Change of concentration of biochemical markers of dysfunction of endothelium at intake of inhibitors of tyrosinekinase of I and II generations at patients with a chronic myeloid leukemia as risk factor of development of cardiovascular complications

CML), the accepting inhibitors tyrosine of kinases (TKI) I and the II generations (TKI1 and TKI2 respectively), and development of arterial hypertension.Material and methods. Examination of 137 patients with CML in the chronic phase (CP) is conducted, the median of age — 47 years. 24 of them were with for the first time the verified diagnosis of CML and earlier did not accept TKI, they have made group of control. Other patients accepted TKI: 39 patients — imatinib 400 mg/day, 36 — dasatinib 100 mg/day, 38 — nilotinib 800 mg/day) more than 6 months. In biochemical analysis of blood indicators of lipidic range were defined. Level detection of ET-1 and VEGF was made by means of enzyme immunoassay. To all patients measurement of the heart rate (HR) and the arterial blood pressure (ABP) on both hands at an interval of 2 minutes from previous was once taken.Results. In group of patients from CML accepting nilotinib authentically significant increase in levels of systolic and diastolic ABP (р<0,001) in comparison with group of control, with group of the patients accepting imatinib and dasatinib is noted. The most serious changes of lipidic range are noted at the patients accepting nilotinib. In all groups statistically significant increase in level of C-reactive protein, fibrinogen, homocysteine, endothelin-1 and VEGF in comparison with group of control is revealed. The most expressed changes are found in group of the patients accepting nilotinib, values of parameters of C-reactive protein, fibrinogen, homocysteine, endothelin-1 and VEGF are changed authentically (р<0,001) and statistically significantly differ in comparison with group for the first time of the revealed patients with CML and groups of reception of imatinib and dazatinib.Conclusion. As a result of the conducted research endothelium variation of a function at patients from CML accepting TKI1 and TKI2 is revealed. The above-stated indicators can be used as additional diagnostic criteria for assessment of risk of development of arterial hypertension in patients with CML at reception of TKI.

A Change of Scale Formula for Wiener Integrals about the First Variation on the Product Abstract Wiener Space

We shall prove the existence of the Wiener integral and the analytic Wiener and Feynman integral and we obtain those relationships and later, we prove the change of scale formula for the Wiener integral about the first variation of a function defined on the product abstract Wiener space. Later, we obtain those relationships in the Fresnel class as it’s corollaries.

On the generalized absolute convergence of Fourier series

In the present paper the sufficient conditions are obtained for the generalized r-absolute convergence ( {0<r<2} ) of the single Fourier trigonometric series in terms of the modulus of δ-variation of a function. It is proved that these conditions are unimprovable in a certain sense. The classical results of Berstein, Szasz, Zygmund and others, related to the absolute convergence of single trigonometric Fourier series, were previously generalized by [L. Gogoladze and R. Meskhia, On the absolute convergence of trigonometric Fourier series, Proc. A. Razmadze Math. Inst. 141 2006, 29–40].

Regularization of ill-posed problems by using stabilizers in the form of the total variation of a function and its derivatives

Under the assumption that the solution of a linear operator equation is presented in the form of a sum of several components with various smoothness properties, a modified Tikhonov regularization method is studied. The stabilizer of this method is the sum of three functionals, where each one corresponds to only one component. Each such functional is either the total variation of a function or the total variation of its derivative. For every component, the convergence of approximate solutions in a corresponding normed space is proved and a general discrete approximation scheme for the regularizing algorithm is justified.

Fractional variation of Hölderian functions

The paper demonstrates the basic properties of the local fractional variation operators (termed fractal variation operators). The action of the operators is demonstrated for local characterization of Hölderian functions. In particular, it is established that a class of such functions exhibits singular behavior under the action of fractal variation operators in infinitesimal limit. The link between the limit of the fractal variation of a function and its derivative is demonstrated. The paper presents a number of examples, including the calculation of the fractional variation of Cauchy sequences leading to the Dirac’s delta-function.

On the Total Variation of a Function

There are a number of theories which assign to a function defined on the real line a measure that reflects somehow the variation of that function. The most familiar of these is, of course, the Lebesgue-Stieltjes measure associated with any monotonie function. The problem in general is to provide a construction of a measure from a completely arbitrary function in such a way that the values of this measure provide information about the total variation of the function over sets of real numbers and from which useful inferences can be drawn.

Generalized Riemann Integration and an Intrinsic Topology

In generalized Riemann integration theory it is becoming increasingly clear that a particular collection of sets has some properties of a topology; it is a useful topology when general requirements hold, and the present paper examines the background. Thomson [23, 24] altered my original theory of the variation and Riemann-type integration that has Lebesgue properties, defining the variation of a function of interval-point pairs over the whole of a space T by using partial divisions of T instead of divisions covering T entirely, and also defining a Lebesgue-type integral. His reason might have been that a decomposable division space seems impossible in a general compact or locally compact space. McGill mentioned this to me, and in [15] connected Thomson's setting with topological measure and Topsøfe [25], giving an interesting theorem on the variation of the limit of a monotone increasing generalized sequence of open sets.