Research and Applications Towards Mathematics and Computer Science Vol. 1

The stuff of internet users increasing with the every moment of time, due to this huge lead of traffic grows on the wide area networks. Some users have crime category behavior and have attitudes of criminals like hacking the site, blocking the mail, chatting unauthorized users etc. Every service provider wants to increase his traffic share and way, which creates the competition among the providers. When users get the connectivity he initiates the crime activity. In this paper invested the effect of different categories crime users on the internet traffic sharing under the Markov Chain model. There are two groups of users (i) Crime users (ii) Noncrime users. Further crime users divided into two group Fully-crime users and Partially Crime users. Simulation study is performing to analysis the better proportion of traffic by the users.

This chapter introduces generalized exponential and extorial functions arrived from exponential and extorial functions. These two types of functions are special types of continuous and discrete hyper geometric functions. These functions are applied to arrive find solutions of higher order differential and difference equations. The results are supported by relevant instances.

In this research work, we propose a new technique for RGB colour image encryption based on permutation matrix. The colour image is encrypted into Red, Green and Blue channels where each channel uses a double permutation key technique for assigning a new colour to every pixel of RGB colour image. Each channel is encrypted with a technique known as double permutation key encoding, which assigns a different color to each pixel of an RGB color image.  Additionally, we present a novel approach of partite block encryption. The number of possible encryptions is supplied along with a detailed study of the encryption of a 9-pixel image. Additionally, the Matrix representation effectively conveys the decryption process.

If each edge in \(E(G)\) of a subgraph of \(G\) is isomorphic to \(H\), the graph \(G\) has an \(H\)-covering. A bijection \(f: V(G) \cup E(G) \rightarrow\{1,2, \ldots, p+q\}\) is \(H\) - \(E\)-super magic graceful labeling (H-E-SMGL) with the property \(f(E(G))=\{1,2, \ldots, q\}\) and for each subgraph \(H^{\prime}\) of \(G\) isomorphic to \(H, \sum_{v \in V\left(H^{\prime}\right)} f(v)-\sum_{e \in E\left(H^{\prime}\right)} f(e)=M\) for some positive integer \(M\).Applying the definition of \(H\)-E-SMGL, in this article we study \(C_k\)-E-super magic labeling of some families of graphs such as generalized fan graph and generalization of a graph attained at connecting of a star \(K_{1, n}\) with one isolated vertex.

In this study, we define coupled fixed point for a mapping in complex valued G_b metric space, prove a few coupled fixed point theorems in this space, and give an illustration to illustrate our main theorem. Fixed point theory has great importance in science and mathematics. Since this area has been developed very fast over the past two decades due to huge applications in various fields such as nonlinear analysis, topology and engineering problems, it has attracted considerable attention from researchers. In this paper, we proved a coupled fixed point theorem in complex valued G_b-metric space which genealized the result of Kumar and Vashistha [1] and many others.  

The objective of this study is to improve the accuracy of brain tumor diagnosis and segmentation, with the aim of aiding physicians in identifying specific brain tumors. Brain tumors are solid neoplasms within the skull. These tumors are caused by uncontrolled growth of abnormal cells. Classification of brain tumors is divided based on the location of the tumor, the type of tissue produced, and whether the tumor is malignant (malignant) or benign (benign) and several other considerations. In addition, a surgical biopsy of the suspected tissue (tumor) is required to obtain more information about the type of tumor. Biopsy takes 10 to 15 days for laboratory testing. With the advantages of machine learning algorithms, especially the CNN method in classifying brain tumors and contour detection, this research was conducted on the performance of machine learning on MRI image results for patients with brain tumor using transfer learning EfficientNet-B7 and U-Net.

