Determine the value of the variable in each equation.

Basic Algebra = 代数学入門

Commutative rings I

How external debt led to economic growth in South Asia: A policy perspective analysis from quantile regression

Chemical reaction network theory is an area of applied mathematics that attempts to model the behavior of real world chemical systems. Since its foundation in the 1960s, it has attracted a growing research community, mainly due to its applications in biochemistry and theoretical chemistry. It has also attracted interest from pure mathematicians due to the interesting problems that arise from the mathematical structures involved. In this report, we compute newly defined topological indices, namely, Arithmetic-Geometric index (AG1 index), SK index, SK1 index, and SK2 index of the Honey Comb Derived Networks. We also compute sum connectivity index and modified Randić index. Moreover we give geometric comparison of our results. Mathematics Subject Classification: 05C12, 05C90.

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The Study of Honey Comb Derived Network via Topological Indices

Two Star Operations and Their Induced Lattices

Topological descriptors are numerical parameters of a molecular graph which characterize its molecular topology and are usually graph invariant In QSAR/QSPR study, physico-chemical properties and 

Computing topological polynomials of mesh-derived networks

Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as the Randic, the atom-bond connectivity (ABC) and the geometric-arithmetic (GA) indices are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study poly honeycomb networks which are generated by a honeycomb network of dimension n and derive analytical closed results for the general Randic index $$R_\alpha (G)$$
 for different values of $$\alpha $$
 , for a David derived network $$(\textit{DD}(n))$$
 of dimension n, a dominating David derived network $$(\textit{DDD}(n))$$
 of dimension n as well as a regular triangulene silicate network of dimension n. We also compute the general first Zagreb, ABC, GA, $$\textit{ABC}_4$$
 and $$\textit{GA}_5$$
 indices for these poly honeycomb networks for the first time and give closed formulas of these degree based indices in case of poly honeycomb networks.

On topological properties of poly honeycomb networks

The objective of this paper is to derive the bounds of fractional integral operators which contain Mittag-Leffler functions in the kernels. By using (s, m)-convex functions bounds of these operators are evaluated which lead to obtain their boundedness and continuity. Moreover the presented results can be used to get various results for known fractional integrals and functions deducible from (s, m)-convexity. Also a version of Hadamard type inequality is established for (s, m)-convex functions via generalized fractional integrals.

Boundedness of fractional integral operators containing Mittag-Leffler functions via ( s,m )-convexity

A recent subject of study linking commutative ring theory with graph theory has been the concept of the zero divisor graph of a commutative ring The zero divisor graph of a commutative ring exhibi

Computing the size of zero divisor graphs

Counting polynomials are those polynomials having at exponent the extent of a property partition and coefficients the multiplicity/occurrence of the corresponding partition. In this paper, Omega, Sadhana and PI polynomials are computed for Multilayer Hex-Cells nanotubes, One Pentagonal Carbon nanocones and Melem Chain nanotubes. These polynomials were proposed on the ground of quasi-orthogonal cuts edge strips in polycyclic graphs. These counting polynomials are useful in the topological description of bipartite structures as well as in counting some single number descriptors, i.e. topological indices. These polynomials count equidistant and non-equidistant edges in graphs. In this paper, analytical closed formulas of these polynomials for Multi-layer Hex-Cells MLH (k, d) nanotubes, One Pentagonal Carbon CNC5 (n) nanocones and Melem Chain MC (n) nanotubes are derived.

Shafiq Ur Rehman

Papers

Computing topological polynomials of mesh-derived networks

On topological properties of poly honeycomb networks

Boundedness of fractional integral operators containing Mittag-Leffler functions via ( s,m )-convexity

Computing the size of zero divisor graphs

Computing topological polynomials of certain nanostructures