Theoretical investigation on the threshold value of stimulated Brillouin scattering in terms of laser intensity

The threshold value of stimulated Brillouin scattering (SBS) was investigated theoretically basing on a new concept of real gain length (RGL). It shows that for ideal steady-state SBS or ideal transient SBS, the threshold values are both constants and the later is five orders of magnitude larger than the former. Under general conditions, whether steady-state SBS or transient SBS will occur is determined by RGL. The SBS occurred in a long material may not be steady-state SBS.     

Analysis of ferroelectric switching in sodium nitrite:poly(vinyl alcohol) nanocomposite films

The Fourier transform infrared (FTIR) spectra and switching current response in sodium nitrite:poly(vinyl alcohol) nanocomposite films have been studied as a function of composition of NaNO₂. The switching current data fitted well to infinite-grain model (IGM) in the region t<t _s and to finite-grain model (FGM) in the region t≥t _s . The microscopic parameters like the dimensionality, the domain wall velocity, and the nucleation rate have been evaluated which provide more physical insight of the switching phenomena in the composite films. The polarization current and nucleation rate are optimum in 50 wt.% composite film and have been discussed in terms of grain size and strain variations with the composition. The effect of applied field and pulse width variation on the switching behavior of 50 wt.% composition has also been studied. The exponential field dependence of the domain wall velocity and the nucleation rate indicate that nucleation mechanism is responsible for switching phenomena in the composite films. The writing pulse width affects significantly on the switching behavior of the composite films.     

Analysis of serum from type II diabetes mellitus and diabetic complication using surface-enhanced Raman spectra (SERS)

In this paper, we show surface-enhanced Raman spectra (SERS) of serums from type II diabetes mellitus and diabetic complication (coronary disease, glaucoma and cerebral infarction), and analyze the SERS through the multivariate statistical methods of principal component analysis (PCA). In particular, we find that there exist many adenines in these serums, which maybe come from DNA (RNA) damage. The relative intensity of the band at 725±2 cm⁻¹ assigned to adenine is higher for patients than for the healthy volunteers; therefore, it can be used as an important ‘fingerprint’ in order to diagnose these diseases. It is also shown that serums from type II diabetes mellitus group, diabetic complication group and healthy volunteers group can be discriminated by PCA.     

Enhanced field emission from pulsed laser deposited nanocrystalline ZnO thin films on Re and W

Nanocrystalline ZnO thin films have been deposited on rhenium and tungsten pointed and flat substrates by pulsed laser deposition method. An emission current of 1 nA with an onset voltage of 120 V was observed repeatedly and maximum current density ∼1.3 A/cm² and 9.3 mA/cm² has been drawn from ZnO/Re and ZnO/W pointed emitters at an applied voltage of 12.8 and 14 kV, respectively. In case of planar emitters (ZnO deposited on flat substrates), the onset field required to draw 1 nA emission current is observed to be 0.87 and 1.2 V/μm for ZnO/Re and ZnO/W planar emitters, respectively. The Fowler–Nordheim plots of both the emitters show nonlinear behaviour, typical for a semiconducting field emitter. The field enhancement factor β is estimated to be ∼2.15×10⁵ cm⁻¹ and 2.16×10⁵ cm⁻¹ for pointed and 3.2×10⁴ and 1.74×10⁴ for planar ZnO/Re and ZnO/W emitters, respectively. The high value of β factor suggests that the emission is from the nanometric features of the emitter surface. The emission current–time plots exhibit good stability of emission current over a period of more than three hours. The post field emission surface morphology studies show no significant deterioration of the emitter surface indicating that the ZnO thin film has a very strong adherence to both the substrates and exhibits a remarkable structural stability against high-field-induced mechanical stresses and ion bombardment. The results reveal that PLD offers unprecedented advantages in fabricating the ZnO field emitters for practical applications in field-emission-based electron sources.     

Applications of operator identities to the multiple q-binomial theorem and q-Gauss summation theorem

In this paper, we first give an interesting operator identity. Furthermore, using the q-exponential operator technique to the multiple q-binomial theorem and q-Gauss summation theorem, we obtain some transformation formulae and summation theorems of multiple basic hypergeometric series.     

Path bundles on n-cubes

A path bundle is a set of 2^a paths in an n-cube, denoted Q_n, such that every path has the same length, the paths partition the vertices of Q_n, the endpoints of the paths induce two subcubes of Q_n, and the endpoints of each path are complements. This paper shows that a path bundle exists if and only if n>0 is odd and 0?a?n-⌈log₂(n+1)⌉.     

The resolvent algebra: A new approach to canonical quantum systems

The standard C^∗-algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does it incorporate pertinent physical observables such as (bounded functions of) the Hamiltonian. Here a novel C^∗-algebra of the canonical commutation relations is presented which does not suffer from such problems. It is based on the resolvents of the canonical operators and their algebraic relations. The resulting C^∗-algebra, the resolvent algebra, is shown to have many desirable analytic properties and the regularity structure of its representations is surprisingly simple. Moreover, the resolvent algebra is a convenient framework for applications to interacting and to constrained quantum systems, as we demonstrate by several examples.     

Order preserving transformations of the Hilbert grassmannian (note on the complex case)

Let H be a separable complex Hilbert space and be the Grassmannian of closed subspaces with infinite dimension and codimension. We show that every order preserving bijective transformation of is induced by an invertible bounded semi-linear operator. Received: 23 October 2007     

On the Cowen-Douglas Class for Banach Space Operators

In [3], M. J. Cowen and R. G. Douglas prove that the adjoint of a Hilbert space operator T is in the class if and only if T is unitarily equivalent with the operator M _z on a Hilbert space -valued analytic functions, where M _z denotes the operator of multiplication by the independent variable. The proof involves holomorphic vector bundles and Grauert’s theorem. In this paper we use a theorem by I. Gohberg and L. Rodman [4] to give a more elementary proof of this fact, which also works for Banach space operators.      

A note on holomorphic approximation in Banach spaces

Given a complex Banach space X and a holomorphic function f on its unit ball B, we discuss the problem whether f can be approximated, uniformly on smaller balls, by functions g holomorphic on all of X. Research partially supported by NSF grant DMS0700281.