Nondissipative curves in Hilbert spaces having a limit of the corresponding correlation function

In this work a class of nondissipative curves in Hilbert spaces whose correlation functions have a limit ast± is presented. These curves correspond to a class of nondissipative basic operators that are a coupling of a dissipative operator and an antidissipative one. The wave operators and the scattering operator for the couple (A ^*, A) ( ) are obtained. The present work is a continuation and a generalization of the investigations of K.Kirchev and V.Zolotarev [1, 2, 3] on the model representations of curves in Hilbert spaces where the respective semigroup generator is a dissipative operator. This article includes four parts. A new form of the triangular model of M.S. Livic ([4, 5]) for the considered operators is introduced in the first part by the help of a suitable representation of the selfadjoint operatorL. This allows us to describe the studied class of nondissipative curves. The second part studies some results concerning the application of the analogue for multiplicative integrals of the well-known Privalov's theorem ([6]) about the limit values in the scalar case. This analogue is a reconstruction of measure by limit values in Stieltjes-Perron's style and it is obtained by L.A. Sakhnovich ([7]). Another problem, considered in the second part is the analogue inC ^m of the classical gamma-function and several properties for further consideration. In the third part the asymptotics of the studied curves corresponding to the nondissipative operators-couplings of a dissipative and an antidissipative operator with absolutely continuous real spectra and the limits of their correlation functions are obtained In the fourth part a scattering theory of a couple (A ^*, A) with a nondissipative operatorA from is constructed as in the selfadjoint case ([8, 9, 10]) and in the dissipative case ([7]). These results show an interesting new effect: the studied nondissipative case is near to the dissipative one.Partially supported by Grant MM-810/98 of MESC     

Charge accumulation in ultrathin Cs / n - GaN and Cs / n - InGaN interfaces

We report on the observation of new phenomena that arise under Cs adsorption on n-GaN(0001) and n-InGaN(0001) surfaces. First, an extremely highly quantum efficient photoemission has been found by excitation with visible light in the transparency region of GaN and InGaN. The photoemission is revealed to appear due to the formation of an electron accumulation layer in the vicinity of the surfaces. Second, a large variety of band bending and potential wells are provided by the Cs coverages. The accumulated charge density at the n-InGaN surface is much stronger than that at the n-GaN surface. Third, a new effect is revealed, namely, the appearance of an oscillation structure in the spectral dependences of the threshold photoemission. A model concept is proposed for photocurrent oscillations that takes into account the formation of an accumulation layer and the multiple-beam interference in parallel-sided GaN or InGaN samples.     

Multigrid method for solving convection-diffusion problems with dominant convection

A modification of the multigrid method for the solution of linear algebraic equation systems with a strongly nonsymmetric matrix obtained after difference approximation of the convection-diffusion equation with dominant convection is proposed. Specially created triangular iterative methods have been used as the smoothers of the multigrid method. Some theoretical and numerical results are presented.     

Experimental and computational studies of the macrocyclic effect of an auxiliary ligand on electron and proton transfers within ternary copper(II)-Histidine complexes

The dissociation of [Cu^II(L)His]^•2+ complexes [L=diethylenetriamine (dien) or 1,4,7-triazacyclononane (9-aneN₃)] bears a strong resemblance to the previously reported behavior of [Cu^II(L)GGH]^•2+ complexes. We have used low-energy collision-induced dissociation experiments and density functional theory (DFT) calculations at the B3LYP/6-31+G(d) level to study the macrocyclic effect of the auxiliary ligands on the formation of His^•+ from prototypical [Cu^II(L)His]^•2+ systems. DFT revealed that the relative energy barriers of the same electron-transfer (ET) dissociation pathways of [Cu^II(9-aneN₃)His]^•2+ and [Cu^II(dien)His]^•2+ are very similar, with the ET reactions of [Cu^II(9-aneN₃)His]^•2+ leading to the generation of two distinct His^•+ species; in contrast, the proton transfer (PT) dissociation pathways of [Cu^II(9-aneN₃)His]^•2+ and [Cu^II(dien)His]^•2+ differ considerably. The PT reactions of [Cu^II(9-aneN₃)His]^•2+ are associated with substantially higher barriers (>13 kcal/mol) than those of [Cu^II(dien)His]^•2+. Thus, the sterically encumbered auxiliary 9-aneN₃ ligand facilitates ET reactions while moderating PT reactions, allowing the formation of hitherto nonobservable histidine radical cations.