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Generalized Analytic Network Process with Path Restriction by the Distance Matrix and transition functions

INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING 2023年第0期

作者： Huang, Jih-Jeng Chen, Chin-Yi Soochow Univ Dept Comp Sci & Informat Management 56 Sect 1Kueiyang St Taipei City 100 Taiwan Chung Yuan Christian Univ Dept Business Adm 200 Chung Pei Rd Taoyuan 320 Taiwan

The analytic network process (ANP) is a generalized analytic hierarchy process used to handle the interdependency and feedback effects between criteria in various multi-criteria decision-making problems. However, problems regarding the ANP have been proposed because of its restrictions and limitations when used in practice. In this paper, we focus on the issues of path restriction between criteria and the transition functions of the supermatrix. It has been postulated that with regard to path restriction between criteria, a criterion with a longer path to another criterion should have less influence, which is likewise assumed in the conventional ANP. In addition, we add transition functions into the supermatrix to calculate the steady-state weights of the criteria. transition functions are beneficial because they allow the consideration of the supermatrix's nonlinear transition instead of the linear situation. The numerical examples in this study show that our proposed method is a generalization of the ANP and reduces to the conventional ANP if the path restriction is released, and the transition function is linear.

关键词： Analytic network process (ANP) multi-criteria decision making (MCDM) path restrictions transition functions

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Existence and Uniqueness of Denumerable Markov Processes with Instantaneous States

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JOURNAL OF THEORETICAL PROBABILITY 2024年第1期37卷 511-532页

作者： Wu, Xiaohan Chen, Anyue Li, Junping Liaocheng Univ Sch Math Sci Liaocheng 252059 Peoples R China Harbin Inst Technol Dept Math Harbin 150001 Peoples R China Southern Univ Sci & Technol Dept Math Shenzhen 518055 Peoples R China Southern Univ Sci & Technol Dept Math Xue Yuan Blvd 1088 Shenzhen 518055 Peoples R China Univ Liverpool Dept Math Sci Peach St Liverpool L69 7ZL England Cent South Univ Sch Math & Stat Changsha 410083 Peoples R China

Based on the resolvent decomposition theorems presented very recently by Chen (J Theor Probab 33:2089-2118, 2020), in this paper we focus on investigating the fundamental problems of existence and uniqueness criteria for Denumerable Markov Processes with finitely many instantaneous states. Some elegant sufficient and necessary conditions are obtained for this less-investigated topic. A few important examples including the generalized Kolmogorov models are presented to illustrate our general results.

关键词： Denumerable Markov processes transition functions Resolvent Taboo probabilities Existence Uniqueness

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Influence of Different transition Modes on the Performances of a Hydraulic Turbine

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Fluid Dynamics & Materials Processing 2023年第10期19卷 2481-2497页

作者： Fengxia Shi Yucai Tang Dedong Ma Xiangyun Shi Guangbiao Zhao School of Energy and Power Engineering Lanzhou University of TechnologyLanzhou730050China Key Laboratory of Fluid Machinery and Systems of Gansu Lanzhou730050China

In order to analyze the response of a hydraulic turbine to a variation in the operating conditions,different laws of variation in time of the massﬂow rate have been *** validating the overall numerical framework through comparison with relevant experiments,the performances of the considered turbine have been analyzed from aﬂuid-dynamic point of *** results show that different time proﬁles of the massﬂow rate(in this work,for simplicity,referred to as“transition functions”)have a varying inﬂuence on the transient behavior of the *** a quadratic function is considered for the case of largeﬂow,the transient head and torque increase gradually with time,theﬂuctuation amplitude of the transient hydraulic efﬁciency at the main frequency is the largest,and theﬂuctuation amplitude of the radial force is the *** the smallﬂow case,the time proﬁle with exponential nature leads to the best *** transient head and torque decrease gradually with time,the pulsation amplitude of the transient hydraulic efﬁciency is the largest at the main frequency,and the pulsation amplitude of the radial force is the smallest.

