• Title/Summary/Keyword: multidimensional operators

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LIOUVILLE THEOREMS FOR THE MULTIDIMENSIONAL FRACTIONAL BESSEL OPERATORS

  • Galli, Vanesa;Molina, Sandra;Quintero, Alejandro
    • Communications of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.1099-1129
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    • 2022
  • In this paper, we establish Liouville type theorems for the fractional powers of multidimensional Bessel operators extending the results given in [6]. In order to do this, we consider the distributional point of view of fractional Bessel operators studied in [12].

GENERALIZED SYMMETRICAL SIGMOID FUNCTION ACTIVATED NEURAL NETWORK MULTIVARIATE APPROXIMATION

  • ANASTASSIOU, GEORGE A.
    • Journal of Applied and Pure Mathematics
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    • v.4 no.3_4
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    • pp.185-209
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    • 2022
  • Here we exhibit multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝN, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the generalized symmetrical sigmoid function. The approximations are point-wise and uniform. The related feed-forward neural network is with one hidden layer.

PARAMETRIZED GUDERMANNIAN FUNCTION RELIED BANACH SPACE VALUED NEURAL NETWORK MULTIVARIATE APPROXIMATIONS

  • GEORGE A. ANASTASSIOU
    • Journal of Applied and Pure Mathematics
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    • v.5 no.1_2
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    • pp.69-93
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    • 2023
  • Here we give multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝN, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by a parametrized Gudermannian sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer.

Multidimensional Analysis of XML Documents using XML Cubes (XML 큐브를 이용한 다차원 XML 문서 분석)

  • Park, Byung-Kwon
    • Proceedings of the Korea Association of Information Systems Conference
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    • 2005.05a
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    • pp.65-78
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    • 2005
  • Nowadays, large amounts of XML documents are available on the Internet. Thus, we need to analyze them multi-dimensionally in the same way as relational data. In this paper, we propose a new frame-work for multidimensional analysis of XML documents, which we call XML-OLAP. We base XML-OLAP on XML warehouses where every fact data as well as dimension data are stored as XML documents. We build XML cubes from XML warehouses. We propose a new multidimensional expression language for XML cubes, which we call XML-MDX. XML-MDX statements target XML cubes and use XQuery expressions to designate the measure data. They specify text mining operators for aggregating text constituting the measure data. We evaluate XML-OLAP by applying it to a U.S. patent XML warehouse. We use XML-MDX queries, which demonstrate that XML-OLAP is effective for multi-dimensionally analyzing the U.S. patents.

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Extending the Multidimensional Data Model to Handle Complex Data

  • Mansmann, Svetlana;Scholl, Marc H.
    • Journal of Computing Science and Engineering
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    • v.1 no.2
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    • pp.125-160
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    • 2007
  • Data Warehousing and OLAP (On-Line Analytical Processing) have turned into the key technology for comprehensive data analysis. Originally developed for the needs of decision support in business, data warehouses have proven to be an adequate solution for a variety of non-business applications and domains, such as government, research, and medicine. Analytical power of the OLAP technology comes from its underlying multidimensional data model, which allows users to see data from different perspectives. However, this model displays a number of deficiencies when applied to non-conventional scenarios and analysis tasks. This paper presents an attempt to systematically summarize various extensions of the original multidimensional data model that have been proposed by researchers and practitioners in the recent years. Presented concepts are arranged into a formal classification consisting of fact types, factual and fact-dimensional relationships, and dimension types, supplied with explanatory examples from real-world usage scenarios. Both the static elements of the model, such as types of fact and dimension hierarchy schemes, and dynamic features, such as support for advanced operators and derived elements. We also propose a semantically rich graphical notation called X-DFM that extends the popular Dimensional Fact Model by refining and modifying the set of constructs as to make it coherent with the formal model. An evaluation of our framework against a set of common modeling requirements summarizes the contribution.

