Some binomial sums involving absolute values

We consider several families of binomial sum identities whose definition involves the absolute value function. In particular, we consider centered double sums of the form $$S_{\alpha,\beta}(n) := \sum_{k,\;\ell}\binom{2n}{n+k}\binom{2n}{n+\ell} |k^\alpha-\ell^\alpha|^\beta,$$ obtaining new results in the cases $\alpha = 1, 2$. We show that there is a close connection between these double sums in the case $\alpha=1$ and the single centered binomial sums considered by Tuenter.Comment: 15 pages, 19 reference

Apollo asteroids (1566) Icarus and 2007 MK6: Icarus family members?

Although it is more complicated to search for near-Earth object (NEO) families than main belt asteroid (MBA) families, since differential orbital evolution within a NEO family can cause current orbital elements to drastically differ from each other, we have found that Apollo asteroids (1566) Icarus and the newly discovered 2007 MK6 are almost certainly related. Specifically, their orbital evolutions show a similar profile, time shifted by only ~1000 yr, based on our time-lag theory. The dynamical relationship between Icarus and 2007 MK6 along with a possible dust band, the Taurid-Perseid meteor swarm, implies the first detection of an asteroidal NEO family, namely the "Icarus asteroid family".Comment: 11 pages, 1 figure, to appear on Astrophysical Journal Letters (journal info added

Synthesis and characterization of phenylethynylcarbonyl terminated novel thermosetting imide compound

Phenylethynyl terminated novel imide compound based on 1,3-bis(3-aminophenoxy)benzene (APB) and phenylethynyl trimellitic anhydride (PETA) were prepared. The curing behavior of phenylethynyl terminated imide compound was investigated by differential scanning calorimetry and Fourier transform infrared spectrometry. The curing reaction of phenylethynylcarbonyl end group completed at 220°C, and proceeded much faster than that of phenylethynyl end group. Glass transition temperature of the thermosetting resin from phenylethynylcarbonyl terminated novel imide compound determined by dynamic mechanical analysis was almost the same as that of o-cresolnovolac type epoxy resin. In addition, the thermosetting resin from phenylethynylcarbonyl terminated novel imide compound exhibited excellent thermal and dimensional stabilities. These excellent properties of these phenylethynyl terminated imide compound might be due to the incorporation of alkene group or aromatic ring substitutes in the backbones, which might enhance the chain interaction (molecular packing) and reduce the molecular chain mobility

Antisymmetrization of a Mean Field Calculation of the T-Matrix

The usual definition of the prior(post) interaction $V(V^\prime )$ between projectile and target (resp. ejectile and residual target) being contradictory with full antisymmetrization between nucleons, an explicit antisymmetrization projector ${\cal A}$ must be included in the definition of the transition operator, $T\equiv V^\prime{\cal A}+V^\prime{\cal A}GV.$ We derive the suitably antisymmetrized mean field equations leading to a non perturbative estimate of $T$. The theory is illustrated by a calculation of forward $\alpha$-$\alpha$ scattering, making use of self consistent symmetries.Comment: 30 pages, no figures, plain TeX, SPHT/93/14

Sign-changing tower of bubbles for a sinh-Poisson equation with asymmetric exponents

Motivated by the statistical mechanics description of stationary 2D-turbulence, for a sinh-Poisson type equation with asymmetric nonlinearity, we construct a concentrating solution sequence in the form of a tower of singular Liouville bubbles, each of which has a different degeneracy exponent. The asymmetry parameter $\gamma\in(0,1]$ corresponds to the ratio between the intensity of the negatively rotating vortices and the intensity of the positively rotating vortices. Our solutions correspond to a superposition of highly concentrated vortex configurations of alternating orientation; they extend in a nontrivial way some known results for $\gamma=1$. Thus, by analyzing the case $\gamma\neq1$ we emphasize specific properties of the physically relevant parameter $\gamma$ in the vortex concentration phenomena