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In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer. In previous studies, this eigenvalue problem was analyzed with one conductive boundary parameter whereas we will consider the case of two parameters. We prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the physical parameters. We are able to prove monotonicity of the first transmission eigenvalue with respect to the parameters and consider the limiting procedure as the second boundary parameter vanishes. Lastly, we provide extensive numerical experiments to validate the theoretical work.
BACKGROUND
Immunosuppression is often considered as an indication for antibiotic prophylaxis to prevent surgical site infections (SSI) while performing skin surgery. However, the data on the risk of developing SSI after dermatologic surgery in immunosuppressed patients are limited.
PATIENTS AND METHODS
All patients of the Department of Dermatology and Allergology at the University Hospital of RWTH Aachen in Aachen, Germany, who underwent hospitalization for a dermatologic surgery between June 2016 and January 2017 (6 months), were followed up after surgery until completion of the wound healing process. The follow-up addressed the occurrence of SSI and the need for systemic antibiotics after the operative procedure. Immunocompromised patients were compared with immunocompetent patients. The investigation was conducted as a retrospective analysis of patient records.
RESULTS
The authors performed 284 dermatologic surgeries in 177 patients. Nineteen percent (54/284) of the skin surgery was performed on immunocompromised patients. The most common indications for surgical treatment were nonmelanoma skin cancer and malignant melanomas. Surgical site infections occurred in 6.7% (19/284) of the cases. In 95% (18/19), systemic antibiotic treatment was needed. Twenty-one percent of all SSI (4/19) were seen in immunosuppressed patients.
CONCLUSION
According to the authors' data, immunosuppression does not represent a significant risk factor for SSI after dermatologic surgery. However, larger prospective studies are needed to make specific recommendations on the use of antibiotic prophylaxis while performing skin surgery in these patients.
The available data on complications after dermatologic surgery have improved over the past years. Particularly, additional risk factors have been identified for surgical site infections (SSI). Purulent surgical sites, older age, involvement of head, neck, and acral regions, and also the involvement of less experienced surgeons have been reported to increase the risk of the SSI after dermatologic surgeries.1 In general, the incidence of SSI after skin surgery is considered to be low.1,2 However, antibiotics in dermatologic surgeries, especially in the perioperative setting, seem to be overused,3,4 particularly regarding developing antibiotic resistances and side effects.
Immunosuppression has been recommended to be taken into consideration as an additional indication for antibiotic prophylaxis to prevent SSI after skin surgery in special cases.5,6 However, these recommendations do not specify the exact dermatologic surgeries, and were not specifically developed for dermatologic surgery patients and treatments, but adopted from other surgical fields.6 According to the survey conducted on American College of Mohs Surgery members in 2012, 13% to 29% of the surgeons administered antibiotic prophylaxis to immunocompromised patients to prevent SSI while performing dermatologic surgery on noninfected skin,3 although this was not recommended by Journal of the American Academy of Dermatology Advisory Statement. Indeed, the data on the risk of developing SSI after dermatologic surgery in immunosuppressed patients are limited. However, it is possible that due to the insufficient evidence on the risk of SSI occurrence in this patient group, dermatologic surgeons tend to overuse perioperative antibiotic prophylaxis.
To make specific recommendations on the use of antibiotic prophylaxis in immunosuppressed patients in the field of skin surgery, more information about the incidence of SSI after dermatologic surgery in these patients is needed. The aim of this study was to fill this data gap by investigating whether there is an increased risk of SSI after skin surgery in immunocompromised patients compared with immunocompetent patients.
The propagation of mechanical waves in plates of isotropic elastic material is investigated. After a short introduction to the understanding of focussing of stress waves in a plate with a curved boundary the method of characteristics is applied to a plate of hyperelastic material. Using this method the propagation of acceleration waves is discussed. Based on this a numerical difference scheme is developed for solving initial-boundary-value problems and applied to two examples: propagation of a point disturbance in a homogeneously finitely strained non-linear elastic plate and geometrical focussing in al linear elastic plate.
