bluuebunny/crossref_metadata_2025_split huggingface dataset:
Search algorithm for Ramsey graphs by union of group orbits
Authors: Radziszowski Stanisław P. , Kreher Donald L. 
Published: June 2007

AbstractAn algorithm for the construction of Ramsey graphs with a given automorphism group G is presented. To find a graph on n vertices with no clique of k vertices, Kk, and no independent set of l vertices, ¯Kl, k, l ≤ n, with an automorphism group G, a Boolean formula α based on the G‐orbits of k‐subsets and l‐subsets of vertices is constructed from incidence matrices belonging to G. This Boolean formula is satisfiable if and only if the desired graph exists, and each satisfying assignment to α specifies a set of orbits of pairs of vertices whose union gives the edges of such a graph. Finding these assignments is basically equivalent to the conversion of α from CNF to DNF (conjunctive to disjunctive normal form). Though the latter problem is NP‐hard, we present an “efficient” method to do the conversion for the formulas that appear in this particular problem. When G is taken to be the dihedral group Dn for n ≤ 101, this method matches all of the previously known cyclic Ramsey graphs, as reported by F. R. K. Chung and C. M. Grinstead [“A Survey of Bounds for Classical Ramsey Numbers,” Journal of Graph Theory, 7 (1983), 25–38], in dramatically smaller computer time when compared to the time required by an exhaustive search. Five new lower bounds for the classical Ramsey numbers are established: R(4, 7) ⩾ 47, R(4, 8) ⩾ 52, R(4, 9) ⩾ 69, R(5,7) ⩾ 76, and R(5, 8) ⩾ 94. Also, some previously known cyclic graphs are shown to be unique up to isomorphism.
On resolvable tree‐decompositions of complete graphs
Authors: Lonc Zbigniew 
Published: June 2007

AbstractA partition of the edge set of a graph H into subsets inducing graphs H1,…,Hs isomorphic to a graph G is said to be a G‐decomposition of H. A G‐decomposition of H is resolvable if the set {H1,…,Hs} can be partitioned into subsets, called resolution classes, such that each vertex of H occurs precisely once in each resolution class. We prove that for every graceful tree T of odd order the obvious necessary conditions for the existence of a resolvable T‐decomposition of a complete graph are asymptotically sufficient. This generalizes the results of Horton and Huang concerning paths and stars.
On the interval number of a chordal graph
Authors: Scheinerman Edward R. 
Published: June 2007

AbstractThe interval number of a (simple, undirected) graph G is the least positive integer t such that G is the intersection graph of sets, each of which is the union of t real intervals. A chordal (or triangulated) graph is one with no induced cycles on 4 or more vertices. If G is chordal and has maximum clique size ω(G) = m, then i(G) ⩽ [1 + o(1)]m/log2 m and this result is best possible, even for split graphs (chordal graphs whose complement is also chordal).
Some results on odd factors of graphs
Authors: Yuting Cui , Kano Mikio 
Published: June 2007

AbstractA {1, 3, …,2n − 1}‐factor of a graph G is defined to be a spanning subgraph of G, each degree of whose vertices is one of {1, 3, …, 2n − 1}, where n is a positive integer. In this paper, we give a sufficient condition for a graph to have a {1, 3, …, 2n − 1}‐factor.
Existence of Δλ‐cycles and Δλ‐paths
Authors: Broersma H. J. 
Published: June 2007

AbstractA Cycle C of a graph G is called a Dλ‐cycle if every component of G − V(C) has order less than λ A Dλ‐path is defined analogously. Dλ‐cycles and Dλ‐paths were introduced by Veldman. Here a cycle C of a graph G is called a Δλ‐cycle if all vertices of G are at distance less than λ from a vertex of C. A Δλ‐path is defined analogously. In particular, in a connected graph, a Δλ‐cycle is a Δλ‐Cycle and a Δλ‐Path is a Δ‐path. Furthermore, a Δ1‐cycle is a Hamilton cycle and a Δ1path is a Hamilton path. Necessary conditions and sufficient conditions are derived for graphs to have a Δλ‐cycle or Δλ‐path. The results are analogues of theorems on Dλ‐cycles and Dλ‐paths. In particular, a result of Chvátal and Erdös on Hamilton cycles and Hamiiton paths is generalized. A recent conjecture of Bondy and Fan is settled.
An extremal problem on Kr‐free graphs
Authors: Frankl Peter , Pach János 
Published: June 2007

AbstractLet r, t ⩾ 2 be integers and c a constant, 0 < c ⩽ (r ‐ 2)/(r − 1). Suppose that G is a Kr‐free graph on n vertices in which any t distinct vertices have at most cn common neighbors. Here an asymptotically best bound is obtained for the maximal number of edges in such graphs. This solves a problem of Babai et al. in a more general form.
A note on graphs with diameter‐preserving spanning trees
Authors: Buckley Fred , Lewinter Martin 
Published: June 2007

