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The major objectives of this research article are to introduce the notion of ($ \alpha, \psi $)-contraction in the context of $ \mathfrak{F} $-bipolar metric space and establish fixed point theorems. In this way, coupled fixed point results are obtained by applying the leading theorems. Some non-trivial examples are also furnished to show the validity of established results. As applications of the main result, we investigate the solution of an integral equation and a homotopy problem.

This paper introduces the concept of proximal (α,F)-contractions in F-metric spaces. We establish novel results concerning the existence and uniqueness of best proximity points for such mappings. The validity of our findings is corroborated through a non-trivial example. Furthermore, we demonstrate the applicability of these results by proving the existence of solutions for Volterra integral equations related to population growth models. This approach not only extends best proximity theory, but also paves the way for further research in applied mathematics and beyond.

We study the split fixed point problem with multiple output sets in nonlinear spaces, particularly in CAT(0) spaces. We modify the existing self-adaptive algorithm for solving the split common fixed point problem with multiple output sets in the settings of generalized structures. We also present the consequences of our main theorem in terms of the split feasibility problem and the split common fixed point problem.

This paper aims to introduce a novel variation of almost Hardy–Rogers ψ,ϕ-type multivalued contraction and ϑ-type contraction mappings. The main focus is on proving new fixed point (FP) results in M℘-metric space (M℘-MS). Additionally, several consequences are derived from our main findings. To elucidate the recency of our outcomes, various examples are provided. Finally, we utilize the obtained results to scrutinize the existence of solutions for nonlinear fourth-order differential equations (NFODEs).

ABSTRACT Background and Objective: A global increase in the prevalence of diabetes mellitus (DM) is associated with increased morbidity and mortality. Oxidative stress is a fundamental component in the pathogenesis of DM Ajwa dates are known to have a high antioxidant content, especially in their seeds. Hence this study was designed to determine the preventive effects of Ajwa date fruit on alloxan-induced diabetes in an experimental rat model. Methods: This experimental study was conducted at the Post Graduate Medical Institute, Lahore, Pakistan. A total of forty Sprague-Dawley rats were divided into five groups with eight animals in each. Rats in group A were normal control, whereas rats in group B were induced with intraperitoneal alloxan (160 mg/kg body weight) to develop diabetes. Groups C, D, and E rats were fed on a diet supplemented with Ajwa flesh, seed, and whole Ajwa respectively for 1 week. Blood and urine glucose levels were measured on days 0, 7 (pre-alloxan) and 11, 14, 19 (post-alloxan). Serum insulin, homeostatic model assessment (HOMA) for β-cell function (HOMA-β), and insulin resistance (HOMA[1]IR) were estimated terminally. Results: Diabetes was induced successfully in animals of all experimental groups except the normal control group. Rats of the Ajwa-seed group (D) showed relative resistance to diabetes induction with three non-diabetic rats on day 19. In group E, rats had lower blood sugar levels than rats in group C (p = 0.010). Serum insulin, HOMA-β and HOMA-IR, revealed partial beta cells restoration in the experimental animals of groups D and C. Insulin resistance was significantly higher, despite the highest insulin level (3.77 µIU/ml; p value Conclusion: Ajwa date seed powder appears to provide relative protection against the development of diabetes in rats induced by alloxan.

Jleli and Samet introduced the notion of F-metric space as a generalization of traditional metric space and proved Banach contraction principle in the setting of these generalized metric spaces. The aim of this article is to utilize F-metric space and establish some common α-fuzzy fixed point theorems for rational (β-ϕ)-contractive conditions. Our results extend, generalize and unify some well-known results in the literature. As application of our main result, we discuss the solution of fuzzy integrodifferential equations in the setting of a generalized Hukuhara derivative.

In this research article, we give the notion of graphic F-contraction in the setting of F-metric space and establish some fixed point results. We also supply some examples to demonstrate the brilliance of the established results. We also establish some fixed point results for orbitally continuous and orbitally G -continuous graphic F-contractions as applications of our main results. Also, we discuss the existence and the uniqueness of solutions of functional equations involving in dynamic programming.

