In this paper, we define and study the notion of the real-valued functions on a frame $L$. We show that $F(L) $, consisting of all frame homomorphisms from the power set of $mathbb{R}$ to a frame $ L$, is an $f$-ring, as a generalization of all functions from a set $X$ into $mathbb R$. Also, we show that $F(L) $ is isomorphic to a sub-$f$-ring of $mathcal{R}(L)$, the ring of real-valued continu...

This paper proposes an algorithm which, given a set of observations of an existing concurrent system that has repetitive sub-functions, constructs a Message Sequence Charts (MSC) graph where repetitive sub-functions of the concurrent system are identified. This algorithm makes fewer assumptions than previously published work, and thus requires fewer and easier to generate observations to constr...

Given a set of observations of an existing concurrent system with repetitive sub-functions, we consider the construction of an MSC graph representing the functionality of the concurrent system. We first introduce a formal structure that we call ”lattice of repetitive subfunctions”. This lattice provides us with a global view of all the repetitive sub-functions of the system and all the compatib...

Abstract Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the concept of an asymptotically linear estimator and the associated influence function leads to optimal sampling procedures for a wide class of popula...

We use Levinson's method and the work of Blomer Harcos on $\mathrm{GL}_2$ shifted convolution problem to prove that at least 6.96% zeros L-function any holomorphic or Maass cusp form lie critical line.

BACKGROUND To examine the safety and efficacy of topical use of tranexamic acid (TA) in total knee arthroplasty (TKA). METHODS An electronic literature search of PubMed Medline; Ovid Medline; Embase; and the Cochrane Library was performed, identifying studies published in any language from 1966 to February 2013. The studies enrolled adults undergoing a primary TKA, where topical TA was used. ...