705 research outputs found
A threshold phenomenon for embeddings of into Orlicz spaces
We consider a sequence of positive smooth critical points of the
Adams-Moser-Trudinger embedding of into Orlicz spaces. We study its
concentration-compactness behavior and show that if the sequence is not
precompact, then the liminf of the -norms of the functions is greater
than or equal to a positive geometric constant.Comment: 14 Page
Quantization for an elliptic equation of order 2m with critical exponential non-linearity
On a smoothly bounded domain we consider a sequence of
positive solutions in to
the equation subject to Dirichlet
boundary conditions, where . Assuming that
we
prove that is an integer multiple of
\Lambda_1:=(2m-1)!\vol(S^{2m}), the total -curvature of the standard
-dimensional sphere.Comment: 33 page
Renormalization and blow up for charge one equivariant critical wave maps
We prove the existence of equivariant finite time blow up solutions for the
wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the
sum of a dynamically rescaled ground-state harmonic map plus a radiation term.
The local energy of the latter tends to zero as time approaches blow up time.
This is accomplished by first "renormalizing" the rescaled ground state
harmonic map profile by solving an elliptic equation, followed by a
perturbative analysis
Collision cross sections of high-mannose N-glycans in commonly observed adduct states – identification of gas-phase conformers unique to [M − H]<sup>-</sup> ions
We report collision cross sections (CCS) of high-mannose N-glycans as [M + Na]+, [M + K]+, [M + H]+, [M + Cl]-, [M + H2PO4]- and [M − H]- ions, measured by drift tube (DT) ion mobility-mass spectrometry (IM-MS) in helium and nitrogen gases. Further analysis using traveling wave (TW) IM-MS reveal the existence of distinct conformers exclusive to [M − H]- ions
Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system
We describe the asymptotic behavior as time goes to infinity of solutions of
the 2 dimensional corotational wave map system and of solutions to the 4
dimensional, radially symmetric Yang-Mills equation, in the critical energy
space, with data of energy smaller than or equal to a harmonic map of minimal
energy. An alternative holds: either the data is the harmonic map and the
soltuion is constant in time, or the solution scatters in infinite time
N-glycan microheterogeneity regulates interactions of plasma proteins
Altered glycosylation patterns of plasma proteins are associated with autoimmune disorders and pathogenesis of various cancers. Elucidating glycoprotein microheterogeneity and relating subtle changes in the glycan structural repertoire to changes in protein–protein, or protein–small molecule interactions, remains a significant challenge in glycobiology. Here, we apply mass spectrometry-based approaches to elucidate the global and site-specific microheterogeneity of two plasma proteins: α1-acid glycoprotein (AGP) and haptoglobin (Hp). We then determine the dissociation constants of the anticoagulant warfarin to different AGP glycoforms and reveal how subtle N-glycan differences, namely, increased antennae branching and terminal fucosylation, reduce drug-binding affinity. Conversely, similar analysis of the haptoglobin–hemoglobin (Hp–Hb) complex reveals the contrary effects of fucosylation and N-glycan branching on Hp–Hb interactions. Taken together, our results not only elucidate how glycoprotein microheterogeneity regulates protein–drug/protein interactions but also inform the pharmacokinetics of plasma proteins, many of which are drug targets, and whose glycosylation status changes in various disease states
KAM for the quantum harmonic oscillator
In this paper we prove an abstract KAM theorem for infinite dimensional
Hamiltonians systems. This result extends previous works of S.B. Kuksin and J.
P\"oschel and uses recent techniques of H. Eliasson and S.B. Kuksin. As an
application we show that some 1D nonlinear Schr\"odinger equations with
harmonic potential admits many quasi-periodic solutions. In a second
application we prove the reducibility of the 1D Schr\"odinger equations with
the harmonic potential and a quasi periodic in time potential.Comment: 54 pages. To appear in Comm. Math. Phy
On a functional satisfying a weak Palais-Smale condition
In this paper we study a quasilinear elliptic problem whose functional
satisfies a weak version of the well known Palais-Smale condition. An existence
result is proved under general assumptions on the nonlinearities.Comment: 18 page
On Singularity formation for the L^2-critical Boson star equation
We prove a general, non-perturbative result about finite-time blowup
solutions for the -critical boson star equation in 3 space dimensions. Under
the sole assumption that the solution blows up in at finite time, we
show that has a unique weak limit in and that has a
unique weak limit in the sense of measures. Moreover, we prove that the
limiting measure exhibits minimal mass concentration. A central ingredient used
in the proof is a "finite speed of propagation" property, which puts a strong
rigidity on the blowup behavior of .
As the second main result, we prove that any radial finite-time blowup
solution converges strongly in away from the origin. For radial
solutions, this result establishes a large data blowup conjecture for the
-critical boson star equation, similar to a conjecture which was
originally formulated by F. Merle and P. Raphael for the -critical
nonlinear Schr\"odinger equation in [CMP 253 (2005), 675-704].
We also discuss some extensions of our results to other -critical
theories of gravitational collapse, in particular to critical Hartree-type
equations.Comment: 24 pages. Accepted in Nonlinearit
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