Microscopic picture of the entrance hole of gunshot wounds

Forensic medical examination should always be based on incontestable provisions, proven by appropriate scientific development. In some cases, the scientific development of individual issues available to date turns out to be insufficient and we have to look for new evidence that will facilitate the exact resolution of the questions posed to the examination. This is the position now on the issue of gunshot injuries.

A note on super Koszul complex and the Berezinian

We construct the super Koszul complex of a free supercommutative A-module V of rank p|q and prove that its homology is concentrated in a single degree and it yields an exact resolution of A. We then study the dual of the super Koszul complex and show that its homology is concentrated in a single degree as well and isomorphic to $$\Pi ^{p+q} A$$ Π p + q A , with $$\Pi $$ Π the parity changing functor. Finally, we show that, given an automorphism of V, the induced transformation on the only non-trivial homology class of the dual of the super Koszul complex is given by the multiplication by the Berezinian of the automorphism, thus relating this homology group with the Berezinian module of V.

A NOVEL ANALYTIC METHOD FOR SOLVING LINEAR AND NON-LINEAR TELEGRAPH EQUATION

The modeling of many phenomena in various fields such as mathematics, physics, chemistry, engineering, biology, and astronomy is done by the nonlinear partial differential equations (PDE). The hyperbolic telegraph equation is one of them, where it describes the vibrations of structures (e.g., buildings, beams, and machines) and are the basis for fundamental equations of atomic physics. There are several analytical and numerical methods are used to solve the telegraph equation. An analytical solution considers framing the problem in a well-understood form and calculating the exact resolution. It also helps to understand the answers to the problem in terms of accuracy and convergence. These analytic methods have limitations with accuracy and convergence. Therefore, a novel analytic approximate method is proposed to deal with constraints in this paper. This method uses the Taylors' series in its derivation. The proposed method has used for solving the secondorder, hyperbolic equation (Telegraph equation) with the initial condition. Three examples have presented to check the effectiveness, accuracy, and convergence of the method. The solutions of the proposed method also compared with those obtained by the Adomian decomposition method (ADM), and the Homotopy analysis method (HAM). The technique is easy to implement and produces accurate results. In particular, these results display that the proposed method is efficient and better than the other methods in terms of accuracy and convergence.

Exact resolution function for double-disk chopper neutron time-of-flight spectrometers: application to reflectivity

The exact resolution function of the transfer vector for the HERMÈS reflectometer at the Laboratoire Léon Brillouin is calculated as an example of a neutron time-of-flight spectrometer with a double-disk chopper. The calculation accounts for the wavelength distribution of the incident beam, the tilt of the chopper axis, collimation and gravity, without an assumption of Gaussian distributions or the independence of these different contributions. A numerical implementation is provided. It is shown that data fitting using this exact resolution function allows much better results to be reached than with the usual approximation by a Gaussian profile.

An Integer Linear Programming Model to Select and Temporally Allocate Resources for Fighting Forest Fires

Optimal planning of the amount and type of resources needed for extinguishing a forest fire is a task that has been addressed in the literature, using models obtained from operational research. In this study, a general integer linear programming model is proposed, which addresses the allocation of resources in different time periods during the planning period for extinguishing a fire, and with the goal of meeting Spanish regulations for the non-negligence of fronts and periods of rest for pilots and brigades. A computer program and interface were developed using the R language. By means of an example using historical data, we illustrate the model at work and its exact resolution. Then, we carry out a simulation study to analyze the obtained objective functions and resolution times. Our simulation study shows that an exact solution can be obtained very quickly without requiring heuristic algorithms, provided that the planning period does not exceed five hours.

The capacitated m two node survivable star problem

In this paper, we address the problem of network design with redundant connections, often faced by operators of telephone and internet services. The network connects customers with one master node and is built by taking into account the rules that shape its construction, such as number of customers, number of components and types of links, in order to meet operational needs and technical constraints. We propose a combinatorial optimization problem called CmTNSSP (Capacitated m Two-Node-Survivable Star Problem), a relaxation of CmRSP (Capacitated m Ring Star Problem). In this variant of CmRSP, the rings are not constrained to be cycles; instead, they can be two-node connected components. The contributions of this paper are: (a) the introduction and definition of a new problem, (b) the specification of a mathematical programming model of the problem to be treated, and (c) the approximate resolution thereof through a GRASP metaheuristic, which alternates local searches that obtain incrementally better solutions, and exact resolution local searches based on mathematical programming models, particularly Integer Linear Programming ones. Computational results obtained by the developed algorithms show robustness and competitiveness when compared to results of the literature relative to benchmark instances. Likewise, the experiments show the relevance of considering the specific variant of the problem studied in this work.