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We give necessary and sufficient conditions for a regular sine family of continuous linear set-valued functions associated with a regular cosine family of continuous linear set-valued functions, to be continuous. Then we show that the continuity and Hukuhara differentiability of regular sine and cosine families are equivalent. As an application, we prove the existence and uniqueness of a solution of a second order differential problem. Our results are a much stronger version of results in [5], [6] and [10] that are valid for Banach spaces. [ABSTRACT FROM AUTHOR]

Cracking and isomerization of n-alkanes, employing bifunctional catalysts, are vital reactions in various refinery processes for producing different high-quality fuels. These catalysts consist of a specific metal component and a specific acid function. The metal component is used for dehydrogenation and hydrogenation constituted from a specific noble metal such as palladium and platinum. The acid function, on the other hand, is used for cracking and isomerization aims. In this work, a number of mesoporous catalysts with different ratios of Si/Ti based on MSU containing Platinum were synthesized and characterized with XRF, XRD, NH3–TPD, and BET tests. These catalysts were applied in n-heptane hydroconversion process in a fixed bed microreactor to see their performance in an actual process. In the microreactor, the pressure was constant (atmospheric), and the temperature varies in the range of 250–600°C. The performance of each of the catalysts was investigated in different ratios of hydrogen to hydrocarbon (5, 10, 15, 20, and 25) and in two values of Weight Hour Space Velocity (WHSV) (1.5 and 2.5 h–1). Products analysis carried out to check out the activity and selectivity of each of the catalysts. The result showed that all samples have a high surface area, favorable pore distribution, and high acidity. The outcome of the study showed that the CAT-D catalyst has the highest activity for normal heptane conversion. This catalyst also has the highest selectivity for isomerization products at moderate temperatures (350°C) and WHSV = 1.5 h–1. [ABSTRACT FROM AUTHOR]

We give an extension of the Mazur-Ulam theorem for isometries from real metrizable topological vector spaces into real normed spaces. [ABSTRACT FROM AUTHOR]

Improving yield, diseases resistance, abiotic stress tolerance, seed quality and other agronomic traits are the most important aims of faba bean breeding. Stemphylium blight, a fungal disease caused by Stemphylium botryosum and S. vesicarium, causes great devastation in faba bean production in Golestan province. The levels of resistance to Stemphylium blight disease were evaluated in 99 faba bean genotypes. The experiment was conducted during the 2011-2012 cropping season in Gorgan, Iran. The experiment was laid out in randomized complete block design with three replications. Treatment variables studied were disease severity, area under disease progress curve (AUDPC), plant height, yield component and grain yield. Plants which scored for resistance on a 1 to 9 severity scale. The results revealed significant differences between genotypes for all studied traits. There was significant variability for resistance to Stemphylium blight disease among faba bean cultivars. According to Principal Component Analysis (PCA), the first two components explained about 98 % of genetic variation. The PC indicated that grain yield and biological yield per plant were important traits for classification. While AUDPC was important in PC. Based on Cluster analysis, 99 genotypes were divided into three clusters. Cluster II showed maximum grain yield per plant and biological yield harvest index. Diversity in the resistance of faba beans to Stemphylium blight determines their potential for improved efficiency in order providing diseases management in this crop, and crossing nurseries for faba bean improvement. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the continuity of linear and sublinear correspondences defined on cones in normed spaces. We also generalize some known results for sublinear correspondences. [ABSTRACT FROM AUTHOR]