Duality for <Emphasis Type="Italic">ε</Emphasis>-Variational Inequality

In this paper, following the method in the proof of the composition duality principle due to Robinson and using some basic properties of the ε-subdifferential and the conjugate function of a convex function, we establish duality results for an ε-variational inequality problem. Then, we give Fenchel duality results for the ε-optimal solution of an unconstrained convex optimization problem. Moreover, we present an example to illustrate our Fenchel duality results for the ε-optimal solutions. The authors thank the referees for valuable suggestions and comments. This work was supported by Grant No. R01-2003-000-10825-0 from the Basic Research Program of KOSEF.     

A colorimetric method for the assay of lipoyl dehydrogenase

Microchimica Acta - A colorimetric method for the direct assay of lipoyl dehydrogenase is described. Enzyme reaction is stopped by ethanol precipitation. This is followed by the displacement of...     

The impact properties of laminated composites containing ultrahigh carbon (UHC) steels

An ultrahigh carbon (UHC) steel/mild steel laminated composite and a UHC steel/UHC steel laminate have been successfully manufactured by a roll-bonding procedure. Impact properties of these laminates, as well as of monolithic samples of the steels contained in these laminates, have been determined in the crackarrestor orientation over the temperature range 25 to ?196°C. Both notched and unnotched samples of the laminated composite and laminate have been tested. Extremely low ductile-to-brittle temperatures of ?140°C, and very high shelf energies (>325 J), have been found both for the laminated composites and the laminates. This remarkably good behavior is shown to be a result of notch blunting by delamination within the laminates.     

Aberrant proteins in the saliva of patients with oral squamous cell carcinoma

Confirmation of oral squamous cell cancer (OSCC) currently relies on histological analysis, which does not provide clear indication of cancer development from precancerous lesions. In the present study, whole saliva proteins of patients with OSCC (n = 12) and healthy subjects (n = 12) were separated by 2DE to identify potential candidate biomarkers that are much needed to improve detection of the cancer. The OSCC patients’ 2DE saliva protein profiles appeared unique and different from those obtained from the healthy subjects. The patients’ saliva α1‐antitrypsin (AAT) and haptoglobin (HAP) β chains were resolved into polypeptide spots with increased microheterogeneity, although these were not apparent in their sera. Their 2DE protein profiles also showed presence of hemopexin and α‐1B glycoprotein, which were not detected in the profiles of the control saliva. When subjected to densitometry analysis, significant altered levels of AAT, complement C3, transferrin, transthyretin, and β chains of fibrinogen and HAP were detected. The increased levels of saliva AAT, HAP, complement C3, hemopexin, and transthyretin in the OSCC patients were validated by ELISA. The strong association of AAT and HAP with OSCC was further supported by immunohistochemical staining of cancer tissues. The differently expressed saliva proteins may be useful complementary biomarkers for the early detection and/or monitoring of OSCC, although this requires validation in clinically representative populations.     

On Implicit Vector Variational Inequalities

In this paper, we study the existence of solutions of implicit vector variational inequalities for multifunctions. Generalized pseudomonotonicity concepts are introduced. Our results extend and unify corresponding earlier existence results of many authors for vector variational inequalities under the Hausdorff topological vector space setting.     

On general best proximity pairs and equilibrium pairs in free abstract economies

In this paper, using Lassonde’s fixed point theorem for Kakutani factorizable multifunctions and Park’s fixed point theorem for acyclic factorizable multifunctions, we will prove new existence theorems for general best proximity pairs and equilibrium pairs for free abstract economies, which generalize the previous best proximity theorems and equilibrium existence theorems due to Srinivasan and Veeramani [P.S. Srinivasan, P. Veeramani, On best approximation pair theorems and fixed point theorems, Abstr. Appl. Anal. 2003 (1) (2003) 33–47; P.S. Srinivasan, P. Veeramani, On existence of equilibrium pair for constrained generalized games, Fixed Point Theory Appl. 2004 (1) (2004) 21–29], and Kim and Lee [W.K. Kim, K.H. Lee, Existence of best proximity pairs and equilibrium pairs, J. Math. Anal. Appl. 316 (2006) 433–446] in several aspects.     

Comparison of anthocyanins present in grapes of Vitis vinifera L. varieties and interspecific hybrids grown in the Czech Republic

Anthocyanins present in the grapes of nine grapevine (Vitis vinifera L.) varieties and ten interspecific hybrids were compared. Total anthocyanin levels were determined in fresh grapes and the values ranged from 0.50 g kg^?1 to 4.99 g kg^?1. A total of twenty-two different anthocyanins were identified. Malvidin 3-glucoside was the most abundant anthocyanin, with concentrations ranging from 30 % to 64 % of the totals observed. The ratio of acetylated to coumaroylated malvidin and peonidin derivatives ranged from 0.09 (variety: Regent) to 1.34 (variety: Cerason), depending on the variety. Diglucosylated anthocyanins were not found in particular interspecific hybrids such as the teinturier XIV 26–56, Laurot, Merlan, and Nativa.     

Some Generalization for an Operator Which Preserving Inequalities Between Polynomials

For a polynomial p(z) of degree n which has no zeros in |z| 1, Dewan et al.,(K. K. Dewan and Sunil Hans, Generalization of certain well known polynomial inequalities, J. Math. Anal. Appl., 363(2010), 38–41) established zp′(z) +nβ2p(z) ≤n2{( β2 + 1+β2)max|z|=1|p(z)|-( 1+β2- β2)min|z|=1|p(z)|},for any complex number β with |β|≤ 1 and |z| = 1. In this paper we consider the operator B, which carries a polynomial p(z) into B[ p(z)] := λ0p(z) + λ1(nz2)p′(z)1!+ λ2(nz2)2 p′′(z)2!,where λ0, λ1, and λ2are such that all the zeros of u(z) = λ0+c(n,1)λ1z+c(n,2)λ2z2lie in the half plane |z| ≤ |z-n/2|. By using the operator B, we present a generalization of result of Dewan. Our result generalizes certain well-known polynomial inequalities.