Recent Advances in Mathematical Research and Computer Science Vol. 2

To improve car security, this study presents an SMS-controlled car security system by incorporating image capturing and voice recording techniques. The device is operated by a mobile phone and is connected to a PIC, GPS, and GSM modem. The entire system is made up of two sections: the transmitting and receiving sections.  The transmitting part is made up of the microcontroller, which serves as the system's brain, the global positioning system (GPS), which is used to obtain precise location and time, a GSM modem (Siemens TC35) that sends and receives messages and voice call, extremely small snapshot camera which takes the pictures of the car thieves, process it into Jpeg file and forward it to the PIC through a serial port, and voice recording device which receives the conversation of the car thief and also  forward it to the receiving part for storage.

The nRF2401 receiver and the memory card that serves as a storage device for data files make up the receiving ends. This device can carry out commands sent to it via text and SMS from a mobile phone. The modem is queried by the microcontroller to see whether there are any messages from the users through the hidden condense microphone, the user can make a voice call and listen to  the thieves conversation. This advanced vehicle security system is ideal for tracking stolen vehicles and their intruders.

Main objective of writing this paper is to adopt and create a common database from multiple databases in an Integrated Software System of a particular domain of interest. This will result in reducing data redundancy, in reducing database maintenance time, in simplifying the development phase of the front-end interface, in minimizing the size of the system, in maximizing the database throughput and in implementing of a transaction pool. The transaction pool is used to optimize the database processing. The system can pool the database transactions. Transaction pooling maximizes database throughput while controlling the number of database connections that can be open at one time. We can also say the transaction pool will reduce the number of times new connection objects are created, will promote connection object reuse, will quicken the process of getting a connection and will control the amount of resources spent on maintaining connections. We also illustrate some examples of a transaction pool to connect transaction databases with a common database. We have also illustrated how to create non-visual transaction objects within the system. Practically, we have implemented this approach in our one integrated software system.

Background: The twin prime conjecture is regarded as a classic puzzle in number theory and one of the most well-known conjectures that has always perplexed us. Mathematician David Hilbert presented 23 key mathematical problems and conjectures to be solved at the International Congress of Mathematicians in 1900. He included the Bernhard Riemann conjecture, the Twin Prime Conjecture, and the Goldbach's conjecture in the eighth of 23 mathematical problems.

Methods: Based on the "Differential Incremental Equilibrium Theory" [1], the infinite set of infinite prime numbers is divided, the increment equation of infinite prime numbers is established, and the tree-like set of prime numbers is obtained. Find the twin primes with a minimum unit [1\(\to\)1] of 2.

Results: When a set of prime numbers is infinitely divided, there are 2[1\(\to\)1] pairs of prime numbers whose gap is equal to 2 and gap is not equal to 2. We gives a complete proof of the twin prime conjecture. It shows that the importance of "Differential Incremental Equilibrium Theory" [1] and infinite classification in twin prime conjecture. In a higher-level ideology, the set infinite partition classification confirms that the minimum unit is 2. It's a new way to prove Twin Prime Conjecture.

Conclusion: This paper gives a complete proof of the establishment of the Twin Prime Conjecture.

The aim of this study was to investigate the Impact of Information Security Policies on Security Beach incidences in Kenyan public universities. Information security policies are designed to safeguard network resources from security breaches.  The objectives of the study were: to investigate if there is a relationship between network security policies and information security breach incidents, to determine the relationship between server security policies and information security breach incidents, to investigate if there is a relationship between application security policies and information security breach incidents and to investigate the impact of information security policies on information security breach incidents. The study utilized a questionnaire to collect primary data from IT personnel in public universities with regard to their perceptions of how information security policies affect computer security breach incidents. A simple random sampling was used to identify 200 IT employees from public universities in Kenya. Pearson correlation analysis was used to study the relationships between the variables. Independent t-tests (2-tailed) and ANOVA test were used to determine the level of significance. According to the results of the study, there is a weak relationship between information security policies and security breach incidences. The study hopes to add to the body of academic knowledge in the public educational institutions in Kenya where information repository is a resource.

