An Exponential-Type Distribution for Modeling Failure Rate.

In this paper we introduced the Truncated Exponential Skew Symmetric Gumbel II (TESSG II) distribution which generalizes the Gumbel II distribution using the method proposed by Nadarajah et al (2013). Unlike the Gumbel II distribution which exhibits a monotone decreasing failure rate, the new distribution is useful for modeling unimodal (Bathtub-shaped) failure rates which has a wider class of applications in solving real life problems. Structural properties of the new distribution namely, density function, hazard function, moments and moment generating function were obtained. The maximum likelihood was employed to estimate parameters of the new distribution. Real data set for failures of Air conditional system of Jet air planes were used to validate its tractability, we discovered that the Truncated Exponential Skew Symmetric Gumbel II (TESSG II)  has a better fit than Gumbel II distribution. Keywords: Quantile function, Bathtub-shaped failure rate, Renyl entropy, moment

Symmetric Integer Matrices Having Integer Eigenvalues

We provide characterization of symmetric integer matrices for rank at most 2 that have integer spectrum and give some constructions for such matrices of rank 3. We also make some connection between Hanlon’s conjecture and integer eigenvalue problem

Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation

A sufficient literature is available for the wavelet error of approximation of certain functions in the L2-norm. There is no work in context of multiresolution approximation of a function in the sense of sup-error. In this paper, for the first time, wavelet estimator for the approximation of a function f belonging to Lipα[a,b] class under supremum norm has been obtained. Working in this direction, four new theorems on the wavelet approximation of a function f belonging to Lipα,0<α≤1 class using the projection Pmf of its wavelet expansions have been estimated. The calculated estimator is best possible in wavelet analysis

Double Laplace Transform Method for Solving Space and Time Fractional Telegraph Equations

Double Laplace transform method is applied to find exact solutions of linear/nonlinear space-time fractional telegraph equations in terms of Mittag-Leffler functions subject to initial and boundary conditions. Furthermore, we give illustrative examples to demonstrate the efficiency of the method

Almost and Nearly Isosceles Pythagorean Triples

This work is about extended pythagorean triples, called NPT, APT, and AI-PT. We generate infinitely many NPTs and APTs and then develop algorithms for infinitely many AI-PTs. Since AI-PT (a,b,c) is of a-b=1, we ask generally for PT (a,b,c) satisfying |a-b|=k for any k∈N. These triples are solutions of certain diophantine equations

A 4-Point Block Method For Solving Higher Order Ordinary Differential Equations Directly

An alternative block method for solving fifth-order initial value problems (IVPs) is proposed with an adaptive strategy of implementing variable step size. The derived method is designed to compute four solutions simultaneously without reducing the problem to a system of first-order IVPs. To validate the proposed method, the consistency and zero stability are also discussed. The improved performance of the developed method is demonstrated by comparing it with the existing methods and the results showed that the 4-point block method is suitable for solving fifth-order IVPs

An Optimal Treatment Control of TB-HIV Coinfection

An optimal control on the treatment of the transmission of tuberculosis-HIV coinfection model is proposed in this paper. We use two treatments, that is, anti-TB and antiretroviral, to control the spread of TB and HIV infections, respectively. We first present an uncontrolled TB-HIV coinfection model. The model exhibits four equilibria, namely, the disease-free, the HIV-free, the TB-free, and the coinfection equilibria. We further obtain two basic reproduction ratios corresponding to TB and HIV infections. These ratios determine the existence and stability of the equilibria of the model. The optimal control theory is then derived analytically by applying the Pontryagin Maximum Principle. The optimality system is performed numerically to illustrate the effectiveness of the treatments

Modal Logic Axioms Valid in Quotient Spaces of Finite CW-Complexes and Other Families of Topological Spaces

In this paper we consider the topological interpretations of L□, the classical logic extended by a “box” operator □ interpreted as interior. We present extensions of S4 that are sound over some families of topological spaces, including particular point topological spaces, excluded point topological spaces, and quotient spaces of finite CW-complexes

Application of ADM Using Laplace Transform to Approximate Solutions of Nonlinear Deformation for Cantilever Beam

We investigate semianalytical solutions of Euler-Bernoulli beam equation by using Laplace transform and Adomian decomposition method (LADM). The deformation of a uniform flexible cantilever beam is formulated to initial value problems. We separate the problems into 2 cases: integer order for small deformation and fractional order for large deformation. The numerical results show the approximated solutions of deflection curve, moment diagram, and shear diagram of the presented method