Cornerstones of Sampling of Operator Theory

This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of the subject back to the original work of the third-named author in the late 1950s and early 1960s, and to the innovations in spread-spectrum communications that preceded that work. We give a brief overview of the NOMAC (Noise Modulation and Correlation) and Rake receivers, which were early implementations of spread-spectrum multi-path wireless communication systems. We examine in detail the original proof of the third-named author characterizing identifiability of channels in terms of the maximum time and Doppler spread of the channel, and do the same for the subsequent generalization of that work by Bello. The mathematical limitations inherent in the proofs of Bello and the third author are removed by using mathematical tools unavailable at the time. We survey more recent advances in sampling of operators and discuss the implications of the use of periodically-weighted delta-trains as identifiers for operator classes that satisfy Bello's criterion for identifiability, leading to new insights into the theory of finite-dimensional Gabor systems. We present novel results on operator sampling in higher dimensions, and review implications and generalizations of the results to stochastic operators, MIMO systems, and operators with unknown spreading domains

Constructing Exactly Solvable Pseudo-hermitian Many-particle Quantum Systems by Isospectral Deformation

A class of non-Dirac-hermitian many-particle quantum systems admitting entirely real spectra and unitary time-evolution is presented. These quantum models are isospectral with Dirac-hermitian systems and are exactly solvable. The general method involves a realization of the basic canonical commutation relations defining the quantum system in terms of operators those are hermitian with respect to a pre-determined positive definite metric in the Hilbert space. Appropriate combinations of these operators result in a large number of pseudo-hermitian quantum systems admitting entirely real spectra and unitary time evolution. Examples of a pseudo-hermitian rational Calogero model and XXZ spin-chain are considered.Comment: To appear in the Special Issue PHHQP 2010, International Journal of Theoretical Physics; 16 pages, LateX, no figur

Combined heterozygosity for methylenetetrahydrofolate reductase (MTHFR) mutations C677T and A1298C is associated with abruptio placentae but not with intrauterine growth restriction

Objective: This study was undertaken to investigate the involvement of MTHFR gene mutations C677T and A1298C implicated in vascular disease, in patients with abruptio placentae and intrauterine growth restriction (IUGR). Study Design: DNA was extracted from blood samples of 54 patients with placental vasculopathy (18 patients with abruptio placentae and 36 with IUGR) and 114 control patients and amplified by the polymerase chain reaction (PCR). The resulting fragments were subjected to restriction enzyme analysis and resolved by gel electrophoresis. Results: A significant association could be demonstrated between mutation A1298C and both abruptio placentae and IUGR. Combined heterozygosity for mutations C677T and A1298C was detected in 22.2% of abruptio placentae cases. Conclusions: Combined heterozygosity for MTHFR mutations C677T and A1298C may represent a genetic marker for abruptio placentae. Copyright © 2001 Elsevier Science Ireland Ltd.Objective: This study was undertaken to investigate the involvement of MTHFR gene mutations C677T and A1298C implicated in vascular disease, in patients with abruptio placentae and intrauterine growth restriction (IUGR). Study Design: DNA was extracted from blood samples of 54 patients with placental vasculopathy (18 patients with abruptio placentae and 36 with IUGR) and 114 control patients and amplified by the polymerase chain reaction (PCR). The resulting fragments were subjected to restriction enzyme analysis and resolved by gel electrophoresis. Results: A significant association could be demonstrated between mutation A1298C and both abruptio placentae and IUGR. Combined heterozygosity for mutations C677T and A1298C was detected in 22.2% of abruptio placentae cases. Conclusions: Combined heterozygosity for MTHFR mutations C677T and A1298C may represent a genetic marker for abruptio placentae. Copyright © 2001 Elsevier Science Ireland Ltd.ArticleArticl

Identification of a suicide victim by facial reconstruction

Facial reconstruction is used in an attempt to identify an individual by a three dimensional representation of the facial features using the skull as the foundation after metrical and non-metrical analysis to determine age, race and gender. The skeletonized remains of a female who was reported missing six years previously were recovered from the summit of Table Mountain in Cape Town. Some personal possessions were also recovered, one of which was a shark tooth pendant which the victim's parents recognized. Although there were distinctive dental features, the antemortem dental records had been lost during the initial investigation which therefore precluded identification by this means. However, positive identification was required and facial reconstruction on the skull was undertaken which the parents duly identified. The method used for facial reconstruction is described.Articl

Evaluation of models for assessing Medicago sativa L. hay quality

A study was conducted to evaluate current proposed models for assessingMedicago sativa L. hay quality, using near infrared reflectance spectroscopy (NIRS) analyses and Cornell Nett Carbohydrate and Protein System (CNCPS) milk production prediction as a criterion of accuracy. Application of the theoretically-based summative total digestible nutrients (TDNlig) model of Weiss et al. (1992), using lignin to determine truly digestible NDF, explained almost all of the variation in milk yield (MY) (r² = 0.98). However, this model involves high analysis costs to develop and maintain NIRS calibrations and several of its components were poorly predicted by NIRS and therefore, not suited for quality assessment in practice. Current available models (forage quality index (FQI), relative forage quality (RFQ); relative feed value (RFV)) for assessing Medicago sativa L. hay quality revealed lower accuracies (r² = 0.83, r² = 0.76, r² = 0.61, respectively), especially when protein was included in the model (total forage quality index (TFI); r² < 0.49). The developed empirical equation named lucerne milk value (LMV), including ADF, ash and lignin (Y = b0 – b1ADF – b2ash – b3lignin) (r² = 0.96), proved to be the most practical, simplistic, economical and accurate quality evaluation model for commercial application

