جستجوی مقالات مرتبط با کلیدواژه « همگرایی » در نشریات گروه « علوم پایه »

In this paper, we extend the collocation method for the numerical solution of two-dimensional Volterra integral equations. For this purpose, we first prove the existence and uniqueness of the solution of these types of equations and present a resolvent kernel representation for their solution. Then, we extend the collocation method using piecewise polynomials to solve the mentioned equations and obtain the corresponding algebraic system of equations and show that the system has a unique solution. We also prove the convergence of the method and obtain the order of convergence of the method by proving a theorem. Finally, we present some numerical examples to show the efficiency of the method and confirm the obtained theoretical results.

Operational risk is one of the identified risks in organizations, especially in banks, and Basel committees on banking supervision pay special attention to it. In this paper, the mathematical model based on the advanced operational risk model is considered to calculate the probability of survive as a partial Volterra integro-differentail equation. This equation has been solved numerically by applying the finite differences method with trapezoidal rule to estimate its integral part and the effect of changing the model parameters on the output of the problem has been investigated. In addition, the stability and convergence of the method are discussed and its numerical results are presented.

In this Article, proposes an approximation for the solution of the Riccati equation based on the use of exponential spline functions. Then the exponential spline equations are obtained and the differential equation of the fractional Riccati is discretized. The effect of performing this mathematical operation is obtained from an algebraic system of equations. To illustrate the benefits of the method proposed here the error analysis and convergence article are also discussed based on this exponential spline. Finally, a second-order method is obtained. One of the benefits of this proposed method is that it is not only for solving fractional Riccati equations, but also for a variety of Fractional equations that can be used. To illustrate the effectiveness of this method by solving numerical examples and a comparison of the results obtained from the implementation of this proposed method with the results of other existing numerical methods proves the claim that the proposed method is a good approximation for the fractional Riccati equations.

In this study, experiments are carried out to determine the deviation flow into the intake in a 90º convergent bend, aiming to investigate the effect of flow characteristics on deviation flow with and without submerged vanes. The effective variables include Froude number, convergence, and submerged vanes’ angle. For this research, a Rectangular channel with a 90º arc was used, which was studied using four different discharges, four different angles of submerged vanes and four degrees of convergence of the end of the channel. According to the results, the deviation flow to the intake increases by converging the laboratory flume. As the end of the flume is converged, the deviation flow is further increased. As the flume is converged (b/B) from 0 to 0.75, the deviation flow is increased from 64.9 to 81.4%, showing a 16.5% increase. Deviation flow is decreased by installing submerged vanes. A decrease in submerged vanes’ angle reduces the deviation flow. Compared to the model without a submerged vane, deviation flow is decreased by 14.9, 9.9, 6.8, and 2.3% by installing submerged vanes at angles of 25, 30, 45 and 60º, respectively. Deviation flow is also decreased by increasing the Froude number, such that it decreases by 5.3% with the increase of Froude number from 0.14 to 0.23.

In this paper, we develop some stationary iterative schemes in block forms for solving double saddle point problem. To this end, we first generalize the Jacobi iterative method and study its convergence under certain condition. Moreover, using a relaxation parameter, the weighted version  of the Jacobi method together with its convergence analysis are considered. Furthermore, we extend a method from the class of Gauss-Seidel iterative method and establish its convergence properties under a certain condition. In addition, the block successive overrelaxation (SOR) method is used to construct an iterative scheme to solve the mentioned double saddle point problem and its convergence properties are analyzed. In order to illustrate the efficiency of the proposed methods, we report some numerical experiments  for a class of saddle point problems arising from the modeling of liquid crystal directors using finite elements../files/site1/files/52/2.pdf

