Credibilistic fuzzy clustering based on evolutionary method of crazy cats

The problem of fuzzy clustering of large datasets that are sent for processing in both batch and online modes, based on a credibilistic approach, is considered. To find the global extremum of the credibilistic fuzzy clustering goal function, the modification of the swarm algorithm of crazy cats swarms was introduced, that combined the advantages of evolutionary algorithms and a global random search. It is shown that different search modes are generated by a unified mathematical procedure, some cases of which are known algorithms for both local and global optimizations. The proposed approach is easy to implement and is characterized by the high speed and reliability in problems of multi-extreme fuzzy clustering.

The Effect of Multi-Stage Discussion with Google Classroom and WhatsApp in Learning Physics on Problem Solving Ability

This research describes the effect of applying multi-stage discussion with Google Classroom and WhatsApp in learning physics on students' problem-solving abilities. Google Classroom media was used for large group discussions and WhatsApp for small group discussions. The design in this research used a pre-experimental design in the form of a one-group pretest-posttest design with apurposive sampling technique for three meetings on Newton’s Law of Motion with experimented classes with a total sample of 60 students. Data were analyzed using paired sample t-test.The results showed a difference in the average students’ problem-solving abilities before and after treatment with a Sig. (2-tailed) value of 0.000. After implementinglearning multi-stage discussion with Google Classroom and WhatsApp, students' problem-solving ability in the experimental class increased from the very low to moderate category with an average N-gain of 0.66. The highest increase occurred in theindicators of physics approach and mathematical procedure with an average N-gain of 0.71 and the lowest increase in thehelpful indicator description with an average of 0.63. This increase shows that the application oflearning multi-stage discussion with Google Classroom and WhatsApp on Newton's Laws of Motion has a moderate effect on students' problem-solving abilities.

Utility Maximization of Bangladeshi Consumers within Their Budget: A Mathematical Procedure

A consumer is considered as a person or a group of people who uses purchased goods, products, or services only for personal use, and not for manufacturing or resale. Consumers usually purchase valuable and useful commodities or goods by spending all or partial of their income. The property of a commodity that enables it to satisfy human wants is called utility. Producers must be conscious to increase the utility among the consumers. This study has considered the maximization of utility problem of consumers of Bangladesh subject to two constraints; namely, budget constraint and coupon constraint. Consequently, in the study two Lagrange multipliers are used and interpreted these with mathematical analysis. Prediction of consumer behavior will help both producers and consumers to take decision of their future economic productions and consumptions, respectively. This article is ornamented with sufficient theorems and economic analyses. So that all the readers find interest when go through the economic analysis of utility maximization.

Theory of Functional Connections Applied to Linear ODEs Subject to Integral Constraints and Linear Ordinary Integro-Differential Equations

This study shows how the Theory of Functional Connections (TFC) allows us to obtain fast and highly accurate solutions to linear ODEs involving integrals. Integrals can be constraints and/or terms of the differential equations (e.g., ordinary integro-differential equations). This study first summarizes TFC, a mathematical procedure to obtain constrained expressions. These are functionals representing all functions satisfying a set of linear constraints. These functionals contain a free function, g(x), representing the unknown function to optimize. Two numerical approaches are shown to numerically estimate g(x). The first models g(x) as a linear combination of a set of basis functions, such as Chebyshev or Legendre orthogonal polynomials, while the second models g(x) as a neural network. Meaningful problems are provided. In all numerical problems, the proposed method produces very fast and accurate solutions.

Implementasi Algoritma Smarter for the Determination of the Thesis Supervisor

Decision making is a basis for determination / unanimity that has a value or criteria that have a weight that can describe a person's ability and intellectual (Ananta dan Winiarti, 2013)..This study aims to design and implement a simple multi attribute attribute rating technique exploiting rank (SMARTER) for the determination of the supervisor lecturer. This SMARTER method is a multi-criteria method which consists of several criteria where each criterion contains values and weights that are used to compare the values between the criteria for lecturers and others. The calculation method data is analyzed and designed using the Rank-Order Centroid (ROC) method with a simple mathematical procedure and produces a major priority of several attributes in the form of a range. The results of the study can be concluded that the greatest utility value of each lecturer can be determined as a supervisor. This system only discusses the selection of thesis supervisors and there is no gender separation for students and supervisors. The database uses SQL Server 2005 and programming using the Visual Basic 2008 language.

