A categorification of finite-dimensional irreducible representations of quantum \mathfraksl2{\mathfrak{sl}_2} and their tensor products

The purpose of this paper is to study categorifications of tensor products of finite-dimensional modules for the quantum group for . The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie algebra . For the special case of simple modules we naturally deduce a categorification via modules over the cohomology ring of certain flag varieties. Further geometric categorifications and the relation to Steinberg varieties are discussed.We also give a categorical version of the quantised Schur–Weyl duality and an interpretation of the (dual) canonical bases and the (dual) standard bases in terms of projective, tilting, standard and simple Harish-Chandra bimodules.     

A categorification of the Casimir of quantum sl(2)

We categorify the Casimir element of the idempotented form of quantum sl(2).     

Uniaxial exchange flows of two Bingham fluids in a cylindrical duct

Buoyancy driven flows of two Bingham fluids in an inclined ductare considered, providing a simplified model for many oilfieldcementing processes. The flows studied are near-uniaxial andstratified, with the heavy fluid moving down the incline, displacingthe lighter fluid upwards. Existence and uniqueness resultsare obtained for quite general flows and for those which satisfyan axial flow rate constraint. Parametric dependence of thesolutions on the axial pressure gradient is studied. Flows whichsatisfy a zero net axial flow constraint result from an axialpressure gradient which minimizes the viscous dissipation, butnot the plastic dissipation. A regularization method is usedto compute solutions to these problems for (more or less) arbitraryfluid-fluid interfaces and duct-cross sections. Examples relatedto a number of practical applications are presented.     

Diagrammatic categorification of the Chebyshev polynomials of the second kind

We develop a diagrammatic categorification of the polynomial ring Z[x], based on a geometrically defined graded algebra. This construction generalizes to categorification of some special functions, such as Chebyshev polynomials. Diagrammatic algebras featured in these categorifications lead to the first topological interpretations of the Bernstein-Gelfand-Gelfand reciprocity property.     

Non-Volatile Threshold Adaptive Transistors with Embedded RRAM

We propose a novel nonvolatile threshold adaptive transistor （TAT） for neuromorphic circuits. The threshold adaptive transistor is achieved by embedding a resistive random-access memory （RRAM） material stack between the gate electrode and gate dielectric. During operation, the embedded RRAM device is kept at a high resistance state, which makes it act as a nonvolatile capacitor. The threshold could be nonlinearly adjusted by the voltage pulses applied on the gate of the transistor. We quantitatively estimate the range of the capacitance variation of the RRAM device. The threshold voltage of the TAT is simulated and shows expected variation. The simulated output of an inverter using a TAT shows a nonlinear adaptive behavior.     

Coherence resonance near a Hopf bifurcation

We report on the observation of coherence resonance for a semiconductor laser with short optical feedback close to Hopf bifurcations. Noise-induced self-pulsations are documented by distinct Lorentzian-like features in the power spectrum. The character of coherence is critically related to the type of the bifurcation. In the supercritical case, spectral width and height of the peak are monotonic functions of the noise level. In contrast, for the subcritical bifurcation, the width exhibits a minimum, translating into resonance behavior of the correlation time in the pulsation transients. A theoretical analysis based on the generic model of a self-sustained oscillator demonstrates that these observations are of general nature and are related to the fact that the damping depends qualitatively different on the noise intensity for the subcritical and supercritical case.     

火焰原子吸收光谱法测定鱼腥草、西洋参和茯苓中的铜含量

用硝酸-高氯酸混合酸(4∶1)消化鱼腥草、西洋参和茯苓,在波长324.8nm处,利用火焰原子吸收光谱法测定鱼腥草、西洋参和茯苓中铜的含量。线性回归方程为A=0.1708C 0.0004,相关系数r=0.9997,线性范围为0—5μg/mL,检出限为0.0035μg/mL,测定结果的相对标准偏差为0.09%,加标回收率为98.0%—104.2%。     

Sensitivity to initial conditions and lyapunov exponent of a quasiperiodic system

The dynamics of a quasiperiodic map is analyzed both in the presence and in the absence of weak noise. It is shown that, in the presence of weak noise, a strange chaotic attractor with a negative Lyapunov exponent and sensitive dependence of trajectories on the initial conditions can exist in the system. This means that the types of motion of a fluctuating system cannot be classified only by the sign of the leading Lyapunov exponent.     

Changes in Ion Selectivity Following the Asymmetrical Addition of Charge to the Selectivity Filter of Bacterial Sodium Channels

Voltage-gated sodium channels (NaVs) play fundamental roles in eukaryotes, but their exceptional size hinders their structural resolution. Bacterial NaVs are simplified homologues of their eukaryotic counterparts, but their use as models of eukaryotic Na⁺ channels is limited by their homotetrameric structure at odds with the asymmetric Selectivity Filter (SF) of eukaryotic NaVs. This work aims at mimicking the SF of eukaryotic NaVs by engineering radial asymmetry into the SF of bacterial channels. This goal was pursued with two approaches: the co-expression of different monomers of the NaChBac bacterial channel to induce the random assembly of heterotetramers, and the concatenation of four bacterial monomers to form a concatemer that can be targeted by site-specific mutagenesis. Patch-clamp measurements and Molecular Dynamics simulations showed that an additional gating charge in the SF leads to a significant increase in Na⁺ and a modest increase in the Ca²⁺ conductance in the NavMs concatemer in agreement with the behavior of the population of random heterotetramers with the highest proportion of channels with charge −5e. We thus showed that charge, despite being important, is not the only determinant of conduction and selectivity, and we created new tools extending the use of bacterial channels as models of eukaryotic counterparts.