Nonlocal Problem for a Mixed Type Fourth-Order Differential Equation with Hilfer Fractional Operator

In this paper, we consider a non-self-adjoint boundary value problem for a fourth-order differential equation of mixed type with Hilfer operator of fractional integro-differentiation in a positive rectangular domain and with spectral parameter in a negative rectangular domain. The mixed type differential equation under consideration is a fourth order differential equation with respect to the second variable. Regarding the first variable, this equation is a fractional differential equation in the positive part of the segment, and is a second-order differential equation with spectral parameter in the negative part of this segment. A rational method of solving a nonlocal problem with respect to the Hilfer operator is proposed. Using the spectral method of separation of variables, the solution of the problem is constructed in the form of Fourier series. Theorems on the existence and uniqueness of the problem are proved for regular values of the spectral parameter. For sufficiently large positive integers in unique determination of the integration constants in solving countable systems of differential equations, the problem of small denominators arises. Therefore, to justify the unique solvability of this problem, it is necessary to show the existence of values of the spectral parameter such that the quantity we need is separated from zero for sufficiently large n. For irregular values of the spectral parameter, an infinite number of solutions in the form of Fourier series are constructed. Illustrative examples are provided

Improved Technology To Prevent Nuclear Proliferation And Counter Nuclear Terrorism

As the world moves into the 21st century, the possibility of greater reliance on nuclear energy will impose additional technical requirements to prevent proliferation. In addition to proliferation resistant reactors, a careful examination of the various possible fuel cycles from cradle to grave will provide additional technical and nonproliferation challenges in the areas of conversion, enrichment, transportation, recycling and waste disposal. Radiation detection technology and information management have a prominent role in any future global regime for nonproliferation. As nuclear energy and hence nuclear materials become an increasingly global phenomenon, using local technologies and capabilities facilitate incorporation of enhanced monitoring and detection on the regional level. Radiation detection technologies are an important tool in the prevention of proliferation and countering radiological/nuclear terrorism. A variety of new developments have enabled enhanced performance in terms of energy resolution, spatial resolution, passive detection, predictive modeling and simulation, active interrogation, and ease of operation and deployment in the field. For example, various gamma ray imaging approaches are being explored to combine spatial resolution with background suppression in order to enhance sensitivity many-fold at reasonable standoff distances and acquisition times. New materials and approaches are being developed in order to provide adequate energy resolution in field use without the necessity for liquid nitrogen. Different detection algorithms enable fissile materials to be distinguished from other radioisotopes

On a Hilfer Type Fractional Differential Equation with Nonlinear Right-Hand Side

In this article we consider the questions of one-valued solvability and numerical realization of initial value problem for a nonlinear Hilfer type fractional differential equation with maxima. By the aid of uncomplicated integral transformation based on Dirichlet formula, this initial value problem is reduced to the nonlinear Volterra type fractional integral equation. The theorem of existence and uniqueness of the solution of given initial value problem in the segment under consideration is proved. For numerical realization of solution the generalized Jacobi–Galerkin method is applied. Illustrative examples are provided

On a Hilfer Type Fractional Differential Equation with Nonlinear Right-Hand Side

In this article we consider the questions of one-valued solvability and numerical realization of initial value problem for a nonlinear Hilfer type fractional differential equation with maxima. By the aid of uncomplicated integral transformation based on Dirichlet formula, this initial value problem is reduced to the nonlinear Volterra type fractional integral equation. The theorem of existence and uniqueness of the solution of given initial value problem in the segment under consideration is proved. For numerical realization of solution the generalized Jacobi-Galerkin method is applied. Illustrative examples are provided

Uzbekistan Radiation Portal Monnitoring System

The work proposed in this presentation builds on the foundation set by the DTRA funded demonstration project begun in 2000 and completed in December of 2003. This previous work consisted of two phases whose overall objective was to install portal radiation monitors at four select ports-of-entry in Uzbekistan (Tashkent International Airport, Gisht-Kuprik (Kazakhstan border), Alat (Turkmenistan border), and Termez (Afghanistan border)) in order to demonstrate their effectiveness in preventing the illicit trafficking of nuclear materials. The objectives also included developing and demonstrating capabilities in the design, installation, operation, training, and maintenance of a radiation portal monitoring system. The system and demonstration project has proved successful in many ways. An effective working relationship among the Uzbekistan Customs Services, Uzbekistan Border Guards, and Uzbekistan Institute of Nuclear Physics has been developed. There has been unprecedented openness with the sharing of portal monitor data with Lawrence Livermore National Laboratory. The system has proved to be effective, with detection of illicit trafficking, and, at Alat, an arrest of three persons illegally transporting radioactive materials into Turkmenistan. The demonstration project has made Uzbekistan a model nonproliferation state in Central Asia and, with an expanded program, places them in a position to seal a likely transit route for illicit nuclear materials. These results will be described. In addition, this work is currently being expanded to include additional ports-of-entry in Uzbekistan. The process for deciding on which additional ports-of-entry to equip will also be described

