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Tougeron’s implicit function theorem and Hensel’s lemma are well known representatives concerning 2?-approximation/?-nondegeneracy implying existence of solutions with identity of order ?. This note aims to extend this
principle to equations ?[?] = 0 in Banach spaces, using ?-transversality concepts, which may geometrically be interpreted as generalized cones spanned by
submanifolds, each characterized by a certain expansion rate.
The number of manifolds in the cone, as well as their expansion rates, is recursively increased until an appropriate desingularization of the cone is build up
with linearization expressed by first ? + 1 derivatives of the singular operator
at the base point.
Along these lines, a well-defined submersion is constructed in the cone with
uniformly bounded inverse when approaching the singularity. The techniques
are restricted to curves, possibly touching by high order the singular locus of ?, but ultimately traversing it, in this way defining an isolated singularity of the
operator family given by the linearization along the curve.
The fine resolution of the cone by the manifolds represents an improvement
compared to measuring the variation of the nonlinear operator exclusively by
the overall behaviour of the determinant.
In case of finite dimensions, each half-cone is characterized by a constant topological degree that can be used to investigate a solution curve in general position with respect to secondary bifurcation.
The core of all considerations is given by some characteristic patterns, valid in
the system of undetermined coefficients that allow for detailed analysis of the
power series resulting from plugging the power series of the ansatz into the
power series of the nonlinear operator.
Open Source
(2020)
In der IT-Branche hat sich Open-Source-Software (OSS) heute durchgesetzt, führende IT-Konzerne verwenden Open-Source-Code und entwickeln ihn auch selbst. Doch auch für Unternehmen anderer Branchen bietet Open-Source-Software Potenzial. In diesem Beitrag erfahren Sie, dass Open-Source-Software nicht nur ein Schlagwort, sondern genau definiert ist,was es mit den Risiken von Open Source auf sich hat und wie man damit umgeht, welche Vorteile und Potenziale Open-Source-Software auch für Nicht-IT-Firmen bietet.
Im Projekt KWK-Flex untersuchte die Hochschule Kempten innovative Methoden und Anlagenbetriebsstrategien zur flexiblen, stromgeführten Fahrweise von Kraft-Wärme-Kopplungs-(KWK)-Anlagen in Fernwärmeverbundnetzen im Kontext steigender Anteile erneuerbarer Energien. Solche KWK-Anlagenverbunde im Leistungsbereich ab einigen MW werden in Deutschland aufgrund ihrer hohen Brennstoffnutzungsgrade und der daraus folgenden Ressourcen- und Klimafreundlichkeit von mehreren hundert Stadtwerken bzw. Fernwärmeversorgern betrieben.
Bei der Methodenentwicklung und den daraus resultierenden optimierten Anlagenbe-triebsstrategien standen neben den Zielgrößen Dynamik und Flexibilität der Strombe-reitstellung insbesondere die Ressourceneffizienz, d.h. hohe Wirkungsgrade, geringe Emissionen und hohe Wirtschaftlichkeit, sowie eine hohe Versorgungssicherheit im Fokus. Als Schwerpunkte des Forschungsvorhabens wurde Untersuchungen zur in-stationären Prozesssimulation von KWK-Kraftwerken mit dem Ziel der Erhöhung der stromseitigen Anlagendynamik mit dem Einsatz numerischer Methoden zur optimierten Anlageneinsatzplanung der Kraftwerke in KWK-Verbunden kombiniert.
Das Projekt wurde am Institut für Energie- und Antriebstechnik (IEAT) der Hochschule Kempten mit Unterstützung der beiden assoziierten gewerblichen Partner Fernwärme Ulm GmbH (FUG) und ZAK Energie GmbH (ZAK) sowie dem Fernwärmeversorgerdachverband AGFW | Der Energieeffizienzverband für Wärme, Kälte u. KWK e.V. durchgeführt.
Die verstärkte Einbindung fluktuierender erneuerbarer Energien erfordert hochflexible thermische Kraftwerke zur Netzstabilisierung und bedarfsgerechten Abdeckung der verbleibenden Netzlasten. Für einen effizienten Anlageneinsatz spielt dabei die möglichst genaue Kenntnis der zu erwartenden Fernwärmelast eine zentrale Rolle. Für die Fernwärmelastprognose können innovative Verfahren unter Verwendung moderner maschineller Lernverfahren zum Einsatz kommen, die im Folgenden vorgestellt werden.
