Induction and foundation in the theory of hereditarily finite sets

The paper contains an axiomatic treatment of the intuitionistic theory of hereditarily finite sets, based on an induction axiom-schema and a finite set of single axioms. The main feature of the principle of induction used (due to Givant and Tarski) is that it incorporates Foundation. On the analogy of what is done in Arithmetic, in the axiomatic system selected the transitive closure of the membership relation is taken as a primitive notion, so as to permit an immediate adaptation of the theory to cases of restricted induction (in particular primitive recursive induction). At the end of the paper several different forms of induction, which play an important role in the development of the theory, are compared. An alternative axiomatization of the theory, which is of intrinsic interest, is also discussed.     

Metal derivatives of azoles,part VII. Pyrazolato-bridged dinuclear complexes containing either cyclopalladated or -platinated trimesitylphosphine or -arsine

Summary The halogen bridges of the dimeric, cyclometallated trimesityl-arsine and -phosphine complexes of palladium(II) and platinum(II), where M=Pd or Pt and E=P or As have been replaced with pyrazolate groups to give the corresponding and less symmetric pyrazolato-bridged complexes, where M=Pd or Pt, E=P or As, Pz=pyrazolato anion, and M=Pd, E=As, Pz=3,5-dimethylpyrazolato anion. In the case of the palladium complexes,¹H. n.m.r. clearly indicates the presence of only one isomer which is most likely to have thetrans configuration while the platinum complexes are mixtures of bothcis andtrans forms.Part VI, ref. 3c     

Analysis of Plant–Plant Interactions Reveals the Presence of Potent Antileukemic Compounds

A method to identify anticancer compounds in plants was proposed based on the hypothesis that these compounds are primarily present in plants to provide them with an ecological advantage over neighboring plants and other competitors. According to this view, identifying plants that contain compounds that inhibit or interfere with the development of other plant species may facilitate the discovery of novel anticancer agents. The method was developed and tested using Magnolia grandiflora, Gynoxys verrucosa, Picradeniopsis oppositifolia, and Hedyosmum racemosum, which are plant species known to possess compounds with cytotoxic activities. Plant extracts were screened for growth inhibitory activity, and then a thin-layer chromatography bioautography assay was conducted. This located the major antileukemic compounds 1, 2, 4, and 5 in the extracts. Once the active compounds were located, they were extracted and purified, and their structures were determined. The growth inhibitory activity of the purified compounds showed a significant correlation with their antileukemic activity. The proposed approach is rapid, inexpensive, and can easily be implemented in areas of the world with high biodiversity but with less access to advanced facilities and biological assays.     

Distinguishing between Decaffeinated and Regular Coffee by HS-SPME-GC×GC-TOFMS,Chemometrics, and Machine Learning

Coffee, one of the most popular beverages in the world, attracts consumers by its rich aroma and the stimulating effect of caffeine. Increasing consumers prefer decaffeinated coffee to regular coffee due to health concerns. There are some main decaffeination methods commonly used by commercial coffee producers for decades. However, a certain amount of the aroma precursors can be removed together with caffeine, which could cause a thin taste of decaffeinated coffee. To understand the difference between regular and decaffeinated coffee from the volatile composition point of view, headspace solid-phase microextraction two-dimensional gas chromatography time-of-flight mass spectrometry (HS-SPME-GC×GC-TOFMS) was employed to examine the headspace volatiles of eight pairs of regular and decaffeinated coffees in this study. Using the key aroma-related volatiles, decaffeinated coffee was significantly separated from regular coffee by principal component analysis (PCA). Using feature-selection tools (univariate analysis: t-test and multivariate analysis: partial least squares-discriminant analysis (PLS-DA)), a group of pyrazines was observed to be significantly different between regular coffee and decaffeinated coffee. Pyrazines were more enriched in the regular coffee, which was due to the reduction of sucrose during the decaffeination process. The reduction of pyrazines led to a lack of nutty, roasted, chocolate, earthy, and musty aroma in the decaffeinated coffee. For the non-targeted analysis, the random forest (RF) classification algorithm was used to select the most important features that could enable a distinct classification between the two coffee types. In total, 20 discriminatory features were identified. The results suggested that pyrazine-derived compounds were a strong marker for the regular coffee group whereas furan-derived compounds were a strong marker for the decaffeinated coffee samples.     

Generic robustness of spectral decompositions

We prove that given a compact n-dimensional boundaryless manifold M, n?2, there exists a residual subset R of Diff¹(M) such that if f∈R admits a spectral decomposition (i.e., the non-wandering set admits a partition into a finite number of transitive compact sets), then this spectral decomposition is robust in a generic sense (tame behavior). This implies a C¹-generic trichotomy that generalizes some aspects of a two-dimensional theorem of Mañé [Topology 17 (1978) 386-396].Lastly, Palis [Astérisque 261 (2000) 335-347] has conjectured that densely in Diff^k(M) diffeomorphisms either are hyperbolic or exhibit homoclinic bifurcations. We use the aforementioned results to prove this conjecture in a large open region of Diff¹(M).     

Qualitative and quantitative analysis of the unsaponifiable fraction of vegetable oils by using comprehensive 2D GC with dual MS/FID detection

The present investigation is focused on the development of a comprehensive two-dimensional GC (GC?×?GC) method, with dual MS/FID detection, for the qualitative and quantitative analysis of the entire unsaponifiable fraction of vegetable oils. The unsaponifiable fraction forms a minor, highly specific part of a vegetable oil, and can be used as an indicator of genuineness. The column set used consisted of a low-polarity first dimension, and a medium-polarity secondary one, both characterized by a high thermal stability. The use of dual detection enabled the attainment of both mass spectral information and relative % FID data. The complexity of the fingerprint, generated by the unsaponifiable fraction, fully justified the employment of the two-dimensional GC technology. Furthermore, two other GC?×?GC benefits contributed greatly to the attainment of promising results, namely sensitivity enhancement and the formation of group-type patterns. The method herein proposed could potentially open a new opportunity for the more in-depth knowledge of the unsaponifiable fraction of vegetable oils.