bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the discrepancy of 3 permutations
Authors: Bohus Géza 
Published: May 2007

AbstractConsider different orderings of an n‐element set and the hypergraph consisting of the intervals of these orderings. A conjecture of J. Beck states that in the case of three orderings this hypergraph has bounded discrepancy. We show that for any constant number of orderings the discrepancy is O(log n). the proof also gives an efficient algorithm to determine such a coloring.
Poisson approximation for large deviations
Authors: Janson Svante 
Published: May 2007

AbstractUpper and lower bounds are given for P(S ≤ k), 0 ≤ k ≤ ES, where S is a sum of indicator variables with a special structure, which appears, for example, in subgraph counts in random graphs. in typical cases, these bounds are close to the corresponding probabilities for a Poisson distribution with the same mean as S. There are no corresponding general bounds for P(S ≥ k), k > ES, but some partial results are given.
A correlation inequality and a poisson limit theorem for nonoverlapping balanced subgraphs of a random graph
Authors: Suen W. C. Stephen 
Published: May 2007

AbstractWe consider non‐overlapping subgraphs of fixed order in the random graph Kn, p(n). Fix a strictly strongly balanced graph G. A subgraph of Kn, p(n) isomorphic to G is called a G‐subgraph. Let Xn be the number of G‐subgraphs of Kn, p(n) vertex disjoint to all other G‐subgraphs. We show that if E[Xn]→∞ as n→, then Xn/E[Xn] converges to 1 in probability. Also, if E[Xn]→c as n→∞, then Xn satisfies a Poisson limit theorem. the Poisson limit theorem is shown using a correlation inequality similar to those appeared in Janson, Łuczak, and Ruciñski[8] and Boppana and Spencer [4].
Matchings in random spanning subgraphs of cubelike graphs
Authors: Kostochka Alexandr V. 
Published: May 2007

AbstractA question about the evolution of random spanning subgraphs Gp of bipartite regular so called cubelike graphs G is considered. It is shown that for Gp of any large enough cubelike graph G the threshold to have a 1‐factor is the same as the threshold to have no isolated vertices. This generalizes a conjecture of K. Weber.
Quasi‐random classes of hypergraphs
Authors: Chung Fan R. K. 
Published: May 2007

AbstractWe investigate the relations among a number of different graph properties for k‐uniformhypergraphs, which are shared by random hypergraphs. Various graph properties form equivalence classes which in turn constitute a natural hierarchy. The analogues for binary functions on k‐tuples and for hypergraphs with small density are also considered. Several classes are related to communication complexity and expander graphs.
Small cliques in random graphs
Authors: Barbour A. D. , Janson Svante , Karoński Michal , Ruciński Andrzej 
Published: May 2007

AbstractFor d ≥ 1, a d‐clique in a graph G is a complete d‐vertex subgraph not contained in any larger complete subgraph of G. We investigate the limit distribution of the number of d‐cliques in the binomial random graph G(n, p), p = p(n), n→∞.
A note on bipartite subgraphs of triangle‐free graphs
Authors: Shearer James B. 
Published: May 2007

AbstractLet G be a triangle‐free graph on n points with m edges and vertex degrees d1, d2,…, dn. Let k be the maximum number of edges in a bipartite subgraph of G. In this note we show that k ⩾ m/2 + Σ √di. It follows as a corollary that k ⩾ m/2 + cm3/4.
Random recursive forests
Authors: Balińska Krystyna T. , Quintas Louis V. , Szymański Jerzy 
Published: May 2007

AbstractA random recursive forest is defined as a union of random recursive trees. We find the expected number of trees in the uniform random recursive forest as well as the number of vertices of given degree, the maximum degree, the height of vertices, the order of branches, the root of the component containing a given vertex, and the last root of such forests. © 1994 John Wiley & Sons, Inc.
Note on independent sets in steiner systems
Authors: Rödl Vojtěch , Šinajová Edita 
Published: May 2007

