On the Number of Distinct Multinomial Coefficients

We study M(n), the number of distinct values taken by multinomial coefficients with upper entry n, and some closely related sequences. We show that both pP(n)/M(n) and M(n)/p(n) tend to zero as n goes to infinity, where pP(n) is the number of partitions of n into primes and p(n) is the total number of partitions of n. To use methods from commutative algebra, we encode partitions and multinomial coefficients as monomials.Comment: 16 pages, to be published in the Journal of Number Theor

Plasmaphysikalische Charakterisierung einer magnetfeldgestützten Hohlkathoden-Bogenentladung und ihre Anwendung in der Vakuumbeschichtung

Die vorliegende Dissertation behandelt Charakterisierung, Modellbildung sowie Anwendung einer magnetfeldgestützten Hohlkathoden-Bogenentladung. Hohlkathoden sind seit den 1960er Jahren Gegenstand grundlagen- sowie anwendungsorientierter Forschung und werden seit 20 Jahren am Fraunhofer-Institut für Elektronenstrahl- und Plasmatechnik für die Anwendung auf dem Gebiet der Vakuumbeschichtung weiterentwickelt. Ziel dieser Arbeit ist es, die technologischen Fortschritte physikalisch zu verstehen und gezielte Weiterentwicklungen für spezifische Einsatzgebiete zu ermöglichen. In der untersuchten Hohlkathodenbauform ist das aus Tantal bestehende, vom Arbeitsgas Argon durchströmte Kathodenröhrchen koaxial von einer Ringanode sowie von einer Magnetfeldspule umgeben. Die Entladung wird durch Hochspannungspulse gezündet, worauf sich ein diffuser Bogen im Röhrchen (internes Plasma) ausbildet. Das Röhrchen wird von Plasmaionen auf hohe Temperaturen geheizt, die eine thermionische Emission von Elektronen ermöglichen, welche das Plasma speisen. Das technologisch nutzbare externe Plasma wird im Vakuumrezipienten durch Wechselwirkung der Gasteilchen mit Strahlelektronen aus der Kathode erzeugt. Bei starker Reduktion des Arbeitsgasflusses wird die Entladung durch das Magnetfeld der Spule stabilisiert. Der experimentelle Befund, dass dadurch Plasmadichte und -reichweite sowie ggf. die Ladungsträgerenergien im Rezipienten aufgrund des intensiveren Elektronenstrahls wesentlich gesteigert werden können, wird durch ortsaufgelöste Langmuir-Sondenmessung, optische Emissionsspektroskopie und energieaufgelöste Massenspektrometrie ausführlich belegt und nach der Lösung von Strom- und Wärmebilanzgleichungen durch die Verhältnisse im Kathodenröhrchen begründet. Neben Argon werden auch typische Reaktivgase der Vakuumbeschichtung im Hohlkathodenplasma betrachtet: zum einen Stickstoff und Sauerstoff, die in reaktiven PVD-Prozessen (physikalische Dampfphasenabscheidung) zur Beschichtung mit Oxid- bzw. Nitridschichten zum Einsatz kommen und durch Ionisation, Dissoziation und Anregung im Hohlkathodenplasma verbesserte Schichteigenschaften ermöglichen; zum anderen Azetylen, das bei PECVD (plasmagestützte chemische Dampfphasenabscheidung) von amorphen wasserstoffhaltigen Kohlenstoffschichten z. B. für tribologische oder biokompatible Beschichtungen genutzt wird. Azetylen wird durch Streuprozesse mit Elektronen und Ionen im Plasma aufgespalten, wodurch schichtbildende Spezies erzeugt werden, die am Substrat kondensieren. Durch die Wahl der Plasmaparameter sowie durch abgestimmte Substratbiasspannung und Substratkühlung lassen sich die Beschichtungsrate einstellen sowie polymer-, graphit- oder diamantartige Eigenschaften erzielen. Neben der Plasmadiagnostik mittels energieaufgelöster Massenspektrometrie werden die erzeugten Kohlenstoffschichten vorgestellt und hinsichtlich Härte, Zusammensetzung und Morphologie analysiert.In the present thesis, characterization, modeling and application of a magnetically enhanced hollow cathode arc discharge are presented. Since the 1960s, hollow cathodes are being studied in basic and applied research. At Fraunhofer Institute for Electron Beam and Plasma Technology, further development concerning the application in vacuum coating technology has been carried out for about twenty years. The present work targets on physically understanding the technological progress in order to enable specific further development and application. In the investigated hollow cathode device, a ring-shaped anode and a magnetic field coil are arranged coaxially around the tantalum cathode tube, which is flown through by argon as the working gas. The discharge is ignited by high voltage pulses establishing a diffuse arc within the cathode tube (internal plasma). The cathode is being heated by the plasma ions to high temperatures, which leads to thermionic emission of electrons sustaining the plasma. The external plasma in the vacuum chamber, which can be used for technological applications, is generated by collisions of gas atoms with beam electrons originating from the cathode. In the case of strongly reduced working gas flow, the discharge is stabilized by the magnetic field of the coil; the related experimental findings such as significantly increased plasma density and range as well as higher charge carrier energies in the external plasma are extensively proved by spatially resolved Langmuir probe measurements, optical emission spectroscopy, and energy-resolved ion mass spectrometry. Furthermore, the results are correlated to the conditions within the cathode tube by solving the current and heat balance equations. Besides argon, typical reactive gases used in vacuum coating are examined in the hollow cathode plasma, too. First, nitrogen and oxygen, which are applied in PVD (physical vapor deposition) processes for the deposition of oxide and nitride layers, are ionized, dissociated, and excited by plasma processes. In the case of practical application, this plasma activation leads to improved film properties. Second, acetylene is used as a precursor for PECVD (plasma-enhanced chemical vapor deposition) of amorphous hydrogenated carbon films, e.g. for tribological or biocompatible applications. Acetylene is cracked by electron and ion scattering in the plasma providing film-forming species to be deposited on the substrate. The deposition rate as well as the polymeric, graphitic, or diamond-like properties can be controlled by plasma parameters, a defined substrate bias, and substrate cooling. The hollow cathode-generated acetylene plasma has been characterized by energy-resolved ion mass spectrometry, and the carbon films obtained are analyzed regarding hardness, film composition, and morphology

