On a Kelvin-Voigt Viscoelastic Wave Equation with Strong Delay

An initial-boundary value problem for a viscoelastic wave equation subject to a strong time-localized delay in a Kelvin & Voigt-type material law is considered. Transforming the equation to an abstract Cauchy problem on the extended phase space, a global well-posedness theory is established using the operator semigroup theory both in Sobolev-valued $C^{0}$- and BV-spaces. Under appropriate assumptions on the coefficients, a global exponential decay rate is obtained and the stability region in the parameter space is further explored using the Lyapunov's indirect method. The singular limit $\tau \to 0$ is further studied with the aid of the energy method. Finally, a numerical example from a real-world application in biomechanics is presented.Comment: 34 pages, 4 figures, 1 set of Matlab code

Armoede tussen de plooien: aanvullingen en correcties op EU-SILC voor verborgen groepen armen

Jaar na jaar publiceren de Belgische en Europese overheden armoedestatistieken op basis van de EU-SILC survey, een grootschalige enquête naar de inkomsten en levensomstandigheden van gezinnen in Europa. Niettegenstaande de schat aan gegevens die EU-SILC oplevert, liggen er ook addertjes onder het gras: selectieve non-respons bij kansarme groepen, en zelfs a priori uitsluiting van groepen zoals daklozen en mensen zonder papieren. Wat is de mogelijke vertekening in de armoedestatistieken als gevolg hiervan? Op welke manier kunnen deze cijfers recht getrokken worden? En wat zijn dan de levensomstandigheden van deze groepen in vergelijking met andere armen in België

Localization effects in a periodic quantum graph with magnetic field and spin-orbit interaction

A general technique for the study of embedded quantum graphs with magnetic fields and spin-orbit interaction is presented. The analysis is used to understand the contribution of Rashba constant to the extreme localization induced by magnetic field in the T3 shaped quantum graph. We show that this effect is destroyed at generic values of the Rashba constant. On the other hand, for certain combinations of the Rashba constant and the magnetic parameters another series of infinitely degenerate eigenvalues appears.Comment: 25 pages, typos corrected, references extende

Exponential stability of the wave equation with memory and time delay

We study the asymptotic behaviour of the wave equation with viscoelastic damping in presence of a time-delayed damping. We prove exponential stability if the amplitude of the time delay term is small enough

Motivic Serre invariants, ramification, and the analytic Milnor fiber

We show how formal and rigid geometry can be used in the theory of complex singularities, and in particular in the study of the Milnor fibration and the motivic zeta function. We introduce the so-called analytic Milnor fiber associated to the germ of a morphism f from a smooth complex algebraic variety X to the affine line. This analytic Milnor fiber is a smooth rigid variety over the field of Laurent series C((t)). Its etale cohomology coincides with the singular cohomology of the classical topological Milnor fiber of f; the monodromy transformation is given by the Galois action. Moreover, the points on the analytic Milnor fiber are closely related to the motivic zeta function of f, and the arc space of X. We show how the motivic zeta function can be recovered as some kind of Weil zeta function of the formal completion of X along the special fiber of f, and we establish a corresponding Grothendieck trace formula, which relates, in particular, the rational points on the analytic Milnor fiber over finite extensions of C((t)), to the Galois action on its etale cohomology. The general observation is that the arithmetic properties of the analytic Milnor fiber reflect the structure of the singularity of the germ f.Comment: Some minor errors corrected. The original publication is available at http://www.springerlink.co

X-Ray Microanalysis of Calcium Containing Organelles in Resin Embedded Tissue

The localization of calcium in cell organelles at the electron microscope level is often achieved through cytochemical techniques, and verified by X-ray microanalysis. Various methods have been used to cytochemically detect calcium or calcium-binding sites : calcium loading, calcium substitution by strontium, barium, or even lead, and calcium precipitation by oxalate, phosphate, fluoride, or pyroantimonate. Their results may have heuristic value, particularly in preliminary studies of poorly known cell types. A complementary and more physiological approach is offered by quantitative measurement of the total calcium content of organelles after cryofixation. Resin embedding is less demanding than cryomicrotomy and gives better images : it can be used after cryosubstitution in the presence of oxalic acid. This technique was tested, and applied to several cell types

