Hardy Spaces, Regularized BMO Spaces and the Boundedness of Calderón–Zygmund Operators on Non-homogeneous Spaces

One defines a non-homogeneous space (X,μ) as a metric space equipped with a non-doubling measure μ so that the volume of the ball with center x, radius r has an upper bound of the form r ⁿ for some n>0. The aim of this paper is to study the boundedness of Calderón–Zygmund singular integral operators T on various function spaces on (X,μ) such as the Hardy spaces, the L ^p spaces, and the regularized BMO spaces. This article thus extends the work of X. Tolsa (Math. Ann. 319:89–149, 2011) on the non-homogeneous space (? ⁿ ,μ) to the setting of a general non-homogeneous space (X,μ). Our framework of the non-homogeneous space (X,μ) is similar to that of Hytönen (2011) and we are able to obtain quite a few properties similar to those of Calderón–Zygmund operators on doubling spaces such as the weak type (1,1) estimate, boundedness from Hardy space into L ¹, boundedness from L ^∞ into the regularized BMO, and an interpolation theorem. Furthermore, we prove that the dual space of the Hardy space is the regularized BMO space, obtain a Calderón–Zygmund decomposition on the non-homogeneous space (X,μ), and use this decomposition to show the boundedness of the maximal operators in the form of a Cotlar inequality as well as the boundedness of commutators of Calderón–Zygmund operators and BMO functions.     

Combined effect of the perpendicular magnetic field and dilute charged impurity on the electronic phase of bilayer AA-stacked hydrogenated graphene

We address the electronic phase engineering in the impurity-infected functionalized bilayer graphene with hydrogen atoms (H-BLG) subjected to a uniform Zeeman magnetic field, employing the tight-binding model, the Green's function technique, and the Born approximation. In particular, the key point of the present work is focused on the electronic density of states (DOS) in the vicinity of the Fermi energy. By exploiting the perturbative picture, we figure out that how the interaction and/or competition between host electrons, guest electrons, and the magnetic field potential can lead to the phase transition in H-BLG. Furthermore, different configurations of hydrogenation, namely reduced table-like and reduced chair-like, are also considered when impurities are the same and/or different. A comprehensive information on the various configurations provides the semimetallic and gapless semiconducting behaviors for unfunctionalized bilayer graphene and H-BLGs, respectively. Further numerical calculations propose a semimetal-to-metal and gapless semiconductor-to-semimetal phase transition, respectively, when only turning on the magnetic field. Interestingly, the results indicate that the impurity doping alone affects the systems as well, leading to semimetal-to-metal and no phase transition in the pristine system and hydrogenated ones, respectively. However, the combined effect of charged impurity and magnetic field shows that the pristine bilayer graphene is not influenced much as the functionalized ones and phase back transitions appear. Tuning of the electronic phase of H-BLG by using both types of electronic and magnetic perturbations play a decisive role in optical responses.     

Nonlinear spectral-spatial control and localization of supercontinuum radiation

We present the first observation of spatiospectral control and localization of supercontinuum light through the nonlinear interaction of spectral components in extended periodic structures. We use an array of optical waveguides in a LiNbO3 crystal and employ the interplay between diffraction and nonlinearity to dynamically control the output spectrum of the supercontinuum radiation. This effect presents an efficient scheme for optically tunable spectral filtering of supercontinua.     

Pulse propagation in an autoionization medium with double Fano profile

We discuss the propagation of a short laser pulse in an auto- ionizing (AI) medium with degenerate double Fano model. By solving numerically the coupled equations for atoms and fields we show that by the proper choice of Fano parameters involved in the problem (contrary to the case considered in (E. Paspalakis, N. J. Kylstra, and P. L. Knight, Phys. Rev. A60 (1999)) we have now two Fano asymmetry parameters) one can eliminate almost completely the absorption in the pulse propagation. It means that we have the transparency in the medium. From the connection between population trapping in short pulsed laser field and transparency in the propagation of the laser pulse which has been fixed by Paspalakis et al., Phys. Rev. A60 (1999) we conclude that this proper choice leads to the presence of the population trapping (or the existence of the “dark” states) in the atomic system. Moreover, instead of one value of the laser detuning for which the dark states exist in the case of one AI level, we find numerically two such values in the case of two AI levels.     

