Systems of mutually unbiased Hadamard matrices containing real and complex matrices

We use combinatorial and Fourier analytic arguments to prove various non-existence results on systems of real and com- plex unbiased Hadamard matrices. In particular, we prove that a complete system of complex mutually unbiased Hadamard ma- trices (MUHs) in any dimension cannot contain more than one real Hadamard matrix. We also give new proofs of several known structural results in low dimensions

A Preliminary Study of Three-dimensional Sonographic Measurements of the Fetus

OBJECTIVES: This study was aimed at establishing an ideal method for performing three-dimensional measurements of the fetus in order to improve the estimation of fetal weight. METHODS: The study consisted of two phases. Phase I was a prospective cross-sectional study performed between 28 and 40 weeks\u27 gestation. The study population (n=110) comprised low-risk singleton pregnancies who underwent a routine third-trimester sonographic estimation of fetal weight. The purpose of this phase was to establish normal values for the fetal abdominal and head volumes throughout the third trimester. Phase II was a prospective study that included patients admitted for an elective cesarean section or for induction of labor between 38 and 41 weeks\u27 gestation (n=91). This phase of the study compared the actual birth weight to two- (2D) and three-dimensional (3D) measurements of the fetus. Conventional 2D ultrasound fetal biometry was performed measuring the biparietal diameter (BPD), head circumference (HC), abdominal circumference (AC), and femur diaphysis length (FL). Volume estimates were computed utilizing Virtual Organ Computer-aided AnaLysis (VOCAL), and the correlation between measured volumes and actual neonatal weight was calculated. RESULTS: Overall, this longitudinal study consisted of 110 patients between 28 and 41 weeks\u27 gestation. Normal values were computed for the fetal abdomen and head volume throughout the third trimester. Ultrasound examination was performed within three days prior to delivery on 91 patients. A good correlation was found between birth weight and abdominal volume (r=0.77) and between birth weight and head volume (r=0.5). Correlation between bidimensional measurements and actual fetal weights was found to be comparable with previously published correlations. CONCLUSION: Volume measurements of the fetus may improve the accuracy of estimating fetal size. Additional studies using different volume measurement of the fetus are necessary

Is gastro-oesophageal reflux a factor in exercise-induced asthma?

AbstractExercise-induced bronchoconstriction (EIB) occurs in the majority of patients with asthma. The relationship between asthma and gastro-oesophageal reflux (GER) is well defined, and the reports of exertional gastro-oesophageal acid reflux in healthy subjects, prompted us to study the relationship between EIB and GER.Following an overnight fast and medication withholding, 15 asthmatics and 15 normal subjects were placed on continuous monitoring of oesophageal pH and ECG. After baseline monitoring of oesophageal pH, at rest, for 30 min, spirometry was performed. Thereafter, the subjects underwent rigorous treadmill exercise for 8 min followed by spirometry, 10 min after running.Twelve out of 15 asthmatics and none in the control group demonstrated significant fall in FEV1 in response to exercise. However, only six out of 15 normal subjects and three in the asthmatic group had evidence of GER during or following exercise.We concluded that there is no significant correlation between EIB and GER in patients with asthma

Deciphering nonfemtoscopic two-pion correlations in p+pp+p collisions with simple analytical models

A simple model of nonfemtoscopic particle correlations in proton-proton collisions is proposed. The model takes into account correlations induced by the conservation laws as well as correlations induced by minijets. It reproduces well the two-pion nonfemtoscopic correlations of like-sign and unlike-sign pions in proton-proton collision events at $\sqrt{s} = 900$ GeV analyzed by the ALICE Collaboration. We also argue that similar nonfemtoscopic correlations can appear in the hydrodynamic picture with event-by-event fluctuating nonsymmetric initial conditions that are typically associated with nonzero higher-order flow harmonics.Comment: 21 pages, 10 figures, misprints correcte

The Conformal Willmore Functional: a Perturbative Approach

The conformal Willmore functional (which is conformal invariant in general Riemannian manifold $(M,g)$) is studied with a perturbative method: the Lyapunov-Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3, g_\epsilon)$ -where $g_\epsilon$ is a metric close and asymptotic to the euclidean one. With the same technique a non existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.Comment: 34 pages; Journal of Geometric Analysis, on line first 23 September 201

The Fractal Properties of the Source and BEC

Using simple space-time implementation of the random cascade model we investigate numerically influence of the possible fractal structure of the emitting source on Bose-Einstein correlations between identical particles. The results are then discussed in terms of the non-extensive Tsallis statistics.Comment: LaTeX file and 2 PS files with figures, 8 pages altogether. Talk presented at the 12th Indian Summer School "Relativistic Heavy Ion Physics, Prague, Czech Republic, 30 August-3 Sept. 1999; to be published in Czech J. Phys. (1999). Some typos correcte

Large Extra Dimensions from a Small Extra Dimension

Models with extra dimensions have changed our understanding of the hierarchy problem. In general, these models explain the weakness of gravity by diluting gravity in a large bulk volume, or by localizing the graviton away from the standard model. In this paper, we show that the warped geometries necessary for the latter scenario can naturally induce the large volumes necessary for the former. We present a model in which a large volume is stabilized without supersymmetry. We comment on the phenomenology of this scenario and generalizations to additional dimensions.Comment: Some formulae altered, conclusions unchange