Boundary rigidity and stability for generic simple metrics

We study the boundary rigidity problem for compact Riemannian manifolds with boundary : is the Riemannian metric uniquely determined, up to an action of diffeomorphism fixing the boundary, by the distance function known for all boundary points and ? We prove in this paper local and global uniqueness and stability for the boundary rigidity problem for generic simple metrics. More specifically, we show that there exists a generic set of simple Riemannian metrics such that for any , any two Riemannian metrics in some neighborhood of having the same distance function, must be isometric. Similarly, there is a generic set of pairs of simple metrics with the same property. We also prove Hölder type stability estimates for this problem for metrics which are close to a given one in .     

Synthesis of some novel 11b-substituted pyrimido[6,1-a]-isoquinoline derivatives

A series of novel 11b-substituted 1,6,7,11b-tetrahydropyrimido[6,1-a]- isoquinoline-2,4-diones and 4-thioxo-1,3,4,6,7,11b-hexahydropyrimido[6,1-a]isoquinolin-2- ones were synthesized, utilizing two alternative strategies for ring closure of tetrahydroisoquinoline intermediates obtained from N-phenethyl enaminones.     

On the identities of the Grassmann algebras in characteristicp>0

In this note we exhibit bases of the polynomial identities satisfied by the Grassmann algebras over a field of positive characteristic. This allows us to answer the following question of Kemer: Does the infinite dimensional Grassmann algebra with 1, over an infinite fieldK of characteristic 3, satisfy all identities of the algebraM ₂(K) of all 2×2 matrices overK? We give a negative answer to this question. Further, we show that certain finite dimensional Grassmann algebras do give a positive answer to Kemer's question. All this allows us to obtain some information about the identities satisfied by the algebraM ₂(K) over an infinite fieldK of positive odd characteristic, and to conjecture bases of theidentities ofM ₂(K).     

Applicability of density functional theory in reproducing accurate vibrational spectra of surface bound species

The structural equilibrium parameters, the adsorption energies, and the vibrational frequencies of the nitrogen molecule and the hydrogen atom adsorbed on the (111) surface of rhodium have been investigated using different generalized‐gradient approximation (GGA), nonlocal correlation, meta‐GGA, and hybrid functionals, namely, Perdew, Burke, and Ernzerhof (PBE), Revised‐RPBE, vdW‐DF, Tao, Perdew, Staroverov, and Scuseria functional (TPSS), and Heyd, Scuseria, and Ernzerhof (HSE06) functional in the plane wave formalism. Among the five tested functionals, nonlocal vdW‐DF and meta‐GGA TPSS functionals are most successful in describing energetics of dinitrogen physisorption to the Rh(111) surface, while the PBE functional provides the correct chemisorption energy for the hydrogen atom. It was also found that TPSS functional produces the best vibrational spectra of the nitrogen molecule and the hydrogen atom on rhodium within the harmonic formalism with the error of ?2.62 and ?1.1% for the N? N stretching and Rh? H stretching frequency. Thus, TPSS functional was proposed as a method of choice for obtaining vibrational spectra of low weight adsorbates on metallic surfaces within the harmonic approximation. At the anharmonic level, by decoupling the Rh? H and N? N stretching modes from the bulk phonons and by solving one‐ and two‐dimensional Schrödinger equation associated with the Rh? H, Rh? N, and N? N potential energy we calculated the anharmonic correction for N? N and Rh? H stretching modes as ?31 cm^?1 and ?77 cm^?1 at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments. © 2014 Wiley Periodicals, Inc.     

Anode Catalysts for Direct Hydrazine Fuel Cells: From Laboratory Test to an Electric Vehicle

Novel highly active electrocatalysts for hydrazine hydrate fuel cell application were developed, synthesized and integrated into an operation vehicle prototype. The materials show in both rotating disc electrode (RDE) and membrane electrode assembly (MEA) tests the world highest activity with peak current density of 16 000 A g^?1 (RDE) and 450 mW cm^?2 operated in air (MEA).     

Cathode Spot Phenomena in Low Current Vacuum Arcs on Arc-Cleaned Electrode Surfaces. II. Spot Dynamics

Part II of the paper presents results of high temporal and spatial resolution experiments with vacuum arcs on pre-arced surfaces. Immobile spots, continuous spot motion and spot position oscillations have been observed. Tentative explanations of these phenomena are offered.     

A SUCCESSIVE LEAST SQUARES METHOD FOR STRUCTURED TOTAL LEAST SQUARES

A new method for Total Least Squares (TLS) problems is presented. It differs from previous approaches and is based on the solution of successive Least Squares problems.The method is quite suitable for Structured TLS (STLS) problems. We study mostly the case of Toeplitz matrices in this paper. The numerical tests illustrate that the method converges to the solution fast for Toeplitz STLS problems. Since the method is designed for general TLS problems, other structured problems can be treated similarly.     

Smoothness of solutions of nonlinear ODE

Smoothness of a -function f is measured by (Carleman) sequence we say if with As an extension of our results in [2] we prove the following type statements: Let u be -function on [0,1] such that where is an entire function of order 1, finite type, on z and of a nonanalytic Carleman class on t. Then u is in the same Carleman class. Received: 16 January 2001 / Revised version: 10 August 2001 / Published online: 6 August 2002