Exact lower bounds to the ground-state energy of spin systems: The two-dimensional S=1/2 antiferromagnetic Heisenberg model

We present a very simple but fairly unknown method to obtain exact lower bounds to the ground-state energy of any Hamiltonian that can be partitioned into a sum of sub-Hamiltonians. The technique is applied, in particular, to the two-dimensional spin-1/2 antiferromagnetic Heisenberg model. Reasonably good results are easily obtained and the extension of the method to other systems is straightforward.

A Rotating black ring solution in five dimensions

The vacuum Einstein equations in five dimensions are shown to admit a solution describing a stationary asymptotically flat spacetime regular on and outside an event horizon of topology S1S2. It describes a rotating black ring. This is the first example of a stationary asymptotically flat vacuum solution with an event horizon of nonspherical topology. The existence of this solution implies that the uniqueness theorems valid in four dimensions do not have simple five-dimensional generalizations. It is suggested that increasing the spin of a spherical black hole beyond a critical value results in a transition to a black ring, which can have an arbitrarily large angular momentum for a given mass.

Microscopic entropy of the black ring

A surprising new seven-parameter supersymmetric black ring solution of five-dimensional supergravity has recently been discovered. In this paper, M theory is used to give an exact microscopic accounting of its entropy.

Continued fraction solution for the radiative transfer equation in three dimensions

Starting from the radiative transfer equation, we obtain an analytical solution for both the free propagator along one of the axes and an arbitrary phase function in the Fourier-Laplace domain. We also find the effective absorption parameter, which turns out to be very different from the one provided by the diffusion approximation. We finally present an analytical approximation procedure and obtain a differential equation that accurately reproduces the transport process. We test our approximations by means of simulations that use the Henyey-Greenstein phase function with very satisfactory results.

EFFECT OF RICE STRAW AND NITRATE LEVELS IN SOIL SOLUTION ON NITROUS OXIDE EMISSION

Among the greenhouse gases, nitrous oxide (N2O) is considered important, in view of a global warming potential 296 times greater than that of carbon dioxide (CO2) and its dynamics strongly depend on the availability of C and mineral N in the soil. The understanding of the factors that define emissions is essential to develop mitigation strategies. This study evaluated the dynamics of N2O emissions after the application of different rice straw amounts and nitrate levels in soil solution. Pots containing soil treated with sodium nitrate rates (0, 50 and 100 g kg-1 of NO−3-N) and rice straw levels (0, 5 and 10 Mg ha-1), i.e., nine treatments, were subjected to anaerobic conditions. The results showed that N2O emissions were increased by the addition of greater NO−3 amounts and reduced by large straw quantities applied to the soil. On the 1st day after flooding (DAF), significantly different N2O emissions were observed between the treatments with and without NO−3 addition, when straw had no significant influence on N2O levels. Emissions peaked on the 4th DAF in the treatments with highest NO−3-N addition. At this moment, straw application negatively affected N2O emissions, probably due to NO−3 immobilization. There were also alterations in other soil electrochemical characteristics, e.g., higher straw levels raised the Fe, Mn and dissolved C contents. These results indicate that a lowering of NO−3 concentration in the soil and the increase of straw incorporation can decrease N2O emissions.

Effects of Pig Slurry Application and Crops on Phosphorus Content in Soil and the Chemical Species in Solution

