Inverse spectral theory for Jacobi matrices and their almost periodicity

In this paper we consider the inverse problem for bounded Jacobi matrices with nonempty absolutely continuous spectrum and as an application show the almost periodicity of some random Jacobi matrices. We do the inversion in two different ways. In the general case we use a direct method of reconstructing the Green functions. In the special case where we show the almost periodicity, we use an alternative method using the trace formula for points in the orbit of the matrices under translations. This method of reconstruction involves analyzing the Abel-Jacobi map and solving of the Jacobi inversion problem associated with an infinite genus Riemann surface constructed from the spectrum.     

Quantifier elimination for algebraic -groups

We prove that if is an algebraic -group (in the sense of Buium over a differentially closed field of characteristic , then the first order structure consisting of together with the algebraic -subvarieties of , has quantifier-elimination. In other words, the projection on of a -constructible subset of is -constructible. Among the consequences is that any finite-dimensional differential algebraic group is interpretable in an algebraically closed field.

     

Cyclic oligofurans: one-pot synthesis of 30pi and 40pi expanded porphyrinoids

Acid-catalyzed condensation of furan and pentafluorobenzaldehyde yielded conjugated macrocycles with six and eight furan rings. They represent systems similar to annulenes with 30pi and 40pi electrons. From their structural analyses, it was found that furan rings in both the molecules were inverted in an alternative fashion and displayed nontwisted conformations. [structure: see text].     

Wavelet domain non-linear filtering for MRI denoising

Feature-preserved denoising is of great interest in medical image processing. This article presents a wavelet-based bilateral filtering scheme for noise reduction in magnetic resonance images. Undecimated wavelet transform is employed to provide effective representation of the noisy coefficients. Bilateral filtering of the approximate coefficients improves the denoising efficiency and effectively preserves the edge features. Denoising is done in the square magnitude domain, where the noise tends to be signal independent and is additive. The proposed method has been adapted specifically to Rician noise. The visual and the diagnostic quality of the denoised image is well preserved. The quantitative and the qualitative measures used as the quality metrics demonstrate the ability of the proposed method for noise suppression.     

Optofluidic system for three-dimensional sensing and identification of micro-organisms with digital holographic microscopy

Optofluidic devices offer flexibility for a variety of tasks involving biological specimen. We propose a system for three-dimensional (3D) sensing and identification of biological micro-organisms. This system consists of a microfluidic device along with a digital holographic microscope and relevant statistical recognition algorithms. The microfluidic channel is used to house the micro-organisms, while the holographic microscope and a CCD camera record their digital holograms. The holograms can be computationally reconstructed in 3D using a variety of algorithms, such as the Fresnel transform. Statistical recognition algorithms are used to analyze and identify the micro-organisms from the reconstructed wavefront. Experimental results are presented. Because of computational reconstruction of wavefronts in holographic imaging, this technique offers unique advantages that allow one to image micro-organisms within a deep channel while removing the inherent microfluidic-induced aberration through interferometery.     

Effect of gravity on subject-specific human lung deformation

A biomechanical model of human lung is developed and used to investigate the effect of gravity on lung deformation. The lung is assumed to behave as a poro-elastic medium with spatially dependent elastic property. Finite element analysis is performed on a three-dimensional (3D) lung geometry reconstructed from a four-dimensional Computed Tomography (4DCT) scan dataset of human patient. The spatially dependent Young’s modulus (YM) values are estimated using inverse analysis from a linear elastic deformation model. The predicted deformation of selected landmarks is monitored with and without gravity, and compared with data obtained from 4DCT registration. The results show that gravity indeed significantly affects the magnitude and distribution of lung deformation with the maximum displacement enhanced by 54% in the direction of gravity, for the conditions investigated. In summary, the accuracy of predicted deformation is improved through incorporation of gravity in the biomechanical model of lung.     

Intensification of oxidation capacity using chloroalkanes as additives in hydrodynamic and acoustic cavitation reactors

The effect of the presence and absence of the chloroalkanes, dichloromethane (CH(2)Cl(2)), chloroform (CHCl(3)) and carbon tetrachloride (CCl(4)) on the extent of oxidation of aqueous I(-) to I(3)(-) has been investigated in (a) a liquid whistle reactor (LWR) generating hydrodynamic cavitation and (b) an ultrasonic probe, which produces acoustic cavitation. The aim has been to examine the intensification achieved in the extent of oxidation due to the generation of additional free radicals/oxidants in the reactor as a result of the presence of chloroalkanes. It has been observed that the extent of increase in the oxidation reaction is strongly dependent on the applied pressure in the case of the LWR. Also, higher volumes of the chloroalkanes favour the intensification and the order of effectiveness is CCl(4)>CHCl(3)>CH(2)Cl(2). However, the results with the ultrasonic probe suggest that an optimum concentration of CH(2)Cl(2) or CHCl(3) exists beyond which there is little increase in the extent of observed intensification. For CCl(4), however, no such optimum concentration was observed and the extent of increase in the rates of oxidation reaction rose with the amount of CCl(4) added. Stage wise addition of the chloroalkanes was found to give marginally better results in the case of the ultrasonic probe as compared to bulk addition at the start of the run. Although CCl(4) is the most effective, its toxicity and carcinogenicity may mean that CH(2)Cl(2) and CHCl(3) offer a safer viable alternative and the present work should be useful in establishing the amount of chloroalkanes required for obtaining a suitable degree of intensification.     

Rotating Detonation Combustor Research at the University of Cincinnati

Rotating detonation combustors (RDC) are at the forefront of pressure gain combustion (PGC) research. The simplicity in design and the ease of assembly makes it a promising technology that could be integrated into existing combustor architectures. This is, however, coupled with the considerable complexities of the detonation-based flow field, and the associated modes and coupling mechanisms. The current paper is an overview of the research done at the University of Cincinnati to address some of the challenges and questions pertaining to the physics of RDC operation. Issues such as combustor geometry, injection schemes and mixing, varied reactants behavior and modes of RDC operation are discussed. The effects of pressurization of the combustor, along with other detonation enhancement strategies are also deliberated upon. When appropriate, parallels are drawn to the phenomena of high frequency combustion instabilities to address the similarities in observations between the two fields.     

Radiochemical studies using 59Fe and 35S provide evidence for iron-regulated uptake of sulfur in wheat

Ecological half-lives of radiocesium were observed on Izu-Oshima Island, Japan, a place which experiences typhoons annually. The estimated ecological half-lives (uncertainty) based on the observations above an asphalt and a bare surface were 1.6 year (31.6%) and 1.9 year (14.4%), respectively; those of ¹³⁴Cs and ¹³⁷Cs in soil were 1.5 year (7.2%) and 4.0 year (5.9%), respectively. The radiation level was quickly returned to the original level compared to other locations that do not experience such typhoon activity.