Periodic solutions for nonautonomous second order differential inclusions systems with p- Laplacian

Using the nonsmooth variant of minimax point theorems, some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

Sôbre u'a modificação do meio de Monteverde

It is well known that the culture media used in the presumptive diagnosis of suspiciuous colonies from plates inoculated with stools for isolation of enteric organisms do not always correctly indicate the major groups of enterobacteria. In an effort to obtain a medium affording more exact indications, several media (1-9) have been tested. Modifications of some of these media have also been tested with the result that a satisfactory modification of Monteverde's medium was finaly selected. This proved to be most satisfactory, affording, as a result of only one inoculation, a complete series of basic indications. The modification involves changes in the formula, in the method of preparation and in the manner of storage. The formulae are: A. Thymol blue indicator: NaOH 0.1/N .............. 34.4 ml; Thymol blue .............. 1.6 g; Water .................... 65.6 ml. B. Andrade's indicator. C. Urea and sugar solution: Urea ..................... 20 g; Lactose ................... 30 g; Sucrose ................... 30 g; Water .................... 100 ml. The mixture (C.) should be warmed slightly in order to dissolve the ingredients rapidly. Sterilise by filtration (Seitz). Keep stock in refrigeratior. The modification of Monteverde's medium is prepared in two parts. Semi-solid part - Peptone (Difco) 2.0 g; NaCl 0.5 g; Agar 0.5 g; Water 100.0 ml. Boil to dissolve the ingredients. Adjust pH with NaOH to 7.3-7.4. Boil again for precipitation. Filter through cotton. Ad indicators "A" 0.3 ml and "B" 1.0 ml. Sterilise in autoclave 115ºC, 15 minutes in amounts not higher than 200 ml. Just before using, add solution "C" asseptically in amounts of 10 ml to 200 ml of the melted semi-solid medium, maintained at 48-50ºC. Solid part - Peptone (Difco) 1.5 g; Trypticase (BBL) 0.5 g; Agar 2.0 g; Water 100,00 ml. Boil to dissolve the ingredients. Adjust pH with NaOH to 7.3-7.4. Boils again. Filter through cotton. Add indicators "A" 0.3 ml and "B" 1.0 ml; ferrous ammonium sulfate 0.02 g; sodiun thiosulfate 0.02 g. Sterilise in autoclave 115ºC, 15 minutes in amounts not higher than 200 ml. Just before using, add solution "C" asseptically in amounts of 10 ml to 200 ml of the melted solid medium, maintained at 48-50ºC. Final medium - The semi-solid part is dispensed first (tubes about 12 x 120 mm) in 2.5 ml amounts and left to harden at room temperature, in vertical position. The solid part is dispensed over the hardened semi-solid one in amounts from 2.0 ml to 2.5 ml and left to harden in slant position, affording a butt of 12 to 15 mm. The tubes of medium should be subjected to a sterility test in the incubator, overnight. Tubes showing spontaneous gas bubbles (air) should then be discarded. The medium should be stored in the incubator (37ºC), for not more than 2 to 4 days. Storage of the tubes in the ice-box produces the absorption of air which is released as bubbles when the tubes are incubated at 37ºC after inoculation. This fact confirmed the observation of ARCHAMBAULT & McCRADY (10) who worked with liquid media and the aplication of their observation was found to be essential to the proper working conditions of this double-layer medium. Inoculation - The inoculation is made by means of a long straight needle, as is usually done on the triple sugar, but the needel should penetrate only to about half of the height of the semi-solid column. Indol detection - After inoculation, a strip of sterelized filter papaer previously moistened with Ehrlich's reagent, is suspended above the surface of the medium, being held between the cotton plug and the tube. Indications given - In addition to providing a mass of organisms on the slant for serological invetigations, the medium gives the following indications: 1. Acid from lactose and/or sucrose (red, of yellowsh with strains which reduce the indicators). 2. Gas from lactose and/or sucrose (bubbles). 3. H[2]S production, observed on the solid part (black). 4. Motility observed on the semi-solid part (tubidity). 5. Urease production, observed on solid and semi-solid parts (blue). 6. Indol production, observed on the strip of filter paper (red or purplish). Indol production is not observed with indol positive strains which rapidly acidify the surface o the slant, and the use of oxalic acid has proved to give less sensitive reaction (11). Reading of results - In most cases overnight incubation is enough; sometimes the reactions appear within only a few hours of incubation, affording a definitive orientation of the diagnosis. With some cultures it is necessary to observe the medium during 48 hours of incubation. A description showing typical differential reaction follows: Salmonella: Color of the medium unchanged, with blackening of the solid part when H[2]S is positive. The slant tends to alkalinity (greenish of bluish). Gas always absent. Indol negative. Motility positive or negative. Shigella: Color of the medium unchanged at the beginning of incubation period, but acquiring a red color when the strain is late lactose/sucrose positive. Slant tending to alkalinity (greenish or purplish). Indol positive or negative. Motility, gas and H[2]S always negative. Proteus: Color of the medium generally changes entirely to blue or sometimes to green (urease positive delayed), with blackening of solid part when H[2]S is positive. Motility positive of negative. Indol positive. Gas positive or negative. The strains which attack rapidly sucrose may give a yellow-greenish color to the medium. Sometimes the intense blue color of the medium renders difficult the reading of the H[2]S production. Escherichiae and Klebsiellae: Color of the medium red or yellow (acid) with great and rapid production of gas. Motility positive or negative. Indol generally impossible to observe. Paracoli: Those lactose of sucrose positive give the same reaction as Esherichia. Those lactose or sucrose negatives give the same reactions as Salmonellae. Sometimes indol positive and H[2]S negative. Pseudomonas: Color of the medium unchanged. The slant tends to alkalinity. It is impossible to observe motility because there is no growth in the bottom. Alkaligenes: Color of the medium unchanged. The slant tends to alkalinity. The medium does not alter the antigenic properties of the strains and with the mass of organisms on the slant we can make the serologic diagnosis. It is admitted that this medium is somewhat more laborious to prepare than others used for similar purposes. Nevertheless it can give informations generally obtained by two or three other media. Its use represents much saving in time, labor and material, and we suggest it for routine laboratory work in which a quick presumptive preliminary grouping of enteric organisms is needed.

