Ekedahl–Oort and Newton strata for Shimura varieties of PEL type

We study the Ekedahl–Oort stratification for good reductions of Shimura varieties of PEL type. These generalize the Ekedahl–Oort strata defined and studied by Oort for the moduli space of principally polarized abelian varieties (the “Siegel case”). They are parameterized by certain elements $w$ in the Weyl group of the reductive group of the Shimura datum. We show that for every such $w$ the corresponding Ekedahl–Oort stratum is smooth, quasi-affine, and of dimension $\ell (w)$ (and in particular non-empty). Some of these results have previously been obtained by Moonen, Vasiu, and the second author using different methods. We determine the closure relations of the strata. We give a group-theoretical definition of minimal Ekedahl–Oort strata generalizing Oort’s definition in the Siegel case and study the question whether each Newton stratum contains a minimal Ekedahl–Oort stratum. As an interesting application we determine which Newton strata are non-empty. This criterion proves conjectures by Fargues and by Rapoport generalizing a conjecture by Manin for the Siegel case. We give a necessary criterion when a given Ekedahl–Oort stratum and a given Newton stratum meet.     

Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields

We give a definition, in the ring language, of _Zp${\mathbb{Z}}_p$ inside _Qp${\mathbb{Q}}_p$ and of _Fp[[t]]${\mathbb{F}}_p[[t]]$ inside _Fp((t))${\mathbb{F}}_p((t))$, which works uniformly for all p   and all finite field extensions of these fields, and in many other Henselian valued fields as well. The formula can be taken existential-universal in the ring language, and in fact existential in a modification of the language of Macintyre. Furthermore, we show the negative result that in the language of rings there does not exist a uniform definition by an existential formula and neither by a universal formula for the valuation rings of all the finite extensions of a given Henselian valued field. We also show that there is no existential formula of the ring language defining _Zp${\mathbb{Z}}_p$ inside _Qp${\mathbb{Q}}_p$ uniformly for all p  . For any fixed finite extension of _Qp${\mathbb{Q}}_p$, we give an existential formula and a universal formula in the ring language which define the valuation ring.     

Randomness and changes of heart rate and respiratory frequency during high altitude mountain ascent without acclimatization

The aim of this study was to detect and compare the changes in the time-frequency and fractal scaling behaviors of heart rate (HR) and respiratory frequency (Rf), recorded simultaneously during a high altitude mountain ascent. The time-frequency analysis was performed using the local cosine4 orthonormal bases of Coifman, Malvar and Meyer, whose spectrum is not redundant as those computed with the short Fourier transform. The fractal scaling behavior was obtained using the detrended fluctuation (DFA) and the wavelet leaders (WL) analysis. Results showed that the high altitude mountain ascent differently affected HR and Rf variability. Rf average values increased (p=0.0003) while HR average values did not change. The scaling variability of HR was altered during the mountain ascent, which was detected by the increasing HR short range DFA exponents with altitude (p<0.03). Rf scaling variability remained unchanged. These differences between HR and Rf alterations were also observed for the local cosine4 power law behavior since power law exponents, in absolute values, increased for HR (p<0.003) while those of Rf did not change. Furthermore, the ratio of low over the whole local spectrum energy of Rf decreased with altitude (p=0.04) in contrast to HR. In most of these HR and Rf analyses, one of the two time series was significantly modified but not both. Moreover, the Rf local cosine4 spectrum had higher entropy compared to HR (p<0.01), the difference between the Rf and the HR entropy increased (p=0.04) during the mountain ascent. In consequence, Rf had more randomness than HR and altitude increased this difference.     

Toward an objective measure for a "stream segregation" task

A procedure to estimate the relative contribution of "A" and "B" tones for a stream-segregation task is described. Listeners detected a delay in the penultimate A tone in an A-B-A-B sequence of tones. For small A-B frequency separations, for most listeners, classification models based on both the A and B tones were superior to models based on just the A tones. For large frequency separations, models based on just the A tones were superior, indicating the A and B tones were segregated. The results also revealed individual differences in the strategies adopted to complete the task.     

Introducing axial chirality into mesoionic 4,4'-bis(1,2,3-triazole) dicarbenes

Mesoionic 4,4'-bis(1,2,3-triazole-5,5'-diylidene) Rh(I) complexes having a C2 chiral 4,4'-axis were accessed from 3-alkyltriazolium salts in virtually complete de. Their structure and configurational integrity were assessed by NMR spectroscopy, X-ray crystallography, and chiral HPLC. Computational analysis of the MICs involved in the reaction suggested the formation of a highly stable and unprecedented cation-carbene intermediate species, which could be evidenced experimentally by cyclic voltammetry analysis.     

Dihydrogen generation from amine/boranes: synthesis, FT-ICR, and computational studies

A Fourier transform ion cyclotron resonance spectrometry (FT-ICR) study of the gas-phase protonation of ammonia-borane and sixteen amine/boranes R(1)R(2)R(3)N-BH(3) (including six compounds synthesized for the first time) has shown that, without exception, the protonation of amine/boranes leads to the formation of dihydrogen. The structural effects on the experimental energetic thresholds of this reaction were determined experimentally. The most likely intermediate and the observed final species (besides H(2)) are R(1)R(2)R(3)N-BH(4)(+) and R(1)R(2)R(3)N-BH(2)(+), respectively. Isotopic substitution allowed the reaction mechanism to be ascertained. Computational analyses ([MP2/6-311+G(d,p)] level) of the thermodynamic stabilities of the R(1)R(2)R(3)N-BH(3) adducts, the acidities of the proton sources required for dihydrogen formation, and the structural effects on these processes were performed. It was further found that the family of R(1)R(2)R(3)N-BH(4)(+) ions is characterized by a three-center, two-electron bond between B and a loosely bound H(2) molecule. Unexpected features of some R(1)R(2)R(3)N-BH(4)(+) ions were found. This information allowed the properties of amine/boranes most suitable for dihydrogen generation and storage to be determined.     

Synthesis of platinum(II) metallocycles using microwave-assisted heating

An efficient microwave-assisted self-assembly of dinuclear platinum metallocycles is reported. The reactions proceed to afford the products with high purity and yields within 3-4 h. We have used this methodology to synthesize a new 14.75 ? × 14.75 ? molecular square. The solid-state structure showed a perfect alignment of the squares along the c axis.     

Analytical and numerical methods for the stability analysis of linear fractional delay differential equations

In this paper, several analytical and numerical approaches are presented for the stability analysis of linear fractional-order delay differential equations. The main focus of interest is asymptotic stability, but bounded-input bounded-output (BIBO) stability is also discussed. The applicability of the Laplace transform method for stability analysis is first investigated, jointly with the corresponding characteristic equation, which is broadly used in BIBO stability analysis. Moreover, it is shown that a different characteristic equation, involving the one-parameter Mittag-Leffler function, may be obtained using the well-known method of steps, which provides a necessary condition for asymptotic stability. Stability criteria based on the Argument Principle are also obtained. The stability regions obtained using the two methods are evaluated numerically and comparison results are presented. Several key problems are highlighted.