In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

Gypseous soil covers approximately 30% of Iraqi lands and is widely used in geotechnical and construction engineering as it is. The demand for residential complexes has increased, so one of the significant challenges in studying gypsum soil due to its unique behavior is understanding its interaction with foundations, such as strip and square footing. This is because there is a lack of experiments that provide total displacement diagrams or failure envelopes, which are well-considered for non-problematic soil. The aim is to address a comprehensive understanding of the micromechanical properties of dry, saturated, and treated gypseous sandy soils and to analyze the interaction of strip base with this type of soil using particle image

In this paper, we study the incorporation of the commensalism interaction and harvesting on the Lotka–Volterra food chain model. The system provides one commensal prey, one harvested prey, and two predators. A set of preliminary results in local bifurcation analysis around each equilibrium point for the proposed model is discussed, such as saddle-node, transcritical and pitchfork. Some numerical analysis to confirm the accruing of local bifurcation is illustrated. To back up the conclusions of the mathematical study, a numerical simulation of the model is carried out with the help of the MATLAB program. It can be concluded that the system's coexistence can be achieved as long as the harvesting rate on the second prey population is

major goal of the next-generation wireless communication systems is the development of a reliable high-speed wireless communication system that supports high user mobility. They must focus on increasing the link throughput and the network capacity. In this paper a novel, spectral efficient system is proposed for generating and transmitting twodimensional (2-D) orthogonal frequency division multiplexing (OFDM) symbols through 2- D inter-symbol interference (ISI) channel. Instead of conventional data mapping techniques, discrete finite Radon transform (FRAT) is used as a data mapping technique due to the increased orthogonality offered. As a result, the proposed structure gives a significant improvement in bit error rate (BER) performance. Th

Orthogonal Frequency Division Multiplexing (OFDM) is an efficient multi-carrier technique.The core operation in the OFDM systems is the FFT/IFFT unit that requires a large amount of hardware resources and processing delay. The developments in implementation techniques likes Field Programmable Gate Array (FPGA) technologies have made OFDM a feasible option. The goal of this paper is to design and implement an OFDM transmitter based on Altera FPGA using Quartus software. The proposed transmitter is carried out to simplify the Fourier transform calculation by using decoder instead of multipliers. After programming ALTERA DE2 FPGA kit with implemented project, several practical tests have been done starting from monitoring all the results of