On uncertainty bounds and growth estimates for fractional fourier transforms

Gelfand–Shilov spaces are spaces of entire functions defined in terms of a rate of growth in one direction and a concomitant rate of decay in an orthogonal direction. Gelfand and Shilov proved that the Fourier transform is an isomorphism among certain of these spaces. In this article we consider mapping properties of fractional Fourier transforms on Gelfand–Shilov spaces. Just as the Fourier transform corresponds to rotation through a right angle in the phase plane, fractional Fourier transforms correspond to rotations through intermediate angles. Therefore, the aim of fractional Fourier estimates is to set up a correspondence between growth properties in the complex plane versus decay properties in phase space.     

On commutative rings which are strongly prüfer

Abstract

As defined by Nicholson [Nicholson, W. K. (1977). Lifting idempotents and exchange rings. Trans. Amer. Math. Soc. 229:269–278] an element of a ring R is clean if it is the sum of a unit and an idempotent, and a subset A of R is clean if every element of A is clean. It is shown that a semiprimitive Gelfand ring R is clean if and only if Max(R) is zero-dimensional; if and only if for each M ∈ Max(R), the intersection all prime ideals contained in M is generated by a set of idempotents. We also give several equivalent conditions for clean functional rings. In fact, a functional ring R is clean if and only if the set of clean elements is closed under sum; if and only if every zero-divisor is clean; if and only if; R has a clean prime ideal.     

Synthesis,Photophysics and Redox Properties of Aza-BODIPY Dyes with Electron-Donating Groups

A series of novel aza-BODIPY dyes substituted with p-(dimethylamino)phenyl groups were synthesized and their spectral and electrochemical properties were compared. In particular, the impact of p-(Me₂N)Ph- groups on these characteristics was of consideration. For two aza-BODIPYs studied, a near-IR absorption band was observed at circa λ_abs=796 nm. Due to the pronounced intramolecular charge transfer (ICT) exerted by the presence of strongly electron-donating p-(Me₂N)Ph- substituents, the compounds studied were weakly emissive with the singlet lifetimes (τ_S) in the picosecond range. Nanosecond laser photolysis experiments of the brominated aza-BODIPYs revealed T₁→T_n absorption spanning from ca. 350 nm to ca. 550 nm with the triplet lifetimes (τ_T) ranged between 6.0 μs and 8.5 μs. The optical properties of the aza-BODIPYs studied were pH-sensitive. Upon protonation of the dimethylamino groups with trifluoroacetic acid in toluene, a stepwise disappearance of the NIR absorption band at λ_abs=790 nm was observed with the concomitant appearance of a blue-shifted absorption band at λ_abs=652 nm, which was accompanied by a prominent emission band at λ_fl=680 nm. The transformation from a non-emissive to an emissive compound is associated with the inhibition of the ICT. As estimated by CV/DPV measurements, all aza-BODIPYs studied exhibited two irreversible oxidation and two quasi-reversible reduction processes. All compounds studied exhibit extremely high photostability and thermal stability.     

Magnetic field as a means to identify initiating reaction in oxidation of organic substances with molecular oxygen

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Exact multiplicity of solutions and S-shaped bifurcation curves for the p-Laplacian perturbed Gelfand problem in one space variable

We study exact multiplicity of positive solutions and the bifurcation curve of the p-Laplacian perturbed Gelfand problem from combustion theory

     

Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions

We introduce a global wave front set suitable for the analysis of tempered ultradistributions of quasi-analytic Gelfand–Shilov type. We study the transformation properties of the wave front set and use them to give microlocal existence results for pullbacks and products. We further study quasi-analytic microlocality for classes of localization and ultradifferential operators, and prove microellipticity for differential operators with polynomial coefficients.     

Iridium(III) Complexes Bearing Pyrene‐Functionalized 1,10‐Phenanthroline Ligands as Highly Efficient Sensitizers for Triplet–Triplet Annihilation Upconversion

“Chemistry‐on‐the‐complex” synthetic methods have allowed the selective addition of 1‐ethynylpyrene appendages to the 3‐, 5‐, 3,8‐ and 5,6‐positions of Ir^III‐coordinated 1,10‐phenanthroline via Sonogashira cross‐coupling. The resulting suite of complexes has given rise to the first rationalization of their absorption and emission properties as a function of the number and position of the pyrene moieties. Strong absorption in the visible region (e.g. 3,8‐substituted Ir‐3 : λ_abs=481 nm, ?=52 400 m ^?1 cm^?1) and long‐lived triplet excited states (e.g. 5‐substituted Ir‐2 : τ_T=367.7 μs) were observed for the complexes in deaerated CH₂Cl₂. On testing the series as triplet sensitizers for triplet–triplet annihilation upconversion, those Ir^III complexes bearing pyrenyl appendages at the 3‐ and 3,8‐positions ( Ir‐1 , Ir‐3 ) were found to give optimal upconversion quantum yields (30.2 % and 31.6 % respectively).     

On the conjugation length for oligo(ethynylnaphthalene)-based molecular rods

The synthesis is described for a small series of oligomers built from (2, 3, 4 or 6) ethynyl-naphthalene repeat units and end-capped with solubilising 1,2,3-tris-dodecyloxy-benzene groups. These compounds absorb in the near-UV region and exhibit strong fluorescence in both fluid solution and a glassy matrix at 77 K. The spectral profiles are fully consistent with a structurally heterogeneous ground state becoming more planar upon excitation and with the low-temperature glass further stabilising the co-planar orientation. The absorption and fluorescence maxima move towards lower energy with increasing number of repeat units and there is a corresponding increase in the Huang-Rhys factor for the radiative process. The non-radiative rate constants also depend on molecular length and are well explained in terms of the energy-gap law. In contrast, very weak phosphorescence is observed at 77 K for which the peak maximum and lifetime remain insensitive to the number of naphthalene units. The triplet lifetimes recorded at ambient temperature are also independent of the molecular length but the triplet-triplet absorption spectra change throughout the series. These results are discussed in terms of the degree of electronic coupling between adjacent repeat units for each of the relevant excited states. During these studies it was noted that the rate of intersystem crossing to the triplet manifold is but weakly affected by heavy-atom perturbers. A non-fluorescent complex is formed between iodoethane and the molecular rod but the corresponding bimolecular process occurs at well below the diffusion-controlled limit. This behaviour is considered in terms of spin-orbit coupling between the excited states and takes account of the differing conjugation lengths.