CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES

Enhancing Numerical Approximations for Scalar Linear Delay Differential Equations with Constant Delay and Impulsive Self Support Conditions

Yaqeen Falih Khlebus — 2024-02-28

Through the course of this study, a numerical approximation approach was developed for a category of scalar delay differential equations that were subject to impulsive conditions. Each and every one of these equations was taken into consideration. An innovative method of approximation is used, which involves the utilization of delay equations that have piecewise constant arguments. The theoretical convergence of the approximation technique was shown at each and every point, with the exception of the instants of time that were impulsive. Additionally, the numerical method does a decent job of estimating the instants of time that are impulsive. In the event that the β parameter of the problem is positive, we possess the capability to establish the convergence conclusion by imposing an additional condition via the use of an additional condition. Without making the assumption of a self-supporting condition, this condition guarantees that the solution
will cross the line x=c at a temporal interval that is impulsive. The conclusions of the theoretical convergence were shown by the presentation of numerical examples. Through the use of numerical study, we were able to identify the existence of periods in the solution. In this particular solution, the minimal period is defined by being bigger than the delay τ that is associated with the model. We take note of the fact that sufficient conditions are presented to guarantee the existence of periodic solutions; nonetheless, numerical examples illustrate that periodic solutions express themselves under criteria that are considerably less strict than those that guarantee their existence. In light of this, there is a pressing need for more study to be conducted in order to determine whether or not periodic solutions are accessible for this particular set of impulsive equations.

Effectiveness of the Use of Concept Attainment Model on Senior Secondary One Students’ Achievement in Mathematics in Lokoja Metropolis, Kogi State, Nigeria

Dr. Onoge Honmane — 2024-02-19

The purpose of this study was to find out the effectiveness of Concept Attainment Model
on students’ achievement in algebra at senior secondary school one. The research was carried out
in Lokoja Metropolis of Kogi State with a population of 1210 senior secondary one students. 356 SS1
students were sampled out of 1210 students. Quasi-experimental design of nonrandomized pre-test
post-test control group design was adopted. The Instrument of the study was Algebraic
Achievement Test (AAT) which was used for collection of data. The AAT was validated by experts
and this gave a reliability index of 0.82. Two research questions were asked and answered using
means and standard deviations. The two hypotheses formulated were tested at 0.05 level of
significance using Analysis of Covariance. The study found among others that the students taught
using Concept Attainment Model (CAM) improved in their achievement than those taught without
CAM. It was therefore, recommended that Curriculum planners and mathematics textbook writers
should be encouraged to include CAM in their books as complementary to other teaching methods.

Local Aerodynamic Drag in Tubes of a Cotton Harvester

Ganjayev Sh.A — 2024-02-26

The results of calculations for aerodynamic drag in the tubes of a cotton harvester are
presented; different tube materials are considered. Based on the calculations conducted, the best
material for the tubes in cotton harvesters was determined. When modifying cotton harvesters to
improve their performance, it is recommended to manufacture the suction tubes of cotton harvesters
from these materials.

Forecasting the Number of Patients with Kidney Failure in Thi-Qar Governorate using Time Series

Hassan Hopoop Razaq — 2024-03-13

This paper has been used time series models for the study and analysis of monthly data to the number of patients with Kidney Failure in Thi-Qar Province for the period (2020-2023) in order forecasting by the numbers of patients with Kidney Failure for the period (2024-2025). The result of data analysis show that the proper and suitable model is Integrated Autoregressive model of order ARIMA (4, 0, 1) because it has the least mean squares error (MSE). Based on the best model, the number of people with Kidney failure was predicted monthly and for the next two years and the predictive value was consistent with the original values and this indicates the efficiency of the model.

On Weak Parallelogram Constants for Lebesgue Spaces

MhamdHasn Abdulrzaq — 2024-03-25

This paper comprehensively examines fundamental principles pertaining to parallelogram and parallelogram (abbreviated as w.p.) laws. Emphasis is placed on investigating the duality in the w.p. laws, alongside a thorough review and analysis of foundational findings concerning the geometry of w.p. spaces. Additionally, the research delves into the exploration of optimal w.p. constants for Lebesgue spaces. Through rigorous examination and synthesis of pertinent literature, this study aims to provide a comprehensive understanding of the theoretical underpinnings and practical implications of parallelogram laws and their application in Lebesgue spaces.

Priority Based Lightweight Cluster Routing for Efficient Communication in Vehicular Ad Hoc Networks

Raghu Ramamoorthy — 2024-04-22

A vehicular ad hoc network (VANET) is a network that is dynamic and has no infrastructure. In VANET movable autonomous vehicles rely on wireless communication systems to form an autonomous, self-organized, and infrastructure-less network. VANETs are prone to frequent path failure due to their high mobility. High mobility causes the node state to change continuously, so routing and communication between vehicles are challenging tasks in VANET. At this point, to provide efficient routing, this work proposes a priority-based lightweight clustering model (P-LWCM) for cluster-based routing. In the proposed work, stable and efficient cluster heads and members are selected for routing in VANET. The proposed system uses various parameters including mobility, Packet Loss Ratio (PLR), Packet Misrouting Ratio (PMR), and Priority Ratio (PR) to select a vehicle as a cluster head or to include a node as a cluster member. An elected cluster head and members have a long lifetime in the group they belong to and efficient routing is possible. The performance of the proposed model is analyzed in terms of packet delivery ratio (PDR), and end-to-end delay (EED). Simulation results show that the proposed system outperforms the Weighted Clustering Trust model (WCTM) in all aspects.