Solutions for real dispersionless Veselov-Novikov hierarchy

We investigate the dispersionless Veselov-Novikov (dVN) equation based on the framework of dispersionless two-component BKP hierarchy. Symmetry constraints for real dVN system are considered. It is shown that under symmetry reductions, the conserved densities are therefore related to the associated Faber polynomials and can be solved recursively. Moreover, the method of hodograph transformation as well as the expressions of Faber polynomials are used to find exact real solutions of the dVN hierarchy.Comment: 14 page

A comparison of snack serving sizes to USDA guidelines in healthy weight and overweight minority preschool children enrolled in Head Start

Background Obesity disproportionately affects children from low-income families and those from racial and ethnic minorities. The relationship between snacking and weight status remains unclear, although snacking is known to be an important eating episode for energy and nutrient intake particularly in young children. The purpose of this pilot study was to examine the snack intake of minority preschool children enrolled in the Head Start Program in four centers in Detroit, Michigan, and investigate differences by child weight status. Methods This secondary data analysis used snack time food observation and anthropometric data from a convenience sample of 55 African American children (44æ% girls, mean age?=?3.8æyears). Snack intake data was obtained over a mean of 5 days through direct observation of children by dietetic interns, and later converted into food group servings according to the United States Department of Agriculture (USDA) meal patterns and averaged for each child. Height and weight measurements were systematically collected and BMI-for-age percentiles were used to classify children into weight categories. One sample, paired samples and independent samples t-tests were performed to test for differences within and between means. Results Based on BMI-for-age percentiles, 72.7æ% of the sample was under/healthy weight and 27.3æ% was overweight/obese. Average (mean?±?SD) intake of milk (0.76?±?0.34) and overall fruits/vegetables (0.77?±?0.34) was significantly lower than one USDA serving, while average intake of grains and breads (2.04?±?0.89), meat/meat alternates (2.20?±?1.89) and other foods (1.43?±?1.08) was significantly higher than one USDA serving (p???0.05). Children ate more when offered canned versus fresh fruits (0.93?±?0.57 vs. 0.65?±?0.37, p?=?0.007). Except for a significantly higher milk intake in the overweight/obese group compared to the under/healthy weight group (0.86?±?0.48 vs. 0.72?±?0.27, p?=?0.021], no relationship was found between snack food intake and weight category. Only in the overweight/obese group was the intake of milk and fresh fruits not significantly different than one USDA serving. Conclusions Findings suggest that regardless of weight status low-income minority preschool children are consuming larger serving sizes when offered less healthy versus healthier snack foods. Continued efforts should be made to provide healthful snack foods at preschool settings to prevent obesity and promote healthier food habits

Broadband energy-efficient optical modulation by hybrid integration of silicon nanophotonics and organic electro-optic polymer

Silicon-organic hybrid integrated devices have emerging applications ranging from high-speed optical interconnects to photonic electromagnetic-field sensors. Silicon slot photonic crystal waveguides (PCWs) filled with electro-optic (EO) polymers combine the slow-light effect in PCWs with the high polarizability of EO polymers, which promises the realization of high-performance optical modulators. In this paper, a broadband, power-efficient, low-dispersion, and compact optical modulator based on an EO polymer filled silicon slot PCW is presented. A small voltage-length product of V{\pi}*L=0.282Vmm is achieved, corresponding to an unprecedented record-high effective in-device EO coefficient (r33) of 1230pm/V. Assisted by a backside gate voltage, the modulation response up to 50GHz is observed, with a 3-dB bandwidth of 15GHz, and the estimated energy consumption is 94.4fJ/bit at 10Gbit/s. Furthermore, lattice-shifted PCWs are utilized to enhance the optical bandwidth by a factor of ~10X over other modulators based on non-band-engineered PCWs and ring-resonators.Comment: 12 pages, 4 figures, SPIE Photonics West Conference 201

T Oligo-Primed Polymerase Chain Reaction (TOP-PCR): A Robust Method for the Amplification of Minute DNA Fragments in Body Fluids.

Body fluid DNA sequencing is a powerful noninvasive approach for the diagnosis of genetic defects, infectious agents and diseases. The success relies on the quantity and quality of the DNA samples. However, numerous clinical samples are either at low quantity or of poor quality due to various reasons. To overcome these problems, we have developed T oligo-primed polymerase chain reaction (TOP-PCR) for full-length nonselective amplification of minute quantity of DNA fragments. TOP-PCR adopts homogeneous "half adaptor" (HA), generated by annealing P oligo (carrying a phosphate group at the 5' end) and T oligo (carrying a T-tail at the 3' end), for efficient ligation to target DNA and subsequent PCR amplification primed by the T oligo alone. Using DNA samples from body fluids, we demonstrate that TOP-PCR recovers minute DNA fragments and maintains the DNA size profile, while enhancing the major molecular populations. Our results also showed that TOP-PCR is a superior method for detecting apoptosis and outperforms the method adopted by Illumina for DNA amplification

Real-time diagnostics of gas/water assisted injection moulding using integrated ultrasonic sensors

YesAn ultrasound sensor system has been applied to the mould of both the water and gas assisted injection moulding processes. The mould has a cavity wall mounted pressure sensor and instrumentation to monitor the injection moulding machine. Two ultrasound sensors are used to monitor the arrival of the fluid (gas or water) bubble tip through the detection of reflected ultrasound energy from the fluid polymer boundary and the fluid bubble tip velocity through the polymer melt is estimated. The polymer contact with the cavity wall is observed through the reflected ultrasound energy from that boundary. A theoretically based estimation of the residual wall thickness is made using the ultrasound reflection from the fluid (gas or water) polymer boundary whilst the samples are still inside the mould and a good correlation with a physical measurement is observed

On the Miura map between the dispersionless KP and dispersionless modified KP hierarchies

We investigate the Miura map between the dispersionless KP and dispersionless modified KP hierarchies. We show that the Miura map is canonical with respect to their bi-Hamiltonian structures. Moreover, inspired by the works of Takasaki and Takebe, the twistor construction of solution structure for the dispersionless modified KP hierarchy is given.Comment: 19 pages, Latex, no figure

The Gould-Hopper Polynomials in the Novikov-Veselov equation

We use the Gould-Hopper (GH) polynomials to investigate the Novikov-Veselov (NV) equation. The root dynamics of the $\sigma$-flow in the NV equation is studied using the GH polynomials and then the Lax pair is found. In particulr, when $N=3,4,5$, one can get the Gold-fish model. The smooth rational solutions of the NV equation are also constructed via the extended Moutard transformation and the GH polynomials. The asymptotic behavior is discussed and then the smooth rational solution of the Liouville equation is obtained.Comment: 22 pages, no figur