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

Fish are regarded as a crucial indicator of alterations in the aquatic environment due to their position at the apex of the food chain. Monitoring these alterations is crucial for identifying modifications in the aquatic ecosystem. The principal elements influencing fish health are temperature, pH, dissolved oxygen, salinity, pesticide contamination, microplastics, and algal presence. These elements substantially influence fish health regarding development, reproduction, respiration, oxygen stress, and the internal enzymes associated with digesting and other metabolic functions. Alterations in global environmental conditions and anthropogenic pollutants result in modifications to fish populations, their lives, and their behavior and

The rising prevalence of obesity-related glomerulopathy (ORG) occurs in accordance with the rising prevalence of obesity worldwide. Clinically ORG is manifested by slowly progressing microalbuminuria that may develop to clinically evident proteinuria. Pathological characteristics of ORG include glomerular hypertrophy in the presence or absence of focal segmental glomerulosclerosis (FSGS). ORG can develop into clinically overt chronic renal insufficiency or even end-stage kidney disease. This article reviews the most important mechanisms for the development of ORG; that are abnormal renal hemodynamics, stimulation of renin-angiotensin-aldosterone system (RAAS), impairment of insulin sensetivity, ectopic lipid deposition, adipose tissue cy

he assignment model represents a mathematical model that aims at expressing an important problem facing enterprises and companies in the public and private sectors, which are characterized by ensuring their activities, in order to take the appropriate decision to get the best allocation of tasks for machines or jobs or workers on the machines that he owns in order to increase profits or reduce costs and time As this model is called multi-objective assignment because it takes into account the factors of time and cost together and hence we have two goals for the assignment problem, so it is not possible to solve by the usual methods and has been resorted to the use of multiple programming The objectives were to solve the problem of

The majority of Arab EFL (English as a Foreign Language) learners struggle with speaking English fluency. Iraqi students struggle to speak English confidently due to mispronunciation, grammatical errors, short and long pauses while speaking or feeling confused in normal conversations. Collaborative learning is crucial to enhance student’s speaking skills in the long run. This study aims to state the importance of collaborative learning as a teaching method to EFL learners in the meantime. In this quantitative and qualitative study, specific focus is taken on some of Barros’s views of collaborative learning as a teamwork and some of Pattanpichet’s speaking achievements under four categories: academic benefits, social benefits,

 Water represents as a basic intellectual material in the myths of creation and the start of formation, Thus, water has turned into an intellectual material in literary mythological texts in addition to its function in sculptural Mesopotamian sculpture. The research is in three sections: the first section deals with Myth, its concept, peculiarities and types, the second section is about mythological literature, the third section is about the idea of ​​water and mythical literature. The question research question here is that does the idea of water have any impact on mythological literature? And Does it link to sculptural products? The importance of the research is that it shows the human imagination and its relationship to functioni

A piezoelectric cantilever beam with a tip mass at its free end is a common energy harvester configuration. This article introduces a new principle of designing such a harvester that increases the generated power without changing the resonance frequency of the harvester: the attraction force between two permanent magnets is used to add stiffness to the system. This magnetic stiffening counters the effect of the tip mass on the efficient operation frequency. Five set-ups incorporating piezoelectric bimorph cantilevers of the same type in different mechanical configurations are compared theoretically and experimentally to investigate the feasibility of this principle: theoretical and experimental results show that magnetically stiffened harve

In this work, we study several features of the non-zero divisor graphs (ℵZD- graph) for the ring Zn of integer modulo n. For instance, the clique number, radius, girth, domination number, and the local clustering coefficient are determined. Furthermore, we present an algorithm that calculates the clique number and draws the non-zero divisor for the ring Zn.

In all process industries, the process variables like flow, pressure, level, concentration
and temperature are the main parameters that need to be controlled in both set point
and load changes.
A control system of propylene glycol production in a non isothermal (CSTR) was
developed in this work where the dynamic and control system based on basic mass
and energy balance were carried out.
Inlet concentration and temperature are the two disturbances, while the inlet
volumetric flow rate and the coolant temperature are the two manipulations. The
objective is to maintain constant temperature and concentration within the CSTR.
A dynamic model for non isothermal CSTR is described by a first order plus dead
time (FO