This study is on determining the characteristics of the three models commonly used in descriptive
time series analysis when the trending is curve quadratic. The purpose is to provide basis for choosing
the most appropriate decomposition model for any study data. The procedure is based on the row,
column, and overall averages and standard deviation of the Buys-Ballot table proposed by Iwueze and
Nwogu (2004) and Iwueze and Ohakwe (2004). Results show that for the additive model, the joint
plots of the column means and standard deviations against column (j) appear to move upwards, the
column means are greater than standard deviations and hence, the coefficients of variation are less
than 100% and decreased with increasing j. For the mixed model, the joint plots of the column mean
and standard deviation against column (j) appear to follow the seasonal pattern, the column means are
greater than the standard deviations and hence, the coefficients of variation are less than 100% and
decreased with increasing j. And for the multiplicative model, the joint plots of the column mean and
standard deviation against column (j) appear to follow the seasonal pattern, the column means show
no particular pattern of variation with the standard deviations and hence, the coefficients of variation
are less than 100% for some columns and more than 100% for others columns. Therefore, the study
recommends the use of the column means and standard deviations to characterize the decomposition
models when trend-cycle component is quadratic.
keywords: : Decomposition models, Characterization, Buys-Ballot table,column means and standard
deviation, quadratic trend
This study extends the symmetric group Sn (a symmetric group of n objects) to a fuzzy set and investigate
various fuzzy properties. A constructed membership function was design to assign membership values ranging
from 𝟎 to 𝟏, facilitating the examination of fuzzy characteristics. The alpha level set, support, height, and
core of the fuzzy symmetric group were being investigated, providing insights into the fuzzy structure. The
extension of Sn to a fuzzy set allows the capture of uncertainties and ambiguities inherent in permutation-based
problems. The findings of this research contribute to the development of fuzzy group theory and its applications
in algebra, The constructed membership function offers a simple way for assigning membership values, allowing
for exploration of fuzzy properties. This work serves as an insight on fuzzy set in permutation and also allows
further research in fuzzy group theory and its potential applications in various fields.
keywords: fuzzy set, alpha cut level, support, core, permutation.
This study presents a modified Atbash cipher that consists of special characters and utilizes a stack data structure to
significantly enhance its security. The traditional Atbash cipher, which substitutes letters with their alphabetical
inverses, is limited by its simplicity and vulnerability to frequency analysis attacks. To address these weaknesses,
we introduce special characters into the cipher's alphabet and employ a stack to store and process the encrypted
characters. Furthermore, we replace the conventional modulo 26 with modulo 31, increasing the cipher's key space
and resistance to cryptanalysis. The modified cipher has improved the security and resistance to attacks, making it a
more reliable choice for confidential communication. The integration of special characters and stack
implementation adds complexity and depth to the encryption process, ensuring the confidentiality and integrity of
sensitive information. This enhanced Atbash cipher has significant implications for secure communication and data
protection. keywords: Atbash cipher, encryption, decryption, algorithm, stack process.
It will be shown that to recover the initial condition and finding the solution of a hyperbolic equation with
Cauchy conditions can be solved in two steps writing the hyperbolic equation as an integral equation,
which can be solved numerically applying the techniques of inverse generalized moments problem. In a
first step, the initial condition is found in approximate form, and in a second step we numerically
approximate the solution of the hyperbolic equation using the initial condition found.
The method is illustrated with examples.
keywords: hyperbolic equation, integral equations, generalized moment problem, inverse problem.
This study investigates the application of the finite difference method (FDM) to model one-dimensional
conductive heat transfer with variable thermal conductivity. Traditional models often assume constant
conductivity, which limits accuracy in materials with non-homogeneous properties or significant
temperature gradients. We develop a numerical model using finite difference method to handle the
variability in conductivity, discretizing the spatial domain and solving the resulting algebraic equations
iteratively. The model accommodates various boundary conditions and is validated against analytical
solutions and experimental data. Results highlight the substantial impact of variable conductivity on
temperature profiles and heat flux distributions, demonstrating the model’s robustness. This approach
aids in designing thermal insulation, analyzing heat exchangers, and optimizing high-temperature
materials. Our research provides a valuable tool for predicting heat transfer in systems with complex
thermal properties.
keywords: Finite difference method (FDM), one-dimensional heat transfer, variable thermal
conductivity, numerical modeling, thermal conductivity
Boundary value problems (BVPs) occur frequently in the fields of engineering and science such as gas
dynamics, nuclear physics, atomic structures and chemical reactions. In this paper,I proposed Taylor
wavelets based Galerkin method (TWGM) for the Numerical solution of BVPs. Here, I used weight
functions as Taylor wavelets that are assumed basis elements which allow us to obtain the numerical
solution of the BVPs. Obtained numerical solutions using this method are compared with some existing
methods and exact solution. Some BVPs are taken to demonstrate the applicability and validity of the
proposed method.
