QPECgen, a MATLAB Generator for Mathematical Programs with Quadratic Objectives and Affine Variational Inequality Constraints

We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, first-level constraints are linear, and second-level (equilibrium) constraints are given by a parametric affine variational inequality or one of its specialisations. The generator, written in MATLAB, allows the user to control different properties of the QPEC and its solution. Options include the proportion of degenerate constraints in both the first and second level, ill-conditioning, convexity of the objective, monotonicity and symmetry of the second-level problem, and so on. We believe these properties may substantially effect efficiency of existing methods for MPEC, and illustrate this numerically by applying several methods to generator test problems. Documentation and relevant codes can be found by visiting http://www.ms.unimelb.edu.au/danny/qpecgendoc.html.     

Characterizing domain mixing effects in hydrogen bond-compatibilized polymer blends

The nature and extent of phase mixing in blends of hydroxyl-functionalized polystyrene and poly(ethyl acrylate) (PS/PEA), where the driving force for mixing is hydrogen bonding, are characterized by several techniques. Small-angle x-ray scattering (SAXS) shows a reduction in average domain size with increasing functionalization level, a result also evident from scanning electron microscopy (SEM). Together, the two techniques reveal a very broad distribution of domain sizes. At high functionalization levels, both SAXS and SEM indicate a high degree of “in-domain” mixing, with little or no pure PS or PEA remaining in the blends. Mathematical modeling of dynamic mechanical thermal analysis (DMTA) data is employed to quantify this progression. Initially, mixing is primarily interfacial, but as the functionalization level increases, the mixed interphase rapidly grows to occupy the entire material. In agreement with the SAXS and SEM results, DMTA modeling shows that further increases in the functionalization level suppress the amplitude of composition variations in the sample. The onset of extensive in-domain mixing coincides with the marked changes in stress-strain behavior observed previously in these materials. © 1994 John Wiley & Sons, Inc.     

Sputtering of ordered nickel-aluminium alloys: II. Preferential sputtering of NiAl single crystals and discussion

Atom-probe field-ion microscopy together with X-ray photoelectron spectroscopy and secondary ion mass spectrometry have been applied to the microanalysis of fully ordered NiAl single crystals subjected to 3 keV inert gas ion bombardment. As with the studies of Ni₃Al (the companion paper) aluminium was found to be preferentially sputtered by both argon and xenon bombardment. Comparisons between depth profiles through Ni₃Al and NiAl targets have provided information about the role of binding energies in the selective sputtering process. These data have also permitted conclusions to be drawn about the correct choice of bombarding species for sample cleaning and depth-profiling applications in surface analysis. Examination of field-ion images from specimens after bombardment suggests that the surface is microroughened and this has been confirmed using transmission electron microscopy.     

Stereoelectronic properties of photosynthetic and related systems: Ab initio configuration interaction calculations on the ground and lower excited singlet and triplet states of magnesium chlorin and chlorin

Ab initio configuration interaction wavefunctions and energies are reported for the ground state and many low-lying singlet and triplet states of magnesium chlorin and chlorin, and are employed in an analysis of the electronic absorption spectra of these systems.In chlorin, the calculated visible spectrum consists of two ${}^1\text{(π, π}{}^1\text{)}$ states, the lower energy, y-polarized state exhibiting moderate absorption intensity in contrast to the very weak absorption of the higher energy x-polarized state. The configurational composition of both states is well described by the four-orbital model. Five ${}^1\text{(π, π}{}^1\text{)}$ states are responsible for the Soret band envelope. A moderately intense y-state lies under the low energy edge of the band envelope, while two x-polarized states of moderate and strong intensity, respectively, are responsible for the band maximum. The final two ${}^1\text{(π, π}{}^1\text{)}$ states lie at the high energy edge of the Soret band and introduce a measure of asymmetry into the band envelope. Two ${}^1\text{(n, π}{}^1\text{)}$ states of very weak oscillator strength are also found in this region of the spectrum. All the Soret states are of complex configurational composition, and several of the higher lying states contain contributions from doubly excited configurations.The calculated visible spectrum of magnesium chlorin also consists of two ${}^1\text{(π, π}{}^1\text{)}$ states, with the weakly absorbing x-polarized state lying approximately 200 cm^?1 lower in energy than the moderately intense y-polarized state. The configurational composition of both states is well described by the four-orbital model. Four ${}^1\text{(π, π}{}^1\text{)}$ states constitute the bulk of the intensity in the Soret band envelope. In distinction to chlorin, the moderately intense ${}^1\text{(π, π}{}^1\text{)}$ state at the low energy edge of the band envelope is x-polarized. Two intense ${}^1\text{(π, π}{}^1\text{)}$ states of y- and x-polarization, respectively, constitute the band maximum region, and a single x-polarized state of moderately strong intensity can be assigned to the high energy shoulder of the band envelope. Two other weakly absorbing ${}^1\text{(π, π}{}^1\text{)}$ states are also found in this region, along with another weakly absorbing state of mixed in-plane and out-of-plane polarization. No clearly defined ${}^1\text{(n, π}{}^1\text{)}$ states are observed. As was the case for chlorin, all the Soret states are of complex configurational composition, and some of the higher energy states contain significant contributions from doubly excited configurations.Chlorin and magnesium chlorin both possess three ${}^3\text{(π, π}{}^1\text{)}$ states which lie below S₁ and a single ${}^3\text{(π, π}{}^1\text{)}$ which lies slightly above S₂. All four of the low-lying ${}^3\text{(π, π}{}^1\text{)}$ states in each molecule are well described by the four-orbital model, with T₁ being essentially a single configuration in each case. The remainder of the ${}^3\text{(π, π}{}^1\text{)}$ states are clustered in the same energetic region as the comparable ${}^1\text{(π, π}{}^1\text{)}$ Soret states, with comparably complex configurational compositions.Dipole moments and charge distributions for low-lying singlet and triplet states are also reported, and are used to rationalize chemical reactivity characteristics.     

