A result on the Gelfand-Kirillov dimension of representations of classical groups

Let be the reductive dual pair . We show that if is a representation of (respectively ) obtained from duality correspondence with some representation of (respectively ), then its Gelfand-Kirillov dimension is less than or equal to
(respectively ).

     

Synthesis and magnetic properties of CoFe2O4 ferrite nanoparticles

CoFe₂O₄ ferrite nanoparticles were prepared by a modified chemical coprecipitation route. Structural and magnetic properties were systematically investigated. X-ray diffraction results showed that the sample was in single phase with the space group . The results of field-emission scanning electronic microscopy showed that the grains appeared spherical with diameters ranging from 20 to 30 nm. The composition determined by energy-dispersive spectroscopy was stoichiometry of CoFe₂O₄. The Curie temperature in the process of increasing temperature was slightly higher than that in the process of decreasing temperature. This can be understood by the fact that heating changed Co²⁺ ion redistribution in tetrahedral and in octahedral sites. The coercivity of the synthesized CoFe₂O₄ samples was lower than the theoretical values, which could be explained by the mono-domain structure and a transformation from ferrimagnetic to superparamagnetic state.     

A hierarchy of Hamiltonian lattice equations associated with the relativistic Toda type system

By considering a discrete iso-spectral problem, a hierarchy of bi-Hamiltonian relativistic Toda type lattice equations are revisited. After introducing a semi-direct sum Lie algebras of four by four matrices, integrable coupling system associated with the relativistic Toda type lattice are derived. It is shown that the resulting lattice soliton hierarchy possesses Hamiltonian structures and infinitely many common commuting symmetries as well infinitely many conserved functions. The Liouville integrability of the resulting system is then demonstrated.     

Using a partially observable Markov chain model to assess colonoscopy screening strategies – A cohort study

Colorectal cancer (CRC) is notoriously hard to combat for its high incidence and mortality rates. However, with improved screening technology and better understanding of disease pathways, CRC is more likely to be detected at early stage and thus more likely to be cured. Among the available screening methods, colonoscopy is most commonly used in the U.S. because of its capability of visualizing the entire colon and removing the polyps it detected. The current national guideline for colonoscopy screening recommends an observation-based screening strategy. Nevertheless, there is scant research studying the cost-effectiveness of the recommended observation-based strategy and its variants. In this paper, we describe a partially observable Markov chain (POMC) model which allows us to assess the cost-effectiveness of both fixed-interval and observation-based colonoscopy screening strategies. In our model, we consider detailed adenomatous polyp states and estimate state transition probabilities based on longitudinal clinical data from a specific population cohort. We conduct a comprehensive numerical study which investigates several key factors in screening strategy design, including screening frequency, initial screening age, screening end age, and screening compliance rate. We also conduct sensitivity analyses on the cost and quality of life parameters. Our numerical result demonstrates the usability of our model in assessing colonoscopy screening strategies with consideration of partial observation of true health states. This research facilitates future design of better colonoscopy screening strategies.     

Photonic EPR State from Quadratic Waveguide Array with Alternating Positive and Negative Couplings

We propose the generation of photonic EPR state from quadratic waveguide array. Both the propagation constant and the nonlinearity in the array are designed to possess a periodical modulation along the propagation direction.This ensures that the photon pairs can be generated efficiently through the quasi-phase-matching spontaneous parametric down conversion by holding the spatial EPR entanglement in the fashion of correlated position and anticorrelated momentum. The Schmidt number which denotes the degree of EPR entanglement is calculated and it can approach a high value when the number of illuminated waveguide channels and the length of the waveguide array are properly chosen. These results suggest the quadratic waveguide array as a compact platform for engineering photonic quantum states in a high-dimensional Hilbert space.     

Design of diamond-shaped transient thermal cloaks with homogeneous isotropic materials

Transformation thermodynamics as a major extension of transformation optics has recently received considerable attention. In this paper, we present two-dimensional (2D) and three-dimensional (3D) diamond-shaped transient thermal cloaks with non-singular homogeneous material parameters. The absence of singularity in the parameters results from the fact that the linear coordinate transformation is performed by expanding a line segment rather than a point into a region, while the mechanism behind the homogeneity is the homogeneous stretching and compression along orthogonal directions during the transformation. Although the derived parameters remain anisotropic, we further show that this can be circumvented by considering a layered structure composed of only four types of isotropic materials based on the effective medium theory. Numerical simulation results confirm the good performance of the proposed cloaks.     

A brief review of co-doping

Dopants and defects are important in semiconductor and magnetic devices. Strategies for controlling doping and defects have been the focus of semiconductor physics research during the past decades and remain critical even today. Co-doping is a promising strategy that can be used for effectively tuning the dopant populations, electronic properties, and magnetic properties. It can enhance the solubility of dopants and improve the stability of desired defects. During the past 20 years, significant experimental and theoretical efforts have been devoted to studying the characteristics of co-doping. In this article, we first review the historical development of co-doping. Then, we review a variety of research performed on co-doping, based on the compensating nature of co-dopants. Finally, we review the effects of contamination and surfactants that can explain the general mechanisms of co-doping.     

Surface-enhanced Raman scattering from silver nanostructures with different morphologies

Scanning electron microscopy and X-ray diffraction reveal that four different types of crystalline silver nanostructures including nanoparticles, nanowires, nanocubes, and bipyramids are synthesized by a solvothermal method by reducing silver nitrate with ethylene glycol using poly(vinylpyrrolidone) as an adsorption agent and adding different quantities of sodium chloride to the solution. These nanostructures which exhibit different surface plasma resonance properties in the ultraviolet–visible region are shown to be good surface-enhanced Raman scattering (SERS) substrates using rhodamine 6G molecules. Our results demonstrate that the silver nanocubes, bipyramids with sharp corners and edges, and aggregated silver nanoparticles possess better SERS properties than the silver nanowires, indicating that they can serve as high-sensitivity substrates in SERS-based measurements.