The aim of this paper is to construct the parabolic version of the Donaldson–Uhlenbeck compactification for the moduli space of parabolic stable bundles on an algenraic surface with parabolic structures along a divisor with normal crossing singularities. We prove the non–emptiness of the moduli space of parabolic stable bundles of rank 2 and also prove the existence of components with smooth po...

The article considers a parabolic-type boundary value problem with divergent principal part, when the condition contains time derivative of required function: { u t − d/dx i ( x,t,u, ∇ )+ )=0, 0 + )cos( v,x )= g ),( x,t )∈ S , x,0 x ), ∈ Ω Such nonclassical problems conditions containing desired function arise in study number applied problems, for example, surface body, whose temperature is sam...

These notes contain a short exposition of selected results about parabolic equations: Schauder estimates for linear parabolic equations with Hölder coefficients, some existence, uniqueness and regularity results for viscosity solutions of fully nonlinear parabolic equations (including degenerate ones), the Harnack inequality for fully nonlinear uniformly parabolic equations. MSC. 35K55, 35D40, ...

To reduce the processing time for in-line carburizing, we performed ultra-rapid carburizing and quenching using induction heating. Conventional gas vacuum (low-pressure carburizing) are treated at 1203–1323 K, which is lower than eutectic temperature. In contrast, in this study, temperature of 1523 K was higher speeding up process. The SCM420 sample rapidly heated to treatment by CH4 N2 were mi...

Parabolic triples of the form (E∗, θ, σ) are considered, where (E∗, θ) is a parabolic Higgs bundle on a given compact Riemann surface X with parabolic structure on a fixed divisor S, and σ is a nonzero section of the underlying vector bundle. Sending such a triple to the Higgs bundle (E∗, θ) a map from the moduli space of stable parabolic triples to the moduli space of stable parabolic Higgs bu...

This work introduces a new operator-splitting method for solving the two-dimensional (2D) and three-dimensional (3D) parabolic equations. The aim is to reduce the computational complexity without loss of accuracy. Firstly, we split the 2D and 3D parabolic equations into a sequence of one-dimensional (1D) parabolic equations respectively, then we solve each 1D parabolic equation by using finite ...

This article focuses on the complex processing of quarry tuffs-stone to extract metals (iron, titanium, copper, silver, etc.) and obtain raw materials for construction agriculture. The issue tuff-stone softening was investigated analytical dependence regularity at water saturation established, which indicates that increases with increasing mass sample according logarithmic law, dehydration proc...

The concept of the iterative parabolic approximation based on the multiscale technique is discussed. This approach is compared with the traditional ways to derive the wide-angle parabolic equation. While the latter fail in the nonlinear case, the multiscale derivation technique leading to iterative parabolic equations can be easily adapted to handle it. The nonlinear iterative parabolic approxi...

Following Parreau’s work in 1951-52, we give a unified definition of parabolic Riemann surfaces, with or without boundary. A surface is parabolic under the unified definition implies that it is either relative parabolic or parabolic under the classical definitions. Then we study the conformal structures of noncompact, proper, branched minimal surfaces in R and prove several criteria of such sur...

considering great medicinal value of hyssopus officinalis l. and possibility of its mass production through in vitro culture, two individual experiments was conducted. effect of various concentrations (0, 2.2, 4.4 and 11 µmol) of tdz and bap in combination with 1 µmol of iaa on direct regeneration from nodal explants were assessed. significant difference between treatments was observed (p≤ 0.01...