• Title, Summary, Keyword: Dirichlet space

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On Efficient Algorithms for Generating Fundamental Units and their H/W Implementations over Number Fields (효율적인 수체의 기본단수계 생성 알고리즘과 H/W 구현에 관한 연구)

  • Kim, Yong-Tae
    • The Journal of the Korea institute of electronic communication sciences
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    • v.12 no.6
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    • pp.1181-1188
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    • 2017
  • The unit and fundamental units of number fields are important to number field sieves testing primality of more than 400 digits integers and number field seive factoring the number in RSA cryptosystem, and multiplication of ideals and counting class number of the number field in imaginary quadratic cryptosystem. To minimize the time and space in H/W implementation of cryptosystems using fundamental units, in this paper, we introduce the Dirichlet's unit Theorem and propose our process of generating the fundamental units of the number field. And then we present the algorithm generating our fundamental units of the number field to minimize the time and space in H/W implementation and implementation results using the algorithm over the number field.

Comparing Two Approaches of Analyzing Mixed Finite Volume Methods

  • Chou, So-Hsiang;Tang, Shengrong
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.5 no.1
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    • pp.55-78
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    • 2001
  • Given the anisotropic Poisson equation $-{\nabla}{\cdot}{\mathcal{K}}{\nabla}p=f$, one can convert it into a system of two first order PDEs: the Darcy law for the flux $u=-{\mathcal{K}{\nabla}p$ and conservation of mass ${\nabla}{\cdot}u=f$. A very natural mixed finite volume method for this system is to seek the pressure in the nonconforming P1 space and the Darcy velocity in the lowest order Raviart-Thomas space. The equations for these variables are obtained by integrating the two first order systems over the triangular volumes. In this paper we show that such a method is really a standard finite element method with local recovery of the flux in disguise. As a consequence, we compare two approaches in analyzing finite volume methods (FVM) and shed light on the proper way of analyzing non co-volume type of FVM. Numerical results for Dirichlet and Neumann problems are included.

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Development of Simulation Method of Doppler Power Spectrum and Raw Time Series Signal Using Average Moments of Radar Wind Profiler (윈드프로파일러의 평균모멘트 값을 이용한 도플러 파워 스펙트럼 및 시계열 원시신호 시뮬레이션기법 개발)

  • Lee, Sang-Yun;Lee, Gyu-Won
    • The Journal of the Korea institute of electronic communication sciences
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    • v.15 no.6
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    • pp.1037-1044
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    • 2020
  • Since radar wind profiler (RWP) provides wind field data with high time and space resolution in all weather conditions, their verification of the accuracy and quality is essential. The simultaneous wind measurement from rawinsonde is commonly used to evaluate wind vectors from RWP. In this study, the simulation algorithm which produces the spectrum and raw time series (I/Q) data from the average values of moments is presented as a step-by-step verification method for the signal processing algorithm. The possibility of the simulation algorithm was also confirmed through comparison with the raw data of LAP-3000. The Doppler power spectrum was generated by assuming the density function of the skew-normal distribution and by using the moment values as the parameter. The simulated spectrum was generated through random numbers. In addition, the coherent averaged I/Q data was generated by random phase and inverse discrete Fourier transform, and raw I/Q data was generated through the Dirichlet distribution.

A Study on Analysis of Topic Modeling using Customer Reviews based on Sharing Economy: Focusing on Sharing Parking (공유경제 기반의 고객리뷰를 이용한 토픽모델링 분석: 공유주차를 중심으로)

  • Lee, Taewon
    • Journal of the Korea Industrial Information Systems Research
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    • v.25 no.3
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    • pp.39-51
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    • 2020
  • This study will examine the social issues and consumer awareness of sharing parking through the method text mining. In this experiment, the topic by keyword was extracted and analyzed using TFIDF (Term frequency inverse document frequency) and LDA (Latent dirichlet allocation) technique. As a result of categorization by topic, citizens' complaints such as local government agreements, parking space negotiations, parking culture improvement, citizen participation, etc., played an important role in implementing shared parking services. The contribution of this study highly differentiated from previous studies that conducted exploratory studies using corporate and regional cases, and can be said to have a high academic contribution. In addition, based on the results obtained by utilizing the LDA analysis in this study, there is a practical contribution that it can be applied or utilized in establishing a sharing economy policy for revitalizing the local economy.

Empirical Comparison of Word Similarity Measures Based on Co-Occurrence, Context, and a Vector Space Model

  • Kadowaki, Natsuki;Kishida, Kazuaki
    • Journal of Information Science Theory and Practice
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    • v.8 no.2
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    • pp.6-17
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    • 2020
  • Word similarity is often measured to enhance system performance in the information retrieval field and other related areas. This paper reports on an experimental comparison of values for word similarity measures that were computed based on 50 intentionally selected words from a Reuters corpus. There were three targets, including (1) co-occurrence-based similarity measures (for which a co-occurrence frequency is counted as the number of documents or sentences), (2) context-based distributional similarity measures obtained from a latent Dirichlet allocation (LDA), nonnegative matrix factorization (NMF), and Word2Vec algorithm, and (3) similarity measures computed from the tf-idf weights of each word according to a vector space model (VSM). Here, a Pearson correlation coefficient for a pair of VSM-based similarity measures and co-occurrence-based similarity measures according to the number of documents was highest. Group-average agglomerative hierarchical clustering was also applied to similarity matrices computed by individual measures. An evaluation of the cluster sets according to an answer set revealed that VSM- and LDA-based similarity measures performed best.

