Adsorption and ion exchange are examples of fixed-bed sorption processes that show transient behavior. This means that differential equations are needed to design them. As a result, numerical methods are commonly utilized to solve these equations. The solution frequently used in analytical methods is called the Thomas solution. Thomas gave a complete solution that adds a nonlinear equilibrium relationship that depends on second-order reaction kinetics. A computational approach was devised to solve the Thomas model. The Thomas model's validity was established by conducting three distinct sets of experiments. The first entails the adsorption of acetic acid from the air through the utilization of activated carbon. Following

This paper presents results about the existence of best approximations via nonexpansive type maps defined on modular spaces. 

Let/. It :0 ---0 G be any two self maps of a compact connected oriented Lie group G. In this paper, for each positive integer k , we associate an integer with fk,hi . We relate this number with Lefschetz coincidence number. We deduce that for any two differentiable maps f, there exists a positive integer k such that k 5.2+1 , and there is a point x C G such that ft (x) = (x) , where A is the rank of G . Introduction Let G be an n-dimensional com -pact connected Lie group with multip-lication p ( .e 44:0 xG--+G such that p ( x , y) = x.y ) and unit e . Let [G, G] be the set of homotopy classes of maps G G . Given two maps f , f G ---• Jollowing [3], we write f. f 'to denote the map G-.Gdefined by 01.11® =A/WO= fiat® ,sea Given a point g

The concepts of higher Bi- homomorphism and Jordan higher Bi- homomorphism have been introduced and studied the relation between Jordan and ordinary higher Bi- homomorphism also the concepts of Co- higher Bi- homomorphism and  Co- Jordan higher Bi- homomorphism introduced  and the relation between them in Banach algebra have also been studied.

Ureteric obstruction is rarely noted in cases of gastric cancer. Its involvement by distant metastasis from gastric adenocarcinoma without direct invasion is an exceptionally unusual occurrence. This is the story of a 58-year-old man who arrived at the emergency department with acute flank pain and fever. He was initially diagnosed with obstructive pyelonephritis after the discovery of a new onset, complete ureteric obstruction on the left side. Subsequent investigations and follow-up revealed the presence of gastric adenocarcinoma with possible ureteric metastasis bilaterally, flank pain and hydronephrosis were the first and only presentations of gastric cancer. The rarity of the condition and the unusual presentation encouraged us to r

Background : Left main coronary artery (LMCA) disease represents important and serious portion of coronary artery disease(CAD).
Aim: The aim of this study is to estimate the incidence of LMCA disease among patients with CAD undergoing coronary artery angiography and to evaluate clinical characteristics of patients with LMCA disease.
Methods: The study involved review of clinical notes and coronary angiography of 1020 patients with CAD in Ibin Al Bitar hospital for cardiac surgery between April and September 2004.This review included evaluation of electrocardiogram (ECG), echocardiogram(ECHO), ECG exercise test (EET) and coronary angiography.
Results: Among 56 patients proved to have left main corona

It is known that images differ from texts in many aspects, such as high repetition and correlation, local structure, capacitance characteristics and frequency. As a result, traditional encryption methods can not be applied to images. In this paper we present a method for designing a simple and efficient messy system using a difference in the output sequence. To meet the requirements of image encryption, we create a new coding system for linear and nonlinear structures based on the generation of a new key based on chaotic maps.

The design uses a kind of chaotic maps including the Chebyshev 1D map, depending on the parameters, for a good random appearance. The output is a test in several measurements, including the complexity of th