Analysis of segregated boundary-domain integral equations for mixed variable-coefficient BVPs in exterior domains

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2011 Birkhäuser Boston.Some direct segregated systems of boundary–domain integral equations (LBDIEs) associated with the mixed boundary value problems for scalar PDEs with variable coefficients in exterior domains are formulated and analyzed in the paper. The LBDIE equivalence to the original boundary value problems and the invertibility of the corresponding boundary–domain integral operators are proved in weighted Sobolev spaces suitable for exterior domains. This extends the results obtained by the authors for interior domains in non-weighted Sobolev spaces.The work was supported by the grant EP/H020497/1 ”Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients” of the EPSRC, UK

Analysis of some localized boundary-domain integral equations for transmission problems with variable coefficients

This is the post-print version of the Article. The official published version can be found at the links below - Copyright @ 2011 Birkhäuser Boston.Some segregated systems of direct localized boundary-domain integral equations (LBDIEs) associated with several transmission problems for scalar PDEs with variable coefficients are formulated and analyzed for a bounded domain composed of two subdomains with a coefficient jump over the interface. The main results established in the paper are the LBDIE equivalence to the original transmission problems and the invertibility of the corresponding localized boundary-domain integral operators in corresponding Sobolev spaces function spaces.This research was supported by the EPSRC grant EP/H020497/1: ”Mathematical analysis of Localized Boundary-Domain Integral Equations for Variable-Coefficient Boundary Value Problems” and partly by the Georgian Technical University grant in the case of the third author

Localized boundary-domain singular integral equations based on harmonic parametrix for divergence-form elliptic PDEs with variable matrix coefficients

This is the post-print version of the Article. The official publised version can be accessed from the links below. Copyright @ 2013 Springer BaselEmploying the localized integral potentials associated with the Laplace operator, the Dirichlet, Neumann and Robin boundary value problems for general variable-coefficient divergence-form second-order elliptic partial differential equations are reduced to some systems of localized boundary-domain singular integral equations. Equivalence of the integral equations systems to the original boundary value problems is proved. It is established that the corresponding localized boundary-domain integral operators belong to the Boutet de Monvel algebra of pseudo-differential operators. Applying the Vishik-Eskin theory based on the factorization method, the Fredholm properties and invertibility of the operators are proved in appropriate Sobolev spaces.This research was supported by the grant EP/H020497/1: "Mathematical Analysis of Localized Boundary-Domain Integral Equations for Variable-Coefficient Boundary Value Problems" from the EPSRC, UK

Omental Flap Provides Definitive Management for Pediatric Patient With Multiple Tracheoesophageal Fistula Recurrences

A term female infant with tracheoesophageal fistula (TEF) and esophageal atresia (EA) underwent primary operative repair that failed with 3 TEF recurrences, which all presented with feeding and respiratory issues. Recurrences were managed with reoperation and an interpositional flap of pleura and a flap of intercostal muscle on 2 separate occasions. The third recurrence was managed with complete dissection of the esophagus prior to the division of the fistula and the interposition of an omental flap between the esophageal and tracheal repair. We present the use of a viable omental flap and complete esophageal mobilization to prevent subsequent TEF recurrences and avoid the additional morbidity of reconstructive surgery

Colostomy as a bridge to definitive pediatric surgical care: A sub-Saharan African experience

Available data, however, points to a wide variety of surgical conditions, with the majority falling into three major diagnostic categories, injuries, congenital anomalies, and surgical infections.1 In Africa, children constitute more than half the population.2 Despite high patient volume, very few dedicated pediatric surgeons are available, with only one pediatric surgeon to approximately two million children in Africa, compared with 1:100,000 in North America.3 Owing to this dearth of pediatric surgical workforce, surgical disease in children is not often managed, and if managed, is predominantly managed by a general surgeon who may lack familiarity with complex pediatric surgical procedures. There is little information in the literature regarding the clinical indications for pediatric patients receiving colostomies, complications associated with colostomies, and colostomy reversal rates in sub-Saharan Africa. [...]the aim of this study is to describe the characteristics and outcomes of patients receiving colostomies in a sub-Saharan African setting. [...]during our study period, there were only four patients who returned for reversal of their colostomy, with two colostomy takedowns and two pull-through procedures, with an average of 261.3 ± 288.1 days till reversal (range 36 to 654 days)

