. Which is an intermediate class between S-primary ideals and quasi S-primary ideals. Let R be a commutative ring with identity and S be a multiplicative closed subset of R. A proper ideal I of R disjoint from S is called strongly quasi S-primary if there exists an s ∈ S such that whenever x , y ∈ R and xy ∈ I , then either s x 2 ∈ I or sy ∈ I . Many basic properties of strongly quasi S-primary ideals are given, and examples are presented to distinguish the last concept from other classical ideals. Moreover, forms of strongly quasi S-primary ideals in polynomial rings, power series rings and idealization of a module are investigated. [ABSTRACT FROM AUTHOR]

Let K be any field. In this paper, we give a complete list of the indecomposable left injective module over the Jacobson algebra K〈X,Y |XY = 1〉, i.e. the free associative K-algebra on two (non-commuting) generators, modulo the single relation XY = 1. This is the natural continuation of the paper of the second two authors with Gene Abrams on the characterization of the injective envelope of the simple modules over K〈X,Y |XY = 1〉. [ABSTRACT FROM AUTHOR]

It is well known that every subvariety of the variety of semigroups need not be absolutely closed. Thus, identifying those subvarieties that are closed in themselves or in larger varieties is an interesting open problem in the theory of semigroup dominions. The significance of finding such varieties lies in the fact that, in these varieties, epimorphisms are precisely the surjective morphisms. In this paper, we address this problem and demonstrate that for each n∈N, the varieties of semigroups Vn≔x1x2x3=xj1xinxj2xj3, where i ∈ {1, 2, 3} and j is any nontrivial permutation of {1, 2, 3} not fixing 1 when i = 2, are closed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of S‐J‐ideals in both commutative and noncommutative rings. For a commutative ring R and a multiplicatively closed subset S, we show that many properties of J‐ideals apply to S‐J‐ideals and examine their characteristics in various ring constructions, such as homomorphic image rings, quotient rings, cartesian product rings, polynomial rings, power series rings, idealization rings, and amalgamation rings. In noncommutative rings, where S is an m‐system, we define right S‐J‐ideals. We demonstrate the equivalence of S‐J‐ideals and right S‐J‐ideals in commutative rings with identity and provide examples to illustrate the connections between right S‐prime ideals and J‐ideals. [ABSTRACT FROM AUTHOR]

Accurate ultra‐short‐term wind power prediction techniques are crucial for ensuring the efficient and safe operation of wind farms and power systems. Combined models based on data decomposition‐prediction techniques have shown excellent performance in ultra‐short‐term wind power forecasting. This study introduces a novel ultra‐short‐term multi‐step prediction model for wind power, which integrates the sparrow search algorithm (SSA), variational mode decomposition (VMD), gated recurrent unit (GRU), and support vector regression (SVR). An optimization variational mode decomposition technique is developed by adaptively determining VMD hyperparameters using SSA. The optimization VMD decomposes the original wind power sequence into sub‐modes, and the resulting sequence of decomposed sub‐modes calculates permutation entropy (PE) values. Sub‐modes with similar PE values are combined, reorganized, and categorized into high‐frequency and low‐frequency. High‐frequency sub‐modes data with high complexity and non‐stationarity are predicted by the GRU neural network. Low‐frequency sub‐modes data with low complexity and strong nonlinearity are predicted with SVR. The proposed model was evaluated against seven others using three error metrics: MAE, RMSE, and R2, along with their corresponding enhancement percentages. Experimental results indicate that the proposed model extracts detailed and trend information from the wind power series more effectively and stably than the comparison models. It also demonstrates superior multi‐step prediction performance, offering significant value for practical engineering applications. [ABSTRACT FROM AUTHOR]

In this article, we prove that for a convergent sequence of residually absolutely irreducible representations of the absolute Galois group of a number field F with coefficients in a domain, which admits a finite monomorphism from a power series ring over a p -adic integer ring, the set of places of F where some of the representations ramifies has density zero. Using this, we extend a result of Das–Rajan to such convergent sequences. We also establish a strong multiplicity one theorem for big Galois representations. [ABSTRACT FROM AUTHOR]

