Lattices are discrete mathematical objects with widespread applications to integer programs as well as modern cryptography. A fundamental problem in both domains is the Closest Vector Problem (popularly known as CVP). It is well-known that CVP can be easily solved in lattices that have an orthogonal basis if the orthogonal basis is specified. This motivates the orthogonality decision problem: v...

in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...

An orthogonal basis of L which is also an unconditional basis of a functional space F is a kind of optimal basis for compressing, estimating, and recovering functions in F . Simple thresholding operations, applied in the unconditional basis, work essentially better for compressing, estimating, and recovering than they do in any other orthogonal basis. In fact, simple thresholding in an uncondit...

Here we give a simple proof of a new representation for orthogonal polynomials over triangular domains which overcomes the need to make symmetry destroying choices to obtain an orthogonal basis for polynomials of fixed degree by employing redundancy. A formula valid for simplices with Jacobi weights is given, and we exhibit its symmetries by using the Bernstein–Bézier form. From it we obtain th...

In this paper we develop a discrete Hierarchical Basis (HB) to efficiently solve the Radial Basis Function (RBF) interpolation problem with variable polynomial order. The HB forms an orthogonal set and is adapted to the kernel seed function and the placement of the interpolation nodes. Moreover, this basis is orthogonal to a set of polynomials up to a given order defined on the interpolating no...

Quantum chemical computational procedures, like LCAOMO theory and quantum similarity, use non orthogonal function basis sets, which define finite dimensional subspaces of a Hilbert space. Based on the original overlap metric matrices, generated by the chosen finite non orthogonal basis sets, there are several symmetrical overlap and basis set transformations possible. This study tries to find o...

Fractional differentiation systems are characterized by the presence of non-exponential aperiodic multimodes. Although rational orthogonal bases can be used to model any L2[0,∞[ system, they fail to quickly capture the aperiodic multimode behavior with a limited number of terms. Hence, fractional orthogonal bases are expected to better approximate fractional models with fewer parameters. Intuit...