The application of pig slurry rates and plant cultivation can modify the soil phosphorus (P) content and distribution of chemical species in solution. The purpose of this study was to evaluate the total P, available P and P in solution, and the distribution of chemical P species in solution, in a soil under longstanding pig slurry applications and crop cultivation. The study was carried out in soil columns with undisturbed structure, collected in an experiment conducted for eight years in the experimental unit of the Universidade Federal de Santa Maria (UFSM), Santa Maria (RS). The soil was an Argissolo Vermelho distrófico arênico (Typic Hapludalf), subjected to applications of 0, 20, 40, and 80 m3 ha-1 pig slurry. Soil samples were collected from the layers 0-5, 5-10, 10-20, 20-30, 30-40, and 40-60 cm, before and after black oat and maize grown in a greenhouse, for the determination of available P, total P and P in the soil solution. In the solution, the concentration of the major cations, anions, dissolved organic carbon (DOC), and pH were determined. The distribution of chemical P species was determined by software Visual Minteq. The 21 pig slurry applications increased the total P content in the soil to a depth of 40 cm, and the P extracted by Mehlich-1 and from the solution to a depth of 30 cm. Successive applications of pig slurry changed the balance between the solid and liquid phases in the surface soil layers, increasing the proportion of the total amount of P present in the soil solution, aside from changing the chemical species in the solution, reducing the percentage complexed with Al and increasing the one complexed with Ca and Mg in the layers 0-5 and 5-10 cm. Black oat and maize cultivation increased pH in the solution, thereby increasing the proportion of HPO42- and reducing H2PO4- species.

Exact temporal evolution for some non-linear diffusion process

Exact solutions to FokkerPlanck equations with nonlinear drift are considered. Applications of these exact solutions for concrete models are studied. We arrive at the conclusion that for certain drifts we obtain divergent moments (and infinite relaxation time) if the diffusion process can be extended without any obstacle to the whole space. But if we introduce a potential barrier that limits the diffusion process, moments converge with a finite relaxation time.

Strong coupling solution to Schrödinger Equation: the mixing of states

In this paper we give some ideas that can be useful to solve Schrödinger equations in the case when the Hamiltonian contains a large term. We obtain an expansion of the solution in reciprocal powers of the large coupling constant. The procedure followed consists in considering that the small part of the Hamiltonian engenders a motion adiabatic to the motion generated by the large part of the same.

Electrical Conductivity and Chemical Composition of Soil Solution: Comparison of Solution Samplers in Tropical Soils

ABSTRACT Soil solution samplers may have the same working principle, but they differ in relation to chemical and physical characteristics, cost and handling, and these aspects exert influence on the chemical composition of the soil solution obtained. This study was carried out to evaluate, over time, the chemical composition of solutions extracted by Suolo Acqua, with the hydrophilic membrane (HM) as a standard, using soils with contrasting characteristics, and to determine the relationship between electrical conductivity (EC) and concentration of ions and pH of soil solution samples. This study was carried out under laboratory conditions, using three soils samples with different clay and organic matter (OM) contents. Soil solution contents of F−, Cl−, NO−3, Br−, SO42−, Na+, NH4+, K+, Mg2+, Ca2+, were analyzed, as well as inorganic, organic, and total C contents, pH, and EC, in four successive sampling times. Soil solution chemical composition extracted by the Suolo Acqua sampler is similar to that collected by the HM, but the Suolo Acqua extracted more Na+ and soluble organic C than the HM solution. Solution EC, cation and anion concentrations, and soluble C levels are higher in the soil with greater clay and OM contents (Latossolo and Cambissolo in this case). Soil solution composition varied over time, with considerable changes in pH, EC, and nutrient concentrations, especially associated with soil OM. Thus, single and isolated sampling of the soil solution must be avoided, otherwise composition of the soil solution may not be correctly evaluated. Soil solution EC was regulated by pH, as well as the sum of cation and anion concentrations, and the C contents determined in the soil liquid phase.

Novel anesthetics and other treatment strategies for refractory status epilepticus

