Boundedness of Product Type Pseudodifferential Operators on Spaces of Besov Type

In this paper we consider pseudodifferential operators associated with symbols satisfying estimates of product type, and give some sufficient conditions for the operators to be bounded on BESOV spaces and on TRIEBEL —LIZORKIN spaces of product type corresponding to the above estimates. In the proof we use the characterization of these spaces by approximation by entire functions.     

Observation of single Ca ions for trace isotope analysis

We developed an ion trap — laser cooling system for observing the laser induced fluorescence (LIF) of a single ion, in the view of utilizing it for the trace isotope analysis of Ca. We observed stepwise LIF signals, which correspond to the numbers of trapped ⁴⁰Ca⁺ ions (⁴⁰Ca/Ca = 96.9%). The detection efficiency was evaluated and the observation of single ions demonstrated the experimental feasibility of trace isotope analysis. Furthermore, as the next step towards trace isotope analysis, we report observation of the even calcium isotopes, ⁴⁴Ca (⁴⁴Ca/Ca = 2.09%) and ⁴⁸Ca (⁴⁸Ca/Ca = 0.187%), without the use of a selective loading method.     

Effect of molecular weight distribution on the structure and mechanical properties of ultradrawn,ultrahigh-molecular-weight polyethylene cast from solution. II. Drawability and mechanical properties

The effect of molecular weight distribution (MWD) on the ultradrawability and mechanical properties of solution-cast films of ultrahigh-molecular-weight polyethylene (UHMW-PE) has been investigated using tensile and dynamic mechanical measurements. The MWD has a marked effect on ultradrawability and thus on the ultimate mechanical properties such as the tensile modulus. It is proposed that UHMW-PE with a narrow MWD(N-PE) attains the ultimate structure at a lower draw ratio than UHMW-PE with a broad MWD(B-PE) because of the existence in the latter of less fully extended intercrystalline tie chains. It is found that, at the same drawing temperature (100°C), N-PE shows a higher modulus than B-PE at draw ratios up to 150 x, which is assumed to be the ultimate value for N-PE.     

A successive quadratic programming algorithm with global and superlinear convergence properties

This paper presents a successive quadratic programming algorithm for solving general nonlinear programming problems. In order to avoid the Maratos effect, direction-finding subproblems are derived by modifying the second-order approximations to both objective and constraint functions of the problem. We prove that the algorithm possesses global and superlinear convergence properties.This work was supported in part by a Scientific Research Grant-in-Aid from the Ministry of Education, Science and Culture, Japan.     

A microsensor for adenosine-5′-triphosphate pH-sensitive field effect transistors

The sensor for adenosine-5′-triphosphate (ATP) is based on H⁺-ATPase immobilized via a polyvinylbutyral resin on a pH-sensitive field effect transistor. A linear relationship was obtained between the initial rate of change of the differential gate output voltage and the logarithm of the ATP concentration over the range 0.2–1.0 mM ATP. The optimum pH was 9.0 at 40°C but pH 7.0 was preferred for routine measurements. Only slight responses were obtained for 1 mM glucose, creatinine or urea. The ATP-sensing system exhibited a response to 1 mM ATP for at least 18 days.     

Flow-shop scheduling with setup and assembly operations

A scheduling model for a production system including machining, setup and assembly operations is considered. Production of a number of single-item products is ordered. Each product is made by assembling a set of several different parts. First, the parts are manufactured in a flow-shop consisting of multiple machines. Then, they are assembled into products on a single assembly stage. Setup operation and setup time are needed when a machine starts processing the parts or it changes items. The operations are partitioned into several blocks. Each block consists of the machining operations, the setup operations, and the assembly operation(s) for one or several products. The parts of the same item in a block are processed successively. The objective function is the mean completion time for all products. We consider a problem to partition the operations into blocks and sequence the parts in each block so as to minimize the objective function. Solution procedures using pseudo-dynamic programming and a branch-and-bound method are proposed. Computational experiments are carried out to evaluate the performance of the solution procedures. It has been found that a good near-optimal schedule is obtained efficiently by the proposed solution procedures.     

Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints

In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints introduced by Birbil et al. (Math Oper Res 31:739–760, 2006). Firstly, by means of a Monte Carlo method, we obtain a nonsmooth discrete approximation of the original problem. Then, we propose a smoothing method together with a penalty technique to get a standard nonlinear programming problem. Some convergence results are established. Moreover, since quasi-Monte Carlo methods are generally faster than Monte Carlo methods, we discuss a quasi-Monte Carlo sampling approach as well. Furthermore, we give an example in economics to illustrate the model and show some numerical results with this example. The first author’s work was supported in part by the Scientific Research Grant-in-Aid from Japan Society for the Promotion of Science and SRF for ROCS, SEM. The second author’s work was supported in part by the United Kingdom Engineering and Physical Sciences Research Council grant. The third author’s work was supported in part by the Scientific Research Grant-in-Aid from Japan Society for the Promotion of Science.