Minimal Hermite-Type Eigenbasis of the Discrete Fourier Transform

There exist many ways to build an orthonormal basis of \(\mathbb {R}^N\), consisting of the eigenvectors of the discrete Fourier transform (DFT). In this paper we show that there is only one such orthonormal eigenbasis of the DFT that is optimal in the sense of an appropriate uncertainty principle. Moreover, we show that these optimal eigenvectors of the DFT are direct analogues of the Hermite functions, that they also satisfy a three-term recurrence relation and that they converge to Hermite functions as N increases to infinity.

     

Parametric polarization pulse shaping demonstrated for optimal control of NaK

We present a routine for calculating and producing customized/parametric femtosecond laser pulses for investigating molecular processes involving the polarization. It is applied on the ionization of NaK molecules by feedback-loop optimization using the recently introduced double-pass "serial setup" that is capable of phase, amplitude, and polarization modulation. The temporal subpulse encoding uses the parameters distance, intensity, zero order spectral phase, and polarization state.     

The RATIO method for time‐resolved Laue crystallography

A RATIO method for analysis of intensity changes in time‐resolved pump–probe Laue diffraction experiments is described. The method eliminates the need for scaling the data with a wavelength curve representing the spectral distribution of the source and removes the effect of possible anisotropic absorption. It does not require relative scaling of series of frames and removes errors due to all but very short term fluctuations in the synchrotron beam.     

Diamino acid derivatives of PpIX as potential photosensitizers for photodynamic therapy of squamous cell carcinoma and prostate cancer: In vitro studies

Photodynamic therapy (PDT) is an alternative treatment modality involving light activated drugs, called photosensitizers (PSs), to treat cancer and non-cancerous conditions. The search for new compounds which might become effective PSs is the major direction for PDT development. In the present work we have studied the dark toxicity, intracellular localization and photodynamic properties of four potential, water soluble, second generation PSs – PP(Arg)₂, PP(Ser)₂Arg₂, PP(Ala)₂Arg₂, PP(Phe)₂Arg₂, all diamino acid derivatives of protoporphyrin IX. Human prostate cancer (DU-145) and squamous carcinoma (A431) cells were used as experimental model.Among investigated compounds PP(Ser)₂Arg₂ exhibited the lowest dark toxicity and the highest PDT effectiveness towards both cell lines. Fluorescence microscopy revealed the time-dependent changes in intracellular localization of the PS which were related to the phototoxicity. The results show that PP(Ser)₂Arg₂ may be a potential PS for PDT.     

Reactivity of T-Nb2O5 or H-Nb2O5 towards V2O5. Synthesis in the solid state and properties of V4Nb18O55

The IR spectrum of V₄Nb₁₈O₅₅ has been compared with the IR spectra of selected niobates of known structures to show structural relations between these compounds. This comparison shows that V₄Nb₁₈O₅₅ has crystal structure related to T-Nb₂O₅, W16Nb18O94 and Ba₂NaNb₅O₁₅. On the other hand, reaction between V₂O₅ and H-Nb₂O₅ yields a solid solution of V₂O₅ in VNb₉O₂₅. It has been proposed two models of synthesized solid solution with formulas V_1+xNb_9-xO₂₅ or V_1+xNb₉O_25+5x/2.Independently of Nb₂O₅ polymorph, used for synthesis, the metastable compound VNbO5 cannot be synthesized in the solid state below 650°C      

Cascade Mi (i = 1–5) subshell X‐ray emission at incident photon energies across the Lj (j = 1–3) subshell absorption edges of 66Dy