Chronic tubulointerstitial nephritis in children: New approaches to diagnosis and treatment

A survey of 120 children with HTIN, aged from 4 to 15 years, was conducted. Taking into account the clinical variant of HTIN, all patients were divided into 2 groups: group 1 –52 (43%) children with recurrent form of HTIN and group 2 -68 (57%) patients with latent HTIN. Among them, there were 65 boys (54%), 55 girls (46%). The conducted studies have shown that with the development of rHTIN and lHTIN, an important mechanism of damage to interstitial kidney tissue, the development of clinical symptoms and the course of the disease is both a metabolic disorder leading to structural shifts at the level of various elements of the nephron and changes in the functional state of the kidneys, and instability of the cytomembranes of tubular cells. The analysis of the results of the study showed that the method of treatment proposed by the authors is the most effective way of treating HTIN, due to accelerated recovery, both clinical and laboratory parameters of the disease and indicators of protein metabolism, as well as in relation to the restoration of the functional state of the kidneys, which leads to a reduction in the length of hospital stay, a reduction in the number of relapses of exacerbation, prevention complications of the chronic process. All this contributes to preventing the development of disability and reducing the number of child deaths from CRF

ОСОБЛИВОСТІ ЗМІНИ ІМУНОЛОГІЧНИХ ПОКАЗНИКІВ У ДІТЕЙ З ХРОНІЧНИМ БРОНХІТОМ

Aim of investigation was the assessment of the condition of the immune status of children with chronic bronchitis. Changes in the system of not only in cell, but also in humoral immunity have been noted in children with chronic bronchitis which are going to have one-directed immunological shifts characterizing T-cell immunodeficiency. The reliably decreased amount of leucocytes have determined in children with chronic bronchitis in the period of the disease exacerbation. Such indexes as relative and absolute amount of leucocytes have reliably decreased in the comparison with normal parameters. One of the basic indexes of the humoral immunity is immunoglobulins of the blood urea. Including in the chain of the immunologic reactions immunoglobulins have been played a significant role in the pathogenesis of chronic bronchitis. From the point of humoral immunity in children with chronic bronchitis it has been noted significant hypoglobuliemia, extremely increasing of IgM level in the comparison with the practically healthy children, the levels of IgA and IgG have increased mostly in the group of children of the preschool age.Целью исследования явилась оценка состояния иммунного статуса при   хроническом  бронхите у детей. У детей с ХБ отмечаются изменения в системе как клеточного, так и гуморального иммунитета, которые носят однонаправленные иммунологические сдвиги, характеризующие Т-клеточным иммунодефицитом. У детей с хроническим бронхитом в период обострения заболевания установлено достоверное снижение лейкоцитов. Достоверно снижаются по сравнению с нормой такие показатели, как относительное и абсолютное количество лимфоцитов. Одним из основных показателей гуморального иммунитета являются иммуноглобулины сыворотки крови. Включаясь в цепь иммунологических реакций, иммуноглобулины играют определенную роль в патогенезе ХБ. Со стороны гуморального иммунитета у детей, больных ХБ, отмечалась выраженная гипоиммуноглобулинемия, резкое повышение уровня IgМ по сравнению с группой практически здоровых детей, уровень IgA и IgG повышались больше в группе детей дошкольного возраста.Метою дослідження була оцінка стану імунного статусу при хронічному бронхіті у дітей. У дітей із ХБ відзначаються зміни в системі як клітинного, так і гуморального імунітету, що носять односпрямовані імунологічні порушення, які характеризує Т-клітинний імунодефіцит. У дітей з хронічним бронхітом в період загострення захворювання встановлено достовірне зниження лейкоцитів. Достовірно знижуються, порівняно з нормою, такі показники, як відносна й абсолютна кількість лімфоцитів. Одним з основних показників гуморального імунітету є імуноглобуліни сироватки крові. Включаючись в ланцюг імунологічних реакцій, імуноглобуліни відіграють певну роль у патогенезі ХБ. З боку гуморального імунітету в дітей, хворих на ХБ, відмічалися виражена гіпоімуноглобулінемія, різке підвищення рівня IgМ, порівняно з групою практично здорових дітей, рівні IgA і IgG підвищувалися в групі дітей дошкільного віку