The Liouville-Arnold-Nekhoroshev theorem for non-compact invariant manifolds

Under ceratin conditions, generalized action-angle coordinates can be introduced near non-compact invariant manifolds of completely and partially integrable Hamiltonian systems.Comment: 8 page

Geometric quantization of time-dependent completely integrable Hamiltonian systems

We provide quantization of a time-dependent completely integrable Hamiltonian system such that its Hamiltonian and first integrals possess time-independent spectra

Global action-angle coordinates for completely integrable systems with noncompact invariant submanifolds

The obstruction to the existence of global action-angle coordinates of Abelian and noncommutative (non-Abelian) completely integrable systems with compact invariant submanifolds has been studied. We extend this analysis to the case of noncompact invariant submanifolds.Comment: 13 pages, to be published in J. Math. Phys. (2007

Popliteal artery entrapment associated with cannabis arteritis.

OBJECTIVE: To report popliteal artery entrapment in a patient with distal necrosis and cannabis-related arteritis, two rare or exceptional disorders never described in association. To conduct a targeted review and especially to seek information on the clinical presentation with characteristics specific to each disorder so as to hasten the diagnosis and choose appropriate management. MATERIAL AND METHODS: A 19-year-old man who presented with plantar claudication associated with necrosis in a toe underwent diagnostic arteriography and surgery for popliteal artery entrapment type III. RESULTS: Surgical clearance resolved the popliteal artery entrapment but left the clinical symptoms unchanged. Closer questioning disclosed a history of cannabis consumption and intravenous vasodilatory therapy was started. After the 21-day course of vasodilator agents the pain disappeared and the toe necrosis regressed. The patient stopped taking cannabis and had no signs of recurrence. CONCLUSION: Whereas a popliteal artery entrapment, albeit a rare event, is well described and responds to standardized treatment, popliteal artery entrapment associated with cannabis-induced arteritis is an exceptional event that could confuse management. Because young people-the age group mainly at risk for popliteal artery entrapment-increasingly use cannabis, cannabis arteritis could become a more frequent event associated with other arterial disorders that may confuse the diagnosis and complicate management. Our experience in a young patient suggests that coexisting popliteal artery entrapment and distal necrosis in a young patient should raise a strong suspicion of an associated vascular disorder possibly related to cannabis consumption. Intravenous vasodilatation treatment is successful provided that cannabis use is discontinued

Aneurysm of the pancreaticoduodenal arteries with a celiac trunk lesion: Current management

OBJECTIVE: We report a ruptured aneurysm of the pancreaticoduodenal arteries without acute or chronic pancreatitis but associated with a median arcuate ligament division that compressed the celiac trunk, an exceptional event, thus far described in only 11 patients. We also conducted a targeted review to seek information about clinical presentation, to hasten diagnosis and assist in therapeutic management. METHODS: A 54-year-old man with retroperitoneal hemorrhage associated with an arcuate ligament division, documented on computed tomographic scans, underwent diagnostic arteriography and embolization to treat the bleeding aneurysm. In a second elective operation the causative arcuate ligament was sectioned to decompress the celiac artery, to prevent aneurysm recurrence. RESULTS: Embolization stopped the aneurysmal bleeding, and arteriograms showed that surgical sectioning resolved the celiac trunk stenosis. At 1-year follow-up the patient had no signs of complications or recurrence of disease. CONCLUSION: Ruptured aneurysm of the pancreaticoduodenal arteries associated with stenosis of the celiac trunk is a surgical emergency. Although a literature review disclosed no significant difference between outcomes after open surgery and radiologic arterial embolization, our experience in this case suggests immediate embolization during arteriography as the most effective treatment. Later, to prevent recurrence, the arcuate ligament should be surgically sectioned and the celiac artery stenosis treated

Millikelvin magnetic relaxation measurements of alpha-Fe2O3 antiferromagnetic particles

In this paper we report magnetic relaxation data for antiferromagnetic alpha-Fe2O3 particles of 5 nm mean diameter in the temperature range 0.1 K to 25 K. The average spin value of these particles S=124 and the uniaxial anisotropy constant D=1.6x10^-2 K have been estimated from the experimental values of the blocking temperature and anisotropy field. The observed plateau in the magnetic viscosity from 3 K down to 100 mK agrees with the occurrence of spin tunneling from the ground state Sz = S. However, the scaling M vs Tln(nu t) is broken below 5 K, suggesting the occurrence of tunneling from excited states below this temperature.Comment: 4 pages (two columns), 4 figure

Unusual enhancement of effective magnetic anisotropy with decreasing particle size in maghemite nanoparticles

In magnetic nanoparticles (NPs), the observed increase in the effective magnetic anisotropy Keff with the decrease in particle size D is often interpreted, sometimes unsuccessfully, using the equation Keff = Kb + (6KS/D), where Kb is the bulk-like anisotropy of the core spins and KS is the anisotropy of spins in the surface layer. Here, we test the validity of this relation in γ-Fe2O3 NPs for sizes D from 15 nm to 2.5 nm. The samples include oleic acid-coated NPs with D = 2.5, 3.4, 6.3, and 7.0 nm investigated here, with results on 14 other sizes taken from literature. Keff is determined from the analysis of the frequency dependence of the blocking temperature TB after considering the effects of interparticle interactions on TB. For the γ-Fe2O3 NPs with D \u3c 5 nm, an unusual enhancement of Keff with decreasing D, well above the magnitudes predicted by the above equation, is observed. Instead the variation of Keff vs. D is best described by an extension of the above equation by including Ksh term from spins in a shell of thickness d. Based on this core-shell-surface layer model, the data are fit to the equation Keff = Kb + (6KS/D) + Ksh{[1−(2d/D)]−3−1} with Kb = 1.9 × 105 ergs/cm3, KS = 0.035 ergs/cm2, and Ksh = 1.057 × 104 ergs/cm3 as the contribution of spins in the shell of thickness d = 1.1 nm. Significance of this result is discussed