In this research paper, we presented a four-dimensional mathematical system modeling the anaerobic mineralization of phenol in a two-step microbial food-web. The inflowing concentrations of the hydrogen and the phenol are considered in our model. We considered the case of general class of nonlinear growth kinetics, instead of Monod kinetics. Due to some conservative relations, the proposed model was reduced to a two-dimensional system. The stability of the steady states was carried out. Based on the species growth rates and the three main operating parameters of the model, represented by the dilution rate and input concentrations of the phenol and the hydrogen, we showed that the system can have up to four steady states. We gave the necessary and sufficient conditions ensuring the existence and the stability for each feasible equilibrium state. We showed that in specific cases, the positive steady state exists and is stable. We gave numerical simulations validating the obtained results.

The purpose of this article is to establish common fixed point results on complex valued extended b-metric spaces for the mappings satisfying rational expressions on a closed ball. Our investigations generalize some well-known results of literature. Furthermore, we supply a significant example to show the authenticity of established results. As application, we solve Urysohn integral equations by our main results.

Irrigation scheduling techniques is one of the suggested solutions for water scarcity problem. The study aims to show the possibility of using practical and applicable irrigation scheduling program which was designed by Water Resources Department at the University of Baghdad by using Spreadsheet Formulas for Microsoft Excel program, version 2007, with some modification to generalize it and made it applicable to various climatic zone and different soil types, as a salvation for the shortage of irrigation water inside the irrigation projects. Irrigation projects which incidence of Tigris River basin will be taken as an applicable example. This program was based on water budgeting and programmed depending on scientific concepts which facilitate irrigation structures operation and ease the use by farmers. By using the abilities of this program, the monthly and annually water requirements and drainage water were estimated. Finally a comparison is made between the calculated discharges with the designers suggested ones. This comparisons showed that the use of this type of irrigation scheduling (i.e. predicted irrigation scheduling) with itsapplicable constrains require high attention when choosing the cropping pattern for each climate zone. Also it found that this irrigation program is a useful tool for saving water if cropping pattern has been chosen carefully.

BACKGROUND: Pain is as a major concern with dental patients. The dentist-patient interaction can reveal the presence of anxiety and fear, which may result in rise of pain. This study aimed to assess vocabulary communication as support to dental anesthesia on the adult dental patient. MATERIALS AND METHODS: This is a prospective, randomized clinical study, conducted from February 2020 through March 2021. Two hundred individuals (112 males, 88 females) of the age range (16 to 84 years) were separated into two groups for testing the level of pain during dental local anesthesia, with vocal communication and without vocal communication. RESULTS: While the control group showed no difference between males and females, there was a difference between the sexes in the experimental group with past dental visits, VAS and injection type having less anxiety (p=0.0001) while with education/VAS having (p£0.01) as appear in sex to age (p£0.05). There was no difference when data were compared by age, or type of anesthesia (inferior alveolar nerve block or infiltration technique). CONCLUSION: Dental anxiety can be alleviated by talking to the patients before the procedure, which could reduce the amount of pain.

Introduction: Rheumatoid arthritis (RA) is a chronic inflammatory disease of joints with 0.24% global prevalence. Numerous pharmacological agents are available for the management of RA, but they are associated with many adverse effects. Alternative therapies for disease management are urgently needed. Colebrookea oppositifolia (CO) is an important herb with various traditional uses and pharmacological actions. In the present study, anti-arthritic effect of ethanolic extract of Colebrookea oppositifolia (EECO) leaves was evaluated in pristane induced arthritic rats (PIA) and compared to methotrexate by assessing body weight, clinical score of inflammation and histopathology. Aims & Objectives: To study anti-arthritic effect of C. oppositifolia on a rat model of pristane induced arthritis. Place and duration of study: This experimental study was conducted in Animal House of Post Graduate Medical Institute, Lahore from March to September 2019. Material & Methods: Total forty female Sprague Dawley rats were categorized into five equal groups (n=8). Group A (normal control), group B (disease control). Group C and D belonged to low dose (250mg/kg) and high dose (500mg/kg) EECO treated groups respectively, while group E was methotrexate treated group. Arthritis was induced within two weeks by single intradermal injection of pristane on day 0 in groups B, C, D and E. At Day 15, treatment was initiated and at day 28 paw joint sections were taken for histopathology. Data input and analysis was done by using IBM SPSS version • p value ?0.05 was considered significant. Results: At week 4, significant increase (approximately 16%) in body weight was observed in all treated groups as compared to disease control. A significant reduction (more than 50%) in clinical score of arthritis was observed in all treated groups compared to diseased control group in which clinical score was 14.50±0.2. All extract and MTX treated groups showed significant improvement (p

