Exactly solvable models through the generalized empty interval method, for multi-species interactions

Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for $E^{\mathbf a}_n(t)$'s, the expectation value of the product of certain linear combination of the number operators on $n$ consecutive sites at time $t$. The constraints are solved for the single-species left-right-symmetric systems. Also, examples of multi-species system for which the evolution equations of $E^{\mathbf a}_n(t)$'s are closed, are given.Comment: 18 pages, LaTeX2e, no figure

Annihilation-diffusion processes: an exactly solvable model

A family of diffusion-annihilation processes is introduced, which is exactly solvable. This family contains parameters that control the diffusion- and annihilation- rates. The solution is based on the Bethe ansatz and using special boundary conditions to represent the reaction. The processes are investigated, both on the lattice and on the continuum. Special cases of this family of processes are the simple exclusion process and the drop-push model.Comment: 11 pages, LaTe

An Immediate Death by Seat Belt Compression; a Forensic Medicine Report

Although death is a gradual process, sometimes sudden death occurs in a fraction of a minute or seconds. Here we report a 49-year-old man without any underlying disease, which has instantly died in an accident scene due to compression of neck critical elements by a three-point seat belt. The examination of the body and the results of the autopsy, toxicology and pathology tests are described from the viewpoint of forensic medicine

On the phase structure of two--dimensional generalized Yang--Mills theories

The phase structure of the generalized Yang--Mills theories is studied, and it is shown that {\it almost} always, it is of the third order. As a specific example, it is shown that all of the models with the interaction $\sum_j (n_j-j+N)^{2k}$ exhibit third order phase transition. ($n_j$ is the length of the $j$-th row of the Yang tableau corresponding to U($N$).) The special cases where the transition is not of the third order are also considered and, as a specific example, it is shown that the model $\sum_j (n_j-j+N)^2+g\sum_j (n_j-j+N)^{4}$ exhibits a third order phase transition, except for $g=27\pi^2/256$, where the order of the transition is 5/2.Comment: 14 pages, LaTex, one paragraph is added to introduction section, to describe the 5/2 phase transition, accepted for publication in Nucl. Phys. B (2001

Sequential importance sampling for estimating expectations over the space of perfect matchings

This paper makes three contributions to estimating the number of perfect matching in bipartite graphs. First, we prove that the popular sequential importance sampling algorithm works in polynomial time for dense bipartite graphs. More carefully, our algorithm gives a $(1-\epsilon)$-approximation for the number of perfect matchings of a $\lambda$-dense bipartite graph, using $O(n^{\frac{1-2\lambda}{8\lambda}+\epsilon^{-2}})$ samples. With size $n$ on each side and for $\frac{1}{2}>\lambda>0$, a $\lambda$-dense bipartite graph has all degrees greater than $(\lambda+\frac{1}{2})n$. Second, practical applications of the algorithm requires many calls to matching algorithms. A novel preprocessing step is provided which makes significant improvements. Third, three applications are provided. The first is for counting Latin squares, the second is a practical way of computing the greedy algorithm for a card guessing game with feedback, and the third is for stochastic block models. In all three examples, sequential importance sampling allows treating practical problems of reasonably large sizes

A Review of Common Problems in Design and Installation of Water Spray Cooling and Low Expansion Foam System to Protect Storage Tanks Containing Hydrocarbons Against Fires

Tank fires are rare but carry significant potential risk to life and property. For this reason fire protection of tanks is critical. Fixed Low expansion foam and water spray cooling systems are one of the most effective and economical ways to reduce damages to a tank from fire. Such systems are currently installed in many companies but are not effective enough and require involvement of firefighters which in turn threaten their lives. This paper studies in a systematic way the problems of foam and cooling systems currently installed in a few domestic companies which operate storage tanks with focus on floating and fixed roof atmospheric tanks containing hydrocarbons and offers possible solutions for more efficient installation, design and operation of such systems

On the solvable multi-species reaction-diffusion processes

A family of one-dimensional multi-species reaction-diffusion processes on a lattice is introduced. It is shown that these processes are exactly solvable, provided a nonspectral matrix equation is satisfied. Some general remarks on the solutions to this equation, and some special solutions are given. The large-time behavior of the conditional probabilities of such systems are also investigated.Comment: 13 pages, LaTeX2

Exactly solvable models through the generalized empty interval method: multi-species and more-than-two-site interactions

Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for $E^{\mathbf a}_n(t)$'s, the expectation value of the product of certain linear combination of the number operators on $n$ consecutive sites at time $t$.Comment: 10 pages, LaTe

Spin 0 and spin 1/2 particles in a spherically symmetric static gravity and a Coulomb field

A relativistic particle in an attractive Coulomb field as well as a static and spherically symmetric gravitational field is studied. The gravitational field is treated perturbatively and the energy levels are obtained for both spin 0 (Klein-Gordon) and spin 1/2 (Dirac) particles. The results are shown to coincide with each other as well as the result of the nonrelativistic (Schrodinger) equation in the nonrelativistic limit.Comment: 12 page

Diagnostic Accuracy of Ultrasonography and Radiography in Initial Evaluation of Chest Trauma Patients

Introduction: Application of chest radiography for all multiple trauma patients is associated with a significant increase in total costs, exposure to radiation, and overcrowding of the emergency department. Ultrasound has been introduced as an alternative diagnostic tool in this regard. The aim of the present study is to compare the diagnostic accuracy of chest ultrasonography and radiography in detection of traumatic intrathoracic injuries. Methods: In the present prospective cross-sectional study, patients with traumatic intrathoracic injuries, who were referred to the emergency department from December 2013 to December 2014, were assessed. The patients underwent bedside ultrasound, radiographic and computed tomography (CT) scan examinations based on ATLS recommendations. Screening performance characteristics of ultrasonography and radiography were compared using SPSS 21.0. Chest CT scan was considered as gold standard. Results: 152 chest trauma patients with a mean age of 31.4 ± 13.8 years (range: 4 ‒ 67), were enrolled (77.6% male). Chest CT scan showed pulmonary contusion in 48 (31.6%) patients, hemothorax in 29 (19.1%), and pneumothorax in 55 (36.2%) cases. Area under the ROC curve of ultrasonography in detection of pneumothorax, hemothorax, and pulmonary contusion were 0.91 (95% CI: 0.86‒0.96), 0.86 (95% CI: 0.78‒0.94), and 0.80 (95% CI: 0.736‒0.88), respectively. Area under the ROC curve of radiography was 0.80 (95% CI: 0.736‒0.87) for detection of pneumothorax, 0.77 (95% CI: 0.68‒0.86) for hemothorax, and 0.58 (95% CI: 0.5‒0.67) for pulmonary contusion. Comparison of areas under the ROC curve declared the significant superiority of ultrasonography in detection of pneumothorax (p = 0.02) and pulmonary contusion (p < 0.001). However, the diagnostic value of the two tests was equal in detection of hemothorax (p = 0.08). Conclusion: The results of the present study showed that ultrasonography is preferable to radiography in the initial evaluation of patients with traumatic injuries to the thoracic cavity