AbstractA partial Steiner (n, k, l)‐system or briefly (n, k, l)‐system is a pair (V, S), where V is an n‐set and S is a collection of k‐subsets of V, such that every l‐subset of V is contained in at most one k‐subset of S. A subset X ⊂ V is called independent if [X]k ∩ S = 0. The size of the largest independent set in S is denoted by α(S). Define

The purpose of this note is to prove that for every k, l, k > l

holds, where c, d are positive constants depending on k and l only.
Ansätze zur Lösung der Grundgleichungen der Elastizitätstheorie
Authors: Marguerr K. 
Published: May 2007

AbstractIn den letzten Jahren sind zahlreiche Probleme der Elastizitätstheorie in 2 und 3 Dimensionen gelöst worden. Die Lösungsansätze, scheinbar ganz verschiedener Natur, erweisen sich bei näherem Zusehen als miteinander nahe verwandt: letzten Endes versucht man die Lösung aus Potentialfunktionen aufzubauen. Die vorliegende Arbeit stellt die Beziehungen zwischen einer großen Zahl solcher Ansätze her, und ergänzt sie durch einen didaktisch naheliegenden neuen. Ein Anhang gibt die wichtigsten Vektor‐ und Tensor‐Rechenregenl.
Inversion of a perfectly elastic spherical shell
Authors: Ericksen J. L. 
Published: May 2007

AbstractThe problem of inversion of a spherical shell which is made of an incompressible, perfectly elastic material is solved in full generality. It is shown that, if the strain energy is of the form assumed in the Mooney‐Rivlin theory for rubber, then the surfaces of the deformed shell may be left free of surface tractions.
Ein praktisches Verfahren zur Lösung biquadratischer Gleichungen mit nur komplexen Wurzeln
Authors: Ludwig Rudolf 
Published: May 2007

AbstractFür die biquadratische Gleichung erhält man für komplexe Wurzeln durch Trennung von Real‐ und Imaginärteil zwei reelle Gleichungen, deren Resultante die Realteile als Wurzeln hat. Es wird ein praktisches Rechenverfahren angegeben zur iterativen Ermittlung von Näherungswerten der reellen Wurzeln dieser Resultante, bei dem man nur das vollständige, reelle Horner‐Schema der gegebenen Gleichung benötigt. Die zugehörigen Imaginärteile sind einfach auszurechnen.
The Film Combustion of Liquid Fuel
Authors: Emmons H. W. 
Published: May 2007

AbstractFür Tröpfchen, die größer als, sagen wir, 10−1 Zoll sind, entfernen Wärmeleitungs‐ und Diffusionsprozesse die chemische Reaktionszone weit genug vom Tröpfchen dorthin, wo sie für die Effekte des Tröpfchens selbst weniger sensibel ist, und daher die Verbrennungsgeschwindigkeit von den Wärmeleitungs‐ und Massenprozessen selbst gesteuert wird. Dieses Problem wird in dieser Arbeit untersucht und teilweise gelöst.
Die dicke Platte mit nichtlinearer Spannungsverteilung
Authors: Koppe Eberhard 
Published: May 2007

AbstractAm Beispiel der dicken Platte mit nichtlinearer Spannungsverteilung wird dargelegt, wie man ausgehend von den Invarianten des Problems einen bequemen und allgemeinen Weg zu strengen Lösungen findet. An den Seitenrändern der Platte können dabei unabhängig voneinander Normal‐ und Tangentialkräfte, Randscherkräfte, Randbiege‐ und Randdrillmomente vorgeschrieben werden. Für zwei sehr allgemeine und praktisch wichtige Klassen von Belastungen werden die Verteilungsfunktionen für die Verschiebungen über die Plattendicke ausgerechnet.
Zum Differenzenverfahren bei parabolischen Differentialgleichungen
Authors: Albrecht Julius 
Published: May 2007

