Recasting the (Synchrosqueezed) Short-Time Fourier Transform as an Instantaneous Spectrum

In a previous work, we proposed a time-frequency analysis called instantaneous spectral analysis (ISA), which generalizes the notion of the Fourier spectrum and in which instantaneous frequency is utilized to the fullest extent. In this paper, we recast both the Fourier transform (FT) and filterbank (FB) interpretations of the short-time Fourier transform (STFT) as instantaneous spectra. We show that to recast the FB interpretation of STFT as an instantaneous spectrum with valid structure, frequency reassignment is a fundamental necessity, thus demonstrating that this IS is closely related to the synchrosqueezed STFT. This result provides a new theoretical motivation for the synchrosqueezed STFT. Finally, we illustrate through example the instantaneous spectra corresponding to the FT and FB interpretations of STFT using two closed-form examples.     

Non-classical law of the iterated logarithm behaviour for trimmed sums

Summary We study the law of the iterated logarithm for the partial sum of i.i.d. random variables when the r _n largest summands are excluded, where r _n=o(log logn). This complements earlier work in which the case log log_n=O(r_n) was considered. A law of the iterated logarithm is again seen to prevail for a wide class of distributions, but for reasons quite different from previously.Research supported in part by NSF Grant DMS-8501732     

Catalytic Hydrocyanation of Activated Terminal Alkynes

A universal, practical and scalable organocatalytic hydrocyanation manifold to provide β-substituted acrylonitriles bearing an electron-withdrawing functionality has been implemented. The catalytic manifold operates under the reactivity generation principle “a good nucleophile generates a strong base”, and it uses 1,4-diazabicyclo[2.2.2]octane (DABCO) as the catalyst, activated terminal alkynes as substrates and acetone cyanohydrin as the cyanide source. The acrylonitriles obtained as E,Z mixtures are straightforwardly resolved by simple flash chromatography delivering the pure isomers in preparative amounts.     

Measurement of the hydrodynamic radii of PEE-G dendrons by diffusion spectroscopy on a benchtop NMR spectrometer

Benchtop nuclear magnetic resonance (NMR) spectroscopy is a useful tool for the rapid determination of the self-diffusion coefficient and the hydrodynamic radius of dendrons. The self-diffusion coefficients of the first four generations of poly ethoxy ethyl glycinamide (PEE-G) dendrons are measured by diffusion-ordered spectroscopy (DOSY) on a benchtop NMR equipped with diffusion gradient coils. The hydrodynamic radii of the dendrons are calculated via the Stokes–Einstein equation. The effects of solvent and pH are determined with the hydrodynamic radius increasing with generation and decreasing upon neutralization of an acidic solution. These measurements provide valuable information for biological and pharmaceutical applications of dendrons.     

An experimental study of airfoil instability tonal noise with trailing edge serrations

This paper presents an experimental study of the effect of trailing edge serrations on airfoil instability noise. Detailed aeroacoustic measurements are presented of the noise radiated by an NACA-0012 airfoil with trailing edge serrations in a low to moderate speed flow under acoustical free field conditions. The existence of a separated boundary layer near the trailing edge of the airfoil at an angle of attack of 4.2 degree has been experimentally identified by a surface mounted hot-film arrays technique. Hot-wire results have shown that the saw-tooth surface can trigger a bypass transition and prevent the boundary layer from becoming separated. Without the separated boundary layer to act as an amplifier for the incoming Tollmien–Schlichting waves, the intensity and spectral characteristic of the radiated tonal noise can be affected depending upon the serration geometry. Particle Imaging Velocimetry (PIV) measurements of the airfoil wakes for a straight and serrated trailing edge are also reported in this paper. These measurements show that localized normal-component velocity fluctuations that are present in a small region of the wake from the laminar airfoil become weakened once serrations are introduced. Owing to the above unique characteristics of the serrated trailing edges, we are able to further investigate the mechanisms of airfoil instability tonal noise with special emphasis on the assessment of the wake and non-wake based aeroacoustic feedback models. It has been shown that the instability tonal noise generated at an angle of attack below approximately one degree could involve several complex mechanisms. On the other hand, the non-wake based aeroacoustic feedback mechanism alone is sufficient to predict all discrete tone frequencies accurately when the airfoil is at a moderate angle of attack.     