Optical emission spectroscopy for rate and composition control of plasma-assisted EBPVD processes

Currently, EB-PVD of YSZ layers is the standard process for TBC on turbine components. Due to the similar vapor pressures of yttria and zirconia, processing is relatively uncomplicated, and the good performance of this material in various aspects is not easy to beat. However, the increasing need for enhanced turbine efficiency and reduced emissions requires new approaches and developments. This calls for improved TBC systems or ceramic-based turbine components coated with EBC systems, which go hand in hand with the use of new admixed materials and more complex coating compositions. Consequently, the corresponding PVD processes become more challenging as well and should be aided by enhanced monitoring and control means therefore. Plasma activation of various PVD processes has been shown to be key to success in order to combine high-rate film growth with the requested film properties. The vapor and the reactive gas species are excited, ionized, and dissociated. The energy of charged particles impinging the substrate surface can be tuned resulting in layers with desired density, composition, hardness, or microstructure. The effect of plasma activation by using a hollow cathode arc discharge onto the morphology of YSZ layers [1,2] and its potential for coating of dense EBC’s [3] have been discussed previously. In this paper, another aspect of utilizing a plasma discharge in the vapor cloud will be discussed. Due to excitation of neutrals and ions, element-specific light emission occurs which can be analyzed by optical emission spectroscopy (OES). The spectrum can be used to monitor and control the PVD process. As an example, YSZ has been evaporated by EB-PVD, and an emission line of excited zirconium neutrals has been used to maintain a constant deposition rate. Moreover, metallic zirconium and yttrium have been co-evaporated in oxygen atmosphere by spotless arc-assisted EB-PVD [4], and the vapor species have been monitored by OES. In another project, co-evaporation of several metallic ingots has been performed by the jumping beam method, and an OES-based control loop is being developed to automatically control the EB power input and feeding speed of the individual ingots. This plasma-based OES control method has a considerable potential for the development of reliable, well-defined deposition processes. In addition, the co-evaporation approach may be of increased interest to deposit new complex TBC and EBC systems. [1] G. Mattausch et al.: 55th SVC Annual Technical Conference Proceedings, 179-185 (2012) [2] B. Zimmermann et al.: Poster presentation at ECI Thermal Barrier Coatings IV, Irsee, Germany (2014) [3] B. Zimmermann et al.: Poster presentation at ECI Advanced Ceramic Matrix Composites, Santa Fe, USA (2017) [4] B. Scheffel et al.: Surface & Coatings Technology 316, 155–161 (2017

