Mohammad Azram

Parametric Cox's Model for Partly Interval-Censored Data with Application to AIDS Studies

 Abstract—The Parametric Coxs Proportional Hazard Model based on Expectation-Maximization (EM) algorithm for partly interval-censored data is studied. We mean by partly interval-censored data that the observed data include both the exact and interval-censored observations on the survival time of interest. Through the simulation data and real data, we demonstrate that the resulting estimate of regression coefficient and its associated standard error. Our proposal is easily implemented by using SAS software in the present of partly interval-censored data.

Joint Channel Assignment and Routing in Multiradio Multichannel Wireless Mesh Networks

Multiradio wireless mesh network is a promising architecture that improves the network capacity by exploiting multiple radio channels concurrently. Channel assignment and routing are underlying challenges in multiradio architectures since both determine the traffic distribution over links and channels. The interdependency between channel assignments and routing promotes toward the joint solutions for efficient configurations. This paper presents an in-depth review of the joint approaches of channel assignment and routing in multiradio wireless mesh networks. First, the key design issues, modeling, and approaches are identified and discussed. Second, existing algorithms for joint channel assignment and routing are presented and classified based on the channel assignment types. Furthermore, the set of reconfiguration algorithms to adapt the network traffic dynamics is also discussed. Finally, the paper presents some multiradio practical implementations and test-beds and points out the future research directions.

New Algorithms for Numerical Assessment of Nonlinear Integro-Differential Equations of Second-Order using Haar Wavelets

This paper deals with the extended design for Fredholm and Volterra integral equations and design for Fredholm and Volterra integro-differential equations of first-order to second-order nonlinear Fredholm and second-order nonlinear Volterra integro-differential equations having square integrable kernels. This approach utilizes the inherent dynamics of the Haar wavelet. The Haar wavelet is used to provide a single platform for the proposed method. The method is tested on problems from literature, and numerical results are compared with existing methods. The numerical results indicate that the accuracy of the method is reasonably high, even on a coarse grid.

Arithmetic version of Boolean algebra

In this article we will discuss that the logical results in Boolean algebra can equally be derived with ordinary algebraic operations. We will establish arithmetic versions of the common logical propositions inclusive of Sheffer stroke (Nand connective) and Peirces arrow (Nor connective) which are very important to design circuit diagrams. We will present the comparison of some basic logical Boolean expressions and their arithmetic version through the truth tables. Finally we will establish the fundamental logical equivalent propositions via arithmetic versions.

Equivalence of dual graphs

Abstract—Because of interesting and useful geometric as well as topological properties, alternating knots (links) were regarded to have an important role in knot theory and 3-manifold theory. Many knots with crossing number less than 10 are alternating. It was the properties of alternating knots that enable the earlier knot tabulators to construct tables with relatively few mistakes or omissions. Graphs of knots (links) have been repeatedly employed in knot theory. This article is devoted to establish relationship between knots and planar graphs. This relationship not only enables us see the equivalence of the graphs corresponding to black regions and the dual graph corresponding to white regions.

Cauchy integral formula

Cauchy-Goursat integral theorem is a pivotal, fundamentally important, and well celebrated result in complex integral calculus. It requires analyticity of the function inside and on the boundary of the simple closed curve. In this study we will investigate the condition(s) under which even though the function is not analytic at a point inside C. Consequently, we will extend the above notion to a finite numbers of points and will present an easy and simple proof of unquestionably the most important, significant and pivotal result known as Cauchy integral formula.