Remark on the strong unique continuation property for parabolic operators

We consider solutions , in a neighbourhood of , to a parabolic differential equation with variable coefficients depending on space and time variables. We assume that the coefficients in the principal part are Lipschitz continuous and that those in the lower order terms are bounded. We prove that, if vanishes of infinite order at , then .

     

Schrödinger Operators on Lattices. The Efimov Effect and Discrete Spectrum Asymptotics

The Hamiltonian of a system of three quantum mechanical particles moving on the three-dimensional lattice and interacting via zero-range attractive potentials is considered. For the two-particle energy operator h(k), with the two-particle quasi-momentum, the existence of a unique positive eigenvalue below the bottom of the continuous spectrum of h(k) for k 0 is proven, provided that h(0) has a zero energy resonance. The location of the essential and discrete spectra of the three-particle discrete Schrödinger operator H(K), being the three-particle quasi-momentum, is studied. The existence of infinitely many eigenvalues of H(0) is proven. It is found that for the number N(0, z) of eigenvalues of H(0) lying below the following limit exists with Moreover, for all sufficiently small nonzero values of the three-particle quasi-momentum K the finiteness of the number of eigenvalues of H(K) below the essential spectrum is established and the asymptotics for the number N(K, 0) of eigenvalues lying below zero is given. Communicated by Gian Michele GrafSubmitted 19/11/03, accepted 08/03/04     

Low reheating temperature and the visible sterile neutrino

We present here a scenario, based on a low reheating temperature T(R)<100 MeV at the end of (the last episode of) inflation, in which the coupling of sterile neutrinos to active neutrinos can be as large as experimental bounds permit (thus making this neutrino "visible" in future experiments). In previous models this coupling was forced to be very small to prevent a cosmological overabundance of sterile neutrinos. Here the abundance depends on how low the reheating temperature is. For example, the sterile neutrino required by the Liquid Scintillator Neutrino Detector result may not have any cosmological problem within our scenario.     

Subcritical statistics in rupture of fibrous materials: experiments and model

We study experimentally the slow growth of a single crack in a fibrous material and observe stepwise growth dynamics. We model the material as a lattice where the crack is pinned by elastic traps and grows due to thermally activated stress fluctuations. In agreement with experimental data we find that the distribution of step sizes follows subcritical point statistics with a power law (exponent 3/2) and a stress-dependent exponential cutoff diverging at the critical rupture threshold.     

Fresh Inflation with Nonminimally Coupled Inflaton Field

I study a fresh inflationary model with a scalar field nonminimally coupled to gravity. An example is examined. I find that, as larger is the value of p (a t ^p ), as smaller (but larger in its absolute value) is the necessary value of the coupling to the inflaton field fluctuations can satisfy a scale invariant power spectrum.     

The formation of ReS(2) inorganic fullerene-like structures containing Re(4) parallelogram units and metal-metal bonds

The encapsulation of ReO(x) within ReS(2) inorganic fullerene-like cages is described for the first time. The encapsulate was prepared by the sulfidization of both hand-milled and ball-milled samples of ReO(2); partial conversion of the oxide to the sulfide was achieved with the degree of sulfidization depending on the exposure to the sulfidizing agent, H(2)S.     

LETTER: BTZ Black Hole from (3+1) Gravity

We propose an approach for constructing spatial slices of (3+1) spacetimes with cosmological constant but without a matter content, which yields (2+1) vacuum with solutions. The reduction mechanism from (3+1) to (2+1) gravity is supported on a criterion in which the Weyl tensor components are required to vanish together with a dimensional reduction via an appropriate foliation. By using an adequate reduction mechanism from the Plebaski–Carter[A] solution in (3+1) gravity, the (2+1) BTZ solution can be obtained.     

Synthesis and isolation of iodocarbazoles. Direct iodination of carbazoles by N‐iodosuccinimide and N‐iodosuccinimide‐silica gel system

Carbazole ( 1 ) undergoes electrophilic aromatic substitution with various iodinating reagents. Although, 3‐iodocarbazole ( 1b ) and 3,6‐diiodocarbazole ( 1d ) obtained by iodination of carbazole were isolated and characterized sometime ago, 1‐iodocarbazole ( 1a ), 1,6‐diiodocarbazole ( 1c ) and 1,3,6‐triiodocarbazole ( 1e ) had never been isolated from the reaction mixture. The preparation and subsequent isolation and characterization of 1a, 1b, 1c, 1d and 1e are reported (mp, t_r, R_f, ¹H‐nmr, ¹³C‐nmr and ms). As iodinating reagents, NaIO₄/I₂ and NaIO₄/KI mixtures in (i) ethanol doped with catalytical amount of sulfuric acid and in (ii) acetic acid, and N‐odosuccinimide and N‐iodosuccinimide‐silica gel in dichloromethane and in chloroform have been used and their uses have been compared. The iodination reaction of different carbazole derivatives such as 2‐acetoxycarbazole ( 2 ), 3‐bromocarbazole (3) and 3‐nitrocarbazole ( 4 ) was also studied and the corresponding iododerivatives, 2a, 2b, 2c, 3a, 3b, 4a and 4b , are described for the first time. Semiempirical PM3 calculations have been performed in order to predict reactivity of carbazole ( 1 ), substituted carbazoles (2‐4) and iodocarbazoles ( 1a‐1e, 2a‐2c, 3a‐3b, 4a and 4b ) (Scheme 1). Theoretical and experimental results are discussed briefly.     

Synthesis of dihydrolysergol analogues

As a part of a search for novel biological active ergoline derivatives, the indole ring present in the ergoline skeleton (indole[4,3‐f,g]quinoline) was converted into different heterocyclic ring systems such as quinazoline 2 , benzofurane 3 and benzoxazole 4 . Due to the paramount importance of chirality to attain biological activity, natural dihydrolysergic acid 1 was chosen as starting material and a synthetic pathway conservative in term of chirality was followed.