Isolated singularities for some types of curvature equations

AbstractWe consider the removability of isolated singularities for the curvature equations of the form Hk[u]=0, which is determined by the kth elementary symmetric function, in an n-dimensional domain. We prove that, for 1⩽k⩽n−1, isolated singularities of any viscosity solutions to the curvature equations are always removable, provided the solution can be extended continuously at the singularities. We also consider the class of “generalized solutions” and prove the removability of isolated singularities

In Search Of Equilibrium In Laser-produced Cloud: Role Of Pressure, Chemical Quenching, And Plasma Expansion

The properties of laser plasma vary significantly depending on the pressure and composition of the environment, thus it a promising emission source to imitate of radiation from various objects in atmosphere (meteor wake, airglow) and in outer space. We aimed to register spectra of FeO and CaO bands in laser plasma as close as possible to the ones observed during the Benešov bolide event to reconstruct the composition and behavior of meteor wake. We fit synthetic spectra of spontaneous vatying temperatures in the region of 1000-8000 K for the infrared system of CaO molecules to those measured in laser-induced plasma. It was found that the excitation (atomic species), vibrational and rotational temperatures of the experimental spectra indicate the absence of local thermodynamic equilibrium (LTE) and does not coincide with each other. The atomic excitation temperature are close to 10000 , vibrational temperature varies in the range of 3500–5000 K, while the rotational temperature is noticeably lower than ~2000–3000 K. Moreover, the specific values of rotational temperatures vary greatly from band to band. We also found the valuable deviation of lines wavelengths and transition probabilities between model spectra based on EXOMOL data. Calculations of the chemical composition of laser-produced clouds formed by laser heating of Fe and CaCO$_{3}$ targets were performed. Timescales of main reactions with participation of Fe- and Ca- containing species were calculated using rate constants of the reactions. Results of calculations of equilibrium composition of laser-produced and impact-produced clouds are presented. Quenching conditions of chemical reactions in laser-produced and impact-produced clouds are found. This work was supported by the Russian Science Foundation (grant 18-13-00269-$\Pi$)

Singular solutions of fully nonlinear elliptic equations and applications

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of $\mathbb{R}^n$, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragm\'en-Lindel\"of result as well as a principle of positive singularities in certain Lipschitz domains.Comment: 41 pages, 2 figure

Wrong-way-round ionization and hydrophilic liquid chromatography in the analysis of insulin-like growth factors

Активное развитие протеомики и геномики приводит к все большему пониманию проблемы изучения и разработки терапевтических средств на основе пептидов. В последние годы получил широкое распространение ряд низкомолекулярных пептидов, используемых в качестве факторов мышечного роста и официально включенных в список запрещенных ВАДА препаратов. Отдельно стоит отметить, что большинство из них не проходили клинических испытаний и могут быть потенциально опасными для здоровья употребляющих их людей. Рассмотрены наиболее распространенные способы определения некоторых низкомолекулярных инсулиноподобных факторов мышечного роста с использованием метода ВЭЖХ с масс-спектрометрическим детектированием. Показано, что наибольшая эффективность разделения достигается с использованием метода обращенно-фазовой жидкостной хроматографии, при этом предел обнаружения составляет 5 нг/мл. Предложен способ определения некоторых инсулиноподобных факторов мышечного роста с использованием ВЭЖХ-ЭРИ-МС/МС в режиме “Wrong-way round ionization”, обеспечивающим аналогичную чувствительность. В данном режиме ионизация осуществляется в щелочной среде с регистрацией положительных ионов, несмотря на отсутствие явного источника протонов, путем переноса протона из иона аммония в газовой фазе. Показано существенное изменение параметров удерживания определяемых веществ за счет изменения их формы нахождения в анализируемой пробе. Рассмотрена возможность применения гидрофильной хроматографии для разделения изучаемых низкомолекулярных пептидов. Установлено, что в случае применения HILIC возможно определение количества пептидов.The recent advances in genomics and proteomics have led to an increased focus on the development of peptide therapeutics. For the last few years the usage of several low molecular weight peptides, included in WADA prohibited list, has increased dramatically. Most of them had never passed a clinical trial, and potentially can be dangerous for people. In this article, we developed a few methods of determination of several low molecular weight insulin-like growth hormones using UPLC-MS/MS. It was shown that reversed-phase liquid chromatography is the most preferred method for their separation, which can be used to achieve a 5 ng/ml limit of detection using the outlined separation and detection conditions. Wrong-way-round ionization UPLC-ESI-MS/MS method for the determination of some insulin-like human growth hormones was developed with the same sensitivity. This method can be realized in alkaline conditions with the detection of positive ions and despite the apparent lack of protons’ source, which can be taken from the ammonia ion in the gas phase. A significant change in the retention parameters was shown because of their forms of occurrence changing in the analyzed sample. The possibility of using hydrophobic interaction chromatography to separate low molecular weight peptides was studied. It was found that in the case of using HILIC it may define a limited number of peptides.The Ministry of Education of the Russian Federation (Project No 4.873.2014 / K) and RFBR (projects No 16-43-230404 r-a and No 15-03-02453 A) supported this work, which was completed using the scientific CCU KubSU equipment

Local and global behaviour of nonlinear equations with natural growth terms

This paper concerns a study of the pointwise behaviour of positive solutions to certain quasi-linear elliptic equations with natural growth terms, under minimal regularity assumptions on the underlying coefficients. Our primary results consist of optimal pointwise estimates for positive solutions of such equations in terms of two local Wolff's potentials.Comment: In memory of Professor Nigel Kalto