Well-posedness for the fifth order KdV equation

In this paper, we establish the well-posedness for the Cauchy problem of the fifth order KdV equation with low regularity data. The nonlinear term has more derivatives than can be recovered by the smoothing effect, which implies that the iteration argument is not available when initial data is given in $H^s$ for any $s \in \mathbb{R}$. So we give initial data in $H^{s,a}=H^s \cap \dot{H}^a$ when $a \leq s$ and $a \leq 0$. Then we can use the Fourier restriction norm method to obtain the local well-posedness in $H^{s,a}$ when $s \geq \max\{-1/4, -2a-2 \}$, $-3/2<a \leq -1/4$ and $(s,a) \neq (-1/4,-7/8)$. This result is optimal in some sense

Monolithic folded pendulum accelerometers for seismic monitoring and active isolation systems

A new class of very low noise low-frequency force-balance accelerometers is presented. The device has been designed for advanced mirror isolation systems of interferometric gravitational wave detectors. The accelerometer consists of a small monolithic folded pendulum with 2 s of natural period and an in-vacuum mechanical quality factor of 3000. The folded pendulum geometry, combined with the monolithic design, allows a unique 0.01% cross-axis residual coupling. Equipped with a high-resolution capacitance position sensor, it is capable of a noise-equivalent inertial displacement of 1-nm root mean square integrated over all the frequencies above 0.01 Hz. The main features of this new accelerometer are here reviewed. New possible applications of monolithic folded pendula in geophysical instrumentation are discussed

Monolithic folded pendulum accelerometers for seismic monitoring and active isolation systems

A new class of very low noise low-frequency force-balance accelerometers is presented. The device has been designed for advanced mirror isolation systems of interferometric gravitational wave detectors. The accelerometer consists of a small monolithic folded pendulum with 2 s of natural period and an in-vacuum mechanical quality factor of 3000. The folded pendulum geometry, combined with the monolithic design, allows a unique 0.01% cross-axis residual coupling. Equipped with a high-resolution capacitance position sensor, it is capable of a noise-equivalent inertial displacement of 1-nm root mean square integrated over all the frequencies above 0.01 Hz. The main features of this new accelerometer are here reviewed. New possible applications of monolithic folded pendula in geophysical instrumentation are discussed

Presynaptic Molecular Determinants of Quantal Size

The quantal hypothesis for the release of neurotransmitters at the chemical synapse has gained wide acceptance since it was first worked out at the motor endplate in frog skeletal muscle in the 1950s. Considering the morphological identification of synaptic vesicles at the nerve terminals that appeared to be homogeneous in size, the hypothesis proposed that signal transduction at synapses is mediated by the release of neurotransmitters packed in synaptic vesicles that are individually uniform in size; the amount of transmitter in a synaptic vesicle is called a quantum. Although quantal size – the amplitude of the postsynaptic response elicited by the release of neurotransmitters from a single vesicle – clearly depends on the number and sensitivity of the postsynaptic receptors, accumulating evidence has also indicated that the amount of neurotransmitters stored in synaptic vesicles can be altered by various presynaptic factors. Here, I provide an overview of the concepts and underlying presynaptic molecular underpinnings that may regulate quantal size