Review of fluorescence anisotropy decay analysis by frequency-domain fluorescence spectroscopy

This didactic paper summarizes the mathematical expressions needed for analysis of fluorescence anisotropy decays from polarized frequency-domain fluorescence data. The observed values are the phase angle difference between the polarized components of the emission and the modulated anisotropy, which is the ratio of the polarized and amplitude-modulated components of the emission. This procedure requires a separate measurement of the intensity decay of the total emission. The expressions are suitable for any number of exponential components in both the intensity decay and the anisotropy decay. The formalism is generalized for global analysis of anisotropy decays measured at different excitation wavelengths and for different intensity decay times as the result of quenching. Additionally, we describe the expressions required for associated anisotropy decays, that is, anisotropy decays where each correlation time is associated with a decay time present in the anisotropy decay. And finally, we present expressions appropriate for distributions of correlation times. This article should serve as a reference for researchers using frequency-domain fluorometry.     

Application of platinum gauze activated by hydrogen to the adsorption separation of silver traces and their determination by aas or spectrophotometry

A method ("electrosorption") has been developed for separation of silver from copper by its deposition through internal electrolysis with hydrogen adsorbed on a platinum surface. The silver can then be stripped and determined by atomic-absorption spectrometry or the dithizone method. The activation of the platinum surface with adsorbed hydrogen can be achieved either electrolytically or by passing hydrogen gas through the solution in which the platinum is immersed. The method of electrosorption has been successfully applied to determination of trace levels of silver in copper metal.     

Direct experimental limit on neutron-mirror-neutron oscillations

In case a mirror world with a copy of our ordinary particle spectrum would exist, the neutron n and its degenerate partner, the mirror neutron n', could potentially mix and undergo nn' oscillations. The interaction of an ordinary magnetic field with the ordinary neutron would lift the degeneracy between the mirror partners, diminish the n' amplitude in the n wave function and, thus, suppress its observability. We report an experimental comparison of ultracold neutron storage in a trap with and without superimposed magnetic field. No influence of the magnetic field is found and, assuming negligible mirror magnetic fields, a limit on the oscillation time taunn' > 103 s (95% C.L.) is derived.     

SO(2) Symmetry of a Maxwell p-Form Theory

We find a universal SO(2) symmetry of a p-form Maxwell theory for both odd and even p. For odd p, it corresponds to the duality rotations but for even p, it defines a new set of transformations which is not related to duality rotations. In both cases, a symmetry group defines a subgroup of the O(2,1) group of R-linear canonical transformations which has also a natural representation on the level of quantization condition for p-brane dyons.     

Pointwise error estimates for a stabilized Galerkin method: non-selfadjoint problems

Highly localized pointwise error estimates for a stabilized Galerkin method are provided for second-order non-selfadjoint elliptic partial differential equations. The estimates show a local dependence of the error on the derivative of the solution u and weak dependence on the global norm. The results in this paper are an extension of the previous pointwise error estimates for the self-adjoint problems. In order to provide pointwise error estimates in the presence of the first-order term in the differential equations, we prove that the stabilized Galerkin solution is higher order perturbation to the Ritz projection of the true solutions. Then, we proceed to obtain pointwise estimates using the so-called discrete Green’s function. Application to error expansion inequalities and a posteriori error estimators are briefly discussed.     

Quasi-Banach spaces of almost universal disposition

We show that for each p∈(0,1]$p\in (0,1]$ there exists a separable p  -Banach space _Gp${\mathbb{G}}_p$ of almost universal disposition, that is, having the following extension property: for each ε>0$\epsilon >0$ and each isometric embedding g:X→Y$g:X\to Y$, where Y is a finite-dimensional p-Banach space and X   is a subspace of _Gp${\mathbb{G}}_p$, there is an ε  -isometry f:Y→_Gp$f:Y\to {\mathbb{G}}_p$ such that x=f(g(x))$x=f(g(x))$ for all x∈X$x\in X$.     

The K-Quotient

The Rayleigh Quotient and a recently proposed Timoshenko Quotient [1] are upper bounds to the fundamental eigenvalue of a discrete dynamic system. The closeness of these upper bounds to the fundamental eigenvalue depends on the closeness of the trial vectors to the eigenmode used in the calculation. In the present paper, a new quotient is presented. This quotient does not require the closeness of the trial vector to the eigenmode and its accuracy is improvable by raising the numerical value of the parameter p.     

SOME PROPERTIES OF HOLOMORPHIC CLIFFORDIAN FUNCTIONS IN COMPLEX CLIFFORD ANALYSIS

In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of Cn+1, so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study polynomial and singular solutions of the equation D△mf=0, obtain the integral representation formula for the complex holomorphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of Cn+1, deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them.     

On the generalized Fréchet functional equation with constant coefficients and its stability

We study a generalization of the Fréchet functional equation, stemming from a characterization of inner product spaces. We show, in particular, that under some weak additional assumptions each solution of such an equation is additive. We also obtain a theorem on the Ulam type stability of the equation. In its proof we use a fixed point result to show the existence of an exact solution of the equation that is close to a given approximate solution.     

Diode-pumped passively Q-switched picosecond Nd:GDxY1-xVO4 self-stimulated raman laser

An efficiency of 8.2% is demonstrated for a diode-pumped passively Q-switched self-stimulated Raman laser with an a-cut mixed vanadate crystal, Nd:Gd0.8Y0.2VO4. At 2.2 W of incident pump power, the self-stimulated Raman laser produces pulses as short as 660 ps at a Stokes wavelength of 1175 nm with 2.7 microJ of energy per pulse at a 66-kHz repetition rate.