A Study on Common Fixed Point and Invariant Approximation Theorems for Mappings Satisfying Generalized Contraction Principle | Chapter 08 | Theory and Applications of Mathematical Science Vol. 3

We prove common fixed point theorems for weakly compatible mappings satisfying a generalized contraction principle by using a control function. As an application, we have established invariant approximation result. Our theorems generalize recent results existing in the literature.

Author(s) Details

Dr. R. Sumitra
Department of Mathematics, Queen Mary’s College, Chennai-600004, Tamilnadu, India.

Dr. V. Rhymend Uthariaraj
Department of Information Technology, MIT Campus (Anna University), Chennai, Tamilnadu, India.

Dr. R. Hemavathy
Department of Mathematics, Queen Mary’s College, Chennai-600004, Tamilnadu, India.

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Estimation of Parameters of Certain Bivariate Distributions with Equal Coefficients of Variation by Concomitants of Order Statistics | Chapter 07 | Theory and Applications of Mathematical Science Vol. 3

For a sample of n pairs of observations from Bivariate normal distribution,Morgenstern type bivariate logistic distribution and morgenstern type bivariate exponential distribution , in which the marginal distributions of random variables X and Y have the same coefficient of variation c, we derive the best linear unbiased estimator of the parameters associated with the Y variable using concomitants of order statistics.

Author(s) Details

N. K. Sajeevkumar
Department of Statistics Government College Kariavattom (Affiliated to University of Kerala), Trivandrum-695 581, India.

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Recent Advancement on Analytical Solution for Linear and Nonlinear Systems of Partial Differential Equations Involving Time Conformable Fractional Derivatives | Chapter 06 | Theory and Applications of Mathematical Science Vol. 3

In this short chapter we apply the conformable fractional reduced differential transform (CFRDTM) method to compute solutions for systems of linear and nonlinear conformable fractional PDEs. The proposed method gives a numerical approximate solution in the form of an infnite series that converges to a closed form solution; which is in many cases the exact solution. We inspect its efficiency in solving systems of CFPDEs by working on several different nonlinear systems. The obtained results show that CFRDTM yielded similar solutions to exact solutions, confirming its proficiency as a competent technique for solving CFPDEs systems. It required very little computational work and hence consumed much less time compared to other numerical methods.

Author(s) Details

Maher Jneid
Departement of Mathematics and Computer Science, Beirut Arab University, Lebanon.

Abir Chaouk
Departement of Mathematics, Bilkent University, Turkey.

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Ergodic Properties of generalized Ornstein – Uhlenbeck Processes | Chapter 05 | Theory and Applications of Mathematical Science Vol. 3

Author(s) Details

Andriy Yurachkivsky
Departement of Mathematics and Computer Science, Beirut Arab University, Lebanon.

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Multiscale Decomposition of Big Data Time Series for Analysis and Prediction of Macroeconomic Data: A Recent Approach | Chapter 04 | Theory and Applications of Mathematical Science Vol. 3

The problem of the extraction of the relevant information for pre- diction purposes in a Big Data time series context is tackled. This issue is especially crucial when the forecasting activity involves macroeconomic time series, i.e. when one is mostly interested in finding leading variables and, at the same time, avoiding overfitted model structures. Unfortunately, the use of big data can cause dangerous overparametrization phenomena in the enter- tained models. In addition, two other drawbacks should be considered: firstly, humandriven handling of big data on a case-by-case basis is an impractical (and generally not viable) option and secondly, focusing solely on the raw time series might lead to suboptimal results. The presented approach deals with these problems using a twofold strategy: i) it expands the data in time scale domain, in the attempt to increase the likelihood of giving emphasis to possibly weak, relevant, signals and ii) carries out a multi-step dimension reduction procedure. The latter task is done by means of crosscorrelation functions (whose employment will be theoretically justified) and a suitable objective function.

Author(s) Details

Livio Fenga
ISTAT, Italian National Institute of Statistics, Italy.

