Recent Studies in Mathematics and Computer Science Vol. 2

By means of the technique of real analysis and the weight functions, a few equivalent statements of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The constant factor related the beta function is proved to be the best possible. As applications, the case of the homogeneous kernel, the operator expressions and a few corollaries are considered.

Privacy emerged as a hot issue again, as the General Data Protection Regulation (GDPR) of EU has become enforceable since May 25, 2018. This paper deals with the problem of health information sharing on a website securely and with preserving privacy. In the context of patient networks (such as ‘PatientsLikeMe’ or ‘USA Patient Network’), we propose the model Secure Information Sharing System (SISS) with the main method of group key cryptosystem. SISS addresses important problems of group key systems. (1) The new developed equations for encryption and decryption can eliminate the rekeying and redistribution process for every membership-change of the group, keeping the security requirements. (2) The new 3D Stereoscopic Image Mobile Security Technology with AR (augmented reality) solves the problem of conspiracy by group members. (3) SISS uses the reversed one-way hash chain to guarantee forward secrecy and backward accessibility (security requirements for information sharing in a group). We conduct a security analysis of SISS according to group information sharing secrecy and an experiment on its performance. Consequently, although current IT paradigm is changing to be more and more ‘complicated’, ‘overlapped’, and ‘virtualized’, SISS makes it possible to securely share sensitive information from collaborative work.

Realization of the tremendous features and facilities provided by Cloud Computing by the geniuses in the world of digital marketing increases its demand. As customer satisfaction is the manifest of this ever shining field, balancing its load becomes a major issue. Various heuristic and meta-heuristic algorithms were applied to get optimum solutions. The current era is much attracted with the provisioning of self-manageable, self-learnable, self-healable, and self-configurable smart systems. To get self-manageable Smart Cloud, various Artificial Intelligence and Machine Learning (AI-ML) techniques and algorithms are revived. In this review, recent trend in the utilization of AI-ML techniques, their applied areas, purpose, their merits and demerits are highlighted. These techniques are further categorized as instance-based machine learning algorithms and reinforcement learning techniques based on their ability of learning. Reinforcement learning is preferred when there is no training data set.  It leads the system to learn by its own experience itself even in dynamic environment.

In day to day life, the computer plays a major role, due to this advancement of technology collection of data from various fields are increasing. A large amount of data is produced by various fields because of IOT sensors for every second and is not easy to process. This large amount of data is called as Big data. A large number of small files also considered as Big data. It's not easy to process and store the small files in Hadoop. In the existing methods Merging technologies and Clustering Techniques are used to combine smaller files to large files up to 128 MB before sending it to HDFS in Hadoop. In the Proposed system CSFC (Clustering Small Files based on Centroid) Clustering Technique is used without mentioning the number of Clusters previously because if the clusters are mentioned before, all the files are clubbed within the limited number of clusters. In proposing system clusters are generated by depending on the number of related files in the dataset. The relevant files are combined up to 128 MB in a cluster. If any file is not relevant to the existing cluster or if the memory size reached 128MB then-new cluster will be generated and the file will be stored. It is easy to process the related files, comparing two relevant files. By using this method fetching data from the data node, it produces efficient result when comparing with other clustering techniques.

Gene expression data clustering is a significant problem to be resolved as it provides functional relationships of genes in a biological process. Finding co-expressed groups of genes is a challenging problem. To identify interesting patterns from the given gene expression data set, a Tanimoto Coefficient Similarity based Mean Shift Gentle Adaptive Boosted Clustering (TCS-MSGABC) Model is proposed. TCS-MSGABC model comprises two processes namely feature selection and clustering. In first process, Tanimoto Coefficient Similarity Measurement based Feature selection (TCSM-FS) is introduced to identify relevant gene features based on the similarity value for performing the genomic expression clustering. Tanimoto Coefficient Similarity Value ranges from is highest similarity. The gene feature with higher similarity value is taken to perform clustering process. After feature selection, Mean Shift Gentle Adaptive Boosted Clustering (MSGABC) algorithm is carried out in TCS-MSGABC model to cluster the similar gene expression data based on the selected features. The MSGABC algorithm is a boosting method for combining the many weak clustering results into one strong learner. By this way, the similar gene expression data are clustered with higher accuracy with minimal time. Experimental evaluation of TCS-MSGABC model is carried out on factors such as clustering accuracy, clustering time and error rate with respect to number of gene data. The experimental results show that the TCS-MSGABC model is able to increases the clustering accuracy and also minimizes clustering time of genomic predictive pattern analytics as compared to state-of-the-art works.