AbstractDiskussion des Differenzenverfahrens bei parabolischen Differentialgleichungen (Wärmeleitungs‐ und Stabschwingungsgleichung): Zusammenhang zwischen Stabilität, Zeitschrittweite und Lage der verwendeten Gitter‐punkte; Genauigkeit (Mehrstellenverfahren); gekrümmte Ränder; Runge‐Kutta‐Prinzip.
Berechnungsergebnisse der radialen Schaufelgitterströmung
Authors: Isay Wolfgang‐Hermann 
Published: May 2007

AbstractIn der vorliegenden im Institut für Angewandte Mathematik der Deutschen Akademie der Wissenschaften zu Berlin durchgeführten Arbeit werden numerische Ergebnisse der radialen Schaufelgitterströmung mitgeteilt und diskutiert. Diese Ergebnisse wurden mit Hilfe der vom Verfasser in früheren Arbeiten veröffentlichten Schaufelgittertheorie erhalten.
Praktische Lösung von Eigenwertaufgaben des Hartree‐Fockschen Typs
Authors: Dettmar H.‐K. , Schlüter A. 
Published: May 2007

AbstractIn der vorliegenden Arbeit wird eine numerische Methode zur genäherten Lösung der Schrödingergleichung des quantenmechanischen Mehrkörperproblems der Elektronen einer Atomhülle beschrieben. Das Hauptaugenmerk wird auf die mathematische Durschführung gelegt, während das physikalische Problem in den Hintergrund tritt. Die herangezogenen mathematischen Hilfsmittel sowie die abgeleiteten Formeln sind möglichst allgemein gehalten und unabhängig von den genannten Problemen in § 1 zusammengestellt.
Über ein Warteproblem aus der Vermittlungstechnik
Authors: Störmer Horand 
Published: May 2007

AbstractDie bekannte, von A. K. Erlang angegebene Verteilung der Wartezeiten, die vor einer zentralen Steuereinrichtung mit konstanter Arbeitszeit T0 auftreten, gilt für den Fall, daß wartende Anrufe in der Reihenfolge ihres Eintreffens abgefertigt werden. In der Praxis ist diese Voraussetzung häufig nicht erfüllt. Die wartenden Anrufe werden vielmehr in einer durch Zufall bestimmten Reihenfolge abgefertigt.In der folgenden Untersuchung wird zunächst die Verteilung der Wartezeiten bei Abfertigung der wartenden Anrufe nach einer bestimmten Rangordnung (m verschiedene Rangstufen) hergeleitet. Dann wird angenommen, daß jedem Anruf zufallsmäßig eine dieser m Rangstufen (Dringlichkeitsstufen) zugeordnet wird. Für m → ∞ ergibt sich ein einfacher geschlossener Ausdruck für die Verteilungsfunktion der Wartezeiten.
Stresses due to Diametral Forces in Tension on an Eccentric Hole of a Circular Disc
Authors: Gupta D. P. 
Published: May 2007

AbstractIn this paper, the problem of determining stresses in a circular disc with an eccentric circular hole is taken up, when the hole is subjected to two equal and opposite forces in tension along the line of centres, the outer boundary of the disc being unstressed. The solution is determined in bipolar coordinates. From the results thus obtained the stresses on a semi‐infinite plate acted upon by two equal and opposite diametral forces in tension on a circular hole in the plate in the direction of the normal to the straight boundary, the latter being kept free, have been deduced.
Zur Frage der Fehlerabschätzung beim Verfahren der harmonischen Balance
Authors: Sagirow P. 
Published: May 2007

AbstractDie harmonische Balance liefert uns für die Frequenz und Amplitude einer periodischen Lösung von (1) gewisse Werte ωhund ah. Die Fehler, mit denen diese Näherungswerte behaftet sind, bleiben jedoch unbekannt.In der vorliegenden Arbeit wird ein Verfahren vorgeschlagen, das in sehr vielen Fällen eine sukzessive Abschätzung des Frequenzfehlers und eine anschließende Abschätzung des Amplitudenfehlers gestattet. Dabei wird festgestellt, daß im allgemeinen schon ein geringer Frequenzfehler einen großen Amplitudenfehler nach sich zieht.Ein Beispiel wird durchgerechnet.
Some Problems in the Small Deflexions of Clamped Thin Isotropic Plates
Authors: Bassali W. A. 
Published: May 2007

