The de Rham Witt complex,cohomological kernels and pm-extensions in characteristic p

In earlier work the authors determined the Brauer kernel of extensions of degree p in characteristic $p>2$ where the Galois group is a semidirect product of order ps for $s|(p?1)$. This result is extended here and tools are developed to compute the cohomological kernels $H_{p^m}^{n+1}(E_m/F)$ for all $n\ge 0$ where $[E_m:F]=p^m$ and the Galois closure is a semidirect product of cyclic groups order $p^m$ and s where $s|(p?1)$. A six-term exact sequence describing the K-theory and cohomology of the extension is obtained. As an application it is shown that any F-division p-algebra of index $p^m$ split in $E_m$ is cyclic; a characteristic p analogue of a result of Vishne. The proofs use the de Rham Witt complex and Izhboldin groups, extending techniques developed earlier for the study of degree 4 extensions in characteristic two. The paper also provides background on the de Rham Witt Complex and Izhboldin groups difficult to track down in the literature.     

John and Uniform Domains in Generalized Siegel Boundaries

Potential Analysis - Given the pair of vector fields X = ?x + |z|2my?t and Y = ?y ?|z|2mx?t,where (x,y,t) = , we give a condition on a bounded domain which ensures...     

Some polynomials associated with the $${\vavec{}}$$-Whitney numbes

In the present article, we study three families of polynomials associated with the r-Whitney numbers of the second kind. They are the r-Dowling polynomials, r-Whitney–Fubini polynomials and the r-Eulerian–Fubini polynomials. Then we derive several combinatorial results by using algebraic arguments (Rota’s method), combinatorial arguments (set partitions) and asymptotic methods.     

Effects of Combination Treatments with Astaxanthin-Loaded Microparticles and Pentoxifylline on Intracellular ROS and Radiosensitivity of J774A.1 Macrophages

Radiation-induced fibrosis (RIF) is a serious, yet incurable, complication of external beam radiation therapy for the treatment of cancer. Macrophages are key cellular actors in RIF because of their ability to produce reactive oxidants, such as reactive oxygen species (ROS) and inflammatory cytokines that, in turn, are the drivers of pro-fibrotic pathways. In a previous work, we showed that phagocytosis could be exploited to deliver the potent natural antioxidant astaxanthin specifically to macrophages. For this purpose, astaxanthin encapsulated into µm-sized protein particles could specifically target macrophages that can uptake the particles by phagocytosis. In these cells, astaxanthin microparticles significantly reduced intracellular ROS levels and the secretion of bioactive TGFβ and increased cell survival after radiation treatments. Here we show that pentoxifylline, a drug currently used for the treatment of muscle pain resulting from peripheral artery disease, amplifies the effects of astaxanthin microparticles on J774A.1 macrophages. Combination treatments with pentoxifylline and encapsulated astaxanthin might reduce the risk of RIF in cancer patients.     

Controlled coherent dynamics of [VO(TPP)], a prototype molecular nuclear qudit with an electronic ancilla

We show that [VO(TPP)] (vanadyl tetraphenylporphyrinate) is a promising system to implement quantum computation algorithms based on encoding information in multi-level (qudit) units. Indeed, it embeds a nuclear spin 7/2 coupled to an electronic spin 1/2 by hyperfine interaction. This qubit–qudit unit can be exploited to implement quantum error correction and quantum simulation algorithms. Through a combined theoretical and broadband nuclear magnetic resonance study, we demonstrate that the elementary operations of such algorithms can be efficiently implemented on the nuclear spin qudit. Manipulation of the nuclear qudit can be achieved by resonant radio-frequency pulses, thanks to the remarkably long coherence times and the effective quadrupolar coupling induced by the strong hyperfine interaction. This approach may open new perspectives for developing new molecular qubit–qudit systems.

By a combined theoretical and broadband nuclear magnetic resonance study, we show that [VOTPP] is a coupled electronic qubit-nuclear qudit system suitable to implement qudit-based quantum error correction and quantum simulation algorithms.     