Much has been said about what and how the ideas of prominent scientists in the world come from different specialties and from different geographical areas. But the nature of science is such that research results and scientific achievements are not so dependent on internal factors and social and political environment conditions. Just as the intellectual and emotional outpourings of sages, mystics, artists, and poets can be a function of the inner and outer conditions, so much they can converge in feeling, understanding, and knowing inside and out, providing many questions. In this article we have tried to interpretations, the explanation and vocabulary of the words in the poems since the original order poet and reality of what has been spoken, and the literal meaning of what is desirable poet, a bridge to be struck. Along with that the convergence of scientific, literary and spiritual concepts with new ways has been considered. The spiritual connection between two thoughtful poets, Goethe from Germany and Hafiz from Iran, who have lived in two different languages and cultures for more than 500 years, demonstrates the possibility of intellectual, cultural and social connection beyond contractual boundaries. Although we were not satisfied with the two, we cite examples of Mowlana, Attar, and Sa'di to show that all the elders in the cupola had a photograph of the scene. We interpret the visage of the mistress as a shared love that knows neither the geographical boundary nor the political or cultural boundary; Not afraid of time or place. Although science also creates such convergence and connection, it brings people together in love, spirit, spirituality, and thought, and avoids disagreements and creates empathy. Today, in spite of the achievement of rationalism, not only the problems of mankind have not been resolved, but also an increase. It may be that everyone thinks of himself as common sense, while everyone is the only one who knows everything and everyone has not yet been born! So, we suggested empathy by speaking it with the language of love, perhaps with this human mechanism achieving promised peace and inner satisfaction.In this soil in this soil, in this clean farmExcept for love and affection, we should not sow any other seed (Mowlana)

on of the efficacious parameters in sketching elements is evaluating the geology dangers of underground excavations including squeezing and rock explosions in tunnels. the water transmission system was constructed from azad dam to degolan- ghorveh plain in order to supply water to dehgolan - ghorveh plains. The squeezing and rock e xplosion phenomena were predicted considering the weekness of rock mass of the tunnel track, the overburden thickness and its settlement in the active zone. in the present research, the tunnel was initialy divided in to 5 zones by using the results of geological and borehole drillings. The squeezing and rock explosion in these 5 zones will be discussed later. The tunnel was situated in non squeezing and extreme squeezing zone. Regarding the previous investigations and also the emorical and semi empirical metheds. The tunnel had low potentidity in the view of rock explosion. finally, the Hook and Marinos and critical strain methods were compared via the Finite Element numerical Method using phase2 software. in order to investigate the occured replacement in the tunnel. based on the previous analysis , it was realized that the critical strain method had the most similarities with the numerical method. as for as the results of numerical and critical strain methods are matched, S3 and S5 zone can be the most unstable zones

In this study, results of experiments about the trajectory and the advance velocity of inclined and convergent rectangular surface jet into stagnant ambient have been presented. In order to discharge process simulation was used a flume with 3.2 m length, 0.6 m width and 0.9 m height and a rectangular channel with 6 cm width. Discharge channel was designed in the four angle of convergence 12.5, 25, 45 and 90 degree. This channel injected the jet stream to form of tangent to the surface of ambient and in three different slopes 0, 4 and 8 percent. Receiving fluid had been prepared from urban water. As well as the jet fluid had been prepared from the salt liquidation in water and in three concentrations 5, 15 and 45 gr/l. After running the experiments and using of images routing process were analyzed the data. In this regard, hydraulic and geometric parameters on the trajectory and the advance velocity of jet was investigated. According to the results, increase the slope and decrease the angle of convergence causes increase in length of trajectory and decrease in the advance velocity of jet. Reduce the densimetric froude number causes decrease in length of trajectory. Also, in order to investigate of influence of convergence on the movement path of flow, by comparison of trajectory in convergent channel and simple channel, More relative advance was seen in convergent channel. Finally, using of the data analysis, relation between advance velocity of jet and dependent parameters was determined with RMSE=0.034.

