The main thrust of the article is to provide interesting example, useful for students of using bitwise operations in the programming languages C ++ and Java. As an example, we describe an algorithm for obtaining a Latin square of arbitrary order. We will outline some techniques for the use of bitwise operations.
Let R be a ring with involution. In the present paper, we characterize biadditive mappings which satisfies some functional identities related to symmetric Jordan (θ,∅)*-biderivation of prime rings with involution. In particular, we prove that on a 2-torsion free prime ring with involution, every symmetric Jordan triple (θ,∅)*-biderivation is a symmetric Jordan (θ,∅)*-biderivation.
In this paper, the Archimedean t-conorm- and t-norm-based interval-valued hesitant fuzzy ordered weighted averaging (A-IVHFOWA) operator and the Archimedean t-conorm- and t-norm-based interval-valued hesitant fuzzy ordered weighted geometric (A-IVHFOWG) operator are given by taking fully account of the different weights associated with the particular ordered positions. Several desirable properties of the developed operators, such as commutativity, idempotency, and boundedness, are studied in detail, and some special cases of these operators are analyzed as well. Furthermore, we apply the proposed operators to develop a method for solving a multi-criteria decision making (MCDM) problem within the context of interval-valued hesitant fuzzy elements (IVHFEs). Finally, a practical example is provided to illustrate the practicality and effectiveness of the developed operators and method.
In linear discriminant analysis, determinant and inverse of the covariance matrix are required to be computed. If number of features is greater than the number of available examples, covariance matrix is no longer invertible. A common approach is to reduce dimensionality due to which some features of interest may be lost. When we are not interested in dimensionality reduction, one approach to solve such problems is to take pseudoinverse of covariance matrix which is not always possible. We propose, in such cases, to project covariance matrix onto a highly correlated space to compute pseudoinverse of the matrix. Proposed solution has been tested for classification of microarray gene expression data of colon’s tumor.
Since its introduction, transfer entropy has become a popular information-theoretic tool for detecting causal inference between two discretized random processes. By means of statistical tools we evaluate the transfer entropy of stationary processes whose continuous probability distributions are known. We study transfer entropy of processes coming from the family of γ-order generalized normal distribution. Applying Kullback-Leibler divergence we provide explicit expressions of the transfer entropy for processes which are normal, as well as for processes from the class of γ-order normal distributions. The results achieved in the paper for continuous time can be applied also to the discrete time case, concretely to the time series whose underlying process distribution is from the discussed classes.
The Enright's third derivative method which is A-stable is derived using multistep collocation approach. The continuous method so obtained are use to generate the main method and the complementary methods to solve standard problems via boundary value techniques such that the numerical solution of a problem is obtained on the domain of integration simultaneously. Numerical result obtained via the implementation of the methods shows that the new method can compete with the existing ones (Enright , Ehigie, Jator, Sofolowe and Okunuga , Jator-Sahi  , Wu-Xia ) in the literature.
Recently, intense research has been on how to reduce the spread of virus on a network of computer systems, which involves the mathematical modelling of the spread of virus based on mathematical epidemiological approach. This is necessary because a threshold cannot be discerned from the data generated on the network, rather it requires a mathematical model to analyze and simulate the virus dynamics on the network. It also enables the calculation of the basic reproductive number (R0) which is an important threshold for determining whether the network is at risk or not. In this paper, we adopt the susceptible- infected-recovered-susceptible (SIRS) model to depict the spread of virus on the network. We qualitatively analyze the model and establish that the virus-free state is locally asymptotically stable provided the basic reproduction number is less than unity. We solved the model numerically and simulate the solution for different scenarios on the network. The findings from our simulations are discussed.