关键词： transition functions hydraulic turbine transition process radial resultant force

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New classes of p-adic evolution equations and their applications

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JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS 2023年第1期14卷 1-19页

作者： Torresblanca-Badillo, Anselmo Bolano-Benitez, Edwin A. Univ Norte Dept Matemat & Estadist Km 5 Via Puerto Colombia Barranquilla Colombia

In this article, we study new classes of evolution equations in the p-adic context. We establish rigorously that the fundamental solutions of the homogeneous Cauchy problem, naturally associated to these equations, are transition density functions of some strong Markov processes (sic) with state space the n-dimensional p-adic unit ball (Z(p)(n)). We introduce a family of operators {T-t}(t >= 0 )(obtained explicitly) that determine a Feller semigroup on C-0(Z(p)(n)). Also, we study the asymptotic behavior of the survival probability of a strong Markov processes (sic) on a ball B--m(n) subset of Z(p)(n), m is an element of N. Moreover, we study the inhomogeneous Cauchy problem and we will show that its mild solution is associated with the mentioned above Feller semigroup.

关键词： Nonlocal evolution equations Heat kernel Strong Markov processes Feller semigroups transition functions p-adic analysis

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Some further classes of pseudo-differential operators in the p-adic context and their applications

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JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS 2023年第2期14卷 24页

作者： Torresblanca-Badillo, Anselmo Albarracin-Mantilla, Adriana. A. A. Univ Norte Dept Matemat & Estadist Km 5 Via Puerto Colombia Barranquilla Colombia Univ Ind Santander Escuela Matemat Cra 27Calle 9 Bucaramanga 680001 Santander Colombia

The purpose of this article is to study new non-Archimedean pseudo-differential operators whose symbols are determined from the behavior of two functions defined on the p-adic numbers. Thanks to the characteristics of our symbols, we can find connections between these operators and new types of non-homogeneous differential equations, Feller semigroups, contraction semigroups and strong Markov processes.

关键词： Pseudo-differential operators Heat kernel Markov processes Feller semigroups transition functions p-Adic analysis

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Simulation of loess gully evolution based on geographic cellular automata

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EARTH SURFACE PROCESSES AND LANDFORMS 2022年第3期47卷 756-777页

作者： Luo, Lanhua Ma, Jin Li, Fayuan Jiao, Haoyang Strobl, Josef Zhu, A-xing Dai, Ziyang Liu, Shuanglin Nanjing Normal Univ Minist Educ Key Lab Virtual Geog Environm Nanjing Peoples R China Nanjing Normal Univ Sch Geog Nanjing 210023 Peoples R China Jiangsu Ctr Collaborat Innovat Geog Informat Reso Nanjing Peoples R China Chongqing Survey Inst Chongqing Peoples R China Univ Salzburg Interfac Dept Geoinformat Salzburg Austria

Gully development is an important topic in the evolution of modern geomorphology. The study of the development process of gullies is key to understanding the genesis, mechanism and spatial differentiation of loess geomorphology. This study explored the mechanism of the development process of gullies whilst taking into account the erosion characteristics of the gully head area, gully slope area and gully bed area. Based on geographic cellular automata (Geo-CA), the transition rules were interacted with the fundamental hydraulic principles for gully evolution simulation. Different sediment transfer rules apply to the gully slope area and gully bed area. A simulation model of the loess gully evolution was constructed and implemented based on the loess simulation small watershed. The superior performance of the model was demonstrated by the accuracy evaluation of the model structure and the comparative analysis of the modelling results. Moreover, the model was validated by natural watershed data, and the analytical results indicated the feasibility of the model.

关键词： DEM geographic cellular automata (Geo-CA) geomorphological process model simulation loess gully development transition functions

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A practical method for computing with piecewise Chebyshevian splines

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2022年第0期406卷 114051-114051页

作者： Beccari, Carolina Vittoria Casciola, Giulio Romani, Lucia Univ Bologna Dept Math Piazza Porta San Donato 5 I-40126 Bologna Italy

A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under knot insertion. The interest in such kind of spaces is justified by the fact that, similarly as for polynomial splines, the related parametric curves exhibit the desired properties of convex hull inclusion, variation diminution and intuitive relation between the curve shape and the location of the control points. For a good-for-design space, in this paper we construct a set of functions, called transition functions, which allow for efficient computation of the B-spline basis, even in the case of nonuniform and multiple knots. Moreover, we show how the spline coefficients of the representations associated with a refined knot partition and with a raised order can conveniently be expressed by means of transition functions. This result allows us to provide effective procedures that generalize the classical knot insertion and degree raising algorithms for polynomial splines. We further discuss how the approach can straightforwardly be generalized to deal with geometrically continuous piecewise Chebyshevian splines as well as with splines having section spaces of different dimensions. From a numerical point of view, we show that the proposed evaluation method is easier to implement and has higher accuracy than other existing algorithms. (c) 2021 Elsevier B.V. All rights reserved.

