In terms of applications, the min discrepancy problem appears in many varied areas of both Computer Science (Computational Geometry, Comb. Optimization, Monte-Carlo simulation, Machine learning, Complexity, Pseudo-Randomness) and Mathematics (Dynamical Systems, Combinatorics, Mathematical Finance, Number Theory, Ramsey Theory, Algebra, Measure Theory,...). One may consult any of the following b...

We present a package for Mathematica computer algebra system which allows the exploitation of local files as sources of random data. We provide the description of the package and illustrate its usage by showing some examples. We also compare the provided functionality with alternative sources of randomness, namely a built-in pseudo-random generator and the package for accessing hardware true ra...

We study lattice Hamiltonian realisations of (3+1)d Dijkgraaf-Witten theory with gapped boundaries. In addition to the bulk loop-like excitations, yields dyonic string-like excitations that terminate at Using a tube algebra approach, we classify such and derive corresponding representation theory. Via dimensional reduction argument, relate this describing (2+1)d boundary point-like interfaces b...

In this paper, we introduce two classes of localized integral operators on L2(Rd) with the Wiener class W and the Kurbatov class K of integral operators as their models. We show that those two classes of localized integral operators are pseudo-inverse closed non-unital subalgebra of B2, the Banach algebra of all bounded operators on L2(Rd) with usual operator norm.

In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using difference operators. The operators are obtained from these symbols via the natural quantisation given by the representation theory. They form an algebra of operators which shares many properties with the...

In this paper, the second in a series of eight we continue our development of the basic tools of the multivector and extensor calculus which are used in our formulation of the differential geometry of smooth manifolds of arbitrary topology. We introduce metric and gauge extensors, pseudo-orthogonal metric extensors, gauge bases, tetrad bases and prove the remarkable golden formula, which permit...

We consider Bézier-like formulas with weights in quaternion and geometric (Clifford) algebra for parametrizing rational curves and surfaces. The simplest non-trivial quaternionic case of bilinear formulas for surface patches is studied in detail. Such formulas reproduce well known biquadratic parametrizations of principal Dupin cyclide patches, and are characterized in general as special Darbou...

In this paper, a procedure is reported that discuss how linear algebra can be used in image compression. The basic idea is that each image can be represented as a matrix. We apply linear algebra (QR ‎factorization and wavelet ‎transformation ‎algorithm‏s) on this matrix and get a reduced matrix out such that the image corresponding to this reduced matrix requires much less storage space than th...

Let S be a locally compact topological foundation semigroup with identity and Ma(S) be its semigroup algebra. In this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $M_a(S)$ of a locally compact topological foundationsemigroup with identity.