When the tunnel passes through the weak and different soil conditions, the soil between the tunnel and the surface of the ground move. And the development of these movements to the surface of the ground will be accompanied with the subsidence of the surface structures. Therefore in order to do necessary planning to create supports considering the conditions of the location of doing the project, providing a decision making model is essential in choosing an appropriate option for tunnel supports in planning phase and designing the tunnel project. The aim of this paper is to offer a useful design to specify and choose suitable options for Karaj subway tunnel supports, as a good model for later stages use. This pattern is formed on the basis of technical, financial, administrating, social and effective factors on the site of doing the project by noticing a variety of criteria. The final goal is selecting the most suitable option aimed all the probable options for choosing subway tunnel supports system and noticing effective and important criteria on which basis and by using multi-criteria decision making and new research methods during the operation, proper options are prioritize and ultimately the best ones are chosen. In AHP and TOPSIS methods, alternative (D) NATM method is selected as the best alternative for support system. On the other hand the results taken by numerical modeling with PLAXIS software shown that alternative D is the best support system with 26mm displacement and 10mm subsidence in the section.

The aim of this paper is to offer a useful design to specify and choose suitable options for Tehran subway tunnel supports, line 3, phase 4 as a good model for later stages use. This pattern is formed on the basis of technical, financial, administrating, social and political and mechanical and effective factors on the site of doing the project by noticing a variety of criteria. Furthermore (on the other hand) subway tunnel supports include lattice girder,cement armed with armature using modular form work (frame work) system, fore poling, corrugated steel sheet and segmental lining in the model. And the final goal is selecting the most suitable option aimed all the probable options for choosing subway tunnel supports system and noticing effective and important criteria on which basis and by using multi-criteria decision making and new research methods during the operation, proper options are prioritize and ultimately the best ones are chosen. In TOPSIS method, alternative (E) is selected as the best alternative for support system.

Inverse theory was developed by scientists and has been used in different scientific applications, such as geophysical tomography, image enhancement, curve fitting and determination of earth structure from geophysical data. Inverse theory provides mathematical techniques to obtain useful information about measurements (data). The information resulting from inversion usually reveals some specific properties of the geological structures, called model parameters. Inverse theory, in contrast to forward theory, which predicts results of measurements on the basis of a suggested model relevant to the problem, uses models that are adjusted and estimates the model parameters by using the data and some general principles. It should be noted that inverse theory provides information about unknown model parameters directly using measured data. In contrast to forward theory, inverse theory doesnt provide a basis for the model itself. Recently, considerable effort has been devoted to the explanation of gravity and magnetic anomalies by employing data inversion in the spatial domain. Three major types of gravity and magnetic data inversion are discussed in geophysical literature. The first is "Inverting data for solving both physical and shape parameters". In this case, the inverse problem is completely non-unique. The non-uniqueness of the problem is visible in the two-dimensional section as a large number of well-defined local minima, some of which are distinguished as unfeasible. In this class, unacceptable solutions can be confined by specifying some of the model parameters. The second type of gravity and magnetic data inversion is "Inverting data for solving physical parameters". In this approach, the earth is divided into a limited number of cells of fixed size with unknown physical parameters, such as density and magnetization. The non-uniqueness of the solution is evident and algorithms have been developed to produce a single model by minimizing an objective function. The third type of gravity and magnetic data inversion is "Inverting data for solving shape parameters". In this class, physical parameters are assumed to be known and nonlinear operators must be design to determine geometry of the geophysical sources. However, geophysical inversion methods are most effective when a linear operator is applied; thus, the problem is usually linearized about some initial model and the inverse problem is solved iteratively. This paper presents a robust, flexible and efficient algorithm to solve large scale non-linear inverse problems in geomagnetic surveys (the third type of gravity and magnetic data inversion). Considering the sensitivity of inverting magnetic data and the high level of noise in data acquisition, the inversion of magnetic data should be performed using advanced methods. These methods have high performance to handle noise data. The method is iterative, and at each iteration a perturbation of model parameters in a P-dimensional subspace of an M-dimensional model space are sought (the primary model is updated using perturbation values of the model parameters at each iteration). This style of iterative subspace procedure is well adapted to non-linear inverse problems with many parameters and can be successfully applied to a variety of geopotential problems. The gradient subspace algorithm utilizes a model of parameterization in which the depth of each block is described as an unknown parameter. Model parameters are allocated to separate subspaces on the basis of different physical dimensionality (in this case, model parameters have the same physical dimension). Basis vectors of P-dimensional subspace are extracted by the SVD of a Hessian matrix (the second derivation of model parameters). M-dimensional model space is projected onto P-dimensional subspace using basis vectors. If effective basis vectors are chosen for inversion procedures, the projected matrix is accurate with respect to original one. In new and small dimensions, inversion can be performed with great speed and is stable against noise. This procedure is very effective in accelerating convergence and obtaining a more accurate solution. Also, the inversion is robust with respect to data errors and poor initial estimations. The efficiency of the method is compared with one of the conventional methods of inversion of non-linear problems (Marquardt-Levenberg); the results show that the gradient subspace has fast and stable convergence in comparison to its performance in the conventional method. The practical effectiveness of this method is demonstrated by inversion of synthetic and real examples. The real magnetic data is acquired over the MOGHAN area, in the northwest of Iran. The results compared with those of seismic interpretation at the study area.

