Novel Copolymers of 4-Fluorostyrene. 3. Some Ring-Substituted 2-Phenyl-1,1-dicyanoethylenes

Novel copolymers of trisubstituted ethylene monomers, ring-substituted 2-phenyl-1,1-dicyanoethylenes, RC₆H₄CH=C(CN)₂ (where R is 4-dimethylamino, 4-diethylamino, 3-phenoxy, 3-benzyloxy, 4-benzyloxy, 4-acetoxy, 2-cyano, 3-cyano, and 4-cyano) and 4-fluorostyrene were prepared at equimolar monomer feed composition by solution copolymerization in the presence of a radical initiator (ABCN) at 70°C. The composition of the copolymers was calculated from nitrogen analysis, and the structures were analyzed by IR, ¹H and ¹³C-NMR. The order of relative reactivity (1/r ₁) for the monomers is 3-benzyloxy (2.9) > 4-cyano (2.7) > 3-phenoxy (1.9) > 4-acetoxy (1.8) > 3-cyano (1.7) > 2-cyano (1.6) > 4-benzyloxy (0.6) > 4-dimethylamino (0.4) = 4-diethylamino (0.4). High T _g of the copolymers, in comparison with that of poly (4-fluorostyrene) indicates a substantial decrease in chain mobility of the copolymer due to the high dipolar character of the trisubstituted ethylene monomer unit. Decomposition of the copolymers in nitrogen occurred in two steps, first in the 290–400°C range with residue, which then decomposition in 400–800°C range.     

Theory of the quantized Hall effect (III)

In the previous paper, we have demonstrated the need for a phase transition as a function of θ in the non-linear σ-model describing the quantized Hall effect. In this work, we present arguments for the occurrence of exactly such a transition. We make use of a dilute gas instanton approximation as well as present a more rigorous duality argument to show that the usual scaling of the conductivity to zero at large distances is altered whenever $\text{σ}{}_{\mathrm{xy}}{}^{\mathrm{(0)}}\text{≈}\text{1}\text{2}\text{ne}{}^2\text{/h}$, n integer. This then completes our theory of the quantized Hall effect.     

Two-dimensional interferogram of an exploding selenium foil using asoft X-ray laser interferometer

We have developed a soft X-ray interferometer capable of probing large high-density plasmas with micron spatial resolutions. A neon-like yttrium X-ray laser operating at 155 Å was combined with the Mach-Zehnder interferometer to obtain electron density profiles of a laser-produced exploding selenium foil plasma. The plasma was produced with one Nova laser beam using a 120-μm line focus, the same conditions used to create a selenium X-ray laser. The interferogram of the selenium plasma was obtained from an end-on perspective     

Theory of the quantized hall effect (II)

We review the derivation that the effective lagrangian describing the critical fluctuations in a two-dimensional disordered electronic system in a transverse magnetic field contains a novel, topological term. We extend this result in several directions. We show how the importance of topological concepts can be seen by examining in detail the nature of the boundary current whenever the Fermi energy lies within a localized state region. This insight allows us to construct a field theoretic quantization argument. Our argument is reminiscent of the Laughlin-Halperin quantization approach, in that we make use of the response of the system to sources with nontrivial gauge topology. This then leads to a discussion of how to use the effective field theory to actually compute the response, and of why localization must break down somewhere within the Landau band. Our methodology unifies the results of Laughlin, Halperin and Thouless with the field theoretic approach to localization pioneered by Wegner.     

High-energy behavior of jet and lepton-pair production

The cross section for jet and lepton-pair production at large transverse momenta has been studied to all orders in QCD perturbation theory. Appropriate moments of these cross sections are seen to factorize short-distance from long-distance dependence, and scale breaking is governed by the anomalous dimensions of twist-two operators.     

Determination of the strong phase in D0-->K+pi- using quantum-correlated measurements

We exploit the quantum coherence between pair-produced D0 and D[over]0 in psi(3770) decays to study charm mixing, which is characterized by the parameters x and y, and to make a first determination of the relative strong phase delta between D0-->K+pi- and D[over]0-->K+pi-. Using 281 pb(-1) of e+e- collision data collected with the CLEO-c detector at Ecm=3.77 GeV, as well as branching fraction input and time-integrated measurements of RM identical with (x2 + y2)/2 and RWS identical with Gamma(D0-->K+pi-)/Gamma(D[over]0-->K+pi-) from other experiments, we find cosdelta=1.03(-0.17)(+0.31)+/-0.06, where the uncertainties are statistical and systematic, respectively. By further including other mixing parameter measurements, we obtain an alternate measurement of cosdelta=1.10+/-0.35+/-0.07, as well as x sindelta=(4.4(-1.8)(+2.7)+/-2.9)x10(-3) and delta=(22(-12-11)(+11+9)) degrees .     

Using block designs in crossing number bounds

The crossing number $\mathrm{\text{CR}}\left(G\right)$ of a graph $G=\left(V,E\right)$ is the smallest number of edge crossings over all drawings of $G$ in the plane. For any $k\ge 1$, the $k$‐planar crossing number of $G,{\mathrm{\text{CR}}}_k\left(G\right)$, is defined as the minimum of $\text{CR}\left(G_1\right)+\text{CR}\left(G_2\right)+?+\text{CR}\left(G_k\right)$ over all graphs $G_1,G_2,\dots ,G_k$ with ${\cup }_{i=1}^k{G}_i=G$. Pach et al [Comput. Geom.: Theory Appl. 68 (2018), pp. 2–6] showed that for every $k\ge 1$, we have ${\text{CR}}_k\left(G\right)\le (2/k^2?1/k^3)\text{CR}\left(G\right)$ and that this bound does not remain true if we replace the constant $2/k^2?1/k^3$ by any number smaller than $1/k^2$. We improve the upper bound to $(1/k^2)\left(1+o\left(1\right)\right)$ as $k\to \infty$. For the class of bipartite graphs, we show that the best constant is exactly $1/k^2$ for every $k$. The results extend to the rectilinear variant of the $k$‐planar crossing number.