An inverse problem of finding the time-dependent diffusion coefficient from an integral condition

We consider the inverse problem of determining the time-dependent diffusivity in one-dimensional heat equation with periodic boundary conditions and nonlocal over-specified data. The problem is highly nonlinear and it serves as a mathematical model for the technological process of external guttering applied in cleaning admixtures from silicon chips. First, the well-posedness conditions for the existence, uniqueness, and continuous dependence upon the data of the classical solution of the problem are established. Then, the problem is discretized using the finite-difference method and recasts as a nonlinear least-squares minimization problem with a simple positivity lower bound on the unknown diffusivity. Numerically, this is effectively solved using the lsqnonlin routine from the MATLAB toolbox. In order to investigate the accuracy, stability, and robustness of the numerical method, results for a few test examples are presented and discussed

Simultaneous determination of time-dependent coefficients and heat source

This article presents a numerical solution to the inverse problems of simultaneous determination of the time-dependent coefficients and the source term in the parabolic heat equation subject to overspecified conditions of integral type. The ill-posed problems are numerically discretized using the finite-difference method. The resulting system of nonlinear equations is solved numerically using the MATLAB toolbox routine lsqnonlin applied to minimizing the nonlinear Tikhonov regularization functional subject to simple physical bounds on the variables. Numerical examples are presented to illustrate the accuracy and stability of the solution

Trends and specifics of electric power industry development in the Russian Federation

At the present stage, given the processes of globalization for the global economy, one of the key industries is energy. And with certainty, we can only talk about the growth of its consumption, despite the negative processes taking place in the economy in the last period. To meet the needs of production and municipal needs, there is a need for a constant increase in the production of energy feedstock, the production of electricity and its distribution. It should be noted that the amount of electricity generated corelates with the level of economic development of the country. However, some countries are forced to import energy resources from abroad without having their own. It is necessary to note such an aspect of energy development as an environmental factor. Indeed, energy is one of the biggest sources of anthropogenic emissions, it is about 42%. Aim of the paper is to study and analyze the trends and specifics of the development of the Russian electric power industry, as one of the main components of the energy complex. Such scientific methods were used, systematization, theoretical generalization and the method of comparison with the use of statistical analysis. Results of the study defines the integral concept of energy, image of the structure of energy complex in the Russian Federation, from various authors, defines the concept of electricity and factors of its development. Prospects for further research: due to further study of the issues of electric power industry development the in Russian Federation, for their subsequent study and search for solutions. Applied value of the material: lies in the possibility of working out problematic issues for further sustainable and effective development

N,N′-Bis[3,5-bis­(2,6-diisopropyl­phen­yl)phen­yl]butane-2,3-diimine

The title mol­ecule, C64H80N2, lies on an inversion center wherein the central butane­diimine fragment [N=C(Me)—C(Me)=N] is essentially planar [maximum deviation = 0.002 (2) Å] and its mean plane forms a dihedral of 70.88 (10)° with the attached benzene ring. In the symmetry-unique part of the mol­ecule, the dihedral angles between the benzene ring bonded to the N atom and the other two benzene rings are 89.61 (6) and 82.77 (6)°

Conservative parabolic problems: Nondegenerated theory and degenerated examples from population dynamics

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/144594/1/mma4901_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144594/2/mma4901.pd

N,N′-Bis(2-amino­benz­yl)ethane-1,2-diaminium bis­(4-methyl­benzene­sulfonate)

The title salt, C16H24N4 2+·2C7H7O3S−, crystallizes with the dication situated on an inversion center and the anion in a general position. The cation contains two ammonium and two free amine groups, and the observed conformation for the chain linking the benzene rings is different from that found in the free tetra­amine and in the fully protonated tetra­amine. All amine and ammonium H atoms of the cation form hydrogen bonds with eight symmetry-related anions, using the sulfonate O atoms as acceptors. This arrangement for the ions precludes any π–π contacts between benzene rings in the crystal

Well-posedness and spectral properties of heat and wave equations with non-local conditions

We consider the one-dimensional heat and wave equations but -- instead of boundary conditions-- we impose on the solution certain non-local, integral constraints. An appropriate Hilbert setting leads to an integration-by-parts formula in Sobolev spaces of negative order and eventually allows us to use semigroup theory leading to analytic well-posedness, hence sharpening regularity results previously obtained by other authors. In doing so we introduce a parametrization of such integral conditions that includes known cases but also shows the connection with more usual boundary conditions, like periodic ones. In the self-adjoint case, we even obtain eigenvalue asymptotics of so-called Weyl's type.Comment: 23 page

