Reversibility of Rings with Respect to the Jacobson Radical

Let R be a ring with identity and J(R) denote the Jacobson radical of R. A ring R is called J-reversible if for any a, \(b \in R\), \(ab = 0\) implies \(ba \in J(R)\). In this paper, we give some properties of J-reversible rings. We prove that some results of reversible rings can be extended to J-reversible rings for this general setting. We show that J-quasipolar rings, local rings, semicommutative rings, central reversible rings and weakly reversible rings are J-reversible. As an application it is shown that every J-clean ring is directly finite.     

Wellposedness of second order backward SDEs

We provide an existence and uniqueness theory for an extension of backward SDEs to the second order. While standard Backward SDEs are naturally connected to semilinear PDEs, our second order extension is connected to fully nonlinear PDEs, as suggested in Cheridito et?al. (Commun. Pure Appl. Math. 60(7):1081–1110, 2007). In particular, we provide a fully nonlinear extension of the Feynman–Kac formula. Unlike (Cheridito et?al. in Commun. Pure Appl. Math. 60(7):1081–1110, 2007), the alternative formulation of this paper insists that the equation must hold under a non-dominated family of mutually singular probability measures. The key argument is a stochastic representation, suggested by the optimal control interpretation, and analyzed in the accompanying paper (Soner et?al. in Dual Formulation of Second Order Target Problems. arXiv:1003.6050, 2009).     

Axially Symmetric Bianchi Type-I Model with Massless Scalar Field and Cosmic Strings in Barber’s Self-Creation Cosmology

Axially symmetric Bianchi type-I space time is considered in the presence of massless scalar field and cosmic strings in Barber’s (Gen. Relativ. Gravit. 14:117, 1982) self-creation theory with two conditions (i) A=B ⁿ and (ii) ε+λ=0. Some physical and kinematical properties of the model, thus obtained, are also discussed.     

Synthesis and antifungal evaluation of 1-aryl-2-dimethyl- aminomethyl-2-propen-1-one hydrochlorides

The development of resistance to current antifungal therapeutics drives the search for new effective agents. The fact that several acetophenone-derived Mannich bases had shown remarkable antifungal activities in our previous studies led us to design and synthesize some acetophenone-derived Mannich bases, 1-8 and 2-acetylthiophene-derived Mannich base 9, 1-aryl-2-dimethylaminomethyl-2-propen-1-one hydrochloride, to evaluate their antifungal activities. The designed chemical structures have α,β-unsaturated ketone moieties, which are responsible for the bioactivities of the Mannich bases. The aryl part was C?H?(1); 4-CH?C?H? (2); 4-CH?OC?H? (3); 4-ClC?H? (4); 4-FC?H? (5); 4-BrC?H? (6); 4-HOC?H? (7); 4-NO?C?H? (8); and C?H?S(2-yl) (9). In this study the designed compounds were synthesized by the conventional heating method and also by the microwave irradiation method to compare these methods in terms of reaction times and yields to find an optimum synthetic method, which can be applied for the synthesis of Mannich bases in further studies. Since there are limited number of studies reporting the synthesis of Mannich bases by microwave irradiation, this study may also contribute to the general literature on Mannich bases. Compound 7 was reported for the first time. Antifungal activities of all compounds and synthesis of the compounds by microwave irradiation were also reported for the first time by this study. Fungi (15 species) were used for antifungal activity test. Amphotericin B was tested as an antifungal reference compound. In conclusion, compounds 1-6, and 9, which had more potent (2-16 times) antifungal activity than the reference compound amphotericin B against some fungi, can be model compounds for further studies to develop new antifungal agents. In addition, microwave irradiation can be considered to reduce reaction period, while the conventional method can still be considered to obtain compounds with higher reaction yields in the synthesis of new Mannich bases.     

Laminar forced convection with viscous dissipation in a concentric annular ductConvection laminaire forcée avec dissipation visqueuse dans un conduit annulaire concentrique

Forced convection heat transfer in fully developed flows of viscous dissipating fluids in concentric annular ducts is analyzed analytically. Special attention has been paid to the effect of the viscous dissipation. Two different cases of the thermal boundary conditions are considered: uniform heat flux at the outer wall and adiabatic inner wall (Case A) and uniform heat flux at the inner wall and adiabatic outer wall (Case B). Solutions for the velocity and temperature distributions and the Nusselt number are obtained for different values of the aspect ratio and the Brinkman number. The present analytical results for the case without the viscous dissipation effect are compared with those available in the literature and an excellent agreement is observed. To cite this article: M. Avc?, O. Ayd?n, C. R. Mecanique 334 (2006).     

Role of diet and trace elements in lithogenesis of renal calculi

Twenty eight stones were characterized for chemical composition and structure. The concentrations of trace elements were determined using INAA while EDXRF was used for determining the calcium contents of the stones. Twenty stones were found to be mainly composed of calcium, six were mixed type and the remaining two were of uric acid type. The concentrations of trace elements namely Zn, Sr, Fe and Cr were lower in uric acid stones as compared to calcium based stones. Diet analysis of 310 patients who were treated for renal stones showed a diet rich in calcium and oxalate and decreased water consumption.

     

Real-time optical imaging and tracking of micron-sized particles

We report real-time imaging and dynamics monitoring of micrometer predefined and random sized particles by time-space-wavelength mapping technology using a single-detector. Experimentally, we demonstrate real-time line imaging of a 5 μm polystyrene microsphere, glass powder particles and patterns such as fingerprints with up to 5 μm resolution at 1 line/50 ns capture rate. By using the same setup, real-time displacement tracking of micrometer-size glass particles with 50 ns temporal resolution and up to 5 μm spatial resolution is achieved. We also show that existing correlation spectroscopy algorithms can be adopted to extract dynamic information in a complex environment.     

Stochastic control for a class of random evolution models

We construct the explicit connection existing between a solvable model of the discrete velocities non-linear Boltzmann equation and the Hamilton-Bellman-Jacobi equation associated with a simple optimal control of a piecewise deterministic process. This study extends the known relation that exists between the Burgers equation and a simple controlled diffusion problem. In both cases the resulting partial differential equations can be linearized via a logarithmic transformation and hence offer the possibility to solve physically relevant non-linear field models in full generality.     

Dehydration kinetics by non-isothermal techniques

The kinetics of thermal degradation of some cementitious calcium aluminates, sulfoaluminates, sulfoferrites and carboaluminates were studied. Activation energies, obtained by Morris and Rogers and Kissinger techniques, were found to be in good agreement with each other.

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Zusammenfassung Die thermische Zersetzungskinetik einiger im Zement befindlicher Kalziumaluminate, Sulfoaluminate, Sulfoferrite und Karboaluminate wurde untersucht. Die nach den Methoden von Morris und Rogers, sowie Kissinger erhaltenen Aktivierungsenergien stimmten gut überein.

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Résumé On a étudié la cinétique de la décomposition thermique de plusieurs constituants du ciment tels les aluminates, sulfoaluminates, sulfoferrites et carboaluminates de calcium. Les énergies d'activation obtenues en appliquant la méthode de Morris et Rogers ainsi que celle de Kissinger sont concordantes.

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Olefination of 3-diazopiperidin-2-one

New conditions have been developed for the olefination of diazo compounds catalysed by methyl trioxorhenium. The new system is suitable for unreactive diazo compounds and its utility is demonstrated by the olefination of 3-diazopiperidin-2-one with a range of aromatic, heterocyclic and alkylaldehydes.