In this chapter, we discuss the stability analysis of mathematical modeling on a typical three species ecology. The system comprises of a commensal (S₁), two hosts S₂ and S₃ ie., S₂ and S₃ both benefit S₁, without getting themselves effected either positively or adversely. Further S₂ is a commensal of S₃ and S₃ is a host of both S₁, S₂. Here all three species are having limited resources quantized by the respective carrying capacities. The mathematical model equations constitute a set of three first order non-linear simultaneous coupled differential equations in the strengths N₁, N₂, N₃ of S₁, S₂, S₃ respectively. In all, eight equilibrium points of the model are identified. The system would be stable, if all the characteristic roots are negative, in case they are real and have negative real parts, in case they are complex. Further, the trajectories of the perturbations over the equilibrium points are illustrated.

We discuss the general technique of estimating the location parameter of certain distributions with known coeffcient of variation by record values.Also we estimate the location parameters of normal distribution,logistic distribution and exponential distribution using upper record values .Al so we include a real life data to estimate the location parameter of a logistic distribution using upper record values.

In this chapter, linear and nonlinear differential equations are solved. The calculations are carried out by using differential transformation method (DTM) which is a semi-numerical–analytical solution technique. By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related initial conditions are transformed into a set of algebraic equations. The properties of differential transformation is briefly introduced, and then applied for the number of problems. The current results are then compared with those derived from the classical Runge-Kutta method (RK4) order to verify the accuracy of the proposed method. The findings disclose that the DTM can achieve more suitable results in predicting the solution of such problems.

In this paper the Modified Equations of Emden type (MEE),  is solved numerically by the differential transform method. This technique doesn’t require any discretization, linearization or small perturbations and therefore it reduces significantly the numerical computation. The current results of this paper are in excellent agreement with those provided by Chandrasekar et al. [1] and thereby illustrate the reliability and the performance of the differential transform method. We have also compared the results with the classical Runge-Kutta 4 (RK4) Method.

For anynonempty family  FsB-Hausdorff Spaces. The Fs- Cartesianproduct topological space is also an FsB-Hausdorff Space.

We need many analyses to come to an inference about any situation. Probability Distributions play very important role in such analyses. We propose one Probability Distribution function of random variable successive arrivals.   

To provide general expression towards the any statistical situation we need many models and also analyses to come to an inference. Probability Distribution plays very important role in such analyses. Among all statistical empirical distributions, several distributions have been developed by some subtle transformations on the existing distributions. We propose one Probability Distribution function of random variable successive departures.   

In recent days, road traffic management and congestion control has become major problems in any busy junction in Hyderabad city. Hence short term traffic flow forecasting has gained greater importance in Intelligent Transport System (ITS). Artificial Neural Network (ANN) models have been fruitfully applied for classification and prediction of time series. In this chapter, an attempt has been made to model and forecast short-term traffic flow at 6.no. junction in Amberpet, Hyderabad, Telangana state, India applying Neural Network models. The traffic data has been considered for peak hours in the morning for 8A.M to 12 Noon, for 5 days. Multilayer Perceptron (MLP) network model is used in this study. These results can be considered to monitor traffic signals and explore methods to avoid congestion at that junction.

This paper proposes the mean for distribution

for the chosen random variable “how likely there are successive departures in a particular interval”.   

Several different distributions have been analyzed by a number of authors. There is still more scope for the probability density functions on arrivals which plays major role in lifetime data analysis. This paper proposes the Mean, Variance and Standard Deviation for the density function

for the chosen random variable “how likely there are successive arrivals” [1,2].