Bulky Polyfluorinated Terphenyldiphenylboranes: Water Tolerant Lewis Acids

Protocols for the synthesis of the bulky polyfluorinated triarylboranes 2,6-(C₆F₅)₂C₆F₃B(C₆F₅)₂ ( 1 ), 2,6-(C₆F₅)₂C₆F₃B[3,5-(CF₃)₂C₆H₃] ( 2 ), 2,4,6-(C₆F₅)₃C₆H₂B(C₆F₅)₂ ( 3 ), 2,4,6-(C₆F₅)₃C₆H₂B[3,5-(CF₃)₂C₆H₃] ( 4 ) were developed. All boranes are water tolerant and according to the Gutmann-Beckett method, 1 – 3 display Lewis acidities larger than that of the prominent B(C₆F₅)₃.     

Energy Spectra of Alpha Particles in the Interaction of $${}^{{56}}$$ Fe Nuclei with Tantalum and Uranium Nuclei at an Energy of 320 MeV

Physics of Atomic Nuclei - The differential cross sections for alpha-particle emission at an angle of 0 $${}^{\circ}$$ in the reactions induced by a 6-MeV/nucleon $${}^{56}$$ Fe beams incident to...     

One-Dimensional Parametric Determining form for the Two-Dimensional Navier–Stokes Equations

The evolution of a determining form for the 2D Navier–Stokes equations (NSE) which is an ODE on a space of trajectories is completely described. It is proved that at every stage of its evolution, the solution is a convex combination of the initial trajectory and a chosen, fixed steady state, with a dynamical convexity parameter \(\theta \), which will be called the characteristic determining parameter. That is, we show a separation of variables formula for the solution of the determining form. Moreover, for a given initial trajectory, the dynamics of the infinite-dimensional determining form are equivalent to those of the characteristic determining parameter \(\theta \) which is governed by a one-dimensional ODE. This one-dimensional ODE is used to show that if the solution to the determining form converges to the fixed state it does so no faster than \({\mathcal {O}}(\tau ^{-1/2})\), otherwise it converges to a projection of some other trajectory in the global attractor of the NSE, but no faster than \({\mathcal {O}}(\tau ^{-1})\), as \(\tau \rightarrow \infty \), where \(\tau \) is the evolutionary variable in determining form. The one-dimensional ODE is also exploited in computations which suggest that the one-sided convergence rate estimates are in fact achieved. The ODE is then modified to accelerate the convergence to an exponential rate. It is shown that the zeros of the scalar function that governs the dynamics of \(\theta \), which are called characteristic determining values, identify in a unique fashion the trajectories in the global attractor of the 2D NSE     

Collapse of the N=28 shell closure in (42)Si

The energies of the excited states in very neutron-rich (42)Si and (41,43)P have been measured using in-beam gamma-ray spectroscopy from the fragmentation of secondary beams of (42,44)S at 39A MeV. The low 2(+) energy of (42)Si, 770(19) keV, together with the level schemes of (41,43)P, provides evidence for the disappearance of the Z=14 and N=28 spherical shell closures, which is ascribed mainly to the action of proton-neutron tensor forces. New shell model calculations indicate that (42)Si is best described as a well-deformed oblate rotor.     

Fish and Chips: a microfluidic perfusion platform for monitoring zebrafish development

We have developed a multi-channel microfluidic perfusion platform for culturing zebrafish embryos and capturing live images of various tissues and organs inside the embryo. The Fish and Chips was micro-fabricated in silicon and glass for reproducibility and accuracy of the microfluidic structure. The microfluidic platform consists of three parts: a microfluidic gradient generator, a row of eight fish tanks, in which the fish embryos are individually placed, and eight output channels. The fluidic gradient generator supports dose-dependent drug and chemical studies. A unique perfusion system ensures a uniform and constant flow of media to the fish tank while the wastes are efficiently removed. The fish tanks restrict the embryo movements, except rotationally, for live imaging of internal tissues and organs. The embryos showed developmental abnormalities under the influence of the drug valproic acid (VPA).     

On Perfectly Generating Projective Classes in Triangulated Categories

We say that a projective class in a triangulated category with coproducts is perfect if the corresponding ideal is closed under coproducts of maps. We study perfect projective classes and the associated phantom and cellular towers. Given a perfect generating projective class, we show that every object is isomorphic to the homotopy colimit of a cellular tower associated to that object. Using this result and the Neeman's Freyd-style representability theorem, we give a new proof of Brown Representability Theorem.     

Schönemann–Eisenstein–Dumas-Type Irreducibility Conditions that Use Arbitrarily Many Prime Numbers

The famous irreducibility criteria of Schönemann–Eisenstein and Dumas rely on information on the divisibility of the coefficients of a polynomial by a single prime number. In this paper, we will use some results and ideas of Dumas to provide several irreducibility criteria of Schönemann–Eisenstein–Dumas-type for polynomials with integer coefficients, criteria that are given by some divisibility conditions for their coefficients with respect to arbitrarily many prime numbers. A special attention will be paid to those irreducibility criteria that require information on the divisibility of the coefficients by two distinct prime numbers.     

FRACTIONAL 2D-STOCHASTIC CURRENTS

Using multiple stochastic integrals and the stochastic calculus for the frac-tional Brownian sheet, we define and we analyze the 2D-fractional stochastic currents.     

Lyapunov operator inequalities for exponential stability of Banach space semigroups of operators

We obtain continuous-time and discrete-time Lyapunov operator inequalities for the exponential stability of strongly continuous, one-parameter semigroups acting on Banach spaces. Thus we extend the classic result of Datko (1970) [2] from Hilbert spaces to Banach spaces.     

Asymptotic Theory for Fractional Regression Models via Malliavin Calculus

We study the asymptotic behavior as n→∞ of the sequence