This paper investigates a competitive location problem with reliability. The reliability is the probability of out of service facilities for customers who cannot be served because of natural causes or human reasons. In this case, for each customer, there are several levels of allocations. If a facility fails to serve a customer, the customer will be served by the facility at the next allocation level. The two , rms determine their optimal location, respectively. The problem is modeled based on a Stackelberg game, in which the leader's and follower's facility locations are determined respectively. The follower chooses the location of his choice according to the leader choice. The object of each competitor is maximizing the pro, t. Demographic parameters are considered as e, ective factors in choosing the location for leaders and followers, which means that the candidate location with more positive demographic factors is a better choice for facility establishment. The behavior of customers in choosing any of the facilities is a, ected by the quality and distance parameters which are considered in the model. According to GRAVITY hu,model, when the distance between costumers and candidate location is shorter and the quality factor is higher, the candidate location is a better choice for establishment. To solve the small part of the problem, the full space searching method is used, in which all possible points in space of answer are investigated. The answers are compared and Pareto optimal solutions are obtained which are shown in , gures. As the problem is NP-hard, NSGA-II meta-heuristics algorithm is used to solve the medium and large size of the problem. Representation of answer and crossover and mutation operator for algorithms also speci, ed for the problem. Ultimately, the numerical problems are randomly generated and Pareto optimal solutions are identi, ed for each problem which is shown in , gures. The answers obtained from both methods for small size problem are also compared.

In this paper, we first review some aspects of the f (R) GRAVITY, and then the concept of the torsion of space-time due to metric-affine formalism in f (R) GRAVITY is studied. Within this formalism, in which the matter action is supposed to be dependent on the connection, we achieve interesting cases including nonzero torsion tensor. Then with the physical interpretation of the torsion of space-time in high energy limit, the MODIFIED expression of Mach’s principle in a very strong gravitational region is obtained.

According to the perturbation order, the equations related to the motion of low-energy string effective action are, in fact, a type of generalization of Einstein equations. Thus, by usingthe conformal transformation of the metric tensor, the lowenergy string effective action into f (T) GRAVITY is shown, with a relationship between the dilaton field and the torsion scalar. Considering a homogeneous and isotropic universe for the canonical Lagrangian of f (T) GRAVITY, we show that this lagrangian is kept invariant under the transformations of the metric tensor and abelian duality (scale factor duality). Finally, by the use of the dualized Lagrangian and also, the invariance of torsion scalar T under the transformation of the scale factor duality a(t) 1/ a(t), the precise form of the f (T) function is obtained.

The current induced by removing a gate separating two fluids of close densities is simulated using a developed Smoothed Particle Hydrodynamic (SPH) model. The simulation is performed for fluids with density ratios between 0.9 and 1.0. To develop the two-phase model, no significant changes are applied to the basic SPH formulations, regarding the low density difference between the two fluids. The classic SPH equations are used with a small change: the speed of sound and the reference density are changed in order to produce the same reference pressure for both phases.In addition, density re-initialization is applied for each phase separately. The resulted in viscid flow has characteristics very close to or the same as the experimental results. The flow depth and the flow front speed are two parameters selected to validate the simulations. The effects caused by the variations in the density differences to the phenomenon and effectiveness of the applied method are evaluated by performing a series of simulations of different density ratios and resolutions.

In this study, in order to eliminate the stripping error from GRACE GRAVITY observations and localization of the signals of this satellite, wavelet analysis instead of Gaussian isotropic filtering approach is used. For this purpose, the scaling functions and wavelets, generated by a so-called cubic polynomial (CuP), are considered and GRAVITY variations for two major earthquakes-Sumatra earthquake and Maule earthquake- are obtained. For the case of Sumatra earthquake- Indonesia, various scale function of CuP are tested and the most precise results of GRAVITY variations with maximum 30 Micro-Gal is acquired in scale 4 which was similar to other studies. This result didn’t change with increasing scale function even higher than 4. Moreover, for the case of Maule earthquake- Chile, the GRAVITY variations before and after of using wavelet is attained which shows many disparity. The maximum GRAVITY variations before applying wavelet is acquired 20 Micro-Gal and after applying that, the maximum of these variations is computed 10 Micro-Gal which was similar to other researches.

In this paper, 3D inversion of GRAVITY data for determination of subsurface density distribution is made using geostatistical co-kriging method. Co-kriging is a mathematical interpolation and extrapolation tool. It uses the spatial correlation between the secondary variables and a primary variable to improve the estimation of the primary variable at un-sampled locations. The Co-kriging method gives weights to the data so as to minimize the estimation variance (the co-kriging variance). In this paper, the primary variable is density, (estimated by ρ *) and the secondary variable is GRAVITY g. For determination of kernel matrix, the subsurface area is divided into large number of rectangular blocks of known sizes and positions. The unknown density contrast of each prism is the parameter that should be estimated. In addition, the weighting matrix has also been used in order to improve the depth resolution. Preconditioned conjugate gradient method has been used for inversion. The computer program has been written in MATLAB and tested on synthetic GRAVITY of a rectangular prism model. The results indicate that the geometry and density of the reconstructed model are close to those of the original model. The GRAVITY data acquired in an area, which includes concealed manganese ore bodies (Safoo mine site), in northwest of Iran. The results show a density distribution in the subsurface from the depth of about 5 to 35-40 m. These results are in good agreement with the results of the borehole drilled in the site.

