Pair of null gravitating shells II. Canonical theory and embedding variables

The study of the two shell system started in our first paper ``Pair of null gravitating shells I'' (gr-qc/0112060) is continued. An action functional for a single shell due to Louko, Whiting and Friedman is generalized to give appropriate equations of motion for two and, in fact, any number of spherically symmetric null shells, including the cases when the shells intersect. In order to find the symplectic structure for the space of solutions described in paper I, the pull back to the constraint surface of the Liouville form determined by the action is transformed into new variables. They consist of Dirac observables, embeddings and embedding momenta (the so-called Kucha\v{r} decomposition). The calculation includes the integration of a set of coupled partial differential equations. A general method of solving the equations is worked out.Comment: 20 pages, Latex file using amstex, some references correcte

The Constraints in Spherically Symmetric General Relativity II --- Identifying the Configuration Space: A Moment of Time Symmetry

We continue our investigation of the configuration space of general relativity begun in I (gr-qc/9411009). Here we examine the Hamiltonian constraint when the spatial geometry is momentarily static (MS). We show that MS configurations satisfy both the positive quasi-local mass (QLM) theorem and its converse. We derive an analytical expression for the spatial metric in the neighborhood of a generic singularity. The corresponding curvature singularity shows up in the traceless component of the Ricci tensor. We show that if the energy density of matter is monotonically decreasing, the geometry cannot be singular. A supermetric on the configuration space which distinguishes between singular geometries and non-singular ones is constructed explicitly. Global necessary and sufficient criteria for the formation of trapped surfaces and singularities are framed in terms of inequalities which relate appropriate measures of the material energy content on a given support to a measure of its volume. The strength of these inequalities is gauged by exploiting the exactly solvable piece-wise constant density star as a template.Comment: 50 pages, Plain Tex, 1 figure available from the authors

CHANGES IN CARBOHYDRATE METABOLISM IN PATIENTS WITH ALCOHOLIC CIRRHOSIS OF THE LIVER ASSOCIATED WITH NON-ALCOHOLIC FATTY LIVER DISEASE DEPENDING ON THE STAGE OF DECOMPENSATION

The purpose of the research was to study the changes in adipocytokines in patients with alcoholic liver cirrhosis (ALC) associated with non- alcoholic fatty liver disease (NAFLD) depending on the stage of decompensation. A significant increase in immunoreactive insulin, the HOMA-IR index and a decrease in the QUICKI index in patients II gr. in comparison with patients I gr. has been detected, that indicating insulin resistance (p<0.05). On the basis of the results of the analysis of the correlation between the levels of leptin, adiponectin, resistin and carbohydrate metabolism, it was found that a stronger correlation was observed in patients suffering from ALC associated with NAFLD.The purpose of the research was to study the changes in adipocytokines in patients with alcoholic liver cirrhosis (ALC) associated with non- alcoholic fatty liver disease (NAFLD) depending on the stage of decompensation. A significant increase in immunoreactive insulin, the HOMA-IR index and a decrease in the QUICKI index in patients II gr. in comparison with patients I gr. has been detected, that indicating insulin resistance (p<0.05). On the basis of the results of the analysis of the correlation between the levels of leptin, adiponectin, resistin and carbohydrate metabolism, it was found that a stronger correlation was observed in patients suffering from ALC associated with NAFLD

IHC characteristics of stem cell markers in PDAC with different degrees of differentiation

Introduction. Cancer stem cells (CSCs) play a key role in the development, progression and metastasis of cancer. Cell surface markers, in particular CD44 and EpCAM, are used to identify CSCs. Marker expression patterns depend on the stage of progression and differentiation. Materials and methods. Histopathological and IHC studies of 49 cases of the pancreas ductal adenocarcinoma (PDAC) of G2, G3 degrees of differentiation. Results of IHC reactions with antibodies against CD44 and EpCAM were estimated by photo digital morphometry and were expressed in immunostained cells relative area (%). Results. Adenocarinoma of the pancreas is characterized by a moderate level of expression of cell surface markers CSC - CD44 and EpCAM. The expression level of CD44 in the І gr. - Me = 34.11% (Q1 = 31.03; Q3 = 38.39), in the II gr. - Me = 43.17% (Q1 = 39.83; Q3 = 47.04), significantly higher than in the I gr. (Kruskal-Wallis test p<0.05). The expression level of EpCAM in the I gr. - Ме=26,10% (Q1=20,42; Q3=31,89), in the II gr. - Ме=31,07% (Q1=27,03; Q3=34,00) (p>0,05). In both groups, the relative area of EpCAM was significantly lower than CD44 (Kruskal-Wallis test p<0.05). Correlation analysis (Pearson's ratio) showed a weak negative relationship between markers at G2 (r = -0.17, p>0.05), at G3 - a weak positive (r = + 0.06, p>0.05)

Зміни тромбоцитарної активності у хворих на ХОЗЛ із супутньою артеріальною гіпертензією при застосуванні L-аргініну

