Parabolic Schemes for Quasi-Linear Parabolic and Hyperbolic PDEs via Stochastic Calculus

We consider two quasi-linear initial-value Cauchy problems on ? ^d : a parabolic system and an hyperbolic one. They both have a first order non-linearity of the form φ(t, x, u)·?u, a forcing term h(t, x, u) and an initial condition u ₀ ∈ L ^∞(? ^d ) ∩ C ^∞(? ^d ), where φ (resp. h) is smooth and locally (resp. globally) Lipschitz in u uniformly in (t, x). We prove the existence of a unique global strong solution for the parabolic system. We show the existence of a unique local strong solution for the hyperbolic one and we give a lower bound regarding its blow up time. In both cases, we do not use weak solution theory but a direct construction based on parabolic schemes studied via a stochastic approach and a regularity result for sequences of parabolic operators. The result on the hyperbolic problem is performed by means of a non-classical vanishing viscosity method.     

6‐Formylindolo[3,2‐b]carbazole (FICZ) is a Very Minor Photoproduct of Tryptophan at Biologically Relevant Doses of UVB and Simulated Sunlight

Exposure to solar UV is at the origin of numerous photodegradation pathways in biomolecules. Tryptophan is readily modified by UVB radiation into ring‐opened and oxidized photoproducts. One of them, 6‐formylindolo[3,2‐b]carbazole (FICZ), has been extensively studied in the recent years because it very efficiently binds to AhR, a major factor in numerous biologic processes, such as metabolism of xenobiotics. Unfortunately, little information is available on the actual yield of FICZ upon exposure to low and biologically relevant doses of UV radiation. In the present work, we used a sensitive and specific HPLC‐tandem mass spectrometry assay to quantify a series of photoproducts induced by UVB and simulated sunlight (SSL) in solutions of tryptophan. FICZ represented only a minute amount of the photoproducts (0.02 and 0.03%, respectively). Experiments were repeated in culture medium where the yield of FICZ was also found to be very low, even when Trp was added. Last, no FICZ could be detected in cytosolic fractions of cultured cells exposed to SSL. Altogether, the present results show that FICZ is a very minor photoproduct and that it cannot be considered the only endogenous photoproduct responsible for the induction of AhR‐dependent responses in UV‐irradiated cells.     

High-bandwidth hybrid quantum repeater

We present a physical- and link-level design for the creation of entangled pairs to be used in quantum repeater applications where one can control the noise level of the initially distributed pairs. The system can tune dynamically, trading initial fidelity for success probability, from high fidelity pairs (F=0.98 or above) to moderate fidelity pairs. The same physical resources that create the long-distance entanglement are used to implement the local gates required for entanglement purification and swapping, creating a homogeneous repeater architecture. Optimizing the noise properties of the initially distributed pairs significantly improves the rate of generating long-distance Bell pairs. Finally, we discuss the performance trade-off between spatial and temporal resources.     

Landau Hamiltonians with Unbounded Random Potentials

We prove the almost sure existence of a pure point spectrum for the two-dimensional Landau Hamiltonian with an unbounded Anderson-like random potential, provided that the magnetic field is sufficiently large. For these models, the probability distribution of the coupling constant is assumed to be absolutely continuous. The corresponding densityg has support equal to , and satisfies , for some > 0. This includes the case of Gaussian distributions. We show that the almost sure spectrum is , provided the magnetic field B0. We prove that for each positive integer n, there exists a field strength B _n , such that for all B>B _n , the almost sure spectrum is pure point at all energies except in intervals of width about each lower Landau level , for m < n. We also prove that for any B0, the integrated density of states is Lipschitz continuous away from the Landau energiesE _n (B). This follows from a new Wegner estimate for the finite-area magnetic Hamiltonians with random potentials.     

Convergent synthesis of (2R,3R,8R,9R)-N-Boc-ADDA

The convergent synthesis of N-Boc-(2R,3R,8R,9R,4E,6E)-3-amino-9-methoxy-2,6,8-trimethyl-10-phenyldecadenoic acid (enantio-N-Boc-ADDA) is reported. Our flexible approach takes advantage of highly efficient non-aldol aldol and cross-metathesis methodologies.     

Efficiency of peroxyderivatives in the chemical modification of polyethylene

The thermal decomposition of dialkyl peroxides, peroxyketals, and peroxyesters was realized in order to study the functionalization of polyethylene in the molten state. Two radicals were produced: one to abstract a hydrogen to the polyolefin, the other to combine with such a macroradical. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2957–2963, 2000     

Rapid state reduction of quantum systems using feedback control

We consider using Hamiltonian feedback control to increase the speed at which a continuous measurement purifies (reduces) the state of a quantum system, and thus to increase the speed of the preparation of pure states. For a measurement of an observable with equispaced eigenvalues, we show that there exists a feedback algorithm which will speed up the rate of state reduction by at least a factor of 2(N + 1)/3.