Mode filters and energy conservation

The discrete form of the mode filtering problem is considered. The relevant equations constitute a linear inverse problem. Solutions to problems of this type are subject to a well-known trade-off between resolution and precision. But unlike the typical linear inverse problem, the correctly formulated mode filtering problem is subject to an energy conservation constraint. This letter focuses on the importance of satisfying, approximately at least, the energy conservation constraint when mode filtering is performed.     

Material transport in dip-pen nanolithography

Dip-pen na.nolithography （DPN） is a useful method for directly printing materials on surfaces with sub-50nm resolution. Because it, involves the physical transport of materials from a scanning probe tip to a surface and the subsequent chemical interaction of that material with the surface, there are many factors to consider when attempting to understand DPN. In this review, we overview the physical and chemical processes that are known to play a role in DPN, Through a detailed review of the literature, we classify inks into three general categories based on their transport properties, and highlight the myriad ways that. DPN can be used to perform chemistry at the tip of a scanning probe.     

Structural Correlations in High-Spin Complexes of [Fe{HC(3,5-Me2pz)3}2]2+: Solid State Structure of [Fe{HC(3,5-Me2pz)3}2][Fe2OCl6]

Abstract  The cation in the solid state structure of [Fe{HC(3,5-Me₂pz)₃}₂][Fe₂OCl₆] (pz = pyrazolyl ring) contains an octahedral iron(II) center with an average Fe–N bond distance of 2.17 Å, indicating that the iron(II) is in the high-spin form. While M–N bond distances of this length with κ³-[HC(3,5-Me₂pz)₃] ligands generally cause tilting of pz to open up the “bite” angle, in this structure the average tilting angle is only 3.1°, a much lower value than observed in earlier structures of this same cation paired with different anions. The crystals are monoclinic, space group P2₁/n, with a = 11.1671(12) Å, b = 10.8091(11) Å, c = 17.4385(17) Å, α = γ = 90°, β = 95.685(2)°, and Z = 2. Graphical Abstract  The cation in the solid state structure of [Fe{HC(3,5-Me₂pz)₃}₂][Fe₂OCl₆] (pz = pyrazolyl ring) contains an octahedral iron(II) center in the high-spin form with unusual orientations of the pyrazolyl rings.      

Synthesis and characterization of a biphenyl perfluorocyclobutyl (BP‐PFCB) polyethylene glycol (PEG) blend compatibilizer

Polyethylene glycol (PEG) end‐capped trifluorovinyl ether (TFVE) telechelomer was synthesized in one step via esterification of 4‐(trifluorovinyloxy) benzoic acid. The new telechelomer was characterized by attenuated total reflectance Fourier transform infrared (ATR‐FTIR), elemental analysis, and by ¹⁹F and ¹H nuclear magnetic resonance (NMR) spectroscopy. The telechelomer and 4,4′‐bis(4‐trifluorovinyloxy)biphenyl (BPVE) were thermally copolymerized via step‐growth [2 + 2] cycloaddition at 160°C. The polymerization afforded PEG enchained biphenyl perfluorocyclobutyl (BP‐PFCB) copolymers that are solution processable and film forming. These copolymers were characterized by ATR‐FTIR, ¹⁹F NMR, and ¹H NMR. Gel permeation chromatography (GPC) gave number‐average molecular weight (M_n) ranging 11,000 to 12,000. Compatibilization of PEG and a commercial polymer BP‐PFCB was achieved utilizing the new PEG BP‐PFCB copolymer, 3‐co2‐4 . It was found that 5 wt% of 3 ‐ co2 ‐ 4 was ideal to reduce interfacial tension by scanning electron microscope (SEM). In addition, phase homogeneity was studied by differential scanning calorimetry (DSC). Copyright © 2016 John Wiley & Sons, Ltd.     

A canonical dilation of the Schrödinger equation

In this paper we shall re-visit the well-known Schrödinger equation of quantum mechanics. However, this shall be realized as a marginal dynamics of a more general, underlying stochastic counting process in a complex Minkowski space. One of the interesting things about this formalism is that its derivation has very deep roots in a new understanding of the differential calculus of time. This Minkowski-Hilbert representation of quantum dynamics is called the Belavkin formalism; a beautiful, but not well understood theory of mathematical physics that understands that both deterministic and stochastic dynamics may be formally represented by a counting process in a second-quantized Minkowski space. The Minkowski space arises as a canonical quantization of the clock, and this is derived naturally from the matrix-algebra representation [1, 2] of the Newton-Leibniz differential time increment, dt. And so the unitary dynamics of a quantum object, described by the Schrödinger equation, may be obtained as the expectation of a counting process of object-clock interactions.     