关键词： (Piecewise) Chebyshevian splines B-spline basis Knot insertion Order elevation Computational algorithms transition functions

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On some generalizations of non-archimedean pseudo-differential operators and their applications

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2022年第2期512卷

作者： Torresblanca-Badillo, Anselmo Univ Norte Dept Matemat & Estadist Km 5 Via Puerto Colombia Barranquilla Colombia

In this article we define and study various generalizations non-archimedean pseudo-differential operators and its connections with probability theory. We provide explicit and sufficient conditions to ensure that these operators can satisfy the positive maximum principle, the heat Kernel or fundamental solution of the Cauchy problem (or heat equation) naturally associated with these operators determine a Feller semigroup and a transition function of some strong Markov processes X with state space the p-adic numbers. Also, we will study the property of Conservation of mass, the Comparison principle and some aspects of these processes including the first passage time problem and the probability of survival. These equations are proposed as mathematical models (connected with energy landscapes) to study the spread of an infectious or contagious disease that takes into account social clusters in a situation of extreme social isolation. (C) 2022 Elsevier Inc. All rights reserved.

关键词： Pseudo-differential operators Heat kernel Markov processes Feller semigroups transition functions p-adic analysis

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Resolvent Decomposition Theorems and Their Application in Denumerable Markov Processes with Instantaneous States

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JOURNAL OF THEORETICAL PROBABILITY 2020年第4期33卷 2089-2118页

作者： Chen, Anyue Southern Univ Sci & Technol Dept Math Xueyuan Blvd 1088 Shenzhen 518055 Peoples R China Univ Liverpool Dept Math Sci Peach St Liverpool L69 7ZL Merseyside England

The basic aim of this paper is to provide a fundamental tool, the resolvent decomposition theorem, in the construction theory of denumerable Markov processes. We present a detailed analytic proof of this extremely useful tool and explain its clear probabilistic interpretation. We then apply this tool to investigate the basic problems of existence and uniqueness criteria for denumerable Markov processes with instantaneous states to which few results have been obtained even until now. Although the complete answers regarding these existence and uniqueness criteria will be given in a subsequent paper, we shall, in this paper, present part solutions of these very important problems that are closely linked with the subtle Williams S and N conditions.

关键词： Denumerable Markov processes transition functions Resolvents Taboo probabilities Existence Uniqueness

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Prediction of post-thinning stem volume in slash pine stands by means of state and transition models

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NEW FORESTS 2019年第4期50卷 663-676页

作者： Fiandino, Santiago Plevich, Jose Tarico, Juan Utello, Marco Gyenge, Javier Natl Univ Rio Cuarto Dept Plant Prod X5804BYA Rio Cuarto Cordoba Argentina Consejo Nacl Invest Cient & Tecn Godoy Cruz 2290C142FQB Buenos Aires DF Argentina INTA EEA Balcarce AER Tandil RA-7000 Buenos Aires DF Argentina

Predicting growth and production is the key to effective forest management, especially in those stands where silvicultural treatments are more intensive, such as silvopastoral systems. The aim of this study was to fit a state and transition model (STM) to predict the stem volume of slash pine silvopastoral systems under different management strategies. Volume growth was modeled by using the dominant height and the Relative Density Index, which can be related to other density indices (such as the Height Factor) through a proportionality factor. This link between density indices is what makes it possible to develop the transition functions, which are used to predict post-thinning stem volume. The transitional functions were established through three different approaches. Although all of them are good predictors of the Relative Density Index pattern, the best results in volume prediction were obtained when fitting the Weibull model to predict the Relative Density Index as a response of the Height Factor. By using this transition function, the differences in the mean volume between the predicted and observed data were less than 7% for all cases. We conclude that the proposed models are valuable management tools to predict the stem volume accumulated in the post-thinning period, and therefore, this finding may improve the management planning of the plantations of the region.

关键词： Density indices Stand volume Silvopastoral systems Thinning transition functions

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