Introduction: Treatment options for rheumatoid arthritis have potentially fatal adverse effects and failure to achieve complete cure. Alternative medicines are, therefore, being researched for this purpose. Berberine is one of such compounds with high antioxidant activity that may prove beneficial in this disease. Aims & Objectives: To compare effects of berberine with methotrexate on pristane induced arthritis in rats. Place and duration of study: Post Graduate Medical Institute, Lahore; March to May 2014. Material & Methods: Forty female Sprague Dawley rats were allotted to five groups including a berberine control. Arthritis developed in 14 days with a single intradermal injection of pristane in arthritis control and experimental groups. Starting Day 15, berberine and methotrexate were administered as single daily intraperitoneal injection for next 14 days. Arthritis resolution was assessed by measuring body weight, clinical score of arthritis on day 0, 14 and 28 and joint histopathology terminally. Data was analyzed using SPSS version 20, p value

We derive a mathematical model that describes the competition of two populations in a chemostat in the presence of a virus. We suppose that only one population is affected by the virus. We also suppose that the substrate is continuously added to the bioreactor. We obtain a model taking the form of an “SI” epidemic model using general increasing growth rates of bacteria on the substrate and a general increasing incidence rate for the viral infection. The stability of the steady states was carried out. The system can have multiple steady states with which we can determine the necessary and sufficient conditions for both existence and local stability. We exclude the possibility of periodic orbits and we prove the uniform persistence of both species. Finally, we give some numerical simulations that validate the obtained results.

A generalized "SVEIR" epidemic model with general nonlinear incidence rate has been proposed as a candidate model for measles virus dynamics. The basic reproduction number $ \mathcal{R} $, an important epidemiologic index, was calculated using the next generation matrix method. The existence and uniqueness of the steady states, namely, disease-free equilibrium ($ \mathcal{E}_0 $) and endemic equilibrium ($ \mathcal{E}_1 $) was studied. Therefore, the local and global stability analysis are carried out. It is proved that $ \mathcal{E}_0 $ is locally asymptotically stable once $ \mathcal{R} $ is less than. However, if $ \mathcal{R} > 1 $ then $ \mathcal{E}_0 $ is unstable. We proved also that $ \mathcal{E}_1 $ is locally asymptotically stable once $ \mathcal{R} > 1 $. The global stability of both equilibrium $ \mathcal{E}_0 $ and $ \mathcal{E}_1 $ is discussed where we proved that $ \mathcal{E}_0 $ is globally asymptotically stable once $ \mathcal{R}\leq 1 $, and $ \mathcal{E}_1 $ is globally asymptotically stable once $ \mathcal{R} > 1 $. The sensitivity analysis of the basic reproduction number $ \mathcal{R} $ with respect to the model parameters is carried out. In a second step, a vaccination strategy related to this model will be considered to optimise the infected and exposed individuals. We formulated a nonlinear optimal control problem and the existence, uniqueness and the characterisation of the optimal solution was discussed. An algorithm inspired from the Gauss-Seidel method was used to resolve the optimal control problem. Some numerical tests was given confirming the obtained theoretical results.

The aim of this paper is to define generalized rational contractions in the setting of graphical b-metric spaces and obtain some fixed-point theorems. Our results are significant generalizations and extensions of some well-known results in the existing theory. We also supply a nontrivial example to show the validity of the obtained theorems. As applications, we obtain some results on rational expressions in the background of graphical metric spaces.

Fly ash acquired from power stations causes removal challenges and environmental concerns. Disposal concerns can be solved by employing these waste materials as a raw source to improve soil stability. Stability of soil refers to the improvement of soil behaviour due to the enhancement of the soil’s geotechnical properties. Water content, strength, plasticity, and density are the most often adjusted properties. Extensive studies have focused on the influence of fly ash on soil stability. Therefore, this investigation discussed some of these studies, drawing a critical review to find out the effect of fly ash additive on soil characteristics. Also, this study focused on the impact of fly ash (FA) mixed with clay soil. Generally, it can be said that fly ash improved the soil stability, especially in terms of CBR values, the permeability of the soil and decreased the potential of volumetric soil changes through a series of experimental tests. This is due to the size and shape of particles; in addition to the treated period, volumetric dilation of the ground is reduced. Considering that the additives are not biodegradable, the behavioural adjustment of the hardened soil does not disappear.