This article describes the fabrication, characterization and application of an epidermal temporary-transfer tattoo-based potentiometric sensor, coupled with a miniaturized wearable wireless transceiver, for real-time monitoring of sodium in the human perspiration. Sodium excreted during perspiration is an excellent marker for electrolyte imbalance and provides valuable information regarding an individual's physical and mental wellbeing. The realization of the new skin-worn non-invasive tattoo-like sensing device has been realized by amalgamating several state-of-the-art thick film, laser printing, solid-state potentiometry, fluidics and wireless technologies. The resulting tattoo-based potentiometric sodium sensor displays a rapid near-Nernstian response with negligible carryover effects, and good resiliency against various mechanical deformations experienced by the human epidermis. On-body testing of the tattoo sensor coupled to a wireless transceiver during exercise activity demonstrated its ability to continuously monitor sweat sodium dynamics. The real-time sweat sodium concentration was transmitted wirelessly via a body-worn transceiver from the sodium tattoo sensor to a notebook while the subjects perspired on a stationary cycle. The favorable analytical performance along with the wearable nature of the wireless transceiver makes the new epidermal potentiometric sensing system attractive for continuous monitoring the sodium dynamics in human perspiration during diverse activities relevant to the healthcare, fitness, military, healthcare and skin-care domains.
The applicability of differential pulse voltammetry (DPV) and adsorptive stripping voltammetry (AdSV) at a non-toxic meniscus-modified silver solid amalgam electrode (m-AgSAE) for the determination of trace amounts of genotoxic substances was demonstrated on the determination of micromolar and submicromolar concentrations of 3-nitrofluoranthene using methanol - 0.01 mol L-1 NaOH (9:1) mixture as a base electrolyte and of Ostazine Orange using 0.01 mol L-1 NaOH as a base electrolyte.
On the basis of bivariate data, assumed to be observations of independent copies of a random vector (S,N), we consider testing the hypothesis that the distribution of (S,N) belongs to the parametric class of distributions that arise with the compound Poisson exponential model. Typically, this model is used in stochastic hydrology, with N as the number of raindays, and S as total rainfall amount during a certain time period, or in actuarial science, with N as the number of losses, and S as total loss expenditure during a certain time period. The compound Poisson exponential model is characterized in the way that a specific transform associated with the distribution of (S,N) satisfies a certain differential equation. Mimicking the function part of this equation by substituting the empirical counterparts of the transform we obtain an expression the weighted integral of the square of which is used as test statistic. We deal with two variants of the latter, one of which being invariant under scale transformations of the S-part by fixed positive constants. Critical values are obtained by using a parametric bootstrap procedure. The asymptotic behavior of the tests is discussed. A simulation study demonstrates the performance of the tests in the finite sample case. The procedure is applied to rainfall data and to an actuarial dataset. A multivariate extension is also discussed.
In a special paired sample case, Hotelling’s T² test based on the differences of the paired random vectors is the likelihood ratio test for testing the hypothesis that the paired random vectors have the same mean; with respect to a special group of affine linear transformations it is the uniformly most powerful invariant test for the general alternative of a difference in mean. We present an elementary straightforward proof of this result. The likelihood ratio test for testing the hypothesis that the covariance structure is of the assumed special form is derived and discussed. Applications to real data are given.
The paper deals with an asymptotic relative efficiency concept for confidence regions of multidimensional parameters that is based on the expected volumes of the confidence regions. Under standard conditions the asymptotic relative efficiencies of confidence regions are seen to be certain powers of the ratio of the limits of the expected volumes. These limits are explicitly derived for confidence regions associated with certain plugin estimators, likelihood ratio tests and Wald tests. Under regularity conditions, the asymptotic relative efficiency of each of these procedures with respect to each one of its competitors is equal to 1. The results are applied to multivariate normal distributions and multinomial distributions in a fairly general setting.