Let A ⊆ B be commutative rings with unity, let S ⊆ T be torsion-free cancellative monoids, and let n ≥ 1 . We give a characterization of when the monoid ring A [ S ] is n-root closed in the monoid ring B [ T ] . For torsion-free cancellative ordered monoids (S , ≤) ⊆ (T , ≤) , we also present sufficient conditions and necessary conditions for the generalized power series ring [ ​ [ A S , ≤ ] ​ ] to be n-root closed in the generalized power series ring [ ​ [ B T , ≤ ] ​ ] . [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with identity. A proper ideal I of R is said to be 2-absorbing if whenever xyz ∈ I for some elements x , y , z ∈ R , then either xy ∈ I or xz ∈ I or yz ∈ I. The ring R is called a two-absorbing factorization ring (TAF-ring) if every proper ideal of R has a two absorbing-factorization that is every ideal is a product of 2-absorbing ideals. In this note, we characterize commutative rings R (respectively, commutative ring extensions A ⊂ B ) for which the ring of formal power series R [ [ X ] ] (respectively, the ring A + XB [ [ X ] ] ) is a TAF-ring. [ABSTRACT FROM AUTHOR]

In recent years, there has been a growing interest among researchers in the study of shallow water waves, driven by their wide applicability across various scientific disciplines. Within this field, the Camassa–Holm equation has garnered significant attention due to its ability to capture complex wave phenomena. However, researchers have extended their investigations to the Modified Camassa–Holm equation (MCH), which incorporates principles from fractional calculus, thereby offering a more comprehensive framework for understanding intricate dynamics. This article focuses on the analytical solution of the Fractional Modified Camassa–Holm (FMCH) equation, an extension of the MCH, achieved through a novel method known as the Residual Power Series Method (RPSM). By utilizing RPSM and initial conditions, the main aim is to unveil an analytical solution for the FMCH, contributing to an improved understanding and modeling of the complex real-world phenomena observed in waves. [ABSTRACT FROM AUTHOR]

The high-thrust linear motor used for the electromagnetic launch is switched by switches composed of anti-shunt thyristors. During the switching process, different current path states will appear, which will lead to changes in motor parameters and current fluctuation. Focusing on the air-core synchronous linear motor with parallel and series power supply, this paper analyzes the change in current path caused by the change in the trigger signal of anti-parallel thyristors in the process of sectionalized stator switching. The motor circuit model of the switching process is derived. A new sectionalized stators switching method is proposed to realize the smooth switching of the sectionalized stators linear motor. Finally, the correctness of the analysis and modeling is verified by simulation, and the effectiveness of the sectionalized stators switching method is tested by using the test prototype. [ABSTRACT FROM AUTHOR]

The Expected Solar Performance and Ramp Rate tool (ESPRR) is an open-source interactive web-based application that reliably calculates ramp rate (RR) statistics and an expected power generation time series for prospective photovoltaic (PV) systems. Users create PV systems by defining site parameters. ESPRR uses those parameters with irradiance data from the National Solar Radiation Database (NSRDB) to create a time series of power output from which RR statistics are calculated. This study rigorously evaluates ESPRR's performance using 5 years of measured power output from a fleet of utility-scale systems and finds that ESPRR calculates stress-case RRs within an error of 0.05 MW/min and 0.42 MW/min for the worst-case RRs. We evaluate the expected AC power output in clear-sky conditions and find an NRMSE of less than 10% and an NMBE of less than 6% for the fleet's largest system. The NRMSE is 10%–15% of system capacity for non-clear-sky conditions, and the NMBE is about zero. The evaluation shows that ESPRR can estimate PV output and RRs that are representative of operational systems, meaning users can use the results from ESPRR in the decision-making process for designing new systems or when adding systems to an existing fleet. Since only system parameters are required to site a proposed system anywhere on a map, users can site and reposition a fleet of PV systems in a way that reduces significant RRs. As the grid-tied PV capacity continues to increase, the mitigation of significant RRs grows in importance. ESPRR can help developers and utilities create geographically diverse fleets of PV systems that will promote grid reliability and avoid significant RRs. ESPRR source code is available at https://github.com/UARENForecasting/ESPRR. [ABSTRACT FROM AUTHOR]

Copyright of Journal of South-Central Minzu University (Natural Science Edition) is the property of Journal of South-Central Minzu University (Natural Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Let R be a commutative ring with identity, X be an indeterminate over R, R[X] be the polynomial ring over R, R[[X]] be the power series ring over R, and Q be a principal prime ideal of R[X] with (Q ∩ R)[X] ⊊ Q. It is well known that if R is an integral domain, then R[X]Q is a DVR and R[X] has infinitely many such principal prime ideals. In this paper, among other things, we show that (i) RQ∩R is a field, (ii) R[X]Q is a DVR, but (iii) there is a ring R such that R[X] has no principal prime ideal. We also study the maximal ideals of R[[X]] that are principal. [ABSTRACT FROM AUTHOR]

