Theory and Applications of Mathematical Science Vol. 3

A study on Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Non-linear Oscillators

D. V. Hieu, N. Q. Hai, D. T. Hung — Mon, 02 Mar 2020 00:00:00 +0000

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), 4^th 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.

An Approach of Second-order Duality for Nondifferentiable Multiobjective Programming Involving (Փ , ρ)-Univexity

Ganesh Kumar Thakur, Bandana Priya — Mon, 02 Mar 2020 00:00:00 +0000

The concepts of (Փ , 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 (Փ , ρ)-univexity conditions.

Generalized Riesz Systems and Ordered Structures of Their Constructing Operators

Hiroshi Inoue — Mon, 02 Mar 2020 00:00:00 +0000

Theory of non-self-adjoint operators and these applications are interested in various fields of mathematics and physics. There are many research results related to pseudo-Hermitian operators. In this field, 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 find constructing operators fitting to each of physical applications.

Multiscale Decomposition of Big Data Time Series for Analysis and Prediction of Macroeconomic Data: A Recent Approach

Livio Fenga — Mon, 02 Mar 2020 00:00:00 +0000

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.

Ergodic Properties of generalized Ornstein – Uhlenbeck Processes

Andriy Yurachkivsky — Mon, 02 Mar 2020 00:00:00 +0000

Let an -valued random process ξ be the solution of an equation of the kind ξ(t) = ξ(0) +, where ξ(0) is a random variable measurable w. r. t. some σ-algebra , S is a random process with-conditionally independent increments, ι is a continuous numeral random process of locally bounded variation, and A is a matrix-valued random process such that for any. Conditions guaranteing the existence of the limiting, as t → ∞, distribution of ξ(t) are found. The characteristic function of this distribution is written explicitly. An ergodic theorem for generalized Ornstein – Uhlenbeck processes is proved.

Recent Advancement on Analytical Solution for Linear and Nonlinear Systems of Partial Dierential Equations Involving Time Conformable Fractional Derivatives

Maher Jneid, Abir Chaouk — Mon, 02 Mar 2020 00:00:00 +0000

In this short chapter we apply the conformable fractional reduced dierential 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 innite series that converges to a closed form solution; which is in many cases the exact solution. We inspect its effciency in solving systems of CFPDEs by working on several dierent nonlinear systems. The obtained results show that CFRDTM yielded similar solutions to exact solutions, conrming its prociency 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.

Estimation of Parameters of Certain Bivariate Distributions with Equal Coecients of Variation by Concomitants of Order Statistics

N. K. Sajeevkumar — Mon, 02 Mar 2020 00:00:00 +0000

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 coecient of variation c, we derive the best linear unbiased estimator of the parameters associated with the Y variable using concomitants of order statistics.

A Study on Common Fixed Point and Invariant Approximation Theorems for Mappings Satisfying Generalized Contraction Principle

R. Sumitra, V. Rhymend Uthariaraj, R. Hemavathy — Mon, 02 Mar 2020 00:00:00 +0000

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.

Quantitative Analysis of Relationship between Three Psychological Parameters Based on Swallowtail Catastrophe Model: A recent perspectives

Asti Meiza, Sutawanir Darwis, Agus Yodi Gunawan, Efi Fitriana — Mon, 02 Mar 2020 00:00:00 +0000

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.