The detour distance of a graph is evaluated in this study, as well as the problems that go along with it. We investigate graph detour eccentricity and average detour eccentricity, as well as some of the features that link self-centered graphs with detour distance. A characterization of tree is also presented.

An efficient DWT-based watermarking technique is proposed in this research to insert gray-scale logos as a watermark in images to attest the owner identify and discourage unauthorised copying. To hide a higher energy hidden watermark in conspicuous picture components, the method converts both the host image and the watermark into the discrete wavelet domain, where their coefficients are fused adaptively based on the Human Visual System (HVS) model. The method merges the watermark coefficients at various resolution levels of the host image, resulting in simultaneous spatial localisation and frequency spread of the watermark, as well as robustness against various attacks. According to the simulation results, the suggested method is robust to a wide range of attacks, including image compression, linear and non-linear filtering, noise addition, image resizing, cropping, and enhancement, among others.

Nowadays, contamination and external exposure by radioactive materials have become frequent and less controlled in different African countries, further to results of mining activities located in affluent areas in sought-after metals, which generate large quantities of solid, gaseous, and liquid products in the environment. We notify that the environmental protection and workers against ionizing radiation seem to be neglected in favour of employers seeking to produce the products sought (Cu, Co, Zn, Ag, etc.). Without mentioning the natural radioelements that can show on the mining site that emit ionizing radiation to protect workers against this radiation by providing them with adequate equipment and without taking the necessary precautions to protect the environment against them.

Indeed, the object of our study is to prevent all risks of contamination with chemical elements and radioactive equipment, because it is healthy a significant danger when we breathe it more or less quantity in the human body on ores site without personal protective equipment.

Hence, to prevent risks due to contamination and external exposure, we opted for technical research based on the interview and questioning of all people working without personal protective clothing and with protective clothing.

In this chapter, the binary quadratic equation x² - 2xy - y² + 2x + 14y = 72 represents a hyperbola is analyzed for its non-zero distinct integer solutions. Also, we obtain a sequence of its integral solutions and present a few interesting relations among them. The recurrence relations satisfied by the solutions x and y are obtained.

In this chapter, three non-extendable Diophantine triples comprises of centered square numbers such that the product of any two members and increased by a non-zero integer or a polynomial with integer co-efficient is a perfect square are exhibited. More precisely, three non-extendable Diophantine triples of the form {a, b, 2(a+b-Square of the difference of the ranks)} involving centered square numbers with property  D(-Square of the difference of the ranks) .

We Present the sum of the Polygonal numbers of even sides are derived from Stella Octangula number and Pronic number using division algorithm.

The fast growing technology has left a great impact on the human life. Many traditional systems are either replaced or running in parallel with their electronic counterpart. As for example: - the traditional postal system is now nearly replaced by mobile phones and emails. The electronic system is providing more functionalities than their traditional counterparts. Due to social media, peoples may communicate with each other, share their thoughts and moments of life in form of texts, images or videos. On the other hand, to enhance technologies and knowledge many research activities are propelled and data from different sources are gathered in large volume for further analysis. In short today’s world is surrounded with large volume of data in different form. This put a requirement for effective management of these billions of terabytes of electronic data generally called BIG DATA. The effective management must be based on proven mathematical concepts so that chance of casualties may be reduced. The study objective of this is to provide a mathematical appraisal for evolution of distribution of file data and explains some basic solution of primitive problems based on probability theory. The probability theory helps us to formalize the basic tree like architecture of distributed file system if we try to solve the problem like Big Data.

