• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제5권2호
• /
• pp.140-144
• /
• 2005

We investigate the P-generating functions, L-generating functions, and A-generating function, respectively induced by product t-norms, Lukasiewicz t-norms and additive semi-groups. Furthermore, we investigate the relations among them.

• 대한수학회지
• /
• 제56권1호
• /
• pp.265-284
• /
• 2019

The main purpose of this paper is to investigate the q-Apostol type Frobenius-Euler numbers and polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive q-integers. By using infinite series representation for q-Apostol type Frobenius-Euler numbers and polynomials including their interpolation functions, we not only give some identities and relations for these numbers and polynomials, but also define generating functions for new numbers and polynomials. Further we give remarks and observations on generating functions for these new numbers and polynomials. By using these generating functions, we derive recurrence relations and finite sums related to these numbers and polynomials. Moreover, by applying higher-order derivative to these generating functions, we derive some new formulas including the Hurwitz-Lerch zeta function, the Apostol-Bernoulli numbers and the Apostol-Euler numbers. Finally, for an application of the generating functions, we derive a multiplication formula, which is very important property in the theories of normalized polynomials and Dedekind type sums.

• 대한수학회지
• /
• 제40권6호
• /
• pp.963-975
• /
• 2003

The aim of this work is to construct twisted q-L-series which interpolate twisted q-generalized Bernoulli numbers. By using generating function of q-Bernoulli numbers, twisted q-Bernoulli numbers and polynomials are defined. Some properties of this polynomials and numbers are described. The numbers $L_{q}(1-n,\;X,\;{\xi})$ is also given explicitly.

• 융합신호처리학회논문지
• /
• 제13권4호
• /
• pp.194-200
• /
• 2012

본 논문에서는 S.Bostas와 V.Kumar[7]에 의하여 제안되고 $GF(2^n)$에서 정의되는 부호계열 발생알고리즘을 분석하고, 길이 n인 이진벡터로 이루어지는 벡터공간 $F_2$으로부터, 두 원소로 정의되는 공간 $F_2$로 사상할 수 있는 부울함수를 이용하여 발생기 구성 함수를 도출하였다. 차수 n=5와 n=7인 두 종류의 최소 다항식을 이용한 피드벡 쉬프트레지스터를 기반으로 Trace 함수로부터 부호계열 발생기 구성 부울함수를 도출하고 발생기를 설계 구성하였으며 이를 이용하여 두 종류의 부호계열 군을 발생하였다. 발생된 부호계열의 주기는 각각 31과 127로서 주기 $L=2^n-1$을 만족하고 ${\tau}=0$을 제외한 자기상관함수 값과 상호상관함수 값이 각각 {-9, -1, 7}과 {-17, -1, 15}로서 상관함수 값 $R_{i,j}({\tau})=\{-2^{(n+1)/2}-1,-1,2^{(n+1)/2}-1\}$의 특성을 만족하였다. 이 결과로부터 부울함수를 이용한 부호계열 발생기 설계와 구성이 타당함을 확인하였다.

• Kyungpook Mathematical Journal
• /
• 제21권1호
• /
• pp.49-52
• /
• 1981

• Kyungpook Mathematical Journal
• /
• 제21권1호
• /
• pp.53-56
• /
• 1981

• 대한수학회지
• /
• 제54권5호
• /
• pp.1595-1604
• /
• 2017

We give a complete formula for the characteristic polynomial of hyperplane arrangements ${\mathcal{J}}_n$ consisting of the hyperplanes $x_i+x_j=1$, $x_k=0$, $x_l=1$, $1{\leq}i$, j, k, $l{\leq}n$. The formula is obtained by associating hyperplane arrangements with graphs, and then enumerating central graphs via generating functions for the number of bipartite graphs of given order, size and number of connected components.

• 대한수학회지
• /
• 제45권2호
• /
• pp.435-453
• /
• 2008

In this paper, by using q-deformed bosonic p-adic integral, we give $\lambda$-Bernoulli numbers and polynomials, we prove Witt's type formula of $\lambda$-Bernoulli polynomials and Gauss multiplicative formula for $\lambda$-Bernoulli polynomials. By using derivative operator to the generating functions of $\lambda$-Bernoulli polynomials and generalized $\lambda$-Bernoulli numbers, we give Hurwitz type $\lambda$-zeta functions and Dirichlet's type $\lambda$-L-functions; which are interpolated $\lambda$-Bernoulli polynomials and generalized $\lambda$-Bernoulli numbers, respectively. We give generating function of $\lambda$-Bernoulli numbers with order r. By using Mellin transforms to their function, we prove relations between multiply zeta function and $\lambda$-Bernoulli polynomials and ordinary Bernoulli numbers of order r and $\lambda$-Bernoulli numbers, respectively. We also study on $\lambda$-Bernoulli numbers and polynomials in the space of locally constant. Moreover, we define $\lambda$-partial zeta function and interpolation function.

• 약학회지
• /
• 제37권2호
• /
• pp.163-171
• /
• 1993

In order to study the functions of vascular endothelial nitric oxide(NO) generating system, we examined the effects of monomethylarginine(MMA) and dimethylarginine(DMA)(asym., sym.), arginine analogues, on modulation of vascular tone. Also, the concentrations of endogenous arginie and MMA were measured by HPLC in rat aortic tissues. The results were as follows. 1. The maximum relaxation induced by Ach (1.5$\times$10$^{-6}$M) was 80% of the contractility of rings of rat aorta induced by phenylephrine and L-Arg causes endothelium-dependent relaxation of the aorta precontracted with phenylephrine and these relaxation were concentration-dependent. 2. Endothelium-dependent contractility of rings of rat aorta induced by MMA (100 $\mu{M}$), DMA (asym., 100 $\mu{M}$) and DMA (sym., 100 $\mu{M}$) were 25.5%, 27.5% and 16.5% of that induced by phenylephrine respectively. 3. The relaxation of rat aortic ring induced by L-Arg was inhibited by MMA, DMA(asym.) and DMA(sym.). The degrees of inhibition induced by MMA, DMA(asym.) and DMA(sym.) were 45.7%, 37.1% and 18.3%, respectively. 4. The endogenous arginine and monomethylarginine contents in rat aorta were 83 pmoles/mg wet tissue, and 34.9 pmoles/mg wet tissue. After stimulation with Ach, the concentrations of L-Arg and MMA were significantly decreased. These results suggest that there are the strong relationships between the endogenous L-Arg and methylated arginines and NO-generating system.

• Journal of applied mathematics & informatics
• /
• 제40권5_6호
• /
• pp.813-830
• /
• 2022

The generating functions of the divisor function σ_s(n) = Σ_0<d|n d^s are quasimodular forms. In this paper, we find the basis of the space of quasimodular forms of weight 6 on Γ₀(10) consisting of Eisenstein series and η-quotients. Then we evaluate the convolution sum Σ_ak+bl+cm=n σ(k)σ(l)σ(m) with lcm(a, b, c) = 10 and Σ_al+bm=n lσ(l)σ(m) and Σ_al+bm=n σ₃(l)σ(m) with lcm(a, b) = 10.