In this paper, we propose some new preconditioners  for solving multilinear system $\mathcal{A}\mathbf{x}^{m-1}=\mathbf{b}$. These preconditioners are based on tensor splitting. We also present some theorems for analyzing and convergence of the preconditioned  Jacobi-, Gauss-Seidel-, and SOR-type iterative methods. Numerical examples are presented to verify the efficiency of the proposed preconditioned methods.

Fee splitting, a clear manifestation of physician's breaching patient' s rights, is the breach of the principle known asbona fide with regard to the patient and the dominance of physician's financial interest on facilitation of treatment process. Yet a question is posed: Can physician's abusing patient's trust or lacks of information, whose manifestation can be observed in fee splitting, justify the necessity of criminalizing fee splitting? In fact, the point of argument is to criminalize or decriminalize fee splitting. Some patients have exposed to high cost of treatment without any medical necessity. Accordingly, the authors of this writing try to identify the necessity of providing criminal protection for this group of patients through studying the arguments posed by advocates of fee splitting and those posed by opponents. This writing then deals with constituent elements of fee splitting and studies necessary principles and features to commit this crime from the viewpoint of teachings of medical criminal law.

During the past years, one of the most important problems has been air pollution in urban areas. In this regard, ozone, as one of the major products of photochemical reactions, has great importance. The term "photochemical" is applied to a number of secohdary pollutants that appear as a result of sun-related reactions, ozone being the most important one. So far various models have been suggested to predict these pollutants. In this paper, we developed the model that has been introduced by Dabir, et al. [4]. In this model model than 48 chemical species and 114 chemical reactions are involved. The resluts of this development, showed good to excellent agreement across the region for coni pounds such as O3, NO, NO2, CO, and SO2 with regard to VOC and NMHC. The results of the simulation were compared with previous work [4] and the effects of increashlg the number of componets and reactions were evaluated. The results of the operator splitting method were compared witll non splitting solving method. The result showed that splitting method with one-tenth time step collapsed with non splitting method (Crank-Nicolson, under-relaxation.iteration method without splitting of the equation terms). Then we developed One dimensional model to 3-D and results were compared witll experimental data.

Given a binary matroid M and a subset T  E(M), Luis A. Goddyn posed a problem that the dual of the splitting of M, i. e., ((MT ) ∗ ) is not always equal to the splitting of the dual of M, ((M ∗ )T ). This persuade us to ask if we can characterize those binary matroids for which (MT ) ∗ = (M ∗ )T. Santosh B. Dhotre answered this question for a two-element subset T. In this paper, we generalize his result for any subset T  E(M) and exhibit a criterion for a binary matroid M and subsets T for which (MT ) ∗ and (M ∗ )T are the equal. We also show that there is no subset T  E(M) for which, the dual of element splitting of M, i. e., ((M ′ T ) ∗ ) equals to the element splitting of the dual of M, ((M ∗ ) ′ T ).

In this study, different methods for shell splitting and the effect of freezing prior to drying on shell splitting percentage of pistachio were investigated. A completely randomized design was used to investigate the effects of different freezing temperatures (0, -6, -12 and -18°C), different drying temperatures (80, 90 and 100°C) and different cultivars (Akbari and Kalehghouchi) on shell splitting percentages. The results showed that both freezing and drying temperature significantly (p £ 0.05) affected the splitting of closed shells into open shells. The effect of cultivar was insignificant. The highest shell splitting percentage (16.56%) was observed with a freezing temperature of -18°C and when a drying temperature of 100°C was used. Freezing and drying temperatures did not significantly increase the number of isolated kernels. However, in most treatments, isolated kernels were observed. Despite the isolated kernels, The shell splitting percentage did not decrease in any of the treatment groups. The results showed that freezing prior to drying can increase the percentage of split pistachio nuts. Thus, by increasing the difference between the temperature of the freezing and the temperature of drying, the percentage of split pistachio increased.

In this paper, some monotonicity-preserving (MP) and positivity-preserving (PP) splitting methods for solving the balance laws of the reaction and diffusion source terms are investigated. To capture the solution with high accuracy and resolution, the original equation with reaction source termis separated through the splitting method into two sub-problems including the homogeneous conservation law and a simple ordinary differential equation (ODE). The resulting splitting methods preserve monotonicity and positivity property for a normal CFL condition. A trenchant numerical analysis made it clear that the computing time of the proposed methods decreases when the so-called MP process for the homogeneous conservation law is imposed. Moreover, the proposed methods are successful in recapturing the solution of the problem with high-resolution in the case of both smooth and non-smooth initial profiles. To show the efficiency of proposed methods and to verify the order of convergence and capability of these methods, several numerical experiments are performed through some prototype examples.