Цель: исследовать влияние L-аргинина на тромбоцитарную активность у больных с ХОЗЛ с сопутствующей артериальной гипертензией. Обследовано 30 больных ХОЗЛ A-D категории в сочетании с гипертонической болезнью (ГБ) I-II стадии в состоянии контроля заболевания. В I гр. (n=20) на фоне базисной терапии пациенты получали препарат L-аргинина (Тивортин) в суточной дозе 4 г в течение 30 дней. Пациенты II гр. (n=10) получали стандартную базисную терапию. Проводилось определение адгезии тромбоцитов (tr), агрегации tr, индуцированной аденозин дифосфатом (AДФ), коллагеном и тромбином (оптический турбидометрический метод агрегатометрии). Дополнительно в I гр. (n=6) – определение уровня активированных, агрегированных, дегранулированных tr, плотности tr гранул (трансмиссионная электронная микроскопия). Под влиянием терапии у пациентов I гр. выявлено снижение степени адгезии tr, степени индуцированной агрегации tr (коллаген, тромбин), скорости агрегации tr (АДФ, тромбин), активности tr фактора фон Виллебрандта (коллаген, тромбин), снижение активированных, агрегированных и дегранулованных tr, повышение плотности упаковки α-гранул (p<0,05). У пациентов II гр. существенных изменений показателей адгезии и индуцированной агрегации tr не выявлено. У коморбидных больных ХОЗЛ и АГ применение препарата L-аргинина (Тивортина) уменьшает тромбоцитарную активность и может способствовать снижению тромбогенного потенциала и риска возникновения тромботических событий. Objective: to investigate the influence of L - arginine on platelets activity in patients with COPD and concomitant arterial hypertension. 30 patients with COPD of A - D category combined with hypertension (Н) I - II stage in the state of disease control were examined. In I gr. (n=20) patients received L – arginine (Tivortin) in a daily dose of 4g as additional medication to the basic therapy for 30 days. Patients of II gr. (n=10) received only basic therapy. The adhesion of platelets (pl), induced with adenosine diphosphate (ADP), collagen and thrombin (optical turbidometric aggregatometry method) were determined. Additionaly, in I gr. (n=6) there were determined the level of activated, aggregated, degranulated pl, packing density of pl granules (transmission electron microscopy). Under the influence of therapy in patients of I gr. degree of pl adhesion, degree of induced pl aggregation (collagen, thrombin), rate of aggregation (ADP, thrombin), activity of pl von Willebrandt factor activity (collagen, thrombin) decreased, level of activated, aggregated and degranulated pl decreased; packing density of α - granules increased (p<0.05). In II gr.of patients significant changes in the indices of adhesion and induced aggregation of pl were not detected. In comorbid patients with COPD and arterial hypertension L-arginine (Tivortin) reduces platelet activity and may reduce thrombogenic potential and risk of thrombotic events

On the complexity of computing Gr\"obner bases for weighted homogeneous systems

Solving polynomial systems arising from applications is frequently made easier by the structure of the systems. Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights $W=(w\_{1},\dots,w\_{n})$, $W$-homogeneous polynomials are polynomials which are homogeneous w.r.t the weighted degree $\deg\_{W}(X\_{1}^{\alpha\_{1}},\dots,X\_{n}^{\alpha\_{n}}) = \sum w\_{i}\alpha\_{i}$. Gr\"obner bases for weighted homogeneous systems can be computed by adapting existing algorithms for homogeneous systems to the weighted homogeneous case. We show that in this case, the complexity estimate for Algorithm~\F5 \left(\binom{n+\dmax-1}{\dmax}^{\omega}\right) can be divided by a factor $\left(\prod w\_{i} \right)^{\omega}$. For zero-dimensional systems, the complexity of Algorithm~\FGLM $nD^{\omega}$ (where $D$ is the number of solutions of the system) can be divided by the same factor $\left(\prod w\_{i} \right)^{\omega}$. Under genericity assumptions, for zero-dimensional weighted homogeneous systems of $W$-degree $(d\_{1},\dots,d\_{n})$, these complexity estimates are polynomial in the weighted B\'ezout bound $\prod\_{i=1}^{n}d\_{i} / \prod\_{i=1}^{n}w\_{i}$. Furthermore, the maximum degree reached in a run of Algorithm \F5 is bounded by the weighted Macaulay bound $\sum (d\_{i}-w\_{i}) + w\_{n}$, and this bound is sharp if we can order the weights so that $w\_{n}=1$. For overdetermined semi-regular systems, estimates from the homogeneous case can be adapted to the weighted case. We provide some experimental results based on systems arising from a cryptography problem and from polynomial inversion problems. They show that taking advantage of the weighted homogeneous structure yields substantial speed-ups, and allows us to solve systems which were otherwise out of reach

The affine Grassmannian and the Springer resolution in positive characteristic

An important result of Arkhipov-Bezrukavnikov-Ginzburg relates constructible sheaves on the affine Grassmannian to coherent sheaves on the dual Springer resolution. In this paper, we prove a positive-characteristic analogue of this statement, using the framework of "mixed modular sheaves" recently developed by the first author and Riche. As an application, we deduce a relationship between parity sheaves on the affine Grassmannian and Bezrukavnikov's "exotic t-structure" on the Springer resolution.Comment: 50 pages; with an appendix joint with Simon Riche. v2: minor correction