Spectrum of the Relativistic Particles in Various Potentials

We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a Schr\"{o}dinger-like equation. For the exactly solvable potentials, eigenvalues are calculated and eigenfunctions are given by confluent hypergeometric functions. It is shown that, our formulation also leads to the study of those potentials in the framework of the supersymmetric quantum mechanics

Effects of Vacuum Polarization in Strong Magnetic Fields with an Allowance Made for the Anomalous Magnetic Moments of Particles

Given the anomalous magnetic moments of electrons and positrons in the one-loop approximation, we calculate the exact Lagrangian of an intense constant magnetic field that replaces the Heisenberg-Euler Lagrangian in traditional quantum electrodynamics (QED). We have established that the derived generalization of the Lagrangian is real for arbitrary magnetic fields. In a weak field, the calculated Lagrangian matches the standard Heisenberg-Euler formula. In extremely strong fields, the field dependence of the Lagrangian completely disappears, and the Lagrangian tends to a constant determined by the anomalous magnetic moments of the particles.Comment: 19 pages, 3 figure

Anisotropic Pressures in Very Dense Magnetized Matter

The problem of anisotropic pressures arising as a consequence of the spatial symmetry breaking introduced by an external magnetic field in quantum systems is discussed. The role of the conservation of energy and momentum of external fields as well as of systems providing boundary conditions in quantum statistics is considered. The vanishing of the average transverse momentum for an electron-positron system in its Landau ground state is shown, which means the vanishing of its transverse pressure. The situation for neutron case and Strange Quark Matter (SQM) in $\beta$-equilibrium is also briefly discussed. Thermodynamical relations in external fields as well as the form of the stress tensor in a quantum relativistic medium are also discussed. The ferromagnetic symmetry breaking is briefly discussed.Comment: 10 page

Трехъярусное внесение удобрений тукопроводом-распределителем глубокорыхлителя

The authors have shown that current methods of soil fertilizing for growing cotton crops in Uzbekistan do not ensure the full supply of nutrients to the root system of plants. Providing the required amount of fertilizers is distributed in tiers in the zone of root development, the ratio of their use and cotton yield will increase. (Research purpose) To determine the design parameters of a spreading funnel of a subsoil tiller for three-tiered fertilizer application. (Materials and methods) The paper provides a design of the developed spreading funnel for three-tier fertilizer application. A subsoil tiller is equipped with a spreading funnel, which consists of a cylindrical and inclined funnel-shaped part, a conductive channel and a lower distributor. Installed in the conductive channel are two branch pipes with reflective plates that cut through the supplied fertilizers and direct them to the corresponding soil horizon. (Results and discussion) The authors have studied the movement of mineral fertilizer granules along the conductive channel; experimentally analyzed the effect of the length of the protruding part of reflective plates of the nozzle and the inclination angle of the funnel spreading pipeline on the distribution of fertilizers and the unevenness of fertilizer supply to the upper, middle and lower tiers. They have also determined the parameters of an intake funnel of the vertical pipeline, branch pipes and movable plates of the upper and middle tiers, and a fertilizer spreader of the lower tier. (Conclusions) The authors have proved that the qualitative distribution of mineral fertilizers at predetermined application depths of the upper and middle tiers is ensured at a length of their nozzles of 260 and 240 millimeters and the protruding part of the reflective plates of the fertilizer channel of 26-30 millimeters and 33-37 millimeters, respectively. At the same time, 40-45 percent of fertilizers is distributed in the lower, i.e. the third tier. The authors have chosen optimal parameters of the lower spreading funnel: a groove inclination angle in the longitudinal-vertical plane of 17-19 degrees; a groove inclination angle in the transverse vertical plane of 29 degrees; a rear edge height of the groove in the middle part of 2.5 millimeters, and at the end – 0.5 millimeters.Показали, что применяемые способы внесения удобрений под хлопчатник в Узбекистане не обеспечивают в полной мере поступление питательных веществ в корневую систему растения. Если распределить удобрения в зоне развития корней ярусно и в нужном соотношении, то коэффициент их использования повышается, увеличивается урожайность хлопчатника. (Цель исследования) Обосновать конструктивные параметры тукопровода-распределителя глубокорыхлителя для трехъярусного внесения удобрений. (Материалы и методы) Представили конструкцию разработанного тукопровода-распределителя для трехъярусного внесения удобрений. Глубокорыхлитель снабдили тукопроводом-распределителем, который состоит из цилиндрической и наклонной воронкообразной части, тукопроводящего канала и нижнего распределителя туков. В тукопроводящем канале установили два патрубка с отражательными пластинами, которые рассекают движущиеся удобрения и направляют их в соответствующий горизонт почвы. (Результаты и обсуждение) Исследовали движение гранул минеральных удобрений по тукопроводящему каналу. Изучили влияние длины выступающей части отражательных пластин патрубков и угла наклона воронки тукопровода-распределителя на распределение удобрений и на неравномерность поступления удобрений в верхний, средний и нижний ярусы. Рассчитали параметры загрузной воронки вертикального тукопровода, патрубков и подвижных пластин верхнего и среднего ярусов, рассеивателя удобрений нижнего яруса. (Выводы) Доказали, что качественное распределение минеральных удобрений на заданных глубинах внесения верхнего и среднего ярусов обеспечивается при длине их патрубков 260 и 240 миллиметров и выступающей части отражательных пластин тукопроводящего канала 26-30 миллиметров и 33-37 миллиметров соответственно. При этом 40-45 процентов удобрений распределяется в нижний, то есть третий ярус. Выбрали рациональные параметры нижнего рассеивателя удобрений: угол наклона желобка в продольно-вертикальной плоскости – 17-19 градусов; угол наклона желобка в поперечно-вертикальной плоскости – 29 градусов; высота заднего обреза желобка в средней части – 2,5 миллиметра, в конце – 0,5 миллиметра