Bone tissue and porous media: common features and differences studied by NMR relaxation

Despite significant differences between bone tissues and other porous media such as oilfield rocks, there are common features as well as differences in the response of NMR relaxation measurements to the internal structures of the materials. Internal surfaces contribute to both transverse (T2) and longitudinal (T1) relaxation of pore fluids, and in both cases the effects depend on, among other things, local surface-to-volume ratio (S/V). In both cases variations in local S/V can lead to distributions of relaxation times, sometimes over decades. As in rocks, it is useful to take bone data under different conditions of cleaning, saturation, and desaturation. T1 and T2 distributions are computed using UPEN. In trabecular bone it is easy to see differences in dimensions of intertrabecular spaces in samples that have been de-fatted and saturated with water, with longer T1 and T2 for larger pores. Both T1 and T2 distributions for these water-saturated samples are bimodal, separating or partly separating inter- and intratrabecular water. The T1 peak times have a ratio of from 10 to 30, depending on pore size, but for the smaller separations the distributions may not have deep minima. The T2 peak times have ratios of over 1000, with intratrabecular water represented by large peaks at a fraction of a ms, which we can observe only by single spin echoes. CPMG data show peaks at about a second, tapering down to small amplitudes by a ms. In all samples the free induction decay (FID) from an inversion-recovery (IR) T1 measurement shows an approximately Gaussian (solid-like) component, exp[-1/2 (T/TGC), with TGC approximately 11.7+/-0.7 micros (GC for "Gaussian Component"), and a liquid-like component (LLC) with initially simple-exponential decay at the rate-average time T(2-FID) for the first 100 micros. Averaging and smoothing procedures are adopted to derive T(2-FID) as a function of IR time and to get T1 distributions for both the GC and the LLC. It appears that contact with the GC, which is presumed to be 1H on collagen, leads to the T2 reduction of at least part of the LLC, which is presumed to be water. Progressive drying of the cleaned and water-saturated samples confirms that the long T1 and T2 components were in the large intertrabecular spaces, since the corresponding peaks are lost. Further drying leads to further shortening of T2 for the remaining water but eventually leads to lengthening of T1 for both the collagen and the water. After the intertrabecular water is lost by drying, T1 is the same for GC and LLC. T(2-FID) is found to be roughly 320/alpha micros, where alpha is the ratio of the extrapolated GC to LLC, appearing to indicate a time tau of about 320 micros for 1H transverse magnetization in GC to exchange with that of LLC. This holds for all samples and under all conditions investigated. The role of the collagen in relaxation is confirmed by treatment to remove the mineral component, observing that the GC remains and has the same TGC and has the same effect on the relaxation times of the associated water. Measurements on cortical bone show the same collagen-related effects but do not have the long T1 and T2 components.     

NMR spectral quantitation by principal component analysis. III. A generalized procedure for determination of lineshape variations

We present a general procedure for automatic quantitation of a series of spectral peaks based on principal component analysis (PCA). PCA has been previously used for spectral quantitation of a single resonant peak of constant shape but variable amplitude. Here we extend this procedure to estimate all of the peak parameters: amplitude, position (frequency), phase and linewidth. The procedure consists of a series of iterative steps in which the estimates of position and phase from one stage of iteration are used to correct the spectra prior to the next stage. The process is convergent to a stable result, typically in less than 5 iterations. If desired, remaining linewidth variations can then be corrected. Correction of (typically) unwanted variations of these types is important not only for direct peak quantitation, but also as a preprocessing step for spectral data prior to application of pattern recognition/classification techniques. The procedure is demonstrated on simulated data and on a set of 992 (31)P NMR in vivo spectra taken from a kinetic study of rat muscle energetics. The proposed procedure is robust, makes very limited assumptions about the lineshape, and performs well with data of low signal-to-noise ratio.     

Spectral Changes Due to Performance Environment in Singers, Nonsingers, and Actors

From postrecording interviews of professional singers, it was hypothesized that recording environments, i.e., sound-treated environment versus an auditorium, may induce different vocal behaviors. To test this hypothesis, three groups consisting of nonsingers, singers, and actors were recorded in two different recording environments: a sound-treated booth (IAC) and an auditorium (AUD). Three recordings were obtained from each participant: recording one (IAC) and two (AUD1) required the participants to read in a normal voice; recording three (AUD2) required participants to pretend that they were "performing" before a full house. Results indicated that only the singers and the actors exhibited significant spectral and/or frequency/duration differences from one recording environment to another, with the most dramatic differences exhibited by the singers. It was concluded that the environment in which we record experimental samples from professional voice users, especially singers, should be considered as a variable that can affect results.     

A rapid method for determining recent sunscreen use in field studies

The role of sunscreens in preventing skin cancer and melanoma is the focus of ongoing research. Currently, there is no objective measure which can be used in field studies to determine whether a person has applied sunscreen to their skin, and researchers must use indirect assessments such as questionnaires. We sought to develop a rapid, non-invasive method for identifying sunscreen on the skin for use in epidemiological studies. Our basic method is to swab the skin, elute any residues which have been adsorbed onto the swab by rinsing in ethanol, and submit the eluted washings for spectrophotometric analysis. In a controlled study, we applied 0.1 ml of sunscreen to a 50 cm(2) grid on both forearms of 21 volunteers. Each forearm was allocated one of 10 different sunscreen brands. The skin was swabbed after intervals of 20 min, 1 h, 2 h and 4 h. In a field study conducted among 12 children aged 2-4 years attending a child care centre, sunscreen was applied to the faces of half the children. Swabs were then taken from the face and back of all children without knowledge of sunscreen status. In the controlled study, sunscreen was clearly detectable up to 2 h after application for all brands containing organic sunscreen, and marginally detectable at 4 h. In the field study, this method correctly identified all children with and without sunscreen. We conclude that spectrophotometric analysis of skin swabs can reliably detect the presence of sunscreen on the skin for up to 2 h after application.