Completely irreducible sequences of meromorphic functions

Given a sequence {fn } of meromorphic functions on a plane domain D, there exists a (possibly empty) open set U■D and a subsequence {f n k } which converges uniformly (with respect to the spherical metric on ) on compact subsets of U, while no subsequence of {f n k } converges uniformly on compact subsets of any larger open subset of D.     

Designing molecules with optimal properties using the linear combination of atomic potentials approach in an AM1 semiempirical framework

The linear combination of atomic potentials (LCAP) approach is implemented in the AM1 semiempirical framework and is used to design molecular structures with optimized properties. The optimization procedure uses property derivative information to search molecular space and thus avoid direct enumeration and evaluation of each molecule in a library. Two tests are described: the optimization of first hyperpolarizabilities of substituted aromatics and the optimization of a figure of merit for n-type organic semiconductors.     

Diferential Inequalities,Normality and Quasi-normality

We prove that ifD is a domain in C,α 1 and C 0,then the family F of functions f meromorphic in D such that |f′(z)|/1 + |f(z)|α C for every z ∈ D is normal in D.For α = 1,the same assumptions imply quasi-normality but not necessarily normality.     

Self-gravitating ring of matter in orbit around a black hole: the innermost stable circular orbit

We study analytically a black-hole-ring system which is composed of a stationary axisymmetric ring of particles in orbit around a perturbed Kerr black hole of mass $M$ . In particular, we calculate the shift in the orbital frequency of the innermost stable circular orbit (ISCO) due to the finite mass $m$ of the orbiting ring. It is shown that for thin rings of half-thickness $r\ll M$ , the dominant finite-mass correction to the characteristic ISCO frequency stems from the self-gravitational potential energy of the ring (a term in the energy budget of the system which is quadratic in the mass $m$ of the ring). This dominant correction to the ISCO frequency is of order $O(\mu \ln (M/r))$ , where $\mu \equiv m/M$ is the dimensionless mass of the ring. We show that the ISCO frequency increases (as compared to the ISCO frequency of an orbiting test-ring) due to the finite-mass effects of the self-gravitating ring.     

Equal moments division of a set

Let be the minimal positive integer , for which there exists a splitting of the set into  subsets, , , ..., , whose first moments are equal. Similarly, let be the maximal positive integer , such that there exists a splitting of into subsets whose first moments are equal. For , these functions were investigated by several authors, and the values of and have been found for and , respectively. In this paper, we deal with the problem for any prime . We demonstrate our methods by finding for any and for .

     

Aggregation via empirical risk minimization

Given a finite set F of estimators, the problem of aggregation is to construct a new estimator whose risk is as close as possible to the risk of the best estimator in F. It was conjectured that empirical minimization performed in the convex hull of F is an optimal aggregation method, but we show that this conjecture is false. Despite that, we prove that empirical minimization in the convex hull of a well chosen, empirically determined subset of F is an optimal aggregation method.     

Remotely scanned multiphoton temporal focusing by axial grism scanning

A simple technique for remote scanning of the focal plane in temporal focusing multiphoton microscopy is demonstrated both theoretically and experimentally. A new on-axis light propagation optical setup design enables this scanning, which was considered not feasible in previous studies. The focal plane is axially displaced by the movement of a remote optical device, consisting of a double prism grating, and optionally a cylindrical lens. The displacement is linear, and its slope is inversely proportional to the square of the optical system's magnification.     

Radioactivity in the Exclusive Economic Zone of east coast Peninsular Malaysia: distribution trends of <Superscript>137</Superscript>Cs in surface seawater

Large volumes of surface seawater samples were collected from thirty locations in the Exclusive Economic Zone (EEZ) of the east coast Peninsular Malaysia on June 2008 to study the activity concentrations of ¹³⁷Cs. The results will serve as additional information to the existing baseline data and is very useful for monitoring fresh input of anthropogenic radionuclide into Malaysian marine environment. In this study, the activity concentrations of ¹³⁷Cs were determined using co-precipitation technique, followed by Gamma Spectrometry measurement. The mean activity concentration of ¹³⁷Cs ranged between 3.40 and 5.89 Bq/m³. Higher activity concentrations were observed at the coastal and towards the south of Peninsular Malaysia and were aligned with the high turbidity. These may due to the rapid diffusion of ¹³⁷Cs from suspended particulates and fine sediments into surface seawater. The activity concentrations of ¹³⁷Cs observed in this study were slightly higher than the concentrations reported in seawater at the Straits of Malacca, Vietnam and Philippines. This might be because the study area received more input of ¹³⁷Cs that originated from global fallout and then deposited on land which later being transported subsequently into the coastal zone due to siltation and erosion processes. It could also be attributed to the intrusion of river waters containing higher concentrations of ¹³⁷Cs.