Solving the problem of contact equilibrium of a punch and an elastic body

The variational problem of contact equilibrium of a punch and an elastic body is considered. An equivalent formulation of the problem is given in variational inequality form. Existence and uniqueness of the solution is investigated in a particular case. A penalty method is proposed for approximate solution of the problem.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 97–103, 1985.     

Estimating a reduced rank regression model for non-normal variables

A method using third order moments for estimating the regression coefficients as well as the latent state scores of the reduced-rank regression model when the latent variable(s) are non-normally distributed is presented in this paper. It is shown that the factor analysis type indeterminacy of the regression coefficient matrices is eliminated. A real life example of the proposed method is presented. Differences of this solution with the reduced-rank regression eigen solution are discussed.     

Stationary turbulent closure via the Hopf functional equation

Exact closed-form solutions are exhibited for the Hopf equation for stationary incompressible 3D Navier-Stokes flow, for the cases of homogeneous forced flow (including a solution with depleted nonlinearity) and inhomogeneous flow with arbitrary boundary conditions. This provides an exact method for computing two- and higher-point moments, given the mean flow.     

A Recursive Algorithm for Order Cycle-time that Minimizes Logistics Cost

A firm's logistics cost, including shipping and inventory-carrying, is a substantial percentage of its sales. Nevertheless, typical inventory-control methods ignore or insufficiently represent the shipping cost. This paper describes a recursive algorithm that determines the reorder cycle-time that minimizes total logistics cost. It allows for a realistic accounting of shipping cost, which is modelled here as a function of shipping distance and weight. The algorithm uses a relaxation procedure to identify a suitable initial approximation to the optimal order cycle-time and then, through a series of recursive steps, moves to the optimal result. We demonstrate the algorithm with a single item, with a group of items that share a common order cycle, and with multi-items when item demands are random variables. Experience with this algorithm indicates that it converges to the optimal result in a very few steps.     

Study of the reaction238U (α, α′f) atE α=480 MeV

The excitation function of the fission probability P _E E _x) for²³⁸U has been measured in the reaction²³⁸U(α, α′ f) at 480 MeV bombarding energy. The reaction mechanism of this reaction is discussed for excitation energies belowB _nf , the threshold for second chance fission, and aboveB _nf up toE _x =37 MeV. In comparing with results from fission induced by photons and by particle transfer reactions the (α, α′f) reaction gives too low values for the fission probabilityP _f at excitation energies well aboveB _nE . The role of the quasi-elastic knock-out process in this reaction is discussed.     

τ-CHEBYSHEV AND τ-COCHEBYSHEV SUBPSACES OF BANACH SPACES

The concepts of quasi-Chebyshev and weakly-Chebyshev and σ-Chebyshev were defined [3 - 7], andas a counterpart to best approximation in normed linear spaces, best coapprozimation was introduced by Franchetti and Furi^[1]. In this research, we shall define τ-Chebyshev subspaces and τ-cochebyshev subspaces of a Banach space, in which the property τ is compact or weakly-compact, respectively. A set of necessary and sufficient theorems under which a subspace is τ-Chebyshev is defined.     

Schmidt analysis of pure-state entanglement

We examine the application of Schmidt mode analysis to pure-state entanglement. Several examples permitting exact analytic calculation of Schmidt eigenvalues and eigenfunctions are included, as well as evaluation of the associated degree of entanglement.     

Observation of the nonlinear effect in relativistic Thomson scattering of electron and laser beams

Thomson scattering of high-power laser and electron beams is a good test of electrodynamics in the high-field region. We demonstrated production of high-intensity X-rays in the head-on collision of a CO₂ laser and 60-MeV electron beams at Brookhaven National Laboratory, Accelerator Test Facility. The energy of an X-ray photon was limited at 6.5 keV in the linear (lowest order) Thomson scattering, but the nonlinear (higher order) process produces higher energy X-rays. We measured the angular distribution of the high-energy X-rays and confirmed that it agrees with theoretical predictions.