ABSTRACT In this paper, a broadband high‐efficiency power amplifier (PA) with filtering characteristics is proposed. This PA is designed using a series of inverse continuous modes (SICMs) and adds a novel coupled microstrip line filter structure. The terminal of this structure is composed of microstrip lines cascaded to improve the out‐of‐band suppression effect. This filter can achieve low in‐band insertion loss, high passband selectivity, as well as deep stopband rejection performance simultaneously. A PA was designed and implemented using a 10 W GaN HEMT device, verifying its wideband characteristics. The measurement result shows that the 39.6–41.6 dBm output power (Pout), 61.6%–73.7% drain efficiency (DE), and 8.6–10.8 dB gain are achieved at 2.2–2.9 GHz. [ABSTRACT FROM AUTHOR]

The study reports on the magnetization, magnetoresistance, and transport properties of superparamagnetic 10% Co-doped Ni/NiO (C10-NN), Graphene Oxide (GO) incorporated 10% Co-doped Ni/NiO (C10-NNG), and 15% Co-doped Ni/NiO (C15-NN) nanoparticles synthesized via a microwave-assisted sol-gel auto-combustion method. All samples show hysteresis in negative Magnetoresistance (M-R) at different temperatures. Resistivity ρ(T) versus temperature plots of samples C10-NN and C15-NN show metallic behavior with applied fields of 0, 1, 5, 8 T, and at 0 T, 1 T respectively. However, the plot of R-T of the C15-NN sample shows a significant difference at 0 T and 1 T. At 0 T for this sample, the metallic behavior is observed for temperature T > TM, with the resistivity falling abruptly at and above TM = 246 K. The resistivity decreases with increasing temperature, exhibiting metallic behavior again above TMM < 276 K. This jump at 276 K, indicating a metal-to metal transition. The Kondo effect is observed for the first time in C10-NNG sample. The upturn of resistivity ρ(T) towards low temperature in the C10-NNG sample is well described by the power series equation and Kondo term. This sample exhibits the upturn resistivity along with a metal–insulator transition above and below the Kondo temperature TK≈ 93.51(2) K at the 0 T, 1 T, 5 T, and 8 T fields. [ABSTRACT FROM AUTHOR]

We investigate the following nonlinear bosonic equation on Euclidean space arising in string theory and cosmology: P − Δ e − c Δ u + m u = f (x , u) , x ∈ R n , where n ≥ 3 , m > 0 , c > 0 and f (x , u) u tends to a positive function h (x) independent of u as u → + ∞ , e − c Δ is given by a power series with Δ is the Euclidean Laplace operator. Here, the nonlinear term f (x , u) does not satisfy the usual condition: AR 0 ≤ F (x , u) : = ∫ 0 u f (x , t) d t ≤ 1 2 + θ f (x , u) u , for θ > 0 and | u | is large, which is important in using the mountain pass theorem, see Alves et al. (J. Differ. Equ. 323:229-252, 2022) and Corrêa et al. (J. Differ. Equ. 363:491-517, 2023). This paper is devoted to discuss how to use the mountain pass theorem to obtain the existence of nontrivial solution to problem (P) without the (AR) condition. [ABSTRACT FROM AUTHOR]

In this paper, we define the concept of generalized graded rings and investigate to study some properties. The class of generalized graded rings contains those of graded rings and power series rings. To study generalized graded rings, we define three kinds of homogeneous type ideals and study some properties. [ABSTRACT FROM AUTHOR]