AbstractConformal mapping methods are applied to find exact solutions in finite terms for the small deflexions of certain thin clamped curvilinear plates subject to symmetrical loading distributed over the area of a circle or acted by isolated forces or couples at arbitrary or specified points. Plates bounded by the inverses of an ellipse with respect to internal or boundary points are included. Regular curvilinear polygonal plates bounded by n equal and very approximately circular arcs are also considered.
Zur Theorie der diskreten unsymmetrischen Irrfahrt
Authors: Henze E. 
Published: May 2007

AbstractFür die unsymmetrische Irrfahrt im ebenen Gitter der Punkte mit ganzzahligen Koordinaten werden das Klassifikationsproblem, die Übergangswahrscheinlichkeit mit ihrer erzeugenden Funktion, das Visitenproblem und die wichtigsten Absorptionswahrscheinlichkeiten behandelt. Als Gebiete werden dabei die unbegrenzte Ebene und die obere Halbebene mit der Abszissenachse als punktweise 1‐absorbierender Berandung zugrunde gelegt und die asymptotischen Ausdrücke für verschwindende Maschenweite des Gitters aufgestellt.
The Influence of Tocopherols on the Oxidation Stability of Methyl Esters
Authors: Fröhlich András , Schober Sigurd 
Published: May 2007

AbstractTocopherols were found to be the principal natural antioxidants in biodiesel grade fatty acid methyl esters. The stabilising effect of α‐, γ‐ and δ‐ tocopherols from 250 to 2,000 mg/kg was evaluated by thermal and accelerated storage induction times based on rapid viscosity increase, in sunflower (SME), recycled vegetable oil (RVOME), rapeseed (RME) and tallow (TME) methyl esters. Both induction times showed that stabilising effect is of the order of δ‐ > γ‐ > α‐tocopherol, and that the stabilising effect increased with concentration. The correlation between the two induction times however was poor, which is probably due to the fact that the time they correspond to two different stages of oxidation. Tocopherols were found to stabilise methyl esters by reducing the rate of peroxide formation while present. The deactivation rates of tocopherols increased with unsaturation of the particular methyl ester and in the present work they were of the order of SME > RME > RVOME > TME. While α‐tocopherol was found to be a relatively weak antioxidants, both γ‐ and δ‐ tocopherols increased induction times significantly and should be added to methyl esters without natural antioxidants.
Volatile compounds produced during deodorization of soybean oil and their flavor significance
Authors: Kao Jian‐Wen , Hammond Earl G. , White Pamela J. 
Published: May 2007

AbstractFreshly deodorized soybean oil has a characteristic nutty flavor but often yields no detectable headspace volatiles. The cause of this flavor was investigated by deodorizing soybean oil in an apparatus with a double cold trap that allowed the volatile compounds formed from the initial decomposition of hydroperoxides to be collected separately from those produced during the normal deodorization process. The chief volatile components from the normal deodorization process were hydrocarbons, which contributed little to no odor to the oil. The compounds with the greatest odor were carbonyls, especially heptanal and cis‐4‐heptenal. Although these comonpents should accumulate at some steady‐state concentration in an oil during its deodorization, none seemed to account for the flavor of the deodorized oil. By using a particle detector, it was shown that small particles could be generated in the human mouth that could provide a mechanism to bring oil with nonvolatile flavor components into contact with the olfactory organ. Attempts to separate possible nonvolatile flavors in deodorized oil from triacylglycerides by chromatography on alumina or reaction with 2,4‐dinitrophenylhydrazine were unsuccessful. Possibly, the flavor is caused by the glycerol esters themselves.
Chloramine T with iodine: A new reagent to determine the iodine value of edible oils
Authors: Nagendrappa Giddappa , Raj Urs S. Subramanya , Rajalakshmi S. 
Published: May 2007