Introduction: Asthma is a chronic disease characterized by recurrent episodes of breathlessness and wheezing. Keeping in view the problems in asthma control and side effects of available medication, there is a need for alternative treatments with better efficacies and fewer side effects. Atorvastatin is a statin that blocks HMG CoA reductase enzyme found in the liver, inhibiting the synthesis of cholesterol. Blockade of this pathway also inhibits production of GTPases which are involved in airway inflammation, airway remodeling and contraction of smooth muscles of the bronchi. Aims & Objectives: To evaluate the symptomatic control in mild to moderate and uncontrolled asthma patients using standard treatment versus its combination with atorvastatin. Place and duration of study: This study was conducted in Pulmonology Department of Lahore General Hospital; Lahore over a 4-week duration from October 2018 till February 2019. Material & Methods: Patients of mild to moderate and uncontrolled asthma were enrolled in this study based on inclusion and exclusion criteria. Patients were divided into two groups by lottery method, Group 1 and Group 2, with 34 patients in each group. Group 1 was continued with standard therapy of asthma and the Group 2 was administered atorvastatin 40 mg, once daily in addition to standard therapy for 4 weeks. The control of asthma before and after treatment was assessed based on Global Initiative for asthma (GINA) guideline questionnaire score. SPSS (Statistical Package for Social Sciences) version 22 was used for analysis of data. P-Value < 0.05 was taken as significant. Results: Nonsignificant results were obtained when comparison between the groups was made based on GINA guidelines questionnaire score by Mann Whitney Utest Conclusion: It was concluded that atorvastatin has no role in symptomatic control in patients of mild to moderate and uncontrolled asthma.

The purpose of this paper is to establish common fixed points of six mappings in the context of bicomplex valued metric spaces. In this way, we generalize some previous well-known results from the literature. Moreover, we provide a non-trivial example to demonstrate the authenticity of established outcomes. As an application, we investigate the solution of an Urysohn integral equation by applying our results.

Foreign body (FB) aspiration in maxillofacial injuries is a life-threatening event. A long-time interval between the aspiration and retrieval results in the formation of granulation tissue and mucosal inflammation around the FB, which could restrict the visual field of bronchoscopy and its retrieval. In addition, it can affect the lung structure with fatal complications. Herein, we present a case of unique FB retrieval (2 joined crown teeth – measuring 19 mm) within 8 h following aspiration in a 24-year-old male polytrauma victim. Further, we discuss our successful modified retrieval technique accordingly without resulting in any complications.

The purpose of this paper is to utilize complex valued extended b-metric space and obtain common α-fuzzy fixed point theorems under Kannan type contractions. As application, we derive common α-fixed point results for multivalued mappings in the context of complex valued extended b-metric space.

Portland cement (PC) is considered the most energy-intensive building material and contributes to around 10% of global warming. It exacerbates global warming and climate change, which have a harmful environmental impact. Efforts are being made to produce sustainable and green concrete as an alternative to PC concrete. As a result, developing a more sustainable strategy and eco-friendly materials to replace ordinary concrete has become critical. Many studies on geopolymer concrete, which has equal or even superior durability and strength compared to traditional concrete, have been conducted for this purpose by many researchers. Geopolymer concrete (GPC) has been developed as a possible new construction material for replacing conventional concrete, offering a clean technological choice for long-term growth. Over the last few decades, geopolymer concrete has been investigated as a feasible green construction material that can reduce CO2 emissions because it uses industrial wastes as raw materials. GPC has proven effective for structural applications due to its workability and analogical strength compared to standard cement concrete. This review article discusses the engineering properties and microstructure of GPC and shows its merits in construction applications with some guidelines and suggestions recommended for both the academic community and the industrial sector. This literature review also demonstrates that the mechanical properties of GPC are comparable and even sometimes better than those of PC concrete. Moreover, the microstructure of GPC is significantly different from that of PC concrete microstructure and can be affected by many factors.

