The neoclassical growth model is tested by use of panel data procedure in this research. In the econometric test, simoultanously time series and cross detection will be compared on the basis of panel data method through which their observed points increase and consequently the estimation efficiency will be increased. The examination of neoclassical growth theory has been done with reference to external & internal factors of 52 selected countries from 1960 to 2000. The independent variable of model has been selected on the basis of the result of previous research which explains the result in three separate models: developed countries, developing countries, and whole countries. These factors are such as: Gross National Products with lag of period, work force age, growth rate, education level, the change of capital accumulation and economic trade volum. The consequences of this research is that: neoclassical growth model can explain the major part of economic growth of the countries with use of internal variables. Also with the use of panel procedure of fixed effect, we can see the fundamental differences and structure of the growth process for different countries; and show how the economic, and social conditions affect on the growth.

Inversion method is very common in the interpretation of practical gravity data. The goal of 3D inversion is to estimate density distribution of an unknown subsurface model from a set of known gravity observations measured on the surface. The regularization parameter is one of the effective parameters for obtaining optimal model in inversion of the gravity data for similar inversion of other geophysical data. For estimation of the optimum regularization parameter the statistical criterion of Akaike’ s Bayesian Information Criterion (ABIC) usually used. This parameter is experimentally estimated in most inversion methods. The choice of the regularization parameter, which balances the minimization of the data misfit and model roughness, may be a critical procedure to achieve both resolution and stability. In this paper the Active Constraint balancing (ACB) as a new method is used for estimating the regularization parameter in two-dimensional (2-D) inversion of gravity data. This technique is supported by smoothness-constrained least-squares inversion. We call this procedure “ active constraint balancing” (ACB). Introducing the Lagrangian multiplier as a spatially-dependent variable in the regularization term, we can balance the regularizations used in the inversion. Spatially varying Lagrangian multipliers (regularization parameters) are obtained by a parameter resolution matrix and Backus-Gilbert spread function analysis. For estimation of regularization parameter by ACB method use must computed the resolution matrix R. The parameter resolution matrix R can be obtained in the inversion process with pseudo-inverse G􀬾 multiplied by the kernel G. 􀜴 = 􀜩 􀬾 􀜩 (1) The spread function, which accounts for the inherent degree of how much the ith model parameter is not resolvable, defined as: 􀜵 􀜲 􀯜 = Σ 􀵫 􀝓 􀯜 􀯝 􀵫 1 − 􀝏 􀯜 􀯝 􀵯 􀜴 􀯜 􀯝 􀯇 􀵯 􀬶 􀯝 􀭀 􀬵 (2) where M is the total number of inversion parameters, 􀝓 􀯜 􀯝 is a weighting factor defined by the spatial distance between the ith and jth model parameters, and 􀝏 􀯜 􀯝 is a factor which accounts for whether the constraint or regularization is imposed on the ith parameter and its neighboring parameters. In other words, the spread function defined here is the sum of the squared spatially weighted spread of the ith model parameter with respect to all of the model parameters excluding ones upon which a smoothness constraint is imposed. In this approach, the regularization parameter λ (x, z) is set by a value from log-linear interpolation. log􁈺 λ 􀭧 􁈻 = log􁈺 λ 􀭫 􀭧 􀭬 􁈻 + 􀭪 􀭭 􀭥 􁈺 􀮛 􀱣 􀱗 􀱮 􁈻 􀬿 􀭪 􀭭 􀭥 􁈺 􀮛 􀱣 􀱟 􀱤 􁈻 􀭪 􀭭 􀭥 􁈺 􀭗 􀭔 􀱣 􀱗 􀱮 􁈻 􀬿 􀭪 􀭭 􀭥 􁈺 􀭗 􀭔 􀱣 􀱟 􀱤 􁈻 × 􁈼 log􁈺 SP􀭧 􁈻 − log􁈺 SP􀭫 􀭧 􀭬 􁈻 􁈽 (3) where 􀜵 􀜲 􀯠 􀯜 􀯡 and 􀜵 􀜲 􀯠 􀯔 􀯫 are the minimum and maximum values of spread function 􀜵 􀜲 􀯜 , respectively, and the 􀟣 􀯠 􀯜 􀯡 and 􀟣 􀯠 􀯔 􀯫 are minimum and maximum values of the regularization parameter λ (x, z), which must be provided by the user. With this method, we can automatically set a smaller value λ (x, z) of the regularization parameter to the highly resolvable model parameter, which corresponds to a smaller value of the spread function SP􀭧 in the inversion process and vice versa. Users can choose these minimum and maximum regularization parameters by setting variables LambdaMin and LambdaMax. For getting the target an algorithm is developed that estimates this parameter. The validity of the proposed algorithm has been evaluated by gravity data acquired from a synthetic model. Then the algorithm used for inversion of real gravity data from Matanzas Cr deposit. The result obtained from 2D inversion of gravity data from this mine shows that this algorithm can provide good estimates of density anomalous structures within the subsurface.