The potential of plasma activation for EB-PVD of EBC systems on CMC components

Gas turbines are subject of intense research and development in order to meet increasing demands on fuel efficiency, reduction of emissions, or enhanced power. One of the major keys is improving the thermal efficiency by increased gas temperature within the turbine. In the hot turbine section, nickel-based superalloy components with thermal barrier coatings are utilized, which are still being refined and improved. Nevertheless, in order to significantly increase temperature capability and turbine efficiency, silicon-based non-oxide ceramics are being investigated and introduced as new base materials, allowing for lower-weight components operating at elevated temperatures. Severe weight losses due to water vapor corrosion, increasing temperature demands and other challenges require protecting environmental barrier coatings (EBC) to be applied on such ceramic components. The development of EBC systems already went through a number of generations, including mullite and barium-strontium-aluminosilicate (BSAS) based layers, various rear earth silicate coatings, hafnia or zirconia doping, and more. Utilizing processing techniques based on plasma spray and EB-PVD methods, tremendous progress has been made regarding the performance of the coating systems. However, improving the thermal, mechanical and chemical stability as well as the resistance against attack from calcia-magnesia-alumina-silica (CMAS) deposits, water vapor corrosion, or damage due to particle impact is still a hot topic of further development. Fraunhofer FEP has been developing PVD processes as well as corresponding hardware such as EB guns and plasma sources in a large field of applications for decades. Selected examples are corrosion protection layers on steel, oxygen and water vapor permeation barrier coatings on plastic webs, hard and wear-resistant coatings on tools, or TBC. In the most cases, plasma activation of the PVD process is the key to success in order to combine high-rate film growth with the requested film properties. The vapor and – if prevalent – the reactive gas species are excited, ionized, and dissociated. The energy of charged particles impinging the substrate surface can be tuned resulting in layers with desired density, composition, hardness, or microstructure. From FEP’s experience, it can be derived that the beneficial effect of plasma activation could complement the above mentioned EBC developments to address the present challenges. Please click Additional Files below to see the full abstract

Intestinal DMBT1 Expression Is Modulated by Crohn’s Disease-Associated IL23R Variants and by a DMBT1 Variant Which Influences Binding of the Transcription Factors CREB1 and ATF-2

Objectives: DMBT is an antibacterial pattern recognition and scavenger receptor. In this study, we analyzed the role of DMBT1 single nucleotide polymorphisms (SNPs) regarding inflammatory bowel disease (IBD) susceptibility and examined their functional impact on transcription factor binding and downstream gene expression. Methods: Seven SNPs in the DMBT1 gene region were analyzed in 2073 individuals including 818 Crohn’s disease (CD) patients and 972 healthy controls in two independent case-control panels. Comprehensive epistasis analyses for the known CD susceptibility genes NOD2, IL23R and IL27 were performed. The influence of IL23R variants on DMBT1 expression was analyzed. Functional analysis included siRNA transfection, quantitative PCR, western blot, electrophoretic mobility shift and luciferase assays. Results: IL-22 induces DMBT1 protein expression in intestinal epithelial cells dependent on STAT3, ATF-2 and CREB1. IL-22 expression-modulating, CD risk-associated IL23R variants influence DMBT1 expression in CD patients and DMBT1 levels are increased in the inflamed intestinal mucosa of CD patients. Several DMBT1 SNPs were associated with CD susceptibility. SNP rs2981804 was most strongly associated with CD in the combined panel (p = 3.0×10−7, OR 1.42; 95% CI 1.24–1.63). All haplotype groups tested showed highly significant associations with CD (including omnibus P-values as low as 6.1×10−18). The most strongly CD risk-associated, non-coding DMBT1 SNP rs2981804 modifies the DNA binding sites for the transcription factors CREB1 and ATF-2 and the respective genomic region comprising rs2981804 is able to act as a transcriptional regulator in vitro. Intestinal DMBT1 expression is decreased in CD patients carrying the rs2981804 CD risk allele. Conclusion: We identified novel associations of DMBT1 variants with CD susceptibility and discovered a novel functional role of rs2981804 in regulating DMBT1 expression. Our data suggest an important role of DMBT1 in CD pathogenesis

