scholarly journals The Discrete Agglomeration Model: Equivalent Problems

2012 ◽  
Vol 03 (11) ◽  
pp. 1702-1718 ◽  
Author(s):  
James L. Moseley
Keyword(s):  
Equivalent Problems

Multiobjective Random Fuzzy Linear Programming Problems Based on the Possibility Maximization Model

2009 ◽  
Vol 13 (4) ◽  
pp. 373-379 ◽  
Author(s):  
Takashi Hasuike ◽  
◽  
Hideki Katagiri ◽  
Hiroaki Ishii ◽  
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fuzzy Programming ◽  
Fuzzy Linear Programming ◽  
Maximization Problem ◽  
Deterministic Equivalent ◽  
Linear Programming Problems ◽  
Previous Solution ◽  
Fuzzy Goal ◽  
Equivalent Problems

Two multiobjective random fuzzy programming problems considered based on the possibility maximization model using possibilistic and stochastic programming are not initially well defined due to the random variables and fuzzy numbers included. To solve them analytically, probability criteria are set for objective functions and chance constraints are introduced. Taking into account the decision maker’s subjectivity and the original plan’s flexibility, a fuzzy goal is introduced for each objective function. The original problems are then changed into deterministic equivalent problems to make the possibility fractile optimization problem equivalent to a linear programming problem. The possibility maximization problem for probability is changed into a nonlinear programming problem, and an analytical solution is constructed extending previous solution approaches.

SOME EFFECTS OF FORMATION ANISOTROPY ON RESISTIVITY MEASUREMENTS IN BOREHOLES

Geophysics ◽  
1958 ◽  
Vol 23 (4) ◽  
pp. 770-794 ◽  
Author(s):  
K. S. Kunz ◽  
J. H. Moran
Keyword(s):  
Anisotropic Medium ◽  
Wide Class ◽  
Anisotropic Media ◽  
Resistivity Measurements ◽  
Potential Problems ◽  
Isotropic Media ◽  
Equivalent Problems ◽  
Resistivity Logging

It is shown that a wide class of potential problems involving anisotropic media can be transformed into equivalent problems involving only isotropic media. By means of such transformations it is possible, in a large number of cases, to determine the apparent resistivities which would be observed in anisotropic formations, using electrode‐type resistivity logging devices. Discussion is given of an infinite, anisotropic medium with and without borehole, of two semi‐infinite anisotropic beds (without borehole), and of a thin isotropic bed bounded by anisotropic adjacent formations (without borehole). An interpretation chart for the normal device is presented for thick, non‐invaded, anisotropic beds penetrated by a borehole.

scholarly journals Inverse Problem for the Sobolev Type Equation of Higher Order

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1647
Author(s):  
Alyona Zamyshlyaeva ◽  
Aleksandr Lut
Keyword(s):  
Inverse Problem ◽  
Bounded Operator ◽  
Type Equation ◽  
Higher Order ◽  
Successive Approximations ◽  
Unknown Coefficient ◽  
Method Of Successive Approximations ◽  
Sobolev Type ◽  
Equivalent Problems ◽  
Sobolev Type Equation

The article investigates the inverse problem for a complete, inhomogeneous, higher-order Sobolev type equation, together with the Cauchy and overdetermination conditions. This problem was reduced to two equivalent problems in the aggregate: regular and singular. For these problems, the theory of polynomially bounded operator pencils is used. The unknown coefficient of the original equation is restored using the method of successive approximations. The main result of this work is a theorem on the unique solvability of the original problem. This study continues and generalizes the authors’ previous research in this area. All the obtained results can be applied to the mathematical modeling of various processes and phenomena that fit the problem under study.

scholarly journals Potential Effect of PISA Equivalent Questions Using the Context of Aceh Traditional Houses

2019 ◽  
Vol 4 (2) ◽  
pp. 89-100
Author(s):  
Uliyatul Usnul ◽  
Rahmah Johar ◽  
Hizir Sofyan
Keyword(s):  
Baseline Level ◽  
Formative Evaluation ◽  
Life Experiences ◽  
Mathematical Reasoning ◽  
Potential Effect ◽  
Reasoning Ability ◽  
Development Research ◽  
Contributing Factors ◽  
Local Contexts ◽  
Equivalent Problems

The achievement of Indonesian students in PISA remains unsatisfactory, as evidenced by their scores that are below the baseline level set in PISA. One of the contributing factors is that Indonesian students are less trained in solving problems with characteristics such as in PISA items. Therefore, it is necessary to familiarize Indonesian students with PISA equivalent problems, but the availability of these questions is still limited, especially concerning reasoning ability. In addition, the use of context is also crucial, especially the local contexts, which can help students understand mathematical phenomena from the perspective of their life experiences. The purpose of this study was to develop the questions of PISA equivalent mathematical reasoning ability using the context of Aceh traditional houses. This research used formative evaluation type development research from Tessmer. The results of this study were 12 mathematical questions equivalent to PISA using the context of Aceh traditional house. The potential effect of the questions developed was analyzed based on the student's responses to the questionnaire, including two aspects: 1) students are interested and seriously working on the questions and 2) the students are interested in using the equivalent PISA questions in the future.

scholarly journals When Instructional Guidance is Needed

2016 ◽  
Vol 33 (2) ◽  
pp. 149-162 ◽  
Author(s):  
Ouhao Chen ◽  
Slava Kalyuga ◽  
John Sweller
Keyword(s):  
Test Performance ◽  
Worked Examples ◽  
School Students ◽  
Element Interactivity ◽  
Worked Example ◽  
Learning Tasks ◽  
Instructional Guidance ◽  
Equivalent Problems ◽  
Facilitated Learning ◽  
Better Than

Studying worked examples providing problem solutions to learners usually leads to better test performance than solving the equivalent problems without guidance, demonstrating the worked-example effect. The generation effect occurs when learners who generate answers without guidance learn better than those who read answers that provide guidance. The contradiction between these results can be hypothesised to be due to differences in the element interactivity of the learning tasks. Primary school students in Year 6 participated in the experiment, which investigated the hypothesis by using geometry materials. A disordinal interaction was obtained between levels of guidance and levels of element interactivity. Higher levels of guidance facilitated learning using high element interactivity information, while lower levels of guidance facilitated learning for low element interactivity information. Cognitive load theory was used to explain these contrasting results. From an educational perspective, it was suggested that when determining levels of guidance, a consideration of element interactivity is essential.

