Positive solutions for singularly perturbed nonlinear elliptic problem on manifolds via Morse theory

Given (M, g0) we consider the problem -{\epsilon}^2Delta_{g0+h}u + u = (u+)^{p-1} with ({\epsilon}, h) \in (0, {\epsilon}0) \times B{\rho}. Here B{\rho} is a ball centered at 0 with radius {\rho} in the Banach space of all Ck symmetric covariant 2-tensors on M. Using the Poincar\'e polynomial of M, we give an estimate on the number of nonconstant solutions with low energy for ({\epsilon}, h) belonging to a residual subset of (0, {\epsilon}0) \times B{\rho}, for ({\epsilon}0, {\rho}) small enough

Methyl 9-(1-methyl-1H-indol-3-yl)-9-oxononanoate

Methyl 9-(1-methyl-1H-indol-3-yl)-9-oxononanoate was synthesized using Friedel-Crafts acylation between N-methyl indole and methyl 9-chloro-9-oxononanoate. The structure of the newly synthesized compound was elucidated using H-1-NMR, C-13-NMR, NOESY-1D, ESI-MS, FT-IR, and UV-Vis spectroscopy

a green synthesis of glycoluril derivatives in aqueous solution with recycle of the waste

Abstract A series of glycoluril derivatives have been synthesized in water at room temperature from urea and 1,2-dicarbonyl compounds in the presence of phosphoric anhydride. The reaction time is about 10 minutes using one mole of 1,2-dicarbonyl compound, three moles of urea, and half mole of P4O10, but the reaction occurs also, even if with longer reaction times, with very small amounts of P4O10 which is recovered at the end of reactions. In fact, several catalytic turnovers can be performed using the same reaction solution obtained after separation by simple filtration of the glycolurils

A compactness result for scalar-flat metrics on low dimensional manifolds with umbilic boundary

Let (M,g) a compact Riemannian $n$-dimensional manifold with umbilic boundary. It is well know that, under certain hypothesis, in the conformal class of g there are scalar-flat metrics that have the boundary of M as a constant mean curvature hypersurface. In this paper we prove that these metrics are a compact set in the case of low dimensional manifolds, that is n=6,7,8, provided that the Weyl tensor is always not vanishing on the boundary.Comment: arXiv admin note: text overlap with arXiv:1903.10990, arXiv:1912.1148

Role of Secondary Motifs in Fast Folding Polymers: A Dynamical Variational Principle

A fascinating and open question challenging biochemistry, physics and even geometry is the presence of highly regular motifs such as alpha-helices in the folded state of biopolymers and proteins. Stimulating explanations ranging from chemical propensity to simple geometrical reasoning have been invoked to rationalize the existence of such secondary structures. We formulate a dynamical variational principle for selection in conformation space based on the requirement that the backbone of the native state of biologically viable polymers be rapidly accessible from the denatured state. The variational principle is shown to result in the emergence of helical order in compact structures.Comment: 4 pages, RevTex, 4 eps figure

Anharmonicity and self-similarity of the free energy landscape of protein G

The near-native free energy landscape of protein G is investigated through 0.4 microseconds-long atomistic molecular dynamics simulations in explicit solvent. A theoretical and computational framework is used to assess the time-dependence of salient thermodynamical features. While the quasi-harmonic character of the free energy is found to degrade in a few ns, the slow modes display a very mild dependence on the trajectory duration. This property originates from a striking self-similarity of the free energy landscape embodied by the consistency of the principal directions of the local minima, where the system dwells for several ns, and of the virtual jumps connecting them.Comment: revtex, 6 pages, 5 figure

Directional translocation resistance of Zika xrRNA

xrRNAs from flaviviruses survive in host cells because of their exceptional dichotomic response to the unfolding action of different enzymes. They can be unwound, and hence copied, by replicases, and yet can resist degradation by exonucleases. How the same stretch of xrRNA can encode such diverse responses is an open question. Here, by using atomistic models and translocation simulations, we uncover an elaborate and directional mechanism for how stress propagates when the two xrRNA ends, 5 \u2032 and 3 \u2032, are driven through a pore. Pulling the 3 \u2032 end, as done by replicases, elicits a progressive unfolding; pulling the 5 \u2032 end, as done by exonucleases, triggers a counterintuitive molecular tightening. Thus, in what appears to be a remarkable instance of intra-molecular tensegrity, the very pulling of the 5 \u2032 end is what boosts resistance to translocation and consequently to degradation. The uncovered mechanistic principle might be co-opted to design molecular meta-materials