Refractory status epilepticus (RSE)-that is, seizures resistant to at least two antiepileptic drugs (AEDs)-is generally managed with barbiturates, propofol, or midazolam, despite a low level of evidence (Rossetti, 2007). When this approach fails, the need for alternative pharmacologic and nonpharmacologic strategies emerges. These have been investigated even less systematically than the aforementioned compounds, and are often used, sometimes in succession, in cases of extreme refractoriness (Robakis & Hirsch, 2006). Several possibilities are reviewed here. In view of the marked heterogeneity of reported information, etiologies, ages, and comedications, it is extremely difficult to evaluate a given method, not to say to compare different strategies among them. Pharmacologic Approaches Isoflurane and desflurane may complete the armamentarium of anesthetics,' and should be employed in a ''close'' environment, in order to prevent intoxication of treating personnel. c-Aminobutyric acid (GABA)A receptor potentiation represents the putative mechanism of action. In an earlier report, isoflurane was used for up to 55 h in nine patients, controlling seizures in all; mortality was, however, 67% (Kofke et al., 1989). More recently, the use of these inhalational anesthetics was described in seven subjects with RSE, for up to 26 days, with an endtidal concentration of 1.2-5%. All patients required vasopressors, and paralytic ileus occurred in three; outcome was fatal in three patients (43%) (Mirsattari et al., 2004). Ketamine, known as an emergency anesthetic because of its favorable hemodynamic profile, is an N-methyl-daspartate (NMDA) antagonist; the interest for its use in RSE derives from animal works showing loss of GABAA efficacy and maintained NMDA sensitivity in prolonged status epilepticus (Mazarati & Wasterlain, 1999). However, to avoid possible neurotoxicity, it appears safer to combine ketamine with GABAergic compounds (Jevtovic-Todorovic et al., 2001; Ubogu et al., 2003), also because of a likely synergistic effect (Martin & Kapur, 2008). There are few reported cases in humans, describing progressive dosages up to 7.5 mg/kg/h for several days (Sheth & Gidal, 1998; Quigg et al., 2002; Pruss & Holtkamp, 2008), with moderate outcomes. Paraldehyde acts through a yet-unidentified mechanism, and appears to be relatively safe in terms of cardiovascular tolerability (Ramsay, 1989; Thulasimani & Ramaswamy, 2002), but because of the risk of crystal formation and its reactivity with plastic, it should be used only as fresh prepared solution in glass devices (Beyenburg et al., 2000). There are virtually no recent reports regarding its use in adults RSE, whereas rectal paraldehyde in children with status epilepticus resistant to benzodiazepines seems less efficacious than intravenous phenytoin (Chin et al., 2008). Etomidate is another anesthetic agent for which the exact mechanism of action is also unknown, which is also relatively favorable regarding cardiovascular side effects, and may be used for rapid sedation. Its use in RSE was reported in eight subjects (Yeoman et al., 1989). After a bolus of 0.3 mg/kg, a drip of up to 7.2 mg/kg/h for up to 12 days was administered, with hypotension occurring in five patients; two patients died. A reversible inhibition of cortisol synthesis represents an important concern, limiting its widespread use and implying a careful hormonal substitution during treatment (Beyenburg et al., 2000). Several nonsedating approaches have been reported. The use of lidocaine in RSE, a class Ib antiarrhythmic agent modulating sodium channels, was reviewed in 1997 (Walker & Slovis, 1997). Initial boluses up to 5 mg/kg and perfusions of up to 6 mg/kg/h have been mentioned; somewhat surprisingly, at times lidocaine seemed to be successful in controlling seizures in patients who were refractory to phenytoin. The aforementioned dosages should not be overshot, in order to keep lidocaine levels under 5 mg/L and avoid seizure induction (Hamano et al., 2006). A recent pediatric retrospective survey on 57 RSE episodes (37 patients) described a response in 36%, and no major adverse events; mortality was not given (Hamano et al., 2006 Verapamil, a calcium-channel blocker, also inhibits P-glycoprotein, a multidrug transporter that may diminish AED availability in the brain (Potschka et al., 2002). Few case reports on its use in humans are available; this medication nevertheless appears relatively safe (under cardiac monitoring) up to dosages of 360 mg/day (Iannetti et al., 2005). Magnesium, a widely used agent for seizures elicited by eclampsia, has also been anecdotally reported in RSE (Fisher et al., 1988; Robakis & Hirsch, 2006), but with scarce results even at serum levels of 14 mm. The rationale may be found in the physiologic blockage of NMDA channels by magnesium ions (Hope & Blumenfeld, 2005). Ketogenic diet has been prescribed for decades, mostly in children, to control refractory