AbstractChloramine T (N‐chloro‐p‐toluenesulfonamide sodium salt) and iodine (2:1, w/w) in carbon tetrachloride and acetic acid (1:1, vol/vol), referred to as reagent (I) was found to be effective for the determination of Iodine value of edible oils. Reagent (I) reacted quantitatively with the double bonds of oils of known weight. The reagent left unreacted after 20–25 min was titrated against standard sodium thiosulfate solution (0.04 M) in presence of potassium iodide (10%, 5 mL). The difference in volume of sodium thiosulfate solution consumed by reagent (I) without and with oil was a basis to calculate the iodine value of oils used. The iodine values of different oils were also determined separately following the standard procedure of Wijs, and calculated iodine value was obtained from the gas chromatographic profile of fatty acids. The iodine value obtained by the new method was in agreement with the results of the standard methods. The results obtained indicate that the method could be a complementary or an alternative to the Wijs method.
Effect of α‐ and γ‐tocopherols on thermal polymerization of purified high‐oleic sunflower triacylglycerols
Authors: Lampi Anna‐Maija , Kamal‐Eldin Afaf 
Published: May 2007

AbstractThe antipolymerization effects of α‐ and γ‐tocopherols were compared in model systems composed of purified high‐oleic sunflower triacylglycerols at 180°C. γ‐Tocopherol was much more effective as an antipolymerization inhibitor than α‐tocopherol, partly due to lower oxidizability/disappearance. Purified triacylglycerols of sunflower, rapeseed, and high‐oleic sunflower oils were less stable than their nonpurified forms containing tocopherols. Results confirmed that tocopherols per se can act as antipolymerization agents in high‐oleic oils at frying temperatures. No synergism was observed when α‐ and γ‐tocopherols were present together although larger amounts of residuals were left for both tocols. Results suggested that high‐oleic/high‐γ‐tocopherol oils (such as high‐oleic canola and high‐oleic soybean oils) may provide better frying oils than high‐oleic/high‐α‐tocopherol oils (such as high‐oleic sunflower oil).
Soybean lipoxygenase is active on nonaqueous media at low moisture: a constraint to xerophilic fungi and aflatoxins?
Authors: Gardner Harold W. , Grove Marilyn J. , Keller Nancy P. 
Published: May 2007

AbstractPrevious workers have reported that certain products of the lipoxygenase pathway are detrimental either to the development and growth of Aspergillus species or to aflatoxin production by these organisms. Since Aspergillus often thrives on “dry” stored grains, depending on the level of the relative humidity, we sought to determine if lipoxygenase could catalyze the oxidation of linoleic acid on these “dry” substrates equilibrated at various relative humidities. A desiccated model system, previously adjusted to pH 7.5, was composed of soybean extract, linoleic acid, and cellulose carrier. The model system was incubated for up to 24 h at four relative humidities ranging between 52 and 95% to determine the extent of oxidation catalyzed by lipoxygenase, compared with heat‐inactivated controls. Oxidation in the active samples was much greater than in the controls at all relative humidities, and oxidation was principally enzymatic as demonstrated by chiral analysis of the linoleate hydroperoxides formed. The main product was 13S‐hydroperoxy‐9Z,11E‐octadecadienoic acid, accompanied by a significant percentage of 9S‐hydroperoxy‐10E,12Z‐octadecadienoic acid. Since the products became more racemic with time of incubation, autoxidation appeared to be initiated by the lipoxygenase reaction in dry media. Additionally, the biological relevance of lipoxygenase activity was tested under these xerophilic conditions. Thus, enzyme‐active and heat‐inactivated defatted soy flour amended either with or without 3.5% by weight linoleic acid was inoculated with fungal spores and incubated at 95% relative humidity. Although fungal growth occurred on all treatments, samples inoculated with Aspergillus parasiticus showed significantly less aflatoxin in the enzyme‐active samples, compared to inactivated flour. Addition of linoleic acid had little effect, possibly because the defatted soy flour was found to contain 1.7% residual linoleic acid as glyceride lipid.
The influence of chemical interesterification on the physicochemical properties of complex fat systems. 2. Morphology and polymorphism
Authors: Rousseau Dérick , Marangoni Alejandro G. , Jeffrey Ken R. 
Published: May 2007

