Recent Advances in Mathematical Research and Computer Science Vol. 1

The primary goal of this paper is to estimate annual mean wind speeds at 10 m, 30 m, and 50 m. The annual mean wind speed is calculated by the PROLOG SWI platform using wind data collected from measurements from 2006 to 2010 at Hiregudda, Bagalkot district, Karnataka state, South India.  Wind speed is measured using cup generator anemometers and the rotational speed (frequency) of the cups is proportional to the wind speed. Three cup anemometers linked to booms on a 50 m lattice met tower were used to measure wind speed at heights of 10 m, 30 m, and 50 m above ground level. The recording interval was set to ten minutes. The findings of mean wind speed data are the first stage in predicting wind speed data at the site in question, and a PROLOG programme was devised and developed to calculate the site's annual mean wind speed data. In order to study the Weibull shape and scale parameters, the statistical wind data set was also analysed using Weibull distributions.

The current study focuses on prospective mathematics teachers' ability to generate problems. A single-item test called the Problem Generating Ability Tool(PGAT). was employed.  Nearly 12% of the prospective mathematics teachers in the sample have a high problem generating ability. The ability to generate problems does not differ considerably by gender or academic qualifications of prospective mathematics teachers. Only the Backward Communities group differed considerably from the Scheduled Castes and Scheduled Tribes categories in terms of social status of prospective mathematics teachers. The social status of the Open Category group did not differ significantly from the other two groups. This study reassures that mathematics teachers possess adequate problem generating ability and hence they can nurture the trait among their wards.

We studied a class of para-Kenmotsu manifolds admitting Weyl-projective curvature tensor of type (1, 3). The present work is organised as follows: Section 2 is equipped with some prerequisites about P-Kenmotsu manifolds. In Section 3, we define W₂-recurrent and semisymmetric para-Kenmotsu manifolds and shown that W₂-recurrent para-Kenmotsu manifold is a semisymmetric manifold. At the end, it is shown that an n-dimensional (n > 2) P-Kenmotsu manifold is Ricci semisymmetric if and only if it is an Einstein manifold.

The term "Artificial Intelligence Plus Plus (AI++)" was coined, invented, and defined in this chapter. Super Computational Intelligence is a sub-field of Artificial Intelligence Plus Plus.

In this chapter, we show students how to use computational modeling to better comprehend and apply mathematical ideas, particularly when dealing with 3D objects like vectors and geometrical shapes. Without any prior coding expertise, students can utilize the Visual Python (VPython) integrated development learning environment to create various 3D objects such as arrows, spheres, and boxes. Building 3D arrows and manipulating by adding or subtracting two or more vectors can help students improve their spatial thinking in a three-dimensional system. The aim of this study is to utilize computational modeling to help students improve their spatial thinking in geometry so that they may better understand and apply mathematical concepts and solve problems. Using VPython, students can adjust the parameters of different vectors, their position, and also attribute different colors based on their preferences. In addition, using mathematical formulas, they will be able to find the solution directly based on some pre-given information. As a result, using VPython provides the educational benefit of empowering students to do more physical modeling and enabling them to better depict processes, both of which help students comprehend concepts better.

Communication networks or information theory have traditionally been used to address cross-layer resource allocation in wireless networks. The allocation of limited resources from network users is a major issue in networking. In a typical layered network, the resource is allotted at the Medium Access Control (MAC) level, and the network layers use bit pipes to deliver data at a fixed rate with some random mistakes. As a result, this study shows how to allocate cross-layer resources in a wireless network using the suggested Social-Sine cosine algorithm (SSCA). The primary goal of this research topic is to use Social Sine Cosine Algorithm (SSCA) to allocate resources between layers. Queue State Information (QSI) and Channel State Interference (CSI) are obtained from the MAC and physical layers, respectively, for Cross_layer optimization. The resource allocation decision is made by the cross-layer optimization entity in order to maximise the network’s sum rate. The Cross_layer entity for optimization adjusts the judgement depending on new input data by altering the channel conditions.

By integrating the Social Ski Driver (SSD) and the Sine Cosine Algorithm (SSA), the suggested SSCA is created. Also, for further refining the resource allocation method, the suggested SSCA considers max-min, hard-fairness, proportional fairness, mixed-bias, and maximum throughput fitness based on energy and fairness. The cross-layer optimization entity decides on resource allocation based on energy and fairness to reduce the network's sum rate. The proposed model's resource allocation performance is measured in terms of energy, throughput, and fairness. The developed model achieves the maximal energy of 258213, maximal throughput of 3.703, and the maximal fairness of 0.868, respectively.

In 2001, Popa and Noiri introduced the notions of minimal structure and m-continuous function as a function defined between a minimal structure and a topological space. In this chapter, we introduce and study the notions of weakly m-semi-I-open sets, weakly m-semi-I-closed sets, weakly m-semi-I-continuity and their related notions in minimal spaces. We prove that any subset of a minimal structure is a weakly m-semi-I-open set if and only if it is a m-\(\delta\)-I-open set. The arbitrary union of weakly m-semi-I-open sets is a weakly m-semi-I-open set and finite intersection of weakly m-semi-I-open sets is a weakly m-semi-I-open set. Also we investigate the decomposition of weakly m-semi-I-open set.