Iran and Afghanistan share deep historical, cultural and civilizational ties. Iran is one of Afghanistan’, s largest trading partners. However, economic sanctions have disrupted bilateral trade between these two neighboring countries through various channels. This paper presents an empirical analysis of the impact of economic sanctions on trade between Iran and Afghanistan in the period 2004-2018 by applying the GRAVITY Model, while the estimation is performed using fully MODIFIED least-squares technique. Findings of the research indicate that the imposition of any strong economic sanctions, in the long run, not only during the sanctions period but also in the post-sanctions period, has increased trade between Iran and Afghanistan. On the other hand, weak sanctions during the sanctions period have reduced trade,nevertheless, weak sanctions in the postsanctions period have increased bilateral trade. Development of trade cooperation between the two countries, facilitation of trade affairs and expansion of joint regional and international cooperation should be on the agenda of economic policymakers in Iran and Afghanistan.

Purpose of this paper is to study generalized quantum chromodynamics ghost dark energy (GDE) in the frame work of Horava–Lifshitz cosmology. Considering interacting and non-interacting scenario of GDE with dark matter in a spatially non-flat universe, we investigate the cosmological implications of this model in detail. We obtain equation of state parameter, deceleration parameter and the evolution of dark energy density to explain the expansion of the universe. Also, we show that the results we calculate have a good compatibility with previous work and restore it in limiting case. Further, we investigate validity of generalized second law of thermodynamics in this scenario. Finally, we find out a cosmological application of our work by evaluating a relation for the equation of state of dark energy for law redshifts.

GRAVITY gradient tensor is a matrix containing the second order derivatives of the Earth’s GRAVITY field, which has numerous applications in geodesy and geophysics. To date, much effort has been done for estimating GRAVITY gradient tensor with reasonable accuracy. This quantity can be estimated via using various methods, and one of these methods is applying finite-difference method to GRAVITY observations. Finite-difference method can estimate GRAVITY gradient tensor directly by using the mathematical concept of gradient, regardless of extra assumptions. This ability of finite-difference method, from theoretical point of view, provides the possibility of accurate estimation of GRAVITY gradient tensor without considering additional assumptions to the problem. This study tends to introduce and evaluate Finite difference method for estimating the gradient tensor and present formulae for determining GRAVITY gradient tensor from land-based GRAVITY observations. In this paper, the proposed equations are numerically tested by means of using a global GRAVITY model of the earth. Global GRAVITY model of the earth (EGM 2008) is a geopotential model of the earth consisting of spherical harmonic coefficients up to degree 2190 and order 2159. There are numerous uses for these high degree potential coefficient models. One of these uses is modeling and estimating GRAVITY gradient tensor.Finally, GRAVITY gradient tensor is estimated by the proposed method for 6350 GRAVITY stations located in Costal Fars region in a northern part of the Persian Gulf, between the latitudes from 26.5 N to 27.27 N and longitudes from 53.41 E to 55.58 E. The target area is about 10000 square kilometers. About 8500 square kilometers of the study area is located in moderate mountainous regions, and about 1500 square kilometers is located in flat coastal areas. The altitudinal distribution and spatial distribution of GRAVITY in study area are shown in figure 1 and 2 respectively. Numerical experiments of this study demonstrate the ability of this method in GRAVITY gradient tensor estimation with acceptable accuracy. For example, numerical experiments showed that the proposed method can estimate diagonal components of GRAVITY gradient tensor (second order derivatives of the Earth’s GRAVITY field in east, north and vertical directions) with the accuracy values of 12.46, 34.49 and 454.82 Eotvos respectively. The spatial distribution of the GRAVITY gradient tensor components obtained from finite difference method in study area are shown in figure 3.Finally, according to the theoretical concepts discussed in this paper, It can be said because the finite difference method using from derivative and difference concepts directly for estimating GRAVITY gradient tensor, it is expected that this method provide accurate estimation of GRAVITY gradient tensor, As this is happen in the simulation conducted. However the accuracy of this method is very dependent on distances between sampling stations and by reducing distance between the stations, the accuracy of proposed method will be increased. The numerical results of this study also showed that the proposed method can provide accurately estimate of GRAVITY gradient tensor components In some stations surrounded by suitable spatial distribution of gravitational observations.