The category of L-domains was discovered by A. Jung while solving the problem of nding maximal cartesian closed categories of algebraic CPO's and continuous functions. In this note we analyse properties of the lossless powerdo-main construction, that is closed on the algebraic L-domains. The powerdomain is shown to be isomorphic to a collection of subsets of the domain on which the construction...

In this project we present detection the motion in video frames using background frame Matching. These document video surveillance systems have become widely available to ensure safety and security in both the public and private sectors due to incidents of terrorist activity and other social problems. This paper proposes a novel motion detection method with a background model module and an obje...

Infinite contexts and their corresponding lattices are of theoretical and practical interest since they may offer connections with and insights from other mathematical structures which are normally not restricted to the finite cases. In this paper we establish a systematic connection between formal concept analysis and domain theory as a categorical equivalence, enriching the link between the t...

Proof: Jf there exists a closed integral curve, then both r* and C* are in the kernel of F*, so F*0. If there is no closed integral curve, let r' be a cycle without contact.3 Any integral curve of F meets r' infinitely often; let P be a point of accumulation of these intersections. We may then construct a C' closed curve C' which differs from the integral curve only in an arbitrarily small neig...

We investigate function classes h#Pi f which are deened as the closure of #P under the operation f and a set of known closure properties of #P, e.g. summa-tion over an exponential range. First, we examine operations f under which #P is closed (i.e., h#Pi f = #P) in every relativization. We obtain the following complete characterization of these operations: #P is closed under f in every rela-tiv...

Proof. (Projection Theorem) Showing that the existence of minimizer implies that V is closed is left as an exercise. So we assume that V is closed. For f ∈ H, let α := infv∈V ‖v − f‖. It is a little easier to work with this in an equivalent form, α2 = infv∈V ‖v − f‖2. Thus, for every ε > 0 there is a vε ∈ V such that α2 ≤ ‖vε − f‖2 < α2 + ε. By choosing ε = 1/n, where n is a positive integer, w...

In this short note, we will show the following weak evidence of S. Lang conjecture over function elds. Let f : X ! Y be a projective and surjective morphism of algebraic varieties over an algebraically closed eld k of characteristic zero, whose generic ber is geometrically irreducible and of general type. If f is not birationally trivial, then there are countably many proper closed varieties fZ...

Proof. [Solution due to Claudiu Raicu] Consider two polynomials f, g ∈ C[X±] such that the spherical graphs they determine intersect transversely at the points where the vectors vi intersect the sphere. This implies that T (f) and T (g) intersect transversely ([1]) at each point and T (f)∩T (g) = Σ. Using the Transverse Intersection Lemma (lemma 3.2, corollary 3.3 of [1]) we get that Σ = T (f, ...

Proof. (Projection Theorem) Showing that the existence of minimizer implies that V is closed is left as an exercise. So we assume that V is closed. For f ∈ H, let α := infv∈V ‖v − f‖. It is a little easier to work with this in an equivalent form, α2 = infv∈V ‖v − f‖2. Thus, for every ε > 0 there is a vε ∈ V such that α2 ≤ ‖vε − f‖2 < α2 + ε. By choosing ε = 1/n, where n is a positive integer, w...

Let f be a diffeomorphism of a closed C∞ manifold M . In this paper, we introduce the notion of the C1-stable specification property for a closed f -invariant set Λ of M , and we prove that f|Λ satisfies a C 1-stable specification property if and only if Λ is a hyperbolic elementary set. As a corollary, the C1-interior of the set of diffeomorphisms of M satisfying the specification property is ...