Quantitative measurements of Ge surface segregation during SiGe alloy growth

Ge segregation during the growth of Si_{1 − x}Ge_x alloys (x = 5, 10, 20, and 40%) was studied using X-ray photoelectron spectroscopy. The alloys were grown in thicknesses up to 20.0 nm at 500°C to measure quantitatively the amount of segregated surface Ge. The length of alloy needed to reach steady-state growth edge was found to decrease with increasing alloy concentration (4.8, 2.8, 2.4, and 2.0 nm, respectively). It was found that each alloy had a complete monolayer of Ge on the surface and an increasing amount of segregated Ge in the second layer (20, 55, 80, and 95%, respectively) during steady-state growth. An increase in the temperature of alloy growth (400–750°C) resulted in an increase in the leading edge of alloy growth but did not change the amount of segregated Ge during steady-state growth. We propose that film stress is responsible for the amount of Ge segregation.     

Application of multiple quench parameters for confirmation of radionuclide identity in radioanalytical quality control

Journal of Radioanalytical and Nuclear Chemistry - Robust and reliable radiochemical analysis is the key factor in the appropriate disposal and management of radioactive wastes arising from the...     

Progress toward the synthesis of piperazimycin A: exploration of the synthesis of γ-hydroxy and γ-chloropiperazic acids

Employing Hamada’s chemistry with MAOS optimization of several steps, an expedient route to key (3S,5S)- and (3R,5R)-γ-hydroxy and (3R,5S)-γ-chloropiperazic acids, was developed en route to a total synthesis of piperazimycin A.     

Precursors to [FeFe]-hydrogenase models: syntheses of Fe2(SR)2(CO)6 from CO-free iron sources

This report describes routes to iron dithiolato carbonyls that do not require preformed iron carbonyls. The reaction of FeCl 2, Zn, and Q 2S 2C n H 2 n (Q (+) = Na (+), Et 3NH (+)) under an atmosphere of CO affords Fe 2(S 2C n H 2 n )(CO) 6 ( n = 2, 3) in yields >70%. The method was employed to prepare Fe 2(S 2C 2H 4)( (13)CO) 6. Treatment of these carbonylated mixtures with tertiary phosphines, instead of Zn, gave the ferrous species Fe 3(S 2C 3H 6) 3(CO) 4(PR 3) 2, for R = Et, Bu, and Ph. Like the related complex Fe 3(SPh) 6(CO) 6, these compounds consist of a linear arrangement of three conjoined face-shared octahedral centers. Omitting the phosphine but with an excess of dithiolate, we obtained the related mixed-valence triiron species [Fe 3(S 2C n H 2 n ) 4(CO) 4] (-). The highly reducing all-ferrous species [Fe 3(S 2C n H 2 n ) 4(CO) 4] (2-) is implicated as an intermediate in this transformation. Reactive forms of iron, prepared by the method of Rieke, also combined with dithiols under a CO atmosphere to give Fe 2(S 2C n H 2 n )(CO) 6 in modest yields under mild conditions. Studies on the order of addition indicate that ferrous thiolates are formed prior to the onset of carbonylation. Crystallographic characterization demonstrated that the complexes Fe 3(S 2C 3H 6) 3(CO) 4(PEt 3) 2 and PBnPh 3[Fe 3(S 2C 3H 6) 4(CO) 4] feature high-spin ferrous and low-spin ferric as the central metal, respectively.     

Reactions of the Dirhenium(II) Complexes Re2 X 4(μ-dppm)2 (X=Cl, Br; dppm=Ph2PCH2PPh2) with Isocyanides. Part XV: A Fifth Structural Isomer of the [Re2Cl3(μ-dppm)2(CO)(CNXyl)2]+ Cation (Xyl = 2, 6-Dimethylphenyl)

The reaction of the unsymmetrical, coordinatively unsaturated dirhenium(II) complex [(XylNC)(OC)CIRe(μ-dppm)₂ReCl₂]O₃SCF₃ (dppm = Ph₂PCH₂PPh₂) with one equivalent of XylNC in CH₂Cl₂ affords a fifth structural isomer of the [Re₂Cl₃(μ-dppm)₂(CO)(CNXyl)₂] ⁺ cation; this is believed to have a CO-bridged structure of the type [(XylNC)ClRe(μ-Cl)(μ-CO)(μ-dppm)₂ReCl(CNXyl)]⁺. The latter complex reacts with a further equivalent of XylNC in the presence of Tl⁺ to form the [Re₂Cl₂(μ-dppm)₂(CO)(CNXyl)₃]²⁺ cation, which has been shown by IR spectroscopy, and by the X-ray crystallographic characterization of its neutral congener Re₂Cl₂(μ-dppm)₂(CO)(CNXyl)₃, to contain a very weak and unsymmetrical CO bridge.