Improving signal-to-noise ratio for the forensic analysis of glass using micro X-ray fluorescence spectrometry

Micro X-ray fluorescence spectrometry (μXRF) is a standard technique used for the elemental analysis of glass fragments in forensic casework. The glass specimens encountered in casework are usually small (<1 mm), thin fragments that are partially transparent to the exciting X-ray beam. In addition to providing fluorescence from the small glass fragments, the primary beam X-rays can scatter within the chamber and provide noise in the measurements. To reduce scatter from the sample stage, the fragments are typically mounted on a thin plastic film and raised on an XRF sample cup (≤3 cm in height). However, at these heights, there may still be significant scatter from the sample stage, which adversely affects the signal-to-noise ratio (SNR) and the limit of detection (LOD). A plastic mount was designed and 3D-printed in-house to allow fragments to be raised as high as possible from the sample stage, thereby minimizing stage scatter. Most elements detected in glass showed an improvement in the SNR when using the 3D-printed mount for analyses. The greatest improvement (>30%) was observed for lower atomic number elements (Na and Mg) and higher atomic number elements (Sr and Zr). Another simple method to improve SNR is the use of primary beam filters; when using primary beam filters during analyses, elements with characteristic lines in the high-energy range (Rb, Sr, and Zr) showed the greatest improvement (>70%) in SNR. The impact of both strategies for the improvement of SNR is presented here.     

Heralded generation of ultrafast single photons in pure quantum States

We present an experimental demonstration of heralded single photons prepared in pure quantum states from a parametric down-conversion source. It is shown that, through controlling the modal structure of the photon pair emission, one can generate pairs in factorable states and thence eliminate the need for spectral filters in multiple-source interference schemes. Indistinguishable heralded photons were generated in two independent spectrally engineered sources and Hong-Ou-Mandel interference observed between them without spectral filters. The measured visibility of 94.4% sets a minimum bound on the mean photon purity.     

Tunability of the multiple-bandpass response of cascaded single-source and continuous-sample microwave photonic filters

We report a theoretical and experimental investigation on the structure and tuning capabilities of cascaded associations of microwave photonic filters composed of a single-source incoherent filter and a continuous-sample filter based on periodically-sliced broadband sources that undergo dispersion after being modulated. We derive the condition that guarantees both incoherent operation and cascading of the radio-frequency responses. This condition implies a lower bound for the ratio between resonance bandwidth (Δf) of the continuous-sample filter and the free spectral range (FSR) of the single-source filter, thus showing the possibility of cascading filters in two complementary regimes, Δf/FSR < 1 and >1. The tunability of the cascaded responses is also explored in a series of proof-of-concept experiments, where a static response of a single-tap, incoherent loop filter is reconfigured by use of a Solc filter. In particular, it is demonstrated a reconfigurable single and dual-bandpass cascaded response, which can be further modified by changes in dispersion, spectral period of the slicing filter, central wavelength or spectral width of the broadband source, and apodization of the resonance. The results are compared with the predictions of the Gaussian model for the degradation of resonances in continuous-sample filters due to second-order dispersion.     

Transmission of microwaves through magnetoactive plasma

The possibility of transmission of microwaves through the plasma layer with an electron concentration of more than critical value is considered. The problem is solved by consideration of the interaction of a microwave with the plane layer of magnetoactive plasma. The problem is formulated by such a way as to obtain the estimation of the greatest lower bound of microwave transmission coefficient through the plasma layer. The results of numerical parametric investigations are applied for the transparency conditions of the shock wave plasma in space communication. The possibility of stable (without interruptions) microwave communication through the shock wave plasma is demonstrated     

Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof

In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming （ADP） algorithm. Via the system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then the novel optimal tracking control method is proposed. It is shown that for the iterative ADP algorithm with finite approximation error, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some convergence conditions. Two examples are given to demonstrate the validity of the proposed optimal tracking control scheme for chaotic systems.     

An improved transmitting multi-layer thin-film filter

The angular resolutions of the phase-shifted Rugate thin-film filters, the ultra-narrow bandpass filters, and a cutoff filter-combination device are discussed, and the electric field distributions of the filters are compared. The results show that the three transmitting multi-layer thin-film filters can realize the same angular resolution, but the electric field in the cutoff filter-combination device is the lowest. Because a lower electric-field distribution corresponds to a higher laser-induced damage threshold of the thin films, the cutoff filter-combination device may replace the traditional spatial filters in high power laser systems.     