Effect of the External Mirror Feedback Strength in the Dynamics and Spectrum of the Injected Semiconductor Lasers

We analytically investigate the effect of an external mirror on the stability of an injected semiconductor laser, the latter treated as injected damped oscillators. In the studied configuration, the injected semiconductor laser with an external mirror is under the influence of a chaotic oscillating optical signal that is generated by a similar semiconductor master laser. We derive our results in terms of the damping rate and resonance frequency. We show that the external mirror can eliminate the unstable modes of the injected laser at low frequencies. Furthermore, the mirror can enhance the damping of the oscillation modes of the injected semiconductor laser; consequently, the driven response of the injected laser may have a broad spectrum, even wider than that of the chaotic driving signal. We also show results for the bandwidths of the injection amplitude and phase increment as functions of the injection rate and feedback strength of the external mirror. In addition, we use bifurcation and time-series curves to describe the dynamical behavior of the injected laser. We identify the feedback strength of injected laser, relative to that of the master laser, which induces synchronization between the injected-laser oscillation modes and the master laser.     

Beyond Schmittel and Myers-Saito cyclizations: rearrangements of 4-heteroatom-1,2-hexa-diene-5-ynes

The thermal rearrangements of 4-heteroatom-1,2-hexadiene-5-ynes (2) were studied at the BLYP/6-311+G//BLYP/6-31G level of theory. Cyclization of 2 to heteroatom-containing cyclopentadienyl structures (6) competes with the Claisen-type rearrangement to acyclic, allenic structures. Cyclizations to cyclobutene (4)- and cyclohexadiene (8)-derived heterocycles are not feasible as a result of high reaction barriers and lower-lying alternative pathways. [structure: see text]     

Structural variability of endotoxins from R-type isogenic mutants of Shigella sonnei

The structural variations in the rough-type endotoxins [lipopolysaccharides (LPSs)] of Shigella sonnei mutant strains (S. sonnei phase II-4303, R41, 562H and 4350) were investigated by Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS) and tandem MS. A series of S. sonnei mutants had previously been the subject of analytical studies on the biosynthesis of heptose components in the core oligosaccharide region of LPSs. This study gives a complete overview on the structures of the full core and lipid A of S. sonnei mutant strains by MS. We found that the LPSs of the isogenic rough mutants were formed in a step-like manner containing 0:1:2:3 heptose in the deep core region of 4350, 562H, R41 and 4303, respectively, and the longest LPS from the mutant S. sonnei 4303 contained also five hexoses. The structural variations in the lipid A moiety and in the oligosaccharide part of the intact LPS were followed by MALDI-TOF-MS/MS. For the dissolution and the ionization of the samples, 2,5-dihydroxybenzoic acid in citric acid solution was applied as matrix. The detailed evaluation of the mass spectra indicates heterogeneity in the lipid part due to the differences in the phosphate and fatty acid composition.     

Structure and catalytic activity of some soluble polyethylene glycol-peptide conjugates

Soluble catalysts for the Juliá-Colonna asymmetric epoxidation reaction have been constructed in three different ways, using NH₂-PEG-OMe as the support system: suitable solvents have been identified and it is shown that the degree of helicity of the conjugates correlates with the extent of conversion and (to a lesser extent) the enantioselectivity of epoxidation.     

Dioscorealides and dioscoreanone,novel cytotoxic naphthofuranoxepins,and 1,4-phenanthraquinone from Dioscorea membranacea Pierre

[structure: see text] Commonly used among ingredients in Thai traditional anticancer preparations, the rhizome of Dioscorea membranacea Pierre was found potently cytotoxic and possibly contributed to such a therapeutic effect. Bioassay-guided isolation resulted in two novel cytotoxic naphthofuranoxepins, dioscorealides A (1) and B (2), and a new 1,4-phenanthraquinone, dioscoreanone (3). The structure determination, achieved mainly by means of NMR and CD spectral and X-ray crystallographic analyses, and cytotoxicity are discussed here.     

Specific ion effects on the electrophoretic mobility of small,highly charged peptides: A modeling study

In this work, we use coarse‐grained modeling to study the free solution electrophoretic mobility of small highly charged peptides (lysine, arginine, and short oligos thereof (up to nonapeptides)) in NaCl and Na₂SO₄ aqueous solutions at neutral pH and room temperature. The experimental data are taken from the literature. A bead modeling methodology that treats the electrostatics at the level of the nonlinear Poisson Boltzmann equation developed previously in our laboratory is able to account for the mobility of all peptides in NaCl, but not Na₂SO₄. The peptide mobilities in Na₂SO₄ can be accounted for by including sulfate binding in the model and this is proposed as one possible explanation for the discrepancy. Oligo arginine peptides bind more sulfate than oligo lysines and sulfate binding increases with the oligo length.