Silica gel is a well-known desiccant. Through dispersion of silica gel in a polymer, films can be made that absorb and desorb water vapor. The water vapor absorption becomes reversible by exposing such films to a water vapor pressure below that of the water vapor pressure during absorption, or by heating the film. The intention of this study was to achieve a better understanding about the water vapor absorption, permeability (H2O, N2, O2, CO2), and mechanical properties of films with dispersed silica gel. Low-density polyethylene (PE-LD) monolayer films with a nominal silica gel concentration of 0.2, 0.4, and 0.6 g dispersed silica gel per 1 g film (PE-LD) were prepared and they absorbed up to 0.08 g water vapor per 1 g of film. The water vapor absorption as a function of time was described by using effective diffusion coefficients. The steady state (effective) water vapor permeation coefficients of the films with dispersed silica gel were a factor of 2 to 14 (8.4 to 60.2·10−12 mg·cm·(cm2·s·Pa)−1, 23 °C) higher than for pure PE-LD films (4.3·10−12 mg·cm·(cm²·s·Pa)−1, 23 °C). On the other hand, the steady state gas permeabilities for N2, O2, and CO2 were reduced to around one-third of the pure PE-LD films. An important result is that (effective) water vapor permeation coefficients calculated from results of sorption and measured by permeation experiments yielded similar values. It has been found that it is possible to describe the sorption and diffusion behavior of water by knowing the permeability coefficient and the sorption capacity of the film (Peff.≈Seff.⋅Deff.). The tensile stress changed only slightly (values between 10 and 14 N mm−2), while the tensile strain at break was reduced with higher nominal silica gel concentration from 318 length-% (pure PE-LD film) to 5 length-% (PE-LD with 0.6 g dispersed silica gel per 1 g film).
Polymers with dispersed desiccants are relevant for various packaging applications to protect packaged goods from water vapor. The intention of this study was to analyze and to describe a relevant system. Therefore, films with calcium oxide (CaO) were investigated, because such materials are hardly described in scientific literature. Monolayer films with 0.14 to 0.51 g dispersed CaO per 1 g film (PE‐LD) were prepared and they absorbed up to 0.2 g water vapor per 1 g of film. The water vapor absorption was described by effective diffusion coefficients. By the use of effective diffusion coefficients and the absorption capacity, the absorption behavior of layers with various thicknesses can be estimated. The steady state (effective) water vapor permeation coefficients of the films with dispersed CaO were a factor of 2 to 24 (8.4 to 101.5 mg cm [cm2 s Pa]–1 × 1012, at 23 °C) higher than for pure PE‐LD films (4.26 mg cm [cm2 s Pa]−1 × 1012, 23 °C). The tensile stress changed only slightly (pure PE‐LD: 9.5 N mm−2; PE‐LD with 0.14 g dispersed CaO per 1 g film: 8.1 N mm−2; PE‐LD with 0.51 g dispersed CaO per 1 g film: 10.5 N mm−2), while the tensile strain at break was reduced with higher CaO concentration from 318% (pure PE‐LD) to 10% (PE‐LD with 0.51 g dispersed CaO per 1 g film). © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47460.
Packaging materials containing certain salts can regulate the humidity of packaged products. This study investigated whether thermoforming of foamed monolayer PP films with dispersed NaCl increases the water vapour sorption capacity and rate. Foamed monolayer PP-films (thickness 630 μm, porosity 0.28) with 6 (g/100 g) dispersed NaCl crystals were thermoformed to cups with depths up to 90 mm. By thermoforming the porosity increased up to 0.63 and the effective water vapour diffusion coefficient elevated by one order of magnitude from 10−11 to 10−10 cm²∙s−1. Therefore, such films absorb and desorb water vapour with a higher rate and they can bind more salt solution which is formed from solid salt crystals by water vapour absorption. Our results are important for packaging producers who thermoform films to cups and trays. This study addresses markets for fresh produce and other products with a high water activity.
