Journal of Informatics and Mathematical Sciences

A Note on Value Distribution of the Product of a Meromorphic Function and Its Higher Order Derivatives

2025-03-23T14:26:53+00:00

In the present note, we consider the value distribution of the product of a meromorphic function and its higher order derivatives and generalise a result of Lahiri and Dewan (Value distribution of the product of a meromorphic function and its derivative, Kodai Mathematical Journal 26 (2003), 95 – 100).

A Numerical Study of Heuristics Time Deviation Technique for Job Sequencing to Minimize Total Elapsed Time and Idle Time

2025-03-29T05:56:27+00:00

Job sequencing refers to the process of determining the most suitable order for performing a number of different jobs across a limited number of available resources, services or facilities to make effective use of these available facilities and achieve greater output with minimum time delay. This study introduces an innovative heuristic technique called the Time Deviation Technique. This technique helps in obtaining the optimal job schedule and also minimizes the total elapsed time and idle time. Here we first apply the new method to the n-jobs, 2 machines problem and extend it to the n-jobs, 3 machines problem. And lastly, we applied this method to the n-jobs, m-machines problem after converting into 2 machines n jobs problems by using the condition of Johnson’s method. The proposed technique is very simple and easy to understand. For this we have given examples numerical illustration of job sequencing problem of n jobs 2 machines, n jobs 3 machines and n jobs m machines problem.

Insights Into the Lucas \(Q\)-Matrix and Its Properties

2025-02-05T18:15:19+00:00

This work proves that the equality
\begin{align*}
\begin{bmatrix} 3 & 1 \\ 1 & 2 \end{bmatrix}^n =
\begin{cases}
5^{\frac{n}{2}}\begin{bmatrix}
F_{n+1} & F_n \\
F_n & F_{n-1}
\end{bmatrix}, & \text{if } n \text{ is even},\\
5^{\frac{n-1}{2}}\begin{bmatrix}
L_{n+1} & L_n \\
L_n & L_{n-1}
\end{bmatrix}, & \text{if } n \text{ is odd},
\end{cases}
\end{align*}
holds for all integer \( n \), where \( \begin{bmatrix} 3 & 1 \\ 1 & 2 \end{bmatrix} \) is the Lucas \( Q \)-matrix introduced by Köken and Bozkurt [2]. While these authors established the case for natural \(n\) using induction, extending the result to integer exponents is considerably more challenging. One cannot simply assume that the formula holds for an arbitrary integer \(n\), since, although Fibonacci and Lucas numbers are defined for negative indices, the proof by mathematical induction does not automatically extend to this setting. To achieve this, we developed several key prerequisites, including new relationships between the Fibonacci and Lucas \( Q \)-matrices, such as \(\begin{bmatrix}L_{n+1} & L_{n} \\ L_{n} & L_{n-1}\end{bmatrix}=\begin{bmatrix}3 & 1 \\ 1 & 2\end{bmatrix}\cdot\begin{bmatrix}F_{n} & F_{n-1} \\ F_{n-1} & F_{n-2}\end{bmatrix}=Q_L \cdot Q_F^{n-1}\), \(n \in \mathbb{Z}\). Additionally, we demonstrate several previously known properties, but in a different way, using our properties. Because this text is also a survey article, we adopted a didactic, step-by-step approach, minimizing omissions whenever possible.

A Note on \(q\)-Sălăgean Type Functions

2025-03-26T06:21:39+00:00

In the present paper, we define certain classes of analytic function in the open disc by using the generalized linear operator \(D_{\lambda,\delta}^{n}\) with help of \(q\) calculus. For functions belonging to these classes we provide coefficient inequalities, distortion theorem.

Distortion of Orbits Under Fluctuating Gravitational Forces

2025-03-23T13:25:49+00:00

The motion of a celestial body under the influence of a central force is considered. The influence of other bodies on the gravitational attraction force of the two-body problem is modeled as fluctuating force perturbations about a mean value. The ordinary differential equation determining the orbits is derived in polar coordinates. The exact analytical solution is given. Three cases, namely the elliptic, parabolic and hyperbolic cases are investigated. The distortion of the orbits under the influence of small perturbational forces are depicted. The equation determining the escape angle is solved numerically by the Newton-Raphson method. Effects of fluctuation frequencies on the distortion of orbits as well as escape angles are studied in detail. It is found that the force fluctuations may alter the nature of the orbits and destroy their symmetries. When the fluctuation frequency is an integer number, the orbits are distorted but the escape angles remain unaffected for the parabolic case. For non-integer frequencies, the escape angles may decrease in magnitude.

