Dispersion properties of coupled waveguides with loss and gain: a full-vectorial analysis

Waveguide structures with a balance of loss and gain have been frequently discussed in the photonic community not only as photonic analogues of quantum-mechanical systems with parity-time (PT) symmetry (breaking), but also as components with potentially interesting technical applications. In this contribution, properties of mutually coupled photonic waveguides with loss and gain are numerically analyzed using our proprietary full-vectorial Fourier modal method. Beside the classical case of a directional coupler with a balance of loss and gain, more general waveguide coupler structures exhibiting the behaviour analogous to PT-symmetry breaking, potentially applicable for photonic switching, are analyzed, too. For applications, simultaneous mutually balanced change of both loss and gain is evidently impractical. For a directional coupler structure with loss in one channel and gain in the other channel it is shown by rigorous numerical modelling that the behaviour analogous to PT-symmetry breaking can be realized by varying gain (or loss) only. Finally, it is confirmed by rigorous numerical modelling that the exceptional point does exist also in a very high-contrast asymmetric structure of a plasmonic directional coupler with strongly localized gain in one channel.     

On orthogonal reduction to Hessenberg form with small bandwidth

Numerous algorithms in numerical linear algebra are based on the reduction of a given matrix A to a more convenient form. One of the most useful types of such reduction is the orthogonal reduction to (upper) Hessenberg form. This reduction can be computed by the Arnoldi algorithm. When A is Hermitian, the resulting upper Hessenberg matrix is tridiagonal, which is a significant computational advantage. In this paper we study necessary and sufficient conditions on A so that the orthogonal Hessenberg reduction yields a Hessenberg matrix with small bandwidth. This includes the orthogonal reduction to tridiagonal form as a special case. Orthogonality here is meant with respect to some given but unspecified inner product. While the main result is already implied by the Faber-Manteuffel theorem on short recurrences for orthogonalizing Krylov sequences (see Liesen and Strakoš, SIAM Rev 50:485–503, 2008), we consider it useful to present a new, less technical proof. Our proof utilizes the idea of a “minimal counterexample”, which is standard in combinatorial optimization, but rarely used in the context of linear algebra. The work of P. Tichy was supported by the Emmy Noether-Program of the Deutsche Forschungsgemeinschaft and by the GAAS grant IAA100300802.     

Hodge theory for elliptic complexes over unital C^*-algebras

For a unital $C^{*}$ -algebra $A$ , we prove that the cohomology groups of $A$ -elliptic complexes of pseudodifferential operators in finitely generated projective $A$ -Hilbert bundles over compact manifolds are finitely generated $A$ -modules and Banach spaces provided the images of certain extensions of the so-called associated Laplacians are closed. We also prove that under this condition, the cohomology groups are isomorphic to the kernels of the associated Laplacians. This establishes a Hodge theory for these structures.     

Fascinating interaction of the ammonium cation with [2.2.2]paracyclophane: experimental and theoretical study

By means of electrospray ionisation mass spectrometry, it was evidenced experimentally that the ammonium cation (NH₄⁺) reacts with the electroneutral [2.2.2]paracyclophane ligand (C₂₄H₂₄) to form the cationic complex [NH₄(C₂₄H₂₄)]⁺. Moreover, applying quantum chemical calculations, the most probable conformation of the proven [NH₄(C₂₄H₂₄)]⁺ complex was solved. In the complex [NH₄(C₂₄H₂₄)]⁺ having a symmetry very close to C₃, the ‘central’ cation NH₄⁺ is coordinated by three strong bifurcated intramolecular hydrogen bonds to the corresponding six carbon atoms from the three benzene rings of [2.2.2]paracyclophane via cation–π interaction. Finally, the interaction energy, E(int), of the considered complex [NH₄(C₂₄H₂₄)]⁺ was evaluated as ?625.8 kJ/mol, confirming the formation of this fascinating complex species as well. It means that the [2.2.2]paracyclophane ligand can be considered as an effective receptor for the ammonium cation in the gas phase.     

Green electrochemical sensors based on boron-doped diamond and silver amalgam for sensitive voltammetric determination of herbicide metamitron

Monatshefte für Chemie - Chemical Monthly - Novel sensitive voltammetric methods for determination of herbicide metamitron were developed using polished and mercury meniscus-modified silver...     

Glyoxal-Linked Nucleotides and DNA for Bioconjugations and Crosslinking with Arginine-Containing Peptides and Proteins

Glyoxal-linked 2’-deoxyuridine 5’-O-mono- and triphosphates were synthesized through a CuAAC click reaction of 4-azidophenylglyoxal or a Sonogashira reaction of 4-bromophenylglyoxal with 5-ethynyl-dUMP or -dUTP. The triphosphates were used as substrates for enzymatic synthesis of modified DNA probes with KOD XL DNA polymerase. The glyoxal-linked nucleotides reacted with arginine-containing peptides to form stable imizadolone-linked conjugates. This reactive glyoxal modification in DNA was used for efficient bioconjugations and crosslinking with Arg-containing peptides or proteins (e. g., histones) and was found to be more reactive than previously reported 1,3-diketone-linked DNA probes.     

