Inhibition of Food Intake by PACAP in the Hypothalamic Ventromedial Nuclei is Mediated by NMDA Receptors

Central injections of pituitary adenylate cyclase-activating polypeptide (PACAP) into the ventromedial nuclei (VMN) of the hypothalamus produce hypophagia that is dependent upon the PAC1 receptor; however, the signaling downstream of this receptor in the VMN is unknown. Though PACAP signaling has many targets, this neuropeptide has been shown to influence glutamate signaling in several brain regions through mechanisms involving NMDA receptor potentiation via activation of the Src family of protein tyrosine kinases. With this in mind, we examined the Src-NMDA receptor signaling pathway as a target for PACAP signaling in the VMN that may mediate its effects on feeding behavior. Under nocturnal feeding conditions, NMDA receptor antagonism prior to PACAP administration into the VMN attenuated PACAP-mediated decreases in feeding suggesting that glutamatergic signaling via NMDA receptors is necessary for PACAP-induced hypophagia. Furthermore, PACAP administration into the VMN resulted in increased tyrosine phosphorylation of the GluN2B subunit of the NMDA receptor, and inhibition of Src kinase activity also blocked the effects of PACAP administration into the VMN on feeding behavior. These results indicate that PACAP neurotransmission in the VMN likely augments glutamate signaling by potentiating NMDA receptors activity through the tyrosine phosphorylation events mediated by the Src kinase family, and modulation of NMDA receptor activity by PACAP in the hypothalamus may be a primary mechanism for its regulation of food intake

Global Well-posedness of the Adiabatic Limit of Quantum Zakharov System in 1D

In this paper, we prove the low-regularity global well-posedness of the adibatic limit of the Quantum Zakharov system and consider its semi-classical limit, i.e., the convergence of the model equation as the quantum parameter tends to zero. We also show ill-posedness in negative Sobolev spaces and discuss the existence of ground-state soliton solutions in high spatial dimensions.Comment: Few Edit

Small Time Behaviour and Summability Methods for the Schr\"odinger Equation on R\mathbb{R}

We consider Carleson's problem regarding small time almost everywhere convergence to initial data for the Schr\"odinger equation, both linear and nonlinear. We show that the (sharp) result proved by Dahlberg and Kenig for initial data in Sobolev spaces still holds when one considers the full Schr\"odinger equation with a certain class of potentials. We also show the same technique used to bound such potential functions works for certain types of nonlinearities as well. As for $s<\frac{1}{4}$, we investigate the $L^p$-unboundedness properties of (localised) maximal operator.Comment: 20 page

Modified Strichartz Estimate of the Periodic Fourth Order NLS

We prove modified Strichartz estimates on the one-dimensional torus, that are adapted to a fourth-order dispersion relation, and use them to show global well-posedness of nonlinear fourth-order Schr\"odinger equations. This extends the (low regularity) existence theory of the adiabatic transition of the Quantum Zakharov system to NLS. We show that the solutions behave continuously with respect to the quantum parameter in every compact time interval. Globally in time, however, we also show that such continuous dependence is generally not uniform.Comment: 15p

Multilinear Weighted Estimates and Quantum Zakharov System

We consider the compact case of one-dimensional quantum Zakharov system, as an initial-value problem with periodic boundary conditions. We apply the Bourgain norm method to show low regularity local well-posedness for a certain class of Sobolev exponents that are sharp up to the boundary, under the condition that Schr\"odinger Sobolev regularity is non-negative. Using the conservation law and energy method, we show global well-posedness for sufficiently regular initial data, without any smallness assumption. Lastly we show the semi-classical limit as $\epsilon \to 0$ on a compact time interval, whereas the quantum perturbation proves to be singular on an infinite time interval.Comment: 18 page

Well-posedness of the mixed-Fractional Nonlinear Schr\"odinger Equation on R2\mathbb{R}^2

We investigate the well-posedness theory of the 2-D fractional nonlinear Schr\"odinger equation (NLSE) with a mixed degree of derivatives. Motivated by models in optics and photonics where the light propagation is governed by non-quadratic, fractional, and anisotropic dispersion profile, this paper presents first results in this direction. Dispersive estimates are developed in the context of anisotropic Sobolev spaces defined by inhomogeneous symbols. The main model is shown to exhibit scattering for small data in the scaling-critical space. Furthermore the continuity of solution with respect to the dispersion parameter is shown on a compact time interval.Comment: Revised Articl

Continuum Limit of 2D Fractional Nonlinear Schr\"odinger Equation

We prove that the solutions to the discrete Nonlinear Schr\"odinger Equation (DNLSE) with non-local algebraically-decaying coupling converge strongly in $L^2(\mathbb{R}^2)$ to those of the continuum fractional Nonlinear Schr\"odinger Equation (FNLSE), as the discretization parameter tends to zero. The proof relies on sharp dispersive estimates that yield the Strichartz estimates that are uniform in the discretization parameter. An explicit computation of the leading term of the oscillatory integral asymptotics is used to show that the best constants of a family of dispersive estimates blow up as the non-locality parameter $\alpha \in (1,2)$ approaches the boundaries.Comment: Revised Articl

Reductive defluorination of aqueous perfluorinated alkyl surfactants : effects of ionic headgroup and chain length

Perfluorinated chemicals (PFCs) are distributed throughout the environment. In the case of perfluorinated alkyl carboxylates and sulfonates, they can be classified as persistent organic pollutants since they are resistant to environmentally relevant reduction, oxidation, and hydrolytic processes. With this in mind, we report on the reductive defluorination of perfluorobutanoate, PFBA (C_3F_7CO_2−), perfluorohexanoate, PFHA (C_5F_(11)CO_2−), perfluorooctanoate, PFOA (C_7F_(15)CO_2−), perfluorobutane sulfonate, PFBS (C_4F_9SO_3−), perfluorohexane sulfonate, PFHS (C_6F_(13)SO_3−), and perfluorooctane sulfonate, PFOS (C_8F_(17)SO_3−) by aquated electrons, eaq−, that are generated from the UV photolysis (λ = 254 nm) of iodide. The ionic headgroup (-SO_3− vs -CO_2−) has a significant effect on the reduction kinetics and extent of defluorination (F index = −[F−]_(produced)/[PFC]_(degraded)). Perfluoroalkylsulfonate reduction kinetics and the F index increase linearly with increasing chain length. In contrast, perfluoroalkylcarboxylate chain length appears to have a negligible effect on the observed kinetics and the F index. H/F ratios in the gaseous fluoro-organic products are consistent with measured F indexes. Incomplete defluorination of the gaseous products suggests a reductive cleavage of the ionic headgroup occurs before complete defluorination. Detailed mechanisms involving initiation by aquated electrons are proposed