The dynamic characteristics.of squeeze film. lubricated on curved circular plates with micropolar .fluid is analysed. The generalised Reynold’s equation governing .squeeze film pressure, load carrying capacity and squeeze film time are derived. The present analysis deals with characteristics of squeezed film between two curved circular plates lubricated with micropolar fluid. The results yields increasing the values of coupling number, couple stress parameter. and upper curvature parameter leads.to increase the squeeze film pressure, load carrying capacity and squeeze film time and decreases for increasing the values of lower curvature parameter.

Cybercrime has increased exponentially in conjunction with the introduction and widespread use of electronic medium. As the technological advancements take shape, so do the systems of evolution of cybercrime. This implies that new forms of cybercrime are emerging to counter the new technological innovations, which has led to an increased concern in the whole endeavor of crime on the internet. Most users of the online applications are weary about the increasing trend of criminal activities, where in real essence, if these harms are not regulated, the use of the internet would be akin to vulnerability to both social and economic risks. This is not just confined to one area, but rather is occurring worldwide. Some progress has been made to counter this type of crime, but criminal legislation which crosses international borders is severely lagging behind. It is imperative that with the increasing advancement in the levels of crime, all the stakeholders must come up with proactive measures that could help resolve this issue for once and for all for a moral definition of the sue of the internet. Some sort of public policy must be adopted, according to individuals, educational institutions, organizations and corporations who are interested in combating this wave of crime.

By the DAG decomposition, we mean the decomposition of a directed acyclic graph G into a minimized set of node-disjoint chains, which cover all the nodes of G. For any two nodes u and v on a chain, if u is above v then there is a path from u to v in G. In this paper, we discuss an efficient algorithm for this problem. Its time complexity is bounded by O(max{k, } ×n²) while the best algorithm for this problem up to now needs O(n³) time, where n is the number of the nodes of G, and k is G’s width, defined to be the size of a largest node subset U of G such that for every pair of nodes x, y Î U, there does not exist a path from x to y or from y to x. k is in general much smaller than n. In addition, by the existing algorithm, Q(n²) extra space (besides the space for G itself) is required to maintain the transitive closure of G to do the task while ours needs only O(k×n) extra space. This is particularly important for some nowadays applications with massive graphs including millions and even billions of nodes, like the facebook, twitter, and some other social networks. 

In this paper, we derive the harmonic centrality of the vertices and the harmonic centralization of products of some important families of graphs. Centrality in graph theory and network analysis is based on the importance of a vertex in a graph. Our goal is to develop formulas that may be used to calculate the harmonic centrality and harmonic centralization of more complicated graphs. We present some results on both the harmonic centrality and harmonic centralization of graphs resulting from some graph products such as Cartesian and direct products of the path  with any of the path , cycle , star , and fan  graphs. For further studies, results can be derived for other families of graphs and other binary operations.

To represent the interaction of the human being with his environment and letting him express it, therefore blending the subject with the object and completing what was missing from Quantum theory. In our polynomial the subjective factor Xo shows up in the numerator and leads to an objective valuation since of a finite degree. Study also revives an approach to elicit human preferences based on the stimuli-response procedure long forgotten. Fifty years ago a new theory, Elementary Catastrophe Theory,(E.C.T.), unfolding a unique Potential in our brain, provided the underlying dynamics needed to fulfill all the desiderata of the so-called school of Psycho-Physics (Weber-Fechner, 1860), seeking to make mathematical sense of the procedure above. The axiomatization of a self-measurement process removes any "a priori" assumptions about human motivation from the explanation of the empirical data. This 5th degree symmetric polynomial exhibits a characteristic (Negative Schwarz' Derivative) that goes a long way to resolve disputes and remove obstacles in the development of Portfolio Theory in addition to meeting the major landmark criteria in the fields of Value and Utility.  Given that chaos theory has the divergence of Newton's Method as a paradigm, we have brought order to a potentially chaotic process because our algorithm ensures local and global convergence through the careful selection of initial points. The possibility of expanding the approach to the complex field is encouraged by the expression of the Schwarz derivative's invariance to the Mobius transformation.