Effect of SP-B peptides on the uptake of liposomes by alveolar cells

Background: Exogenous surfactant has been accepted worldwide as a therapy of RDS in premature and term infants. Exogenous surfactant is usually derived from lung extracts containing phospholipids and the surfactant proteins SP-B and SP-C. Synthetic peptides of SP-B and SP-C are being tested with the aim to develop a completely synthetic surfactant preparation. Nevertheless, the effects of these peptides on the endogenous surfactant metabolism remain unknown. Objectives: The effect of synthetic SP-B peptides on uptake of surfactant-like liposomes was investigated in alveolar cells. Native SP-B and seven SP-B peptides were included: monomeric and dimeric SP-B1-25(Cys-11 → Ala-11), SP-B63-78and Ala-SP-B63-78(Cys-71 → Ala-71;Cys-77 → Ala-77)and their serine mutants. Methods: In vitro, alveolar macrophages (AM) and alveolar type II cells (ATII) were incubated with liposomes containing SP-B or one of its peptides. In vivo, rats received intratracheally various SP-B peptides (SP-B/lipid ratio 1:33 w/w) incorporated in fluorescent surfactant-like liposomes. One hour after instillation, AM and ATII were isolated and cell-associated fluorescence was determined using flow cytometry. Confocal laser microscopy was performed to ensure internalization of the liposomes. Results: In vitro uptake by AM or ATII was not influenced by the SP-B peptides. In vivo, SP-B1-25and Ser-SP-B1-25increased the uptake by AM whereas dSP-B1-25decreased the uptake. Neither SP-B1-25nor dSP-B1-25affected total uptake by ATII. The overall uptake by SP-B63-78variants was not changed. Conclusions: Surface-active synthetic SP-B peptides do not interfere with the normaluptake of surfactant by ATII. Copyrigh

Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order

Abstract We employ computer algebra algorithms to prove a collection of identities involving Bessel functions with half-integer orders and other special functions. These identities appear in the famous Handbook of Mathematical Functions, as well as in its successor, the DLMF, but their proofs were lost. We use generating functions and symbolic summation techniques to produce new proofs for them

Feedback inhibition of the general phenylpropanoid and flavonol biosynthetic pathways upon a compromised flavonol-3-O-glycosylation

Flavonols, phenylalanine-derived secondary metabolites, have protective and regulatory functions in plants. In Arabidopsis thaliana, they are consecutively glycosylated at their 3-OH and 7-OH groups. UGT78D1 and UGT78D2 are the major flavonol 3-O-glycosyltransferases in Arabidopsis leaves. The ugt78d1 ugt78d2 double mutant, which was strongly compromised in the initial 3-O-glycosylation, showed a severe and specific repression of flavonol biosynthesis, retaining only one-third of the wild-type level. This metabolic phenotype was associated with a repressed transcription of several flavonol biosynthetic genes including the committed step chalcone synthase [(CHS) or TRANSPARENT TESTA 4 (TT4)]. Furthermore, the committed step of the upstream, general phenylpropanoid pathway, phenylalanine ammonia-lyase (PAL), was down-regulated in its enzyme activity and in the transcription of the flavonol-related PAL1 and PAL2. However, a complete blocking of flavonoid biosynthesis at CHS released PAL inhibition in a tt4 ugt78d1 ugt78d2 line. PAL activity was even enhanced in the flavonol synthase 1 mutant, which compromises the final formation of flavonol aglycones. The dependence of the PAL feedback inhibition on flavonols was confirmed by chemical complementation of tt4 ugt78d1 ugt78d2 using naringenin, a downstream flavonoid intermediate, which restored the PAL repression. Although aglycones were not analytically detectable, this study provides genetic evidence for a novel, flavonol-dependent feedback inhibition of the flavonol biosynthetic pathway and PAL. It was conditioned by the compromised flavonol-3-O-conjugation and a decrease in flavonol content, yet dependent on a residual, flavonol synthase 1 (FLS1)-related capacity to form flavonol aglycones. Thus, this regulation would not react to a reduced metabolic flux into flavonol biosynthesis, but it might prevent the accumulation of non-glycosylated, toxic flavonols