The total M shell and the M_k (k = ξ, αβ, γ, m) X‐ray production cross sections for ₆₆Dy have been measured at incident photon energies across its L_j (j = 1–3) subshell absorption edge energies, ranging 7.8–9.2 keV. This study aims to investigate the evolution of the probability for cascade decay of L_j subshell vacancies as the tunable incident energy ionizes progressively different ₆₆Dy L_j subshells. The experimental X‐ray production cross sections have been compared with theoretical ones calculated using the nonrelativistic Hartree–Fock–Slater (HFS) model‐based photoionization cross sections; three sets of the X‐ray emission rates, fluorescence and Coster–Kronig yield based on the nonrelativistic Hartree–Slater (NRHS) model, Dirac–Hartree–Slater (DHS) model and Dirac–Fock (DF) model; the L_j (j = 1–3) subshell to the M_i (i = 1–5) subshell vacancy transfer probabilities evaluated in the present work. Presently measured total M shell and the M_αβ X‐ray production cross sections are found to be significantly lower than the theoretical ones evaluated using physical parameters based on the relativistic Dirac–Fock/Dirac–Hartree–Slater model calculations, whereas a much better agreement is observed with respect to the NRHS model‐based calculations; however, the measured X‐ray production cross sections are still systematically lower than the NRHS values.     

Applications of the conformal transformation method in studies of composed superconducting systems

A framework for analytical studies of superconducting systems is presented and illustrated. The formalism, based on the conformal transformation of momentum space, allows one to study the effects of both the dispersion relation and the structure of the pairing interaction in two-dimensional anisotropic high-T _c superconductors. In this method, the number of employed degrees of freedom coincides with the dimension of the momentum space, which is different compared to that in the standard Van Hove scenario with a single degree of freedom. A new function, the kernel of the density of states, is defined and its relation to the standard density of states is explained. The versatility of the method is illustrated by analyzing coexistence and competition between spin-singlet and spin-triplet order parameters in superconducting systems with a tight-binding-type dispersion relation and an anisotropic pairing potential. Phase diagrams of stable superconducting states in the coordinates η (the ratio of hopping parameters) and n (the carrier concentration) are presented and discussed. Moreover, the role of attractive and repulsive on-site interactions for the stability of the s-wave order parameter is explained.     

An Efficient RuII–RhIII–RuII Polypyridyl Photocatalyst for Visible‐Light‐Driven Hydrogen Production in Aqueous Solution

The development of multicomponent molecular systems for the photocatalytic reduction of water to hydrogen has experienced considerable growth since the end of the 1970s. Recently, with the aim of improving the efficiency of the catalysis, single‐component photocatalysts have been developed in which the photosensitizer is chemically coupled to the hydrogen‐evolving catalyst in the same molecule through a bridging ligand. Until now, none of these photocatalysts has operated efficiently in pure aqueous solution: a highly desirable medium for energy‐conversion applications. Herein, we introduce a new ruthenium–rhodium polypyridyl complex as the first efficient homogeneous photocatalyst for H₂ production in water with turnover numbers of several hundred. This study also demonstrates unambiguously that the catalytic performance of such systems linked through a nonconjugated bridge is significantly improved as compared to that of a mixture of the separate components.     

HBr or not HBr? That is the question: crystal structure of 6‐hydroxy‐1,4‐diazepane‐1,4‐diium dibromide redetermined

Liu et al. [Chin. J. Struct. Chem. (1996). 15 , 371–373] reported the structure of 6‐hydroxy‐1,4‐diazepane di(hydrogen bromide), C₅H₁₂N₂O·2HBr, which was interpreted in terms of neutral diazepane and HBr molecules. We found, however, ample evidence that the formation of an organic salt, consisting of a diammonium cation and two bromide anions, is more plausible. This interpretation is also in agreement with thermogravimetric analysis and with the observed solution behaviour. The crystal structure of 6‐hydroxy‐1,4‐diazepane‐1,4‐diium dibromide, C₅H₁₄N₂O²⁺·2Br^?, measured at 142 K, crystallized in the orthorhombic space group P2₁2₁2₁. The structure displays O—H…Br and N—H…Br hydrogen bonding. Contact distances are given. A search in the Cambridge Structural Database for the singly‐bonded H—Br moiety revealed a total of 69 structures. The question, whether these structures really include HBr as neutral molecules or rather Br^? anions and a protonated substrate such as an amine, is addressed.