The Klein-Gordon equation and scattering theory

Using our previously developed theory, we prove the main conclusions of scattering theory for the Klein-Gordon equation under hypotheses weaker than presently known. We consider more general equations and obtain stronger results.     

A subgradient duality theorem

A duality theorem of P. Wolfe for nonlinear differentiable programming is extended to the nondifferentiable case by replacing gradients by subgradients. The dual pair is further simplified in the case that nondifferentiability enters only in the objective functions and then only through a positively homogeneous convex function. A number of previously studied problems appear as special cases.     

Eigenfunction expansions for the Schrödinger operator

We obtain an eigenfunction expansion for the operator ?°+V under assump-tions (1.2)–(1.5) given below.     

Photochemical reactions in an isothermal laminar-flow chemical reactor

Summary The photolysis of a photon sensitive material in a laminar-flow tubular reactor is examined theoretically. Included in the analysis are the coupled effects of diffusion, convection, photon attenuation and reaction rate. The analytical solution to the problem is complex and somewhat tedious to apply. Consequently, an approximate solution, which is simpler, has been devised and the accuracy of the approximation tested.     

Tensor products and joint spectra

We prove that the joint spectrum of the tensor product of several operators is the cartesian product of their spectra.     

Linderstrom-Lang-Schellman's model for protein stabilization revisited

The fact that cleavage of single peptide linkages in proteins often leads to extensive conformational alteration, including regions far removed from the cleavage site is not fully understood. We propose, based on the work of Linderstrom-Lang and Schellman, that disruption primarily occurs within protein structural domains that are stabilized by cooperative interactions and that cleavage of single peptide linkages of the domain perturbs the entire cooperative interaction. For this model we review experimental observations: on fragment complexation (ribonuclease A, staphylococcal nuclease and cytochrome c), destabilized N-terminal large fragments (ribonuclease A and nuclease), cooperative folding and stabilization of proteins (ribonuclease A, nuclease and cytochrome c), the close relationship of the three-dimensional structure between fragment complexes and the original protein (ribonuclease A and nuclease), ligand induced stabilization (nuclease), 3D domain swapping, circular permutation (dihydrofolate reductase), evolutionary conservation (cytochrome c fold). Based on analysis of these observations, we conclude that the cooperative interactions of domains are important for the mechanism of 3D domain swapping as well as for stabilization and thereby, determination of the ground state of native proteins. Furthermore, analysis of the observations reveals that domains generally contain a hydrophobic core. Further, based on studies of cytochrome c and the Tsao, Evans and Wennerstrom model of electrostatic interactions between two hydrophobic monolayers, we propose the model that the hydrophobic core of a domain is polarizable and responds to the surface charges through its polarizability to stabilize the domain, explaining in part the nature of the cooperative interactions.     

An infinite-dimensional linking theorem and applications

In this paper, we establish a new infinite-dimensional linking theorem without (PS)-type assumptions. The new theorem needs a weaker linking geometry and produces bounded (PS) sequences. The abstract result will be applied to the study of the existence of solutions of the strongly indefinite partial differential systems. For the first application, we consider the system

     

Well-defined quasiparticles in interacting metallic grains

We analyze spectral functions of mesoscopic systems with large dimensionless conductance, which can be described by a universal Hamiltonian. We show that an important class of spectral functions are dominated by one single state only, which implies the existence of well-defined (i.e., infinite-lifetime) quasiparticles. Furthermore, the dominance of a single state enables us to calculate zero-temperature spectral functions with high accuracy using the density-matrix renormalization group. We illustrate the use of this method by calculating the tunneling density of states of metallic grains, of which we discuss the crossover from the few-electron to the bulk regime.