EXISTENCE OF WEAK NON-NEGATIVE SOLUTIONS FOR A CLASS OF NONUNIFORMLY BOUNDARY VALUE PROBLEM

  • Hang, Trinh Thi Minh;Toan, Hoang Quoc
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.4
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    • pp.737-748
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    • 2012
  • The goal of this paper is to study the existence of non-trivial non-negative weak solution for the nonlinear elliptic equation: $$-div(h(x){\nabla}u)=f(x,u)\;in\;{\Omega}$$ with Dirichlet boundary condition in a bounded domain ${\Omega}{\subset}\mathbb{R}^N$, $N{\geq}3$, where $h(x){\in}L^1_{loc}({\Omega})$, $f(x,s)$ has asymptotically linear behavior. The solutions will be obtained in a subspace of the space $H^1_0({\Omega})$ and the proofs rely essentially on a variation of the mountain pass theorem in [12].

A Fast Bayesian Detection of Change Points Long-Memory Processes (장기억 과정에서 빠른 베이지안 변화점검출)

  • Kim, Joo-Won;Cho, Sin-Sup;Yeo, In-Kwon
    • The Korean Journal of Applied Statistics
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    • v.22 no.4
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    • pp.735-744
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    • 2009
  • In this paper, we introduce a fast approach for Bayesian detection of change points in long-memory processes. Since a heavy computation is needed to evaluate the likelihood function of long-memory processes, a method for simplifying the computational process is required to efficiently implement a Bayesian inference. Instead of estimating the parameter, we consider selecting a element from the set of possible parameters obtained by categorizing the parameter space. This approach simplifies the detection algorithm and reduces the computational time to detect change points. Since the parameter space is (0, 0.5), there is no big difference between the result of parameter estimation and selection under a proper fractionation of the parameter space. The analysis of Nile river data showed the validation of the proposed method.

SHAPING A NOZZLE WITH A CENTRAL BODY (스파이크 노즐 설계)

  • KIM C. W.
    • 한국전산유체공학회:학술대회논문집
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    • pp.293-298
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    • 2005
  • We calculate the coordinates of an axisymmetric nozzle with a central body. This nozzle ensures a transonic flow with a plane sound surface, which is orthogonal to the symmetry axis and has a wall kink at the sonic point, The Chaplygin transformation in the subsonic part of the flow leads the Dirichlet problem for a system of nonlinear equations. The definition domain of the solution in the velocity-hodograph plane is taken as a rectangle. This enables one to obtain the nozzle with a monotonic distribution of velocity along its subsonic part. In the nonlinear differential equation, the linear Chaplygin operator for plane flows is separated, which allows the iterative calculation of the solution. The supersonic part of the nozzle is calculated under the assumption that the flow at the nozzle exit is uniform and parallel to the symmetry axis; i.e., the supersonic jet outflows to the submerged space with the same pressure. The calculation is performed by the characteristic method. The exact solution of Tricomi equation for near-sonic flows with the straight sonic line is used to 'move away' the sound plane. The velocity distribution alone the supersonic part of the nozzle is also monotonic, which ensures the absence of the boundary-layer separation and, therefore, the adequacy of the ideal-gas model. calculations show that the flow in the supersonic part of the nozzle is continuous (compression shocks are absent)

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ON THE ANALOGS OF BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND ZETA AND L-FUNCTIONS

  • Kim, Tae-Kyun;Rim, Seog-Hoon;Simsek, Yilmaz;Kim, Dae-Yeoul
    • Journal of the Korean Mathematical Society
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    • v.45 no.2
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    • pp.435-453
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    • 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.

QUANTUM MARKOVIAN SEMIGROUPS ON QUANTUM SPIN SYSTEMS: GLAUBER DYNAMICS

  • Choi, Veni;Ko, Chul-Ki;Park, Yong-Moon
    • Journal of the Korean Mathematical Society
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    • v.45 no.4
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    • pp.1075-1087
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    • 2008
  • We study a class of KMS-symmetric quantum Markovian semigroups on a quantum spin system ($\mathcal{A},{\tau},{\omega}$), where $\mathcal{A}$ is a quasi-local algebra, $\tau$ is a strongly continuous one parameter group of *-automorphisms of $\mathcal{A}$ and $\omega$ is a Gibbs state on $\mathcal{A}$. The semigroups can be considered as the extension of semi groups on the nontrivial abelian subalgebra. Let $\mathcal{H}$ be a Hilbert space corresponding to the GNS representation con structed from $\omega$. Using the general construction method of Dirichlet form developed in [8], we construct the symmetric Markovian semigroup $\{T_t\}{_t_\geq_0}$ on $\mathcal{H}$. The semigroup $\{T_t\}{_t_\geq_0}$ acts separately on two subspaces $\mathcal{H}_d$ and $\mathcal{H}_{od}$ of $\mathcal{H}$, where $\mathcal{H}_d$ is the diagonal subspace and $\mathcal{H}_{od}$ is the off-diagonal subspace, $\mathcal{H}=\mathcal{H}_d\;{\bigoplus}\;\mathcal{H}_{od}$. The restriction of the semigroup $\{T_t\}{_t_\geq_0}$ on $\mathcal{H}_d$ is Glauber dynamics, and for any ${\eta}{\in}\mathcal{H}_{od}$, $T_t{\eta}$, decays to zero exponentially fast as t approaches to the infinity.