Shear walls have high strength and stiffness, which could be used at the same time to resist large horizontal loads and weight loads, making them pretty beneficial in several structural engineering applications. The shear walls could be included with openings, such as doors and windows, for relevant functional requirements. In the current study, a building of G + 13 stories with RC shear walls with and without openings has been investigated using ETABS Software. The seismic analysis is carried out for the determination of parameters like shear forces, drift, base shear, and story displacement for numerous models. The regular and staggered openings of the shear wall have been considered variables in the models. The dynamic analysis is carried out with the help of ETABS software. It has been observed that shear walls without openings models perform better than other models, and this is in agreement with the previous studies published in this area. This investigation also shows that the seismic behaviour of the shear wall with regular openings provides a close result to the shear wall with staggered openings. At the roof, the displacement of the model with regular openings was 38.99 mm and approximately 39.163 mm for the model with staggered openings. However, the model without a shear wall experienced a displacement of about 56 mm at the roof. Generally, it can be concluded that the openings have a substantial effect on the seismic behaviour of the shear wall, and that should be taken into consideration during the construction design. However, the type of opening (regular or staggered) has a slight effect on the behaviour of shear walls.

In recent years, steel-concrete composite shear walls have been widely used in enormous high-rise buildings. Due to their high strength and ductility, enhanced stiffness, stable cycle characteristics and large energy absorption, such walls can be adopted in auxiliary buildings, surrounding the reactor containment structure of nuclear power plants to resist lateral forces induced by heavy winds and severe earthquakes. The current study aims to investigate the seismic behaviour of composite shear walls and evaluate their performance in comparison with traditional reinforced concrete (RC) walls when subjected to cyclic loading. A three-dimensional finite element model is developed using ANSYS by emphasising constitutive material modelling and element type to represent the real physical behaviour of complex shear wall structures. The analysis escalates with parametric variation in reinforcement ratio, compressive strength of the concrete wall, layout of shear stud and yield stress of infill steel plate. The modelling details of structural components, contact conditions between steel and concrete, associated boundary conditions and constitutive relationships for the cyclic loading are explained. The findings of this study showed that an up to 3.5% increase in the reinforcement ratio enhanced the ductility and energy absorption with a ratio of 37% and 38%, respectively. Moreover, increasing the concrete strength up to 55 MPa enhanced the ductility and energy absorption with ratios of 51% and 38%, respectively. Thus, this improves the contribution of concrete strength, while increasing the yield stress of steel plate (to 380 MPa) enhanced the ductility (by a ratio of 66%) compared with the reference model. The present numerical research shows that the compressive strength of the concrete wall, reinforcement ratio, layout of shear stud and yield stress of infill steel plate significantly affect ductility and energy absorption. Moreover, this offers a possibility for improving the shear wall’s capacity, which is more important.

The composite shear wall has various merits over the traditional reinforced concrete walls. Thus, several experimental studies have been reported in the literature in order to study the seismic behavior of composite shear walls. However, few numerical investigations were found in the previous literature because of difficulties in the interaction behavior of steel and concrete. This study aimed to present a numerical analysis of smart composite shear walls, which use an infilled steel plate and concrete. The study was carried out using the ANSYS software. The mechanical mechanisms between the web plate and concrete were investigated thoroughly. The results obtained from the finite element (FE) analysis show excellent agreement with the experimental test results in terms of the hysteresis curves, failure behavior, ultimate strength, initial stiffness, and ductility. The present numerical investigations were focused on the effects of the gap, thickness of infill steel plate, thickness of the concrete wall, and distance between shear studs on the composite steel plate shear wall (CSPSW) behavior. The results indicate that increasing the gap between steel plate and concrete wall from 0 mm to 40 mm improved the stiffness by 18% as compared to the reference model, which led to delay failures of this model. Expanding the infill steel plate thickness to 12 mm enhanced the stiffness and energy absorption with a ratio of 95% and 58%, respectively. This resulted in a gradual drop in the strength capacity of this model. Meanwhile, increasing concrete wall thickness to 150 mm enhanced the ductility and energy absorption with a ratio of 52% and 32%, respectively, which led to restricting the model and reduced lateral offset. Changing the distance between shear studs from 20% to 25% enhanced the ductility and energy absorption by about 66% and 32%, respectively.