One possible method is proposed for reducing the problem of isotropic hereditary elasticity to solving a set of similar quasi-static problems in the theory of elasticity and thermoelasticity. The representability of the solution of the problem of linear hereditary elasticity in the form of the sum of solutions of three problems is substantiated: the linear theory of elasticity for imaginary bodies-incompressible and having a zero Poisson’s ratio and stationary uncoupled thermoelasticity for a body whose properties do not depend on temperature. The shear and bulk relaxation kernels are considered independent; the viscoelastic Poisso  ratio is time dependent.

Two theorems that reduce solutions of the general quasi-static problem of linear viscoelasticity theory to a solution of the corresponding problem of elasticity theory are proved. These theorems hold if one of the following conditions is satisfied: 1) the material is close to a mechanically uncompressible material; 2) the mean stress is zero; 3) the shift and volume hereditary functions are equal. The theorems provide free direct and inverse transforms between solutions of viscoelasticity and elasticity problems, which make them convenient in applications. They have been applied to solutions of problems on the pure torsion of a prismatic viscoelastic solid with an arbitrary simply connected cross section. Some examples describing the obtained results have been considered.

The emergence of various data mining algorithms and its application to various fields include medical imaging, network traffic analysis, environment system etc. Environment system now a day is the most important area of people’s concern in today’s world since it has daily impact on human beings life. May it be earthquake, soil erosion, deforesting, increasing summer temperature, rain fall density/intensity, flood occurrences and the most important is the impact of all these ES factors to directly and indirectly on the human beings and their behaviour. The capability of data mining algorithms of finding pattern in a data can be applied to Environment System data which is largely distributed, heterogeneous, sparse, multidimensional and heterogeneous. This paper gives a brief survey of essential steps, related algorithms and details processes that deals in designing and dealing with ES data that are essential in development of data mining tool for finding and interpreting patterns in environment system data set. The design process of ES Tool using data mining techniques ranges from processing of rough data sets to transforming it into pattern for analysis.

Nowadays, the use of the internet is overgrowing throughout the world, which makes security a major concern for users.  Data is any information that is stored on a digital platform. Security is about the protection of data. Data security means digital protective measures which are applied to prevent data from hackers. Data encryption is one of the security measures which is used on data. If somehow anyone steals the data, he could not access the data if data is already encrypted. Data Encryption algorithms are developed in computer science to secure the data of senders and receivers. The security of communication is a crucial issue on the internet. Various encryption algorithms depend on data such as text, voice, picture, video, etc. In daily life, security has become a wide necessity. Information protection is perhaps the most important of all. The data is open to high potential risks in our framework. We adopt diverse methods for various security reasons. Now we are all relying on the security and storage cloud platform but also vulnerable to multiple threats. The data in the cloud is not well-secured because anyone who can enter our credentials can access it, and cloud providers do have fair access to us. This paper discusses various data encryption techniques and much more.

The crossed product of a ring R over a group G under a cross mapping \(\sigma\), that is, the crossed product R#\(_{\sigma}\)G, is explored in this chapter. Next, we deduce that R#\(_{\sigma}\)G and the group-ring R[G] are Morita Equivalent.

In, the recent years, many authors have attracted much attention to the study of existence problems for differential and integrodifferntial equations. In this work, we investigate the existence and regularity of solutions for some partial functional integrodifferential equations with finite delay. The continuous dependence upen initial values and asymptotic stability are also studied. Firstly, we show the existence of the mild solutions. Secondly, we give suffcient conditions ensuring the existence of the strict solutions. The method used treats the equations in the domain of A with the graph norm employing results from linear semigroup theory. To illustrate our abstract result, we conclude this work with an application.

Fatigue and drowsiness are among the main causes of traffic accidents, just behind excessive speed and alcoholism. It is essential to monitoring continuously the driver’s vigilance level to ameliorate their ability to maintain safe and efficient driving.  This paper deals with the problem of road safety. It attempts to present a driver vigilance monitoring system based on a video approach. This work aims at creating an assistive driving application employing eyes closure duration and head posture estimation as performant signs for alertness control. The proposed system can be summarized in three main steps: Eyes' detection and tracking in a video, eyes' state classification and fusion of both sub-systems based on eyes' blinking and head position. To accomplish the previous tasks, we used the Viola and Jones algorithm for interest area detection thanks to its efficiency in real time applications. For the classification step, we used two novel architectures of transfer learning classifier based on fast wavelet transform and separator wavelet networks, which presents our main contribution of this paper. This novel architecture proves its performance compared to the classic version of the transfer learning based on SVM classifier and to our old classifier based only on fast wavelet networks without a deep learning structure. The objective of our study is to test the efficiency of the CNN technique compared to wavelet networks in the classification phase. Also we aim to highlight the interest of fuzzy logic as a tool for merging different inputs, which allows us to have a more accurate system for vigilance control.

In this paper, we study a class of neutral partial functional integrodifferential equations with finite delay in Banach spaces. We are interested in the global existence, uniqueness and regularity of solutions with values in the subspace D(A) . The method used are based on Banach’s fixed point theorem and on the technique of the graph norm. In our work the nonlinear term is treated as a perturbation of the linear equation. As an application, we consider a diffusive neutral partial functional integrodifferential equation.