seizures. Its use in RSE as ''ultima ratio'' has been occasionally described: three of six children (Francois et al., 2003) and one adult (Bodenant et al., 2008) were responders. This approach displays its effect subacutely over several days to a few weeks. Because ''malignant RSE'' seems at times to be the consequence of immunologic processes (Holtkamp et al., 2005), a course of immunomodulatory treatment is often advocated in this setting, even in the absence of definite autoimmune etiologies (Robakis & Hirsch, 2006); steroids, adrenocorticotropic hormone (ACTH), plasma exchanges, or intravenous immunoglobulins may be used alone or in sequential combination. Nonpharmacologic Approaches These strategies are described somewhat less frequently than pharmacologic approaches. Acute implantation of vagus nerve stimulation (VNS) has been reported in RSE (Winston et al., 2001; Patwardhan et al., 2005; De Herdt et al., 2009). Stimulation was usually initiated in the operation room, and intensity progressively adapted over a few days up to 1.25 mA (with various regimens regarding the other parameters), allowing a subacute seizure control; one transitory episode of bradycardia/asystole has been described (De Herdt et al., 2009). Of course, pending identification of a definite seizure focus, resective surgery may also be considered in selected cases (Lhatoo & Alexopoulos, 2007). Low-frequency (0.5 Hz) transcranial magnetic stimulation (TMS) at 90% of the resting motor threshold has been reported to be successful for about 2 months in a patient with epilepsia partialis continua, but with a weaning effect afterward, implying the need for a repetitive use (Misawa et al., 2005). More recently, TMS was applied in a combination of a short ''priming'' high frequency (up to 100 Hz) and longer runs of low-frequency stimulations (1 Hz) at 90-100% of the motor threshold in seven other patients with simple-partial status, with mixed results (Rotenberg et al., 2009). Paradoxically at first glance, electroconvulsive treatment may be found in cases of extremely resistant RSE. A recent case report illustrates its use in an adult patient with convulsive status, with three sessions (three convulsions each) carried out over 3 days, resulting in a moderate recovery; the mechanism is believed to be related to modification of the synaptic release of neurotransmitters (Cline & Roos, 2007). Therapeutic hypothermia, which is increasingly used in postanoxic patients (Oddo et al., 2008), has been the object of a recent case series in RSE (Corry et al., 2008). Reduction of energy demand, excitatory neurotransmission, and neuroprotective effects may account for the putative mechanism of action. Four adult patients in RSE were cooled to 31_-34_C with an endovascular system for up to 90 h, and then passively rewarmed over 2-50 h. Seizures were controlled in two patients, one of whom died; also one of the other two patients in whom seizures continued subsequently deceased. Possible side effects are related to acid-base and electrolyte disturbances, and coagulation dysfunction including thrombosis, infectious risks, cardiac arrhythmia, and paralytic ileus (Corry et al., 2008; Cereda et al., 2009). Finally, anecdotic evidence suggests that cerebrospinal fluid (CSF)-air exchange may induce some transitory benefit in RSE (Kohrmann et al., 2006); although this approach was already in use in the middle of the twentieth century, the mechanism is unknown. Acknowledgment A wide spectrum of pharmacologic (sedating and nonsedating) and nonpharmacologic (surgical, or involving electrical stimulation) regimens might be applied to attempt RSE control. Their use should be considered only after refractoriness to AED or anesthetics displaying a higher level of evidence. Although it seems unlikely that these uncommon and scarcely studied strategies will influence the RSE outcome in a decisive way, some may be interesting in particular settings. However, because the main prognostic determinant in status epilepticus appears to be related to the underlying etiology rather than to the treatment approach (Rossetti et al., 2005, 2008), the safety issue should always represent a paramount concern for the prescribing physician. Conclusion The author confirms that he has read the Journal's position on issues involved in ethical publication and affirms that this paper is consistent with those guidelines.

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$

Von Neumann-Morgenstern solution and convex descompositions of TU games

We study under which conditions the core of a game involved in a convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas¿ five player game with a unique stable set different from the core, are reckoning and analyzed.

Confédération nationale, ou Récit exact & circonstancié de tout ce qui s'est passé à Paris, le 14 juillet 1790, à la fédération ([Reprod.])

Collection : Les archives de la Révolution française ; 6.2.1151