This paper deals with FINITE CAPACITY single server queuing system with vacations. Vacation starts at rate u if the system is empty. Also, the server takes another vacation if upon his arrival to the system, finds the system empty. Customers arrive in the system in Poisson fashion at rate λ0 during vacation, faster rate λf during active service and slower rate λs³0 during the breakdown. Customers are served exponentially with the rate m. Server breakdowns at rate b and it immediately repaired exponentially with the rate r. We derive the explicit formulas for queue length distribution, average queue length, average number of customers in the system and average waiting time for a customer in queue and in the system. Numerical illustrations have been cited to show the model proposed is practically sound.

The lack of Quranic approaches in the production of Quran-based humanities is still felt, despite the predominance of the philosophical approach in critical approaches to modern humanities, which has become very common in the Islamic world and in Iran for several decades. It seems that the CAPACITY of the method of thematic exegesis (al-Tafsīr al-mawdū'ī, Arabic: التفسیر الموضوعیّ) in this regard, can be used to bring the Holy Quran into the field of humanities. Thematic exegesis, according to whether its subject is inside or outside the Qur'an, has several functions in criticizing the structure of modern knowledge and scientific research, as well as the production of Islamic humanities. It is possible to make use of thematic exegesis of the inside of the Holy Book of Quran in order to “fundamental criticism” of the general fundamentals of humanities -the fundamentals of epistemology, axiology, ontology and anthropology- and it is also possible to use thematic exegesis for constructing and producing foundation of humanities obtained from the Holy Quran. It is used by thematic interpretation exegesis of the outside of the Holy Book of Quran -such as Shahīd (martyr) Sadr’s interrogational approach- to answer the problems of humanities and this process faces challenges such as the complexity and multiplicity of the “subject” of the humanities that exist in modern terminology of this field. It can be used in order to solve this issue in some cases to know the process of the change of the components of the modern of the conceptual history’s approach and also by analyzing the issue into several components can be shown that the components are not necessarily a product of the modern era and can be followed up in the Holy Quran and can be found up in the Holy Quran. The perspective of the Holy Quran, after that, regarding the modern subject in the desired field by the “combining” of the results obtained based on the thematic interpretation.

Short packet transmission is one of the topics considered in the new generation of telecommunication systems for low latency connections. In this paper, in order to have a low latency communication, a cooperative system with FINITE block length (FBL) transmission is investigated. In this relay system, a two-way half-duplex (HD) relay replaces data packets between two nodes. The two-way relay functionality is assumed as amplify-and-forward (AF) with fixed gain and variable gains. Due to the importance of delay, the criterion for evaluating system performance is the effective CAPACITY. Therefore, to optimize the performance of the system, the optimal power allocation is used to maximize the effective CAPACITY. The concavity of this power allocation problem under the assumption of constant total available power between nodes and relay is calculated. Finally, the effect of various parameters including packet length, bit error rate and quality-of-service (QoS) is investigated on overall system performance.

The granular pile anchor (GPA) is a relatively new and uncomplicated ground improvement technique that can support tensile loads effectively. In this study, the uplift CAPACITY of GPAs embedded in clay was assessed using FINITE element limit analysis (FELA) with an adaptive mesh. The analysis considered a broad range of parameters, including the GPA’s diameter and length, the undrained shear strength of the surrounding clay, and the friction angle and unit weight of the GPA material. Results showed that the dimensionless uplift CAPACITY generally increased with a higher length-to-diameter ratio. However, the nature of this increase varied for certain cases due to shifts in the failure mechanism of the GPA. Multiple linear regression was applied to establish a practical correlation,, resulting in a predictive equation for dimensionless variables. The model's goodness-of-fit was evaluated using statistical measures such as the ztest, demonstrating its reliability. This study's findings provide valuable insights for designing GPAs in clayey soils and contribute to more effective engineering applications.

