• Title/Summary/Keyword: sum of power p

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ON A QUASI-POWER MODULE

  • PARK CHIN HONG;SHIM HONG TAE
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.679-687
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    • 2005
  • In this paper we shall give a new definition for a quasi-power module P(M) and discuss some properties for P(M). The quasi-power module P(M) is a direct sum of invertible quasi-submodules C(H)'s of P(M) and then the quasi-submodule C(H) is also a direct sum of strongly cyclic quasi-submodules of C(H). When M is a quasi-perfect right R-module, we shall see that the quasi-power module P(M) is invertible.

GENERALIZED EULER POWER SERIES

  • KIM, MIN-SOO
    • Journal of applied mathematics & informatics
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    • v.38 no.5_6
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    • pp.591-600
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    • 2020
  • This work is a continuation of our investigations for p-adic analogue of the alternating form Dirichlet L-functions $$L_E(s,{\chi})={\sum\limits_{n=1}^{\infty}}{\frac{(-1)^n{\chi}(n)}{n^s}},\;Re(s)>0$$. Let Lp,E(s, t; χ) be the p-adic Euler L-function of two variables. In this paper, for any α ∈ ℂp, |α|p ≤ 1, we give a power series expansion of Lp,E(s, t; χ) in terms of the variable t. From this, we derive a power series expansion of the generalized Euler polynomials with negative index, that is, we prove that $$E_{-n,{\chi}}(t)={\sum\limits_{m=0}^{\infty}}\(\array{-n\\m}\)E_{-(m+n),{\chi}^{t^m}},\;n{\in}{\mathbb{N}}$$, where t ∈ ℂp with |t|p < 1. Some further properties for Lp,E(s, t; χ) has also been shown.

IDENTITIES OF SYMMETRY FOR THE HIGHER ORDER q-BERNOULLI POLYNOMIALS

  • Son, Jin-Woo
    • Journal of the Korean Mathematical Society
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    • v.51 no.5
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    • pp.1045-1073
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    • 2014
  • The study of the identities of symmetry for the Bernoulli polynomials arises from the study of Gauss's multiplication formula for the gamma function. There are many works in this direction. In the sense of p-adic analysis, the q-Bernoulli polynomials are natural extensions of the Bernoulli and Apostol-Bernoulli polynomials (see the introduction of this paper). By using the N-fold iterated Volkenborn integral, we derive serval identities of symmetry related to the q-extension power sums and the higher order q-Bernoulli polynomials. Many previous results are special cases of the results presented in this paper, including Tuenter's classical results on the symmetry relation between the power sum polynomials and the Bernoulli numbers in [A symmetry of power sum polynomials and Bernoulli numbers, Amer. Math. Monthly 108 (2001), no. 3, 258-261] and D. S. Kim's eight basic identities of symmetry in three variables related to the q-analogue power sums and the q-Bernoulli polynomials in [Identities of symmetry for q-Bernoulli polynomials, Comput. Math. Appl. 60 (2010), no. 8, 2350-2359].

A Low Power Realization by Eliminating Glitch-Propagation in an ALU with P/G blocks (P/G블록을 가진 ALU에서 글리치 전파제거에 의한 저전력 실현)

  • Ryu, Beom-Seon;Lee, Seong-Hyeon;Lee, Gi-Yeong;Jo, Tae-Won
    • Journal of the Institute of Electronics Engineers of Korea SD
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    • v.38 no.1
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    • pp.55-68
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    • 2001
  • This paper presents a new ALU architecture to minimize glitching power consumption which is appeared in the conventional one with P(carry propagation)/G(carry generation) blocks. In general, A lot of glitches generated once are propagating into the next stage of circuits to make unnecessary power dissipation. Therefore, a new ALU architecture which removes the glitches at the output of P/G blocks is presented in this paper. If a lot of glitches at the output of P/G blocks are removed, then the signal transitions caused by glitches are reduced in the sum generation block and hence power consumption is also reduced. A latch is inserted into the conventional P/G blocks to remove the glitches at the output of P/G blocks. Latch enable signal can make a role in eliminating a lot of glitches at the P/G's outputs by controlling output enable time. Experimental results from HSPICE simulations with implementing 16-b ALU show 28% reduction in glitching power consumption with negligible delay penalty.

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Emergence and Structure of Complex Mutualistic Networks

  • Lee, KyoungEun;Jung, Nam;Lee, Hyun Min;Maeng, Seung Eun;Lee, Jae Woo
    • Proceedings of the National Institute of Ecology of the Republic of Korea
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    • v.3 no.3
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    • pp.149-153
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    • 2022
  • The degree distribution of the plant-pollinator network was identified by analyzing the data in the ecosystem and reproduced by a model of the growing bipartite mutualistic networks. The degree distribution of pollinator shows power law or stretched exponential distribution, while plant usually shows stretched exponential distribution. In the growth model, the plant and the pollinator are selected with probability Pp and PA=1-Pp, respectively. The number of incoming links for the plant and the pollinator is lp and lA, respectively. The probability that the link of the plant selects the pollinator of the existing network given as $A_{k_i}=k^{{\lambda}_A}_i/{\sum}_i\;k^{{\lambda}_A}_i$, and the probability that the pollinator selects the plant is $P_{k_i}=k^{{\lambda}_p}_i/{\sum}_i\;k^{{\lambda}_p}_i$. When the nonlinear growth index is 𝛌X=1 (X=A or P), the degree distribution follows a power law, and if 0≤𝛌X<1, the degree distribution follows a stretched exponential distribution. The cumulative degree distributions of plants and pollinators of 14 empirical plant-pollinators included in Interaction Web Database were calculated. A set of parameters (PA,PP,lA,lP) that reproduces these cumulative degree distributions and a growth index 𝛌X (X=A or P) were obtained. We found that animal takes very heterogenous connections, whereas plant takes a more flexible connection network.

