Logical Entropy of Information Sources.

In this paper, we present the concept of the logical entropy of order , logical mutual information, and the logical entropy for information sources. We found upper and lower bounds for the logical entropy of a random variable by using convex functions. We show that the logical entropy of the joint distributions X1 and X2 is always less than the sum of the logical entropy of the variables X1 and X2.

Hosoya Polynomial for Subdivided Caterpillar Graphs.

Background: Computing Hosoya polynomial for a graph associated with a chemical compound plays a vital role in the field of chemistry. From Hosoya polynomial, it is easy to compute the Weiner index(Weiner number) and Hyper Weiner index of the underlying molecular structure. The Wiener number enables the identifying of three basic features of molecular topology: branching, cyclicity, and centricity (or centrality) and their specific patterns, which are well reflected by the physicochemical properties of chemical compounds.

-polynomial exponential type -convex function with some related inequalities and their applications.

In this paper, the idea and its algebraic properties of -polynomial exponential type -convex function have been investigated. Authors prove new trapezium type inequality for this new class of functions. We also obtain some refinements of the trapezium type inequality for functions whose first derivative in absolute value at certain power are -polynomial exponential type -convex.

Role of key players in paradigm shifts of prostate cancer bone metastasis.

The decreased bone mineral density and compromised bone strength predispose individuals to skeletal osteoporosis. Both prostate cancer and bone metastasis caused by cancer invasion have remained a great challenge to researchers. With the advancement in the fields of biochemistry and biomechanics, the molecular mechanisms that make prostate cancer metastasize to bone have recently been identified, and they provide new molecular targets for drug development.

New generalizations of Popoviciu-type inequalities via new Green's functions and Montgomery identity.

The inequality of Popoviciu, which was improved by Vasić and Stanković (Math. Balk. 6:281-288, 1976), is generalized by using new identities involving new Green's functions.