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.

We prove the Gan–Gross–Prasad conjecture for U(n)×U(n) under some local conditions using a relative trace formula. We deduce some new cases of the Gan–Gross–Prasad conjecture for U(n+1)×U(n) from the case of U(n)×U(n).