Consider the set SG(Qk) of all graphs whose vertices are labeled with non-identity elements of the group Qk = Z2 so that there is an edge between vertices with labels a and b if and only if the vertex labeled a + b is also in the graph. Note that edges always appear in triangles, since a + b = c, b + c = a and a + c = b are equivalent statements for Qk. We define the random cubic sum graph SG(Q...

We introduce quantum-K ($QK$), a measure of the descriptive complexity density matrices using classical prefix-free Turing machines and show that initial segments weak Solovay random quantum Schnorr states are incompressible in sense $QK$. Many properties enjoyed by Kolmogorov ($K$) have analogous versions for $QK$; notably counting condition. Several connections between randomness $K$, includi...

The aim of this paper is to construct (p,q)-calculus on finite intervals. (pk,qk)-derivative and (pk,qk)-integral are defined some basic properties given. Also, (pk,qk)-analogue H?lder, Minkowski integral inequalities proved.

We show that the q-Kneser graph q K2k:k (the graph on the k-subspaces of a 2k-space over G F(q), where two k-spaces are adjacent when they intersect trivially), has chromatic number qk + qk−1 for k = 3 and for k < q log q − q . We obtain detailed results on maximal cocliques for k = 3.

This thesis presents, in full, a simple linear time algorithm for intersecting two convex 3-polyhedra P and Q. This di ers from the rst such algorithm | due to Chazelle | in that it operates entirely in primal space, whereas Chazelle's algorithm relies heavily on duality transforms. We use the hierarchical representations of polyhedra due to Dobkin and Kirkpatrick to induce a cell complexes bet...

in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.

Starting from the most general harmonic superspace action of self-interacting Q+ hypermultiplets in the background of N = 2 conformal supergravity, we derive the general action for the bosonic sigma model with a generic 4n dimensional quaternionic-Kähler (QK) manifold as the target space. The action is determined by the analytic harmonic QK potential and supplies an efficient systematic procedu...

The main purpose of the following article is to introduce a Lie theoretical approach to the problem of classifying pseudo quaternionic-Kähler (QK) reductions of the pseudo QK symmetric spaces, otherwise called generalized Wolf spaces. The history of QK geometry starts with the celebrated Berger’s Theorem [Ber55] which classifies all the irreducible holonomy groups for not locally symmetric pseu...

1. Preliminary The uniform design initially proposed by Wang and Fang (1981) is a space-filling design for computer experiments, but it can also be utilized as a fractional factorial design. In the past two decades, it has been successfully applied to a wide range of areas; for example, in industry, system engineering, pharmaceuticals and natural sciences (see Fang and Lin, 2003). Many uniform ...