In this note, we completely describe the shape of the bisector of two given points in a two-dimensional normed vector space. More precisely, we show that, depending on the position of two given points with respect to the shape of the unit circle, the following holds: the bisector of a non-strict pair of points consists of two cones and a curve, which has properties similar to those of bisectors...

A distinctive feature of modern functional logic languages like Toy or Curry is the possibility of programming non-strict and non-deterministic functions with call-time choice semantics. For almost ten years the CRWL framework [6,7] has been the only formal setting covering all these semantic aspects. But recently [1] an alternative proposal has appeared, focusing more on operational aspects. I...

We discuss some results concerning fixed point equations in the setting of topological *-algebras of unbounded operators. In particular, an existence result is obtained for what we have called weak τ strict contractions, and some continuity properties of these maps are discussed. We also discuss possible applications of our procedure to quantum mechanical systems. Running title: Fixed Points in...

We consider the conic linear program given by a closed convex cone in an Euclidean space and matrix, where vector on right-hand side of inequality constraint defining objective function are subject to change. Using strict feasibility condition, we prove locally Lipschitz continuity obtain some differentiability properties optimal value problem under right-hand-side perturbations. For perturbati...

Usage of a projection system to display large screen images is still relevant in the midst of LED-based display increasing popularity. This is due to that the system itself is a mature technology, reliable and cheaper than the LED counterpart. While various methods had addressed the projection problems on curve surface, projecting image on jagged like surface (zero order geometric continuity) h...

In his [2011], Lionel Shapiro proposes a very interesting deflationist conception of logical consequence, according to which the logical-consequence predicate applying to sentences serves as a merely expressive device allowing us to talk in a generalising way about typically non-linguistic entailment facts (just as, according to a deflationist conception of truth, the truth predicate applying t...

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The ubiquitous schema ‘All Fs are Gs’ dominates much philosophical discussion on laws but rarely is it shown how actual laws mentioned and used in science are supposed to fit it. After consideration of a variety of laws, including those obviously conditional and those superficially not conditional (such as equations), I argue that we have good reason to support the traditional interpretation of...

What is a non-strict functional language? Is a non-strict language necessarily lazy? What additional expressiveness brings non-strictness, with or without laziness? This paper tries to shed some light on these questions. First, in order to characterize non-strictness, di1erent evaluation strategies are introduced: strict, lazy, and lenient. Then, using program examples, how these evaluation str...