Ультразвуковая дифференциальная диагностика кист и кистозных опухолей селезенки

The incidence of focal lesions in the spleen is 3.2–4.2% per 100,000 population. Spleen cysts are rare (incidence 0.75 per 100,000). These are single or multiple, thin- and smooth-walled cavities filled with a transparent liquid. Distinguish between primary (or true) cysts, lined with epithelium, and secondary (or false), devoid of epithelial lining. Among the primary cysts, there are congenital cysts formed in the embryonic period due to the migration of peritoneal cells into the spleen tissue, dermoid and epidermoid cysts. A special group of primary cysts are parasitic cysts. Cystic tumors of the spleen include lymphangioma and lymphoma.The main difficulties in the diagnosis and differential diagnosis of cysts and cystic tumors of the spleen are associated with the rarity of this pathology and, as a consequence, a small number of works, including a significant number of the cases. However, in those works where a large number of the cases are described, most often this is one morphological form and an analysis of its various characteristics.Purpose. Based on the analysis of our own examination data of a significant number of patients with cysts and cystic tumors of the spleen, to assess the possibility of differential diagnosis of individual morphological forms according to ultrasound data.Materials and methods. 323 patients with cysts and cystic tumors of the spleen from 15 to 77 years old (men – 105 (32.5%); women – 218 (67.5%) were treated at A.V. Vishnevsky National Medical Research Center of Surgery for the period from 1980 to 2020. All patients underwent ultrasound during examination. Surgical treatment was carried out in various ways – (85.1%), when making a preoperative diagnosis of an uncomplicated spleen cyst of small size, dynamic observation was carried out (verification by puncture biopsy data).Results. Morphological verification of cysts and cystic tumors of the spleen was presented as follows (taking into account possible difficulties in identifying the epithelial lining): true cyst – 182 (56.4%); dermoid cyst – 3 (0.9%) (malignant – in 1 case); pseudocyst – 16 (5.0%); pancreatogenic – 34 (10.5%); echinococcus – 52 (16.1%); lymphangioma – 24 (7.4%); lymphoma – 10 (3.1%); ovarian cancer metastasis – 2 (0.6%). The article describes the ultrasound signs of the above forms of the lesions with an emphasis on the complexity of diagnosis.Conclusions. Primary and parasitic spleen cysts are well differentiated according to ultrasound; false cysts of the spleen, depending on the cause of their occurrence, can create difficulties in their identification and differentiation (they require careful dynamic control); cystic tumors of the spleen should be differentiated from malignant tumors and metastases of a cystic structure, as a result of which such vigilance should always be present when they are detected.Частота встречаемости очаговых образований селезенки составляет 3,2–4,2% на 100 000 населения. Кисты селезенки встречаются редко (частота 0,75 на 100 000). Это одиночные или множественные, тонко- и гладкостенные полости, заполненные прозрачной жидкостью. Различают первичные (или истинные) кисты, выстланные эпителием, и вторичные (или ложные), лишенные эпителиальной выстилки. Среди первичных кист выделяют врожденные, образующиеся в эмбриональном периоде вследствие миграции перитонеальных клеток в ткань селезенки, дермоидные и эпидермоидные кисты. Особую группу первичных кист составляют паразитарные кисты. К кистозным опухолям селезенки относят лимфангиому и лимфому.Основные трудности в диагностике и дифференциальной диагностике кист и кистозных опухолей селезенки связаны с редкостью данной патологии и, как следствие, небольшим числом работ, включающих значимое число наблюдений. Однако и в тех работах, где описано большое число наблюдений, чаще всего это одна морфологическая форма и разбор различных ее характеристик.Цель исследования: на основании анализа собственных данных обследования значительного числа пациентов с кистами и кистозными опухолями селезенки оценить возможность дифференциальной диагностики отдельных морфологических форм по данным ультразвукового исследования (УЗИ).Материал и методы. В НМИЦ хирургии имени А.В. Вишневского за период с 1980 по 2020 г. было пролечено 323 больных с кистами и кистозными опухолями селезенки в возрасте от 15 до 77 лет (мужчин – 105 (32,5%); женщин – 218 (67,5%)). Всем пациентам при обследовании выполняли УЗИ. Большей части пациентов было проведено оперативное лечение различными способами (85,1%), при постановке дооперационного диагноза неосложненной кисты селезенки незначительных размерах проводили динамическое наблюдение (верификация по данным пункционной биопсии).Результаты. Морфологическая верификация кист и кистозных опухолей селезенки была представлена следующим образом (с учетом возможных сложностей в выявлении эпителиальной выстилки): истинная киста – 182 (56,4%); дермоидная киста – 3 (0,9%) (малигнизированная – в 1 случае); псевдокиста – 16 (5,0%); панкреатогенная – 34 (10,5%); эхинококк – 52 (16,1%); лимфангиома – 24 (7,4%); лимфома – 10 (3,1%); метастаз рака яичника – 2 (0,6%). В статье описаны ультразвуковые признаки представленных выше форм образований с акцентом на сложности диагностики.Выводы. Первичные и паразитарные кисты селезенки хорошо дифференцируются по данным УЗИ; ложные кисты селезенки в зависимости от причины их возникновения могут создавать трудности при их выявлении и дифференциации (они требуют тщательного динамического контроля); кистозные опухоли селезенки следует дифференцировать со злокачественными образованиями и метастазами кистозного строения, вследствие чего при их выявлении всегда должна быть подобная настороженность

Phosphorescent Organic Light-Emitting Devices: Working Principle and Iridium Based Emitter Materials

Even though organic light-emitting device (OLED) technology has evolved to a point where it is now an important competitor to liquid crystal displays (LCDs), further scientific efforts devoted to the design, engineering and fabrication of OLEDs are required for complete commercialization of this technology. Along these lines, the present work reviews the essentials of OLED technology putting special focus on the general working principle of single and multilayer OLEDs, fluorescent and phosphorescent emitter materials as well as transfer processes in host materials doped with phosphorescent dyes. Moreover, as a prototypical example of phosphorescent emitter materials, a brief discussion of homo- and heteroleptic iridium(III) complexes is enclosed concentrating on their synthesis, photophysical properties and approaches for realizing iridium based phosphorescent polymers