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International Journal of Mathematics and Mathematical Sciences publishes research across all fields of mathematics and mathematical sciences, such as pure and applied mathematics, mathematical physics, probability and mathematical statistics.
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International Journal of Mathematics and Mathematical Sciences maintains an Editorial Board of practicing researchers from around the world, to ensure manuscripts are handled by editors who are experts in the field of study.
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A Relation between D-Index and Wiener Index for r-Regular Graphs
For any two distinct vertices and in a connected graph , let be the length of path and the D–distance between and of is defined as: , where the minimum is taken over all paths and the sum is taken over all vertices of path . The D-index of G is defined as . In this paper, we found a general formula that links the Wiener index with D-index of a regular graph G. Moreover, we obtained different formulas of many special irregular graphs.
Exact Solution of Modified Veselov–Novikov Equation and Some Applications in the Game Theory
A method of finding exact solutions of the modified Veselov–Novikov (mVN) equation is constructed by Moutard transformations, and a geometric interpretation of these transformations is obtained. An exact solution of the mVN equation is found on the example of a higher order Enneper surface, and given transformations are applied in the game theory via Kazakh proverbs in terms of trees.
Mathematical Modeling and Analysis of an Alcohol Drinking Model with the Influence of Alcohol Treatment Centers
In this paper, we present a continuous mathematical model of alcohol drinking with the influence of private and public addiction treatment centers. We study the dynamical behavior of this model and we discuss the basic properties of the system and determine its basic reproduction number . We also study the sensitivity analysis of model parameters to know the parameters that have a high impact on the reproduction number . The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at drinking-free equilibrium when . When , drinking present equilibrium exists and the system is locally as well as globally asymptotically stable at alcohol present equilibrium .
Lower Bound for the Class Number of
In this paper, we give an explicit lower bound for the class number of real quadratic field , where is a square-free integer, using which is the number of odd prime divisors of .
Rational Cohomology Algebra of Mapping Spaces between Complex Grassmannians
We consider the complex Grassmannian of k-dimensional subspaces of . There is a natural inclusion . Here, we use Sullivan models to compute the rational cohomology algebra of the component of the inclusion in the space of mappings from to for and in particular to show that the cohomology of contains a truncated algebra , where , for and .
New Bounds on 2-Frameproof Codes of Length 4
Frameproof codes were first introduced by Boneh and Shaw in 1998 in the context of digital fingerprinting to protect copyrighted materials. These digital fingerprints are generally denoted as codewords in , where Q is an alphabet of size q and n is a positive integer. A 2-frameproof code is a code C such that any 2 codewords in C cannot form a new codeword under a particular rule. Thus, no pair of users can frame a user who is not a member of the coalition. This paper concentrates on the upper bound for the size of a q-ary 2-frameproof code of length 4. Our new upper bound shows that when q is odd and .
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