Design and Amplitude Modulation Characteristics with Bias of Class J Power Amplifier for CSB (CSB용 J급 전력증폭기 설계 및 바이어스에 따른 진폭 변조 특성)

  • Su-kyung Kim;Kyung-Heon Koo
    • Journal of Advanced Navigation Technology
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    • v.27 no.6
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    • pp.849-854
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    • 2023
  • In this paper, a high-efficiency power amplifier was designed by applying the operating point Class J using LDMOS(laterally diffused metal oxide semiconductor) and optimizing the output matching circuit so that the second harmonic impedance becomes the reactance impedance. The designed power amplifier has a frequency of 108 ~ 110 MHz, Characteristics of PAE(power added efficiency) is 71.5% at PSAT output (54.5 dBm), 55.5% at P1dB output (51.5 dBm), and 24.38% at 45 dBm. The CSB(carrier with sideband) amplifier, which is the reference signal in the spatial modulation method, has an operating output of 45 dBm ~ 35 dBm, and linear SDM(sum in the depth of modulation) characteristics(40% ± 0.3%) were obtained. We measure the characteristics in amplitude modulation according to the bias operating point of the power amplifier for CSB and propose the optimal operating point to obtain linear modulation characteristics.

EVERY POLYNOMIAL OVER A FIELD CONTAINING 𝔽16 IS A STRICT SUM OF FOUR CUBES AND ONE EXPRESSION A2 + A

  • Gallardo, Luis H.
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.5
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    • pp.941-947
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    • 2009
  • Let q be a power of 16. Every polynomial $P\in\mathbb{F}_q$[t] is a strict sum $P=A^2+A+B^3+C^3+D^3+E^3$. The values of A,B,C,D,E are effectively obtained from the coefficients of P. The proof uses the new result that every polynomial $Q\in\mathbb{F}_q$[t], satisfying the necessary condition that the constant term Q(0) has zero trace, has a strict and effective representation as: $Q=F^2+F+tG^2$. This improves for such q's and such Q's a result of Gallardo, Rahavandrainy, and Vaserstein that requires three polynomials F,G,H for the strict representation $Q=F^2$+F+GH. Observe that the latter representation may be considered as an analogue in characteristic 2 of the strict representation of a polynomial Q by three squares in odd characteristic.

SOME SYMMETRY IDENTITIES FOR GENERALIZED TWISTED BERNOULLI POLYNOMIALS TWISTED BY UNRAMIFIED ROOTS OF UNITY

  • Kim, Dae San
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.2
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    • pp.603-618
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    • 2015
  • We derive three identities of symmetry in two variables and eight in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by unramified roots of unity. The case of ramified roots of unity was treated previously. The derivations of identities are based on the p-adic integral expression, with respect to a measure introduced by Koblitz, of the generating function for the generalized twisted Bernoulli polynomials and the quotient of p-adic integrals that can be expressed as the exponential generating function for the generalized twisted power sums.

Calculation of Carrier Electron Concentration in ZnO Depending on Oxygen Partial Pressure

  • Kim, Eun-Dong;Park, Jong-Mun;Kim, Sang-Cheol;Kim, Nam-Kyun
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2000.05b
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    • pp.222-232
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    • 2000
  • The relationship between carrier electron concentration(n) and atmosphere oxygen partial pressure($P_{O_2}$ for pure ZnO calculated by the mass-action law, well-known as n ${\propto}P^{-1/m}_{O_2}$ where m = 4 or 6 for the single or the double ionization of the native donor defects due to its nonstoichiometry, respectively, is found in competition with the calculation result on the basis that the total defect concentration is the sum of those of unionized and ionized defects. Definitively, it is found inconsistent with the calculation result by employing the Fermi-Dirac(FD) statistics for their ionization processes. By application of the FD statistics law to the ionization while assuming the defect formation is still ruled by the mass-action law, the calculation results shows the concentration is proportional to $P^{-1/2}_{O_2}$ whenever they ionize singly and/or doubly. Conclusively we would like to propose the new theoretical relation n ${\propto}P^{-1/m}_{O_2}$ because the ionization processes of donors in ZnO should be treated with the electronoccupation probability at localized quantum states in its forbidden band created by the donor defects, i.e. the FD statistics

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Evaluation of PTO Severeness for 78 kW-Class Tractor According to Disk Plow Tillage and Rotary Tillage (디스크플라우 및 로타리 작업에 따른 78 kW급 트랙터 PTO 가혹도 평가)

  • Kim, Wan Soo;Kim, Yong Joo;Park, Seong Un;Hong, Soon Jung;Kim, Yeon Soo
    • Journal of Drive and Control
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    • v.16 no.4
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    • pp.23-31
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    • 2019
  • The purpose of this study was to evaluate the PTO severeness for an agricultural tractor during disk plow and rotary tillage. The PTO load measurement system was constructed with data acquisition and a PTO torquemeter. Field experiments were conducted at a combination of traveling speed (L3 Low, L3 High) and PTO speed (P1, P2). The load spectrum was generated using the rain-flow counting method, and the SWT method was used to consider the range and mean of the PTO load. The damage sum was calculated by applying a modified miner rule, which is a cumulative damage law. The relative severeness was expressed as the ratio of the lowest damage sum. Relative severeness was higher with the lower PTO gear stage, and higher driving gear stage and it was approximately 40-102 times higher for rotary tillage than disk plow tillage in the same gear stages. The relative severeness was 1010.12 in the rotary tillage under L3 High P1 based on the disk plow tillage under L3 Low P2.