This paper presents a developed and configured Ku and UHF bands integrated  cloud-connected, multicentre instrumentation system for real time measurement and  storing of  Ku and UHF signals  data across climatic zones of Nigeria for scientist and radio researchers use. The instruments are connected to the computer via USB interfaces, and data is exchanged with the systems using logging software bonded to these interfaces. The logging program plots graphs for the various detected quantities, whereas the viewing software retrieves data from a cloud service, shows its values, and plots graphs in its graphical user interface (GUI). The cloud architecture is housed by Amazon Web Services (AWS), which operates a web application that connects to numerous centers and makes their obtained data available in real time via viewing software.  The system configuration flexibility allows for changes in Ku signal polarization to vertical or horizontal polarization situations, as well as depicting the features of the satellite whose downlink signal is being measured together with other information about its position. Through the web application that connects the locations together, upgrading may be done throughout the logging and view locations from a particular place. Configurations also improve the ability to view information on variations of Ku and UHF signals from any other location in Nigeria's climatic areas from a particular spot. This instrumentation system provides important data for radio scientists and engineers to construct detailed and realistic models of (Ku and UHF) signal fading and attenuation, which will improve the budgeting and planning of terrestrial and satellite communications across  climatic regions of Nigeria.

The Lorenz curve and Gini-concentration co-efficient were used to describe the income inequality of families in the selected village, and the incidence of poverty assessed in Poverty Gap (PG) proposed by Foster-Greer-Thorbecke (FGT) was employed as a poverty indicator. The paper is an attempt to study and examine the problem of poverty and the incidence of income inequality in the study area of Thanga Karang. The paper also aims at analyzing the mode of income distribution among the households of the study area. Thanga Karang, a village of 257 households, is regarded to be selected village. To gather information about poverty, a household survey was conducted. A statistical analysis of PG is performed, and parameters and are fitted to the beta distribution using the method of moments and the maximum likelihood approach. The statistically significant values of \(\alpha\) and \(\beta\) are respectively \(\hat{\alpha}\) = 0.2989 and \(\hat{\beta}\) = 3.4722 by method of moments; \(\hat{\alpha}\) = 1.459 and \(\hat{\beta}\) = 3.001 by method of maximum likelihood. As a result, the PG, a poverty index, best fits the assumed model (i.e. Beta distribution). The Gini concentration co-efficient is 0.5253, according to the research. It suggests that income inequality among the household is observed in 52.53 percentages.

In the theory of rings, the properties of derivations are important. In [1], Jun and Xin applied the notion of derivations in ring and near-ring theory to BCI-algebras, and they also introduced a new concept called a regular derivation in BCI-algebras. They investigated some properties of its. A BCC-algebra is an important class of logical algebras introduced by Y. Komori [2].   In this manuscript, the concept of fuzzy left (right) derivations BCC-ideals in BCC-algebras is introduced and then investigate their basic properties. In connection with the notion of homomorphism, the authors study how the image and the pre-image of fuzzy left (right) derivations BCC-ideals under homomorphism of BCC-algebras become fuzzy left (right) derivations BCC-ideals. Furthermore, the Cartesian product of fuzzy left (right) derivations BCC-ideals in Cartesian product of BCC-algebras is introduced and investigated some related properties.

Cloud computing is the delivery of identical IT capacity (services, software, or infrastructure) via internet technologies on a pay-per-use, self-service basis. File management services based on cloud storage, such as DropBox, Google Drive, OneDrive, and Mega, are utilised by millions of people across the world. Features for rising of external file systems with DropBox, FTP, and GoogleDrive allow users to have all of their file sync and distribution tools in a single interface. To trust our data on other people's data centres, we use cloud storage services such as DropBox, Google Drive, OneDrive, and Mega Cloud. OwnCloud is an open source file sync and share platform that allows us to keep our data on our servers and choose which other public cloud services to integrate into our personal cloud of cloud storage size, security, and used in platform between online public cloud as OneDrive, GoogleDrive, DropBox, Mega, and private cloud storage OwnCloud with public cloud OpenShift and some file related storage analysis between them.

Study objectives:

 The main objectives set forth for current study are:

1. Study on Insecure cloud Storage.
2. Study on Partial Secure Cloud
3. Study on Secure Cloud.

Comparative study on Comparisons of cloud storage and Analysis on Uploaded Files in OneDrive, Google Drive, DropBox, Mega and OwnCloud-OpenShift platforms.