Application of Method of Moments to Acoustic Scattering From Fluid Filled Cylinders Using Three Different Formulations

1995 ◽  
Author(s):  
S. P. Sun ◽  
P. K. Raju ◽  
S. M. Rao
Keyword(s):  
Integral Equation ◽  
Cross Section ◽  
Method Of Moments ◽  
Acoustic Scattering ◽  
Arbitrary Cross Section ◽  
The Body ◽  
Equation Formulation ◽  
Integral Equation Formulation ◽  
Equivalent Problems ◽  
Field Integral

Abstract In this work, we present three different formulations Viz. The pressure field integral equation formulation (PFIE), the velocity field integral equation formulation (VFIE), and the combined field integral equation formulation (CEDE) for solving acoustic scattering problems associated with two dimensional fluid-filled bodies of arbitrary cross section. In particular using the boundary conditions on the surface of the body, two equivalent problems, each valid for the outside and inside regions of the scatterer, are derived. By properly selecting the associated equations for these equivalent problems, the three different formulations are derived. The PFIE, VFIE, and CFIE are then solved by approximating the cylindrical cross section by linear segments and employing the method of moments. Further, it is shown that the moment matrices generated by the PFIE and VFIE are ill-conditioned at resonant frequencies of the cylinder, whereas the CFIE generates a well-conditioned matrix at all frequencies. The solution techniques presented in this work are simple, efficient and applicable to truly arbitrary geometries. Numerical results are presented for certain canonical shapes and compared with other available data.

Search time optimization for random pulse sources with given accuracy

2020 ◽  
Author(s):  
А.Л. Резник ◽  
А.В. Тузиков ◽  
А.А. Соловьев ◽  
А.В. Торгов ◽  
В.А. Ковалев
Keyword(s):  
A Priori ◽  
Search Algorithms ◽  
Point Sources ◽  
Random Point ◽  
Technical Diagnostics ◽  
Optimal Search ◽  
Localization Accuracy ◽  
Random Pulse ◽  
Time Optimal ◽  
Equivalent Problems

Исследуются вопросы построения быстродействующих алгоритмов обнаружения и локализации точечных источников, имеющих случайное распределение и обнаруживающих себя в случайные моменты времени генерацией мгновенных дельта-импульсов. Поиск осуществляется системой, включающей одно либо несколько приемных устройств, и выполняется с соблюдением требований по точности локализации. Предполагается, что все приемные устройства имеют произвольно перестраиваемые во времени окна обзора. Оптимальной считается процедура, которая в статистическом плане (т.е. по ансамблю реализаций) минимизирует среднее время локализации. Показано, что даже при сравнительно невысоких требованиях к точности локализации оптимальная процедура состоит из нескольких этапов, каждый из которых заканчивается в момент регистрации очередного импульса. Вполне допускается ситуация, когда в процессе оптимального поиска часть генерируемых источником импульсов может быть пропущена приемной системой. В работе рассчитаны и систематизированы параметры оптимального поиска в зависимости от количества приемных устройств и требуемой точности локализации. Для случая предельно высоких требований к точности локализации рассчитаны параметры асимптотически оптимальных поисковых алгоритмов. Показана возможность использования полученных результатов в многомерном случае. Purpose. The main goal of the research is to develop time-optimal algorithms for the localization of point sources that have a random spatial distribution and indicate themselves by generating instantaneous delta pulses at random time points. Methods. In many practically important problems requiring the highest reduction in the average time of localization of signal objects, the complexity of constructing optimal search algorithms forces researchers to resort to various kinds of simplifications or to the use of methods of numerical and simulation modelling. The mathematical apparatus used in the article belongs to probabilistic-statistical and non-linear programming methods. In a number of sections of the study (in particular, when constructing optimal control algorithms for multi-receiving search engines), traditional methods of discrete analysis and applied programming were used. Results. The solution of the variational problem is found, which minimizes the average localization time in the class of one-stage search algorithms with a known distribution density and the simultaneous absence of a priori information about the intensity of a random pulse source. For random point sources with a priori known intensity of the instantaneous generation of pulses, physically realizable multistage search algorithms have been constructed that have a significant gain in speed over single-stage algorithms, especially with increased requirements for localization accuracy. For a uniform distribution of a random source, an optimal strategy of multi-stage search was calculated, depending on the required localization accuracy and the number of receivers used. Findings. A distinctive feature of the studies is their universality, since in mathematical terms, the discussed problems and algorithms for the time-optimal search of random point-pulse objects arise in many scientific and technical applications. In particular, such studies are needed when developing methods for intermittent failures troubleshooting in the theory of reliability, in mathematical communication theory and in problems of technical diagnostics. Scientifically equivalent problems appear in the problems of detection, localization and tracking of radiation targets for eliminating malfunctions that manifest themselves in the form of intermittent failures. Scientifically equivalent problems arise in the problems of detecting, localizing and tracking radiation source targets.

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