Real classification of complex quadrics

Canonical forms are given for complex quadric surfaces (and conics) under real changes of variable. The basic idea is to use known results on pairs of real quadratic forms.     

Notes toward higher differential algebra

This paper is a self-contained introduction to a theory of higher differential algebra. The results were originally accumulated in sporadic attempts to forge a link between differential algebra and the study of formal groups, and one trace of that goal is included here as motivation. Primarily, however, the theory is of interest because it preserves for arbitrary rings much of the formal structure of ordinary differential algebra for Ritt algebras. Some of the results have appeared in weaker form in the literature, so it seems worthwhile to put the theory on record.     

Continuous oxygen monitoring of mammalian cell growth on space shuttle mission STS-93 with a novel radioluminescent oxygen sensor

A compact, flow-through oxygen sensor device based on luminescence quenching was used to monitor dissolved oxygen levels during mammalian cell growth on the STS-93 mission of the Columbia space shuttle. Excitation of an oxygen-sensitive ruthenium complex was provided by a radiolumin escent light source (0.9 mm in diameter, 2.5 mm long), and the intensity of the resulting luminescence was measured by a simple photodiode detector. The use of radiolum inescence for the excitation light source is a unique approach that provides many features important for long-term and remote monitoring applications. For the spaceflight experiment, human lung fibroblast cells (WI-38) were grown in hollow-fiber bioreactors. Oxygen concentration was measured in the flow path both before and after the bioreactor cartridge in order to gain information about the metabolism of the cells. The sensor was found to be nonperturbing to cell growth and withstood the challenging physical conditions of shuttle launch and landing while maintaining a stable calibration function. In addition, the sensor provided physically meaningful oxygen predictions.     

Synthesis and Evaluation of 11C-Labeled Triazolones as Probes for Imaging Fatty Acid Synthase Expression by Positron Emission Tomography

Cancer cells require lipids to fulfill energetic, proliferative, and signaling requirements. Even though these cells can take up exogenous fatty acids, the majority exhibit a dependency on de novo fatty acid synthesis. Fatty acid synthase (FASN) is the rate-limiting enzyme in this process. Expression and activity of FASN is elevated in multiple cancers, where it correlates with disease progression and poor prognosis. These observations have sparked interest in developing methods of detecting FASN expression in vivo. One promising approach is the imaging of radiolabeled molecular probes targeting FASN by positron emission tomography (PET). However, although [¹¹C]acetate uptake by prostate cancer cells correlates with FASN expression, no FASN-specific PET probes currently exist. Our aim was to synthesize and evaluate a series of small molecule triazolones based on GSK2194069, an FASN inhibitor with IC₅₀ = 7.7 ± 4.1 nM, for PET imaging of FASN expression. These triazolones were labeled with carbon-11 in good yield and excellent radiochemical purity, and binding to FASN-positive LNCaP cells was significantly higher than FASN-negative PC3 cells. Despite these promising characteristics, however, these molecules exhibited poor in vivo pharmacokinetics and were predominantly retained in lymph nodes and the hepatobiliary system. Future studies will seek to identify structural modifications that improve tumor targeting while maintaining the excretion profile of these first-generation ¹¹C-methyltriazolones.     

Hollow PtFe Alloy Nanoparticles Derived from Pt-Fe3O4 Dimers through a Silica-Protection Reduction Strategy as Efficient Oxygen Reduction Electrocatalysts

The development of efficient and stable electrocatalysts for the oxygen reduction reaction (ORR) is critical for the large-scale production of fuel cells. Platinum (Pt) nanoparticle catalysts show excellent performance for ORR, though the high cost of Pt is a limiting factor that directly impacts fuel cell production costs. Alloying Pt with other transition metals is an effective strategy to reduce Pt utilization whilst maintaining good ORR performance. In this work, novel hollow PtFe alloy catalysts were successfully synthesized by high-temperature pyrolysis of SiO₂-coated Pt-Fe₃O₄ nanoparticle dimers supported on carbon at 900 °C, followed by SiO₂ shell removal and partial dealloying of the PtFe nanoparticles formed using HF. The obtained hollow PtFe nanoparticle catalysts (denoted herein as PtFe-900) showed a 2.3-fold enhancement in ORR mass activity compared to PtFe nanoparticles synthesized without SiO₂ protection, and a remarkable 7.8-fold enhancement relative to a commercial Pt/C catalyst. Further, after 10 000 potential cycles, the ORR mass activity of PtFe-900 remained very high (90.9 % of the initial mass activity). The outstanding ORR performance of PtFe-900 can be attributed to the modification of Pt lattice and electronic structure by alloying with Fe at high temperature under the protection of the SiO₂ coating. This work guides the development of improved, highly dispersed Pt-based alloy nanoparticle catalysts for ORR and fuel cell applications.     

Defining Sets of Full Designs with Block Size Three II

A defining set of a t?(v, k, ??) design is a subcollection of its blocks which is contained in a unique t-design with the given parameters. A minimal defining set is a defining set, none of whose proper subcollections is a defining set. The spectrum of minimal defining sets of a design D is the set {|M| | M is a minimal defining set of D}. The unique simple design with parameters ${{t-\left(v, k, \begin{array}{ll}\left(\begin{array}{ll}v-t\\ k-t\end{array}\right)\end{array}\right)}}$ is said to be the full design on v elements. This paper studies the minimal defining sets of full designs when t = 2 and k = 3. The largest known minimal defining set is given. The existence of a continuous section of the spectrum comprising asymptotically 9v ²/50 values is shown. This gives a quadratic length section of continuous spectrum where only a linear section with respect to v was known before.     

On defining sets of full designs

A defining set of a t-(v,k,λ) design is a subcollection of its blocks which is contained in a unique t-design with the given parameters on a given v-set. A minimal defining set is a defining set, none of whose proper subcollections is a defining set. The spectrum of minimal defining sets of a design D is the set {|M|∣M is a minimal defining set of D}. The unique simple design with parameters is said to be the full design on v elements; it comprises all possible k-tuples on a v set. We provide two new minimal defining set constructions for full designs with block size k≥3. We then provide a generalisation of the second construction which gives defining sets for all k≥3, with minimality satisfied for k=3. This provides a significant improvement of the known spectrum for designs with block size three. We hypothesise that this generalisation produces minimal defining sets for all k≥3.