On orthogonal matrices with constant diagonal

In connection with the problem of finding the best projections of k-dimensional spaces embedded in n-dimensional spaces Hermann König asked: Given m∈$\text{R}$ and n∈$\text{N}$, are there n×n matrices C=(c_ij), i, j=1,…,n, such that c_ii=m for all i, |c_ij|=1 for i≠j, and C²=(m²+n?1)I_n? König was especially interested in symmetric C, and we find some families of matrices satisfying this condition. We also find some families of matrices satisfying the less restrictive condition CC^T=(m²+n?1)I_n.     

Field-theoretic extended particles in two space dimensions

A family of Lagrangian models of two scalar fields in (2 + 1) dimensions is studied. All their localized static classical solutions are obtained, and interpreted as representing systems of extended particles. The models are generalized by taking into account general-relativistic gravirational coupling, for which case the general static solutions are also obtained explicitly.     

Non-skew symmetric orthogonal matrices with constant diagonals

A matrix C of order n is orthogonal if CC^T=dI. In this paper, we restrict the study to orthogonal matrices with a constant m > 1 on the diagonal and ±1's off the diagonal. It is observed that all skew symmetric orthogonal matrices of this type are constructed from skew symmetric Hadamard matrices and vice versa. Some simple necessary conditions for the existence of non-skew orthogonal matrices are derived. Two basic construction techniques for non-skew orthogonal matrices are given. Several families of non-skew orthogonal matrices are constructed by applying the basic techniques to well-known combinatorial objects like balanced incomplete block designs. It is also shown that if m is even and n=0 (mod 4), then an orthogonal matrix must be skew symmetric. The structure of a non-skew orthogonal matrix in the special case of m odd,n=2 (mod 4) and m?1/6n is also studied in detail. Finally, a list of cases with n?50 is given where the existence of non-skew orthogonal matrices are unknown.     

Measurement of the spin parameters A and Ann in pp elastic scattering in the 1–3 GeV/c region

We have measured the asymmetry parameter A and the spin correlation parameter A_nn in pp elastic scattering, using the Argonne ZGS polarized proton beam and a polarized proton target. Angular distributions of A and A_nn for |t| ? 0.2 (GeV/c)²wereobtainedateightmomentabetween 1.10 and 2if2.75 GeV/c. We find significant structure in both the energy and t-dependence of A_nn at these energies. At p_lab ≈ 1.34 GeV/cA_nn reaches a very large value of about 0.8–0.9 near θ_cm = 90°.     

Effects of the n-n potential core on the spectroscopic sum rules for one-nucleon transfer

Previously derived sum rules are shown to have corrections if the potential contains a hard core. The corrections represent a total loss of single-particle strength which also occurs from the low-energy observable region in the soft-core case. Estimates give a reduction of at least 5 % in the total sum rules, but negligible additional spin-dependent corrections to the partial or spin-dependent sum rules. Important consequences of this lack of spin dependence are pointed out for existing and future sum-rule analyses of spectroscopic data.     

Optimization of extinction efficiency of gold‐coated polystyrene bead substrates improves surface‐enhanced Raman scattering effects by post‐growth microwave heating treatment

We report a novel post‐growth microwave treatment approach to selectively modify the surface morphologies of gold (Au) films coated on the polystyrene (PS) bead substrates for effectively improving the surface‐enhanced Raman scattering (SERS) effect on the analytes. The discrete dipole approximation (DDA) model was introduced to evaluate the enhancement effects by calculating the localized electromagnetic field distribution and extinction efficiency based on the sizes of the trenches and voids, and the surface roughness of the modified Au–PS bead substrates. The SERS performance of microwave‐modified Au–PS substrates on rhodamine 6G (Rh 6G) and saliva yields at least 10‐fold improvements in SERS intensities compared to the as‐grown substrates, which is also in agreement with theoretical predictions by DDA modeling. This work demonstrates both experimentally and theoretically the efficacy of the microwave heating treatment on modifying the Au–PS bead substrates for the realization of high SERS performance in biomedical applications. Copyright © 2009 John Wiley & Sons, Ltd.     

Study of spectator tagging in the reaction np → ppπwith a deuteron beam

The reaction has been studied in a kinematically complete experiment at a single beam momentum GeV/c (T = 759MeV). All four ejectiles have been detected in the large-acceptance time-of-flight spectrometer COSY-TOF. We analyzed the data along the lines of the spectator model as a means to isolate the quasi-free reaction. The spectator proton was identified by its momentum and flight direction thus yielding access to the associated Fermi motion of the bound neutron. A comparison is carried out with Monte Carlo simulations based on two different parameterizations of the deuteron wave function. Up to a Fermi momentum of roughly 150MeV/c no significant deviations between experimental and simulated data of various observables were found from which we conclude that the deuteron can indeed be taken as a valid substitute for the neutron.