A Note on the Symmetry of Sequence Spaces

Mathematical Notes - We give a self-contained treatment of symmetric Banach sequence spaces and some of their natural properties. We are particularly interested in the symmetry of the norm and the...     

Screening of threading bis-intercalators binding to duplex DNA by electrospray ionization tandem mass spectrometry

The DNA binding of novel threading bis-intercalators V1, trans-D1, and cis-C1, which contain two naphthalene diimide (NDI) intercalation units connected by a scaffold, was evaluated using electrospray ionization mass spectrometry (ESI-MS) and DNAse footprinting techniques. ESI-MS experiments confirmed that V1, the ligand containing the -Gly3-Lys- peptide scaffold, binds to a DNA duplex containing the 5'-GGTACC-3' specific binding site identified in previous NMR-based studies. The ligand formed complexes with a ligand/DNA binding stoichiometry of 1:1, even when there was excess ligand in solution. Trans-D1 and cis-C1 are new ligands containing a rigid spiro-tricyclic scaffold in the trans- and cis- orientations, respectively. Preliminary DNAse footprinting experiments identified possible specific binding sites of 5'-CAGTGA-5' for trans-D1 and 5'-GGTACC-3' for cis-C1. ESI-MS experiments revealed that both ligands bound to DNA duplexes containing the respective specific binding sequences, with cis-C1 exhibiting the most extensive binding based on a higher fraction of bound DNA value. Cis-C1 formed complexes with a dominant 1:1 binding stoichiometry, whereas trans-D1 was able to form 2:1 complexes at ligand/DNA molar ratios >or=1 which is suggestive of nonspecific binding. Collisional activated dissociation (CAD) experiments indicate that DNA complexes containing V1, trans-D1, and cis-C1 have a unique fragmentation pathway, which was also observed for complexes containing the commercially available bis-intercalator echinomycin, as a result of similar binding interactions, marked by intercalation in addition to hydrogen bonding by the scaffold with the DNA major or minor groove.     

A complete $\mathcal{O}(\alpha_{\mathrm{S}}^{2})$ calculation of the signal–background interference for the Higgs diphoton decay channel

We analyze a noncommutative model of BTZ spacetime based on deformation of the standard symplectic structure of phase space, i.e., a modification of the standard commutation relations among coordinates and momenta in phase space. We find a BTZ-like solution that is nonperturbative in the non-trivial noncommutative structure. It is shown that the use of deformed commutation relations in the modified non-canonical phase space eliminates the horizons of the standard metric.     

Renormalization in theories with modified dispersion relations: Weak gravitational fields

We consider a free quantum scalar field satisfying modified dispersion relations in curved spacetimes, within the framework of Einstein–Aether theory. Using a power counting analysis, we study the divergences in the adiabatic expansion of 〈?²〉$〈{?}^2〉$ and 〈T_μν〉$〈T_{\mu \nu }〉$, working in the weak field approximation. We show that for dispersion relations containing up to 2s powers of the spatial momentum, the subtraction necessary to renormalize these two quantities on general backgrounds depends on s   in a qualitatively different way: while 〈?²〉$〈{?}^2〉$ becomes convergent for a sufficiently large value of s  , the number of divergent terms in the adiabatic expansion of 〈T_μν〉$〈T_{\mu \nu }〉$ increases with s. This property was not apparent in previous results for spatially homogeneous backgrounds.     

Experimental study of high energy electron interactions in a superconducting aluminum alloy resonant bar

Peak amplitude measurements of the fundamental mode of oscillation of a suspended aluminum alloy bar hit by an electron beam show that the amplitude is enhanced by a factor ∼3.5 when the material is in the superconducting state. This result is consistent with the cosmic ray observations performed by the resonant gravitational wave detector NAUTILUS, made of the same alloy, when operated in the superconducting state. A comparison of the experimental data with the predictions of the model describing the underlying physical process is also presented.     

Effect of the gelation process on the production of alginate microbeads by microfluidic chip technology

The present paper reports the production of Ba-alginate microspheres by microfluidic chip technology. The general production strategy is based on the formation of an alginate multiphase flow by a 'Y' junction squeezing mechanism. Special emphasis is given to the relationship existing between the gelation process and the final morphological characteristics of the produced microbeads. A series of different gelation strategies, namely: 'external gelation', 'internal gelation' and 'partial gelation' were compared in terms of size, size distribution and morphology of the produced microbeads.     

Multilinear Marcinkiewicz-Zygmund Inequalities

We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on \(\ell ^r\)-valued extensions of linear operators. We show that for certain \(1 \le p, q_1, \dots , q_m, r \le \infty \), there is a constant \(C\ge 0\) such that for every bounded multilinear operator \(T:L^{q_1}(\mu _1) \times \cdots \times L^{q_m}(\mu _m) \rightarrow L^p(\nu )\) and functions \(\{f_{k_1}^1\}_{k_1=1}^{n_1} \subset L^{q_1}(\mu _1), \dots , \{f_{k_m}^m\}_{k_m=1}^{n_m} \subset L^{q_m}(\mu _m)\), the following inequality holds

$$\begin{aligned} \left\| \left( \sum _{k_1, \dots , k_m} |T(f_{k_1}^1, \dots , f_{k_m}^m)|^r\right) ^{1/r} \right\| _{L^p(\nu )} \le C \Vert T\Vert \prod _{i=1}^m \left\| \left( \sum _{k_i=1}^{n_i} |f_{k_i}^i|^r\right) ^{1/r} \right\| _{L^{q_i}(\mu _i)}. \end{aligned}$$ (1)

In some cases we also calculate the best constant \(C\ge 0\) satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderón-Zygmund operators.