In this paper, we introduce new results of vertex connected dominating set and vertex connected domination polynomial of vertex identification, edge introduced and t-tuple of complete graph, also we determine  new results of vertex connected dominating set and vertex connected domination polynomial of  vertex identification, edge introduced and t-tuple of wheel graph.

This paper outlines an encoding schematic that is dependent on simple Cartesian coordinate transformations. Namely, the change of axes and the rotation of axes. A combination of these two is incorporated after turning singular ASCII values into 2D points. This system is based on multiple private keys that can also act as a potential candidate for threshold cryptography. Comprehensive initial testing has been performed on certain parameters by altering their values within a range. Further testing is required for more insights about the system. For now, the list of parameters that amounts to successful decryption is to be noted down for future use with this system.

Human action recognition is an important research direction in computer vision areas. Its main content is to simulate human brain to analyze and recognize human action in video. It usually includes individual actions, interactions between people and the external environment. Space-time dual-channel neural network can represent the features of video from both spatial and temporal perspectives. Compared with other neural network models, it has more advantages in human action recognition. In this paper, a action recognition method based on improved space-time two-channel convolutional neural network is proposed. First, the video is divided into several equal length non-overlapping segments, and a frame image representing the static feature of the video and a stacked optical flow image representing the motion feature are sampled at random part from each segment. Then these two kinds of images are input into the spatial domain and the temporal domain convolutional neural network respectively for feature extraction, and then the segmented features of each video are fused in the two channels respectively to obtain the category prediction features of the spatial domain and the temporal domain. Finally, the video action recognition results are obtained by integrating the predictive features of the two channels. Through experiments, various data enhancement methods and transfer learning schemes are discussed to solve the over-fitting problem caused by insufficient training samples, and the effects of different segmental number, pre-training network, segmental feature fusion scheme and dual-channel integration strategy on action recognition performance are analyzed. The experiment results show that the proposed model can better learn the human action features in a complex video and better recognize the action.

Numerical integral is one of the mathematical branches that connect between analytical mathematics and computer. Numerical integration is a primary tool used by engineers and scientists to obtain an approximate result for definite integrals that cannot be solved analytically. Numerical double integration is widely used in calculating surface area, the intrinsic limitations of flat surfaces and finding the volume under the surface. A wide range of method is applied to solve numerical double integration for equal data space but the difficulty is arisen when the data values are not equal.  In this paper we have tried to generate a mathematical formula of numerical double integration for unequal data spaces. Trapezoidal rule for unequal space is used to evaluate the formula. We also verified our proposed model by demonstrating some numerical examples and compared the numerical result with the analytical result.

The research is concerned with the development of a mathematical model for predicting the rate of human happiness and to outline factors that influence human happiness. The model was optimized and observation about the model’s extreme value was made. The outcome of the optimization result showed that happiness has neither minimum nor maximum level that should be required in human. It means someone’s happiness could be close to 0% or even be up to 100%. Thereafter, the model was analysed and the collated real-life data were correlated with those of the model data (H model) using suitable statistical tools. The findings from the correlation result showed that the questionnaire result attained a 70% degree of correlation with the estimated model result (H model), and thus recommending the model as a standard measure for predicting the rate of human happiness.