arXiv subjects

Hamza Alzaareer

Publications and source records attributed to Hamza Alzaareer.

3 recordsLinked to original sources

arXiv2019

Optimization and Positivity Certificates of Rational Functions using Bernstein Form

Rational functions of total degree $l$ in n variables have a representation in the Bernstein form defined over $n$ dimensional simplex. The range of a rational function is bounded by the smallest and the largest rational Bernstein coefficients over a simplex. Convergence properties of the bounds to the range are reviewed. Algebraic identities certifying the positivity of a given rational function over a simplex are given. Subsequently, a bound established in this work does not depend on the given dimension.

math.OC↗

arXiv2019

Tubes of coordinate finite type Gauss map in the Euclidean 3-space

In this paper, we consider tubes in the Euclidean 3-space whose Gauss map n is of coordinate finite I-type, i.e., the position vector n satisfies the relation ΔIn = Λn, where ΔI is the Laplace operator with respect to the first fundamental form I of the surface and Λ is a square matrix of order 3. We show that circular cylinders are the only class of surfaces mentioned above of coordinate finite I-type Gauss map.

math.DG↗

arXiv2014

Differentiable mappings on products with different degrees of differentiability in the two factors

We develop differential calculus of $C^{r,s}$-mappings on products of locally convex spaces and prove exponential laws for such mappings. As an application, we consider differential equations in Banach spaces depending on a parameter in a locally convex space. Under suitable assumptions, the associated flows are mappings of class $C^{r,s}$.

math.FA↗