Finite Time Merton Strategy under Drawdown Constraint: A Viscosity Solution Approach

We consider the optimal consumption-investment problem under the drawdown constraint, i.e. the wealth process never falls below a fixed fraction of its running maximum. We assume that the risky asset is driven by the constant coefficients Black and Scholes model and we consider a general class of utility functions. On an infinite time horizon, Elie and Touzi (Preprint, [2006]) provided the value function as well as the optimal consumption and investment strategy in explicit form. In a more realistic setting, we consider here an agent optimizing its consumption-investment strategy on a finite time horizon. The value function interprets as the unique discontinuous viscosity solution of its corresponding Hamilton-Jacobi-Bellman equation. This leads to a numerical approximation of the value function and allows for a comparison with the explicit solution in infinite horizon.     

A New and Efficient Synthesis of α-Amino Cycloalkyl-Phosphonic Acids via Electrophilic Azidation of Cycloalkylphosphonates

α-Amino cyclobutyl-, cyclopentyl-and cyclohexylphosphonic acids (13) were efficiently prepared from the related unsubstituted cycloalkylphosphonates (5), in three steps including electrophilic azidation of the corresponding lithiated carbanions, catalytic hydrogenation of the intermediate α-azido cycloalkyl-phosphonates (10) and acidic hydrolysis of the resulting α-amino cycloalkyl-phosphonates (12).     

Instability of elastic bodies

The study of the equilibrium of systems constitutes an important chapter of applied mechanics. Since Euler’s works on beam buckling, in 1774, many eminent specialists studied the problem of the elastic instability of structures.An examination of many works published in this field shows a large number of approaches or criteria adopted by various authors. The objective of this study is to show through a classical example the link between the different approaches to provide a multi-level basis and to propose a valid global approach for conservative as well as nonconservative systems.     

Observations sur le mémoire précédent

Sans résuméExtrait d'une lettre à M. D. D. Kosambi.     

Practical enantiospecific syntheses of (+) erythro-9- (2s-hydroxy-3r-nonyl) adenine.

Three enantiospecific syntheses of 1S (2S-benzyloxethyl) oxirane (9) from L-ascorbic acid, L(+) tartaric acid, and Z-butene 1,4-diol are reported. The conversion of 9 to 2S-hydroxy-3R-nonylamine (19) is also described.     

A Multicoincidence Study of Fragmentation Dynamics in Collision of γ‐Aminobutyric Acid with Low‐Energy Ions

Fragmentation of the γ‐aminobutyric acid molecule (GABA, NH₂(CH₂)₃COOH) following collisions with slow O⁶⁺ ions (v≈0.3 a.u.) was studied in the gas phase by a combined experimental and theoretical approach. In the experiments, a multicoincidence detection method was used to deduce the charge state of the GABA molecule before fragmentation. This is essential to unambiguously unravel the different fragmentation pathways. It was found that the molecular cations resulting from the collisions hardly survive the interaction and that the main dissociation channels correspond to formation of NH₂CH₂⁺, HCNH⁺, CH₂CH₂⁺, and COOH⁺ fragments. State‐of‐the‐art quantum chemistry calculations allow different fragmentation mechanisms to be proposed from analysis of the relevant minima and transition states on the computed potential‐energy surface. For example, the weak contribution at [M?18]⁺, where M is the mass of the parent ion, can be interpreted as resulting from H₂O loss that follows molecular folding of the long carbon chain of the amino acid.     

A multicoincidence study of fragmentation dynamics in collision of γ-aminobutyric acid with low-energy ions

Fragmentation of the γ-aminobutyric acid molecule (GABA, NH(2)(CH(2))(3)COOH) following collisions with slow O(6+) ions (v≈0.3?a.u.) was studied in the gas phase by a combined experimental and theoretical approach. In the experiments, a multicoincidence detection method was used to deduce the charge state of the GABA molecule before fragmentation. This is essential to unambiguously unravel the different fragmentation pathways. It was found that the molecular cations resulting from the collisions hardly survive the interaction and that the main dissociation channels correspond to formation of NH(2)CH(2)(+), HCNH(+), CH(2)CH(2)(+), and COOH(+) fragments. State-of-the-art quantum chemistry calculations allow different fragmentation mechanisms to be proposed from analysis of the relevant minima and transition states on the computed potential-energy surface. For example, the weak contribution at [M-18](+), where M is the mass of the parent ion, can be interpreted as resulting from H(2)O loss that follows molecular folding of the long carbon chain of the amino acid.     

Toward a structure-activity relationship for apoptolidin: selective functionalization of the hydroxyl group array

[reaction: see text] To investigate the structural basis for the exceptional selectivity and activity of apoptolidin (1), a strategy has been devised that allows for selective functionalization of seven of its eight hydroxyl groups based on progressive silyl protection, derivatization, and deprotection. The syntheses of these derivatives and their ability to inhibit F(0)F(1)-ATPase are reported.     

Elastic scattering of 1-GeV protons by nuclei

The calculated elastic scattering of 1.04-GeV protons by ²⁰⁸Pb, ⁵⁸Ni, and ⁴⁰Ca is compared with experiment. The effects of the spin-orbit potential, Pauli and short-range correlations, variations in the ratio of the real to the imaginary part of the nucleon-nucleon scattering amplitude at 0° are found to have similar effects. Further experiments are required before these effects can be disentangled. Changes of the neutron density compared to the proton density can be distinguished. The proton polarization by elastic scattering by ²⁰⁸Pb and ⁴⁰Ca is calculated omitting the effects of correlations.