Synthesis of γ-functionalized allyltrichlorosilanes and their application in the asymmetric allylation of aldehydes

Isomerically pure trans- and cis-γ-bromoallyltrichlorosilanes 4 and 5 have been synthesized and shown to react with aromatic aldehydes 1 in the presence of Lewis-basic catalysts (e.g., DMF) to produce the corresponding anti- and syn-allylbromohydrins 8 and 9, respectively, as single diastereoisomers. With BINAPO 25 as a chiral catalyst, promising enantioselectivity (?50% ee) has been attained.     

Coordination bonding in dicopper and dichromium tetrakis(μ-acetato)-diaqua complexes: Nature,strength, length,and topology

Geometry optimization, energetics, electronic structure, and topology of electron density of dicopper ( I ) and dichromium ( II ) tetrakis(μ-acetato)-diaqua complexes are studied focusing on the metal–metal interactions. The performance of broken symmetry (BS) single-determinant ab initio (Hartree–Fock, Møller–Plesset perturbation theory to the second and third orders, coupled clusters singles and doubles) and density functional theory (BLYP, B3LYP, B3LYP-D3, B2PLYP, MPW2PLYP) methods is compared to multideterminant ab initio (CASSCF, NEVPT2) methods as well as to the multipole model of charge density from a single-crystal X-ray diffraction experiment (Herich et al., Acta Cryst. 2018, B74, 681–692). In vacuo DFT geometry optimizations (improper axial water ligand orientation) are compared against the periodic ones. The singlet state is found to be energetically preferred. J coupling of ( I ) becomes underestimated for all ab initio methods used, when compared to experiment. It is concluded that the strength of the direct M─M interactions correlates closely with the J coupling magnitude at a given level of theory. The double potential well character of (II) and of the dehydrated form of (II) are considered with respect to the Cr─Cr distance. The physical effective bond order of the metal–metal interaction is small (below 0.1 e) in ( I ) and moderate (0.4 e) in ( II ). The CASSCF results overestimate the electron density of the metal–metal bond critical point by 20% and 50% in ( I ) and ( II ), respectively, when compared to the multipole model. © 2019 Wiley Periodicals, Inc.     

Comparison of tyrosinase biosensor based on carbon nanotubes with DPPH spectrophotometric assay in determination of TEAC in selected Moravian wines

Monatshefte für Chemie - Chemical Monthly - An amperometric biosensor based on carbon paste electrode coated with a thin layer of carbon nanotubes and Nafion film containing the tyrosinase...     

New Chiral and Achiral Imines and Bisimines Derived from 2‐Phenyl‐1H‐imidazole‐4‐carbaldehyde. Synthesis,Structural Studies and Complexation Stability Constants

Synthesis and properties of new imines and bisimines derived from 2‐phenyl‐1H‐imidazole‐4‐carbaldehyde and amines/diamines were studied. (2‐Phenyl‐1H‐imidazole‐4‐yl)methanol was oxidized to 2‐phenyl‐1H‐imidazole‐4‐carbaldehyde with better yield 55% by the modification of literature procedure. This aldehyde was condensed with the following achiral and chiral amines or 1,2‐diamines: ethanamine, propan‐1‐amine, butan‐1‐amine, 2‐methylpropan‐1‐amine, cyclohexanamine, (2R)‐ and (2S)‐3‐methylbutan‐2‐amine, (1R)‐ and (1S)‐1‐cyclohexylethanamine, (S)‐1‐aminopropan‐2‐ol, (S)‐1‐(2‐phenyl‐1H‐imidazol‐4‐yl)ethanamine, (S)‐1‐(2‐phenyl‐1H‐imidazol‐4‐yl)‐2‐methylpropan‐1‐amine, (S)‐1‐(2‐phenyl‐1H‐imidazol‐4‐yl)‐3‐methylbutan‐1‐amine, ethane‐1,2‐diamine, and (1R,2R)‐ and (1S,2S)‐cyclohexane‐1,2‐diamine. Sixteen condensation products, especially chiral imines and bisimines, were prepared by founded procedures in 45–99% of yields and characterized by the ¹H NMR spectroscopy in solution, mass spectrometry, and elemental analyses. The optical rotation values in the case of chiral ones were also observed. Stability constants of Cu(II) complexes of selected prepared imines/bisimines were determined.