Robotic arms have received attention in manufacturing due to their high precision and productivity. As their demand rises, energy consumed by robotic arms in manufacturing applications has become a critical issue. Predicting energy usage of industrial robotic arms is therefore necessary to assess and reduce their energy consumption and costs. However, existing power estimation methods require too many mechanical inputs or focus on only one single robotic arm without considering operational perspectives such as interactions between robotic arms and machines. To tackle these issues, this study proposes a simplified power estimation model for robotic arms and provides energy simulation models in which machines and robotic arms work together. For more accurate results, power data are collected through experiments of central composite design (CCD) using a 7-axis robotic arm. Then, regression models are built to estimate power demand of the robotic arm as three simple inputs: starting point, ending point, and payload. The regression analyses of this study consistently show that the power demand estimation models are very accurate with high R2 values between 0.95 and 0.98. Then, a manufacturing system with milling machines supported by robotic arms is simulated. By applying the proposed method, the activities of robotic arms and machines are simulated with various operational factors, and the time series power is obtained. Further analyses suggest that energy performance of robotic arms can be improved at a maximum of 22% by optimizing two operational parameters: the base and idle positions of robotic arms. The proposed method facilitates energy modeling and simulation processes for robot-assisted manufacturing and enables practitioners and researchers to readily adjust operational parameters and evaluate energy performance for robot applications in manufacturing. [ABSTRACT FROM AUTHOR]

In this article, two-dimensional unsteady incompressible viscous nanofluids magneto-hydrodynamic (MHD) flow among two parallel plates extended infinitely is investigated. The equations that results from the use of similarity transformations for non-linear partial differential system are solved by the new algorithm. The important key to this construct is the derivatives that appear as coefficients in the power series. The effects of apparent physical parameters on velocity concentration and temperature distributions are described using a schematic diagram and interpreted physically. The effects of apparent physical parameters on concentration, temperature, and velocity distributions are described by graphs. For the flow of nanofluids, the results indicate that it is inversely proportional between the rate of mass and heat transfer with nanoparticle size fraction and magnetic parameter. Over time, squeeze number and schmidt number lead to increase the rate of mass transfer. This problem is dissolved numerically by using the Runge-Kutta scheme of fourthorder (RK4S) . [ABSTRACT FROM AUTHOR]

We consider the case of regular singularity for a class of equations with pseudodifferential operator Dα, α > 0, on radial functions t p α D α t p = A t p u t p. Under certain conditions, we prove the existence of a solution specified in the form of a locally absolutely convergent power series. [ABSTRACT FROM AUTHOR]

In this paper, the approximate solutions of the time fractional Harry Dym equation with fractional derivative in the Caputo sense are obtained by using the Residual power series method (RPSM). This equation is a significant dynamical equation that occurs in a variety of physical systems. The suggested method provides good accuracy for the approximate solution when compared numerically with the exact solution. The effectiveness of the proposed method is also illustrated with the aid of numerical results. These results indicate that the RPSM is a power, useful, and applicable for determining the solutions of the time Hary Dym equation. Some of these results are illustrated by 2D and 3D graphics. Besides, the proposed method can be applied to many different differential equations due to its ease of use and reliability. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study of Class‐‐E/F2 and inverse Class‐‐F power amplifiers (PAs) designed for 35–42 GHz millimeter‐wave applications, utilizing a 130 nm CMOS process. The proposed RF PAs are well suited for wide frequency‐band millimeter‐wave and 5G radio transmitters. A comprehensive study of limiting factors in amplifier efficiency is presented in this paper. The study encompasses an analysis of all the factors that restrict the efficiency of the switched power amplifier. The first proposed power amplifier is based on the Class E/F2 architecture, comprising a parallel capacitor, second harmonic resonance circuit, and output matching network. Conversely, the second suggested power amplifier is constructed using the inverse Class‐‐F topology, which includes harmonic termination and matching networks. The harmonic termination circuit incorporates a second harmonic resonance network and utilizes a parasitic capacitor to control the harmonic components. Both the proposed Class E/F2 and inverse Class‐‐F architectures are employed to reshape the drain current and voltage waveforms, aiming to reduce the overlap between them and, consequently, improve efficiency. The suggested power amplifiers comprise a driver Class‐‐AB stage and a power stage constructed based on either the Class E/F2 architecture or inverse Class‐‐F topology, utilizing harmonic termination networks at the output load. Two new designs of high‐Q factor on‐chip finger capacitors have been implemented to improve efficiency and radio frequency performance. Achieving input matching and inter‐stage matching is facilitated by employing two novel on‐chip transformers designed for maximum power transfer. Additionally, an inter‐stage matching inductor is utilized in a cascode configuration to enhance the overall RF performance. The on‐chip transformers, inductors, and finger capacitors are designed using the HFSS software program. S‐parameter files (SNP files) of the designed on‐chip components are extracted and inserted into the simulation tool to ensure accurate results. The proposed Class E/F2 power amplifier achieves a constant power of 14.9 dBm, an extreme power added efficiency (PAE) of 11.7%, and a maximum gain of 13.74 dB. In contrast, the suggested inverse Class‐‐F power amplifier attains a constant power of 15.4 dBm, a peak PAE of 12.6%, and a maximum gain of 14.8 dB. The DC power consumption is 73 and 66 mW for the proposed Class E/F2 and inverse Class‐‐F PAs, respectively, while their active sizes are 0.14 and 0.2 mm2. [ABSTRACT FROM AUTHOR]

