Research Updates in Mathematics and Computer Science Vol. 1

In this paper we prove that, the unique fixed point exists for a mapping satisfying the generalized contractive type conditions in b-metric space. Here the b-metric under consideration need not be continuous function whereas the metric is a continuous function. An example is also given for the verification of the result.

The Security Awareness and Training (SAT) program enables organizational members to understand the organization’s security strategies, know their responsibilities, and control risks that are caused by security incidents. The need for this program has reached an all-time high since COVID-19, which has led organizations to conduct their operations online. One of the most affected fields was the educational field which needed to shift its methods from conventional methods to online learning and teaching pedagogies. Therefore, implementing an SAT program is a critical step for any institution to assure that information assets are appropriately secured. The aim of this chapter is divided into folds: first, to gain an insight and determine the information security awareness and training program levels in the Middle Eastern higher education sector through a case study that examined 182 institute websites over eight countries that were examined before and after COVID-19. Second, to provide recommendations based on the findings that aid information security professionals to establish a new awareness and training program or improve an existing one. Literature showed that no study has been done on the SAT program at the level of the entire Middle Eastern region specifically before COVID-19. However, there was a need for this investigation and therefore, it was a pioneering study at the regional level in the field of information security. The result showed improvements in deploying the SAT program after COVID-19.

We introduce the notion of almost pretopological vector spaces and present some examples of almost pretopological vector spaces. Almost pretopological vector spaces are defined by using regular open sets and pre-open sets.

In this chapter, the new concept vertex sum cube labeling has been introduced and a formula for vertex sum cube labeling has been established. A function \(\theta\) is called a Vertex sum cube labeling of a graph G with edges, if the vertices of G to the set {0,1,2,p-1} such that when each edge \(\mathit{uv}\) is assigned the label \(\theta\)(\(\mathit{uv}\)) = \(\mathit{u^3}\) + \(\mathit{v^3}\) + \(\mathit{3u^2v}\) + \(\mathit{3uv^2}\), then \(\theta\) is a bijective function, then the resulting edge labels are distinct cube numbers. In this chapter, some families of graphs such as Ladder, Stair Str\(_n\), Jelly Fish \(\mathit{J(m,n)}\) and P\(^2_n\) has been established.

Advancements in technology have produced the exploration of blockchain uses in a range of industries, particularly in education, real estate, law enforcement, certification verification, and funding ventures. Blockchain, a decentralized ledger, offers opportunities to revolutionize traditional systems by providing transparency, security, and traceability.

In the education sector, blockchain technology shows promise in enhancing the credibility of online degrees and preventing fraudulent activities by recording accreditations on the blockchain. Similarly, in real estate, the implementation of blockchain models helps mitigate loopholes and brings transparency to property transactions by eliminating intermediaries and reducing fraud potential.

In law enforcement, the fragile nature of digital evidence poses challenges in maintaining integrity and credibility. Blockchain's immutability and traceability offer a promising solution for preserving digital evidence securely, ensuring its authenticity throughout criminal investigations.

Additionally, the project addresses the rampant issue of fraudulent degree certificates by proposing a solution that stores genuine certificates digitally on a blockchain. This system generates unique hashes for verification, detecting any alterations in certificate contents and invalidating tampered documents.

Furthermore, the project introduces a decentralized funding platform for innovative business ventures. Utilizing Ethereum smart contracts, it enables stakeholders to invest in ventures, ensuring transparency and accountability through voting mechanisms for fund disbursement.

By leveraging blockchain's decentralized nature, these projects aim to revolutionize traditional systems, providing secure, transparent, and efficient solutions in education, real estate, law enforcement, certification verification, and venture funding.

The purpose of this paper is to design a dynamic boot loader which removes the BIOS dependency and allows user to boot from USB without changing CMOS settings. Boot Loader is the crucial program that loads the operating system in memory and initializes the system. In today’s world people are constantly on the move and portable system are in demand specially the USB devices due to its portability and accessibility compared to CD/DVD drives. To boot from USB, the user needs to change the boot order and choose the USB to start the booting process from USB. The available boot process is static which is dependent on user changing the BIOS settings. The USB is devised as plug and play portable system with puppy Linux and newly developed dynamic boot loader. The device is experimented on a computer machine with 8 GB RAM, i5 processor, 64-bit Operating system and windows 7 and observed that nearly 50% reduction in booting time i.e., the time spent in changing the boot order is eliminated compared to the static boot loader. The time spent in the BIOS is dependent on the user knowledge in changing the boot priority. The portable system allows the user to work in ease in any environment with minimum requirement of Windows XP and USB 2.0 compatible system. Since the OS runs from the USB and not dependent on the operating system of the machine, the proposed design achieves security for the data stored as well as make the environment secure. The kernel image can be customized as per the requirement of the user. This will greatly improve the loading time of the OS to the host machine.

The decomposition problem is old, and well understood when the function to be decomposed is specified by a truth table or has one output only. The paper consists of the use of some logical function decomposition algorithms with application in the implementation of classical circuits like SSI, MSI and PLD. The decomposition methods use the Boolean matrix calculation. It is calculated the implementation costs emphasizing the most economical solutions. We have considered a circuit PAL10L8, which has 10 inputs, 8 outputs and an AND-OR configuration, each NOR having 2 inputs. One important aspect of serial decomposition is the task of selecting ’best candidate’ variables for the G function. Decomposition is essentially a process of substituting two or more input variables with a lesser number of new variables. This substitution results in the reduction of the number of rows in the truth table. Hence, we look for variables which are most likely to reduce the number of rows in the truth table as a result of decomposition. Let us consider an input variable purposely avoiding all inter-relationships among the input variables. The only available parameter to evaluate its "activity" is the number of ’l’s or ’O’s it has in the truth table. If the variable has only ’1’ s or ’0’ s it is the "best candidate" for decomposition, as it is practically redundant. The paper showed that the use of the Boolean function decomposition method reduces the number of circuits necessary for the implementation.

