We consider the problem of finding for a given N -tuple of polynomials (real or complex) the closest N -tuple that has a common divisor of degree at least d. Extended weighted Euclidean seminorm of the coefficients is used as a measure of closeness. Two equivalent representations of the problem are considered: (i) direct parameterization over the common divisors and quotients (image representat...

We deal with the existence and localization of positive radial solutions for Dirichlet problems involving ϕ $$ \phi -Laplacian operators in a ball. In particular, p Minkowski-curvature equations are considered. Our approach relies on fixed point index techniques, which work thanks to Harnack-type inequality terms seminorm. As consequence result, it is also derived several (even infinitely many)...

In this paper, we study p-tuples of bounded linear operators on a complex Hilbert space with adjoint defined respect to non-zero positive operator A. Our main objective is investigate the joint A-numerical radius p-tuple.We established several upper bounds for it, some which extend and improve upon previous work second author. Additionally, provide sharp inequalities involving classical A-semin...

In this paper, we propose a new hybridized discontinuous Galerkin method for the convection-diffusion-reaction problems with mixed boundary conditions. The coercivity of the convection-reaction part is achieved by adding an upwinding term. We give error estimates of optimal order in the piecewise H1-seminorm. Furthermore, we show that the approximate solution of our scheme is close to that of t...

Definition 1.2 A real vector space X is called a real normed space if there exists a map || · || : X → IR, such that, for all λ ∈ IR and x, y ∈ X, (i) ||x|| = 0⇔ x = 0; (ii) ||λx|| = |λ| ||x||; (iii) ||x + y|| ≤ ||x|| + ||y|| (triangle inequality). The map || · || is called the norm. If || · || only satisfies (ii) and (iii) then it is called a seminorm. Note that X is automatically a metric spa...

We propose a method to evaluate the complexity of probability measures from data that is based on a reproducing kernel Hilbert space seminorm of the logarithm of conditional probability densities. The motivation is to provide a tool for a causal inference method which assumes that conditional probabilities for effects given their causes are typically simpler and smoother than vice-versa. We pre...

Strong stability preserving (SSP) high order time discretizations were developed for solution of semi-discrete method of lines approximations of hyperbolic partial differential equations. These high order time discretization methods preserve the strong stability properties–in any norm or seminorm—of the spatial discretization coupled with first order Euler time stepping. This paper describes th...

Given s ∈ (0, 1), we consider the problem of minimizing the Gagliardo seminorm in H with prescribed condition outside the ball and under the further constraint of attaining zero value in a given set K . We investigate how the energy changes in dependence of such set. In particular, under mild regularity conditions, we show that adding a set A to K increases the energy of at most the measure of ...

In this paper, we deal with Stancu operators which depend on a non-negative integer parameter. Firstly, define Kantorovich extension of the operators. For functions belonging to space Lp [0, 1] , 1 ? p < ?, obtain convergence in norm by sequence Stancu-Kantorovich operators, and give an estimate for rate via first order averaged modulus smoothness. Moreover, operators; search variation detra...