Detection of the hydrogen-bond stretching mode in the low-frequency Raman spectrum of catechol and catechol-D2

Low-frequency Raman spectra of catechol (1,2-dihydroxybenzene) and catechol-d₂ have been measured at 130 K. The stretching mode of the intermolecular hydrogen bond, ν_σ, has been assigned at 187 and 184 cm^?1, respectively. A short discussion of this assignment and its implications with respect to the previously reported guaiacol (2-methoxyphenol) spectra is presented.     

The effect of heat and IR radiation on the fluorescence of cellulose

The emission spectra of pure cellulose samples of various origins were monitored during several heating/cooling cycles. During heating the emission intensity decreased due to the greater probability for internal conversion at higher temperatures. Cooling resulted in an emission recovery that was nearly reversible over several heating/cooling cycles, provided that the final 0temperature was sufficiently low. The change in the relative emission yield with temperature showed two regimes, both with linear decreases but different slopes, suggesting different mechanisms for the internal conversion in these regions. Heating to temperatures higher than 160°C for filter papers and higher than 145°C for microcrystalline cellulose initiated reactions that caused changes in the emission spectra typical of thermal degradation. If the samples were heated beyond these threshold temperatures the emission recovery on cooling after the first heat treatment occurred to a much higher intensity level than that observed initially, indicating the formation of a multitude of new chromophores due to thermal reactions. Exposure of the samples to IR radiation caused a slow increase in the emission intensity for almost 600h.     

A Raman spectroscopic study of the low-frequency vibrations of o-dimethoxybenzene and its methyl deuterated analogues

The low-frequency (100–400 cm⁻¹) Raman spectra of liquid (at 300 K) and solid (at 130 K) veratrole (o-dimethoxybenzene), and its methyl deuterated analogues, have been measured. The methyl and methoxyl torsional transitions have been identified, and the corresponding rotational barriers have been determined. The interpretation of the spectra points to a conformationally mixed situation for solid veratrole, in which both planar and non-planar conformers may co-exist.     

Compact and Weakly Compact Composition Operators on BMOA

Any analytic map φ of the unit disc ${\mathbb{D}}$ into itself induces a composition operator C _φ on BMOA, mapping ${f \mapsto f \circ \varphi}$ , where BMOA is the Banach space of analytic functions ${f\colon \mathbb{D} \to \mathbb{C}}$ whose boundary values have bounded mean oscillation on the unit circle. We show that C _φ is weakly compact on BMOA precisely when it is compact on BMOA, thus solving a question initially posed by Tjani and by Bourdon, Cima and Matheson in the special case of VMOA. As a crucial step of our argument we simplify the compactness criterion due to Smith for C _φ on BMOA and show that his condition on the Nevanlinna counting function alone characterizes compactness. Additional equivalent compactness criteria are established. Furthermore, we prove the unexpected result that compactness of C _φ on VMOA implies compactness even from the Bloch space into VMOA.     

Rigidity of commutators and elementary operators on Calkin algebras

LetA=(A ₁,...,A _n ),B=(B ₁,...,B _n )εL(ℓ ^p ) ⁿ be arbitraryn-tuples of bounded linear operators on (ℓ ^p ), with 1<p<∞. The paper establishes strong rigidity properties of the corresponding elementary operators ε _a,b on the Calkin algebraC(ℓ ^p )≡L(ℓ ^p )/K(ℓ ^p ); , where quotient elements are denoted bys=S+K(ℓ ^p ) forSεL(ℓ ^p ). It is shown among other results that the kernel Ker(ε _a,b ) is a non-separable subspace ofC(ℓ ^p ) whenever ε _a,b fails to be one-one, while the quotient is non-separable whenever ε _a,b fails to be onto. These results extend earlier ones in several directions: neither of the subsets {A ₁,...,A _n }, {B ₁,...,B _n } needs to consist of commuting operators, and the results apply to other spaces apart from Hilbert spaces. Supported by the Academy of Finland, Project 32837.     

Thermoacoustically driven flame motion and heat release variation in a swirl-stabilized gas turbine burner investigated by LIF and chemiluminescence

Laser-induced fluorescence and chemiluminescence, both phase-locked to the dominant acoustic oscillation, are used to investigate phenomena related to thermoacoustic instability in a swirl-stabilized industrial scale gas turbine burner. The observed sinusoidal phase-averaged flame motion in axial (main flow) direction is analyzed using different schemes for defining the flame position. Qualitative agreement between experimental data and theoretical analysis of the observed flame motion is obtained, interpreted as originating primarily from variation of the burning velocity. The heat release variation during an acoustic cycle is determined from the sinusoidally varying total OH* chemiluminescence intensity.

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Compact and inessential perturbations of operators with closed range

The size of the perturbation class {SL(E)S has closed range}+I(E) is studied, whereE is a Banach space andI(E) stands for various classical operator ideals. For instance, it is shown for the ideal consisting of the inessential operators that the resulting perturbation class does not exhaust the class of bounded linear operators under natural structural conditions onE. It is known from a recent result of Gowers and Maurey that some conditions are needed.Partially supported by the Academy of Finland     

On the bounded compact approximation property and measures of noncompactness

The Banach spaces with the bounded compact approximation property are characterized by the completeness of measures of noncompactness. Applications to the theory of semi-Fredholm operators and to the algebraic properties of their canonical images in the Calkin algebra are discussed.     

Duality of the weak essential norm

It is established by an example that the natural quotient norms and are not comparable in general. Hence there is no uniform quantitative version of Gantmacher's duality theorem for weakly compact operators in terms of the preceding weak essential norm. Above stands for the class of weakly compact operators , where and are Banach spaces. The counterexample is based on a renorming construction related to weakly compact approximation properties that is applied to the Johnson-Lindenstrauss space .     

The essential norm of an operator is not self-dual

It is established by an example that the distance of a bounded linear operatorS from the class of compact operators on a Banach space is not always uniformly comparable with that of its adjointS′. This provides a negative solution to an old problem. It is also shown that the seminorms due to Schechter and Weis, that measure the deviation from strict singularity or strict cosingularity of an operator, are not uniformly comparable with the corresponding distance functions. Both results rely on a general construction related to certain approximation properties that are associated with closed ideals of operators.