Eigenvalues of a statistical mechanics matrix

We consider the problem of finding the spectrum of an n × n matrix which arises in the study of a certain model of long-range interactions in a one-dimensional statistical mechanics system. Our analysis exhibits a curious resemblance of the suitably normalized distribution of eigenvalues to the Marčenko–Pastur law in the limit n → ∞.     

Strongly orthogonal geminals: size-extensive and variational reference states

Properties and some applications of strongly orthogonal geminals (APSG) are reviewed emphasizing the motivations for their use and their shortcomings. An overview presents some techniques capable of improving the APSG function.     

Solubility of methane in octane + ethanol at temperatures from 303.15 K to 333.15 K and pressures up to 12.01 MPa

Solubility of methane in octane + ethanol was measured at temperatures ranging from 303.15 K to 333.15 K and pressures ranging from 2.60 MPa to 12.01 MPa. Experimental data were analyzed using the Soave-Redlich-Kwong equation of state with three types of mixing rules, and the estimated average deviation from the experimental solubility data was less than 3.5 %.     

Design of polyglycidol-containing microspheres for biomedical applications

The paper presents a short review on the synthesis, characterisation and selected medical applications of poly(styrene/α-tert-butoxy-ω-vinylbenzyl-polyglycidol) (P(S/PGL)) microspheres. The soap-free emulsion-polymerisation of styrene and α-tert-butoxy-ω-vinylbenzyl-polyglycidol macromonomer (PGL) in water yielded core-shell microspheres with a low particle-diameter dispersity (ratio of the weight average particle diameter and the number average particle diameter). The interfacial fraction of PGL units, estimated by XPS, was in the range of 0–42 mole % depending on the concentration of the macromonomer in the polymerisation feed. The studies of adsorption of model proteins showed that the surface fraction of adsorbed protein was significantly reduced when the PGL interfacial fraction was higher than 40 mole %. The P(S/PGL) particles with covalently immobilised proteins were used for the preparation of photonic crystal assemblies suitable for applications in optical biosensors and the medical diagnostic test for the detection of Helicobacter pylori antibodies in the blood serum.     

A Note on the Legendre Series Solution of the Biharmonic Equation for Cylindrical Problems

The solution of cylindrical problems is addressed. A series solution is considered of the biharmonic equation, in which the series terms of the stress function Φ are expressions based upon Legendre polynomials and logarithmically singular functions. An explicit form of a polynomial supplementing each logarithmically singular part of the series solution is obtained.     

An Incompressible Fluid in a Weakly Deformable Shell. Part I: Analysis of the Model

We consider the flow of a viscous incompressible fluid in a pipe when the boundary is a deformable shell of Naghdi type. We prove that the corresponding system of partial differential equations has a solution when the deformation of the shell is smooth and small enough. We propose an algorithm that uncouples the unknowns and prove its convergence.     

Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos

We apply the recently improved version of the 0–1 test for chaos to real experimental time series of laser droplet generation process. In particular two marginal regimes of dripping are considered: spontaneous and forced dripping. The outcomes of the test reveal that both spontaneous and forced dripping time series can be characterized as chaotic, which coincides with the previous analysis based on nonlinear time series analysis.     

Standard<Emphasis Type="Italic">SU</Emphasis>(5) supergravity grand unification model and predictions

A review is given of the StandardSU(5) supergravity model. This model has passed an important check regarding unification of the electro-weak and the strong couplings using high precision LEP data. It is shown that for a significant domain of the parameter space the model also satisfies constraints on the SUSY spectrum from CDF and LEP, as well as proton stability and cosmological relic density constraints.     

Simulation and design of a bandpass filter on metasubstrates

This work presents an analysis of the microstrip bandpass filter on metamaterial substrates. The filter is composed of two ring resonators with quarter-wavelength side-coupled sections. The filter input is provided, as well as the output port, using a quarter-wavelength side-coupled microstrip line section. Simulations by finite element method have been carried out to verify the effect of the metamaterial substrate properties on the filter performance, and to compare these results to those obtained considering isotropic substrate.     

Direct Images,Fields of Hilbert Spaces,and Geometric Quantization

Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family H _s of Hilbert spaces, and the question arises if the spaces H _s are canonically isomorphic. Axelrod et al. (J. Diff. Geo. 33:787–902, 1991) and Hitchin (Commun. Math. Phys. 131:347–380, 1990) suggest viewing H _s as fibers of a Hilbert bundle H, introduce a connection on H, and use parallel transport to identify different fibers. Here we explore to what extent this can be done. First we introduce the notion of smooth and analytic fields of Hilbert spaces, and prove that if an analytic field over a simply connected base is flat, then it corresponds to a Hermitian Hilbert bundle with a flat connection and path independent parallel transport. Second we address a general direct image problem in complex geometry: pushing forward a Hermitian holomorphic vector bundle ${E \to Y}$ along a non–proper map ${Y \to S}$ . We give criteria for the direct image to be a smooth field of Hilbert spaces. Third we consider quantizing an analytic Riemannian manifold M by endowing TM with the family of adapted Kähler structures from Lempert and Sz?ke (Bull. Lond. Math. Soc. 44:367–374, 2012). This leads to a direct image problem. When M is homogeneous, we prove the direct image is an analytic field of Hilbert spaces. For certain such M—but not all—the direct image is even flat; which means that in those cases quantization is unique.