Transporting Deformations of Face Emotions in the Shape Spaces: A Comparison of Different Approaches

Studying the changes of shape is a common concern in many scientific fields. We address here two problems: (1) quantifying the deformation between two given shapes and (2) transporting this deformation to morph a third shape. These operations can be done with or without point correspondence, depending on the availability of a surface matching algorithm, and on the type of mathematical procedure adopted. In computer vision, the re-targeting of emotions mapped on faces is a common application. We contrast here four different methods used for transporting the deformation toward a target once it was estimated upon the matching of two shapes. These methods come from very different fields such as computational anatomy, computer vision and biology. We used the large diffeomorphic deformation metric mapping and thin plate spline, in order to estimate deformations in a deformational trajectory of a human face experiencing different emotions. Then we use naive transport (NT), linear shift (LS), direct transport (DT) and fanning scheme (FS) to transport the estimated deformations toward four alien faces constituted by 240 homologous points and identifying a triangulation structure of 416 triangles. We used both local and global criteria for evaluating the performance of the 4 methods, e.g., the maintenance of the original deformation. We found DT, LS and FS very effective in recovering the original deformation while NT fails under several aspects in transporting the shape change. As the best method may differ depending on the application, we recommend carefully testing different methods in order to choose the best one for any specific application.

On the correctness of problem solving in ancient mathematical procedure texts

It has been argued in relation to Old Babylonian mathematical procedure texts that their validity or correctness is self-evident. One “sees” that the procedure is correct without it having, or being accompanied by, any explicit arguments for the correctness of the procedure. Even when agreeing with this view, one might still ask about how is the correctness of a procedure articulated? In this work, we present an articulation of the correctness of ancient Egyptian and Old Babylonian mathematical procedure texts – mathematical texts presenting the solution of problems. We endeavor to make explicit and explain how and why the procedures are reliable over and above the fact that their correctness is intuitive.

TRANSFORMADA INVERSA DE LAPLACE PARA ANÁLISE DE SINAIS DE RESSONÂNCIA MAGNÉTICA NUCLEAR DE BAIXO CAMPO

INVERSE LAPLACE TRANSFORM FOR SIGNAL ANALYSIS OF LOW FIELD NUCLEAR MAGNETIC RESONANCE. The objective of this work is to describe the mathematical procedure denominated ‘Inverse Laplace Transform’ used to process Low Field Nuclear Magnetic Resonance signals of experiments as CPMG, Inversion Recovery and Saturation Recovery. Also, we present a developed script, “ILT Origin script” v.1, in the environment of the software Origin Lab 9 to execute it. The presented ILT is executed with an algorithm of non-negative last square, with Tikhonov regularization and singular values decomposition. The main features of the code were tested using simulated and experimental signals, and in order to validate the results the same sets of data were analyzed using similar ILT softwares. The developed scripts for Origin Lab, Matlab and other languages are available for free for scientific and teaching uses.

Reconstruction of falsified election results using Shpilkin integral method

I propose a simple and formal method to reconstruct falsified election results, based on the hypothesis of the mutual independence of the overall turnout and the result of power. This method is a development of the classical method of S.A. Shpilkin, however, it does not require additional assumptions and has no free parameters. In addition, it uniformly reconstructs all key values and uses a simpler and clearer mathematical procedure. Comparison of official and true results of federal elections allows to perform a political science analysis of the development of the institution of electoral frauds in Russia in the 20th century and its impact on the political system.

The Lorentz transformations by way of the wave equations

We prove here, by the rigorous mathematical procedure, that so-called Lorentzian time in the special theory of relativity is defined by the wave equation, where the wave of time is the form of matter and not the Bergson physiological process in S and S′.