The Energy Level Shifts, Wave Functions and the Probability Current Distributions for the Bound Scalar and Spinor Particles Moving in a Uniform Magnetic Field

We discuss the equations for the bound one-active electron states based on the analytic solutions of the Schrodinger and Pauli equations for a uniform magnetic field and a single attractive $\delta({\bf r})$-potential. It is vary important that ground electron states in the magnetic field differ essentially from the analogous state of spin-0 particles, whose binding energy was intensively studied more than forty years ago. We show that binding energy equations for spin-1/2 particles can be obtained without using the language of boundary conditions in the $\delta$-potential model developed in pioneering works. We use the obtained equations to calculate the energy level displacements analytically and demonstrate nonlinear dependencies on field intensity. We show that the magnetic field indeed plays a stabilizing role in considered systems in a case of the weak intensity, but the opposite occurs in the case of strong intensity. These properties may be important for real quantum mechanical fermionic systems in two and three dimensions. We also analyze the exact solution of the Pauli equation for an electron moving in the potential field determined by the three-dimensional $\delta$-well in the presence of a strong magnetic field. We obtain asymptotic expressions for this solution for different values of the problem parameters. In addition, we consider electron probability currents and their dependence on the magnetic field. We show that including the spin in the framework of the nonrelativistic approach allows correctly taking the effect of the magnetic field on the electric current into account. The obtained dependencies of the current distribution, which is an experimentally observable quantity, can be manifested directly in scattering processes, for example.Comment: 31 pages, 10 figure

Magnetism in Dense Quark Matter

We review the mechanisms via which an external magnetic field can affect the ground state of cold and dense quark matter. In the absence of a magnetic field, at asymptotically high densities, cold quark matter is in the Color-Flavor-Locked (CFL) phase of color superconductivity characterized by three scales: the superconducting gap, the gluon Meissner mass, and the baryonic chemical potential. When an applied magnetic field becomes comparable with each of these scales, new phases and/or condensates may emerge. They include the magnetic CFL (MCFL) phase that becomes relevant for fields of the order of the gap scale; the paramagnetic CFL, important when the field is of the order of the Meissner mass, and a spin-one condensate associated to the magnetic moment of the Cooper pairs, significant at fields of the order of the chemical potential. We discuss the equation of state (EoS) of MCFL matter for a large range of field values and consider possible applications of the magnetic effects on dense quark matter to the astrophysics of compact stars.Comment: To appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

Magnetic Oscillations in Dense Cold Quark Matter with Four-Fermion Interactions

The phase structures of Nambu-Jona-Lasinio models with one or two flavours have been investigated at non-zero values of $\mu$ and $H$, where $H$ is an external magnetic field and $\mu$ is the chemical potential. In the phase portraits of both models there arise infinitely many massless chirally symmetric phases, as well as massive ones with spontaneously broken chiral invariance, reflecting the existence of infinitely many Landau levels. Phase transitions of first and second orders and a lot of tricritical points have been shown to exist in phase diagrams. In the massless case, such a phase structure leads unavoidably to the standard van Alphen-de Haas magnetic oscillations of some thermodynamical quantities, including magnetization, pressure and particle density. In the massive case we have found an oscillating behaviour not only for thermodynamical quantities, but also for a dynamical quantity as the quark mass. Besides, in this case we have non-standard, i.e. non-periodic, magnetic oscillations, since the frequency of oscillations is an $H$-dependent quantity.Comment: latex, 29 pages, 8 figure

