Kinetic Stabilization¶of a Nonlinear Sonic Phase Boundary

We consider a system arising in the study of phase transitions in elastodynamics – a system of two conservation laws, in a single space dimension. The system has two hyperbolic regions with an elliptic zone in between. A phase boundary is a strong discontinuity in a solution, with left and right states belonging to different hyperbolic regions. We call such a solution a phase wave. We first address the Riemann problem for initial states close to a fixed sonic phase wave, in the genuinely nonlinear case. This problem is naturally underdetermined. We propose two essentially different types of Reimann problems: a sonic one, which is smooth, and a kinetic one, which is only Lipschitz-continuous. Both problems are well posed owing to a shared stability condition that is of a purely sonic nature. In the kinetic case we prove the global existence of solutions to the Cauchy problem for initial data having small variation and close to a sonic kinetic wave. The crucial issue is the interaction of the phase boundary with a small wave of the same mode. The introduction of a pertinent quantity, called here detonation potential, ensures a balance between ingoing and outgoing waves. The proof is based on a Glimm-type scheme; we define a potential, which includes the detonation potential, along the strong discontinuity, and this potential controls the outbreak of unusual shocks. Accepted: June 9, 1999     

Sm5Ga3

Single crystals of penta­samarium trigallium, Sm₅Ga₃, display tetra­gonal symmetry. The crystal structure was solved and refined in space group P4/ncc. The present work does not confirm the space group I4/mcm previously deduced from powder data measurements. One Sm atom is in a general position, and the other Sm atom and one of the Ga atoms are at sites with fourfold symmetry. The remaining Ga atom is at a site with twofold symmetry.     

Diastereoselective addition of 2H-2-oxo-1,4,2-oxazaphosphinanes to aldehydes and imines

[reaction: see text] Diastereoselective additions of 2-hydrogeno-2-oxo-1,4,2-oxazaphosphinanes to aldehydes and imines are described. alpha,alpha'-Diaminophosphinic and alpha-amino-alpha'-hydroxyphosphinic derivatives were obtained with de's ranging from 24 to 90%.     

Audiogram of a harbor porpoise (Phocoena phocoena) measured with narrow-band frequency-modulated signals

The underwater hearing sensitivity of a two-year-old harbor porpoise was measured in a pool using standard psycho-acoustic techniques. The go/no-go response paradigm and up-down staircase psychometric method were used. Auditory sensitivity was measured by using narrow-band frequency-modulated signals having center frequencies between 250 Hz and 180 kHz. The resulting audiogram was U-shaped with the range of best hearing (defined as 10 dB within maximum sensitivity) from 16 to 140 kHz, with a reduced sensitivity around 64 kHz. Maximum sensitivity (about 33 dB re 1 microPa) occurred between 100 and 140 kHz. This maximum sensitivity range corresponds with the peak frequency of echolocation pulses produced by harbor porpoises (120-130 kHz). Sensitivity falls about 10 dB per octave below 16 kHz and falls off sharply above 140 kHz (260 dB per octave). Compared to a previous audiogram of this species (Andersen, 1970), the present audiogram shows less sensitive hearing between 2 and 8 kHz and more sensitive hearing between 16 and 180 kHz. This harbor porpoise has the highest upper-frequency limit of all odontocetes investigated. The time it took for the porpoise to move its head 22 cm after the signal onset (movement time) was also measured. It increased from about 1 s at 10 dB above threshold, to about 1.5 s at threshold.     

The cut cone III: On the role of triangle facets

The cut polytopeP _n is the convex hull of the incidence vectors of the cuts (i.e. complete bipartite subgraphs) of the complete graph onn nodes. A well known class of facets ofP _n arises from the triangle inequalities:x _ij +x _ik +x _jk ≤2 andx _ij −x _ik −x _jk ≤0 for 1≤i, j, k≤n. Hence, the metric polytopeM _n , defined as the solution set of the triangle inequalities, is a relaxation ofP _n .We consider several properties of geometric type forP _n , in particular, concerning its position withinM _n . Strengthening the known fact ([3]) thatP _n has diameter 1, we show that any set ofk cuts,k≤log₂ n, satisfying some additional assumption, determines a simplicial face ofMn and thus, also, ofP _n . In particular, the collection of low dimension faces ofP _n is contained in that ofM _n . Among a large subclass of the facets ofP _n , the triangle facets are the closest ones to the barycentrum ofP _n and we conjecture that this result holds in general. The lattice generated by all even cuts (corresponding to bipartitions of the nodes into sets of even cardinality) is characterized and some additional questions on the links between general facets ofP _n and its triangle facets are mentioned.     

Variations in model formulations

Mathematical programming models may contain a great deal of variations in their formulations. The same problem can be modeled as different formulations, or different problems can be modeled as the same formulations. In order to handle these variant formulations efficiently and intelligently, a model management system should be able to eliminate or recognize the variations in model formulations. We analyze possible variations involved in model formulations and categorize them into three types-syntactic, semantic and structural.The first author received support for this work from the 1991 Research Fund at Ajou University.     

Synthesis,spectroscopic characterization and in vitro antitumour activity of di-n-butyltin and diethyltin trimethoxybenzoates: X-ray structure analysis of bis[di-n-butyl(3,4,5-trimethoxybenzoato)tin] oxide

Di-n-butyltin(IV) and diethyltin(IV) 2,3,4-, 2,4,5- and 3,4,5-trimethoxybenzoates [(CH₃O)₃C₆H₂COO]₂SnR [Type a] and {[(CH₃O)₃C₆H₂COO]R₂Sn}₂O [Type b] have been synthesized and characterized spectroscopically. The crystal structure of bis[di-n-butyl(3,4,5- trimethoxybenzoato)tin] oxide has been determined. The triclinic unit cell contains one centrosymmetric dimer; a = 15.919(2) Å, b = 11.711(3) Å, c = 13.475(1) Å, and α = 63.63(2)°, β = 67.49(1)°, γ = 76.61(2)°. The geometry of the dimer is very similar to that of bis[di-n-butyl(5-methoxysalicylatotin] oxide), with two different types of five-coordinate tin atoms and one central planar Sn₂O₂ ring.     

Some advantages of high temperature for the separation of pharmaceutical compounds with mass spectrometry detection

The beneficial effects of high temperature on separation and detection of basic compounds, the detection being performed by MS via ESI, are investigated. The influence of various parameters on both separation and detection performances is studied. These parameters include the mobile phase pH, the temperature, and the type of stationary phase. Experiments are performed under gradient elution conditions. The results obtained with four different supports, silica-, zirconia-, carbon-, and polymer-based columns, are compared by means of different criteria including the elution composition, the peak asymmetry, and the S/N. High temperature liquid chromatography at high pH with volatile buffers suitable for MS detection was shown to be an interesting choice for solutes with basic sites.