460 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
Collision cross sections of high-mannose N-glycans in commonly observed adduct states â identification of gas-phase conformers unique to [M â 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 â 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 â H]- ions
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
Existence of solutions to a higher dimensional mean-field equation on manifolds
For we prove an existence result for the equation on a closed Riemannian
manifold of dimension for certain values of .Comment: 15 Page
Chemoenzymatic Synthesis of a New Germacrene Derivative Named Germacrene F
The new farnesyl pyrophosphate (FPP) derivative with a shifted olefinic double bond from C6-C7 to C7-C8 is accepted and converted by the sesquiterpene cyclases protoilludene synthase (Omp7) as well as viridiflorene synthase (Tps32). In both cases, a so far unknown germacrene derivative was found to be formed, which we name âgermacrene Fâ. Both cases are examples in which a modification around the central olefinic double bond in FPP leads to a change in the mode of initial cyclization (from 1â11 to 1â10). For Omp7 a rationale for this behaviour was found by carrying out molecular docking studies. Temperature-dependent NMR experiments, accompanied by NOE studies, show that germacrene F adopts a preferred mirror-symmetric conformation with both methyl groups oriented in the same directions in the cyclodecane ring
Small coupling limit and multiple solutions to the Dirichlet Problem for Yang Mills connections in 4 dimensions - Part I
In this paper (Part I) and its sequels (Part II and Part III), we analyze the
structure of the space of solutions to the epsilon-Dirichlet problem for the
Yang-Mills equations on the 4-dimensional disk, for small values of the
coupling constant epsilon. These are in one-to-one correspondence with
solutions to the Dirichlet problem for the Yang Mills equations, for small
boundary data. We prove the existence of multiple solutions, and, in
particular, non minimal ones, and establish a Morse Theory for this non-compact
variational problem. In part I, we describe the problem, state the main
theorems and do the first part of the proof. This consists in transforming the
problem into a finite dimensional problem, by seeking solutions that are
approximated by the connected sum of a minimal solution with an instanton, plus
a correction term due to the boundary. An auxiliary equation is introduced that
allows us to solve the problem orthogonally to the tangent space to the space
of approximate solutions. In Part II, the finite dimensional problem is solved
via the Ljusternik-Schirelman theory, and the existence proofs are completed.
In Part III, we prove that the space of gauge equivalence classes of Sobolev
connections with prescribed boundary value is a smooth manifold, as well as
some technical lemmas used in Part I. The methods employed still work when the
4-dimensional disk is replaced by a more general compact manifold with
boundary, and SU(2) is replaced by any compact Lie group
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