Integrating long-term care insurance purchase decisions with saving and investment for retirement

Risk related to long-term care (LTC) is high for the elderly. Planning for LTC is now regarded as the ‘third leg’ of retirement planning. In this paper, planning for LTC is integrated with saving and investment decisions for an integrated approach to retirement planning. Optimal LTC insurance purchase decisions are obtained by developing a trade-off between post-retirement LTC costs and LTC insurance premiums paid and coverage received. Integrating insurance purchase with wealth evolution, consisting of saving and investment decisions, allows addressing affordability issues.Two-way branching models are used for the stochastic health events and asset returns. The problem, formulated as a nonlinearly constrained mixed-integer optimization problem, is solved using a heuristic. Sensitivity analyses are performed for initial health and wealth status. Some important aspects of an individual’s behavioral preferences are also addressed in this framework to provide more robust decision support.     

On the non-BoltzmannA-X emission in Na2 following laser excitation of theB state

A ¹Σ _u ⁺ -X ¹Σ _g ⁺ emission in Na₂ is observed following excitation ofB ¹π _u by various lines of an argon ion laser. The excitation energy ofB ¹π _u is collisionally transferred to the (2)¹Σ _g ⁺ which then radiatively populates theA ¹Σ _u ⁺ state. The Na vapour is contained in a stainless steel crossed heat pipe with Ar buffer gas and temperature around 600°C. For all laser lines except 4579 Å, the coarse features ofA-X emission are independent of the laser wavelength. However, at high resolution the finer differences between different laser line excitation are explained. Variousv′-v″ transitions in this emission are identified. Computer simulation is presented to help explain some features of this emission.     

Synthetic,spectroscopic, and structural Studies on Lanthanide Complexes of Diphosphazane Dioxide Ligands

Lanthanide nitrate complexes of diphosphazane dioxides Ph₂P(O)N(Prⁱ)P(O)Ph₂ ( 1 ) and (PhO)₂P(O)N(Me)P(O)(OPh)₂ ( 2 ) have been synthesised and studied by conductometry, IR, multinuclear NMR spectroscopic methods and X-ray diffraction. Ligand 2 is accessible by two different methods, viz., by direct oxidation of the phosp(III)azane ligand or by starting from phosph(V)azane chloro precursor. The structure of 2 is confirmed by X-ray diffraction. Crystallographic data for 2 : Triclinic, Space group P1 , a = 10.078(1), b = 10.575(3), c = 12.364(4) Å, α = 75.70(2)°, α = 75.56(1)°, γ = 77.68(1)°, Z = 2, V = 1 220 ų; structure refined to R_F = 0.0459 on 3 495 data with F > 3σ(F). The diphosphazane dioxide ligand exhibits trans geometry in the solid state. The structure of a lanthanide complex, [Pr(NO₃)₃( 2 )₂] ( 14 ) is also determined by X-ray diffraction. Crystallographic data for 14 : Trigonal, Space group P3₂, a = b = 15.710(2), c = 40.067(2) Å, Z = 6, V = 8 564 ų; structure refined to R_F = 0.0430 on 8 077 data with F > 5σ(F). The two diphosphazane dioxide ligands and the nitrate groups are coordinated to praseodymium in a bidentate chelate fashion. The geometry around the ten coordinated metal is distorted bicapped square antiprism.     

Kinetics and mechanism of polymerization yielding stereoblock poly(methyl methacrylate) with VCl4-Al(C2H5)3 catalyst system

Methyl methacrylate was polymerized at 40°C with the VCl₄–AlEt₃ catalyst system in n-hexane. The rate of polymerization was proportional to the catalyst and monomer concentration at Al/V ratio of 2, indicating a coordinate anionic mechanism of polymerization. NMR spectra were further used to confirm the mechanism of polymerization and stability of active sites responsible for isotacticity.     

Free-energy component analysis of 40 protein-DNA complexes: a consensus view on the thermodynamics of binding at the molecular level

Noncovalent association of proteins to specific target sites on DNA--a process central to gene expression and regulation--has thus far proven to be idiosyncratic and elusive to generalizations on the nature of the driving forces. The spate of structural information on protein--DNA complexes sets the stage for theoretical investigations on the molecular thermodynamics of binding aimed at identifying forces responsible for specific macromolecular recognition. Computation of absolute binding free energies for systems of this complexity transiting from structural information is a stupendous task. Adopting some recent progresses in treating atomic level interactions in proteins and nucleic acids including solvent and salt effects, we have put together an energy component methodology cast in a phenomenological mode and amenable to systematic improvements and developed a computational first atlas of the free energy contributors to binding in approximately 40 protein-DNA complexes representing a variety of structural motifs and functions. Illustrating vividly the compensatory nature of the free energy components contributing to the energetics of recognition for attaining optimal binding, our results highlight unambiguously the roles played by packing, electrostatics including hydrogen bonds, ion and water release (cavitation) in protein-DNA binding. Cavitation and van der Waals contributions without exception favor complexation. The electrostatics is marginally unfavorable in a consensus view. Basic residues on the protein contribute favorably to binding despite the desolvation expense. The electrostatics arising from the acidic and neutral residues proves unfavorable to binding. An enveloping mode of binding to short stretches of DNA makes for a strong unfavorable net electrostatics but a highly favorable van der Waals and cavitation contribution. Thus, noncovalent protein-DNA association is a system-specific fine balancing act of these diverse competing forces. With the advances in computational methods as applied to macromolecular recognition, the challenge now seems to be to correlate the differential (initial vs. final) energetics to substituent effects in drug design and to move from affinity to specificity.     

Polymerization of acrylonitrile with VCl4–Al(C2H5)3 catalyst system in presence of acetonitrile

The polymerization of acrylonitrile with the homogeneous catalyst system of VCl₄–AlEt₃ in acetonitrile at 40°C has been investigated. The rate of polymerization is found to be first-order with respect to monomer and inversely proportional to the catalyst concentration. The overall activation energy for this catalyst system is 10.97 kcal/mole. The inverse proportionality of rate of polymerization with the catalyst concentration is attributed to the permanent complex formation between the catalyst complex and acrylonitrile, and a reaction scheme is proposed.     

A representation theorem for weak automorphisms of a universal algebra

Given a group G and a descending chainG ₀,G ₁,...,G _n, of normal subgroups ofG, we prove that there exists a universal algebra , such that the chain ...W_n( )...W₁( }) W₀( )W( ) is isomorphic to the chain ...G _n ...G ₁G ₀G, where W( ) is the group of weak automorphisms of , and W_n( ) is the group of weak automorphisms of that leaves alln-ary operations fixed.We also prove that there are an infinite number of non-isomorphic algebras that satisfy the above.These results are a generalization of those proved by J. Sichler, in the special case when G=G₀, and G₁=G₂=...=G_n=....Presented by J. Mycielski.This paper comprises part of the author's doctoral dissertation at the University of Notre Dame in 1983. The author wishes to express her deep gratitude to Professor Abraham Goetz for suggesting this problem, for being extremely generous with his time and experience, and for giving her his constant encouragement. The author also thanks the reviewer for his helpful comments.