Regularized gap function as penalty term for constrained minimization problems

By using the regularized gap function for variational inequalities, Li and Peng introduced a new penalty function Pα(x) for the problem of minimizing a twice continuously differentiable function in closed convex subset of the n-dimensional space Rn. Under certain assumptions, they proved that the original constrained minimization problem is equivalent to unconstrained minimization of Pα(x). The main purpose of this paper is to give an in-depth study of those properties of the objective function that can be extended from the feasible set to the whole Rn by Pα(x). For example, it is proved that the objective function has bounded level sets (or is strongly coercive) on the feasible set if and only if Pα(x) has bounded level sets (or is strongly coercive) on Rn. However, the convexity of the objective function does not imply the convexity of Pα(x) when the objective function is not quadratic, no matter how small α is. Instead, the convexity of the objective function on the feasible set only implies the invexity of Pα(x) on Rn. Moreover, a characterization for the invexity of Pα(x) is also given.     

Mesoporous MnO2 synthesized by hydrothermal route for electrochemical supercapacitor studies

Poorly crystalline mesoporous MnO₂, which is suitable for supercapacitor studies, is synthesized from neutral KMnO₄ aqueous solution by hydrothermal route. But it requires a high temperature (180 °C) and also a long reaction time (24 h). Addition of a tri-block copolymer, namely, poly(ethylene glycol)-block-poly(propylene glycol)-block-poly(ethylene glycol) (P123), which is generally used as a soft template for the synthesis of nano-structured porous materials, reduces the hydrothermal temperature to 140 °C and also reaction time to 2 h. When the reaction time is increased, the product morphology changes from nanoparticles to nanorods with a concomitant decrease in BET surface area. Also, the product tends to attain crystallinity. The electrochemical capacitance properties of MnO₂ synthesized under varied hydrothermal conditions are studied in 0.1 M Na₂SO₄ electrolyte. A specific capacitance of 193 F?g^?1 is obtained for the mesoporous MnO₂ sample consisting of nanoparticle and nanorod mixed morphology synthesized in 6 h using P123 at 140 °C.     

Aqua bridged Cu2 dimer of a heptadentate N4O3 coordinating ligand: Synthesis,structure and magnetic properties

The N₄O₃ coordinating heptadentate imidazolidinyl phenolate ligand, H₃L (2-(2′-hydroxyphenyl)-1,3-bis[4-(2-hydroxyphenyl)-3-azabut-3-enyl]-1,3-imidazolidine) forms with Cu(II) a rare aqua bridged complex [{Cu₂(μ-L)(μ-H₂O)}₂](ClO₄)₂ · 4.5H₂O (1 · 4.5H₂O). Complex 1 · 4.5H₂O contains two crystallographically different but chemically equivalent dinuclear [Cu₂(μ-L)(μ-H₂O)]⁺ cationic units in the asymmetric unit. The copper atoms of each dinuclear unit are in a distorted square-pyramidal environment and are held together by phenolate, imidazolidinyl and aqua bridges with a Cu···Cu separation of av. 3.34 Å. The compound exhibits a very weak antiferromagnetic exchange interaction (J = −0.77 cm⁻¹, ? = −2 J?₁?₂) between the two copper(II) (S = 1/2) ions. The ¹H NMR spectrum of the complex shows a total of 17 hyperfine shifted peaks, as expected from the idealized C_s symmetry of the compound, spread over a very large window of chemical shift, spanning about 250 ppm. The complex, having an appropriate intermetallic separation for catechol binding, shows catecholase like activity in MeCN at 25 °C, with the aerobic oxidation of 3,5-di-tert-butylcatechol (3,5-DTBC) to 3,5-di-tert-butylquinone (3,5-DTBQ).     

Application of continuous-time programming problems to a class of variational-type inequalities

In this paper, we establish sufficiency criteria under generalized ρ−(η,θ)-invexity conditions for general continuous-time programming problems with nonlinear equality/inequality constraints. Using this we establish some existence criteria for solutions of a class of variational-type inequalities.     

