Consider a game of drawing balls from a bucket. The game manager tosses a secret coin. If the outcome is heads, the manager places 3 red balls and 2 white balls, and vice versa if the outcome is tails. Each player in his turn draws a ball from the bucket, secretly and at random, and has to announce (to all other players) his guess of the outcome of the original toss. Now, suppose that the rst f...

Consider two unit balls in a d-dimensional flat torus with edge length r, for d ≥ 2. The balls do not move by themselves but they are pushed by a Brownian motion. The balls never intersect—they reflect if they touch. It is proved that the joint distribution of the processes representing the centers of the balls converges to the distribution of two independent Brownian motions when r →∞, assumin...

We study combinatorial bounds for geometric permutations of balls with bounded size disparity in d-space. Our main contribution is the following theorem: given a set S of n disjoint balls in R , if n is sufficiently large and the radius ratio between the largest and smallest balls of S is γ , then the maximum number of geometric permutations of S is O(γ logγ ). When d = 2, we are able to prove ...

Abstract Thanks to their outstanding mechanical properties, Bulk Metallic Glasses (BMGs) are new alternatives traditional crystalline metals for and micromechanical applications including power transmission. However, the tribological properties of BMGs still poorly understood, mostly because amorphous nature induces counter intuitive responses friction wear. In present study, four different (Cu...

We consider the problem of resource allocation in a parallel environment where new incoming resources are arriving online in groups or batches. We study this scenario in an abstract framework of allocating balls into bins. We revisit the allocation algorithm GREEDY[2] due to Azar, Broder, Karlin, and Upfal (SIAM J. Comput. 1999), in which, for sequentially arriving balls, each ball chooses two ...

My project was in part to investigate the variance of playing the Shepp urn under the strategy which maximizes expected value. To this end after much experimentation I was able to conjecture and subsequently prove that if we play the Shepp urn with p postive balls and β(p) negative balls then the variance of our results grows at a rate of roughly √ p. I didn’t see as obvious of a pattern for ot...

Surface mechanical attrition treatment (SMAT) or ultrasonic shot peening method improves properties of metallic materials by causing the plastic deformation on their surface layer workpiece. In this research, an generator, booster, a sonotrode, one hundred steel balls with mean diameter 1 mm, optical microscope, automatic roughness meter, and other supporting accessories are employed to conduct...

Résumé. Cet article montre comment on peut utiliser la construction de Chu afin de simplifier la construction assez complexe de la catégorie ∗-autonome des boules qui sont réflexives et ζ-ζ∗-complètes donnée par le premier auteur dans les articles [Barr, 1976, 1979]. Abstract. This paper shows how the use of the “Chu construction” can simplify the rather complicated construction of the ∗-autono...