A noninvasive hemoglobin monitor in the pediatric intensive care unit

Background Critically ill pediatric patients frequently require hemoglobin monitoring. Accurate noninvasive Hb (SpHb) would allow practitioners to decrease anemia from repeated blood draws, traumatic blood draws, and a decreased number of laboratory Hb (LabHb) medical tests. The Food and Drug Administration has approved the Masimo Pronto SpHb and associated Rainbow probes; however, its use in the pediatric intensive care unit (PICU) is controversial. In this study, we define the degree of agreement between LabHb and SpHb using the Masimo Pronto SpHb Monitor and identify clinical and demographic conditions associated with decreased accuracy. Materials and methods We performed a prospective, observational study in a large PICU at an academic medical center. Fifty-three pediatric patients (30-d and 18-y-old), weighing >3 kg, admitted to the PICU from January-April 2013 were examined. SpHb levels measured at the time of LabHb blood draw were compared and analyzed. Results Only 83 SpHb readings were obtained in 118 attempts (70.3%) and 35 readings provided a result of "unable to obtain." The mean LabHb and SpHb were 11.1 g/dL and 11.2 g/dL, respectively. Bland-Altman analysis showed a mean difference of 0.07 g/dL with a standard deviation of ±2.59 g/dL. Pearson correlation is 0.55, with a 95% confidence interval between 0.38 and 0.68. Logistic regression showed that extreme LabHb values, increasing skin pigmentation, and increasing body mass index were predictors of poor agreement between SpHb and LabHb (P < 0.05). Separately, increasing body mass index, hypoxia, and hypothermia were predictors for undetectable readings (P < 0.05). Conclusions The Masimo Pronto SpHb Monitor provides adequate agreement for the trending of hemoglobin levels in critically ill pediatric patients. However, the degree of agreement is insufficient to be used as the sole indicator for transfusion decisions and should be used in context of other clinical parameters to determine the need for LabHb in critically ill pediatric patients

Analysis of segregated boundary-domain integral equations for BVPs with non-smooth coefficients on Lipschitz domains

Segregated direct boundary-domain integral equations (BDIEs) based on a parametrix and associated with the Dirichlet and Neumann boundary value problems for the linear stationary diffusion partial differential equation with a variable Hölder-continuous coefficients on Lipschitz domains are formulated. The PDE right-hand sides belong to the Sobolev (Bessel potential) space Hs−2(Ω ) or H˜s−2(Ω ) , 12<s<32, when neither strong classical nor weak canonical co-normal derivatives are well defined. Equivalence of the BDIEs to the original BVP, BDIE solvability, solution uniqueness/non-uniqueness, and the Fredholm property and invertibility of the BDIE operators are analysed in appropriate Sobolev spaces. It is shown that the BDIE operators for the Neumann BVP are not invertible; however, some finite-dimensional perturbations are constructed leading to invertibility of the perturbed (stabilised) operators.EPSR

Status of the CCD development for the Dark Energy Spectroscopic Instrument

We describe improvements in CCD performance that have been achieved on 4k×4k, (15 μm)2-pixel, fully depleted CCDs for the Dark Energy Spectroscopic Instrument (DESI) [1]. With respect to our previous work on CCDs for the Dark Energy Camera and the Baryon Oscillation Spectroscopic Survey, our goals for the DESI CCD development were to improve read noise and quantum efficiency, improve the astrometric precision, and decrease pixel-size variations. We report experimental results on recently fabricated CCDs to be used in DESI

Integral potential method for a transmission problem with Lipschitz interface in R^3 for the Stokes and Darcy–Forchheimer–Brinkman PDE systems

The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the non-linear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain with connected boundary, and the other one is the exterior Lipschitz domain R3 n. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces

Study of the B^0 Semileptonic Decay Spectrum at the Upsilon(4S) Resonance

We have made a first measurement of the lepton momentum spectrum in a sample of events enriched in neutral B's through a partial reconstruction of B0 --> D*- l+ nu. This spectrum, measured with 2.38 fb**-1 of data collected at the Upsilon(4S) resonance by the CLEO II detector, is compared directly to the inclusive lepton spectrum from all Upsilon(4S) events in the same data set. These two spectra are consistent with having the same shape above 1.5 GeV/c. From the two spectra and two other CLEO measurements, we obtain the B0 and B+ semileptonic branching fractions, b0 and b+, their ratio, and the production ratio f+-/f00 of B+ and B0 pairs at the Upsilon(4S). We report b+/b0=0.950 (+0.117-0.080) +- 0.091, b0 = (10.78 +- 0.60 +- 0.69)%, and b+ = (10.25 +- 0.57 +- 0.65)%. b+/b0 is equivalent to the ratio of charged to neutral B lifetimes, tau+/tau0.Comment: 14 page, postscript file also available at http://w4.lns.cornell.edu/public/CLN