An audio power amplifier is an electronic device used to amplify a small signal source power at the input into a large signal power at the output that is speaker. In general, audio power amplifiers use class-AB amplifiers. In the process of amplifying the signal power, there will be power losses in the amplifiers which results in relatively lower amplifier power efficiency because there is a difference between the supply and output voltage levels. In this paper a class-G series audio power amplifier for subwoofers is designed to minimize these power losses and increase the power efficiency of the amplifier. The designed amplifier voltage supply is 40 V with a maximum output power of 80 W at an 8 Ω load. The amplifier has frequency response from 20–200 Hz and gain twice. Realization of the power amplifier and measurements were carried out using the circuit maker simulator, and the measurement results of the class-G power amplifier were compared with the class-AB power amplifier. The measurement results show that both power amplifiers meet the design specifications. The proposed class-G amplifier has 0.14% larger total harmonic distortion (THD) but has 10.4% greater power efficiency advantages over the class-AB amplifier. [ABSTRACT FROM AUTHOR]

We define an enrichment of the logarithmic derivative of the zeta function of a variety over a finite field to a power series with coefficients in the Grothendieck–Witt group. We show that this enrichment is related to the topology of the real points of a lift. For cellular schemes over a field, we prove a rationality result for this enriched logarithmic derivative of the zeta function as an analogue of part of the Weil conjectures. We also compute several examples, including toric varieties, and show that the enrichment is a motivic measure. [ABSTRACT FROM AUTHOR]

In this paper, we present Lie symmetry analysis for time fractional Black-Scholes equation with time-dependent coefficients. The group classification is carried out by investigating the time-dependent coefficients σ (t) , r(t) and s(t). Then the obtained group generators are used to reduce the equation under study, some of the reduced equations are fractional ordinary equations with Erdélyi-Kober fractional derivative, and some exact solutions including power series solutions are constructed. [ABSTRACT FROM AUTHOR]

We study the distribution of zeroes of power series with infinite radius of convergence. The coefficients of the series have the form ξ(n)a(n), where a is a smooth sequence of positive numbers, and ξ is a sequence of complex-valued multipliers having binary correlations and no gaps in the spectrum. We show that under certain assumptions on the smoothness of the sequence a and on the binary correlations of the multipliers ξ, the zeroes of the power series are equidistributed with respect to a radial measure defined by the sequence a. We apply our approach to several examples of the sequence ξ: (i) IID sequences, (ii) sequences e(αn² ) with Diophantine α, (iii) random multiplicative sequences, (iv) the Golay–Rudin–Shapiro sequence, (v) the indicator function of the square-free integers, (vi) the Thue–Morse sequence. [ABSTRACT FROM AUTHOR]

The primary objective of this paper is to introduce innovative orthogonal power function series aimed at obtaining accurate nonlinear analytical solutions for axisymmetric circular thin plates. The main features of this paper are as follows: The deflection is expanded by the innovative orthogonal power function series. The Airy stress function, which satisfies the geometric deformation compatibility equation, responds to the nonlinear coupling relationships between the plate deflection and the in-plane force or displacement boundary conditions. The nonlinear algebraic equations are obtained by the energy variational method. Many comparisons are made with the results of related researchers. The present accurate solutions not only allow the problems to be solved perfectly and provide the most reliable basis for engineering design but also set new benchmarks for the verification of various nonlinear numerical and approximate analytical solutions. The developed methodology represents a significant improvement, providing better accuracy and computational efficiency compared to historical approaches. Therefore, the present method is more worthy of promotion. [ABSTRACT FROM AUTHOR]

