Search results for "combinatoric"
showing 10 items of 1776 documents
“Ill-Conditioned” Vertices
1970
The round-off errors tend to increase particularly rapidly after pivoting at “ill-conditioned” vertices. Those vertices where two or more hyperplanes, each representing one constraint, intersect at a very slight angle are considered as “ill-conditioned”. An “ill-conditioned” vertex is for instance given by the intersection of the two constraints: $$\eqalign{ & 3\,{{\rm{x}}_{\rm{1}}}\, + \,{{\rm{x}}_{\rm{2}}}\, \le \,6 \cr & {{\rm{x}}_{\rm{1}}}\, + \,.354\,{{\rm{x}}_{\rm{2}}}\, \le \,2.001 \cr} $$
Perturbations of Jordan Blocks
2019
In this chapter we shall study the spectrum of a random perturbation of the large Jordan block A0, introduced in Sect. 2.4: $$\displaystyle A_0=\begin {pmatrix}0 &1 &0 &0 &\ldots &0\\ 0 &0 &1 &0 &\ldots &0\\ 0 &0 &0 &1 &\ldots &0\\ . &. &. &. &\ldots &.\\ 0 &0 &0 &0 &\ldots &1\\ 0 &0 &0 &0 &\ldots &0 \end {pmatrix}: {\mathbf {C}}^N\to {\mathbf {C}}^N. $$ Zworski noticed that for every z ∈ D(0, 1), there are associated exponentially accurate quasimodes when N →∞. Hence the open unit disc is a region of spectral instability. We have spectral stability (a good resolvent estimate) in \(\mathbf {C}\setminus \overline {D(0,1)}\), since ∥A0∥ = 1. σ(A0) = {0}.
Some Aspects of Vector-Valued Singular Integrals
2009
Let A, B be Banach spaces and \(1 < p < \infty. \; T\) is said to be a (p, A, B)- CalderoLon–Zygmund type operator if it is of weak type (p, p), and there exist a Banach space E, a bounded bilinear map \(u: E \times A \rightarrow B,\) and a locally integrable function k from \(\mathbb{R}^n \times \mathbb{R}^n \backslash \{(x, x): x \in \mathbb{R}^n\}\) into E such that $$T\;f(x) = \int u(k(x, y), f(y))dy$$ for every A-valued simple function f and \(x \notin \; supp \; f.\)
Hilbert Space Embeddings for Gelfand–Shilov and Pilipović Spaces
2017
We consider quasi-Banach spaces that lie between a Gelfand–Shilov space, or more generally, Pilipovi´c space, \(\mathcal{H}\), and its dual, \(\mathcal{H}^\prime\) . We prove that for such quasi-Banach space \(\mathcal{B}\), there are convenient Hilbert spaces, \(\mathcal{H}_{k}, k=1,2\), with normalized Hermite functions as orthonormal bases and such that \(\mathcal{B}\) lies between \(\mathcal{H}_1\; \mathrm{and}\;\mathcal{H}_2\), and the latter spaces lie between \(\mathcal{H}\; \mathrm{and}\;\mathcal{H}^\prime\).
Leading order corrections to the Bethe-Heitler process in the γp→l+l−p reaction
2019
This paper focuses on all one-loop corrections to the Bethe-Heitler process involved in the reaction $\ensuremath{\gamma}\phantom{\rule{0}{0ex}}p\ensuremath{\rightarrow}{l}^{+}\phantom{\rule{0.333em}{0ex}}{l}^{\ensuremath{-}}\phantom{\rule{0}{0ex}}p$. These corrections are of paramount interest as they serve to check the exactness of the so called $l\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n$ $u\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}v\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}i\phanto…
Explanation of theΔ5/2−(1930)as aρΔbound state
2009
We use the $\ensuremath{\rho}\ensuremath{\Delta}$ interaction in the hidden gauge formalism to dynamically generate ${N}^{*}$ and ${\ensuremath{\Delta}}^{*}$ resonances. We show, through a comparison of the results from this analysis and from a quark model study with data, that the ${\ensuremath{\Delta}}_{5/{2}^{\ensuremath{-}}}(1930)$, ${\ensuremath{\Delta}}_{3/{2}^{\ensuremath{-}}}(1940)$, and ${\ensuremath{\Delta}}_{1/{2}^{\ensuremath{-}}}(1900)$ resonances can be assigned to $\ensuremath{\rho}\ensuremath{\Delta}$ bound states. More precisely the ${\ensuremath{\Delta}}_{5/{2}^{\ensuremath{-}}}(1930)$ can be interpreted as a $\ensuremath{\rho}\ensuremath{\Delta}$ bound state whereas the $…
Measurement of the branching fraction forB±→χc0K±
2004
We present a measurement of the branching fraction of the decay ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c0}{K}^{\ifmmode\pm\else\textpm\fi{}}$ from a sample of $89\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ pairs collected by the BABAR detector at the SLAC PEP-II asymmetric-energy B factory. The ${\ensuremath{\chi}}_{c0}$ meson is reconstructed through its two-body decays to ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${K}^{+}{K}^{\ensuremath{-}}.$ We measure $\mathcal{B}{(B}^{\ifmmode\pm\else\textpm\fi{}}\stackrel{\ensuremath{\rightarrow}}{}{\ensuremath{\chi}}_{c0}{K}^{\ifmmode\pm\else\textpm\fi{}})\ifmmode\times\e…
Spectral Asymptotics for $$\mathcal {P}\mathcal {T}$$ Symmetric Operators
2019
\(\mathcal {P}\mathcal {T}\)-symmetry has been proposed as an alternative to self-adjointness in quantum physics, see Bender et al. (J Math Phys 40(5):2201–2229, 1999), Bender and Mannheim (Phys Lett A 374(15–16):1616–1620, 2010). Thus for instance, if we consider a Schrodinger operator on Rn, $$\displaystyle P=-h^2\Delta +V(x), $$ the usual assumption of self-adjointness (implying that the potential V is real valued) can be replaced by that of \(\mathcal {P}\mathcal {T}\)-symmetry: $$\displaystyle V\circ \iota =\overline {V}, $$ where ι : Rn →Rn is an isometry with ι2 = 1≠ι. If we introduce the parity operator \(\mathcal {P}_\iota u(x)=u(\iota (x))\) and the time reversal operator \(\mathc…
Evidence forB+→J/ψpΛ¯and Search forB0→J/ψpp¯
2003
We have performed a search for the decays ${B}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}p\overline{\ensuremath{\Lambda}}$ and ${B}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}p\overline{p}$ in a data set of $(88.9\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $\ensuremath{\Upsilon}(4S)$ decays collected by the BABAR experiment at the PEP-II ${e}^{+}{e}^{\ensuremath{-}}$ storage ring at the Stanford Linear Accelerator Center. Four charged $B$ candidates have been observed with an expected background of $0.21\ifmmode\pm\else\textpm\fi{}0.14$ events. The corresponding branching fraction is $({12}_{\ensuremath{-}6}^{+9})\ifmmode\times\else\texttimes\fi{}{10}^…
Lengths of radii under conformal maps of the unit disc
1999
If E f ( R ) E_{f}(R) is the set of endpoints of radii which have length greater than or equal to R > 0 R>0 under a conformal map f f of the unit disc, then cap E f ( R ) = O ( R − 1 / 2 ) \operatorname {cap} E_{f}(R)=O(R^{-1/2}) as R → ∞ R\to \infty for the logarithmic capacity of E f ( R ) E_{f}(R) . The exponent − 1 / 2 -1/2 is sharp.