A counterexample to the Bartle-Graves selection theorem for multilinear maps

We present an example showing that the multilinear version of the Bartle-Graves Selection Theorem is false, even on finite dimensional spaces.

     

Cationic copolymerization of cycloaliphatic epoxy resin with a spirobislactone with lanthanum triflate as initiator: I. Characterization and shrinkage

3,4‐Epoxycyclohexylmethyl 3,4‐epoxycyclohexane carboxylate (ECH) was cured with different proportions of 1,6‐dioxaspiro [4,4]nonane‐2,7‐dione (s(γ‐BL)) using lanthanum triflate as a catalyst. The shrinkage undergone during curing was monitored by means of thermomechanical analysis (TMA) in isothermal experiments. Fourier transform infrared spectroscopy in attenuated‐total‐reflection mode (FTIR/ATR) was used to study the evolution of lactone, epoxide, and intermediate spiroorthoester (SOE) groups to identify the different reactions that take place during the curing process. DSC was used to study the thermal characteristics of the curing process and to assess the glass‐transition temperature (T_g) of the cured material. The dynamic mechanical properties of the cured material were determined based on the data obtained by DMTA. An increase in the proportion of s(γ‐BL) led to a decrease in the gelation time and the shrinkage after gelation. By combining the data obtained by TMA and FTIR/ATR, it was also possible to identify the reactive processes responsible for the shrinkage. It was observed that an increase in the proportion of s(γ‐BL) also increases the speed of the curing process and modifies the structure of the material, thus giving rise to more flexible materials. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3421–3432, 2005     

Polynomial time approximation schemes for dense instances of minimum constraint satisfaction

It is known that large fragments of the class of dense Minimum Constraint Satisfaction (MIN‐CSP) problems do not have polynomial time approximation schemes (PTASs) contrary to their Maximum Constraint Satisfaction analogs. In this paper we prove, somewhat surprisingly, that the minimum satisfaction of dense instances of kSAT ‐formulas, and linear equations mod 2, Ek‐LIN2, do have PTASs for any k. The MIN‐Ek‐LIN2 problems are equivalent to the k‐ary versions of the Nearest Codeword problem, the problem which is known to be exceedingly hard to approximate on general instances. The method of solution of the above problems depends on the development of a new density sampling technique for k‐uniform hypergraphs which could be of independent interest. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 73–91, 2003     

Forced transverse vibrations of a submerged tensioned string

For a submerged cable, the classical equation of a vibrating string must be modified to account for added mass and damping effects. This can be done with the aid of Morison's formulae. The resulting equation is non-linear. It is solved for the case when one end of the string is forced into sinusoidal transverse motion. The first harmonic approximations for both resonant and non-resonant responses are obtained by the method of matched asymptotic expansions under the assumption that the non-dimensional damping coefficient is small.     

On the maximum cardinality of a consistent set of arcs in a random tournament

For any tournament T on n vertices, let h(T) denote the maximum number of edges in the intersection of T with a transitive tournament on the same vertex set. Sharpening a previous result of Spencer, it is proved that, if T_n denotes the random tournament on n vertices, then, $\text{P}$$\text{(h(T}{}_{\mathrm{n}}\text{) ≤}\text{1}\text{2}\text{(}{}_2{}^{\mathrm{n}}\text{) + 1.73n}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{) → 1}$ as n → ∞.     

Inclusive ηp and ηn charged-current neutrino reactions below 6 GeV

Results are presented of a study of inclusive ηp and ηn interactions from threshold to 6 GeV. The data show a rapid approach to the distributions expected in the naive quark-parton model. The charged-current η deuteron total cross section is fit by the expression σ_T(ηd) = (0.76 ± 0.03) × 10^?38E_η cm² per GeV per nucleon. For E_η > 1.5 GeV, we measure σ_T(ηn)/σ_T(ηp) = (2.02 ± 0.23). The distributions in the scaling variables x and y are given and discussed.