Non-parametric predictive reliability demonstration for failure-free periods

We derive sample sizes for testing as required for reliabilitydemonstration, using non-parametric predictive inference forthe predicted number of future failures on the basis of testinformation. We assume that tests lead to zero failures, asis typical, for example, for high-reliability testing. Optimizationis in terms of failure-free periods for a process after testing,and we also consider total expected cost minimization, withparticular attention to deterministic and Poisson processes.We show that, perhaps surprisingly, the deterministic case isa worst-case scenario with regard to number of tests needed.     

Linear orderings and the sets of periods for star maps

We show that Baldwin's characterization of the set of periods of continuous self maps of the n-star can be expressed in terms of a finite number of linear orderings.     

SIMULTANEOUS SAXS／WAXS／DSC STUDIES ON MICROSTRUCTURE OF CONVENTIONAL AND METALLOCENE-BASED ETHYLENE-BUTENE COPOLYMERS

The fractions of one metallocene-based (mPE) and one conventional (znPE) ethylene-butene copolymer eluted at 80-82℃ from temperature rising elution fractionation were selected for DSC and time-resolved small angle X-ray scattering (SAXS) and wide angle X-ray scattering (WAXS) characterization. The DSC and WAXS results show that two crystal structures exist in both mPE and znPE: structure A with higher melting temperature and structure B with lower melting temperature. It was found that original znPE (s-znPE) contains more highly ordered structure A than original mPE (s-mPE) in spite of the higher comonomer content of znPE. Another structure C is also identified because of higher crystallinity measured by WAXS than by DSC and is attributed to the interfacial region. The SAXS data were analyzed with correlation function and two maxima were observed in s-mPE and s-znPE, in agreement with the conclusion of two crystal populations drawn from DSC and WAXS results. These two crystal populatiorts have close long periods in s-mPE, but very different long periods in s-znPE. In contrast, freshly crystallized mPE and znPE (f-mPE and f-znPE) contain only a single crystal population with a broader distribution of long period     

Low-threshold mid-IR MgO:PPLN optical parametric generation with high reflectivity mirror for signal wavelength

A low-threshold middle-infrared(mid-IR) MgO:PPLN optical parametric generation(OPG)pumped by a laser diode(LDl end-pumped Z-type Nd:YLF laser at 1047 nm is realized with high reflectivity(HR) mirror for signal.At repetition rate of 10 kHz,the OPG threshold of 50μJ has been achieved with HR mirror for signal.Compared with the threshold without mirror,the threshold decreases by 17%.Using HR mirror for pump at output side of crystal,the threshold of 40μJ is achieved.The 2.7-4.1μm continuous tunable output is produced with seven grating periods from 28.5 to 31.5μm and temperatures from 30 to 200℃.When the incident average pump power is 3 W.the OPG idler output power is 0.46 W at 3.26 μm,which corresponds to optical-to-optical conversion efficiency up to 15.3%.     

Rankin-Selberg without unfolding and bounds for spherical Fourier coefficients of Maass forms

We use the uniqueness of various invariant functionals on irreducible unitary representations of in order to deduce the classical Rankin-Selberg identity for the sum of Fourier coefficients of Maass cusp forms and its new anisotropic analog. We deduce from these formulas non-trivial bounds for the corresponding unipotent and spherical Fourier coefficients of Maass forms. As an application we obtain a subconvexity bound for certain -functions. Our main tool is the notion of a Gelfand pair from representation theory.

     

The poisson representation. II Two-time correlation functions

Basic formulas for the two-time correlation functions are derived using the Poisson representation method. The formulas for the chemical system in thermodynamic equilibrium are shown to relate directly to the fluctuationdissipation theorems, which may be derived from equilibrium statistical mechanical considerations. For nonequilibrium systems, the formulas are shown to be generalizations of these fluctuation-dissipation theorems, but containing an extra term which arises entirely from the nonequilibrium nature of the system. These formulas are applied to two representative examples of equilibrium reactions (without spatial diffusion) and to a nonequilibrium chemical reaction model (including the process of spatial diffusion) for which the first two terms in a systematic expansion for the two-time correlation functions are calculated. The relation between the Poisson representation method and Glauber-SudarshanP-representation used in quantum optics is discussed.     

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.     

Multi-modal approach for large natural flexural vibrations of thermally stressed plates

By means of Berger's approximation, suitable for plates with immovable edges, the geometrically nonlinear problem is considerably simplified. Thermally loaded plates with polygonal planform under hard-hinged support conditions are considered, taking into account the effect of shear in transverse isotropy. The class of symmetric vibrations about the flat plate position is represented by a homogeneous and coupled set of Duffing-oscillators as a result of a multi-mode expansion. A unifying non-dimensional closed-form solution for the corresponding nonlinear natural vibration periods is given, which is independent of the special planform. The individual shape of the plate enters the transformation into real time through the linear natural frequencies, or, equivalently, through the linear eigen-values of an effectively prestressed membrane of the same planform.