Most of underground structures are designed and built to withstand the effects of precision penetrating weapons and heavy bombs in the soil. Usually the depth of the structures is high and there is no possibility of missiles to the main structure. Accordingly, the design of these structures is performed for blast loads. The explosion phenomenon is a type of high strain rate problem that requires dynamic analysis to solve. Also, due to the interaction between underground structures and soil, the analysis of these structures is affected by any type of nonlinear analysis. Thus, the analysis of underground structures in simulations affected by the explosion is a high strain rate problem that requires nonlinear dynamic analysis. There are two implicit and explicit solutions to dynamic analysis that, given the explosion problems, their analysis is explicitly integral. The loading of underground structures is often based on the relationships obtained from theoretical and experimental research. Currently, the most important reference for explosive loading in the field of underground structures is the US code (TM5-855-1) provided by the US army. The numerical simulation methods have recently been widely used as a novel method in the calculation of nonlinear dynamic loads. According to the researchers, among the explicit software available in AUTODYN software, due to its ability to solve very high strain rate problems, it yields good results from simulation and explosion problem analysis. On the other hand, the explosive loading of underground structures is often based on theoretical and empirical research. In this study, a numerical simulation method was used to analyze and simulate the effect of the surface explosion on the underground structure. Also, all the simulation steps were performed using AUTODYN hydrocode. In order to analyze the loading and response of underground structures, the effect of the explosive charge weight and the depth of burial of the structure has been studied and the numerical results have been compared with the relationships presented in reliable US scientific and guidance sources. Finally, suggestions are made to improve the loading of these structures. Also, considering the results of the load on the roof of the structure, it was observed that the values of the US code are conservative compared to the other two methods. Therefore, it is recommended not to apply 1. 5 incremental coeficient load to the structure in accordance with this instruction. The numerical simulation results including a comparison of maximum pressure and the velocity values with the values provided in the by code (TM5-855-1) showed that the predicted values for the maximum pressure values larger than of instructions America's Army. The reason for this is that the code assumes that the investigations take place in the full explosion range (mating coefficient f = 1), while in the numerical model under consideration, the explosion is formed at the joint surface of air and soil. Hence the coupling coefficient is equal to (f = 0. 4). In other words, the depth of the explosive charge is almost zero and there is little difference between the results.

For this reason and in order to be registered in the medical sources of the world, we plan to register this new type of terrorism injury in the medical sources of the world under the title “pager explosion trauma" or “pager trauma”. We invite all our colleagues in all countries and especially in Lebanon to publish their articles about the characters of this injury.Based on field observations and expert opinions, it seems that these injuries will cause lifelong disability, and this is a terrible tragedy that needs international response, and these injured patient need urgent specialized treatment at this stage and should be treated in the future.Publishing of experiences and treatments modalities about this injury will help physicians to give better medical services.

In this paper, we consider statistics on permutations of lengthn represented geometrically as bargraphs having the same number of horizontal steps. More precisely, we nd the joint distribution of the descent and up step statistics on the bargraph representations, thereby obtaining a new rened count of permutations of a given length. To do so, we consider the distribution of the parameters on permutations of a more general multiset of which Sn is a subset. In addition to nding an explicit formula for the joint distribution on this multiset, we provide counts for the total number of descents and up steps of all its members, supplying both algebraic and combinatorial proofs. Finally, we derive explicit expressions for the sign balance of these statistics, from which the comparable results on permutations follow as special cases.

In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite Hamiltonian group.

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