Introduction: Studying the effect of slope angle on bearing CAPACITY of foundations on the slope in urban areas is a challenging problem that has been investigated by researchers for years. In general, the analytical approaches for solving this problem can be categorized into limit equilibrium, characteristics and limit analysis methods. In recent years, there have been studies for using the limit analysis within the framework of FINITE element method for geomaterials. In these studies, the soil mass is not considered as rigid and there is no need to predefine a failure surface for the slope. In the performed research, using the upper bound FINITE element limit analysis, bearing CAPACITY of strip foundation on slope have been studied. This analytical method enables the use of the advantages of both methods of limit analysis and FINITE element analysis. In this method, the slip between the two elements is considered. In order to find the critical state of the failure, the rate of power internally dissipated is linearly optimized, by using the interior points method. The advantages of this method are the high convergence rate in comparison with other analytical optimization methods. The effect of different upstream and downstream slopes and foundation depths and also the influence of various mesh discretizations have been evaluated. Finally, the results are compared with those obtained from previous methods available in the literature. Methods: The FINITE element limit analysis method is based on nodal velocities. Considering the principals of the FINITE element method and having the nodal velocities, the velocity at each node of the element can be obtained from corresponding shape functions. The rate of power internally dissipated in each element is defined by multiplying the strain rate on stress in each element. In this method, the slip between the two elements and the rate of internal power dissipated at each discontinuity of two adjacent elements is considered. For this purpose, in each node, four new unknowns’ velocities are defined. To remove the stress from the equations, and provide a linear relationship for linear optimization, a linear approximation to the yield function has been used. For this purpose, the Mohr-Coulomb yield criterion is estimated with a polygon in the stress space. Also, using the reduced strength parameter, the effect of the dilation angle is considered. According to the principles of upper bound limit analysis, the value of plastic strain rate is calculated from the flow rule. The velocity field in elements and discontinuities must satisfy the set of constraints imposed by an associated flow rule. In order to have an acceptable kinematics field, the velocity vectors have to satisfy the boundary conditions. These conditions include zero kinematics velocities along the vertical and horizontal boundaries of the geometry as well as negative vertical unit velocities and zero horizontal velocities at points underneath the rigid foundation. Results and discussion: In order to calculate the bearing CAPACITY of foundation, a set of different uniform and non-uniform mesh has been examined. The results obtained from different uniform mesh sizes indicate a certain divergence in the course of analysis. However, the results between the fine and very fine non-uniform mesh are closely related to each other and are converged. The obtained results show that, by increasing the internal friction angle, the bearing CAPACITY has been increased. At high angles of modified friction, the effect of increasing the internal friction angle on the increase in bearing CAPACITY is more in slopes with lower angles. By increasing the downstream foundation depth, the bearing CAPACITY has been increased. This increase is more important in the case of slopes with lower angles. However, the upstream depth variations didn't present a significant effete on bearing CAPACITY. In order to investigate the effect of upstream angle on the bearing CAPACITY, the upstream mesh is also refined similar to the downstream. The obtained results indicate that variations of the upstream angle have a minor effect on the bearing CAPACITY. This is of course true if the upstream slope is fully stable. The results of the proposed method in this study are an upper bound for the results reported by the limit equilibrium and displacement FINITE element methods. As seen in Figure 1, the suggested method predicts lower bearing capacities compared to rigid block limit analysis method and is indeed a lower bound for the classical limit analysis method. The FINITE element limit analysis with linear optimization has resulted in more bearing CAPACITY than cone optimization. The bearing capacities, obtained from characteristic lines method depending to the slope angles, in some cases is more and in some cases less than those explored by the proposed method. In this paper, the bearing CAPACITY of foundation located on slope was evaluated by FINITE element limit analysis method. In this regard, the effects of different downstream and upstream angles of slope and foundation depths and also, the effect of various mesh discretizations on the bearing CAPACITY were studied. It is shown that an increase in the downstream angle causes a decrease in the bearing CAPACITY and an increase in the downstream foundation depth leads to an increase in the bearing CAPACITY. However, the upstream angle and upstream foundation depth were not much effective on the bearing CAPACITY.

The ultimate bearing CAPACITY of ring footings for different conditions such as internal to external diameter ratio, base roughness and thickness of sand layer were determined in the laboratory. The deformed shape of the soil under footing at failure was investigated, and accordingly a semi-empirical relation for determining the bearing CAPACITY of ring footings was developed. The bearing CAPACITY of ring footings was also determined using FINITE element method. The results of experiments, a semi-empirical relation and numerical methods were compared, and reasonable agreements were observed.

We address the batch arrival m[x]/G/1 systems with FINITE CAPACITY under partial batch acceptance strategy where service times or rates oscillate between two forms according to the evolution of the number of customers in the system. Applying the theory of Markov regenerative processes and resorting to Markov chain embedding, we present a new algorithm for computing limit distributions of the number customers in the system. The numerical results are given in the paper for a clearer expression of the proposed computational methodologies

In this paper, finding Dynamic Load Carrying CAPACITY (DLCC) of flexible link manipulators in point to-point motion was formulated as an optimal control problem. The FINITE element method was employed for modelling and deriving the dynamic equations of the system. The study employed indirect solution of optimal control for system motion planning. Due to offline nature of the method, many difficulties such system nonlinearities and all types of constraints can be catered for and implemented easily. The application of Pontryagin’s minimum principle to this problem was resulted in a standard two-point boundary value problem (TPBVP), solved numerically. Then, the formulation was developed to find the maximum payload and corresponding optimal path. The main advantage of the proposed method is that the various optimal trajectories can be obtained with different characteristics and different maximum payloads. Therefore, the designer can select a suitable path among the numerous optimal paths. In order to verify the effectiveness of the method, a simulation study considering a two-link flexible manipulator was presented in details.