This article reports opto-electronic switching properties of heterostructure GaN/AlGaN lateral Avalanche Transit Time (ATT) diode oscillator. A novel technique has been adopted for the incorporation of 2DEG effect in two-terminal device. This is achieved through the inherent conduction band offset and subsequent application of Cathode Field Plate (CFP) in combination with lateral orientation. The performance superiority of the proposed electrical and optical switches over conventional silicon devices is evidently established and experimentally verified. Under dark condition, maximum RF power output with and without series resistance has been obtained as, RFP SR ∼ 1.5 × 10 11 W / m 2 and R F P ∼ 2.84 × 10 11 W / m 2 at 0.4THz. Also, the mentioned parasitic series resistance has been obtained to be, R Parasitic ∼ 7 × 10 - 10 Ω / m 2 . Under illumination, output power with and without series resistance, have been deduced to be RFP SR ∼ 1 × 10 11 W / m 2 and R F P ∼ 2 × 10 11 W / m 2 at 0.5THz, for M N = 10 . To the best of authors' knowledge this is the first report on electro-optical performance optimization study in connection with exotic type GaN/AlGaN two-terminal ATT oscillator. A power combining technique is used in designing a 3 × 3 array. For the 3 × 3 array structure, the parasitic series resistance is obtained to be R Parasitic ∼ 8.5 × 10 - 10 Ω / m 2 . Value of the series resistance has increased for such array as compared to a single diode, due to circuit loading. In spite of such increase in series resistance, RF output power increases substantially for the array structure, due to enhanced negative conductance. Under dark condition at 0.4THz, RFP SR ∼ 4 × 10 11 W / m 2 and R F P ∼ 7.7 × 10 11 W / m 2 are the RF power output with and without series resistance. Further, for illuminated array structure, peak RF power output, with and without series resistance, is obtained to be RFP SR ∼ 2.4 × 10 11 W / m 2 and R F P ∼ 5.3 × 10 11 W / m 2 at 0.5THz, for M N = 10 . The reported performance enhancement of the newly designed ATT diode is due to the high mobility 2DEG transport region. Such 2DEG has resulted from the quantum confinement caused by GaN/ AlGaN conduction band offset in conjunction with the unique CFP and lateral orientation of the proposed diode. For the first time, quantum confined high mobility 2DEG transport region has been formed in a two-terminal ATT device. [ABSTRACT FROM AUTHOR]

In this paper, an optimal age replacement policy has been studied for a parallel system with a random number of components. The objective functions have been constructed based on the expected cost rate and the availability functions. It is supposed that the lifetime of the system components has a Weibull distribution. Three famous members of the power series class of distributions, namely geometric, zero-truncated Poisson, and logarithmic distributions have been considered for the number of components. The optimal model and the conditions for finding the optimal solution have been studied in terms of the hazard rate function of the system. Numerical and graphical computations have been given. Finally, a real data set has been used to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we have presented the far field pattern in presence and absence of Kerr type nonlinearity for the first higher order mode in Dispersion shifted and dispersion flattened type optical fibers. Our analytical results are based on simple power series expressions for the first higher order (LP11) mode of aforesaid fibers, which have been formulated by Chebyshev formalism. Using the analytical expressions for the linear case, method of iteration is applied in order to predict the concerned propagation parameters in presence of Kerr type nonlinearity. We have taken some typical trapezoidal index, step W and Parabolic W fibers for our study. Our results for the far field pattern have been shown to be in excellent agreement with the exact numerical results computed by rigorous finite element technique. The simplicity and accuracy of our formalism will prove helpful to the designers for setting up of efficient low dispersion optical link. [ABSTRACT FROM AUTHOR]

Copyright of Przegląd Elektrotechniczny is the property of Przeglad Elektrotechniczny and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Let $ \alpha,\beta $ be real parameters and let $ a>0 $. We study radially symmetric solutions of$ \begin{equation*} S_k(D^2v)+\alpha v+\beta\xi\cdot\nabla v = 0,\, v>0\;\; \mbox{in}\;\; \mathbb{R}^n,\; v(0) = a, \end{equation*} $where the dot means the usual scalar product in $ \mathbb{R}^n $ and $ S_k(D^2v) $ denotes the $ k $-Hessian operator of $ v $. For $ \beta>0 $ and $ \alpha\leq\frac{\beta(n-2k)}{k}\;\;\mbox{with}\;\;k