Corrosion resistance of sol–gel alumina coated Mg metal in 3.5 % NaCl solution

Journal of Sol-Gel Science and Technology - This investigation describes the potential of sol–gel derived alumina coating on the corrosion resistance of magnesium metal in 3.5 % NaCl...     

Probiotic Escherichia coli CFR 16 Producing Pyrroloquinoline Quinone (PQQ) Ameliorates 1,2-Dimethylhydrazine-Induced Oxidative Damage in Colon and Liver of Rats

Inflammation of the gastrointestinal tract is associated with reactive oxygen species (ROS) genesis. Alleviation of oxidative stress is achieved by using antioxidants and probiotics. Present study investigates a synergistic effect of the probiotic Escherichia coli CFR 16 containing Vitreoscilla haemoglobin gene (vgb), green fluorescent protein (gfp) gene and pyrroloquinoline quinone (pqq) gene cluster on oxidative stress induced by 1,2-dimethylhydrazine (DMH). Adult virgin Charles foster male rats (3–4 months) weighing 200–250 g were administered with DMH (25 mg/kg body weight, s.c.) twice a week for eight consecutive weeks. Rats receiving only DMH dose showed increased lipid peroxidation in liver and intestinal tissues with reduced activity of antioxidant enzymes, i.e. superoxide dismutase (SOD), catalase (CAT) and glutathione peroxidase (GPx). Oral dose of E. coli CFR 16::vgb-gfp harbouring pqq gene cluster increased rat faecal PQQ concentration by twofold, reduced lipid peroxidation and retained SOD, CAT and GPx activities close to normal levels in liver and colonic tissues following DMH treatment. In addition, significant protection was found in colonic histological sections of these rat groups. This study demonstrates a protective efficacy in the following order: E. coli CFR 16?<?E. coli CFR 16::vgb-gfp?<?vitamin C?=?PQQ?<?E. coli CFR 16::vgb-gfp (pqq).     

Weakly relaxed α-pseudomonotonicity and equilibrium problem in Banach spaces

In this paper, we introduce the weakly relaxed ??-pseudomonotone mapping which generalizes the class of pseudomonotone mappings. Some examples are given which show that the weakly relaxed ??-pseudomonotonicity is a proper generalization of pseudomonotonicity for both scalar and vector valued bi-functions. Using the KKM technique, we establish the existence of solutions of equilibrium problems and vector equilibrium problems with weakly relaxed ??-pseudomonotonicity in the reflexive Banach spaces. The present work extends some corresponding results of the variational-like inequalities (Fang and Huang in J. Optim. Theory Appl. 118:327?C338, 2003; Lee and Lee in J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 11: 231?C242, 2004) to equilibrium problems.     

Nonsmooth ρ ? (η, θ)-invexity in multiobjective programming problems

In this paper we extend Reiland’s results for a nonlinear (single objective) optimization problem involving nonsmooth Lipschitz functions to a nonlinear multiobjective optimization problem (MP) for ρ − (η, θ)-invex functions. The generalized form of the Kuhn–Tucker optimality theorem and the duality results are established for (MP).     

A note on the weight spectrum of the Schubert code $$C_{\alpha }(2, m)$$

We consider the Schubert code \(C_{\alpha }(2, m)\) associated to the \(\mathbb {F}_q\)-rational points of the Schubert variety \(\Omega _{\alpha }(2,m)\) in the Grassmannian \(G_{2,m}\). A correspondence between codewords of \(C_{\alpha }(2, m)\) and skew-symmetric matrices of certain special form is given. Using this correspondence, we give a formula for all possible weights of codewords in \(C_{\alpha }(2, m)\). It is shown that the weight of each codeword is divisible by certain power of q. Further, a formula for the weight spectrum of the Schubert code \(C_{\alpha }(2, m)\) is given.     

On multiobjective generalized symmetric dual programs withρ − (η, θ)-invexity

A pair of multiobjective generalized symmetric dual nonlinear programming problems and weak, strong and converse duality theorems for these problems are established under generalized ρ ? (η, θ)-invexity assumptions. Several known results are obtained as special cases.