On set systems with restricted intersections modulo p and p-ary t-designs

We consider bounds on the size of families ℱ of subsets of a v-set subject to restrictions modulo a prime p on the cardinalities of the pairwise intersections. We improve the known bound when ℱ is allowed to contain sets of different sizes, but only in a special case. We show that if the bound for uniform families ℱ holds with equality, then ℱ is the set of blocks of what we call a p-ary t-design for certain values of t. This motivates us to make a few observations about p-ary t-designs for their own sake

Set Systems with No Singleton Intersection

Let $\mathcal{F}$ be a $k$-uniform set system defined on a ground set of size $n$ with no singleton intersection; i.e., no pair $A,B\in\mathcal{F}$ has $|A\cap B|=1$. Frankl showed that $|\mathcal{F}|\leq\binom{n-2}{k-2}$ for $k\geq4$ and $n$ sufficiently large, confirming a conjecture of Erdős and Sós. We determine the maximum size of $\mathcal{F}$ for $k=4$ and all $n$, and also establish a stability result for general $k$, showing that any $\mathcal{F}$ with size asymptotic to that of the best construction must be structurally similar to it

On t -designs

Introduction and preliminaries An incidence structure is a triple S=(X, <J,9 S} where X and JL are disjoint sets andc^ci^fX^?. Elements x^X are called points and elements A^JL are called blocks of S. A point x and a block ^4 are incident iff (#, ^4)ec?. For any block A, (A) will denote the set of points incident with A

SOME TESTS OF THE ECONOMIC THEORY OF COOPERATIVES: METHODOLOGY AND APPLICATION TO COTTON GINNING

Little progress has been made in testing the often conflicting hypotheses generated from theoretical research on cooperatives. This paper addresses the deficiency by describing and applying (to California cotton ginning cooperatives) a methodology to test key hypotheses concerning (a) cooperativesÂ’ price-output equilibrium, (b) allocative efficiency, and (c) utilization of capital inputs. The empirical results (a) are consistent with predictions from the game theory model of cooperative behavior, (b) reject the null hypothesis of absolute allocative efficiency, and (c) indicate absolute overutilization of capital inputs among the sample cooperatives.Agribusiness, Crop Production/Industries,

Space Electrochemical Research and Technology

Individual papers presented at the conference address the following topics: development of a micro-fiber nickel electrode for nickel-hydrogen cell, high performance nickel electrodes for space power application, bending properties of nickel electrodes for nickel-hydrogen batteries, effect of KOH concentration and anions on the performance of a Ni-H2 battery positive plate, advanced dependent pressure vessel nickel hydrogen spacecraft cell and battery design, electrolyte management considerations in modern nickel hydrogen and nickel cadmium cell and battery design, a novel unitized regenerative proton exchange membrane fuel cell, fuel cell systems for first lunar outpost - reactant storage options, the TMI regenerable solid oxide fuel cell, engineering development program of a closed aluminum-oxygen semi-cell system for an unmanned underwater vehicle, SPE OBOGS on-board oxygen generating system, hermetically sealed aluminum electrolytic capacitor, sol-gel technology and advanced electrochemical energy storage materials, development of electrochemical supercapacitors for EMA applications, and high energy density electrolytic capacitor

Power-Ups in Digital Games: The Rewarding Effect of Phantom Game Elementson Player Experience

Power-ups are a type of game reward that allow the player tocustomise their experience by altering gameplay for a shortperiod of time. Despite the wide use of power-ups in videogames, little is known about their effect on gaming experiences.To explore this, we conducted an experimental study that compares the experiences of players depending on their exposureto power-ups in a recreational video game. The results show that players who collected power-ups felt significantly more immersed in the game, experienced more autonomy, but didnot feel more competent or challenged than those who played the game without these collectables. Interestingly, a similareffect was observed for those players who picked up ‘placebo ’power-ups, despite the items having no effect on the gameplay. We provide a discussion of these results and their implications both for games user researchers and game designers

A Reply to H. S. Gutowsky and E. M. Peterson Regarding the Ozone Spectrum

To avoid unnecessary confusion regarding the ozone spectrum it appears desirable to point out that the analysis of the infra-red spectrum based upon an acute angled molecular model proposed by Gutkowsky and Peterson (1) appears to be completely excluded on at least two different grounds. (Incidentally the heading of columns 2 and 3 of the Table I appear to be interchanged)