Circular hollow steel tube columns are widely used in high-rise buildings and bridges due to their ductility and lower weight compared to reinforced concrete. The use of this type of steel section has several advantages over using reinforced concrete members. The present study investigates the bending behavior of steel circular hollow sections when subjected to bending loads. The variations in material characteristics with regard to position along the cross-section of a steel tube member is first considered in this experimental study, providing for a more accurate definition of the material behavior in the model. A supported beam tested by two-point loads is the loading type that is used to study the bending performance of steel tubes. Ten circular hollow beam specimens were prepared and tested up to and post the failure stage with the following dimensions: thickness (2, 3, and 6 mm), diameter (76.2, 101.6, and 219 mm), and span (1000, 1500, and 2000 mm). A finite element analysis has been conducted for these ten specimens using the ANSYS program. The finite element model is compared to experimentally obtained data to verify that both local and global behaviors are correctly considered. The load-deflection results of this analysis showed a good agreement with the experimental results. A parametric study also was performed that considered two variables, which were the effect of the presence of circular rings and the change of opening location in the length direction on the specimens’ behavior. This study showed that the presence of the circular rings in the specimen led to an increase in its ultimate strength (of 53.24%) compared with the non-presence of these rings. In contrast, the presence of openings at 30, 40, and 50% from the specimen length reduced the strength capacity by 8.76, 14.23, and 17.88%, respectively.

The estimation of recharge to ground water is the important basics to improve the use of ground water with other available resources, and to save ground water resource from depletion, especially when using large quantity of ground water during a long time such as for agricultural purposes. Al-Wand River Basin in Iraq suffers from water shortage of its requirement of Blajo–Al-Wand Project, and to cover this shortage, the ground water plays a good role to overcome this problem. In this study, three methods were used to estimate the recharge and ground water storage for Al-Wand Basin, these methods are: Water Table Fluctuation (WTF), Water Balance of Climatic for Basin, and Water Table Balance for Basin. The results showed differences between the methods used to estimate recharging and ground storage for this basin. The approximated values between drawl water from production wells and water balance of climate for basin method make it better the other methods, which the difference percentage was large with drawls water. Also, classifying the methods by assumptions found make (WTF) better method, because it contains less assumptions compared to the other methods.

Iraq depends mainly on Tigris and Euphrates Rivers to provide high percentage of agricultural water use for thousands years. At last years, Iraq is suffering from shortage in water resources due to global climate changes and unfair water politics of the neighboring countries, which affected the future of agriculture plans for irrigation, added to that the lack of developed systems of water management in the irrigation projects and improper allocation of irrigation water, which reduces water use efficiency and lead to losing irrigation water and decreasing in agricultural yield. This study aims at studying the usability of irrigation and leaching scheduling within the irrigating projects and putting a complete annual or seasonal irrigation program as a solution for the scarcity of irrigation water, the increase of irrigation efficiency, lessening the salinity in the projects and preparing an integral irrigation calendar through field measurements of soil physical properties and chemical for project selected and compared to the results of the irrigation scheduling and leaching with what is proposed by the designers. The process is accomplished by using a computer program which was designed by Water Resources Department at the University of Baghdad, with some modification to generalize it and made it applicable to various climatic zone and different soil types. Study area represented by large project located at the Tigris River, and this project was (Al-Amara) irrigation project. Sufficient samples of project's soil were collected so as to identify soil physical and chemical properties and the salinity of soil and water as well as identifying the agrarian cycles virtually applied to this project. Finally, a comparison was conducted between the calculated water quantities and the suggested ones by the designers. The research results showed that using this kind of scheduling (previously prepared irrigation and leaching scheduling) with its properties which made it applicable requires an intense care when using the plant distribution pattern, the agrarian cycle, its agrarian areas and agricultural intensity within all climatic regions. Also, it was found that this program was an instrumental tool for providing water if the plant distribution pattern was well-selected.

Applying conjunctive use between surface water and ground water is getting widely used at many regions in the world, due to the increasing need of water resources, especially when large quantities of water and for long time are used for irrigation purposes to meet agricultural production requirements. The linear programming has been formulated to optimize the optimum allocation of water. An economic analysis of conjunctive use for Al-Wand project in Iraq has been done for a certain cropping pattern using two scenarios of management and operation of ground water and surface water. One suggested scenario was to use ground tank to save the water during the period of water excess to be used during the shortage period. The other scenario was to operate the reservoir dam to supply the water requirements during the agriculture years. The main concerns of this research were: the fluctuation of the ground water and how to estimate the deficit of yield which is caused by using the decreased water in irrigation. The economic analysis has been done by calculating the overall cost and the annual estimation of return. It can be concluded that the operation of surface water at (60 and 70%) from total available surface is a compromise, because some of the water still flow in the river and canals and the ground water reservoirs were not affected especially its storage capacity.

