A damping preconditioner for time-harmonic wave equations in fluid and elastic material

A physical damping is considered as a preconditioning technique for acoustic and elastic wave scattering. The earlier preconditioners for the Helmholtz equation are generalized for elastic materials and three-dimensional domains. An algebraic multigrid method is used in approximating the inverse of damped operators. Several numerical experiments demonstrate the behavior of the method in complicated two-dimensional and three-dimensional domains.     

Multiple‐element spectrometer for non‐resonant inelastic X‐ray spectroscopy of electronic excitations

A multiple‐analyser‐crystal spectrometer for non‐resonant inelastic X‐ray scattering spectroscopy installed at beamline ID16 of the European Synchrotron Radiation Facility is presented. Nine analyser crystals with bending radii R = 1 m measure spectra for five different momentum transfer values simultaneously. Using a two‐dimensional detector, the spectra given by all analysers can be treated individually. The spectrometer is based on a Rowland circle design with fixed Bragg angles of about 88°. The energy resolution can be chosen between 30–2000 meV with typical incident‐photon energies of 6–13 keV. The spectrometer is optimized for studies of valence and core electron excitations resolving both energy and momentum transfer.     

Oligonucleotides Featuring a Covalently Mercurated 6-Phenylcarbazole Residue as High-Affinity Hybridization Probes for Thiopyrimidine-Containing Sequences

Short oligonucleotides incorporating either 1-mercuri-6-phenylcarbazole, 8-mercuri-6-phenylcarbazole, or 1,8-dimercuri-6-phenylcarbazole C-nucleoside in the middle of the chain have been synthesized and studied for their potential as hybridization probes for sequences containing thiopyrimidine nucleobases. All of these oligonucleotides formed very stable duplexes with complementary sequences pairing the organometallic moiety with either 2- or 4-thiothymine. The isomeric monomercurated oligonucleotides were also able to discriminate between 2- and 4-thiothymine based on the different melting temperatures of the respective duplexes. DFT-optimized structures of the most stable mononuclear Hg^II-mediated base pairs featured a coordinated covalent bond between Hg^II and either S2 or S4 and a hydrogen bond between the carbazole nitrogen and N3. The dinuclear Hg^II-mediated base pairs, in turn, were geometrically very similar to the one previously reported to form between 1,8-dimercuri-6-phenylcarbazole and thymine and had one Hg^II ion coordinated to a thio and the other one to an oxo substituent.     

Weak $$A_\infty $$ Weights and Weak Reverse Hölder Property in a Space of Homogeneous Type

In the Euclidean setting, the Fujii–Wilson-type \(A_\infty \) weights satisfy a reverse Hölder inequality (RHI), but in spaces of homogeneous type the best-known result has been that \(A_\infty \) weights satisfy only a weak reverse Hölder inequality. In this paper, we complement the results of Hytönen, Pérez and Rela and show that there exist both \(A_\infty \) weights that do not satisfy an RHI and a genuinely weaker weight class that still satisfies a weak RHI. We also show that all the weights that satisfy a weak RHI have a self-improving property, but the self-improving property of the strong reverse Hölder weights fails in a general space of homogeneous type. We prove most of these purely non-dyadic results using convenient dyadic systems and techniques.     

Quantitative weighted estimates for rough homogeneous singular integrals

We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space L ²(w), we obtain a bound that is quadratic in A ₂ constant \({\left[ w \right]_{{A_2}}}\). We do not know if this is sharp, but it is the best known quantitative result for this class of operators. The proof relies on a classical decomposition of these operators into smooth pieces, for which we use a quantitative elaboration of Lacey's dyadic decomposition of Dini-continuous operators: the dependence of constants on the Dini norm of the kernels is crucial to control the summability of the series expansion of the rough operator. We conclude with applications and conjectures related to weighted bounds for powers of the Beurling transform.     

Singular convolution integrals with operator-valued kernel

We study operators \(f\mapsto Kf\) of the form \((Kf)(t)=\int_{{\bf R}^{n}} k(t-s)f(s) {\rm d}s\), where f is a vector-valued function and k an operator-valued singular kernel. Sufficient conditions for boundedness on L ^p -spaces of UMD-valued functions are given in terms of a Hörmander-type condition involving R-boundedness. The results cover large classes of kernels and also provide new proofs of recent operator-valued Fourier multiplier theorems. Moreover, they give new information about families of singular integral operators.     

1,8-Dimercuri-6-Phenyl-1H-Carbazole as a Monofacial Dinuclear Organometallic Nucleobase

A C-nucleoside with 6-phenyl-1H-carbazole as the base moiety has been synthesized and incorporated in the middle of an oligonucleotide. Mercuration of this modified residue at positions 1 and 8 gave the first example of an oligonucleotide featuring a monofacial dinuclear organometallic nucleobase. The dimercurated oligonucleotide formed stable duplexes with unmodified oligonucleotides placing either cytosine, guanine, or thymine opposite to the organometallic nucleobase. A highly stabilizing (ΔT_m=7.3 °C) Hg^II-mediated base pair was formed with thymine. According to DFT calculations performed at the PBE0DH level of theory, this base pair is most likely dinuclear, with the two Hg^II ions coordinated to O2 and O4 of the thymine base.     

On the Carleson duality

As a tool for solving the Neumann problem for divergence-form equations, Kenig and Pipher introduced the space ${\mathcal{X}}$ of functions on the half-space, such that the non-tangential maximal function of their L ₂ Whitney averages belongs to L ₂ on the boundary. In this paper, answering questions which arose from recent studies of boundary value problems by Auscher and the second author, we find the pre-dual of ${\mathcal{X}}$ , and characterize the pointwise multipliers from ${\mathcal{X}}$ to L ₂ on the half-space as the well-known Carleson-type space of functions introduced by Dahlberg. We also extend these results to L _p generalizations of the space ${\mathcal{X}}$ . Our results elaborate on the well-known duality between Carleson measures and non-tangential maximal functions.     

Non-homogeneous Tb Theorem and Random Dyadic Cubes on Metric Measure Spaces

We prove a Tb theorem on quasimetric spaces equipped with what we call an upper doubling measure. This is a property that encompasses both the doubling measures and those satisfying the upper power bound ??(B(x,r))??Cr ^d . Our spaces are only assumed to satisfy the geometric doubling property: every ball of radius r can be covered by at most N balls of radius r/2. A key ingredient is the construction of random systems of dyadic cubes in such spaces.