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Quantitative Analysis of Relationship between Three Psychological Parameters Based on Swallowtail Catastrophe Model: A recent perspectives | Chapter 09 | Theory and Applications of Mathematical Science Vol. 3

A sudden jump in the value of the state variable in a certain dynamical system can be studied through a catastrophe model. This paper presents an application of catastrophe model to solve a psychological problems. Since we will have three psychological aspects or parameters. Intelligence (I), Emotion (E), and Adversity (A), a Swallowtail catastrophe model  is considered to be an appropriate one. Our methodology consists of three steps : solving the Swallowtail potential function, finding the critical points up to and including three-fold degenerates and fitting the model into our measured data. Using a polynomial curve fitting derived from the potential function of Swallowtail Catastrophe Model, relations among three parameters combinations are analyzed. Results show that there are catastrophe phenomena for each relations, meaning that a small change in one psychological aspect may cause a dramatically change in another aspect.

Author(s) Details

Dr. Asti Meiza
Faculty of Psychology, UIN Sunan Gunung Djati Bandung, Indonesia.

Sutawanir Darwis
Statistical Research Division, Faculty of Mathematics, Natural Bandung Institute of Technology, Indonesia.

Agus Yodi Gunawan
Industrial and Finance Research Division of Mathematics, Natural Faculty Bandung Institute of Technology, Indonesia.

Efi Fitriana
Faculty of Psychology, Padjadjaran University, Indonesia.

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Generalized Riesz Systems and Ordered Structures of Their Constructing Operators | Chapter 03 | Theory and Applications of Mathematical Science Vol. 3

Theory of non-self-adjoint operators and these applications are interested in various felds of mathematics and physics. There are many research results related to pseudo-Hermitian operators. In this feld, generalized Riesz systems can be used to construct some physical operators. From this fact, it seems to be important to consider under what conditions biorthogonal sequences are generalized Riesz systems. In this chapter, we shall focus the construction of generalized Riesz systems from biorthogonal sequences and the properties of constructing operators for generalized Riesz systems. In details, we shall investigate under what conditions the ordered set of all constructing operators for a generalized Riesz system has maximal elements, minimal elements, the largest element and the smallest element in order to fnd constructing operators ftting to each of physical applications.

Author(s) Details

Hiroshi Inoue
Center for Advancing Pharmaceutical Education, Daiichi University of Pharmacy, 22-1 Tamagawacho, Minami-ku, Fukuoka 815-8511, Japan.

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An Approach of Second-order Duality for Nondifferentiable Multiobjective Programming Involving ( Φ, ρ)-Univexity | Chapter 02 | Theory and Applications of Mathematical Science Vol. 3

The concepts of ( Φ, ρ)invexity have been given by Carsiti, Ferrara and Stefanescu [1]. We consider a second-order dual model associated to a  multiobjective programming problem involving support functions and a weak duality result is established under appropriate second-order ( Φ, ρ) univexity conditions.

Author(s) Details

Dr. Ganesh Kumar Thakur
Department of Applied Sciences, Krishna Engineering College, Ghaziabad, India.

Dr. Bandana Priya
Department of Applied Sciences, G. L. Bajaj Institute of Technology and Management, KP-III, Greater Noida, UP, India.

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A study on Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Non-linear Oscillators | Chapter 01 | Theory and Applications of Mathematical Science Vol. 3

In this paper, the Equivalent Linearization Method (ELM) with a weighted averaging is applied to analyse five undamped oscillator systems with nonlinearities. The results obtained via this method are compared with the ones achieved by Parameterized Perturbation Method (PPM), Min-Max Approach (MMA), Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Energy Balance Method (EBM), Hanormic Balance Method (HBM), 4th order Runge-Kutta Method and the exact ones. The obtained results demonstrate that this method is very convenient for solving nonlinear equations and also can be successfully exerted to a lot of practical engineering and physical problems.

Author(s) Details

D. V. Hieu
Thai Nguyen University of Technology, Thai Nguyen, Vietnam

N. Q. Hai
Hanoi Architectural University, Hanoi, Vietnam

D. T. Hung
Thai Nguyen University of Technology, Thai Nguyen, Vietnam

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