Determination of the central density on the basis of its moments

The value of the central density is of key importance for annihilation processes. For the ground state we discuss its determination from the moments of the ground state density. We first review the way of reaching the moments from the spectrum. In particular we show how to get the lowest moments in D = 3, namely 〈r⁻²〉 and 〈r⁻¹〉 from the series expansion of the Laplace transform of the density. We then recall a method to obtain the central density based on the Stieltjes moment problem. If the number of known moments is finite, this technique yields a lower bound. We investigate the possibilities to estimate the accuracy of the bound and the corresponding asymptotic value. An application to the muonic ²⁰⁸Pb atom is presented.     

Quick assessment methodology for reliability of solder joints in ball grid array (BGA) assembly—Part I: Creep constitutive relation and fatigue model

In this study, a new unified creep constitutive relation and a modified energy-based fatigue model have been established respectively to describe the creep flow and predict the fatigue life of Sn−Pb solders. It is found that the relation successfully elucidates the creep mechanism related to current constitutive relations. The model can be used to describe the temperature and frequency dependent low cycle fatigue behavior of the solder. The relation and the model are further employed in part II to develop the numerical simulation approach for the long-term reliability assessment of the plastic ball grid array (BGA) assembly. The project supported by the National Natural Science Foundation of China (59705008)     

Influence of surface tension on damping of the oscillations of a viscous incompressible fluid in a cylindrical channel

A numerical calculation is made of small oscillations of a viscous incompressible fluid that fills half of a horizontal cylindrical channel. The calculation is made with and without allowance for surface tension. The results of the calculation show that allowance for surface tension increases the damping of the oscillations. The general properties of problems of the normal oscillations of a heavy and capillary viscous incompressible fluid were studied in [1–3], in which the possibility of applying the Bubnov-Galerkin method to these problems was pointed out. A method for calculating the oscillations of a viscous incompressible fluid that partly fills an arbitrary vessel at large Reynolds numbers was developed in [3–5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–132, May–June, 1980.     

Development of a microfluidic platform for single-cell secretion analysis using a direct photoactive cell-attaching method

A precise understanding of individual cellular processes is essential to meet the expectations of most advanced cell biology. Therefore single-cell analysis is considered to be one of possible approach to overcome any misleading of cell characteristics by averaging large groups of cells in bulk conditions. In the present work, we modified a newly designed microchip for single-cell analysis and regulated the cell-adhesive area inside a cell-chamber of the microfluidic system. By using surface-modification techniques involving a silanization compound, a photo-labile linker and the 2-methacryloyloxyethyl phosphorylcholine (MPC) polymer were covalently bonded on the surface of a microchannel. The MPC polymer was utilized as a non-biofouling compound for inhibiting non-specific binding of the biological samples inside the microchannel, and was selectively removed by a photochemical reaction that controlled the cell attachment. To achieve the desired single-macrophage patterning and culture in the cell-chamber of the microchannel, the cell density and flow rate of the culture medium were optimized. We found that a cell density of 2.0 × 10(6) cells/ml was the appropriate condition to introduce a single cell in each cell chamber. Furthermore, the macrophage was cultured in a small size of the cell chamber in a safe way for 5 h at a flow rate of 0.2 μl/min under the medium condition. This strategy can be a powerful tool for broadening new possibilities in studies of individual cellular processes in a dynamic microfluidic device.     

Cohen–Macaulayness of monomial ideals and symbolic powers of Stanley–Reisner ideals

We present criteria for the Cohen–Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of graph theory and of linear programming to study the Cohen–Macaulayness of monomial ideals which are intersections of prime ideal powers. We can characterize the Cohen–Macaulayness of the second symbolic power or of all symbolic powers of a Stanley–Reisner ideal in terms of the simplicial complex. These characterizations show that the simplicial complex must be very compact if some symbolic power is Cohen–Macaulay. In particular, all symbolic powers are Cohen–Macaulay if and only if the simplicial complex is a matroid complex. We also prove that the Cohen–Macaulayness can pass from a symbolic power to another symbolic powers in different ways.     

Multiwavelength Raman fiber lasers with equalized peak power using a sampled chirped fiber Bragg grating

Two novel multiwavelength Raman fiber lasers using a ring cavity and a linear cavity are proposed and demonstrated experimentally. Both laser configurations include a sampled chirped fiber Bragg grating used in the reflection mode. By adjusting the polarization controller (PC) in the cavities, up to ten stable lasing wavelengths with 0.8 nm spacing and equalized peak power are achieved at room temperature. It is observed that the output spectrum depends upon which port of the grating is connected to the cavity. These two fiber ring lasers offer advantages such as, stable room temperature operation, simple structure, low loss, multiwavelength lasing lines with moderate output power. PACS 42.55.Wd; 42.55.Ye; 42.81.-i     

Wave scattering functions and their application to multiple scattering problems

Scattering functions arise naturally in standard treatments of the effects of a material object or surface embedded in a uniform field. The most commonly used scattering function describes the far-field modulation imparted at large distances to a spherical wavefront eminating from the scatterer. The purpose of this is to develop the properties of the spectrum of scattered plane waves as an exact generalized scattering function. The linearity of the wave equations guarantees that such a representation exists; moreover, it is possible to derive the generalized scattering function from the far-field scattering function by analytic continuation. Although these properties are known, recent theoretical developments have motivated us to reexplore the interrelations among the far-field scattering function, the Green's function and various forms of the generalized scattering function as well as the symmetry properties of the generalized scattering function imposed by reciprocity. For multiple-scattering objects that can be separated by parallel planes, a system of difference equations is developed that fully accommodates the mutual interaction among the scatterers. The mutual interaction equations were developed earlier, but we show here that they can be transformed into the form that would be obtained by using the Foldy-Lax-Twersky formalism. This reinforces the equivalence between wave-space and configuration space formulations of the scattering problems.