Molecular description for magnesium iodide

Graph theory, which has become a powerful area of mathematics, owns much advancement in the field of mathematical chemistry. Recently, chemical graph theory has turned into a very popular area among researchers because of its wide-ranging applications in the field of mathematical chemistry. The manipulation and inspection of chemical structural information is made feasible using molecular descriptors. The molecular topological descriptors are the numerical invariants of a molecular graph and are valuable for predicting their bioactivity. An abundant variety of such indices are taken into consideration and used in pharmaceutical researchers, in theoretical chemistry, in drugs and in several other fields. A topological index actually relates a chemical structure by means of a numeric number. In this recent research work, we have considered the chemical graph of magnesium iodide. We computed degree based topological indices. Mainly, we addressed atom-bond connectivity index (ABC), geometric arithmetic index (GA), fourth atom-bond connectivity index (ABC4), The fifth geometric-arithmetic index (GA5), general Randic' index Ra(G) and First Zagreb index M1(G), Second Zagreb index M2(G) for magnesium iodide, MgI2. Furthermore, the results are analysed and we have provided general formulas for all these above mentioned families of graphs that are in fact very helpful in studying the underlying topologies

New FxLMAT-Based Algorithms for Active Control of Impulsive Noise

In the presence of non-Gaussian impulsive noise (IN) with a heavy tail, active noise control (ANC) algorithms often encounter stability problems. While adaptive filters based on the higher-order error power principle have shown improved filtering capability compared to the least mean square family algorithms for IN, however, the performance of the filtered-x least mean absolute third (FxLMAT) algorithm tends to degrade under high impulses. To address this issue, this paper proposes three modifications to enhance the performance of the FxLMAT algorithm for IN. To improve stability, the first alteration i.e. variable step size FxLMAT (VSSFxLMAT)algorithm is suggested that incorporates the energy of input and error signal but has slow convergence. To improve its convergence, the second modification i.e. filtered x robust normalized least mean absolute third (FxRNLMAT) algorithm is presented but still lacks robustness. Therefore, a third modification i.e. modified filtered-x RNLMAT (MFxRNLMAT) is devised, which is relatively stable when encountered with high impulsive noise. With comparable computational complexity, the proposed MFxRNLMAT algorithm gives better robustness and convergence speed than all variants of the filtered-x least cos hyperbolic algorithm, and filtered-x least mean square algorithm

Existence theories and exact solutions of nonlinear PDEs dominated by singularities and time noise

The current research deals with the exact solutions of the nonlinear partial differential equations having two important difficulties, that is, the coefficient singularities and the stochastic function (white noise). There are four major contributions to contemporary research. One is the mathematical analysis where the explicit a priori estimates for the existence of solutions are constructed by Schauder’s fixed point theorem. Secondly, the control of the solution behavior subject to the singular parameter ϵ when ϵ → 0. Thirdly, the impact of noise that is present in the differential equation has been successfully handled in exact solutions. The final contribution is to simulate the exact solutions and explain the plots

Construction of nonlinear component of block cipher using coset graph

In recent times, the research community has shown interest in information security due to the increasing usage of internet-based mobile and web applications. This research presents a novel approach to constructing the nonlinear component or Substitution Box (S-box) of block ciphers by employing coset graphs over the Galois field. Cryptographic techniques are employed to enhance data security and address current security concerns and obstacles with ease. Nonlinear component is a keystone of cryptography that hides the association between plaintext and cipher-text. Cryptographic strength of nonlinear component is directly proportional to the data security provided by the cipher. This research aims to develop a novel approach for construction of dynamic S-boxes or nonlinear components by employing special linear group $PSL(2, \mathbb{Z})$ over the Galois Field $GF\left({2}^{10}\right)$. The vertices of coset diagram belong to $GF\left({2}^{10}\right)$ and can be expressed as powers of α, where α represents the root of an irreducible polynomial $p\left(x\right) = {x}^{10}+{x}^{3}+1$. We constructed several nonlinear components by using ${GF}^{*}\left({2}^{10}\right)$. Furthermore, we have introduced an exceptionally effective algorithm for optimizing nonlinearity, which significantly enhances the cryptographic properties of the nonlinear component. This algorithm leverages advanced techniques to systematically search for and select optimal S-box designs that exhibit improved resistance against various cryptographic attacks

Some Applications of Generalized Char-Sets of Ordinary Differential Polynomial Sets

The notion of characteristic sets, which are a special kind of triangular sets, is introduced by J. F Ritt and W.T. Wu. Wu extended Ritt’s work and developed the characteristic set method not only in theory but in algorithms, efficiency and its numerous applications. Triangular sets are widely considered as a good representation for the solution of polynomial systems. After the introduction of characteristic sets by Ritt, triangular sets have become an alternative tool for representing the ideal besides the Gröbner bases. This paper is about implementation and applications of generalized characteristic sets of ordinary differential polynomial sets defined by author

M-polynomial and topological indices of zigzag edge coronoid fused by starphene

Chemical graph theory is a subfield of graph theory that studies the topological indices for chemical graphs that have a good correlation with chemical properties of a chemical molecule. In this study, we have computed M-polynomial of zigzag edge coronoid fused by starphene. We also investigate various topological indices related to this graph by using their M-polynomial

Effect of Simulated Chemistry Practicals on Students’ Performance at Secondary School Level

The study was conducted to compare the performance of students working in chemistry laboratory with those working in chemistry laboratory supplemented with simulations at secondary school level. The study was experimental in nature and post-test only control group design was used. The sample comprised of 55 males and 60 female students and 02 Chemistry teachers of class IX of Public schools. At the end of the treatment, practical examination was conducted on the pattern of Peshawar Board of Intermediate and Secondary Education. The scores of both control and experimental groups were compared by using independent sample t-test in three main areas i.e. written, viva voce and notebook. The result of independent sample t test of school No 1(male) indicated that there is a significance difference between the performance of control group (M=8.9, SD=2.13) and experimental group (M=10.5, SD=3.04) at α=0.05 and df=53. The result of independent sample t test of school No 2(female) indicated that there is a significance difference between the performance of control group (M=10, SD=1.91) and experimental group (M=11.7, SD=2.13) at α=0.05 and df=58. The qualitative data was collected by means of interviews from chemistry teachers. Both the interviewees were motivated and showed keen interest in the simulated software. The performance of the students of experimental groups showed improvement results in the rejection of hypotheses that there is no significant difference between the performance of students taught by conventional demonstration in laboratory and laboratory work facilitated with simulation

Design and Implementation of Novel LMI-Based Iterative Learning Robust Nonlinear Controller

An iterative learning robust fault-tolerant control algorithm is proposed for a class of uncertain discrete systems with repeated action with nonlinear and actuator faults. First, by defining an actuator fault coefficient matrix, we convert the iterative learning control system into an equivalent unknown nonlinear repetitive process model. Then, based on the mixed Lyapunov function approach, we describe the stability of the nonlinear repetitive mechanism on time and trial indices and have appropriate conditions for the repeated control system’s stability in terms of linear matrix inequality theory. Through LMI techniques, we have obtained satisfactory results and controller stability, and robustness against fault tolerance is also discussed in detail. Finally, the simulation results of the output tracking control of the two exemplary models verify the effectiveness of the proposed algorithm