We develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. First, using the notion seminorm, we propose a geometric framework for introduce matrix semimeasures characterize their properties. show that spectral abscissa is infimum over weighted semimeasures. For dynamical systems, use semimeasure Jacobian to contractivity properties trajectories. ...

Abstract We study a PDE-constrained optimal control problem that involves functions of bounded variation as controls and includes the TV seminorm in objective. apply path-following inexact Newton method to problems arise from smoothing adding an $$H^1$$ H 1 regularizati...

 Let $R$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎A right $R$-module $M$ is called $(n‎, ‎d)$-projective if $Ext^{d+1}_R(M‎, ‎A)=0$ for every $n$-copresented right $R$-module $A$‎. ‎$R$ is called right $n$-cocoherent if every $n$-copresented right $R$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $R$-module is $(n‎, ‎d)$-projective‎. ‎$R$...

In this paper, we develop a gradient recovery based linear (GRBL) finite element method (FEM) and Hessian FEM for second-order elliptic equations in non-divergence form. The equation is casted into symmetric weak formulation, which derivatives of the unknown function are involved. We use operators to calculate approximations. Although, thanks low degrees freedom elements, implementation propose...

MNDO semi-empirical SCF MO calculations are used to study the pyramidal nitrogen atom inversion and configurational equilibria in the title compounds.

We define the stable 4–genus of a knot K ⊂ S, gst(K), to be the limiting value of g4(nK)/n, where g4 denotes the 4–genus and n goes to infinity. This induces a seminorm on the rationalized knot concordance group, CQ = C ⊗ Q. Basic properties of gst are developed, as are examples focused on understanding the unit ball for gst on specified subspaces of CQ. Subspaces spanned by torus knots are use...

In this document I develop a weight function theory of positive order basis function interpolants and smoothers. In Chapter 1 the basis functions and data spaces are defined directly using weight functions. The data spaces are used to formulate the variational problems which define the interpolants and smoothers discussed in later chapters. The theory is illustrated using some standard examples...

This paper deals with the approximate solution of a linear regularly-elliptic 2mth-order boundary-value problem Lu = f, with / 6 Hr(Q) for r > —m. Suppose that the problem is indefinite, i.e., the variational form of the problem involves a weaklycoercive bilinear form. Of particular interest is the quality of the finite element method (FEM) of degree k using n inner products of /. The error of ...

Given a passive tracer distribution $f(x,y)$ , what is the simplest unstirred pattern that may be reached under incompressible advection? This question partially motivated by recent studies of three-dimensional (3-D) magnetic reconnection, in which patterns topological invariant called field line helicity greatly simplify until reaching relaxed state. We test two approaches: variational method ...

Let $\mathbb{B}(\mathcal{H})$ denote the $C^{\ast}$-algebra of all bounded linear operators on a Hilbert space $\big(\mathcal{H}, \langle\cdot, \cdot\rangle\big)$. Given positive operator $A\in\B(\h)$, and number $\lambda\in [0,1]$, seminorm ${\|\cdot\|}_{(A,\lambda)}$ is defined set $\B_{A^{1/2}}(\h)$ in $\B(\h)$ having an $A^{1/2}$-adjoint. The combination sesquilinear form ${\langle \cdot, \...