AbstractPalm oil‐soybean oil (POSBO) blends and lard‐canola oil (LCO) blends were chemically interesterified with sodium methoxide. Changes in crystal morphology using polarized light microscopy and crystal polymorphic behavior using X‐ray diffraction spectroscopy (XRD) were studied. Spherulitic crystalline particles, measuring 10–20 µm, were detected in palm oil (PO). These spherulitic particles were characterized by a dense core surrounded by a lower‐density halo region. PO fat‐crystal morphology was not greatly altered on addition of soybean oil (SBO), except for a gradual reduction in spherulite size as the amount of SBO in the blends was increased. Chemical interesterification (IE) did not alter PO or POSBO blend fat‐crystal morphology significantly. Irregular particles and spherulites of different sizes and shapes were observed in lard, from small crystals to irregular, angular crystal aggregates. Changes in lard fat‐crystal morphology due to the addition of canola oil (CO) were concentration‐dependent. In general, spherulite diameter decreased with increasing CO addition. IE dramatically altered lard fat‐crystal morphology—IE induced the formation of more symmetrical spherulitic crystalline particles, and the halo‐to‐core ratio was increased significantly. XRD spectroscopic analysis of POSBO blends revealed small changes in the long spacings of PO fat crystals with either blending or IE; all values were close to 45 Å. Short spacings of fat crystals in noninteresterified (NIE) POSBO blends suggested the predominance of β′ polymorphs. IE led to an increase in the proportion of the β polymorph in PO and POSBO blends. Long spacings of NIE lard fat crystals suggested the presence of a bilayer structure in their unit cells (45 Å). Dilution with ≥10% canola oil led to the appearance of a second reflection at 35 Å. β′ polymorphs were predominantly detected in NIE lard and NIE LCO blends. The β polymorph became more evident with increasing addition of CO. Fat crystals in IE lard and IE LCO blends displayed a single long‐spacing reflection at 40 Å. IE of lard and LCO blends induced the formation of β polymorphs.
A fully robotic method for the determination of acid values in olive oil without titration
Authors: Velasco‐Arjona A. , Luque de Castro M. D. 
Published: May 2007

AbstractA method for the determination of acid values (AV) in olive oil without titration is proposed, based on pH measurements on an oil sample emulsion in a suitable reagent and fully automated using a robotic station. The robot performs the weighing of the sample, adds the reagent, emulsifies both, and measures the pH of the emulsion. The data are acquired and treated by the computer. After optimization, two versions of the measurement step (interpolation within a calibration curve and addition of standard) are developed and applied to 51 oil samples with AV values that also have been determined by the standard method based on potentiometric titration. Both versions are statistically compared with the standard method, and no significant differences are found. Excellent correlation (R>0.99) between all three methods demonstrates the usefulness of the fully automated approach that works at a sample rate of 15 sample h−1 with relative standard deviations lower than 2.5%.
Triglyceride analysis by gas chromatography in assessment of authenticity of goat milk fat
Authors: Fontecha J. , Díaz V. , Fraga M. J. , Juárez M. 
Published: May 2007

AbstractThe triglyceride (TG) composition of 35 samples of milk collected at different times of year from five herds of goats was analyzed using short capillary column‐gas chromatography. The distribution of TG in goat milk fat was unimodal, peaking at C40 (12.6%); the sum of TG from C38 to C44 accounted for about 50%, whereas the three classes of TG from C48 to C52 did not exceed 6% each. These results were compared with the corresponding data for cow milk fat. Significant differences between herds were observed, mainly in long‐chain TG. To detect foreign fats in goat milk fat, two multiple regression equations based on TG content of the goat milk fat were proposed. Analysis of known mixtures of tallow, palm oil, and cow milk fat with goat milk fat have experimentally confirmed the accuracy of the equations.