Inverse spectral problems for energy-dependent Sturm-Liouville equations

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.Comment: AMS-LaTeX, 28 page

Improvement of the Process of Mechanical Dehydration of Five-Layer Semi-finished Wet Leather Products

To improve the process of mechanical dehydration of semi-finished wet leather products, a multilayer dehydration using felt materials – monshons was experimentally investigated. The process is conducted by vertical feed of semi-finished wet leather products on a base plate between rotating squeezing rollers. The D-optimal method of mathematical planning of the experiment and the Kano design matrix were used for conducting experiments. The multi-layer package consists of five layers of semi-finished wet leather products and two layers of moistureremoving materials between each layer, folded over the base plate. The studies were carried out in laboratory conditions on an experimental bench, taking into account the production parameters of processing. As a result of the study, mathematical dependences of the amount of removed moisture for each of five layers of semifinished wet leather product on the feed speed and the pressure of the squeezing rollers were derived. The analysis of the results showed that, with the existing parameters of mechanical dehydration, it was possible to simultaneously squeeze out moisture from five layers of the semi-finished leather product with a minimum pressure of the squeezing rollers and an average feed speed. The productivity of the technological process was more than five times higher in comparison with the productivity of similar roller machines. In the near future, this research methodology will be used to determine the technological factors affecting the extraction of excess moisture from a package consisting of ten semi-finished wet leather products and moisture-removing materials

Beyond single-photon localization at the edge of a Photonic Band Gap

We study spontaneous emission in an atomic ladder system, with both transitions coupled near-resonantly to the edge of a photonic band gap continuum. The problem is solved through a recently developed technique and leads to the formation of a ``two-photon+atom'' bound state with fractional population trapping in both upper states. In the long-time limit, the atom can be found excited in a superposition of the upper states and a ``direct'' two-photon process coexists with the stepwise one. The sensitivity of the effect to the particular form of the density of states is also explored.Comment: to appear in Physical Review

Entanglement Sudden Death in Band Gaps

Using the pseudomode method, we evaluate exactly time-dependent entanglement for two independent qubits, each coupled to a non-Markovian structured environment. Our results suggest a possible way to control entanglement sudden death by modifying the qubit-pseudomode detuning and the spectrum of the reservoirs. Particularly, in environments structured by a model of a density-of-states gap which has two poles, entanglement trapping and prevention of entanglement sudden death occur in the weak-coupling regime

Spatial optical solitons in nonlinear photonic crystals

We study spatial optical solitons in a one-dimensional nonlinear photonic crystal created by an array of thin-film nonlinear waveguides, the so-called Dirac-comb nonlinear lattice. We analyze modulational instability of the extended Bloch-wave modes and also investigate the existence and stability of bright, dark, and ``twisted'' spatially localized modes in such periodic structures. Additionally, we discuss both similarities and differences of our general results with the simplified models of nonlinear periodic media described by the discrete nonlinear Schrodinger equation, derived in the tight-binding approximation, and the coupled-mode theory, valid for shallow periodic modulations of the optical refractive index.Comment: 15 pages, 21 figure

Effects of hospital facilities on patient outcomes after cancer surgery: an international, prospective, observational study

Background Early death after cancer surgery is higher in low-income and middle-income countries (LMICs) compared with in high-income countries, yet the impact of facility characteristics on early postoperative outcomes is unknown. The aim of this study was to examine the association between hospital infrastructure, resource availability, and processes on early outcomes after cancer surgery worldwide.Methods A multimethods analysis was performed as part of the GlobalSurg 3 study-a multicentre, international, prospective cohort study of patients who had surgery for breast, colorectal, or gastric cancer. The primary outcomes were 30-day mortality and 30-day major complication rates. Potentially beneficial hospital facilities were identified by variable selection to select those associated with 30-day mortality. Adjusted outcomes were determined using generalised estimating equations to account for patient characteristics and country-income group, with population stratification by hospital.Findings Between April 1, 2018, and April 23, 2019, facility-level data were collected for 9685 patients across 238 hospitals in 66 countries (91 hospitals in 20 high-income countries; 57 hospitals in 19 upper-middle-income countries; and 90 hospitals in 27 low-income to lower-middle-income countries). The availability of five hospital facilities was inversely associated with mortality: ultrasound, CT scanner, critical care unit, opioid analgesia, and oncologist. After adjustment for case-mix and country income group, hospitals with three or fewer of these facilities (62 hospitals, 1294 patients) had higher mortality compared with those with four or five (adjusted odds ratio [OR] 3.85 [95% CI 2.58-5.75]; p<0.0001), with excess mortality predominantly explained by a limited capacity to rescue following the development of major complications (63.0% vs 82.7%; OR 0.35 [0.23-0.53]; p<0.0001). Across LMICs, improvements in hospital facilities would prevent one to three deaths for every 100 patients undergoing surgery for cancer.Interpretation Hospitals with higher levels of infrastructure and resources have better outcomes after cancer surgery, independent of country income. Without urgent strengthening of hospital infrastructure and resources, the reductions in cancer-associated mortality associated with improved access will not be realised

The Improvement of the Rheological Model of Leather

Fibrous capillary-porous materials, such as woven materials and leather, used in the light industry for clothing and footwear, differ sharply from metallic materials. These differences manifest themselves in a complex relationship between stress and strain, which depends on the strain rate and loading time. A method for determining the identified new rheological parameter of the inert resistance of a capillary-porous material (for example, leather) of accelerated deformation is presented in the article; it consists in determining the indentation force of a conical indenter at a constant speed and the coefficient that considers shear zones, and the angle formed by the boundaries of the material deformation zone and application of force value. An equation for an improved rheological model of leather is derived; it consists of the Kelvin model, the Bingham-Shvedov model, and the Khusanov model, expressed in terms of the rheological parameter in the form of a deformation inertness coefficient. The inclusion of the model of deformation inertness in the form of a coefficient into the rheological model of leather will allow the mathematical description of the rheological parameters of leather and the development of engineering methods for their calculation. The implementation of the developed method will allow obtaining numerical values of the rheological parameter of the inert resistance of the capillary-porous material under its accelerated deformation, namely, a new property of the capillary-porous material, which must be taken into account in various technological processing operations, for example, when treating moisture-saturated leather