In this paper, the Lie symmetry analysis method is applied to the high dimensional fractional Zakharov-Kuznetsov equation. All Lie symmetries and the corresponding conserved vectors for the equation are obtained. The one-dimensional optimal system is utilized to reduce the aimed equation with Riemann-Liouville fractional derivative to a low dimensional fractional partial differential equation with Erdélyi-Kober fractional derivative. Then the power series solution of the reduced equation is given. Moreover, some other low-dimensional reduced fractional differential equations with Riemann-Liouville fractional derivatives are obtained and can be solved by different methods in the literatures herein. [ABSTRACT FROM AUTHOR]

Since power systems are designed to work at the fundamental frequency, the presence of other frequencies from various sources may induce series and parallel resonances, leading to damage. The behavior of the power system in the presence of harmonics becomes evident with knowledge of harmonic impedance. Measurement offers the most accurate means of estimating harmonic impedance. However, when precise data of the power system parameters are available, highly satisfactory results can be achieved through calculation methods, particularly regarding loads, which are unknown and always change. This paper presents a study on estimating harmonic impedance using the Electromagnetic Transients Program Alternative Transient Program Draw (EMTP-ATPDraw) program, applied to an authentic network of Petrovice line 67, 22/0.4 kV, located in the Czech Republic. Hypothetically, the network was subjected to harmonic injection from a source (3rd, 5th, 7th, 9th, and 11th harmonics), and the harmonic impedance was calculated for three different variants: individual harmonics, all harmonics, and all except the 9th harmonic. The results show that the presence of the 9th harmonic can lead to a parallel resonance. This study is the first to employ EMTP-ATPDraw for programming this network. It gives the possibility to create a network database for different operating conditions, offering an asset for future project planning. [ABSTRACT FROM AUTHOR]

We consider a class of n th -order linear ordinary differential equations with a large parameter u. Analytic solutions of these equations can be described by (divergent) formal series in descending powers of u. We demonstrate that, given mild conditions on the potential functions of the equation, the formal solutions are Borel summable with respect to the parameter u in large, unbounded domains of the independent variable. We establish that the formal series expansions serve as asymptotic expansions, uniform with respect to the independent variable, for the Borel re-summed exact solutions. Additionally, we show that the exact solutions can be expressed using factorial series in the parameter, and these expansions converge in half-planes, uniformly with respect to the independent variable. To illustrate our theory, we apply it to an n th -order Airy-type equation. [ABSTRACT FROM AUTHOR]

Real-time simulations of laser-driven electron dynamics contain information about molecular optical properties through all orders in response theory. These properties can be extracted by assuming convergence of the power series expansion of induced electric and magnetic multipole moments. However, the accuracy relative to analytical results from response theory quickly deteriorates for higher-order responses due to the presence of high-frequency oscillations in the induced multipole moment in the time domain. This problem has been ascribed to missing higher-order corrections. We here demonstrate that the deviations are caused by nonadiabatic effects arising from the finite-time ramping from zero to full strength of the external laser field. Three different approaches, two using a ramped wave and one using a pulsed wave, for extracting electrical properties from real-time time-dependent electronic-structure simulations are investigated. The standard linear ramp is compared to a quadratic ramp, which is found to yield highly accurate results for polarizabilities, and first and second hyperpolarizabilities, at roughly half the computational cost. Results for the third hyperpolarizability are presented along with a simple, computable measure of reliability. [ABSTRACT FROM AUTHOR]

In this work, the author reviews the origination of normalized tails of the Maclaurin power series expansions of infinitely differentiable functions, presents that the ratio between two normalized tails of the Maclaurin power series expansion of the exponential function is decreasing on the positive axis, and proves that the normalized tail of the Maclaurin power series expansion of the exponential function is absolutely monotonic on the whole real axis. [ABSTRACT FROM AUTHOR]

Solutions to most nonlinear ordinary differential equations (ODEs) rely on numerical solvers, but this gives little insight into the nature of the trajectories and is relatively expense to compute. In this paper, we derive analytic solutions to a class of nonlinear, homogeneous ODEs with linear and quadratic terms on the right-hand side. We formulate a power series expansion of each state variable, whose function depends on the eigenvalues of the linearized system, and solve for the coefficients using some linear algebra and combinatorics. Various experiments exhibit quickly decaying coefficients, such that a good approximation to the true solution consists of just a few terms. [ABSTRACT FROM AUTHOR]

