Vector Variational Inequalities for Nondifferentiable Convex Vector Optimization Problems

In this paper, we consider a nondifferentiable convex vector optimization problem (VP), and formulate several kinds of vector variational inequalities with subdifferentials. Here we examine relations among solution sets of such vector variational inequalities and (VP). Mathematics Subject classification (2000). 90C25, 90C29, 65K10 This work was supported by the Brain Korea 21Project in 2003. The authors wish to express their appreciation to the anonymous referee for giving valuable comments.     

A limit on the lepton-family number violating process π → μe

A FNAL E799 Collaboration has carried out a search for the lepton-family number violating decay π⁰ → μ^±e using π⁰'s produced from K_L → π⁰π⁰π⁰ decays in flight. No events were observed. Assuming that lepton-family number violation is charge independent, the 90% confidence level upper limit on

Full-size image

was determined to be 8.6 × 10⁻⁹.     

Synthesis of metallic ReO3 nanowires

We present the synthesis of highly crystalline metallic rhenium trioxide (ReO₃) nanowires via a simple physical vapor transport at 300 °C for the first time. Based on HRTEM, the ReO₃ nanowires exhibit a core of perfect cubic perovskite‐type single crystal structure with a shell of thin amorphous and disordered structures of less than 2 nm in the near surface layers. Possibly this is due to proton intercalation induced by the surface reaction of single crystal ReO₃ with water.

     

On relations between weak approximation properties and their inheritances to subspaces

It is shown that for the separable dual X^∗ of a Banach space X, if X^∗ has the weak approximation property, then X^∗ has the metric weak approximation property. We introduce the properties W^∗D and MW^∗D for Banach spaces. Suppose that M is a closed subspace of a Banach space X such that M^⊥ is complemented in the dual space X^∗, where for all m∈M}. Then it is shown that if a Banach space X has the weak approximation property and W^∗D (respectively, metric weak approximation property and MW^∗D), then M has the weak approximation property (respectively, bounded weak approximation property).     

Extended application of a chiral stationary phase based on (+)-(1 8-crown-6)-2,3,11,12-tetracarboxylic acid to the resolution of N-(substituted benzoyl)-alpha-amino acid amides

A chiral stationary phase (CSP 1) based on (+)-(18-crown-6)-2,3,11,12-tetracarboxylic acid was applied to the resolution of N-(substituted benzoyl)-alpha-amino acid amides and esters. N-(Substituted benzoyl)-alpha-amino acid amides were well resolved using a mixture of acetic acid-triethylamine-acetonitrile (0.01:0.05:100, v/v/v) as an optimum mobile phase while N-(substituted benzoyl)-alpha-amino acid esters were not resolved at all. In contrast, both N-(substituted benzoyl)-alpha-amino acid amides and esters were not resolved at all or resolved very poorly on another CSP (CSP 2), which lacks the two N-H hydrogens of the amide tethers of CSP 1. Among the substituents on the benzoyl group of analytes, the nitro group was the best for good resolution of analytes on CSP 1. From these results, the two N-H hydrogens of the amide tethers of CSP 1, the carbonyl oxygen of the amide group of analytes, and the nitro group on the benzoyl group of analytes were concluded to play significant roles in chiral recognition. In addition, various N-(3,5-dinitrobenzoyl)leucine amides with different lengths of N-alkylamide chains were resolved on CSP 1 and N-(3,5-dinitrobenzoyl) leucine N-propylamide was found to show the best chiral recognition in terms of the separation (alpha = 1.30) and the resolution factor (Rs= 3.17).     

An alternative theorem for set-valued maps via set relations and its application to robustness of feasible sets

Abstract

This paper contains a generalized Gordan-type alternative theorem for set-valued maps which characterizes set relations without any convexity assumptions using certain evaluation functions. As a direct consequence and as a good example, we discuss robustness (or stability) of linear programming problems for modelling error. Moreover, this theorem can be utilized for that of general vector optimization problems in special cases due to reformation of the evaluation functions.     

Upper semicontinuity result for the solution mapping of a mixed parametric generalized vector quasiequilibrium problem with moving cones

In this paper, we give sufficient conditions for the upper semicontinuity property of the solution mapping of a parametric generalized vector quasiequilibrium problem with mixed relations and moving cones. The main result is proven under the assumption that moving cones have local openness/local closedness properties and set-valued maps are cone-semicontinuous in a sense weaker than the usual sense of semicontinuity. The nonemptiness and the compactness of the solution set are also investigated.     

Modeling special-day effects for forecasting intraday electricity demand

We propose and apply a novel approach for modeling special-day effects to predict electricity demand in Korea. Notably, we model special-day effects on an hourly rather than a daily basis. Hourly specified predictor variables are implemented in the regression model with a seasonal autoregressive moving average (SARMA) type error structure in order to efficiently reflect the special-day effects. The interaction terms between the hour-of-day effects and the hourly based special-day effects are also included to capture the unique intraday patterns of special days more accurately. The multiplicative SARMA mechanism is employed in order to identify the double seasonal cycles, namely, the intraday effect and the intraweek effect. The forecast results of the suggested model are evaluated by comparing them with those of various benchmark models for the following year. The empirical results indicate that the suggested model outperforms the benchmark models for both special- and non-special day predictions.