This paper highlights a Novel GMTDS Algorithm for Dynamic Management of Transaction under Different Workload Condition. In today’s scenario large enterprise world spread across different locations, continents or having a diverse presence over the globe, where data is enormous and handling such large data over distributed computing becomes critical in real-time database system. Transaction processing ensures that related data is added to or deleted from the database simultaneously, thus preserving data integrity in your application. In transaction processing, data is not written to the database until a commit command is issued. Ensuring that the sequence of updates in the stable warehouses at various locations is safely confirmed or canceled as a single full item of work is a critical task for the distributed environment's transaction management system. Working with Real-Time Database System (RTDBS) and that to on a distributed computing system is a tough task. When we work with distributed environment over larger database, we need to take care of the transaction time period as well as number of transactions that are actually executed (committed) and number of transactions fail. The application on dynamic RTDBS becomes more complex when certain deadlines need to be completed. In this paper, we had carried out the test of CRUD (Create, Read, Update, and Delete) operation on transactional Real-time databases in real time dynamic distributed environment by using the existing EDF, GEDF algorithm and we had compared these algorithms with our proposed GMTDS (Generic Multi-dimensional Transaction Management under Dynamic Settings) algorithm in standalone and distributed environment with a dynamic self adaptive approach for management of transactions.

To validate the efficacy of the GMTDS algorithm, comprehensive simulations were conducted under various workload scenarios. Comparative analysis against existing transaction management algorithms showcase the advantages and improvements offered by GMTDS in terms of response times, throughput, and adaptability.

This Chapter deals with basic introductory concepts on translating the Entity-Relationship Data Model relationship types from an enriched XML schema to an object-oriented one. Database migration is a process wherein all the components of a source database are converted to their equivalents in the environment of the target one.

We chose oriented object database as a target database because there are many common characteristics between XML and object-oriented model, Thus the mapping from XML data into object-oriented databases is more interesting; also the object-oriented data bases have become very widespread and acceptable, they offer an evolutionary approach, so we agree that it is time to develop a translation between XML and OO databases. Our work is focused on preserving Semantics transformation of association relationships, we describe set of rules to create ODL classes from an enriched XML schema, the experimental show that the approach is feasible, and results are the same, the source database is transformed into target one without loss of data. Our future work, will be on developing a better mapping taking into account the definition ODL allowing to establish correspondences between concepts that were not taken into account such as inheritance relationship, besides the addition of these concepts allows to specifically identifies semantic links between elements.

We present an approach to inverstigation of the solutions of the boundary value problem for the Cauchy-Riemann equation on the curvelinear strip in the real plane. Here the boundary conditions are in the special type and are fundamental with respect to the direction solutions are used. As a result, an analytic form of the solution of considered boundary value problem is obtained.

The coefficient of variation (CV) serves as a dimensionless metric commonly employed to assess the variability within a population in relation to its standard deviation. It is conventionally expressed as a percentage (1). When considering the percent coefficient of variation (%CV) for data subjected to logarithmic transformation, it becomes crucial to apply the appropriate %CV formulation designed for lognormally distributed data. A thorough examination of various journals reveals a recurring issue where the %CV formula for log-transformed data is inaccurately applied, particularly in cases involving naturally exponential distributions that undergo transformation to linearity (i.e., lognormal distributions). This chapter establishes a framework for the accurate application of the mathematical formula for %CV in the context of data derived from a lognormal probability distribution.

Network interface cards come from the factory with a unique MAC address associated with the hardware. MAC is unique, but now we know the way of making MAC address clone of any PC or Router. Every network interface has a media access control (MAC) address. Most network cards and routers allow one to set a custom MAC address, overriding the MAC address present in the hardware. On the other hand if the ISP blocked the Mac address of the original device, changing Mac address is efficient way to communicate to the internet. Another function of cloning MAC address is used to jam the network with the IP address conflict associated with two devices.

Purpose: Agricultural development banks (ADB) record marginal profits with some running at a loss. Due to poor allocation and loan disbursement, the banks are not able to optimize profits from loans. The main aim of this study is to develop a Linear Programming (LP) model to help the Agriculture Development Bank, Sunyani branch in the Brong Ahafo Region to allocate their funds to prospective loan seekers in order to maximize profits.

Methodology: To achieve this aim, secondary data was extracted from the annual reports and financial statements of the bank. Based on these empirical data, the LP model was formulated. The results were found after nine iterations. A computerized software application called LP Solver based on the Revised Simplex Algorithm was used to solve the problem.

Results: The results from the model showed that ADB, Sunyani branch would be making an annual profit of GH¢ 476732.00 on loans alone as against GH¢ 190693.00 in 2011 if they stick to the model. The policymakers and the loan officers at Sunyani ADB should allocate more funds to personal loans since they contributed 34.79% significantly to the bank’s profit.

Unique Contribution to Theory, Practice and Policy: From the study, it was realized that the Scientific method used to develop the proposed model can have a significant increase in the Bank’s profit margin if put into use. Banks and other financial institutions should adopt the use of mathematical tools and methods to improve efficiency in their work.