• 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 L_p,E(s, t; χ) be the p-adic Euler L-function of two variables. In this paper, for any α ∈ ℂ_p, |α|_p ≤ 1, we give a power series expansion of L_p,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 ∈ ℂ_p with |t|_p < 1. Some further properties for L_p,E(s, t; χ) has also been shown.

• East Asian mathematical journal
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• v.14 no.1
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• pp.63-76
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• 1998

we consider the hp-version to solve non-constant coefficients elliptic equations $-div(a{\nabla}u)=f$ with Dirichlet boundary conditions on a bounded polygonal domain $\Omega$ in $R^2$. In [6], M. Suri obtained an optimal error-estimate for the hp-version: ${\parallel}u-u^h_p{\parallel}_{1,\Omega}{\leq}Cp^{(\sigma-1)}h^{min(p,\sigma-1)}{\parallel}u{\parallel}_{\sigma,\Omega}$. This optimal result follows under the assumption that all integrations are performed exactly. In practice, the integrals are seldom computed exactly. The numerical quadrature rule scheme is needed to compute the integrals in the variational formulation of the discrete problem. In this paper we consider a family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties, which can be used for calculating the integrals. Under the numerical quadrature rules we will give the variational form of our non-constant coefficients elliptic problem and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_{1,\Omega}$.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.553-567
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• 2023

There are real life situations in our lives where the things are changing continuously or from time to time. It is a very important problem for one whether to continue the existing relationship or to form a new one after some occasions. That is, people, companies, cities, countries, etc. may change their opinion or position rapidly. In this work, we think of the problem of changing relationships from a mathematical point of view and think of an answer. In some sense, we comment these changes as power changes. Our number theoretical model will be based on this idea. Using the convolution sum of the restricted divisor function E, we obtain the answer to this problem.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.537-564
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• 2023

In this paper, we are mainly concerned with two-sided estimates for transition probabilities of symmetric Markov chains on ℤ^d, whose one-step transition probability is comparable to |x - y|^-dϕ_j (|x - y|)^-1 with ϕ_j being a positive regularly varying function on [1, ∞) with index α ∈ [2, ∞). For upper bounds, we directly apply the comparison idea and the Davies method, which considerably improves the existing arguments in the literature; while for lower bounds the relation with the corresponding continuous time symmetric Markov chains are fully used. In particular, our results answer one open question mentioned in the paper by Murugan and Saloff-Coste (2015).

• 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.

• Computational Structural Engineering
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• v.10 no.4
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• pp.267-280
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• 1997

This paper deals with the development of simplified methods to predict the creep deformation of reinforced concrete beams. The layer approach based on a degenerate kernel of compliance function in form of Dirichlet series is mentioned and a simplified analytical method derived from the equilibrium equations and compatibility conditions is proposed to overcome the sophisticated calculation procedures in the classical creep analysis. Correlation studies between analytical and experimental results and design codes are conducted with the objective to establish the validity of the proposed methods. Besides, various parameter studies are conducted with the objective to identify the effects of cracking, steel ratio and sectional shape in the creep deformation and the obtained results are discussed.

• Smart Media Journal
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• v.12 no.10
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• pp.38-46
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• 2023

Farming activities are transforming from traditional skill-based agriculture into knowledge-based and technology-driven digital agriculture. The use of intelligent information and communication technology introduces the idea of smart farming that enables farmers to collect weather data, monitor crop growth remotely and detect crop diseases easily. The introduction of Plantix, a pest and disease management tool in the form of a mobile application has allowed farmers to identify pests and diseases of the crop using their mobile devices. Hence, this study collected the reviews of Plantix to explore the response of the users on the Google Play Store towards the application through Latent Dirichlet Allocation (LDA) topic modeling. Results indicate four latent topics in the reviews: two positive evaluations (compliments, appreciation) and two suggestions (plant options, recommendations). We found the users suggested the application to additional plant options and additional features that might help the farmers with their difficulties. In addition, the application is expected to benefit the farmer more by having an early alert of diseases to farmers and providing various substitutes and a list of components for the remedial measures.

• Journal of KIISE
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• v.41 no.9
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• pp.652-665
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• 2014

Many important terminologies in biomedical text are expressed as abbreviations or acronyms. We newly suggest a semantic link topic model based on the concepts of topic and dependency link to disambiguate biomedical abbreviations and cluster long form variants of abbreviations which refer to the same senses. This model is a generative model inspired by the latent Dirichlet allocation (LDA) topic model, in which each document is viewed as a mixture of topics, with each topic characterized by a distribution over words. Thus, words of a document are generated from a hidden topic structure of a document and the topic structure is inferred from observable word sequences of document collections. In this study, we allow two distinct word generation to incorporate semantic dependencies between words, particularly between expansions (long forms) of abbreviations and their sentential co-occurring words. Besides topic information, the semantic dependency between words is defined as a link and a new random parameter for the link presence is assigned to each word. As a result, the most probable expansions with respect to abbreviations of a given abstract are decided by word-topic distribution, document-topic distribution, and word-link distribution estimated from document collection though the semantic dependency link topic model. The abstracts retrieved from the MEDLINE Entrez interface by the query relating 22 abbreviations and their 186 expansions were used as a data set. The link topic model correctly predicted expansions of abbreviations with the accuracy of 98.30%.

• Journal of the Korean Institute of Landscape Architecture
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• v.49 no.5
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• pp.46-58
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• 2021

Parks became essential to people after the introduction of modern parks in Korea. Following mayoral elections by popular vote, issues surrounding parks, such as the creation of parks, have arisen and have been publicized by the media, allowing for the formation of discourse. Accordingly, this study conducted a topic analysis by collecting news articles from major media outlets in Korea that addressed issues related to parks since 1995, after the introduction of mayoral elections by popular vote, and analyzed changes over time in the discourse on parks through semantic network analysis. As a result of a Latent Dirichlet allocation topic modeling analysis, the following five topics were classified: urban park expansion (Topic 1), historical and cultural parks (Topic 2), use programs (Topic 3), zoo event (Topic 4), and conflicts in the park creation process (Topic 5). The park-related discourse addressed by the media is as follows. First, the creation process and conflicts regarding the quantitative expansion of parks are treated as the central discourse. Second, the names of parks appear as keywords every time a new park is created, and they are mentioned continuously from then on, thereby playing an important role in the formation of discourse. Third, 'residents' form discourse about the public nature of the park as the principal agent in park-related media. This study has significance in that it examines how parks are interpreted and how discourse is formed and changed by the media. It is expected that discourse on parks will be addressed from various perspectives in further research focusing on other media, such as regional and specialized magazines.

• Smart Media Journal
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• v.12 no.8
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• pp.9-17
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• 2023

The development of information and communication technology and the improvement of the development and dissemination of smart devices have caused changes in the form of tourism, and the concept of smart tourism has since emerged. In this regard, researches related to smart tourism has been conducted in various fields such as policy implementation and surveys, but there is a lack of research on application reviews. This study collects Trip Advisor application review data in the Google Play Store to identify usage of the application and user satisfaction through Latent Dirichlet Allocation (LDA) topic modeling. The analysis results in four topics, two of which are positive and the other two are negative. We found that users were satisfied with the application's recommendation system, but were dissatisfied when the filters they set during search were not applied or that reviews were not published after updates of the application. We suggest more categories can be added to the application to provide users with different experiences. In addition, it is expected that user satisfaction can be improved by identifying problems within the application, including the filter function, and checking the application environment and resolving the error occurring during the application usage.