Mathematics Interdisciplinary Research
Volume:7 Issue: 3, Summer 2022

The Mathieu group M24 has a maximal subgroup of the form G ̅=N:G, where N=26 and G=3. S6 ≅ 3. PGL2 (9). Using Atlas, we can see that M24 has only one maximal subgroup of type 26:(3. S6). The group is a split extension of an elementary abelian group, N=26 by a non-split extensionmgroup, G=3. S6. The Fischer matrices for each class representative of G are computed which together with character tables of inertia factor groups of G lead to the full character table of G ̅. The complete fusion of G ̅ into the parent group M24 has been determined using the technique of set intersections of characters.

A non-empty set S ⊆ V is a dominating set, if every vertex not in S is adjacent to at least one vertex in S, and S is a total dominating set, if every vertex of V is adjacent to some vertices of S. We enumerate dominating sets, non-split dominating sets and total dominating sets in several classes of cactus chains.

We present a study of high efficient terahertz (THz) wave generation in DASB/GaAs, DASC/GaAs, and DAST/GaAs multilayer structures at 1.5THz via difference frequency generation (DFG) process with 1.5µm femtosecond laser pulses. We also compare the conversion efficiency in proposed structures with DASB/SiO2, DASC/SiO2, and DAST/SiO2 multilayer structures and bulk crystals DASB, DASC, and DAST. These structures compensate for phase mismatching in bulk crystals DASB, DASC, and DAST and increase conversion efficiency from 10-5 in bulk organic crystals up to 10-3 in multilayer structures. We show that DASC/GaAs is the best structure to generate 1.5THz waves.

In this paper we study the dependence of solutions of uncertain initial value problems (UIVP) on the initial values. Introducing a contraction mapping and using Banach Fixed Point Theorem (BFPT), the existence and uniqueness (EaU) of solutions of the UIVP will be proven. We show that under appropriate assumptions, the solutions of UIVP are continues and differentiable with respect to initial conditions (ICs). The paper will be ended by proving a theorem about the existence of solutions of an autonomous UIVP under weaker conditions. This theorem is a generalization of PeanoTheorem to UDEs.

In the era of information technology and the expansion of global networks, digital document management systems play a crucial role in providing services. The use of digital instead of paper documents has become more common to reduce the administrative costs in small and large organizations. One of the most significant concerns of such systems, though, is the security of documents against alteration or distortion. There are various ways to increase the security of digital documents and this paper is aimed at providing a new framework of the combination of steganography and cryptography to increase the security of digital documents.The proposed method first has been tested and reviewed with MATLAB 2018 software on standard images such as Lena, Baboon and Pepper. Then, it has been tested on digital documents of the Social Security Organization through the proposed conceptual model which utilizes a combination of unique image features to generate messages. The evaluation of results indicates the effectiveness of the proposed method and its applicability in digital document management systems.

This study concentrated on the numerical solution of a nonlinear Volterra integral equation. The approach is accorded to a type of orthogonal wavelets named the Chebyshev cardinal wavelets. The undetermined solution is extended concerning the Chebyshev cardinal wavelets involving unknown coefficients. Hence, a system of nonlinear algebraic equations is drawn out by changing the introduced expansion to the predetermined problem, applying the generated operational matrix, and supposing the cardinality of the basis functions. Conclusively, the estimated solution is achieved by figuring out the mentioned system. Relatively, the convergence of the founded procedure process is reviewed in the Sobolev space. In addition, the results achieved from utilizing the method in some instances display the applicability and validity of the method.