Search results for "Combinatorics"
showing 10 items of 1770 documents
Theoretical description of the decays Λb→Λ(*)(12±,32±)+J/ψ
2017
We calculate the invariant and helicity amplitudes for the transitions ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}^{(*)}({J}^{P})+J/\ensuremath{\psi}$, where the ${\mathrm{\ensuremath{\Lambda}}}^{(*)}({J}^{P})$ are $\mathrm{\ensuremath{\Lambda}}(sud)$-type ground and excited states with ${J}^{P}$ quantum numbers ${J}^{P}={\frac{1}{2}}^{\ifmmode\pm\else\textpm\fi{}}$, ${\frac{3}{2}}^{\ifmmode\pm\else\textpm\fi{}}$. The calculations are performed in the framework of a covariant confined quark model previously developed by us. We find that the values of the helicity amplitudes for the ${\mathrm{\ensuremath{\Lambda}}}^{*}(1520,{\frac{3}{2}}^{\ensu…
The Neumann Problem for the Total Variation Flow
2004
This chapter is devoted to prove existence and uniqueness of solutions for the minimizing total variation flow with Neumann boundary conditions, namely $$ \left\{ \begin{gathered} \frac{{\partial u}} {{\partial t}} = div\left( {\frac{{Du}} {{\left| {Du} \right|}}} \right) in Q = (0,\infty ) \times \Omega , \hfill \\ \frac{{\partial u}} {{\partial \eta }} = 0 on S = (0,\infty ) \times \partial \Omega , \hfill \\ u(0,x) = u_0 (x) in x \in \Omega , \hfill \\ \end{gathered} \right. $$ (2.1) where Ω is a bounded set in ℝ N with Lipschitz continuous boundary ∂ Ω and u0 ∈ L1(Ω). As we saw in the previous chapter, this partial differential equation appears when one uses the steepest descent method …
Color- and motion-specific units in the tectum opticum of goldfish
2016
Extracellular recordings were performed from 69 units at different depths between 50 and [Formula: see text]m below the surface of tectum opticum in goldfish. Using large field stimuli (86[Formula: see text] visual angle) of 21 colored HKS-papers we were able to record from 54 color-sensitive units. The colored papers were presented for 5[Formula: see text]s each. They were arranged in the sequence of the color circle in humans separated by gray of medium brightness. We found 22 units with best responses between orange, red and pink. About 12 of these red-sensitive units were of the opponent "red-ON/blue-green-OFF" type as found in retinal bipolar- and ganglion cells as well. Most of them w…
Periodic Orbits in the Isosceles Three-Body Problem
1991
The Saturn’s satellites Janus and Epimetheus are the first known bodies in the Solar System that has horseshoe orbits in a frame that rotates with uniform angular velocity. Both satellites have similar masses and orbital elements when they are far from one another. Moreover, their orbits are nearly symmetric. In fact, in the past, they have been identify as a unique satellite and afterwards, some mathematical theories about their orbits has been necessaries to understand why they do not collide. In particular, the interest in planar three-body problem with two small masses has increased6. We assume that the two small masses have similar symmetric initial conditions. The aim of this paper is…
Scaling behavior of an airplane-boarding model
2013
An airplane-boarding model, introduced earlier by Frette and Hemmer [Phys. Rev. E 85, 011130 (2012)], is studied with the aim of determining precisely its asymptotic power-law scaling behavior for a large number of passengers $N$. Based on Monte Carlo simulation data for very large system sizes up to $N={2}^{16}=65\phantom{\rule{0.16em}{0ex}}536$, we have analyzed numerically the scaling behavior of the mean boarding time $\ensuremath{\langle}{t}_{b}\ensuremath{\rangle}$ and other related quantities. In analogy with critical phenomena, we have used appropriate scaling Ans\"atze, which include the leading term as some power of $N$ (e.g., $\ensuremath{\propto}$${N}^{\ensuremath{\alpha}}$ for …
Dissipative operators and differential equations on Banach spaces
1991
If we consider the initial value problem Inline Equation $$x'(t) = f(t,x(t)),{\text{ }}x(0) = {x_0}$$ on the real line, it is well known that one—sided bounds like Inline Equation $$\left[ {f(t,x) - f\left( {t,y} \right)} \right]\left( {x - {\text{y}}} \right) \leqslant \omega {\left( {x - y} \right)^2}$$ give much better information about the behaviour of solutions than the Lipschitz- type estimates Inline Equation $$ \left| {f\left( {t,x} \right) - f\left( {t,y} \right)} \right| \leqslant L\left| {x - y} \right|,$$ because ω, unlike L, may be negative.
Structure of Kac-Moody groups
2008
For a phys ic i s t , a Kac-Moody algebra is the current algebra of a quantum f i e l d theory model in I + I space-time dimensions with an in terna l symmetry group G [ I ] . A More p rec ise ly , l e t ~ be the Lie algebra of G . The Kac-Moody algebra g is a one-dimensional central extension of the loop algebra Map(S I , g ) . I f f l ' f2 C Map(S I ,~ ) , then the commutator is defined point -wise,
Introduction to Homotopy Theory
2001
Consider two manifolds X and Y together with a set of continuous maps f, g,... $$ f:X \to Y,x \to f(x) = y;x \in X,y \in Y. $$
“Ill-Conditioned” Vertices
1970
The round-off errors tend to increase particularly rapidly after pivoting at “ill-conditioned” vertices. Those vertices where two or more hyperplanes, each representing one constraint, intersect at a very slight angle are considered as “ill-conditioned”. An “ill-conditioned” vertex is for instance given by the intersection of the two constraints: $$\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}.