Influence of interparticle interactions on the kinetics of self-assembly and mechanical strength of nanoparticulate aggregates

Computer simulations based on Discrete Element Method have been performed in order to investigate the influence of interparticle interactions on the kinetics of self-assembly and the mechanical strength of nanoparticle aggregates.Three different systems have been considered.In the first system the interaction between particles has been simulated using the JKR (Johnson,Kendall and Roberts) contact theory,while in the second and third systems the interaction between particles has been simulated using van der Waals and electrostatic forces respectively.In order to compare the mechanical behaviour of the three systems,the magnitude of the maximum attractive force between particles has been kept the same in all cases.However,the relationship between force and separation distance differs from case to case and thus,the range of the interparticle force.The results clearly indicate that as the range of the interparticle force increases,the self-assembly process is faster and the work required to produce the mechanical failure of the assemblies increases by more than one order of magnitude.     

Turbulent Flow and Dispersion of Inertial Particles in a Confined Jet Issued by a Long Cylindrical Pipe

In this work we examine first the flow field of a confined jet produced by a turbulent flow in a long cylindrical pipe issuing in an abrupt angle diffuser. Second, we examine the dispersion of inertial micro-particles entrained by the turbulent flow. Specifically, we examine how the particle dispersion field evolves in the multiscale flow generated by the interactions between the large-scale structures, which are geometry dependent, with the smaller turbulent scales issued by the pipe which are advected downstream. We use Large-Eddy-Simulation (LES) for the flow field and Lagrangian tracking for particle dispersion. The complex shape of the domain is modelled using the immersed-boundaries method. Fully developed turbulence inlet conditions are derived from an independent LES of a spatially periodic cylindrical pipe flow. The flow field is analyzed in terms of local velocity signals to determine spatial coherence and decay rate of the coherent K–H vortices and to make quantitative comparisons with experimental data on free jets. Particle dispersion is analyzed in terms of statistical quantities and also with reference to the dynamics of the coherent structures. Results show that the particle dynamics is initially dominated by the Kelvin–Helmholtz (K–H) rolls which form at the expansion and only eventually by the advected smaller turbulence scales.     

On the convergence of successive Galerkin approximation for nonlinear output feedback <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control

Although the formulation of the nonlinear theory of H _∞ control has been well developed, solving the Hamilton–Jacobi–Isaacs equation remains a challenge and is the major bottleneck for practical application of the theory. Several numerical methods have been proposed for its solution. In this paper, results on convergence and stability for a successive Galerkin approximation approach for nonlinear H _∞ control via output feedback are presented. An example is presented illustrating the application of the algorithm.     

On the Nitroxide Quasi‐Equilibrium in the Alkoxyamine‐Mediated Radical Polymerization of Styrene

Summary: The range of validity of two popular versions of the nitroxide quasi‐equilibrium (NQE) approximation used in the theory of kinetics of alkoxyamine mediated styrene polymerization, are systematically tested by simulation comparing the approximate and exact solutions of the equations describing the system. The validity of the different versions of the NQE approximation is analyzed in terms of the relative magnitude of (dN/dt)/(dP/dt). The approximation with a rigorous NQE, k_c[P][N] = k_d[P N], where P, N and P N are living, nitroxide radicals and dormant species respectively, with kinetic constants k_c and k_d, is found valid only for small values of the equilibrium constant K (10⁻¹¹–10⁻¹² mol · L⁻¹) and its validity is found to depend strongly of the value of K. On the other hand, the relaxed NQE approximation of Fischer and Fukuda, k_c[P][N] = k_d[P N]₀ was found to be remarkably good up to values of K around 10⁻⁸ mol · L⁻¹. This upper bound is numerically found to be 2–3 orders of magnitude smaller than the theoretical one given by Fischer. The relaxed NQE is a better one due to the fact that it never completely neglects dN/dt. It is found that the difference between these approximations lies essentially in the number of significant figures taken for the approximation; still this subtle difference results in dramatic changes in the predicted course of the reaction. Some results confirm previous findings, but a deeper understanding of the physico‐chemical phenomena and their mathematical representation and another viewpoint of the theory is offered. Additionally, experiments and simulations indicate that polymerization rate data alone are not reliable to estimate the value of K, as recently suggested.

Validity of the rigorous nitroxide quasi‐equilibrium assumption as a function of the nitroxide equilibrium constant.