ESR identification of a new N2− defect in X-ray irradiated NaN3

A relatively weak ESR spectrum is observed in single crystals of NaN₃ after X-ray irradiation at 77 K. This spectrum, which has an anisotropic g value and exhibits a resolved 5-line hyperfine structure with components in the ratio 1:2:3:2:1, corresponds to a single unpaired electron interacting symmetrically with two spin-one nuclei, in three inequivalent sites. The spin-Hamiltonian parameters are: g_x = 2.0054 ± 0.0005, g_y = 2.0045 ± 0.0005, g_z = 1.9688 ± 0.0005, |A_x| = 4.0 ± 0.2 G, |A_y| = 20.0 ± 0.2 G, and |A_z| = 4.9 ± 0.2 G, c-axis, and y is perpendicular to the c-axis. This spectrum, which is clearly different from that of substitutional N₂^?reported by Gelerinter and Silsbee, is attributed to interstitial N₂^?.     

Chemical reactivity and surface-enhanced raman scattering

A mechanism is proposed for surface-enhanced Raman scattering for pyridine which explains the enhancement, the anodizalion “activation”, the significance of silver, the photographitization of coordinated pyridine and formate, the participation of surface roughness, and the irreversibly held yet liquid-like nature of surface pyridine.     

Linear maps that preserve matrices annihilated by a polynomial

Let M_n be the algebra of n×n matrices over an algebraically closed field of characteristic zero. Let f(x) be a polynomial over $\text{F}$ with at least two distinct roots. Then all nonsingular linear maps L:M_n→M_n that map matrix roots of F(x)=0 into matrix roots of f(x}=0 are found.     

Symmetry rules for predicting the course of chemical reactions

Rules are given for a reaction of any molecularity which show whether it is allowed or forbidden by orbital symmetry properties. The rules are based on a rigorous treatment, but correspond to simple concepts in practice. A rough MO sequence for the reactants is all that is needed.

---

Zusammenfassung Für Reaktionen beliebiger Molekularität werden Regeln dafür angegeben, ob die Reaktion aus Symmetriegründen erlaubt oder verboten ist. Diese Regeln werden streng hergeleitet, sind jedoch in der Praxis einfach anwendbar. Benötigt wird lediglich die Reihenfolge der MO der Reaktionen.

---

Résumé On donne des règles de sélection pour une réaction de molécularité arbitraire selon les propriétés de symétrie orbitale. Les règles sont basées sur un traitement rigoureux mais correspondent en practique à des concepts simples. On a seulement besoin de connaître l'ordre des orbitales moléculaires des réactants.

     

AB initio calculations of the electronic properties of N4− in KN3

The energies of the ground state and low-lying excited states of the N₄^? defect in KN₃ have been calculated using ab initio techniques. A rectangular equilibrium geometry with dimensions X = 2.76 and Z = 2.47 a.u. and ground state symmetry of Γ₄⁺ was determined by calculating N₄^? as a free radical. For this ground state the unpaired electron is in a π orbital which is consistent with the experimental hyperfine tensor only if one edge of the N₄^? radical is parallel to the c axis in KN₃. These results were used to calculate the X²Γ₄⁺ state of N₄^? in the crystal field of KN₃, yielding an energy of ?217.899 Hartrees. The isotropic hyperfine constant was calculated to be a = 2.1 G and the components of the anisotropic hyperfine tensor as B_xx = ?3.4 G, B_yy = 7.0 G and B_zz = ?3.6 G, in good agreement with experimental and INDO results. Several excited states were calculated for the N₄^? defect in KN₃. When an estimate was made of the correlation energy, the transition energy of the X²Γ₄⁺→A²Γ₃^? transition agreed well with the peak energy of the 780 nm absorption band which has been attributed to N₄^?.