In this paper we used orthogonal basis functions and expansion coefficients for inverse modeling of magnetic data. The basis functions chosen are normalized eigenvectors of second derivation of the objective function (Hessian matrix) calculate for an initial model. Limited number of basis vectors obtained in this way defines a new subspace in model parameters space. A new objective function is defined in term of these new parameters and minimized in subspace of original space. As in geophysical inverse problems we need to inverse matrixes that are functions data and geometry of data and model parameters. The matrix inversion in new subspace of the original space will be better conditions due to less dimensionality in the inversion. Since the most significant eigenvectors corresponding the largest eigen values in Singular Value Decomposition (SVD) of matrixes. Others eigenvectors have less influence in fitting data or lead inversion procedures to local minima. With apply subspace method inversion will be fast and stable against the noise. The efficiency of the method is tested with synthetic and real magnetic data (acquired from Moghan area, north-west of Iran). The results proved fast convergence and stability of inversion against the noise.

Nowadays water, as a competitive and favored element and at the same time a worrisome factor in the life and existence of mankind’s descendants, has appeared into the governments’ affairs and disputes. Considering the various values of water, it is of concern for the governments and nations as a valuable item; which due to its constant increasing demand, has been discussed as a political element and is assumed a significant political merit. Only about 2.5% of the world’s waters are sweet water and the rest are saltwater, while from the overall sweet waters just around 0.3% can be recycled. Access to this water is difficult due to the following factors; irregular consumption as a result of population increase, industrialization, change in consumption model, lack of steady distribution of water in the world countries, evacuation, pollution of the underground sweet water resources, in addition to it becoming salty, the high pollution of surface fresh waters through mankind’s activities including economical activities, the collaboration of water resources among several countries, the dominance of upper countries and the dependence of lower part countries related to international rivers etc. Water, which is known as a strategic substance, a rare source, the source of life, and water is one of the competitive tools among countries and one of the world’s challenges which will cause wars and strife in future. The issue of access to water resources has become so important that many countries, including Israel, consider interference in the origin, path and destination of the water resources lawful within the neighboring countries. In this article we intend to survey the strategic role of the Nile River in the countries’ convergence or divergence and the extent to which the Zionistic Regime and the U.S. influence it within a descriptive-analytic method.

Inversion of gravity data is one of the most interesting numerical tools for obtaining 3-D images of geological structure. In this study, modeling of gravity anomalies is performed by new linear modeling Method (Compact Inversion). The principle used is to minimize the volume of causative body which is equivalent to maximizing its compactness. The anomalous density distribution is obtained using an iterative technique which is numerically stable and rapidly convergent. The principle can also be adapted to include modeling of gravity anomalies by single density sources. The treatment of noise in data fits naturally into formulations of the inversion procedure. The method is illustrated by inversion of noise-free data and noisy data.The practical effectiveness of this methods is demonstrated by inversion of synthetic and real example. The real data is acquired over chromite ore in Hormozgan province of Iran. The results obtained are compared with existing outcrop and available superficial drilling.