Der moderne Karosseriebau ist geprägt durch den Wunsch nach einer schlanken Prozesskette, die sich durch hohe Prozesssicherheit auszeichnet. Im Umfeld der Fügetechnik rücken zur Erreichung dieses Ziels vermehrt sogenannte „unmittelbare Verbindungen“ in den Vordergrund. Hierbei handelt es sich um Fügeverbindungen, zu deren Erzeugung keine zusätzlichen Verbindungsmittel wie Schrauben oder Niete bereitgestellt werden müssen. Daher werden spezielle Schnappelemente für den Karosseriebau entwickelt, die als integraler Bestandteil aus dem Fügeteil ausgeformt werden. Durch den Einsatz derartiger Schnappelemente lässt sich die Teilevielfalt signifikant reduzieren. Das Fügen derartiger Teile erfolgt hierbei mit geringstem Zeitaufwand und nur mit der ohnehin zur Zuführung des Fügeteils benötigten Handhabungsvorrichtung.
Die assistierte Querführung wie das Spurhalteassistenzsystem ist ein Schlüssel zur erfolgreichen Einführung des hochautomatisierten Fahrens. Was empfindet der Kunde beim Einsatz von Spurhalteassistenzsystemen, und welche psychischen und physischen Belastungen lösen die verschiedenen Fahrsituationen aus? Welche Erwartungen hat er an das Fahrerlebnis? Was wird als angenehm und unangenehm empfunden, was wird akzeptiert, und welche Attribute sind inakzeptabel? Die Hochschule Kempten und MdynamiX sind diesen Fragen in breit angelegten Studien mit insgesamt 120 Probanden im Realeinsatz nachgegangen.
Support prospect of success in mathematics for first-year students in engineering by early feedback
(2020)
Providing students with the necessary mathematical skills is a growing challenge in German engineering degree courses. This is due to manifold mostly pre-university reasons, for example, inadequate or heterogeneous secondary education in Germany. Preparatory courses, a common remedy offered by many universities, often turn out to lack the expected effect. However, implying an early, mandatory test that scans the basic mathematical skills defined as entrance standard, showed positive results, as it detects the individual knowledge gaps of first-year students and motivates them to take action. For this purpose, we coupled the test with detailed, individual feedback and a cluster of affiliated support offers - preparatory to the test as well as attendant to the first year. Being mandatory, the test already pushes more students in our preparatory math courses. Whereas its detailed, individual feedback enables students to choose among the subsequent support offers and to cope with remaining gaps. The support offers range from transition workshops, co-learning tutorials, an online exercise platform, video tutorials up to conventional worksheets and consultation hours. This setup of mandatory test, early and detailed feedback and versatile supporting offers, tackling the missing skills, significantly increased the success in the basic mathematics and mathematics dependent modules of our engineering bachelor courses. In the process, this setup generates several additional, statistical outcomes, like a rating of the different German pre-university school systems, which helps to further work on measures dealing with the decreasing skills of beginners.
Church bells are exposed to severe loading conditions during ringing, which results in different damage modes due to material wear, fatigue loading, material deficiencies, different clapper-to-bell layouts, etc. As part of the activities of an EU-funded project called Maintenance and Protection of Bells (PROBELL), experimental investigations and finite-element simulations of the local contact between the clapper and the bell were carried out to study the wear-related damage to bells. First a simplified model was built to assess under the laboratory-controlled conditions the consequences of the repetitive impacts between a spherical body made from steel and a flat block made from bronze. After the results of the finite-element simulations for a simplified model were in reasonable agreement with the measured data a full-scale finite-element model for simulating the repetitive clapper-to-bell strokes was built. The simulations with the full-scale model were performed for variations of the parameters that influence the structural behaviour of the bell and the clapper: the clapper material, the clapper mass, the relative impact velocity of the clapper, the shape of the clapper, the clapper's pin support, the clapper's impact angle, the clapper's guide accuracy, the bell's sound-burp thickness and the coefficient of friction between the clapper and the bell. The agreement between the simulated and the measured results and the relation between the local stress–strain state and the damage to the bell in the contact area are discussed.
