Field transfer decay and interferometry in coupled waveguides with stochastic sources

Coupled waveguides, such as those used as optical filters, switches, or couplers, are investigated in the context of coherence theory. A stochastic source is introduced to the standard coupled-mode model. Decay in the power transferred between the waveguides as a function of distance is predicted. Application of this result in the form of an interferometric spectrometer is explored.     

Quaternionic theta constants

We investigate the six quaternionic theta constants introduced by Freitag and Hermann. More precisely we investigate their restrictions to the Hermitian resp. Siegel half-space of degree 2. It turns out that these theta constants generate the graded ring of symmetric Hermitian modular forms for the principal congruence subgroup of level 1 + i over the Gaussian number field resp. of Siegel modular forms for the principal congruence subgroup of level 2 and even weight. As an application we obtain a simple construction of Igusa’s Siegel modular form of degree 2 and weight 30 with respect to the non-trivial character.     

3D atom probe assisted by femtosecond laser pulses

The 3DAP allows to image a material in 3D on a nearly atomic scale. It is based on the field evaporation occurring at the surface of a biased tip like shape specimen with an end radius of 50 nm. Surface atoms are removed one by one from the tip by means of fs laser pulses so that the physical process involved in this laser enhanced field evaporation might correspond to the very early stages of the ablation process. This technique makes possible to distinguish between different regimes of material removal such as thermal evaporation or in the case of metals or semiconductors an evaporation assisted by the rectification of the optical field at the surface. In this paper the principle of the 3DAP is presented and the underlying physics involved in the field evaporation assisted by femtosecond laser pulses is discussed.     

Preparation and Characterization of a π-Conjugated Donor–Acceptor System Containing the Strongly Electron-Accepting Tetraphenylborolyl Unit

A novel thiophene-bridged donor–acceptor system was synthesized with a carbazole as donor and a borole as acceptor unit. The borole group was successfully installed via the tin–boron exchange reaction of 1,1-dimethyl-2,3,4,5-tetraphenylstannole with 9-(5-(dibromoboryl)thiophen-2-yl)carbazole. The effect of the borole on the optoelectronic properties of the donor–acceptor system was explored by spectroscopic (UV/Vis and fluorescence spectroscopy), electrochemical (cyclic voltammetry) and theoretical (TD-DFT) methods as well as by modifying its structure. The corresponding donor–acceptor compound bearing the widely employed dimesitylboryl acceptor group was also synthesized for comparison.     

Targeted Photodynamic Therapy of Human Head and Neck Squamous Cell Carcinoma with Anti-epidermal Growth Factor Receptor Antibody Cetuximab and Photosensitizer IR700DX in the Mouse Skin-fold Window Chamber Model

Targeted photodynamic therapy (PDT) in head/neck cancer patients with a conjugate of the anti-epidermal growth factor receptor (EGFR) antibody, Cetuximab and a phthalocyanine photosensitizer IR700DX is under way, but the exact mechanisms of action are still not fully understood. In this study, the EGFR-overexpressing human head/neck OSC-19-luc2-cGFP tumor with transfected GFP gene was used in a skin-fold window chamber model in BALB/c nude mice. The uptake and localization of the conjugate in the tumor and its surrounding normal tissues were studied by an intravital confocal laser scanning microscopy with image analyses. The tumor was also irradiated with 690 nm laser light 24 h after conjugate administration. The vascular and tumor responses were examined by morphological evaluation and immunohistochemistry (IHC). The amount of conjugate in the tumor peaked at 24–48 h after injection. Image analyses of colocalization correlation parameters demonstrated a high fraction of the conjugate IR700DX colocalized in the GFP-expressing tumor cells. PDT-treated tumors showed extensive necrotic/apoptotic destruction with little vascular damage, while IHC showed no HIF-1α expression and decreased EGFR and Ki67 expression with activated caspase-3 overexpression, indicating a direct killing of tumor cells through both necrotic and apoptotic cell death.     

Reconciling Electrostatic and n→π* Orbital Contributions in Carbonyl Interactions

Interactions between carbonyl groups are prevalent in protein structures. Earlier investigations identified dominant electrostatic dipolar interactions, while others implicated lone pair n→π* orbital delocalisation. Here these observations are reconciled. A combined experimental and computational approach confirmed the dominance of electrostatic interactions in a new series of synthetic molecular balances, while also highlighting the distance-dependent observation of inductive polarisation manifested by n→π* orbital delocalisation. Computational fiSAPT energy decomposition and natural bonding orbital analyses correlated with experimental data to reveal the contexts in which short-range inductive polarisation augment electrostatic dipolar interactions. Thus, we provide a framework for reconciling the context dependency of the dominance of electrostatic interactions and the occurrence of n→π* orbital delocalisation in C=O⋅⋅⋅C=O interactions.     

App-based scaffolds for writing two-column proofs

This paper presents apps designed to assist students in understanding and developing proofs in geometric theorems. These technologies focus on triangle congruence, triangle similarity and properties of parallelograms. Focus group discussions and initial testing of the apps revealed that the apps offered a more engaging medium for learning proving and were capable of facilitating proof-writing skills in geometry.     

Analysis of and numerical schemes for a mouse population model in Hantavirus epidemics

This paper considers a non-linear system of ordinary differential equations, which arises in the study of hantavirus epidemics. The system has the property that the total population obeys the logistic equation. For this system, we use linearization and the dynamical properties of the logistic equation to analyze the dynamics of the subpopulation system. In view of the usual numerical instabilities associated with standard finite difference methods used for simulating such systems, we construct non-standard finite difference (NSFD) schemes, which preserve the dynamic properties of the system, and may therefore be used for its simulation.     

Self‐Sufficient Formaldehyde‐to‐Methanol Conversion by Organometallic Formaldehyde Dismutase Mimic

The catalytic networks of methylotrophic organisms, featuring redox enzymes for the activation of one‐carbon moieties, can serve as great inspiration in the development of novel homogeneously catalyzed pathways for the interconversion of C₁ molecules at ambient conditions. An imidazolium‐tagged arene–ruthenium complex was identified as an effective functional mimic of the bacterial formaldehyde dismutase, which provides a new and highly selective route for the conversion of formaldehyde to methanol in absence of any external reducing agents. Moreover, secondary amines are reductively methylated by the organometallic dismutase mimic in a redox self‐sufficient manner with formaldehyde acting both as carbon source and reducing agent.     

Vibrational spectra and quantum chemical calculations of 3,4-diaminobenzoic acid.

The Fourier Transform Raman and Fourier Transform infrared spectra of 3,4-diaminobenzoic acid (3,4-DABA) were recorded in the solid phase. Geometry optimizations were done without any constraint and harmonic-vibrational wave numbers and several thermodynamic parameters were calculated for the minimum energy conformer at ab initio and DFT levels invoking 6-311++G(d,p) basis set. The results were compared with the experimental values with the help of specific scaling procedures, the observed vibrational wavenumbers in FT-IR and FT-Raman spectra were analyzed and assigned to different normal modes of the molecule. Most of the modes have wavenumbers in the expected range, the error obtained was in general very low. The appropriate theoretical spectrograms for the IR and Raman spectra of the title molecule were also constructed.