Application of NMR Spectroscopy and Imaging in Heterogeneous Biocatalysis

Heterogeneously catalyzed enzymatic glucose isomerization was considered as a model process to extend the application of nuclear magnetic resonance (NMR) and magnetic resonance imaging techniques to the studies of biocatalytic processes and heterogeneous biocatalysts. It has been demonstrated that the T ₂ times of glucose are different for its aqueous solution in the pores of an unmodified porous support and in a heterogeneous biocatalyst, comprising bacterial cells immobilized on the same support. This observation has been used to map the spatial distribution of the active component within a packed bed of biocatalyst in a model reactor. ¹³C NMR spectroscopy was applied to follow the progress of glucose isomerization catalyzed by the heterogeneous biocatalyst in a batch reactor. The utilization of proton spin decoupling and nuclear Overhauser effect was shown to be necessary to obtain high signal-to-noise ratio in the natural abundance ¹³C NMR spectra of a glucose–fructose syrup present in the packed bed of biocatalyst. The spectra thus obtained were suitable for the quantification of the glucose-to-fructose ratio achieved in the biocatalytic reaction.     

Evolutionary game theory in growing populations

Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We present here a generic stochastic model which combines the growth dynamics of the population and its internal evolution. Our model thereby accounts for the fact that both evolutionary and growth dynamics are based on individual reproduction events and hence are highly coupled and stochastic in nature. We exemplify our approach by studying the dilemma of cooperation in growing populations and show that genuinely stochastic events can ease the dilemma by leading to a transient but robust increase in cooperation.     

Negative normal restitution coefficient found in simulation of nanocluster collisions

The oblique impacts of nanoclusters are studied theoretically and by means of molecular dynamics. In simulations we explore two models--Lennard-Jones clusters and particles with covalently bonded atoms. In contrast with the case of macroscopic bodies, the standard definition of the normal restitution coefficient yields for this coefficient negative values for oblique collisions of nanoclusters. We explain this effect and propose a proper definition of the restitution coefficient which is always positive. We develop a theory of an oblique impact based on a continuum model of particles. A surprisingly good agreement between the macroscopic theory and simulations leads to the conclusion that macroscopic concepts of elasticity, bulk viscosity, and surface tension remain valid for nanoparticles of a few hundred atoms.     

Soliton propagation in tapered silicon core fibers

Numerical simulations are used to investigate soliton-like propagation in tapered silicon core optical fibers. The simulations are based on a realistic tapered structure with nanoscale core dimensions and a decreasing anomalous dispersion profile to compensate for the effects of linear and nonlinear loss. An intensity misfit parameter is used to establish the optimum taper dimensions that preserve the pulse shape while reducing temporal broadening. Soliton formation from Gaussian input pulses is also observed--further evidence of the potential for tapered silicon fibers to find use in a range of signal processing applications.     

Multilayer metal/metal-oxide diffractive structure for photonic temperature sensing

We designed and fabricated multilayer metal/metal-oxide surface relief diffractive grating structures by growing alternating Pt and SnO(x) layers. Optical interrogation at 633 nm reveals the temperature dependence of their reflection and transmission diffractive effects. This function is explored here in the context of a remote, spatially localized, photonic temperature sensing operation, achieving sensitivity of 10% per °C for the zeroth-order in the transmission mode. The experimental demonstration is found to be in good agreement with the results of rigorous coupled wave analysis of the composite metal/metal-oxide element.     

On a functional equation by Baak,Boo and Rassias

In Baak et al. (J Math Anal Appl 314(1):150–161, 2006) the authors considered the functional equation

$$\begin{aligned} r f\left( \frac{1}{r}\,\sum _{j=1}^{d}x_j\right)+ & {} \sum _{i(j)\in \{0,1\} \atop \sum _{1\le j\le d} i(j)=\ell }r f\left( \frac{1}{r}\,\sum _{j=1}^d (-1)^{i(j)}x_j\right) \\= & {} \left( {d-1\atopwithdelims ()\ell }-{d-1\atopwithdelims ()\ell -1} +1\right) \sum _{j=1}^{d} f(x_j) \end{aligned}$$

where \(d,\ell \in \mathbb {N}\), \(1<\ell <d/2\) and \(r\in \mathbb {Q}{\setminus }\{0\}\). The authors determined all odd solutions \(f:X\rightarrow Y\) for vector spaces X, Y over \(\mathbb {Q}\). In Oubbi (Can Math Bull 60:173–183, 2017) the author considered the same equation but now for arbitrary real \(r\not =0\) and real vector spaces X, Y. Generalizing similar results from (J Math Anal Appl 314(1):150–161, 2006) he additionally investigates certain stability questions for the equation above, but as for that equation itself for odd approximate solutions only. The present paper deals with the general solution of the equation and the corresponding stability inequality. In particular it is shown that under certain circumstances non-odd solutions of the equation exist.

     

Trace formulas for relative Schatten class perturbations

We derive trace formulas for a pair of self-adjoint operators $H+V$ and H under the assumption that ${(H?\mathrm{i})}^{?1}V$ is in a Schatten class. This extends the trace formulas of [8], where V alone is assumed to be in a Schatten class. Our trace formulas apply, in particular, in the setting of differential operators and are based on Taylor-like approximations of operator functions. This significantly improves non-Taylor based trace formulas of [10].     

Groups in which every subgroup of infinite rank is almost permutable

In this paper, the structure of locally finite groups of infinite rank whose subgroups of infinite rank are permutable in a subgroup of finite index is investigated.     

Partition identities and quiver representations

We present a particular connection between classical partition combinatorics and the theory of quiver representations. Specifically, we give a bijective proof of an analogue of A. L. Cauchy’s Durfee square identity to multipartitions. We then use this result to give a new proof of M. Reineke’s identity in the case of quivers \({\mathcal {Q}}\) of Dynkin type A. Our identity is stated in terms of the lacing diagrams of S. Abeasis–A. Del Fra, which parameterize orbits of the representation space of \({\mathcal {Q}}\) for a fixed dimension vector.