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Covering families of triangles by convex sets
Krajči, Samuel ; Kynčl, Jan (advisor) ; Soukup, Jan (referee)
A convex universal cover of a family M of sets in the plane is a convex set that contains a congruent copy of every element of M. Park and Cheong conjecture that for every family of triangles with bounded diameter there exists a triangle that is a smallest universal cover of this family. We prove this conjecture for every family of all triangles with the lengths of their two sides fixed, every family of all triangles with the length of a side and the size α of the opposite angle fixed (where α is from an interval (0, λ]∩[3π/7, π) with λ being approximately 0.396π), every finite subfamily of a family of all triangles with the length of a side and the size α of the opposite angle fixed (where α ≥ π/2). 1
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Unfolding some classes of polycubes
Minařík, Josef ; Kynčl, Jan (advisor) ; Tiwary, Hans Raj (referee)
An unfolding of a polyhedron is a cutting along its surface such that the surface remains connected and it can be flattened to the plane without any overlap. An edge- unfolding is a restricted kind of unfolding, we are only allowed to cut along the edges of the faces of the polyhedron. A polycube is a special case of orthogonal polyhedron formed by glueing several unit cubes together face-to-face. In the case of polycubes, the edges of all cubes are available for cuts in edge-unfolding. We focus on one-layer polycubes and present several algorithms to unfold some classes of them. We show that it is possible to edge-unfold any one-layer polycube with cubic holes, thin horizontal holes and separable rectangular holes. The question of edge-unfolding general one-layer polycubes remains open. We also briefly study some classes of multi-layer polycubes. 1
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The analysis of marketing communications of the Prague Spring International Music Festival 2009
Kyncl, Jan ; Dolanská, Nora (advisor) ; Čeňková, Jana (referee)
Bachelor thesis "The analysis of marketing communications of The Prague Spring International Music Festival 2009" deals with the method how basic marketing principles are applied in the field of arts. The major goal of this study is: 1. to make a list of the main features marketing of an art organization should include, 2. to name the reasons why marketing policy should be adopted by such organization's management, 3. to indicate conditions needed for success in arts marketing. The theoretical part is based upon the relevant art marketing publications available, and on the major marketing literature which creates a framework for modern marketing theory. The second part deals with the marketing campaign of the The Prague Spring International Music Festival 2009 which is widely considered to be the most significant cultural event within the Czech republic and Central Europe as well. The analysis consists of detailed description of the marketing planning proces, characterization of the campaign's communication mix, and the evaluation of it's effectiveness. There's also a short resumé at the end of the text which provides a brief review of festival camping. Complex overview of all the information gained by writing the diploma thesis and studying the subject is also included.
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