In the paper, we refine and extend Cusa-Huygens inequality by simple functions. particular, determine sharp bounds for $$\sin x /x$$ of form $$(2+\cos x)/3 -(2/3-2/\pi )\Upsilon (x)$$ , where $$\Upsilon (x)>0$$ $$x\in (0, \pi /2)$$ (0)=0$$ (\pi /2)=1$$ such that x/x$$ proposed coincide at $$x=0$$ $$x=\pi /2$$ . The hierarchy obtained is discussed, along with a graphical study. Also, alternative...

This paper describes some design refinements on marking menus and shows how these refinements embody interesting and relevant design principles for HCI. These refinements are based on the design principles of: (1) maintaining visual context, (2) hiding unnecessary information, and (3) supporting skill development by graphical feedback. The result is a new graphical representation and a more eff...

For every $1leq s< n$, the $s^{th}$ derivative of a polynomial $P(z)$ of degree $n$ is a polynomial $P^{(s)}(z)$ whose degree is $(n-s)$. This paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. Besides, our result gives interesting refinements of some well-known results.

Today’s notions of encapsulation are very restricted — a module or component contains only source code. What we really need is for modules or component to encapsulate not only source code that will be installed when the component is used, but also encapsulate corresponding changes to documentation, formal properties, and performance properties — i.e., changes to the central concerns of software...

Programs written in dynamic languages make heavy use of features— run-time type tests, value-indexed dictionaries, polymorphism,and higher-order functions — that are beyond the reach of type sys-tems that employ either purely syntactic or purely semantic reason-ing. We present a core calculus, System D, that merges these twomodes of reasoning into a single powerful mecha...

Sequential programs and algorithms are usually specified by means of preconditions and postconditions. This is not possible for concurrent and reactive programs, since their behaviour during execution is more interesting than their final states, even when termination is desirable. There are two schools in the way behaviours of concurrent and reactive programs are described. In the process algeb...

Rule-based modelling is particularly effective for handling the highly combinatorial aspects of cellular signalling. The dynamics is described in terms of interactions between partial complexes, and the ability to write rules with such partial complexes -i.e., not to have to specify all the traits of the entitities partaking in a reaction but just those that matteris the key to obtaining compac...

Metric refinements of qualitative topological relations not only provide more details of distinctions between spatial entities, but also theoretical interests and applications. This paper developed an alternative way of metric refinements for improving the identification of the eight topological relations with the aid of the extension of convex hull concept to defining relations between two spa...