Prediction of chemical composition of South African Medicago sativa L. hay from a near infrared reflectance spectroscopy spectrally structured sample population

The near infrared reflectance spectroscopy (NIRS) to predict chemical and digestibility parameters was investigated. Samples (n = 168) representing the spectral characteristics of the South AfricanMedicago sativa L. hay population were chemically analysed for the development of calibration equations. Values for r² and ratio of prediction to deviation (RPD) used as estimates of calibration accuracy for these parameters were classified as follows: good for dry matter (DM) (r² = 0.97; RPD = 4.84), crude protein (CP) (r² = 0.97; RPD = 4.57), acid detergent fibre (ADF) (r² = 0.95; RPD = 3.97), neutral detergent fibre (NDF) (r² = 0.95; RPD = 3.99), lignin (r² = 0.94; RPD = 3.61), ash (r² = 0.93; RPD = 3.12) and chloride (Cl) (r² = 0.95; RPD = 3.74); intermediate for NDF-crude protein (NDF-CP) (r² = 0.91; RPD = 2.96), sugar (r² = 0.91; RPD = 2.82), in vitro organic matter digestibility at 24 hr (IVOMD24) (r² = 0.90; RPD = 2.84) and 48 hr (IVOMD48) (r² = 0.89; RPD = 2.70); and low (RP

The nutritive value of South African Medicago sativa L. hay

A study was conducted to evaluate the variation and expand the existing and limiting nutritive value database ofMedicago sativa L. hay (168 near-infrared reflectance spectroscopy spectrally selected samples) in South Africa. The highest moisture content recorded (140 g/kg) was safely below the critical moisture level of 160 g/kg for effective storage. Coefficient of variation (CV) ranged from 1.2% for dry matter (DM) up to 66.2% for acid detergent fibre-crude protein (ADF-CP). The average ash content was 130 g/kg (73 to 295 g/kg), indicating soil contamination. Fibre fractions varied as follows: acid detergent fibre (ADF) (213 to 473 g/kg), neutral detergent fibre (NDF) (289 to 659 g/kg), lignin (43 to 163 g/kg), cellulose (163 to 364 g/kg) and hemicellulose (53 to 199 g/kg). The mean IVOMD for both 24 and 48 h (693 and 732 g/kg DM, respectively), was representative (CV = ± 8%) of the Medicago sativa L. hay population. Crude protein (CP) (average = 207 g/kg DM) consists of 76.9% true protein. According to ADF-CP, 6% of the samples were heat damaged. High mean Ca (13.5 g/kg), P (25.3 g/kg) and Fe (874 mg/kg) values were recorded

ANALYSIS OF TRANSPORT PHENOMENA IN THE COATING OF FIBERS BY CVD

Inorganic coated fibers produced by chemical vapor deposition find several technological applications. In this CVD process, a fiber core is mounted in a reactor between two electrodes. Reactive gases flow over the substrate and react near or on the fiber surface to form the desired coating. Experience has shown that quality deposition can only be obtained over a small range of the governing parameters : these parameters are, however, difficult to control. In the present study, a mathematical model is developed for the reactor configuration under consideration. The different mass and energy transport mechanism are compared and their influence on the reactor performance is evaluated for horizontal reactor arrangements. Numerical results, showing sharp temperature and concentration gradient close to the fiber surface, suggest that heat and mass transfer in this region are controlled by conduction and diffusion mechanisms. In the bulk region, heat and mass transfer via the convection and conduction/diffusion mechanisms can be of equal importance. Numerical results show how bulk properties are affected by both transversal and longitudinal rolls

A model for assessing Medicago Sativa L. hay quality

A study was conducted to identify chemical parameters and/or models for assessingMedicago sativa L. (L) hay quality, using near infrared reflectance spectroscopy (NIRS) analysis and Cornell Net Carbohydrate and Protein System (CNCPS) milk prediction as a criterion of accuracy. Milk yield (MY) derived from the CNCPS model, by replacing the average L hay in a complete diet with 168 representative South African L hay samples, was used as a criterion to evaluate and/or develop models for L hay quality grading. The best single predictor of MY was the acid detergent fibre (ADF) content of L hay, which explained 67% of the measured variation. A multiple linear equation (Y = 64.18 – b1ADF – b2ash – b3lignin) explains 96% of the measured variation in MY. The relatively poor performance of crude protein (CP) (r² = 0.04) and other protein related parameters (r²< 0.25; adjusted-crude protein, ADF-CP, neutral detergent fibre-CP and soluble protein) in predicting MY suggests that protein content of L hay is an unreliable indicator of L hay quality. It is clear that MY derived from the CNCPS model by replacing L hay in a basal diet with others in the South African L hay population can be significantly predicted with high accuracy by the developed empirical model named lucerne milk value (LMV) consisting of only ADF, ash and lignin