Cotangent cohomology of Stanley-Reisner rings

Simplicial complexes X provide commutative rings A(X) via the Stanley- Reisner construction. We calculated the cotangent cohomology, i.e., T¹ and T² of A(X) in terms of X. These modules provide information about the deformation theory of the algebro geometric objects assigned to X.     

Torsion of differentials on toric varieties

We introduce an invariant for semigroups with cancellation property. When the semigroup equals the set of lattice points in a rational, polyhedral cone, then this invariant describes the torsion of the differential sheaf on the associated toric variety. Finally, as an example, we present the case of two-dimensional cones (corresponding to two-dimensional cyclic quotient singularities).     

Using Inquiry to Improve Pedagogy through K‐12/University Partnerships

This article focuses on the impact a collaborative project between university graduate fellows and K‐12 classroom teachers had on improved pedagogy in the classroom and in the future at the university. Nine teams participated in a yearlong professional development project to improve pedagogy and communication skills of the participants. This study shows that the participants, the fellows and the K‐12 teacher partners, made changes in planning, implementation, and even motivation for using inquiry‐based methods in their classroom. External observations of the teams further support the individuals' claims of improved pedagogy using inquiry and impact on student conceptual understanding. The Horizon Classroom Observation instrument was used for these observations. The teams showed an overall increase in scores, as well as overall effective and exemplarily implementation of their planning. The program design, the implementation, and the results of this three‐year study will be elaborated in this article.     

Harmonic and intermodulation distortion modeling in IM-DD multi-band radio over fiber links exploiting injection locked lasers

A comprehensive numerical tool has been developed for the evaluation of the performances of Radio over Fiber (RoF) links intended for wireless signal distribution.At the transmitter end an appropriate set of rate equations allows to model the optical source as a solitary laser or as an appropriately injection locked laser. The optical channel is modeled putting into account the combined effect of fiber dispersion, laser source non ideal performances (e.g. non-linear effects, frequency chirp), and quadratic detection of the receiving photodiode. The simulation model developed can be a useful tool at the design stage allowing a preliminary evaluation of the characteristics of real RoF links.     

Study of the spectrum of cherenkov light

It is pessible to study experimentally Cherenkov light spectra in a liquid scintillation spectrometer with colour filters. Cherenkov light spectra of⁶⁰Co,¹⁹⁸Au,¹¹⁵Cd,¹⁴³Ce,¹⁴⁰La,³²P,⁸⁶Rb,⁷⁶As,⁴²K and an external standard were studied in a Packard 3375 type liquid scintillation spectrometer, using 11 various Kodak Wratten filters. The absorption maxima of the filters ware in the 410–796 nm interval.     

Momentum-resolved bremsstrahlung isochromat spectroscopy of silver surfaces

Angle-resolved bremsstrahlung isochromat spectra of the Ag(100), Ag(110) and Ag(111) surfaces have been measured. Our work extends and complements several earlier investigations of other authors. The data are summarized in the form of final state dispersionsE(k ). Comparison is made to the available theoretical and experimental information. The results for the bulk as well as for the surface-specific features are in excellent to reasonable agreement among each others and with recent calculations.     

Application of solid phase peptide synthesis to engineering PEO–peptide block copolymers for drug delivery

This work describes a simple, versatile solid-phase peptide-synthesis (SPPS) method for preparing micelle-forming poly(ethylene oxide)-block-peptide block copolymers for drug delivery. To demonstrate its utility, this SPPS method was used to construct two series of micelle-forming block copolymers (one of constant core-composition and variable length; the other of constant core length and variable composition). The block copolymers were then used to study in detail the effect of size and composition on micellization. The various block copolymers were prepared by a combination of SPPS for the peptide block, followed by solution–phase conjugation of the peptide block with a proprionic acid derivative of poly(ethylene oxide) (PEO) to form the PEO-b-peptide block copolymer. The composition of each block component was characterized by mass spectrometry (MALDI and ES-MS). Block copolymer compositions were characterized by ¹H NMR. All the block copolymers were found to form micelles as judged by transmission electron microscopy (TEM) and light scattering analysis. To demonstrate their potential as drug delivery systems, micelles prepared from one member of the PEO-b-peptide block copolymer series were physically loaded with the anticancer drug doxorubicin (DOX). Micelle static and dynamic stability were found to correlate strongly with micelle core length. In contrast, these same micellization properties appear to be a complex function of core composition, and no clear trends could be identified from among the set of compositionally varying, fixed length block copolymer micelles. We conclude that SPPS can be used to construct biocompatible block copolymers with well-defined core lengths and compositions, which in turn can be used to study and to tailor the behavior of block copolymer micelles.     

Controlled Double-Bond Migration in Palladium-Catalyzed Intramolecular Arylation of Enamidines

Palladium-catalyzed intramolecular cyclization of N-(N'-tert-butylformimidoyl)-6-[2-(2-iodophenyl)ethyl]-1,2,3,4-tetrahydropyridine (1a) and N-(N'-tert-butylformimidoyl)-6-[3-(2-iodophenyl)propyl]-1,2,3,4-tetrahydropyridine (1b) respectively results in formation of spiro compounds 1'-(N-tert-butylformimidoyl)-3',4'-dihydrospiro[indan-1,2'(1'H)-pyridine] (4a), 1'-(N-tert-butylformimidoyl)-1',6'-dihydrospiro[indan-1,2'(3'H)-pyridine] (5a), and 1'-(N-tert-butylformimidoyl)-5',6'-dihydrospiro[indan-1,2'(1'H)-pyridine] (6a) and 1'-(N-tert-butylformimidoyl)-3,3',4,4'-tetrahydrospiro[naphthalene-1(2H),2'(1'H)-pyridine] (4b), 1'-(N-tert-butylformimidoyl)-1',3,4,6'-tetrahydrospiro[naphthalene-1(2H),2'(3'H)-pyridine] (5b), and 1'-(N-tert-butylformimidoyl)-3,4,5',6'-tetrahydrospiro[naphthalene-1(2H),2'(1'H)-pyridine] (6b). The double-bond migration process can be controlled, and any of the three double-bond isomers can be prepared by employing proper ligands. A combination of BINAP and the amidine function was required to obtain the isomers 5a and 5b with the double bond in the homoallylic position relative to the aryl group. An electrospray ionization mass spectrometric study was conducted to support suggested reaction intermediates.