The commutator equation problem forSL (3,Z)

1982 ◽  
Vol 38 (1) ◽  
pp. 204-205
Author(s):  
K. W. Weston
Keyword(s):  
Equation Problem ◽  
Commutator Equation

scholarly journals New Properties of Modified Second Kind Chebyshev Polynomials

2020 ◽  
Vol 55 (3) ◽  
Author(s):  
Semaa Hassan Aziz ◽  
Mohammed Rasheed ◽  
Suha Shihab
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Chebyshev Polynomial ◽  
Chebyshev Polynomials ◽  
Digital Computer ◽  
Higher Order ◽  
Algebraic Equations ◽  
Equation Problem ◽  
Higher Order Differential Equations

Modified second kind Chebyshev polynomials for solving higher order differential equations are presented in this paper. This technique, along with some new properties of such polynomials, will reduce the original differential equation problem to the solution of algebraic equations with a straightforward and computational digital computer. Some illustrative examples are included. The modified second kind Chebyshev polynomial is calculated using only a small number of the modified second kind Chebyshev polynomials, which leads to attractive results.

scholarly journals Indirect Analogical Reasoning Components

2021 ◽  
Vol 4 (1) ◽  
pp. 13
Author(s):  
K Kristayulita
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Problem Solving ◽  
Word Problem ◽  
Analogical Reasoning ◽  
Quadratic Equation ◽  
Target Problem ◽  
Equation Problem ◽  
Analogical Problem ◽  
Verbal Analogies

If using different instruments obtained a different analogical reasoning component. With use  people-piece analogies, verbal analogies, and geometric analogies, have analogical reasoning component consists of encoding, inferring, mapping, and application. Meanwhile,  with use analogical problems (algebra, source problem and target problem is equal), have analogical reasoning components consist of structuring, mapping, applying, and verifying. The instrument used was analogical problems consisting of two problems where the source problem was symbolic quadratic equation problem and the target problems were trigonometric equation problem and a word problem. This study aims to provide information analogical reasoning process in solving indirect analogical problems. in addition, to identify the analogical reasoning components in solving indirect analogical problems. Using a qualitative design approach, the study was conducted at two schools in Mataram city of Nusa Tenggara Barat, Indonesia. The results of the study provide an overview of analogical reasoning of the students in solving indirect analogical problems and there is a component the representation and mathematical model in solving indirect analogical problems.  So the analogical reasoning component in solving indirect analogical problems is the representation and mathematical modeling, structuring, mapping, applying, and verifying. This means that there are additional components of analogical reasoning developed by Ruppert. Analogical reasoning components in problem-solving depend on the analogical problem is given.

scholarly journals A Maximum Entropy Procedure to Solve Likelihood Equations

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 596
Author(s):  
Antonio Calcagnì ◽  
Livio Finos ◽  
Gianmarco Altoé ◽  
Massimiliano Pastore
Keyword(s):  
Logistic Regression ◽  
Maximum Likelihood ◽  
Maximum Entropy ◽  
Probability Distributions ◽  
Score Function ◽  
Likelihood Estimation ◽  
Likelihood Equation ◽  
Equation Problem ◽  
Standard Procedures ◽  
Data Separation

In this article, we provide initial findings regarding the problem of solving likelihood equations by means of a maximum entropy (ME) approach. Unlike standard procedures that require equating the score function of the maximum likelihood problem at zero, we propose an alternative strategy where the score is instead used as an external informative constraint to the maximization of the convex Shannon’s entropy function. The problem involves the reparameterization of the score parameters as expected values of discrete probability distributions where probabilities need to be estimated. This leads to a simpler situation where parameters are searched in smaller (hyper) simplex space. We assessed our proposal by means of empirical case studies and a simulation study, the latter involving the most critical case of logistic regression under data separation. The results suggested that the maximum entropy reformulation of the score problem solves the likelihood equation problem. Similarly, when maximum likelihood estimation is difficult, as is the case of logistic regression under separation, the maximum entropy proposal achieved results (numerically) comparable to those obtained by the Firth’s bias-corrected approach. Overall, these first findings reveal that a maximum entropy solution can be considered as an alternative technique to solve the likelihood equation.