Well-Posedness and Symmetries of Strongly Coupled Network Equations

We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered interactions take place at the boundary, i. e., in the nodes of the network. We discuss well-posedness of the associated initial value problem as well as contractivity and positivity properties of its solutions. Finally, we discuss qualitative properties that can be formulated in terms of invariance of linear subspaces of the state space, i. e., of symmetries of the associated physical system. Applications to a neurobiological model as well as to a system of linear Schroedinger equations on a quantum graph are discussed.Comment: 25 pages. Corrected typos and minor change

Quantum ergodicity for graphs related to interval maps

We prove quantum ergodicity for a family of graphs that are obtained from ergodic one-dimensional maps of an interval using a procedure introduced by Pakonski et al (J. Phys. A, v. 34, 9303-9317 (2001)). As observables we take the L^2 functions on the interval. The proof is based on the periodic orbit expansion of a majorant of the quantum variance. Specifically, given a one-dimensional, Lebesgue-measure-preserving map of an interval, we consider an increasingly refined sequence of partitions of the interval. To this sequence we associate a sequence of graphs, whose directed edges correspond to elements of the partitions and on which the classical dynamics approximates the Perron-Frobenius operator corresponding to the map. We show that, except possibly for subsequences of density 0, the eigenstates of the quantum graphs equidistribute in the limit of large graphs. For a smaller class of observables we also show that the Egorov property, a correspondence between classical and quantum evolution in the semiclassical limit, holds for the quantum graphs in question.Comment: 20 pages, 1 figur

In-patient treatment in functional and sectorised care: patient satisfaction and length of stay.

BACKGROUND: Debate exists as to whether functional care, in which different psychiatrists are responsible for in- and out-patient care, leads to better in-patient treatment as compared with sectorised care, in which the same psychiatrist is responsible for care across settings. Aims To compare patient satisfaction with in-patient treatment and length of stay in functional and sectorised care. METHOD: Patients with an ICD-10 diagnosis of psychotic, affective or anxiety/somatoform disorders consecutively admitted to an adult acute psychiatric ward in 23 hospitals across 11 National Health Service trusts in England were recruited. Patient satisfaction with in-patient care and length of stay (LoS) were compared (trial registration ISRCTN40256812). RESULTS: In total, 2709 patients were included, of which 1612 received functional and 1097 sectorised care. Patient satisfaction was significantly higher in sectorised care (β = 0.54, 95% CI 0.35-0.73, P<0.001). This difference remained significant when adjusting for locality and patient characteristics. LoS was 6.9 days shorter for patients in sectorised care (β = -6.89, 95% CI -11.76 to -2.02, P<0.001), but this difference did not remain significant when adjusting for clustering by hospital (β = -4.89, 95% CI -13.34 to 3.56, P = 0.26). CONCLUSIONS: This is the first robust evidence that patient satisfaction with in-patient treatment is higher in sectorised care, whereas findings for LoS are less conclusive. If patient satisfaction is seen as a key criterion, sectorised care seems preferable. Declarations of interest None.European Commission 7th Framework Programme. Grant agreement number 602645

Recent Trends in the Diagnostic and Surgical Management of Benign Prostatic Hyperplasia in the U.S. from 2004 to 2017: Annual Changes in the Selection of Treatment Options and Medical Costs

Background: Transurethral resection of the prostate (TURP) is the gold-standard treatment for benign prostatic hyperplasia (BPH). However, laser surgery techniques (e.g., photoselective vaporization of the prostate (PVP), holmium laser, thulium laser enucleation of the prostate (HoLEP or ThuLEP)), and minimally invasive treatment options (e.g., UroLift) are increasingly replacing TURP. This study seeks to report the annual incidence, management trends, and costs of BPH procedures in the U.S. Methods: Data analyses of U.S. health insurance claims from 2004 to 2017, collected from the de-identified Optum Clinformatics Claims Database, were performed to determine the number of BPH patients and the treatment selected. Results: A total of 51,448 patients underwent BPH procedures from 2004 to 2017. There was a significant increase in the annual rate from 770 in 2004 to 6571 in 2017. The mean patient age (±SD) increased from 67.6 years old (±8.4) in 2004 to 73.4 years old (±8.4) in 2017. More than 60% of patients underwent cystourethroscopy and a post-void residual urine check for workup prior to surgical management. TURP was the most-common, and PVP was the second-most-common BPH procedure. Medical and total treatment costs increased, while the detection rate of prostate cancer after BPH surgery gradually decreased from 19.87% in 2004 to 5.78% in 2017. Conclusions: Our study demonstrates a recent trend in BPH management that replaces the traditional TURP technique with alternative methods. Due to rising costs, future studies should assess whether these newer methods are cost effective over the long ter