We study properties of the semilinear elliptic equation ∆u = 1 u on domains in R, with an eye toward nonnegative singular solutions as limits of positive smooth solutions. We prove the nonexistence of such solutions in low dimensions when we also require them to be stable for the corresponding variational problem. The problem of finding singular solutions is related to the general study of sing...

Assume that Ω is a bounded domain in Rn with n ≥ 2. We study positive solutions to the problem, ∆u = up in Ω, u(x)→∞ as x→ ∂Ω, where p > 1. Such solutions are called boundary blow-up solutions of ∆u = up. We show that a boundary blow-up solution exists in any bounded domain if 1 < p < n n−2 . In particular, when n = 2, there exists a boundary blow-up solution to ∆u = up for all p ∈ (1,∞). We al...

Consider a cubic unit u of positive discriminant. We present a computational proof of the fact that u is a fundamental unit of the order Z[u] in most cases and determine the exceptions. This extends a similar (but restrictive) result due to E. Thomas. Introduction Let f(X) := X + aX + bX ± 1 ∈ Z[X] be irreducible in Z[X] and with three (distinct) real roots. We think of the order R := Z[u], obt...

In heavy ion collisions at Coulomb barrier energies the two collision partners can be brought into nuclear contact. During their closest approach the two nuclei form a dinuclear system (nuclear molecule) which is seen by the electrons as a common charge centre. The lifetime of the di-nuclear system (nuclear contact time) is correlated with the energy dissipation during the collision. While the ...

We rewrite the system ∆u − Wu(u) = 0, for u : R n → R n , in the form div T = 0, where T is an appropriate stress-energy tensor, and derive certain a priori consequences on the solutions. In particular, we point out some differences between two paradigms: the phase-transition system, with target a finite set of points, and the Ginzburg–Landau system, with target a connected manifold.

In this paper, we study the construction of cyclic DNA codes by cyclic codes over the finite chain ring     2 4 1 F u u  . First, we establish a 1-1 correspondence  between DNA pairs and the 16 elements of the ring     2 4 1 F u u  . Considering the biology features of DNA codes, we investigate the structure and properties of selfreciprocal complement cyclic codes. Hamming minimum di...

Full-overlap U+U collisions provide significantly larger initial energy densities at comparable spatial deformation, and significantly larger deformation and volume at comparable energy density, than semi-central Au+Au collisions. We show quantitatively that this provides a long lever arm for studying the hydrodynamic behavior of elliptic flow in much larger and denser collision systems and the...

A quark interaction with topologically nontrivial gluonic fields, instantons and sphalerons, violates P and CP symmetry. In the strong magnetic field of a noncentral nuclear collision such interactions lead to the charge separation along the magnetic field, the so-called chiral magnetic effect (CME). Recent results from the STAR collaboration on charge dependent correlations are consistent with...

We consider the 3D equation $u_{yy} = u_{tx} + u_yu_{xx} - u_xu_{xy}$ and its 2D reductions: (1) (u_y+y)u_{xx}-u_xu_{xy}-2$ (which is equivalent to Gibbons-Tsarev equation) (2) (u_y+2x)u_{xx} (y-u_x)u_{xy} -u_x$. Using reduction of known Lax pair for equation, we describe nonlocal symmetries of~(1) and~(2) show that Lie algebras these are isomorphic Witt algebra.