In this paper we show that all supergravity billiards corresponding to σ-models on any U/H non compact-symmetric space and obtained by compactifying supergravity to D = 3 are fully integrable. The key point in establishing the integration algorithm is provided by an upper triangular embedding of the solvable Lie algebra associated with U/H into sl(N,R) which always exists. In this context we es...

Let L and K be two full rank lattices in R. We prove that if v(L) = v(K), i.e. they have the same volume, then there exists a measurable set Ω such that it tiles R by both L and K. A counterexample shows that the above tiling result is false for three or more lattices. Furthermore, we prove that if v(L) ≤ v(K) then there exists a measurable set Ω such that it tiles by L and packs by K. Using th...

If (fn) is a sequence of elements of an infinite dimensional Hilbert space H and (en) is an orthonormal basis for H , we define the preframe operator T : H → H by: Ten = fn. It follows that for any f ∈ H , T ∗f = ∑ n〈f, fn〉en. Hence, (fn) is a frame if and only if T ∗ is an isomorphism (called the frame transform) and in this case S = TT ∗ is an invertible operator on H called the frame operato...

in this paper, we study b-focal curves of biharmonic b -general helices according to bishop frame in the heisenberg group heis   finally, we characterize the b-focal curves of biharmonic b- general helices in terms of bishop frame in the heisenberg group heis

An element z ∈CPd−1 is called fiducial if {gz : g ∈G} is a set of lines with only one angle between each pair, where G∼= Zd × Zd is the one-dimensional finite Weyl-Heisenberg group modulo its centre. We give a new characterization of fiducial vectors. Using this characterization, we show that the existence of almost flat fiducial vectors implies the existence of certain cyclic difference sets. ...

Abstract. We provide a detailed development of a function valued inner product known as the bracket product and used effectively by de Boor, Devore, Ron and Shen to study translation invariant systems. We develop a version of the bracket product specifically geared to Weyl-Heisenberg frames. This bracket product has all the properties of a standard inner product including Bessel’s inequality, a...

The idea of magnetic translation groups, appearing in considerations of movement of electron in an external magnetic field, was proposed independently by Brown [1] and Zak [2]. From those works follows that the magnetic translation group is an image of Weyl–Heisenberg group [3] obtained by imposing the Born–von Kármán periodic boundary conditions. The general description of similar problems has...

In 1990, Daubechies proved a fundamental identity for WeylHeisenberg systems which is now called the Weyl-Heisenberg Frame Identity. WH-Frame Identity: If g ∈ W (L∞, L), then for all continuous, compactly supported functions f we have: ∑ m,n | < f, EmbTnag > | = 1 b ∑

1. Introduction. Arithmetic physics, or better, arithmetic quantum theory, is a term that refers to a collection of ideas and partial results, loosely held together, that suggests that there are connections between the worlds of quantum physics and number theory and that onw should try to discover and develop these connections. At one extreme is the modest idea that one should try to formulate ...

in this paper, we study spacelike dual biharmonic curves. we characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the lorentzian dual heisenberg group . we give necessary and sufficient conditions for spacelike dual biharmonic curves in the lorentzian dual heisenberg group . therefore, we prove that all spacelike dual biharmonic curves are spacelike dual heli...