Among a variety of approaches introduced in the literature to establish duality theory, Fenchel duality was of great importance in convex analysis and optimization. In this paper we establish some conditions to obtain classical strong Fenchel duality for evenly convex optimization problems defined in infinite dimensional spaces. The objective function of the primal problem is a family of (possible) infinite even convex functions. The strong duality conditions we present are based on the consideration of the epigraphs of the c-conjugate of the dual objective functions and the ε-c-subdifferential of the primal objective functions.

Let G be a graph, each edge e of which is given a weight w(e). The shortest path problem is a path of minimum weight connecting two specified vertices a and b, and from it we have a pre-topology. Furthermore, we study the restriction and separators in pre-topology generated by the shortest path problems. Finally, we study the rate of liaison in pre-topology between two subgraphs. It is formally shown that the new distance measure is a metric

• The problem of infertility considers one of the chronic problem a which faced the
  individual & families equally . This problem causes a negative effects in psychological ,
  social and development fields. The infertility contributes in weakening the human
  development, when the human development has become as a centre point which centered
  about individual preparing , rehabilitation, training and knowledge toreach to the required
  excellence.
  We think that , the infertility destroys the socially development; therefore the socially and
  scientific institutions are working hard to find successful solution to resolve the problem
  infertility through sophisticated and scientific methods. This problem

High-performance liquid chromatographic methods are used for the determination of water-soluble vitamins with UV-Vis. Detector. A reversed-phase high-performance liquid chromatographic has been developed for determination of water-soluble vitamins. Identification of compounds was achieved by comparing their retention times and UV spectra with those of standards solution. Separation was performed on a C18 column, using an isocratic 30% (v/v) acetonitril in dionozed water as mobile phase at pH 3.5 and flow rate 1.0m/min. The method provides low detection and quantification limits, good linearity in a large concentration interval and good precision. The detection limits ranged from 0.01 to 0.025µg/ml. The accuracy of the method was

Background: Poly (methyl methacrylate) has been widely utilized for fabrication of dentures for many years as it has good advantages but not achieved all demands of the mechanical properties such as low transverse strength, low impact strength, low surface hardness, high water solubility and high water sorption. Material and method: To provide bonding between ZrO2 nanoparticles and PMMA matrix, the ZrO2 Nano-fillers were surface-treated with a saline coupling agent. Plasma surface treatment of polyethylene (PE) fiber was done to change surface fiber by using DC- glow discharge system. For characterization of interring any functional groups, the (FTIR) spectrum were done .then the mechanical properties studied to choose the appropriate perc

This paper addresses the factors responsible for changes in crude oil prices, in real market and financial sector. In order to prepare the analytical background for further investigation, it highlights the patterns of correlations of the real oil price and the most related prices of assets, exchange rate and government bond yield. The paper reviews the statistical behavior of oil price, quantities and the  global macroeconomic environment. Topics discussed include the theory of differential rent and scarcity effect ,the role of  future market and speculation, strategies of energy of the major economies to investigate the prospects of oil market and the potential demand for  OPEC's oil.  The paper explores the

This study included isolation and characterization of extremely halophilic bacteria from Al-Massab Al-Aam region in South of Iraq Fifty isolates were identified by using numerical taxonomy 40 strains belonged to the genus Halobacterium which inclucted Hb. halobium Hb. cutirubrum Hb. salinarium Hb. saccharovorum Hb. valismortis and Hb. volcanii. Ten strains belonged to the genus Halococcus which included Hc. morrhuae Hc. saccharolyticus. Growth curves were sensitive mutants determined for wild type and salt Generation time in logarthmic phase was measured and found to be (10.37 2hr 7 0.59) for Hb. salinarium / 18 (6.490 hr 0.24) for Hb. cutirubrum / 32, (6.700 hr + 0.488) for Hb. valismortis / 20, (11.243 hr + 0.96) for Hb. volcanii / 7. (7

The aim of this work was to develop and validate a rapid and low cost method for estimation of ibuprofen in pharmaceutical suspensions using Reverse-Phase High Performance Liquid Chromatography. The proposed method was conducted and validated according to International Conference on Harmonization (ICH) requirements. The chromatographic parameters were as follows: column of octyldecylsilyl C18 with dimensions (150 × 4.6) mm, mobile phase composed of acetonitrile with phosphoric acid with a ratio of 50 to 50 each using isocratic mode, flow rate of 1.5 mL/min and injection volume of 5 μL. The detection was carried out using UV detector at 220 nm. The method was validated and showed short retention time for ibuprofen peak at 7.651 min, wit

The importance of specifying proper aggregate grading for achieving satisfactory performance in pavement applications has long been recognized. To improve the specifications for superior performance, there is a need to understand how differences in aggregate gradations within the acceptable limits may affect unbound aggregate base behavior. The effects of gradation on strength, modulus, and deformation characteristics of high-quality crushed rock base materials are described here. Two crushed rock types commonly used in constructing heavy-duty granular base layers in the State of Victoria, Australia, with three different gradations each were used in this study. The gradations used represent the lower, medium, and upper gradation li

Hypothesis Nanofluid flooding has been identified as a promising method for enhanced oil recovery (EOR) and improved Carbon geo-sequestration (CGS). However, it is unclear how nanoparticles (NPs) influence the CO2-brine interfacial tension (γ), which is a key parameter in pore-to reservoirs-scale fluid dynamics, and consequently project success. The effects of pressure, temperature, salinity, and NPs concentration on CO2-silica (hydrophilic or hydrophobic) nanofluid γ was thus systematically investigated to understand the influence of nanofluid flooding on CO2 geo-storage. Experiments Pendant drop method was used to measure CO2/nanofluid γ at carbon storage conditions using high pressure-high temperature optical cell. Findings CO2/nano