On the volumes and affine types of trades

A $[t]$-trade is a pair $T=(T_+, T_-)$ of disjoint collections of subsets (blocks) of a $v$-set $V$ such that for every $0\le i\le t$, any $i$-subset of $V$ is included in the same number of blocks of $T_+$ and of $T_-$. It follows that $|T_+| = |T_-|$ and this common value is called the volume of $T$. If we restrict all the blocks to have the same size, we obtain the classical $t$-trades as a special case of $[t]$-trades. It is known that the minimum volume of a nonempty $[t]$-trade is $2^t$. Simple $[t]$-trades (i.e., those with no repeated blocks) correspond to a Boolean function of degree at most $v-t-1$. From the characterization of Kasami--Tokura of such functions with small number of ones, it is known that any simple $[t]$-trade of volume at most $2\cdot2^t$ belongs to one of two affine types, called Type\,(A) and Type\,(B) where Type\,(A) $[t]$-trades are known to exist. By considering the affine rank, we prove that $[t]$-trades of Type\,(B) do not exist. Further, we derive the spectrum of volumes of simple trades up to $2.5\cdot 2^t$, extending the known result for volumes less than $2\cdot 2^t$. We also give a characterization of "small" $[t]$-trades for $t=1,2$. Finally, an algorithm to produce $[t]$-trades for specified $t$, $v$ is given. The result of the implementation of the algorithm for $t\le4$, $v\le7$ is reported.Comment: 30 pages, final version, to appear in Electron. J. Combi

Storage stability of encapsulated barberry's anthocyanin and its application in jelly formulation

The barberry (Berberis vulgaris) extract which is a rich source of anthocyanin was used for encapsulation with three different wall materials i.e., combination of gum Arabic and maltodextrin (GA+MD), combination of maltodextrin and gelatin (MD+GE) and maltodextrin (MD) by spray drying process. In this context, the storage stability of encapsulated pigments was investigated under four storage temperatures (4, 25, 35 and 42 °C), four relative humidities (20, 30, 40 and 50%) and light illumination until 90 days. All wall materials largely increased the half-life of the encapsulated pigments during storage compared with non-encapsulated anthocyanins. MD+GA showed the highest encapsulation efficiency, lower degradation rate in all temperatures and was found as the most effective wall material in stabilizing the pigments. The encapsulated pigments were utilized in coloring jelly powder as an alternative of synthetic color. Sensory evaluation were run to identify best encapsulated natural color concentration in jelly powder formulation according to acceptability by consumers. A jelly with added 7% encapsulated color had higher scores than the commercial jelly containing synthetic color for all the sensory attributes evaluated. Physicochemical properties of produced jelly including moisture content, hygroscopicity, acidity, ash content and texture were not significantly different with control sample while, syneresis and solubility of the samples prepared with encapsulated color was significantly reduced. © 2016 Elsevier Ltd

Characteristics of Male Pre-Service Elementary Education Candidates in North Dakota: An Exploratory Study

In 2003 the National Education Association annual survey revealed that male teachers currently make up 35% of America\u27s kindergarten through 12 th grade classroom teaching cadre. In grades kindergarten through sixth grade, men comprise 9% of the classroom teachers, and only 2% of classroom teachers inkindergarten through third grade are men. In 1994 Sadker and Sadker published Failing at Fairness, which examined gender biases in American kindergarten through 12th grade classrooms, including the effects of the overwhelmingly-female faculties. At the National Education Association\u27s 2002 Representative Assembly, members adopted a measure to identify, recognize, recruit and retain, more male teachers, particularly elementary and minority male teachers. The purpose of this study was to investigate the characteristics of pre-service elementary and early childhood male and female teaching candidatesthrough the use of the Important Concepts of a Career Scale developed by Galbraith (1992) and through the use of certain demographic data. This studyexamined the hypothesis that men who pursue nontraditional careers find the relational aspects of their work more important than the financial, power and prestige rewards. After the data (n = 63) were collected from the online demographic survey and Important Concepts of a Career Scale, descriptive statistics based on the demographic survey were displayed. The pre-service male teaching candidates came from familial backgrounds of lower educational levels with 50% of paternal parents having high school diplomas as their highest level of education. Standard statistical methodologies were used to report if male pre-service teaching candidates valued three relational aspects, general relationships, relationship with students, and relationships with peers, of their prospective careers over the financial, power and prestige aspects and if there were differences between male and female candidates\u27 responses, as well as differences among the male candidates\u27 responses. Participants rated items on the Important Concepts of a Career Scale on a four-point Likert Scale. Results indicated that male pre-service teaching candidates valued the financial aspect of their career as more important than did the female pre-serviceteaching candidates. Male pre-service teaching candidates did not value general relationships as highly as did the female pre-service teaching candidates. There were no statistical differences between the male and female pre-service teaching candidates on rating relationships with students, relationships with peers, power, and prestige aspects. There were no differences on any of the items on the scale among the male respondents