Global, regional, and national burden of chronic kidney disease, 1990–2017 : a systematic analysis for the Global Burden of Disease Study 2017

Background Health system planning requires careful assessment of chronic kidney disease (CKD) epidemiology, but data for morbidity and mortality of this disease are scarce or non-existent in many countries. We estimated the global, regional, and national burden of CKD, as well as the burden of cardiovascular disease and gout attributable to impaired kidney function, for the Global Burden of Diseases, Injuries, and Risk Factors Study 2017. We use the term CKD to refer to the morbidity and mortality that can be directly attributed to all stages of CKD, and we use the term impaired kidney function to refer to the additional risk of CKD from cardiovascular disease and gout. Methods The main data sources we used were published literature, vital registration systems, end-stage kidney disease registries, and household surveys. Estimates of CKD burden were produced using a Cause of Death Ensemble model and a Bayesian meta-regression analytical tool, and included incidence, prevalence, years lived with disability, mortality, years of life lost, and disability-adjusted life-years (DALYs). A comparative risk assessment approach was used to estimate the proportion of cardiovascular diseases and gout burden attributable to impaired kidney function. Findings Globally, in 2017, 1·2 million (95% uncertainty interval [UI] 1·2 to 1·3) people died from CKD. The global all-age mortality rate from CKD increased 41·5% (95% UI 35·2 to 46·5) between 1990 and 2017, although there was no significant change in the age-standardised mortality rate (2·8%, −1·5 to 6·3). In 2017, 697·5 million (95% UI 649·2 to 752·0) cases of all-stage CKD were recorded, for a global prevalence of 9·1% (8·5 to 9·8). The global all-age prevalence of CKD increased 29·3% (95% UI 26·4 to 32·6) since 1990, whereas the age-standardised prevalence remained stable (1·2%, −1·1 to 3·5). CKD resulted in 35·8 million (95% UI 33·7 to 38·0) DALYs in 2017, with diabetic nephropathy accounting for almost a third of DALYs. Most of the burden of CKD was concentrated in the three lowest quintiles of Socio-demographic Index (SDI). In several regions, particularly Oceania, sub-Saharan Africa, and Latin America, the burden of CKD was much higher than expected for the level of development, whereas the disease burden in western, eastern, and central sub-Saharan Africa, east Asia, south Asia, central and eastern Europe, Australasia, and western Europe was lower than expected. 1·4 million (95% UI 1·2 to 1·6) cardiovascular disease-related deaths and 25·3 million (22·2 to 28·9) cardiovascular disease DALYs were attributable to impaired kidney function. Interpretation Kidney disease has a major effect on global health, both as a direct cause of global morbidity and mortality and as an important risk factor for cardiovascular disease. CKD is largely preventable and treatable and deserves greater attention in global health policy decision making, particularly in locations with low and middle SDI

Predicting the environmental suitability for onchocerciasis in Africa as an aid to elimination planning

Recent evidence suggests that, in some foci, elimination of onchocerciasis from Africa may be feasible with mass drug administration (MDA) of ivermectin. To achieve continental elimination of transmission, mapping surveys will need to be conducted across all implementation units (IUs) for which endemicity status is currently unknown. Using boosted regression tree models with optimised hyperparameter selection, we estimated environmental suitability for onchocerciasis at the 5 × 5-km resolution across Africa. In order to classify IUs that include locations that are environmentally suitable, we used receiver operating characteristic (ROC) analysis to identify an optimal threshold for suitability concordant with locations where onchocerciasis has been previously detected. This threshold value was then used to classify IUs (more suitable or less suitable) based on the location within the IU with the largest mean prediction. Mean estimates of environmental suitability suggest large areas across West and Central Africa, as well as focal areas of East Africa, are suitable for onchocerciasis transmission, consistent with the presence of current control and elimination of transmission efforts. The ROC analysis identified a mean environmental suitability index of 0.71 as a threshold to classify based on the location with the largest mean prediction within the IU. Of the IUs considered for mapping surveys, 50.2% exceed this threshold for suitability in at least one 5×5-km location. The formidable scale of data collection required to map onchocerciasis endemicity across the African continent presents an opportunity to use spatial data to identify areas likely to be suitable for onchocerciasis transmission. National onchocerciasis elimination programmes may wish to consider prioritising these IUs for mapping surveys as human resources, laboratory capacity, and programmatic schedules may constrain survey implementation, and possibly delaying MDA initiation in areas that would ultimately qualify