To investigate the combustion and emission behavior of straight vegetable oils (SVO), jatropha oil, soybean oil, and diesel fuel were tested. For this research, a 2.2L common-rail engine with a two-stage turbocharging concept was equipped with a cylinder pressure indication system, an exhaust-gas analyzer, an AVL Micro Soot sensor and a Scanning Mobility Particle Sizer 3936 (SMPS) device to detect the particle-size-distribution (PSD). At a low- and mid-load engine-operating point (EOP), the thermodynamic and emissions were investigated under various exhaust gas recirculation (EGR) rates with respect to the PSD. Moreover, the injection behavior of the three test fuels was analyzed separately using an injection rate analyzer. This procedure facilitates the thermodynamic investigations of the engine process and allows the calculation of the hydraulic delay (HD) as well as the ignition delay (ID). The ID of the SVO fuels compared to diesel fuel was found to be lower at all engine-operating modes, while jatropha oil always showed the shortest ID. In the particulate-nitrogen oxide (NOX) trade-off, the SVO fuels showed higher particulate matter (PM) emissions at the low-load EOP, whereas the PM emissions of diesel fuel overtop the SVO fuels at a higher engine load. With increased EGR-rates, a rise in the particle size was observed for all fuels. At the low-load EOP, the SVO fuels showed larger particles for high EGR-rates. This effect also changed by increasing the engine-load to the mid-load EOP, wherein the particle size of the diesel fuel emissions is higher by applying elevated EGR-rates.
A scanning Kerr microscope with a temporal resolution of <230 fs and a spatial resolution of 210 nm is presented. Equipped with a large temporal and spatial scanning range of 8 ns and 320 μm, respectively, the microscope allows studying nonuniform magnetization dynamics on many different time scales over a large area. For demonstration, we study the magnetization dynamics in Fe/Gd multilayer dot arrays exhibiting a spin reorientation transition (SRT) on three different time scales, namely, femtosecond, picosecond, and nanosecond scales. The dynamics on all time scales varies from one dot to another. This is attributed to the high sensitivity of the SRT to the variations of the layer thicknesses and the Fe/Gd interface structure.
The oxygen permeability of films is relevant for packaging related and technical applications. An increasingly used test method for the measurement of oxygen permeability is the optical test method, because it allows a simple and cost-efficient measurement setup. This method is based on optical chemical sensors. However, not much is known about its validity. Therefore, method validation is necessary which is subject of this study. The optical method is compared with the carrier gas method for a variety of film samples. In the tested permeability range of 0.5–2500 cm3 (STP)·(m2 d bar)−1 both methods deviated less than 20% for zero and 50% relative humidity.
Oxygen scavengers are used in food packaging to protect oxygen-sensitive food products. A mixture of gallic acid (GA) and sodium carbonate was used as an oxygen scavenger (OSc) in bio-based multilayer packaging films produced in a three-step process: compounding, flat film extrusion, and lamination. We investigated the film surface color as well as oxygen absorption at different relative humidities (RHs) and temperatures, and compared the oxygen absorption of OSc powder, monolayer films, and multilayer films. The films were initially brownish-red in color but changed to greenish-black during oxygen absorption under humid conditions. We observed a maximum absorption capacity of 447 mg O2/g GA at 21 °C and 100% RH. The incorporation of GA into a polymer matrix reduced the rate of oxygen absorption compared to the GA powder because the polymer acted as a barrier to oxygen and water vapor diffusion. As expected, the temperature had a significant effect on the initial absorption rate of the multilayer films; the corresponding activation energy was 75.4 kJ/mol. Higher RH significantly increased the oxygen absorption rate. These results demonstrate for the first time the production and the properties of a bio-based multilayer packaging film with GA as the oxygen scavenger. Potential applications include the packaging of food products with high water activity (aw > 0.86).
Water loss, gain or transfer results in a decline in the overall quality of food. The aim of this study was to form a uniform layer of sodium alginate-based edible coating (1.25% sodium alginate, 2% glycerol, 0.2% sunflower oil, 1% span 80, 0.2% tween 80, (w/w)) and investigate the effects on the water barrier characteristics of fresh-cut cantaloupe and strawberries. To this end, a uniform and continuous edible film formation was achieved (0.187 ± 0.076 mm and 0.235 ± 0.077 mm for cantaloupe and strawberries, respectively) with an additional immersion step into a calcium solution at the very beginning of the coating process. The coating application was effective in significantly reducing the water loss (%) of the cantaloupe pieces. However, no significant effect was observed in water vapor resistance results and weight change measurements in a climate chamber (80%→60% relative humidity (RH) at 10 °C). External packaging conditions (i.e., closed, perforated, and open) were not significantly effective on water activity (aw) values of cantaloupe, but were effective for strawberry values. In general, the coating application promoted the water loss of strawberry samples. Additionally, the water vapor transmission rate of stand-alone films was determined (2131 g·100 µm/(m2·d·bar) under constant environmental conditions (23 °C, 100%→50% RH) due to the ability to also evaluate the efficacy in ideal conditions.
