The equation of state and heat of fusion of poly(ether ether ketone)

The pressure-volume-temperature properties of poly(ether ether ketone) (PEEK) were studied experimentally at temperatures of 400°C and pressures to 200 MPa. Specific volume data were fitted successfully to the empirical Tait equation for T < T_g and T > T_m and to the theoretical Simha-Somcynsky equation of state for the melt. The pressure dependence of the glass-transition temperature is about 0.57–0.59°C/MPa and that of the melting point 0.483°C/MPa. The pressure dependence of the melting point, the specific volume of the melt at T_m, and the specific volume of the crystal at T_m determined from x-ray diffraction data at elevated temperatures were combined in the Clapeyron equation to calculate a heat of fusion of 161 ± 20 J/g for the PEEK crystal. This value is somewhat higher than the previously reported value of 130 J/g.     

An Unconstrained Quadratic Binary Programming Approach to the Vertex Coloring Problem

The vertex coloring problem has been the subject of extensive research for many years. Driven by application potential as well as computational challenge, a variety of methods have been proposed for this difficult class of problems. Recent successes in the use of the unconstrained quadratic programming (UQP) model as a unified framework for modeling and solving combinatorial optimization problems have motivated a new approach to the vertex coloring problem. In this paper we present a UQP approach to this problem and illustrate its attractiveness with preliminary computational experience.     

The heat of fusion of copolymers of tetrafluoroethylene and hexafluoropropylene

The Clapeyron equation has been applied to determine the heat of fusion of two copolymers of tetrafluoroethylene and hexafluoropropylene. The values obtained are within experimental uncertainty of that for the homopolymer, PTFE. This study supports the conclusion of earlier workers that the CF₃ side groups are included in the crystal lattice. In both PTFE and polyethylene, C₁ side groups are included in the crystal but have little if any effect on its density. We believe that the same relationship between the crystallinity and the heat of fusion can be used for both PTFE and copolymers of TFE and HFP.     

Cross sections for the 11.08 (3+) and 11.096 MeV (4+) states in 16O by 12C(6Li,d) and 13C(6Li,t)

Particle and particle-γ measurements were performed to determine the cross sections for population of the 8.87 (2^?), 10.35 (4⁺), 11.08 (3⁺) and 11.096 MeV (4⁺) states in ¹⁶O by the ¹²C(⁶Li, d) and ¹³C(⁶Li, t) reactions in the energy range from 20—34 MeV. In general, statistical compound nuclear calculations correctly predict the magnitude of the cross sections of the unnatural parity states and underpredict those for the natural parity states. The population of the 10.35 MeV 4⁺ state in the ¹³C(⁶Li, t) reaction is correctly predicted by these calculations. These measurements support earlier claims that the large ¹²C(⁶Li, d) cross section to the 11.096 MeV 4⁺ state is a result of multistep processes.     

Possible heavy lepton signals at pp colliders

If a new sequential heavy lepton L exists with mass below that of the W boson, it will give rise to the following decay chains: W → Lν_Lwith $\text{L}\text{→}\text{e}\text{ν}{}_{\mathrm{<mtext>e</mtext>}}\text{ν}{}_{\mathrm{<mtext>L</mtext>}}$ or $\text{L}\text{→}\text{Q}\text{qν}{}_{\mathrm{<mtext>L</mtext>}}$. We critically study, and quantify, the possibility of identifying this heavy lepton signal against the various backgrounds in high energy p?p collision. We find that the leptonic decay signal is plagued by serious b?b, W → eν, and W → τν backgrounds, whereas the hadronic decay mode leads to a distinctive signature, after selected cuts are applied. We discuss how the mass of such a lepton may be determined.     

Aggregating diophantine equations

Summary Mathews [1897] has given a theorem for aggregating two diophantine equations with positive integer coefficients into a single equation that has the same solution set as its parents over the nonnegative integers. Building on this result,Elmaghraby andWig [1970] show how to shrink the inequality constraints of a bounded variable integer program to a single constraint equation. However, such applications are limited, as we show, by a greater than exponential growth in coefficient size as successive constraints are aggregated into one. To mitigate this situation, we give new theorems and implementation procedures that provide exponential order reductions in the coefficient growth attending the aggregation process.

---

Zusammenfassung Mathews [1897] hat ein Theorem zur Zusammenfassung zweier diophantischer Gleichungen mit positiven ganzzahligen Koeffizienten zu einer einzigen Gleichung mit derselben Lösungsmenge wie die beiden ursprünglichen Gleichungen entwickelt. Aufbauend auf dieses Ergebnis zeigtenElmaghraby undWig [1970] eine Möglichkeit, die Ungleichungen eines ganzzahligen Optimierungsproblems mit begrenzten Variablen sukzessive auf eine einzige Gleichung zu reduzieren. Die praktische Anwendbarkeit ist jedoch begrenzt. Bei der sukzessiven Zusammenfassung der Nebenbedingungen zu einer einzigen wachsen die Koeffizienten stärker als exponentiell an. Um diesen Nachteil zu mindern, werden hier neue Theoreme und Anwendungsprozeduren entwickelt. Diese gewährleisten, daß das Anwachsen der Koeffizienten im Verlaufe des Aggregationsprozesses um einen Faktor exponentieller Ordnung geringer ist.

     

Experimental and shell-model studies of the reactions 91Zr(d,p)92Zr and 90Zr(t,p)92Zr

The results of high-resolution studies of the ⁹¹Zr(d, p) reaction at E_d = 12 MeV and the ⁹⁰Zr(t, p) reaction at E_t = 11.85 MeV are presented. Absolute cross sections have been measured for both reactions and (d, p) spectroscopic factors determined. A comparison of these results with earlier data has been made, and although many of the previous assignments have been confirmed, many new features concerning the structure of ⁹²Zr have been discovered. Shell-model calculations have been performed for ⁹¹Zr and ⁹²Zr using a neutron space which includes the $\text{2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, $\text{3}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{2}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, $\text{1}\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ and $\text{1}\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ orbits and a proton space comprising the $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ and $\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ orbits. Realistic proton-neutron and neutron-neutron interactions based on the Sussex matrix elements were used in the calculations. Spectroscopic factors have been calculated for the ⁹⁰Zr(d, p) and ⁹¹Zr(d, p) reactions and cross sections calculated for the ⁹⁰Zr(t, p) reaction. In general, good agreement between the theoretical and the experimental results has been obtained.     

Polyhedral annexation in mixed integer and combinatorial programming

Polyhedral annexation is a new approach for generating all valid inequalities in mixed integer and combinatorial programming. These include the facets of the convex hull of feasible integer solutions. The approach is capable of exploiting the characteristics of the feasible solution space in regions both “adjacent to” and “distant from” the linear programming vertex without resorting to specialized notions of group theory, convex analysis or projective geometry. The approach also provides new ways for exploiting the “branching inequalities” of branch and bound.