Microlens arrays etched into glass and silicon

Microlens arrays fabricated by melting photoresist were transferred by reactive ion etching (RIE) into glass (SiO₂) and silicon (Si). By controlling the etching rates of the mask and the substrate material, radii of curvature and focal lengths within a wide range can be achieved. For example, glass lenses with diameter 120 μm and focal lengths between 500 μm and 1500 μm were made. The scaling possibilities of microlens arrays, given the use of RIE, are discussed.     

Second-order optimality conditions for nondominated solutions of multiobjective programming with C 1,1 data

We examine new second-order necessary conditions and sufficient conditions which characterize nondominated solutions of a generalized constrained multiobjective programming problem. The vector-valued criterion function as well as constraint functions are supposed to be from the class C ^1,1. Second-order optimality conditions for local Pareto solutions are derived as a special case.     

Development of Counting Skills: Role of Spontaneous Focusing on Numerosity and Subitizing-Based Enumeration

Children differ in how much they spontaneously pay attention to quantitative aspects of their natural environment. We studied how this spontaneous tendency to focus on numerosity (SFON) is related to subitizing-based enumeration and verbal and object counting skills. In this exploratory study, children were tested individually at the age of 4-5 years on these skills. Results showed 2 primary relationships in children's number skills development. Performance in a number sequence production task, which is closely related to ordinal number sequence without reference to cardinality, is directly associated with SFON. Second, the association of SFON and object counting skills, which require relating cardinal and ordinal aspects of number, is mediated by subitizing-based enumeration. This suggests that there are multiple pathways to enumeration skills during development.     

A Theorem of Ludwig Revisited

Using a recent result of Busch and Gudder, we reconsider a theorem of Ludwig which allows one to identify a class of effect automorphisms as the symmetry transformations in quantum mechanics.     

Quasihyperbolic boundary conditions and capacity: Uniform continuity of quasiconformal mappings

We prove that quasiconformal maps onto domains which satisfy a suitable growth condition on the quasihyperbolic metric are uniformly continuous when the source domain is equipped with the internal metric. The obtained modulus of continuity and the growth assumption on the quasihyperbolic metric are shown to be essentially sharp. As a tool, we prove a new capacity estimate.     

Communication: Manipulating the singlet-triplet equilibrium in organic biradical materials

We investigated the tunability of the singlet-triplet equilibrium population in the organic biradical 1,4-phenylenedinitrene via magneto-optical spectroscopy. A rich magnetochromic response occurs because applied field increases the concentration of the triplet state species, which has a unique optical signature by comparison with the singlet biradical and the precursor molecule. A Curie-like analysis of the magneto-optical properties allows us to extract the spin gap, which is smaller than previously supposed. These measurements establish the value of local-probe photophysical techniques for magnetic property determination in open-shell systems such as biradicals where a traditional electron paramagnetic resonance Curie law analysis has intrinsic limitations.     

Absolute Continuity of Quasiconformal Mappings on Curves

We show that a quasiconformal mapping between two proper, locally Ahlfors Q-regular metric spaces, Q > 1, is absolutely continuous on almost every curve. We further relax the limes superior in the definition of quasiconformality to a limes inferior and verify that exceptional sets analogous to the Euclidean setting can be allowed. The authors were supported by grants from the Swiss NSF and the Academy of Finland. Part of the research was done while S.R. was visiting at the University of Bern. Received: August 2005 Accepted: January 2006     

Solid-state photochemical generation of stable radical pairs from bis(aryloxy)phosphine azide precursors

Two types of radical pairs, stable at room temperature, were found in monocrystals of 2,6-di-tert-butyl-4-methylphenol doped with bis(2,6-di-tert-butyl-4-methoxyphenoxy) phosphine azide after photoirradiation using a Xe arc lamp. One pair consists of two 2,6-di-tert-butyl-4-methoxyphenoxyls (RP₁), the other of 2,6-di-tert-butyl-4-methoxyphenoxyl and 2,6-di-tert-butyl-4-methylphenoxyl (RP₂), as indicated by their EPR hyperfine splitting. In the temperature range of 120–200 K RP₁ accumulates 7 times faster than at 77 K. Explanations for this photoaccumulation as well as a mechanism of RP formation are proposed.     

Coexistence and Joint Measurability in Quantum Mechanics

This talk is a survey of the question of joint measurability of coexistent observables and it is based on the monograph Operational Quantum Physics (Busch et al., Springer-Verlag, Berlin, 1997) and on the papers (Lahti et al., Journal of Mathematical Physics 39, 6364–6371, 1998; Lahti and Pulmannova, Reports on Mathematical Physics 39, 339–351, 1997; 47, 199–212, 2001).     

A semiempirical investigation of interelectronic exchange coupling in bisected poly(1,4-phenylene) polycation model systems

AM 1 SCF -MO -CI computations find the bisected biphenyl dication to have nearly degenerate triplet and singlet states, with the lowest-energy state being a quininoid singlet planar dication. The bisected perchlorobiphenyl dication favors a triplet ground state by a small amount (0.4-1.9 kcal/mol), in qualitative agreement with recent experimental findings and with theoretical expectations that such an orthogonal open-shell pi-system should exhibit ferromagnetic exchange coupling. The higher oligomeric bisected para-linked phenylenes polycations do not show an appreciable computational preference for a high-spin multiplicity ground state either with or without perchlorine substitution. Chlorine substitution para to the 1,1′-linkage may lend a unique stabilization to the biphenyl system, which is not available in higher oligomeric analogs of poly(1,4-phenylene)s. The small magnitude of ferromagnetic exchange in these systems suggests that small geometric or substituent effects may confound experimental efforts to design polymeric ferromagnetic materials by this strategy. © 1992 John Wiley & Sons, Inc.