Borel-Hirzebruch type formula for the graph equivariant cohomology of a projective bundle over a GKM-graph

In this paper, we introduce the GKM theoretical counterpart of the equivariant complex vector bundles as the ``leg bundle''. We also provide a definition for the projectivization of a leg bundle and prove the Borel-Hirzebruch type formula for its graph equivariant cohomology, assuming that the projectivization is again a GKM graph. Moreover, we investigate the conditions under which the projective GKM fiber bundle, in the sense of Guillemin-Sabatini-Zara, can be obtained from the projectivization of a leg bundle. If we consider the category of leg bundles to leg bundles with Q-coefficient axial functions, then every projective GKM fiber bundle can be obtained by the projectivization of some Q-leg bundle.Comment: 20 pages, 7 figures; 2nd version, rewrite the heavy notations and add the new result

Role of membrane lipids in the regulation of erythrocytic oxygen-transport function in cardiovascular diseases

The composition and condition of membrane lipids, the morphology of erythrocytes, and hemoglobin distribution were explored with the help of laser interference microscopy (LIM) and Raman spectroscopy. It is shown that patients with cardiovascular diseases (CVD) have significant changes in the composition of their phospholipids and the fatty acids of membrane lipids. Furthermore, the microviscosity of the membranes and morphology of the erythrocytes are altered causing disordered oxygen transport by hemoglobin. Basic therapy carried out with the use of antiaggregants, statins, antianginals, beta-blockers, and calcium antagonists does not help to recover themorphofunctional properties of erythrocytes. Based on the results the authors assume that, for the relief of the ischemic crisis and further therapeutic treatment, it is necessary to include, in addition to cardiovascular disease medicines, medication that increases the ability of erythrocytes’ hemoglobin to transport oxygen to the tissues. We assume that the use of LIM and Raman spectroscopy is advisable for early diagnosis of changes in the structure and functional state of erythrocytes when cardiovascular diseases develop

Physical and chemical processes and the morphofunctional characteristics of human erythrocytes in hyperglycaemia

Background: This study examines the effect of graduated hyperglycaemia on the state and oxygen-binding ability of hemoglobin, the correlation of phospholipid fractions and their metabolites in the membrane, the activity of proteolytic enzymes and the morphofunctional state of erythrocytes. Methods: Conformational changes in the molecule of hemoglobin were determined by Raman spectroscopy. The structure of the erythrocytes was analyzed using laser interference microscopy (LIM). To determine the activity of NADN-methemoglobinreductase, we used the P.G. Board method. The degree of glycosylation of the erythrocyte membranes was determined using a method previously described by Felkoren et al. Lipid extraction was performed using the Bligh and Dyer method. Detection of the phospholipids was performed using V. E. Vaskovsky method. Results: Conditions of hyperglycaemia are characterized by a low affinity of hemoglobin to oxygen, which is manifested as a parallel decrease in the content of hemoglobin oxyform and the growth of deoxyform, methemoglobin and membrane-bound hemoglobin. The degree of glycosylation of membrane proteins and hemoglobin is high. For example, in the case of hyperglycaemia, erythrocytic membranes reduce the content of all phospholipid fractions with a simultaneous increase in lysoforms, free fatty acids and the diacylglycerol (DAG). Step wise hyperglycaemia in incubation medium and human erythrocytes results in an increased content of peptide components and general trypsin-like activity in the cytosol, with a simultaneous decreased activity of µ-calpain and caspase 3. Conclusions: Metabolic disorders and damage of cell membranes during hyperglycaemia cause an increase in the population of echinocytes and spherocytes. The resulting disorders are accompanied with a high probability of intravascular haemolysis.</p

Explicit constructions of bordism of Milnor hypersurface H1,n and CP1 × CPn−

In the present paper we construct two new explicit complex bordisms between any two projective bundles over CP1 of the same complex dimension, including the Milnor hypersurface H1,n and CP1 ×CPn−1. These constructions reduce the bordism problem to the null-bordism of some projective bundle over CP1 with the non-standard stably complex structure. © 2020 The Mathematical Society of Japa

EXPLICIT GEOMETRIC CONSTRUCTIONS OF BORDISM OF MILNOR HYPERSURFACE AND CP3×CPN-

In the present paper we construct two new explicit complex bordisms between any two projective bundles over C P 1 of the same complex dimension, including the Milnor hypersurface H 1 ,n and C P 1 ×C P n -1. These constructions reduce the bordism problem to the null-bordism of some projective bundle over C P 1 with the non-standard stably complex structure