Some Fixed Point Theorems Using Different Spaces in Banach Algebras

2025-02-27T12:35:42+00:00

In this paper, it expands and generalize several fixed point theorems on multiple spaces and prove the existence and some operations of fixed points for nonlinear operators over Banach algebras. Results are extensions, proofs and generalizations of well-known findings from the literature. These findings represent Das et al. [7] generalized findings.

Effortless Calculations of Arithmetic Progression Through Vedic Sutras

2025-01-30T03:00:33+00:00

To finding the \(n\)th term and the sum of \(n\) terms in Arithmetic Progression is very easy if the number of term's small but the it is bulky if the number of term's are lager and so its take's larger time and also take our large affects and difficulties. On the other hand, the Vedic Mathematics work's opposite as the modern mathematics so if we using the Vedic Mathematics sutra \(^{3}\)Urdhwatiryagbhyam, sutra \(^{7}\)sankalan-vyavkalanabyam, Up-sutra \(^{9}\)Antyyoravto finding the \(n\)th term and the sum of \(n\) terms in Arithmetic Progression it takes our large affects reduced around 60-65% and also take's small time comparatively modern mathematics. The arithmetic pattern is one of the easiest series to study. It contains adding or subtracting from a common difference \((d)\), for generating a string of the numbers that are interrelated to each other. Thus, in this document we present the comparison to find the \(n\)th term and the sum of \(n\) terms in Arithmetic Progression by using the modern mathematics and Vedic mathematics.

Rough identity-summand graph and its applications

2025-02-24T03:43:04+00:00

This work aims to obtain various Gray code constructions from the structural properties of a rough
identity-summand graph. To establish the nature of the rough identity-summand graph defined for
the filters of a rough bi-Heyting algebra, the enumeration of distinct complete bipartite graphs from
G(FX(T)) will be presented in detail. Then it will be proved that the union of these distinct complete
bipartite graphs forms the subgraph of G(FX(T)). This subgraph will be considered in identifying the
various lengths of the Gray codes through two approximation transition sequences.

A STUDY ON NEUTROSOPHIC ANTI-FUZZY SUBSEMIRING OF A SEMIRING

2025-03-28T03:54:43+00:00

In this research, we endeavor to explore the algebraic properties of neutrosophic anti-fuzzy subsemirings (NAFSSR) within a semiring (SR), and we present several theorems related to NAFSSR in the context of a semiring (SR).

Reviewing the green building concepts along with the applications of AI and IoT for environmental monitoring and designing sustainable Infrastructures

2025-02-21T10:51:25+00:00

This academic article explores the ever-evolving field of smart green building technologies, with a particular emphasis on the ways in which artificial intelligence (AI) and Internet of Things (IoT) are integrated into and affect sustainable architecture. The study is based on background of changing green building principles, which are highlighted by rapid development of smart technologies that are changing face of contemporary architecture. With goal of comprehending how AI and IoT might improve building performance and sustainability with simultaneous reduction in carbon footprints, the study takes a methodological approach that is based on a thorough assessment of the literature and qualitative analysis. It looks at how AI and IoT work together, how difficult it is to deploy them, how they affect society and environment, how much it will cost to invest in these technologies. The primary conclusions show that combining AI and IoT improves building performance, increases energy efficiency, promoting environmental sustainability. The study showcases cutting-edge IoT building management technologies and to create more sustainable and effective living environments. It also notes impediments to the uptake of these technologies, such as financial limitations and the requirement for highly qualified personnel. In summary, the study suggests a multimodal strategy to address these issues, with a focus on legislative changes, educational programs, and creation of affordable green building technologies. In-depth investigation of AI and IoT integration in sustainable building designs is presented in this study, along with insights into how these technologies may transform the construction sector and advance sustainable urban development.