A bi-Gamma distribution model is proposed to determine the probability density function (PDF) of broadband non-Gaussian random stress rainflow ranges during vibration fatigue. A series of stress Power Spectral Densities (PSD) are provided, and the corresponding Gaussian random stress time histories are generated using the inverse Fourier transform and time-domain randomization methods. These Gaussian random stress time histories are then transformed into non-Gaussian random stress time histories. The probability density values of the stress ranges are obtained using the rainflow counting method, and then the bi-Gamma distribution PDF model is fitted to these values to determine the model's parameters. The PSD parameters and the kurtosis, along with their corresponding model parameters, constitute the neural network input–output dataset. The neural network model established after training can directly provide the parameter values of the bi-Gamma model based on the input PSD parameters and kurtosis, thereby obtaining the PDF of the stress rainflow ranges. The predictive capability of the neural network model is verified and the effects of non-Gaussian random stress with different kurtosis on the structural fatigue life are compared for the same stress PSD. And all life predicted results were within the second scatter band. [ABSTRACT FROM AUTHOR]

The Ratio Test and the Root Test for absolute convergence/divergence of series of numbers $ \sum _{n=0}^{\infty }a_n $ ∑n=0∞an are frequently discussed and proved independently in Calculus courses. The Root Test is stronger (verifies convergence for more series) than the Ratio Test. This relation inspires introduction of some intermediate strength tests (stronger than the Ratio Test and weaker than the Root Test) that we call Power Mean Tests (they, in particular, include the Arithmetic Mean Test). We show the connection between the Root, the Power Mean and the Ratio Tests. We also note that all these tests are related to the test that we formulate and call Generalised f-mean Test (or Kolmogorov–Nagumo–de Finetti mean Test). We provide an example of an infinite series, where the Arithmetic Mean test is the test that should be used for convergence verification, because the Root and the Ratio Tests are not easy to apply. We conclude this work with the statement emphasising why it is ‘fair’ to include the summarising Corollary 3.1 in our Calculus course. [ABSTRACT FROM AUTHOR]

ABSTRACT Power quality issues encompass a spectrum of disturbances that affect the stability and reliability of the power supply. This study explores voltage‐related anomalies, including sags, surges, flickers, unbalances, harmonics, interruptions, and swells, examining their origins, characteristics, and repercussions. These issues arise from a myriad of sources, such as load fluctuations, equipment malfunctions, and grid dynamics. The ramifications of these disturbances extend to equipment malfunctions, reduced operational efficiency, and financial losses. Dynamic voltage restorer (DVRs) are series custom power devices for mitigating these voltage‐related anomalies and use real‐time monitoring and control to quickly inject exact voltages into the grid during disruptions, restoring voltage levels to acceptable levels. This study demonstrates the capacity of DVRs to successfully alleviate power quality concerns, hence improving equipment dependability and system stability by analyzing case studies and simulation findings. The control system used to supply switching signals to the voltage source converter (VSC) of the DVR is based on adaptive Bateman polynomial (ABMP). Traditional DVR control techniques often rely on fixed or linear control strategies, which may not adequately handle varying load conditions and disturbances. ABMP offers an adaptive approach where the control parameters can adjust dynamically based on real‐time system conditions. This adaptive capability enhances the accuracy of voltage restoration, ensuring that the DVR responds optimally to varying loads and disturbances. During voltage sag and swell conditions at the grid side, the VSC injects the compensating voltage in series with the feeder with a constant switching frequency. A battery energy‐supported system (BESS) based DVR is considered for the proposed system. The supply is connected to the critical and sensitive loads. The proposed control scheme is validated through extensive simulation and experimental results. [ABSTRACT FROM AUTHOR]

Copper oxide (CuO) is considered a promising material for pseudocapacitor electrodes in supercapacitors. In this study, binder-free CuO/Ni7S6 composite electrode materials were prepared on nickel foam using a two-step electrodeposition method. The test results show that the CuO/Ni7S6-1:1–20 composite material has the best electrochemical performance. It displays an areal capacitance of 8644.3 mF cm−2 at a current density is 1 mA cm−2. The assembled CuO/Ni7S6-1:1–20‖PVDF/KOH‖CuO/Ni7S6-1:1–20 devices can reach a maximum energy density (Ea) and power density (Pa) of 112.5 μW h cm−2 and 4200 μW cm−2 respectively while retaining 58.3% of their initial capacitance after 3000 charge/discharge cycles. Two devices connected in series can power an LED lamp for up to 15 minutes. The results demonstrate that CuO/Ni7S6 materials have significant potential for application in supercapacitors. [ABSTRACT FROM AUTHOR]