Achieving high quality of a coated food product is mostly dependent on the characteristics of the food material to be coated, the properties of the components in the coating solution, and the obtained coating material. In the present study, usability and effectiveness of various components as well as their concentrations were assessed to produce an effective coating material. For this purpose, different concentrations of gelling agent (sodium alginate 0–3.5%, w/w), plasticizers (glycerol and sorbitol (0–20%, w/w), surfactants (tween 40, tween 80, span 60, span 80, lecithin (0–5%, w/w), and vegetable oils (sunflower oil, olive oil, rapeseed oil (0–5%, w/w) were used to prepare edible coating solutions. Formulations were built gradually, and characteristics of coatings were evaluated by analyzing surface tension values and its polar and dispersive components, emulsion droplet size, and optical appearance in microscopic scale. The results obtained showed that 1.25% sodium alginate, 2% glycerol, 0.2% sunflower oil, 1% span 80, and 0.2% tween 40 or tween 80 can be used in formulation to obtain an effective coating for hydrophobic food surfaces. Three formulations were designed, and their stability (emulsion droplet size, optical characteristics, and creaming index) and wettability tests on strawberry showed that they could be successfully used in coating applications
The water vapour transmission rate (WVTR) of packaging materials and edible coatings is one of their critical parameters for the shelf life of many food products. The water vapour transmission rates of flat bodies such as films are determined by permeation measurements which are a steady-state method. Another method is based on water vapour sorption measurements which is a non-steady-state method. It can be used only for mono-material flat bodies. It allows using smaller sample areas compared to permeation measurements. However, not much is known about how well both methods correlate with each other. Therefore, the aim of this study was to compare the WVTR results of different materials determined by both methods. The results of both methods differed by up to factor of three, measured at identical samples. In a few cases the difference was up to factor five. The exact reasons for these differences are unknown. Nonetheless, the water vapour sorption method is a suitable method to determine the magnitue of order of the water vapour transmission rate but not its exact value.
For “on board” diagnosis purposes of the injected fuel quantity flow sensitive elements based on the thermo-resistive measurement principle were integrated into finished Common Rail injection nozzles of valve-covered orifice (VCO) or mini-sac hole (MSH) class. Electron-discharge machining as well as electron beam welding technique are key technologies for a reliable integration procedure. To demonstrate negligible influence on the hydraulic performance of the nozzle after modification an optical measurement set-up is used to record temporally resolved the propagation of the spray patterns ejected from the six injection holes simultaneously. From these investigations the impact on the structural distortion of the valve caused by the welding seam is proved as its position can be directly linked to any chances in spray performance of each individual injection hole. Reducing the energy input during the electron beam welding lowers substantially the asymmetry in spray patterns from hole to hole as the needle uncovers the six injection holes more symmetrically. Besides this important finding, the numerical calculations indicate that the implementation of the sensor chip slightly amplifies the asymmetry induced by the welding process due to an additional weakening of the nozzle body which is confirmed experimentally. Despite these challenges, however, it is demonstrated that appropriate parameters for the integration procedure can be found affecting the hydraulic performance negligible compared to the original state.
Alginate is a naturally occurring polysaccharide used in the bio industry. It is mainly derived from brown algae species. Alginate-based edible coatings and films attract interest for improving/maintaining quality and extending the shelf-life of fruit, vegetable, meat, poultry, seafood, and cheese by reducing dehydration (as sacrificial moisture agent), controlling respiration, enhancing product appearance, improving mechanical properties, etc. This paper reviews the most recent essential information about alginate-based edible coatings. The categorization of alginate-based coatings/film in food packaging concept is formed gradually with the explanation of the most important titles. Emphasis will be placed on active ingredients incorporated into alginate-based formulations, edible coating/film application methods, research and development studies of coated food products and mass transfer and barrier characteristics of the alginate-based coatings/films. Future trends are also reviewed to identify research gaps and recommend new research areas. The summarized information presented in this article will enable researchers to thoroughly understand the fundamentals of the coating process and to develop alginate-based edible films and coatings more readily.