We show that for a system $$ x'(t)=g(x(t-d_1(Lx_t)),\dots,x(t-d_k(Lx_t))) $$ of $n$ differential equations with $k$ discrete state-dependent delays the solution manifold, on which solution operators are differentiable, is nearly as simple as a graph over a closed subspace in $C^1([-r,0],\mathbb{R}^n)$. The map $L$ is continuous and linear from $C([-r,0],\mathbb{R}^n)$ onto a finite-dimensional vectorspace, and $g$ as well as the delay functions $d_{\kappa}$ are assumed to be continuously differentiable.

Tibor Krisztin Hans-Otto Walther

Let $r>0, n\in\mathbb{N}, {\bf k}\in\mathbb{N}$. Consider the delay differential equation $$ x'(t)=g(x(t-d_1(Lx_t)),\ldots,x(t-d_{{\bf k}}(Lx_t))) $$ for $g:(\mathbb{R}^n)^{{\bf k}}\supset V\to\mathbb{R}^n$ continuously differentiable, $L$ a continuous linear map from $C([-r,0],\mathbb{R}^n)$ into a finite-dimensional vectorspace $F$, each $d_k:F\supset W\to[0,r]$, $k=1,\ldots,{\bf k}$, continuously differentiable, and $x_t(s)=x(t+s)$. The solutions define a semiflow of continuously differentiable solution operators on the submanifold $X_f\subset C^1([-r,0],\mathbb{R}^n)$ which is given by the compatibility condition $\phi'(0)=f(\phi)$ with $$ f(\phi)=g(\phi(-d_1(L\phi)),\ldots,\phi(-d_{{\bf k}}(L\phi))). $$ We prove that $X_f$ has a finite atlas of at most $2^{{\bf k}}$ manifold charts, whose domains are almost graphs over $X_0$. The size of the atlas depends solely on the zerosets of the delay functions $d_k$.

Hans-Otto Walther

Data are presented on the reaction pbar-p -> omega-omega-pizero at rest from the Crystal Barrel detector. These data identify a strong signal due to f2(1565) -> omega-omega. The relative production from initial pbar-p states 3P2, 3P1 and 1S0 is well determined from omega-omega decay angular correlations; P-state annihilation dominates strongly. A combined fit is made with data on pbar-p -> 3pizero at rest, where f2(1565) -> pizero-pizero is observed.

C. A. Baker B. M. Barnett C. J. Batty K. Braune D. V. Bugg O. Cramer V. Crede N. Djaoshvili W. Dunnweber M. A. Faessler N. P. Hessey P. Hidas C. Hodd D. Jamnik H. Kalinowsky J. Kisiel E. Klempt C. Kolo L. Montanet B. Pick W. Roethel A. Sarantsev I. Scott C. Strassburger U. Thoma C. Volker S. Wallis D. Walther K. Wittmack B. S. Zou

5$\mu$m thick NdFeB films have been sputtered onto 100 mm Si substrates using high rate sputtering (18 $\mu$m/h). Films were deposited at ≤ 500 C and then annealed at 750 C for 10 minutes. While films deposited at temperatures up to 450 C have equiaxed grains, the size of which decreases with increasing deposition temperature, the films deposited at 500 C have columnar grains. The out-of-plane remanent magnetization increases with deposition temperature, reaching a maximum value of 1.4 T, while the coercivity remains constant at about 1.6 T. The maximum energy product achieved (400 kJ/m3) is comparable to that of high-quality NdFeB sintered magnets.

N. M. Dempsey Arnaud Walther Frederic May Dominique Givord Kirill Khlopkov Oliver Gutfleisch

Ta (100 nm) / NdFeB (5 $\mu$m) / Ta (100 nm) films have been deposited onto Si substrates using triode sputtering (deposition rate ~ 18 $\mu$m/h). A 2-step procedure was used : deposition at temperatures up to 400 C followed by ex-situ annealing at higher temperatures. Post-deposition annealing temperatures above 650 C are needed to develop high values of coercivity. The duration of the annealing time is more critical in anisotropic samples deposited onto heated substrates than in isotropic samples deposited at lower temperatures. For a given set of annealing conditions (750 C/ 10'), high heating rates (≥ 2000 C / h) favour high coercivity in both isotropic and anisotropic films. The shape and size of Nd2Fe14B grains depend strongly on the heating rate.

Arnaud Walther Kirill Khlopkov Oliver Gutfleisch Dominique Givord Nora M. Dempsey

This is a collection of statements gathered on the occasion of the Quantum Physics of Nature meeting in Vienna.

M. Arndt M. Aspelmeyer H. J. Bernstein R. Bertlmann C. Brukner J. P. Dowling J. Eisert A. Ekert C. A. Fuchs D. M. Greenberger M. A. Horne T. Jennewein P. G. Kwiat N. D. Mermin J. -W. Pan E. M. Rasel H. Rauch T. G. Rudolph C. Salomon A. V. Sergienko J. Schmiedmayer C. Simon V. Vedral P. Walther G. Weihs P. Zoller M. Zukowski

We consider the maximal function of oscillatory integrals and prove a global estimate for radial test functions which is almost sharp with respect to the Sobolev regularity.

Björn G. Walther

We extend the result of K. Karlander [Math. Scand. 80 (1997)] regarding finite dimensionality of spaces of absolutely convergent Fourier transforms.

Björn G. Walther

In this survey we discuss various aspects of the singularity invariants with differential origin derived from the $D$-module generated by $f^s$.

Anton Leykin Uli Walther

In the classical phase retrieval problem in the Paley-Wiener class $PW_L$ for $L>0$, i.e. to recover $f\in PW_L$ from $|f|$, Akutowicz, Walther, and Hofstetter independently showed that all such solutions can be obtained by flipping an arbitrary set of complex zeros across the real line. This operation is called zero-flipping and we denote by $\mathfrak{F}_a f$ the resulting function. The operator $\mathfrak{F}_a$ is defined even if $a$ is not a genuine zero of $f$, that is if we make an error on the location of the zero. Our main goal is to investigate the effect of $\mathfrak{F}_a$. We show that $\mathfrak{F}_af$ is no longer bandlimited but is still wide-banded. We then investigate the effect of $\mathfrak{F}_a$ on the stability of phase retrieval by estimating the quantity $\inf_{|c|=1}\|cf-\mathfrak{F}_af\|_2$. We show that this quantity is in general not well-suited to investigate stability, and so we introduce the quantity $\inf_{|c|=1}\|c\mathfrak{F}_bf-\mathfrak{F}_af\|_2$. We show that this quantity is dominated by the distance between $a$ and $b$.

Philippe Jaming Karim Kellay Rolando Perez