Assembly Line production is one of the widely used basic principles in production system. The problem of Assembly Line balancing deals with the distribution of activities among the workstations so that there will be maximum utilization of human resources and facilities without disturbing the work sequence. Research works reported in the literature mainly deals with minimization of idle time i.e. balancing, subject to precedence constraints. Lack of uniqueness in their optimum solutions has led to the present work where minimization of both balancing loss and system loss has been envisaged under the usual precedence constraints. The researchers suggest a generic approach for designing of an assembly line where, with a given number of workstations, one can efficiently arrive at the desired solution under different methods of search like simulation, heuristic etc. Thus, the main aim of this paper is to redefine the objective of the Assembly Line balancing Problem and sequentially handle balancing Loss and System Loss. A numerical example has been added to demonstrate the generic nature of the researcher's approach and improvement in the solution set when compared with different standard line balancing methods available so far in the literature.

Gravity data inversion is one of the important steps in the interpretation of practical gravity data. The inversion result can be obtained by minimization of the Tikhonov objective function. The determination of an optimal regularization parameter is highly important in the gravity data inversion. In this work, an attempt was made to use the active constrain balancing (ACB) method to select the best regularization parameter for a 3D inversion of the gravity data using the Lanczos bidiagonalization (LSQR) algorithm. In order to achieve this goal, an algorithm was developed to estimate this parameter. The validity of the proposed algorithm was evaluated by the gravity data acquired from a synthetic model. The results of the synthetic data confirmed the correct performance of the proposed algorithm. The results of the 3D gravity data inversion from this chromite deposit from Cuba showed that the LSQR algorithm could provide an adequate estimate of the density and geometry of sub-surface structures of mineral deposits. A comparison of the inversion results with the geologic information clearly indicated that the proposed algorithm could be used for the 3D gravity data inversion to estimate precisely the density and geometry of ore bodies. All the programs used in this work were provided in the MATLAB software environment.

The main goal of this paper is to develop a new generalization of balancing and Lucas-balancing sequences namely balancing and Lucas-balancing p-numbers and derive several identities related to them. Some combinatorial forms of these numbers are also presented.

Todays gamma knife radiosurgery is used widely for treatment of very small brain tumors. In order to investigate accuracy of dosimetry and treatment planning calculations, using Monte Carlo simulation with dedicated code named as beamnrc including non-CT data and CT data options is necessary. The aim of this study is choosing the best options in order to have an accurate tools based on their advantages and disadvantages. In this study, gamma knife unit 4C along with standard water equivalent phantom and EBT3 films were used to obtain dose distributions. Monte Carlo simulation was done with non-CT data and CT data options of the code and their resulting dose were compared. Comparison the calculated and measured dose distributions at X, Y and Z axis showed gamma value below 1 which verified Monte Carlo simulations. Also comparing the dose distributions from both non-CT data and CT data with each other implies that there is no significant difference between two methods. Based on the obtained results using non-CT data and CT data results in the same dose distribution. So for simplicity, using non CT data for regular phantom shapes is preferred.