Metal-based rugate filters with strong visible and near-infrared reflectivity

Metallic rugate filters are theoretically investigated for the first time. Our model builds on randomly dispersed metallic nanorod arrays with sinusoidally varying porosities along the film thickness. It was found that metallic rugate filters can display strong optical response in the visible and near-infrared regions for both TE and TM polarizations and for a wide range of incident angles. Moreover, the optical features of a metallic rugate filter can be fine tuned by adjusting its structural features. Interestingly, multiple-peak rugate filters can be conveniently achieved by combining different periodicities in one rugate structure. The interesting optical behaviors of the novel metal-based reflectors, combined with the many desirable properties of metals (e.g. electric, thermal, magnetic, mechanical, and chemical properties) are bound to lead to various multi-functional optical devices.     

Notes on Joint Measurability of Quantum Observables

For sharp quantum observables the following facts hold: (i) if we have a collection of sharp observables and each pair of them is jointly measurable, then they are jointly measurable all together; (ii) if two sharp observables are jointly measurable, then their joint observable is unique and it gives the greatest lower bound for the effects corresponding to the observables; (iii) if we have two sharp observables and their every possible two outcome partitionings are jointly measurable, then the observables themselves are jointly measurable. We show that, in general, these properties do not hold. Also some possible candidates which would accompany joint measurability and generalize these apparently useful properties are discussed.     

逼近积分点数下限的五阶容积卡尔曼滤波定轨算法

为了在保持滤波定轨精度不变的条件下提高定轨计算的实时性,提出一种新的逼近积分点个数下限的五阶容积卡尔曼滤波定轨算法.首先,采用一种数值容积准则对非线性函数的高斯加权积分进行近似,该准则所需的积分点个数仅比五阶代数精度容积准则积分点个数的理论下限多一个积分点,并在贝叶斯滤波算法框架下推导出本文算法的更新步骤.然后,给出实时定轨所需的状态方程和量测方程,在状态方程中考虑了J2项引力摄动和大气阻力摄动,在量测方程中利用坐标系转换推导了轨道状态与测量元素之间的非线性关系.仿真实验结果表明,本文所提算法在定轨精度方面与已有的五阶滤波算法相当,但所需的积分点个数最少,计算实时性最高,从而验证了本文算法的有效性.     

On estimates for short wave stability and long wave instability in three-layer Hele-Shaw flows

We consider the linear stability of three-layer Hele-Shaw flows with each layer having constant viscosity and viscosity increasing in the direction of a basic uniform flow. While the upper bound results on the growth rate of long waves are well known from our earlier works, lower bound results on the growth rate of short stable waves are not known to date. In this paper, we obtain such a lower bound. In particular, we show the following results: (i) the lower bound for stable short waves is also a lower bound for all stable waves, and the exact dispersion curve for the most stable eigenvalue intersects the dispersion curve based on the lower bound at a wavenumber where the most stable eigenvalue is zero; (ii) the upper bound for unstable long waves is also an upper bound for all unstable waves, and the exact dispersion curve for the most unstable eigenvalue intersects the dispersion curve based on the upper bound at a wavenumber where the most unstable eigenvalue is zero. Numerical results are provided which support these findings.     

Design of Narrowband Optical Filters Using Binary Number Sequence Photonic Crystals

A theory to design narrow band optical filters by using a new photonic crystal structure is presented. This new photonic crystal structure is composed of low index layers and high index layers arranged in mod. 4 up and down binary number sequence. The new structure exhibits narrow transmission peaks in the forbidden frequency gap region with high optical transmission (greater than 99.98%) at C.W.D.M. (Coarse Wavelength Division Multiplexing) center wavelengths. The proposed filters use only 8 layers. These new binary number sequence photonic crystal narrowband optical filters are much smaller in size, lower in cost and easier to fabricate as compared to narrowband photonic crystal optical filters based on defect Fractal Cantor multilayers, suggested recently by a group of researchers.     

Bounds to the wave-vector dependent susceptibility of the ising model

It is shown that rigorous upper and lower bounds to the wave-vector dependent susceptibility of the Ising Model are obtained either when an upper bound to the spin pair correlation function and a lower bound to the susceptibility at zero wave-vector are given, or when a lower bound to the former and an upper bound to the latter are given. An example of the numerical computation of the bounds is presented for the Ising model on the sc lattice.     

Bound States in the continuum in photonics

With examples of two parallel dielectric gratings and two arrays of thin parallel dielectric cylinders, it is shown that the interaction between trapped electromagnetic modes can lead to scattering resonances with practically zero width. Such resonances are the bound states in the radiation continuum first discovered in quantum systems by von Neumann and Wigner. Potential applications of such photonic systems include: large amplification of electromagnetic fields within photonic structures and, hence, enhancement of nonlinear phenomena, biosensing, as well as perfect filters and waveguides for a particular frequency, and impurity detection.     

