Abstract. In 2007, Andrews and Paule introduced the family of functions ∆k(n) which enumerate the number of broken k–diamond partitions for a fixed positive integer k. In that paper, Andrews and Paule proved that, for all n ≥ 0, ∆1(2n + 1) ≡ 0 (mod 3) using a standard generating function argument. Soon after, Shishuo Fu provided a combinatorial proof of this same congruence. Fu also utilized th...

Bacterial panicle blight (BPB) caused by Burkholderia glumae has become the most important disease of ‘Bengal’ rice in Arkansas. Many arthropods with the capability to vector bacteria are commonly found in rice fields; however, no link has been made to any arthropod vectors of BPB. This study sampled rice fields for the presence of BPB and any small arthropods typically implicated in disease ve...

We study the computational complexity of finding stable outcomes in hedonic games, which are a class of coalition formation games. We restrict our attention to a nontrivial subclass of such games, which are guaranteed to possess stable outcomes, i.e., the set of symmetric additively-separable hedonic games. These games are specified by an undirected edge-weighted graph: nodes are players, an ou...

PURPOSE The purpose of this study was to evaluate whether surface treatments affect the translucency of laminate veneers with different shades and thicknesses. MATERIALS AND METHODS A total of 224 disc-shaped ceramic veneers were prepared from A1, A3, HT (High Translucent) and HO (High Opaque) shades of IPS e.max Press (Ivoclar Vivadent) with 0.5 mm and 1.0 mm thicknesses. The ceramics were d...

In this work we study the problem of private set-intersection in the multi-party setting and design two protocols with the following improvements compared to prior work. First, our protocols are designed in the so-called star network topology, where a designated party communicates with everyone else, and take a new approach of leveraging the 2PC protocol of [FNP04]. This approach minimizes the ...

When secure arithmetic is required, computation based on secure multiplication (MULT) is much more efficient than computation based on secure boolean circuits. However, a typical application can also require other building blocks, such as comparison, exponentiation and the modulo (MOD) operation. Secure solutions for these functions proposed in the literature rely on bit-decomposition or other ...

Besides speed and period length, the quality of uniform random number generators is usually assessed by measuring the uniformity of their point sets, formed by taking vectors of successive output values over their entire period length. For F2-linear generators, the commonly adopted measures of uniformity are based on the equidistribution of the most significant bits of the output. In this paper...

in this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. a numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. truncation errors are derived for both continuous and discontinuous problems. parameter uni...