Nonlinearity Management in Higher Dimensions

In the present short communication, we revisit nonlinearity management of the time-periodic nonlinear Schrodinger equation and the related averaging procedure. We prove that the averaged nonlinear Schrodinger equation does not support the blow-up of solutions in higher dimensions, independently of the strength in the nonlinearity coefficient variance. This conclusion agrees with earlier works in the case of strong nonlinearity management but contradicts those in the case of weak nonlinearity management. The apparent discrepancy is explained by the divergence of the averaging procedure in the limit of weak nonlinearity management.Comment: 9 pages, 1 figure

Natural population movement and COVID-19: data from Russia

The COVID-19 pandemic is highly infectious, so it paralyzed the health systems of many countries causing a high mortality rate. Official data on COVID-19 deaths at many sites are questioned, and the figures are considered several times higher than official data. In this sense, the objective of the study was to determine the impact of the COVID-19 pandemic on the natural movement of the population and, in addition, to evaluate the real mortality rate from COVID-19 in Russia from the construction of predictive mortality models. The study used data from the World Health Organization and the Statistical Service of the Federal State of Russia; se used linear and polynomial models to construct mortality models. The study revealed an underestimation of the official COVID-19 death rate by 2.4 to 6.8 times, depending on the data source. There was a sharp increase in mortality in Russia in 2020 among people over 50 years of age, and with the increase in age, mortality increased. The main reasons for the sharp increase in mortality were coronary heart disease, cerebrovascular diseases, and respiratory diseases, among others

Fast atomic transport without vibrational heating

We use the dynamical invariants associated with the Hamiltonian of an atom in a one dimensional moving trap to inverse engineer the trap motion and perform fast atomic transport without final vibrational heating. The atom is driven non-adiabatically through a shortcut to the result of adiabatic, slow trap motion. For harmonic potentials this only requires designing appropriate trap trajectories, whereas perfect transport in anharmonic traps may be achieved by applying an extra field to compensate the forces in the rest frame of the trap. The results can be extended to atom stopping or launching. The limitations due to geometrical constraints, energies and accelerations involved are analyzed, as well as the relation to previous approaches (based on classical trajectories or "fast-forward" and "bang-bang" methods) which can be integrated in the invariant-based framework.Comment: 10 pages, 5 figure

New Data on the Anomalies of Tailless Amphibians of the Volga Basin

This paper presents new findings on abnormal specimens of amphibians in the Volga basin. Some anomalies have been noted for the first time: macrophthalmia, eardrum anomalies in marsh frogs (P. ridibundus), the absence of a tympanic membrane in green toads and ectromelia in spadefoot Pallas samples (P. vespertinus)

Enchanced preoperative rehabilitation as part of the complex perioperative rehabilitation of patients with super-obesity and obstructive sleep apnea syndrome (clinical outlook)

Obesity is a global social and economic problem. The bariatric surgery is a most effective treatment for obesity. The presented clinical case demonstrates the usage of principles of enchanced perioperative rehabilitation for the preoperative preparation of a patient with super obesity and with severe obstructive sleep apnea and alveolar hypoventilation syndrome.A 54-year-old patient was hospitalized with complaints of obesity, impossibility of persistent weight loss conservatively, severe daytime sleepiness, frequent nocturnal awakenings (up to 8 times per night). The patient’s weight was 230 kg with a height of 157 cm (BMI 93.5 kg / m2). The examination revealed a syndrome of sleep apnea of mixed genesis of extremely severe degree, chronic night hypoxemia of an extremely severe degree. Preoperative preparation was performed in accordance with the program of enchanced perioperative rehabilitation. The duration of preoperative preparation was 19 days; weight loss — 40 kg (%WL -17,4), compensation of comorbidities was achieved as well. After that the patient underwent a laparoscopic sleeve gastrectomy. There were no complications in the postoperative period. Length of postoperative hospital stay was 6 days. At follow-up examination one year after surgery, body weight dropped from 230 to 153 kg (% WL-33.5), a significant improvement of the quality of life was achieved.The enchanced perioperative rehabilitation program can be successfully used as an effective method for preoperartive preparation of the patients with morbid obesity in combination with severe obstructive sleep apnea syndrome.and obesity hypoventilation. It can be a reasonable alternative to the standard program with preoperative intragastric balloon treatment. The use of this technique allows to increase the effectiveness of treatment of these high-risk patients, as well as to reduce the risk of perioperative complications

Comorbidity of tics and epilepsy in children and adolescents

Tics are the most common forms of hyperkinesis among children and adolescents, the etiology of which is not fully clear. A study has shown a high comorbidity of tic disorders and epilepsy, as evidenced by video-EEG monitoring. In patients with tics even in the absence of epileptic seizures, epileptiform activity is an adverse predictor and a determinant of the potential risk of comorbid epilepsy especially during neuroleptic therapy. Antiepileptic drugs are the drugs of choice to treat this category of patients

Lie symmetries for two-dimensional charged particle motion

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The associated electromagnetic fields satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding four classes of electromagnetic fields compatible with Lie point symmetries

Generalized Hamiltonian structures for Ermakov systems

We construct Poisson structures for Ermakov systems, using the Ermakov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations, the existence of Casimir functions can give rise to superintegrable Ermakov systems. Finally, we characterize the cases where linearization of the equations of motion is possible