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

Limit Cycles for a class of three dimensional polynomial differential systems

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Periodic orbits in complex Abel equation

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Polynomial and linearized normal forms for almost periodic differential systems

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Multiplicity of limit cycles and analytic m-solutions for planar differential systems

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Dynamics of the third order Lyness' difference equation

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Dysproteinaemia in the differential diagnosis of kala-azar

Serum protein abnormalities were examined in six kala-azar (KA) patients, six controls with positive immunofluorescence tests with Leishmania donovani antigens, and six seronegative controls. KA patients were clearly distinguishable from controls by several parameters, including A/G ratio, albumin and globulin levels, IgM and IgG titers, and positive rheumatoid factor (RF) tests. A positive relationship was noted between RF titers and serum levels of IgM. The diagnostic value and possibel pathologic significance of serum abnormalities in KA is discussed.

On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities

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The equation xpyq=zr and groups that act freely on Λ-trees

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Differential effect of culture epimastigotes and blood-form Trypamastigotes on normal mouse splenocyte responsiveness to mitogens

Blood form trypomastigotes of the Y strain of T. cruzi, produced a strong inhibition of the blastogenic response to T and B cell mitogens, of the C3H/He, C57BLand BALB/cJ strains of mice, while culture epimastigotes of the Y strain kept in a medium that allows parasite growth at 26°. 30° and 37°C produced a strong stimulatory effect that was even higher than the effect of the mitogens alone. Both the inhibitory or the stimulatory effects were dose-dependent. The stimulatory effect of epimastigotes was also temperature-dependent producing increasedstimulation indexes as the temperature of parasite cultures was raised. Metabolically active,living parasites seemed to be necessary for an improved lymphocyte stimulation suggesting a potential role of secreted metabolites as polyclonal activators of mouse lymphocytes.

Differential effects of two anti-apo-cytochrome c-specific monoclonal antibodies on the function of apo-cytochrome c-specific murine T cell clones.

A murine monoclonal antibody (SJL 2-4) specific for the antigen apo-cytochrome c was shown to inhibit both antigen-induced proliferation and lymphokine secretion by an apo-cytochrome c-specific BALB/c helper T cell clone. The inhibition was specific because additional apo-cytochrome c-specific T cell clones were not inhibited by the same monoclonal antibody. Time course studies of the inhibition indicated that the initial 8 hr of contact between T cell clones and antigen-presenting cells were critical for activation of the T cell clones. Inhibition of T cell functions by antigen-specific antibodies appeared to correlate with the antibody-antigen binding constant because a second monoclonal antibody (Cyt-1-59), with identical specificity but with a lower affinity constant for apo-cytochrome c, had very little inhibitory effect on the proliferation or lymphokine secretion of apo-cytochrome c-specific T cell clones.

A curious example of two model categories and some associated differential graded algebras

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