Construction of pseudo-gradient vector field and sign-changing multiple solutions involving p-Laplacian

Existence of multiple and sign-changing solutions for a problem involving p-Laplacian and jumping nonlinearities are considered via the construction of descent flow in . Sign-changing and multiple solutions are obtained under additional assumption on the nonlinearity. The uniqueness of positive (negative) solution theorem is included too.     

Transmission problems and spectral theory for singular integral operators on Lipschitz domains

We prove the well-posedness of the transmission problem for the Laplacian across a Lipschitz interface, with optimal non-tangential maximal function estimates, for data in Lebesgue and Hardy spaces on the boundary. As a corollary, we show that the spectral radius of the (adjoint) harmonic double layer potential K∗ in is less than , whenever is a bounded convex domain and 1<p?2.     

Boundary blow-up solutions with a spike layer

We prove that for large λ>0, the boundary blow-up problem

     

Large time behavior of the heat kernel

In this paper we study the large time behavior of the (minimal) heat kernel k_P^M(x,y,t) of a general time-independent parabolic operator Lu=u_t+P(x,∂_x)u which is defined on a noncompact manifold M. More precisely, we prove that

     

Polynomial sequences of bounded operators

The basic results of spectral theory are obtained using the sequence of powers of a bounded linear operator T,T²,…,Tⁿ,…. In this paper, we replace the powers Tⁿ by certain polynomials p_n(T), and make use of special properties of the polynomial sequence to derive some new results concerning operators. For example, using an arbitrary polynomial sequence , we obtain “binomial” spectral radii and semidistances, which reduce, in the case of the sequence of powers, to the usual spectral radius and semidistance.     

Explicit exact solutions for a new generalized Hamiltonian amplitude equation with nonlinear terms of any order

Making use of a proper transformation and a generalized ansatz, we consider a new generalized Hamiltonian amplitude equation with nonlinear terms of any order, iu_x + u_tt + (|u|^p + |u|^2p)u + u_xt = 0. As a result, many explicit exact solutions, which include kink-shaped soliton solutions, bell-shaped soliton solutions, periodic wave solutions, the combined formal solitary wave solutions and rational solutions, are obtained.Received: April 4, 2002     

I.I. Rabi: The Two Cultures and the Universal Culture of Science

I set forth and discuss I.I. Rabis views on the nature of science and society, focusing specifically on Rabis views on science and government, science and education, and science and religion. I also explore the influence of Rabi and C.P. Snow on each other. In the 1960s, Rabi set forth his mature and boldest positions, advocating science as the center of education and science as the replacement for religion. His positions culminate in science as the universal culture. I highlight Rabi not only as a scientist and public servant, but also as a public intellectual actively engaged with and connected to major issues of his time.Michael A. Day is Professor of Physics at Lebanon Valley College. He holds doctorates in both physics and philosophy.     

tBuP(NH2)2--a reactive synthon for the synthesis of molecular imidophosphinates of group 13 metals

Reactions of tBuP(NH(2))(2) with Group 13 trialkyls MR(3) (M=Al, Ga, In; R=Me, tBu) were investigated in detail. According to variable-temperature (VT) NMR investigations, the reaction proceeds stepwise with the initial formation of aminophosphane adducts, which subsequently react to give iminophosphorane adducts and finally the heterocyclic metallonitridophosphinates. BP86/TZVPP (DFT) calculations were performed to verify this reaction pathway, to elucidate the influence of the central Group 13 element on the stability of the reaction intermediates and the heterocycles, as well as to assess the thermodynamics of their formation. The relative stability of free and complexed aminophosphane RP(NH(2))(2) and iminophosphorane R(H(2)N)(H)P=NH (adducts) with P(III) and P(V) centers was studied in more detail with DFT and MP2 methods. In addition, the influence of the substituent R was investigated by variation of R from H to Me, tBu, F, and NH(2). In general, the aminophosphane form was found to be favored for the free ligand, however, upon complexation with MR(3) (M=Al, Ga; R=alkyl) both forms are almost equal in energy.     

Addition of secondary phosphines to a vinyl ether of diacetone-d-glucose: a new approach to optically active phosphines and their derivatives

Secondary phosphines react readily with a vinyl ether of diacetone-d-glucose under radical initiation conditions to give, in high yield, anti-Markovnikov adducts, diorganyl{2-[3-O-(1,2:5,6-di-O-isopropylidene)-d-glucofuranosyloxy]ethyl}phosphines, which oxidize almost quantitatively upon reacting with air oxygen or elemental sulfur to form the corresponding optically active phosphine oxides or sulfides.