A SIC consists of N equiangular unit vectors in an N dimensional Hilbert space. The frame potential is a function of N unit vectors. It has a unique global minimum if the vectors form a SIC, and this property has been made use of in numerical searches for SICs. When the vectors form an orbit of the Heisenberg group the frame potential becomes a function of a single fiducial vector. We analytica...

We derive the relation between the Hilbert space of certain geometries under the Bohr-Sommerfeld quantization and the perturbative prepotentials for the supersymmetric five-dimensional SU(N) gauge theories with massive fundamental matters and with one massive adjoint matter. The gauge theory with one adjoint matter shows interesting features. A five-dimensional generalization of Nekrasov’s part...

In a previously proposed architecture, the mobile user is able to look up and connect to the wireless technology that best matches his context. In order to support such an architecture, the mobile user needs to access information about wireless cells across different management domains and about different access technologies.The P2P overlay aggregates meta-data of heterogeneous cellular network...

In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...

Controlled frames in Hilbert spaces have been recently introduced by P. Balazs and etc. for improving the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper we develop a theory based on g-fusion frames on Hilbert spaces, which provides exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In part...

How can one compute the dimension of a projective algebraic subset, given by a system of equations? There are different definitions, and their equivalence is part of the classical dimension theory in algebraic geometry. The game is then the following: to make some definition of dimension effective enough to get an algorithm. A first method consists to think algebraically and to use the Hilbert ...

In this paper we consider a number of sequence and function spaces that are known to be homeomorphic to the countable product of the linear space σ. The spaces we are interested in have a canonical imbedding in both a topological Hilbert space and a Hilbert cube. It turns out that when we consider these spaces as subsets of a Hilbert cube then there is only one topological type. For imbeddings ...

Hilbert transform of wavelets has been used to approximate functions in L2(R) . It is proved that Hilbert transform of wavelets with many vanishing moments does a good job in approximating smooth functions in L2(R) . We also prove that Hölder continuity of a function helps in the decay of wavelet coefficients and thereby helps in approximating it. Finally, we give a result that relates the Hilb...

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.