A large time asymptotics for transparent potentials for the Novikov-Veselov equation at positive energy

In the present paper we begin studies on the large time asymptotic behavior for solutions of the Cauchy problem for the Novikov--Veselov equation (an analog of KdV in 2 + 1 dimensions) at positive energy. In addition, we are focused on a family of reflectionless (transparent) potentials parameterized by a function of two variables. In particular, we show that there are no isolated soliton type waves in the large time asymptotics for these solutions in contrast with well-known large time asymptotics for solutions of the KdV equation with reflectionless initial data

Monosynaptic pathway from rat vibrissa motor cortex to facial motor neurons revealed by lentivirus-based axonal tracing

The mammalian motor cortex typically innervates motor neurons indirectly via oligosynaptic pathways. However, evolution of skilled digit movements in humans, apes, and some monkey species is associated with the emergence of abundant monosynaptic cortical projections onto spinal motor neurons innervating distal limb muscles. Rats perform skilled movements with their whiskers, and we examined the possibility that the rat vibrissa motor cortex (VMC) projects monosynaptically onto facial motor neurons controlling the whisker movements. First, single injections of lentiviruses to VMC sites identified by intracortical microstimulations were used to label a distinct subpopulation of VMC axons or presynaptic terminals by expression of enhanced green fluorescent protein (GFP) or GFP-tagged synaptophysin, respectively. Four weeks after the injections, GFP and synaptophysin-GFP labeling of axons and putative presynaptic terminals was detected in the lateral portion of the facial nucleus (FN), in close proximity to motor neurons identified morphologically and by axonal back-labeling from the whisker follicles. The VMC projections were detected bilaterally, with threefold larger density of labeling in the contralateral FN. Next, multiple VMC injections were used to label a large portion of VMC axons, resulting in overall denser but still laterally restricted FN labeling. Ultrastructural analysis of the GFP-labeled VMC axons confirmed the existence of synaptic contacts onto dendrites and somata of FN motor neurons. These findings provide anatomical demonstration of monosynaptic VMC-to-FN pathway in the rat and show that lentivirus-based expression of GFP and GFP-tagged presynaptic proteins can be used as a high-resolution neuroanatomical tracing method

The investigation of speed on idling power of a drive of cutting machine Unimat 23 EL

Experimental values of capacity at idling of a quadrilateral milling machine Unimat 23 EL cutting drive are defined at various tool rotation speed and various tool types. It is experimentally established that dependence of cutting drive idling capacity on tool rotation speed has curvilinear character, and dependence of cutting drive idling capacity on tool rotation speed square is close to the linear. It contradicts the theoretical data received by a way of calculations by a technique for metalcutting machines. Accordingly, the idling capacity calculating technique is inapplicable to woodcutting machines not only owing to big divergence of calculated and experimental values, but also because of character discrepancy of experimental and settlement dependences

Promising effects of oxytocin on social and food-related behaviour in young children with Prader-Willi syndrome: A randomized, double-blind, controlled crossover trial

Background: Prader-Willi syndrome (PWS) is known for hyperphagia with impaired satiety and a specific behavioural phenotype with stubbornness, temper tantrums, manipulative and controlling behaviour and obsessive

Towards an Inverse Scattering theory for non decaying potentials of the heat equation

The resolvent approach is applied to the spectral analysis of the heat equation with non decaying potentials. The special case of potentials with spectral data obtained by a rational similarity transformation of the spectral data of a generic decaying potential is considered. It is shown that these potentials describe $N$ solitons superimposed by Backlund transformations to a generic background. Dressing operators and Jost solutions are constructed by solving a DBAR-problem explicitly in terms of the corresponding objects associated to the original potential. Regularity conditions of the potential in the cases N=1 and N=2 are investigated in details. The singularities of the resolvent for the case N=1 are studied, opening the way to a correct definition of the spectral data for a generically perturbed soliton.Comment: 22 pages, submitted to Inverse Problem