Methods for scheduling irrigation are important aspects of good crop and plant management. Irrigation scheduling process is concerned with quantity and date of irrigation. In this paper Time Domain Reflectometer (TDR) is used as a soil moisture tool to measure the trend of the soil moisture in the root zone of Cherries in Michigan State/ United State of America for three years of measurements. The study analyzes the effect of irrigation process by using trickle system on the variation and trends of the soil moisture. Furthermore, the study compares the quantities of the applied water with the soil water content to get the soil water depletion and the actual crop evapotranspiration. The results show that there is no fixed and clear irrigation schedule within the years of the study (2009, 2010 and 2011). Over irrigation in some months the soil becomes in saturated conditions. On other hands, in some months and during the years of study, the soil moisture deficit be more than the allowable depletion and sometimes close to limit of permanent wilting point, and this is due to apply a deficit irrigation, knowing that the root depth of this study is 1.22 meter only, which means that the crop may be extract the water by roots that are deeper than 1.22 meter. Knowing that the saving water and energy is very important and also system evaluation and its maintenance are required.

The role of drain in agricultural lands is to remove excess surface and subsurface water to create a good environment for root growth and to increase crops yield. The main objective of this research was to evaluate the performance of closed drains when using textile filter instead of crushed gravel filter. The research has been executed in the laboratory using a sand tank model and by using two types of the soil. One of soils was light soil (sandy soil) and the other heavy soil (loamy soil). The tests were classified into four cases; each case was supplied discharge during 10 days. The results showed that the amount of out flow when using graded crushed gravel filter is greater than the amount of out flow in case of using textile filter for the same soil; and the amount of sediment in applying graded crushed gravel filter for the two types of soils was greater than using textile filter. The entrance resistance for textile filter was greater than graded crushed gravel filter and the entrance resistance increase for the two types of filters with time. From the results it can be concluded that the graded crushed gravel is more efficient than the textile filter in sandy soil, while when using the two types of filters with loamy soil the results showed that the two types of filter exhibited low work efficiency.

The estimation of recharge to ground water is the important basics to improve the use of ground water with other available resources, and to save ground water resource from depletion, especially when using large quantity of ground water during a long time such as for agricultural purposes. Al-Wand River Basin in Iraq suffers from water shortage of its requirement of Blajo–Al-Wand Project, and to cover this shortage, the ground water plays a good role to overcome this problem. In this study, three methods were used to estimate the recharge and ground water storage for Al-Wand Basin, these methods are: Water Table Fluctuation (WTF), Water Balance of Climatic for Basin, and Water Table Balance for Basin. The results showed differences between the methods used to estimate recharging and ground storage for this basin. The approximated values between drawl water from production wells and water balance of climate for basin method make it better the other methods, which the difference percentage was large with drawls water. Also, classifying the methods by assumptions found make (WTF) better method, because it contains less assumptions compared to the other methods.

This paper introduces the concept of proximal (α , F) -contractions in F -metric spaces. We establish novel results concerning the existence and uniqueness of best proximity points for such mappings. The validity of our findings is corroborated through a non-trivial example. Furthermore, we demonstrate the applicability of these results by proving the existence of solutions for Volterra integral equations related to population growth models. This approach not only extends best proximity theory, but also paves the way for further research in applied mathematics and beyond. [ABSTRACT FROM AUTHOR]

This paper aims to introduce a novel variation of almost Hardy–Rogers (ψ, ϕ)‐type multivalued contraction and ϑ‐type contraction mappings. The main focus is on proving new fixed point (FP) results in M℘‐metric space (M℘‐MS). Additionally, several consequences are derived from our main findings. To elucidate the recency of our outcomes, various examples are provided. Finally, we utilize the obtained results to scrutinize the existence of solutions for nonlinear fourth‐order differential equations (NFODEs). [ABSTRACT FROM AUTHOR]

We study the split fixed point problem with multiple output sets in nonlinear spaces, particularly in CAT(0) spaces. We modify the existing self-adaptive algorithm for solving the split common fixed point problem with multiple output sets in the settings of generalized structures. We also present the consequences of our main theorem in terms of the split feasibility problem and the split common fixed point problem. [ABSTRACT FROM AUTHOR]