Search results for "combinatoric"

A Generalized Synthesis of 3-Amino-5-aryl-, 3-Amino-5-polyfluorophenyl-, and 3-Amino-5-alkyl-1,2,4-oxadiazoles through Ring-degenerate Rearrangements

2002

A generalized synthesis of 3-amino-5-aryl-, 3-amino-5-poly- fluorophenyl- and 3-amino-5-alkyl-1,2,4-oxadiazoles has been developed starting from the 3-amino-5-methyl-1,2,4-oxadiazole as a common synthon. Aroylation or alkanoylation of this aminooxadiazole, followed by thermally- induced ring-degenerate equilibration of resulting 3-acylamino compounds, and final acid hydrolysis of the 3-acetylamino-5-aryl- (or 5-polyfluorophenyl-), or 3- acetylamino-5-alkyl-1,2,4-oxadiazoles counterpart which is formed, gave the expected 3-amino-5-substituted 1,2,4-oxadiazoles. In the case of some 3- aroylamino compounds, yields of final 3-amino-5-aryloxadiazoles are higher than that expected on the basis of…

Sur les Codes ZigZag et Leur Décidabilité

1990

AbstractThis paper deals with zigzag factorizations and zigzag codes. The language of “zigzag” over a regular language is represented by constructing a special family of two-way automata. Decidability of zigzag codes, previously shown for the finite languages, is proved here for all regular languages by the analysis of the set of “crossing sequences” produced by a two-way automation in the family. We also obtain that it is decidable whether or not a two-way automation of a certain type is non-ambiguous.RésuméDans ce papier on reprend les notions de factorisation zigzag et de code zigzag. On construit pour tout langage rationnel, une famille d'automates bilatéres lesquels reconnaissent les m…

The ⊥-Illusion Is Not a T-Illusion

2020

Variants of the capital Latin letter T were prepared with the straight strokes replaced by J-, C-, or S-curves, mimicking handwritten Ts. These were used to test the hypothesis that the overestimation of the length of the T&rsquo

Closure to “Stage–Discharge Relationship for an Upstream Inclined Grid with Transversal Bars” by C. Di Stefano and V. Ferro

2016

Untangling CP violation and the mass hierarchy in long baseline experiments

2004

In the overlap region, for the normal and inverted hierarchies, of the neutrino-antineutrino bi-probability space for $\nu_\mu \to \nu_e$ appearance, we derive a simple identity between the solutions in the ($\sin^2 2\theta_{13}$, $\sin \delta$) plane for the different hierarchies. The parameter $\sin^2 2\theta_{13}$ sets the scale of the $\nu_\mu \to \nu_e$ appearance probabilities at the atmospheric $\delta m^2_{atm} \approx 2.4 \times 10^{-3}$ eV$^2$ whereas $\sin \delta $ controls the amount of CP violation in the lepton sector. The identity between the solutions is that the difference in the values of $\sin \delta$ for the two hierarchies equals twice the value of $\sqrt{\sin^2 2\theta…

On a class of singular measures satisfying a strong annular decay condition

2018

A metric measure space $(X,d,\mu)$ is said to satisfy the strong annular decay condition if there is a constant $C>0$ such that $$ \mu\big(B(x,R)\setminus B(x,r)\big)\leq C\, \frac{R-r}{R}\, \mu (B(x,R)) $$ for each $x\in X$ and all $0<r \leq R$. If $d_{\infty}$ is the distance induced by the $\infty$-norm in $\mathbb{R}^N$, we construct examples of singular measures $\mu$ on $\mathbb{R}^N$ such that $(\mathbb{R}^N, d_{\infty},\mu)$ satisfies the strong annular decay condition.

Approximation of the Maxwell equations in anisotropic inhomogeneous media

1996

Let Ω ∈ L be in ℝ 2. We consider the initial-boundary value problem $$ \begin{array}{l}rot\,E\left( {x,t} \right) + \mu \left( x \right)\frac{\partial }{{\partial t}}H\left( {x,t} \right) = J\left( {x,t} \right), \\\left( {x,t} \right) \in \Omega \, \times \,(0,T], \\curl\,H\left( {x,t} \right) - \varepsilon \left( {\frac{\partial }{{\partial t}}} \right)E\left( {x,t} \right) = k\left( {x,t} \right), \\n \wedge E\left( {x,t} \right) = 0, \\\left( {x,t} \right) \in \partial \Omega \, \times \,(0,T], \\\left( {E\left( {x,0} \right),H\left( {x,0} \right)} \right) = \left( {{E_0}\left( x \right),\,{H_0}\left( x \right)} \right), \\x \in \bar \Omega \\\end{array} $$ (13.1) .

Exercises, Hints and Selected Solutions

2016

1.1. Prove the formula (1.8a) in Sect. 1.3, $$\displaystyle{ \int \mathrm{d}^{n}x\; =\int _{ 0}^{+\infty }\!\!\!\mathrm{d}r\;r^{n-1}\int _{ 0}^{2\pi }\!\!\!\mathrm{d}\phi \prod _{ k=1}^{n-2}\int _{ 0}^{\pi }\!\!\!\mathrm{d}\theta _{ k}\sin ^{k}(\theta _{ k}) }$$ (1.1) by means of induction.

Asymptotic Behaviour and Qualitative Properties of Solutions

2004

The purpose of this chapter is to give some qualitative properties of the flow $$ frac{{\partial u}}{{\partial t}} = div\left( {\frac{{Du}}{{\left| {Du} \right|}}} \right) in\;]0,\infty [ \times {\mathbb{R}^N} $$ (4.1) .

Indefinitely growing self-avoiding walk.

1985

We introduce a new random walk with the property that it is strictly self-avoiding and grows forever. It belongs to a different universality class from the usual self-avoiding walk. By definition the critical exponent $\ensuremath{\gamma}$ is equal to 1. To calculate the exponent $\ensuremath{\nu}$ of the mean square end-to-end distance we have performed exact enumerations on the square lattice up to 22 steps. This gives the value $\ensuremath{\nu}=0.57\ifmmode\pm\else\textpm\fi{}0.01$.