Predicting the path of a changing sound: velocity tracking and auditory continuity

Three studies demonstrate listeners' ability to use the rate of a sound's frequency change (velocity) to predict how the spectral path of the sound is likely to evolve, even in the event of an occlusion. Experiments 1 and 2 use a modified probe-signal method to measure attentional filters and demonstrate increased detection to sounds falling along implied paths of constant-linear velocity. Experiment 3 shows listeners perceive a suprathreshold tone as falling along a trajectory of constant velocity when the frequency is near to the region of greatest detection as measured in Experiments 1 and 2. Further, results show greater accuracy and decreased bias in the use of velocity information with increased exposure to a constant-velocity sound. As the duration of occlusion lengthens, results also show a downward shift (relative to a trajectory of constant velocity) in the frequency at which listeners' detection and experience of a continuous trajectory are greatest. A preliminary model of velocity processing is proposed to account for this downward shift. Results show listeners' use of velocity in extrapolating sounds with dynamically changing spectral and temporal properties and provide evidence for its role in perceptual auditory continuity within a noisy acoustic environment.     

Observable estimation of bipartite mixed-state entanglement

An analytic lower bound is presented for bipartite mixed-state entanglement which is obtained from convex roof construction of a variational definition of pure-state negativity. It is shown that this lower bound can be directly measured by one single projection operator or a few local observables in experiments without the requirement of simultaneous multiple copies of states. In particular, we show that the lower bound can serve as an exact entanglement measure for isotropic states.     

Upper and lower bounds for fundamental natural frequency of beams

A better upper bound than the Rayleigh quotient is the Timoshenko quotient, the evaluation of which depends on a pair of compatible admissible moment and displacement functions. Based on both Rayleigh and Timoshenko quotients, a lower bound is readily computed. By means of an iteration procedure, both the upper and lower bound converge to the fundamental natural frequency.     

Variational Bounds for the Generalized Random Energy Model

We compute the pressure of the random energy model (REM) and generalized random energy model (GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra’s “broken replica symmetry bounds,” and identify the random probability cascade as the appropriate random overlap structure for the model. For the REM the lower bound is obtained, in the high temperature regime using Talagrand’s concentration of measure inequality, and in the low temperature regime using convexity and the high temperature formula. The lower bound for the GREM follows from the lower bound for the REM by induction. While the argument for the lower bound is fairly standard, our proof of the upper bound is new.     

Some Properties of D-Concurrence

In this note,we give a new lower bound for the concurrence,which is related to D-concurrence.For the Werner states,we compare that this D-concurrence bound with the other known bound.In addition,some of new upper and lower bounds of D-concurrence are given.     

Acoustically dependent latency shifts of BSER (wave V) in man

The latencies of wave V in Brain Stem Evoked Responses (BSER) elicited by a set of acoustic transients were measured. The stimuli were produced by delivering pulses to two filters, arranged in series. The filters were set so that the maximum acoustic energy in the transients, i.e., filtered clicks, occurred at 0.5, 1, 2, 4, or 8 kHz. The filtered clicks were presented via earphones at a rate of 30/s at 20, 40, or 60 dB HL to ten subjects with normal hearing. The latencies of wave V varied systematically with center frequency of the filtered clicks when they were each at the same HL. Stimuli presented at 40 dB HL produced the greatest opportunity for relating stimulus frequency to latency. The latencies for a smaller set of responses to stimuli presented at 10/s were the same as those for the principal data taken at 30/s. The changes in latency of wave V due to frequency are similar to those observed by other investigators in whole-nerve responses recorded in man.     

Achievable accuracy of parameter estimation for multidimensional NMR experiments

A fundamental issue in NMR spectroscopy is the estimation of parameters such as the Larmor frequencies of nuclei, J coupling constants, and relaxation rates. The Cramer-Rao lower bound provides a method to assess the best achievable accuracy of parameter estimates resulting from an unbiased estimation procedure. We show how the Cramer-Rao lower bound can be calculated for data obtained from multidimensional NMR experiments. The Cramer-Rao lower bound is compared to the variance of parameter estimates for simulated data using a least-squares estimation procedure. It is also shown how our results on the Cramer-Rao lower bound can be used to analyze whether an experimental design can be improved to provide experimental data which can result in parameter estimates with higher accuracy. The concept of nonuniform averaging in the indirect dimension is introduced and studied in connection with nonuniform sampling of the data.