It is shown that the formula for the Chern classes (in the Chow ring) of blow-ups of algebraic varieties, due to Porteous and Lascu-Scott, also holds (in the cohomology ring) for blow-ups of symplectic and complex manifolds. This was used by the second-named author in her solution of the geography problem for 8-dimensional symplectic manifolds. The proof equally applies to real blow-ups of arbi...

The blow-up of a graph is obtained by replacing every vertex with a finite collection of copies so that the copies of two vertices are adjacent if and only if the originals are. If every vertex is replaced with the same number of copies, then the resulting graph is called a balanced blow-up. We show that any graph which contains the maximum number of induced copies of a sufficiently large balan...

This paper concerns with blow-up behaviors for semilinear parabolic systems coupled in equations and boundary conditions in half space. We establish the rate estimates for blow-up solutions and prove that the blow-up set is ∂R+ under proper conditions on initial data. Furthermore, for N = 1, more complete conclusions about such two topics are given.  2004 Elsevier Inc. All rights reserved.

We study finite blow-up solutions of the heat equation with nonlinear boundary conditions. We provide a sufficient condition for the single point blow-up at the origin and a precise spacial singularity of the blow-up profile. Mathematics subject classification (2010): 35K20, 35B44.

In this paper, I consider nonlinear parabolic problems under nonlinear boundary conditions. I establish respectively the conditions on nonlinearities to guarantee that ( , ) u x t exists globally or blows up at some finite time. If blow-up occurs, an upper bound for the blow-up time is derived, under somewhat more restrictive conditions, lower bounds for the blow-up time are also derived.

A multi layered feed forward neural network model is being developed for the prediction of end blow oxygen in the LD converter using a two step process. In the first step intermediate stopping temperature is being predicted and using this as an input the end blow oxygen is predicted. In both the cases two hidden layers had given the best results compared to the single layer neural network. Inte...

In the paper, several problems on the periodic Degasperis-Procesi equation with weak dissipation are investigated. At first, the local well-posedness of the equation is established by Kato’s theorem and a precise blow-up scenario of the solutions is given. Then, several criteria guaranteeing the blow-up of the solutions are presented. Moreover, the blow-up rate and blow-up set of the blowing-up...

We use techniques from reaction-diffusion theory to study the blow-up and existence of solutions of the parabolic Monge–Ampère equation with power source, with the following basic 2D model 0.1 (0.1) ut = −|Du|+ |u|u in R × R+, where in two-dimensions |D2u| = uxxuyy − (uxy) and p > 1 is a fixed exponent. For a class of “dominated concave” and compactly supported radial initial data u0(x) ≥ 0, th...

We study the asymptotic behavior of a semidiscrete numerical approximation for a pair of heat equations ut = ∆u, vt = ∆v in Ω × (0, T ); fully coupled by the boundary conditions ∂u ∂η = up11vp12 , ∂v ∂η = up21vp22 on ∂Ω× (0, T ), where Ω is a bounded smooth domain in Rd. We focus in the existence or not of non-simultaneous blow-up for a semidiscrete approximation (U, V ). We prove that if U blo...

This paper focuses on the technological characteristics of Keilmesser with a lateral tranchet blow modification on the cutting edge. It examines the underlying technological production of these bifacial objects: this implies the evaluation of their working stage succession, as well as produced forms necessary for the execution of tranchet blow performance. Furthermore, it offers a techno-morpho...