ε-AMDA Algorithm and Its Application to Decision Making (ε-AMDA 알고리즘과 의사 결정에의 응용)

  • Choi, Dae-Young
    • The KIPS Transactions:PartB
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    • v.16B no.4
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    • pp.327-331
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    • 2009
  • In fuzzy logic, aggregating uncertainties is generally achieved by means of operators such as t-norms and t-conorms. However, existing aggregation operators have some disadvantages as follows : First, they are situation-independent. Thus, they may not be properly applied to dynamic aggregation process. Second, they do not give an intuitional sense to decision making process. To solve these problems, we propose a new $\varepsilon$-AMDA (Aggregation based on the fuzzy Multidimensional Decision Analysis) algorithm to reflect degrees of strength for option i (i = 1, 2, ..., n) in the decision making process. The $\varepsilon$-AMDA algorithm makes adaptive aggregation results between min (the most weakness for an option) and max (the most strength for an option) according to the values of the parameter representing degrees of strength for an option. In this respect, it may be applied to dynamic aggregation process. In addition, it provides a mechanism of the fuzzy multidimensional decision analysis for decision making, and gives an intuitional sense to decision making process. Thus, the proposed method aids the decision maker to get a suitable decision according to the degrees of strength for options (or alternatives).

An Efficient Query Transformation for Multidimensional Data Views on Relational Databases (관계형 데이타베이스에서 다차원 데이타의 뷰를 위한 효율적인 질의 변환)

  • Shin, Sung-Hyun;Kim, Jin-Ho;Moon, Yang-Sae
    • Journal of KIISE:Databases
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    • v.34 no.1
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    • pp.18-34
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    • 2007
  • In order to provide various business analysis methods, OLAP(On-Line Analytical Processing) systems represent their data with multidimensional structures. These multidimensional data are often delivered to users in the horizontal format of tables whose columns are corresponding to values of dimension attributes. Since the horizontal tables nay have a large number of columns, they cannot be stored directly in relational database systems. Furthermore, the tables are likely to have many null values (i.e., sparse tables). In order to manage the horizontal tables efficiently, we can store them as the vertical format of tables which has dimension attribute names as their columns thus transforms the columns of horizontal tables into rows. In this way, every queries for horizontal tables have to be transformed into those for vertical tables. This paper proposed a technique for transforming horizontal table queries into vertical table ones by utilizing not only traditional relational algebraic operators but also the PIVOT operator which recent DBMS versions are providing. For achieving this goal, we designed a relational algebraic expression equivalent to the PIVOT operator and we formally proved their equivalence. Then, we developed a transformation technique for horizontal table queries using the PIVOT operator. We also performed experiments to analyze the performance of the proposed method. From the experimental results, we revealed that the proposed method has better performance than existing methods.

A Canonical Correlation Analysis of Customer Satisfaction for Family Restaurant Dining in Sunchon City (순천시 패밀리레스토랑 이용고객들의 외식만족에 대한 정준상관분석)

  • Kang, Jong-Heon
    • Journal of the Korean Society of Food Culture
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    • v.17 no.2
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    • pp.120-130
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    • 2002
  • The purpose of this study is to investigate whether a group of predictor variables which constitute four determinants of dining satisfaction do exert a significant influence on messures of dining satisfaction in family restaurant. Canonical correlation analysis is used to achieve the purpose of this study. This technique enables the researcher to test for the effects of a set of predictor variables upon a multidimensional measure of dining satisfaction in family restaurant. Results suggest that multiple determinants are important in determining dining satisfaction in family restaurant. No one determinant can fully explain its complexities. The four determinants also appear to vary in terms of importance. Individual variables within four determinants also appear to vary in terms of importance. Finally, the results of the study provide some insight into the types of marketing strategies that can be successfully used by operators who manage family restaurants.

Solving Time-dependent Schrödinger Equation Using Gaussian Wave Packet Dynamics

  • Lee, Min-Ho;Byun, Chang Woo;Choi, Nark Nyul;Kim, Dae-Soung
    • Journal of the Korean Physical Society
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    • v.73 no.9
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    • pp.1269-1278
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    • 2018
  • Using the thawed Gaussian wave packets [E. J. Heller, J. Chem. Phys. 62, 1544 (1975)] and the adaptive reinitialization technique employing the frame operator [L. M. Andersson et al., J. Phys. A: Math. Gen. 35, 7787 (2002)], a trajectory-based Gaussian wave packet method is introduced that can be applied to scattering and time-dependent problems. This method does not require either the numerical multidimensional integrals for potential operators or the inversion of nearly-singular matrices representing the overlap of overcomplete Gaussian basis functions. We demonstrate a possibility that the method can be a promising candidate for the time-dependent $Schr{\ddot{o}}dinger$ equation solver by applying to tunneling, high-order harmonic generation, and above-threshold ionization problems in one-dimensional model systems. Although the efficiency of the method is confirmed in one-dimensional systems, it can be easily extended to higher dimensional systems.