Douglas' + Sebestyén's lemmas = a tool for solving an operator equation problem

2020 ◽  
Vol 482 (2) ◽  
pp. 123599 ◽  
Author(s):  
Dragana Cvetković-Ilić ◽  
Qing-Wen Wang ◽  
Qingxiang Xu
Keyword(s):  
Operator Equation ◽  
Equation Problem

Parametric Study on Economic Feasibility of Microturbine Cogeneration Systems by an Optimization Approach

2005 ◽  
Vol 127 (2) ◽  
pp. 389-396 ◽  
Author(s):  
Satoshi Gamou ◽  
Ryohei Yokoyama ◽  
Koichi Ito
Keyword(s):  
Energy Demand ◽  
Unit Cost ◽  
Maximum Energy ◽  
Optimal Number ◽  
Economic Feasibility ◽  
Optimization Approach ◽  
Energy Demands ◽  
Equation Problem ◽  
Numerical Studies ◽  
Cogeneration System

Economic feasibility of microturbine cogeneration systems is investigated by analyzing relationships between the optimal number of microturbine units and the maximum energy demands under various conditions. For this purpose, a method to obtain the maximum energy demand at which the optimal number changes is proposed by combining a nonlinear equation problem and an optimal unit sizing problem hierarchically. Based on the proposed method, a map expressing the aforementioned relationships can be illustrated. Through numerical studies carried out on systems installed in hotels by changing the electrical generating efficiency and the capital unit cost of the microturbine cogeneration unit as parameters, the influence of the parameters on the economic feasibility of the microturbine cogeneration system is clarified.

Markov jump processes with a singularity

2000 ◽  
Vol 32 (03) ◽  
pp. 779-799 ◽  
Author(s):  
Ole E. Barndorff-Nielsen ◽  
Fred Espen Benth ◽  
Jens Ledet Jensen
Keyword(s):  
State Space ◽  
Laser Cooling ◽  
Quantum Physics ◽  
Jump Processes ◽  
Main Question ◽  
Markov Jump ◽  
Markov Jump Processes ◽  
Equation Problem ◽  
Continuous State Space ◽  
Continuous State

Certain types of Markov jump processes x(t) with continuous state space and one or more absorbing states are studied. Cases where the transition rate in state x is of the form λ(x) = |x|δ in a neighbourhood of the origin in ℝ d are considered, in particular. This type of problem arises from quantum physics in the study of laser cooling of atoms, and the present paper connects to recent work in the physics literature. The main question addressed is that of the asymptotic behaviour of x(t) near the origin for large t. The study involves solution of a renewal equation problem in continuous state space.

Applications of Compressive Sensing Technique in Structural Health Monitoring

2013 ◽  
Vol 558 ◽  
pp. 561-566
Author(s):  
Yue Quan Bao ◽  
Hui Li ◽  
Jin Ping Ou
Keyword(s):  
Data Acquisition ◽  
Compressive Sensing ◽  
Sampling Rate ◽  
Random Sets ◽  
Moving Loads ◽  
Software Complexity ◽  
Equation Problem ◽  
Acceleration Data ◽  
Application Potential ◽  
Sparse Solutions

Compressive sampling also called compressive sensing (CS) is a emerging information theory proposed recently. CS provides a new sampling theory to reduce data acquisition, which says that sparse or compressible signals can be exactly reconstructed from highly incomplete random sets of measurements. CS broke through the restrictions of the Shannon theorem on the sampling frequency, which can use fewer sampling resources, higher sampling rate and lower hardware and software complexity to obtain the measurements. Not only for data acquisition, CS also can be used to find the sparse solutions for linear algebraic equation problem. In this paper, the applications of CS for SHM are presented including acceleration data acquisition, lost data recovery for wireless sensor and moving loads distribution identification. The investigation results show that CS has good application potential in SHM.

scholarly journals TEACHING HIGH SCHOOL STUDENTS TO SOLVE DIFFERENTIAL EQUATIONS USING PYTHON AT MATH CLASS

2020 ◽  
pp. 38-43
Author(s):  
K.B. Alkhan ◽  
◽  
Z.E. Shaimova ◽  
Keyword(s):  
Differential Equation ◽  
High School ◽  
Information Technology ◽  
High School Students ◽  
School Students ◽  
Equation Problem ◽  
The Difference ◽  
Basic Characteristics ◽  
Time And Energy ◽  
Math Class

The article discusses examples of the differential equation problem in Python with a graph for high school students. The basic characteristics of some tools for solving problems in mathematics using information technology are given. The difference between the two modern-known computer programs Python and Pascal is briefly explained. The article uses illustrative examples of built-in and manually entered functions that can be repeated by readers in Python to recreate graphs of trigonometric, differential, and other functions. In conclusion, it describes how the program can save time and energy for solving graphic problems in mathematics using the Python program. The article concludes that it is important for students to use logic to solve problems with improvised tools, where there are built-in functions, compared to remembering programming language algorithms for solving problems.

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