keywords: : Boundary value problems; Taylor wavelets; Galerkin method
GestureNet addresses the quintessential challenge of seamless human-computer interaction (HCI) by
interpreting human gestures and vocal commands, thereby eliminating the tactile interface. This
innovation is particularly pertinent in mitigating pathogen transmission in shared spaces, a significant
concern in the post-pandemic world. Leveraging the synergy of OpenCV Python for computer vision
and the YOLOv8 algorithm or real-time object detection, GestureNet pioneers an intuitive interface. It
integrates a virtual mouse, keyboard, canvas, and volume control into a cohesive system, setting a new
benchmark for HCI. The core of GestureNet’s ingenuity lies in its algorithmic architecture that
overcomes egronomic limitations, efficient computational cost, recognition precision that gives best
performance in worst condition that also in cheap rate. The system employs advanced machine learning
models and natural language processing to interpret complex gestures and auditory commands,
translating them into precise digital responses. GestureNet is underpinned by robust theoretical
frameworks in computer vision and machine learning, ensuring its adaptability and scalability. The
system’s design principles are rooted in fostering inclusivity and democratizing access to technology.
GestureNet is poised to revolutionize smart education in India by providing an inclusive platform that
empowers students with disabilities. Its contactless nature not only enhances pedagogical interaction
but also serves as a bulwark against the spread of contact-based pathogens. The novelty of GestureNet
lies in its amalgamation of cutting-edge technologies to create a cost-effective and universally
accessible HCI system that provides best solution in worst case. Its innovative use of the YOLOv8
algorithm within the OpenCV framework represents a leap forward in the domain of gesture
recognition, setting a precedent for future research and development. GestureNet is not merely a
technological breakthrough; it is a visionary stride towards a more connected and capable society,
embodying the spirit of progress and acting as a catalyst for societal transformation.
keywords: Gesture Recognition, OpenCV, Machine Learning, Human Computer Interaction.
1Department of Mathematics,
Institute of Natural and Applied Sciences
Dicle University, Diyarbakır, Turkey 2Department of Mathematics
Dicle University, Diyarbakır, Turkey
This work focuses on the Petrovsky equation with a variable coefficient delay term. Firstly by using the
Faedo-Galerkin method, we prove the global existence of the solution under suitable conditions. Later, we
establish a decay estimate for the energy by using the Martinez lemma.
keywords: Decay, Global existence, Petrovsky equation, Variable coefficients, time-varying delay
In this paper, we have developed the matrix representation of the (p,q)-generalized Fibonacci sequence by expressing the homogeneous linear recurrence relations
Vn(p,q,a,b)=pVn-1+qVn-2 as Vn(p,q,a,b)=Tn-1(p,q)V2+qTn-2(p,q)V1
,
TnTn-1
=
p q1 0
n-2
p1
, n>=3 T0,=0,T=p,T2=1.
p,q,V1 = a and V2 = b
are arbitrary integers. Employing these, sequence is characterized in the form of
generalized matrix, which is used to investigate the new results and generalized the exiting results,
reducing them as special cases. Selecting any suitable values of (p,q) initial terms and n, general matrix
is utilized for encryption of data in the form of second order matrix.
keywords: Recurrence relations, generalized, Fibonacci sequence, encryption
Thermal conductivity plays a significant role in thermal transmission and engineering processes,
particularly when the fluid serves as an energy source. Against the popular notion that thermal
conductivity should be kept constant, recent trends in experimental findings reveal that, most often,
thermal conductivity varies in relation to temperature, pressure, etc. Therefore, this paper is aimed at
exploring the impact of variable thermal conductivity and Casson fluid flow on a magnetized
oscillatory system within a permeable plate immersed in a porous material. The flow is affected by the
non-uniform wall heating condition. The solutions of the resultant nonlinear dimensionless equations
have been determined using regular perturbation. In view of the assumed oscillatory pressure gradient,
the nonlinear partial differential equations were reduced to a boundary-valued problem where the
unsteady flow is superimposed on the mean steady flow. The physical flow behavior of velocity,
temperature, shear stress, and heat transfer rate are demonstrated graphically and discussed
thoroughly in view of the embedded parameters. It is concluded from this computational analysis that
the involvement of variable thermal conductivity improves the temperature and velocity components
more effectively compared to the commonly assumed constant thermal conductivity. The action of the
Casson fluid parameter is to suppress the fluid velocity. Interestingly, the results obtained for the
limiting case in this research are consistent with previous literature, thereby establishing the accuracy
and validity of the present analysis.
keywords: : variable thermal conductivity, casson fluid parameter, magnetized oscillatory flow,
darcy porous number, slip parameter
We consider the problem of finding a pair of functions 𝑟(𝑥,𝑡)and 𝑤(𝑥,𝑡)that satisfy the equation w𝑡(𝑥,𝑡) = 𝑤𝑥𝑥(𝑥,𝑡) + 𝑟(𝑥,𝑡) under Cauchy boundary conditions. We will see that an approximate
solution can be found using the techniques of generalized inverse problem of moments and find dimensions
for the error of the estimated solution.
keywords: generalized moment problem; integral equations; Parabolic equation, inverse source.
