Extended Superposed Quantum State Initialization Using Disjoint Prime Implicants (ESQUID) is a new algorithm for generating quantum arrays for the purpose of initializing a desired quantum superposition. The quantum arrays generated by this algorithm almost always use fewer gates than other algorithms and in the worst case use the same number of gates. These improvements are achieved by allowin...

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

The equilibria of strategic games with many semi-anonymous players have a strong ex-post Nash property. Even with perfect hindsight about the realized types and selected actions of all his opponents, no player has an incentive to revise his own chosen action. This is illustrated for normal form and for one shot Baysian games with statistically independent types, provided that a certain continui...

Byzantine Fault Tolerant (BFT) systems are considered to be state of the art with regards to providing reliability in distributed systems. Despite over a decade of research, however, BFT systems are rarely used in practice. In this paper, we describe our experience, from an application developer’s perspective, trying to leverage the publicly available, highlystudied and extended “PBFT” middlewa...

Let $G$ be a finitely generated abelian group and $M$ be a $G$-graded $A$-module. In general, $G$-associated prime ideals to $M$ may not exist. In this paper, we introduce the concept of $G$-attached prime ideals to $M$ as a generalization of $G$-associated prime ideals which gives a connection between certain $G$-prime ideals and $G$-graded modules over a (not necessarily $G$-graded Noetherian...

Let E be an optimal elliptic curve overQ of prime conductorN . We show that if for an odd prime p, the mod p representation associated to E is reducible (in particular, if p divides the order of the torsion subgroup of E(Q)), then the p-primary component of the ShafarevichTate group of E is trivial. We also state a related result for more general abelian subvarieties of J0(N) and mention what t...

A method for approximate model checking of stochastic hybrid systems with provable approximation guarantees is proposed. We focus on the probabilistic invariance problem for discrete time stochastic hybrid systems and propose a two-step scheme. The stochastic hybrid system is first approximated by a finite state Markov chain. The approximating chain is thenmodel checked for probabilistic invari...

We will study the complexity of QMA proof systems with inverse exponentially small promise gap. We will show that this class, QMAexp, can be exactly characterized by PSPACE, the class of problems solvable with a polynomial amount of memory. As applications we show that a “precise” version of the Local Hamiltonian problem is PSPACE-complete, and give a provable setting in which the ability to pr...

In this paper, we define prime (semiprime) hyperideals and prime(semiprime) fuzzy hyperideals of semihypergroups. We characterize semihypergroupsin terms of their prime (semiprime) hyperideals and prime (semiprime)fuzzyh yperideals.