Poisson transform for the Heisenberg group and eigenfunctions of the sublaplacian

We define an analogue of Poisson transform on the Heisenberg group and use it to characterise joint eigenfunctions of the sublaplacian and T=i∂_t in terms of certain analytic functionals.     

miR-27 regulates mitochondrial networks by directly targeting the mitochondrial fission factor

Mitochondrial morphology is dynamically regulated by forming small, fragmented units or interconnected networks, and this is a pivotal process that is used to maintain mitochondrial homeostasis. Although dysregulation of mitochondrial dynamics is related to the pathogenesis of several human diseases, its molecular mechanism is not fully elucidated. In this study, we demonstrate the potential role of miR-27 in the regulation of mitochondrial dynamics. Mitochondrial fission factor (MFF) mRNA is a direct target of miR-27, whose ectopic expression decreases MFF expression through binding to its 3′-untranslated region. Expression of miR-27 results in the elongation of mitochondria as well as an increased mitochondrial membrane potential and mitochondrial ATP level. Our results suggest that miR-27 is a novel regulator affecting morphological mitochondrial changes by targeting MFF.     

Engineered C–N Lyase: Enantioselective Synthesis of Chiral Synthons for Artificial Dipeptide Sweeteners

Aspartic acid derivatives with branched N-alkyl or N-arylalkyl substituents are valuable precursors to artificial dipeptide sweeteners such as neotame and advantame. The development of a biocatalyst to synthesize these compounds in a single asymmetric step is an as yet unmet challenge. Reported here is an enantioselective biocatalytic synthesis of various difficult N-substituted aspartic acids, including N-(3,3-dimethylbutyl)-l -aspartic acid and N-[3-(3-hydroxy-4-methoxyphenyl)propyl]-l -aspartic acid, precursors to neotame and advantame, respectively, using an engineered variant of ethylenediamine-N,N′-disuccinic acid (EDDS) lyase from Chelativorans sp. BNC1. This engineered C–N lyase (mutant D290M/Y320M) displayed a remarkable 1140-fold increase in activity for the selective hydroamination of fumarate compared to that of the wild-type enzyme. These results present new opportunities to develop practical multienzymatic processes for the more sustainable and step-economic synthesis of an important class of food additives.     

Enantiocomplementary Epoxidation Reactions Catalyzed by an Engineered Cofactor-Independent Non-natural Peroxygenase

Peroxygenases are heme-dependent enzymes that use peroxide-borne oxygen to catalyze a wide range of oxyfunctionalization reactions. Herein, we report the engineering of an unusual cofactor-independent peroxygenase based on a promiscuous tautomerase that accepts different hydroperoxides (t-BuOOH and H₂O₂) to accomplish enantiocomplementary epoxidations of various α,β-unsaturated aldehydes (citral and substituted cinnamaldehydes), providing access to both enantiomers of the corresponding α,β-epoxy-aldehydes. High conversions (up to 98 %), high enantioselectivity (up to 98 % ee), and good product yields (50–80 %) were achieved. The reactions likely proceed via a reactive enzyme-bound iminium ion intermediate, allowing tweaking of the enzyme's activity and selectivity by protein engineering. Our results underscore the potential of catalytic promiscuity for the engineering of new cofactor-independent oxidative enzymes.     

A multiplier theorem for the sublaplacian on the Heisenberg group

A multiplier theorem for the sublaplacian on the Heisenberg group is proved using Littlewood-Paley-Stein theory ofg-functions.     

Oscillating multipliers for some eigenfunction expansions

Let P be a non-negative, self-adjoint differential operator of degree d on ℝⁿ. Assume that the associated Bochner-Riesz kernel s _R ^δ satisfies the estimate, |s _R ^δ (x, y)| ≤ C R^n/d(1+R^1/d|x - y|^-αδ+β)for some fixed constants a>0 and β. We study L^p boundedness of operators of the form m(P), m coming from the symbol class S _p ^−α . We prove that m(P) is bounded on L^P if . We also study multipliers associated to the Hermite operator H on ℝⁿ and the special Hermite operator L on ℂⁿ given by the symbols . As a special case we obtain L^p boundedness of solutions to the Wave equation associated to H and L.     

A parametric study of negative feedback Nd:YAG laser

The output pulse parameters of a mode-locked Nd:YAG laser with a passive negative feedback element were studied experimentally. The pulse evolution within the train was experimentally recorded using a modified second harmonic generation autocorrelator. By comparing the laser operation with and without an acousto-optic modulator, we found that with the later there is a significant increase in the mode locking probability and the pulse acquires a temporally Gaussian symmetric pulse shape. Further with the active modulator there is a relaxation in alignment tolerances and increase in the range of permissible dye concentrations for stable mode locking. It was also observed that the pulse width of the negative feedback laser depends on the saturation intensity of the mode locking dye and reduces for a dye with higher saturation intensity. The pulse width was also found to reduce linearly as the initial transmission of the dye is reduced.     

Hardy's inequalities for Hermite and Laguerre expansions

Hardy's inequalities are proved for higher-dimensional Hermite and special Hermite expansions of functions in Hardy spaces. Inequalities for multiple Laguerre expansions are also deduced.

     

Riesz transform and Riesz potentials for Dunkl transform

Analogues of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weight functions that are invariant under a reflection group. The L^p$L^p$ boundedness of these operators is established in certain cases.     

An Uncertainty Principle for Eigenfunction Expansions

In this paper, we extend a theorem of Hardy’s on Fourier transform pairs to: (a) a noncompact-type Riemannian symmetric space of rank one, with respect to the eigenfunction expansion of the invariant Laplacian; (b) a compact Riemannian manifold with respect to the eigenfunction expansion of a positive elliptic operator; and (c) Rⁿ with respect to Hermite and Laguerre expansions.