Expand all Collapse all | Results 1 - 12 of 12 |
1. CMB 2013 (vol 56 pp. 673)
Diophantine Approximation for Certain Algebraic Formal Power Series in Positive Characteristic In this paper, we study rational approximations for certain algebraic power series over a finite field.
We obtain results for irrational elements of strictly positive degree
satisfying an equation of the type
\begin{equation}
\alpha=\displaystyle\frac{A\alpha^{q}+B}{C\alpha^{q}}
\end{equation}
where $(A, B, C)\in
(\mathbb{F}_{q}[X])^{2}\times\mathbb{F}_{q}^{\star}[X]$.
In particular,
we will give, under some conditions on the polynomials $A$, $B$
and $C$, well approximated elements satisfying this equation.
Keywords:diophantine approximation, formal power series, continued fraction Categories:11J61, 11J70 |
2. CMB 2011 (vol 56 pp. 337)
Certain Properties of $K_0$-monoids Preserved by Tracial Approximation We show that the following $K_0$-monoid properties of $C^*$-algebras
in the class $\Omega$ are inherited by simple unital $C^*$-algebras in
the class $TA\Omega$: (1) weak comparability, (2) strictly
unperforated, (3) strictly cancellative.
Keywords:$C^*$-algebra, tracial approximation, $K_0$-monoid Categories:46L05, 46L80, 46L35 |
3. CMB 2011 (vol 55 pp. 752)
Approximation of Holomorphic Solutions of a System of Real Analytic Equations We prove the existence of an approximation function for holomorphic
solutions of a system of real analytic equations. For this we use
ultraproducts and Weierstrass systems introduced by J. Denef and L.
Lipshitz. We also prove a version of the PÅoski smoothing theorem in
this case.
Keywords:Artin approximation, real analytic equations Categories:13B40, 13L05, 14F12 |
4. CMB 2011 (vol 55 pp. 762)
Smooth Approximation of Lipschitz Projections We show that any Lipschitz projection-valued function
$p$ on a connected closed Riemannian manifold
can be approximated uniformly by smooth
projection-valued functions $q$ with Lipschitz constant
close to that of $p$.
This answers a question of Rieffel.
Keywords:approximation, Lipschitz constant, projection Category:19K14 |
5. CMB 2011 (vol 54 pp. 566)
Non-uniform Randomized Sampling for Multivariate Approximation by High Order Parzen Windows We consider approximation of multivariate functions in Sobolev
spaces by high order Parzen windows in a non-uniform sampling
setting. Sampling points are neither i.i.d. nor regular, but are
noised from regular grids by non-uniform shifts of a probability
density function. Sample function values at sampling points are
drawn according to probability measures with expected values being
values of the approximated function. The approximation orders are
estimated by means of regularity of the approximated function, the
density function, and the order of the Parzen windows, under
suitable choices of the scaling parameter.
Keywords:multivariate approximation, Sobolev spaces, non-uniform randomized sampling, high order Parzen windows, convergence rates Categories:68T05, 62J02 |
6. CMB 2010 (vol 53 pp. 614)
The Mean Width of Circumscribed Random Polytopes
For a given convex body $K$ in ${\mathbb R}^d$, a random polytope
$K^{(n)}$ is defined (essentially) as the intersection of $n$
independent closed halfspaces containing $K$ and having an isotropic
and (in a specified sense) uniform distribution. We prove upper and
lower bounds of optimal orders for the difference of the mean widths
of $K^{(n)}$ and $K$ as $n$ tends to infinity. For a simplicial
polytope $P$, a precise asymptotic formula for the difference of the
mean widths of $P^{(n)}$ and $P$ is obtained.
Keywords:random polytope, mean width, approximation Categories:52A22, 60D05, 52A27 |
7. CMB 2009 (vol 53 pp. 11)
Approximation and Interpolation by Entire Functions of Several Variables Let $f\colon \mathbb R^n\to \mathbb R$ be $C^\infty$ and let $h\colon
\mathbb R^n\to\mathbb R$ be positive
and continuous. For any unbounded nondecreasing sequence $\{c_k\}$
of nonnegative real numbers and for any sequence without
accumulation points $\{x_m\}$ in $\mathbb R^n$, there exists an entire
function $g\colon\mathbb C^n\to\mathbb C$ taking real values on $\mathbb R^n$ such that
\begin{align*}
&|g^{(\alpha)}(x)-f^{(\alpha)}(x)|\lt h(x), \quad |x|\ge c_k, |\alpha|\le k,
k=0,1,2,\dots,
\\
&g^{(\alpha)}(x_m)=f^{(\alpha)}(x_m), \quad |x_m|\ge c_k, |\alpha|\le k,
m,k=0,1,2,\dots.
\end{align*}
This is a version for functions of several variables of the
case $n=1$ due to L. Hoischen.
Keywords:entire function, complex approximation, interpolation, several complex variables Category:32A15 |
8. CMB 2009 (vol 52 pp. 28)
Right and Left Weak Approximation Properties in Banach Spaces New necessary and sufficient conditions are established for Banach
spaces to have the approximation property; these conditions are
easier to check than the known ones. A shorter proof of a result
of Grothendieck is presented, and some properties of a weak
version of the approximation property are addressed.
Keywords:approximation property, quasi approximation property, weak approximation property Categories:46B28, 46B10 |
9. CMB 2008 (vol 51 pp. 372)
Picard's Iterations for Integral Equations of Mixed Hammerstein Type A new semilocal convergence result for the Picard method is presented,
where the main required condition in the contraction mapping principle is relaxed.
Keywords:nonlinear equations in Banach spaces, successive approximations, semilocal convergence theorem, Picard's iteration, Hammerstein integral equations Categories:45G10, 47H99, 65J15 |
10. CMB 2007 (vol 50 pp. 434)
MKZ Type Operators Providing a Better Estimation on $[1/2,1)$ In the present paper, we introduce a modification of the Meyer-K\"{o}nig and
Zeller (MKZ) operators which preserve the test functions $f_{0}(x)=1$ and
$f_{2}(x)=x^{2}$, and we show that this modification provides a better estimation
than the classical MKZ operators on the interval $[\frac{1}{2},1)$ with
respect to the modulus of continuity and the Lipschitz class functionals.
Furthermore, we present the $r-$th order generalization of our operators and
study their approximation properties.
Keywords:Meyer-KÃ¶nig and Zeller operators, Korovkin type approximation theorem, modulus of continuity, Lipschitz class functionals Categories:41A25, 41A36 |
11. CMB 2006 (vol 49 pp. 237)
Approximation by Rational Mappings, via Homotopy Theory Continuous mappings defined from compact subsets $K$ of complex
Euclidean space $\cc^n$ into complex projective space $\pp^m$ are
approximated by rational mappings. The fundamental tool employed
is homotopy theory.
Keywords:Rational approximation, homotopy type, null-homotopic Categories:32E30, 32C18 |
12. CMB 2002 (vol 45 pp. 80)
Approximation On Arcs and Dendrites Going to Infinity in $\C^n$ On a locally rectifiable arc going to infinity, each continuous
function can be approximated by entire functions.
Keywords:tangential approximation, Carleman Categories:32E30, 32E25 |