AbstractThe distance between a pair of vertices u, v in a graph G is the length of a shortest path joining u and v. The diameter diam(G) of G is the maximum distance between all pairs of vertices in G. A spanning tree T of G is diameter preserving if diam(T) = diam(G). In this note, we characterize graphs that have diameter‐preserving spanning trees.
Edge‐connectivity in p‐partite graphs
Authors: Volkmann Lutz 
Published: June 2007

AbstractLet G = (V, E) be a finite, simple p‐partite graph with minimum degree δ and edge‐connectivity γ. It is proved that if |V| ⩽ (2pδ)/(p ‐ 1) ‐ 2 or in special cases that if |V| ⩽ (2pδ)/(p ‐ 1) ‐ 1, then λ = δ. It is further shown that this result is best possible.
Graphs with intrinsic s3 convexities
Authors: Bandelt Hans‐Jürgen 
Published: June 2007

AbstractSeparation properties for some intrinsic convexities of graphs are investigated. The most natural convexities defined on a graph are the induced path convexity and the geodesic convexity. A set A of vertices is convex with respect to the former convexity if A contains every induced path connecting two vertices of A. In particular, a characterization of those graphs is given in which all such convex sets are the intersections of halfspaces (i.e., convex sets with convex complements).
A strengthening of Kikustapos;s theorem
Authors: Hendry George R. T. 
Published: June 2007

AbstractWe consider connected, locally connected graphs in which the maximum and minimum degrees differ by at most one and do not exceed five. It is shown that if C is a nonhamiltonian cycle in such a graph G, then there exists a cycle Capos; in G such that V(C) ⊆ V(Capos;) and /V(Capos;) = /(C) + 1.
Reduced graphs of diameter two
Authors: Lai Hong‐Jian 
Published: June 2007

AbstractA graph H is collapsible if for every subset X ⊆ V(H), H has a spanning connected subgraph whose set of odd‐degree vertices is X. In any graph G there is a unique collection of maximal collapsible subgraphs, and when all of them are contracted, the resulting contraction of G is a reduced graph. Interest in reduced graphs arises from the fact [4] that a graph G has a spanning closed trail if and only if its corresponding reduced graph has a spanning closed trail. The concept can also be applied to study hamiltonian line graphs [11] or double cycle covers [8]. In this article, we characterize the reduced graphs of diameter two. As applications, we obtain prior results in [12] and [14], and show that every 2‐edge‐connected graph with diameter at most two either admits a double cycle cover with three even subgraphs or is isomorphic to the Petersen graph.
The chromaticity of complete bipartite graphs with at most one edge deleted
Authors: Teo C. P. , Koh K. M. 
Published: June 2007

AbstractLet K(p, q), p ≤ q, denote the complete bipartite graph in which the two partite sets consist of p and q vertices, respectively. In this paper, we prove that (1) the graph K(p, q) is chromatically unique if p ≥ 2; and (2) the graph K(p, q) ‐ e obtained by deleting an edge e from K(p, q) is chromatically unique if p ≥ 3. The first result was conjectured by Salzberg, López, and Giudici, who also proved the second result under the condition that q ‐ p ≤ 1.
Maximal chromatic polynomials of connected planar graphs
Authors: Tomescu Ioan 
Published: June 2007

AbstractIn this paper we obtain chromatic polynomials of connected 3‐ and 4‐chromatic planar graphs that are maximal for positive integer‐valued arguments. We also characterize the class of connected 3‐chromatic graphs having the maximum number of p‐colorings for p ≥ 3, thus extending a previous result by the author (the case p = 3).
Zur iterativen Lösungseinschließung bei Anfangswertproblemen mittels Intervallmethoden
Authors: Bauch H. 
Published: June 2007

AbstractIn der vorliegenden Arbeit werden Voraussetzungen für iterative Verfahren zur intervallanalytischen Lösungseinschließung bei Anfangswertproblemen von Systemen gewöhnlicher Differentialgleichungen 1. Ordnung untersucht und Möglichkeiten zur Konvergenzbeschleunigung angegeben.
Über fast homogene turbulente Scherströmungen
Authors: Szablewski W. 
Published: June 2007

AbstractAuf der Grundlage einfacher mathematischer Ansätze für die Komponenten des Energieaustausches sowie für die Komponenten der Dissipation erhält man eine explizite Beschreibung der Entwicklung einer fast homogenen turbulenten Scherströmung, die mit kürzlich publizierten Messungen in Übereinstimmung steht. Aus der Gleichung der turbulenten Schubspannung folgt formelmäßig eine Abhängigkeit der Komponenten des Energieaustausches von der relativen Schubspannung (Schubspannung relativ zur Turbulenzenergie), die anscheinend durch vorliegende Messungen bestätigt wird.
Sensitivity Analysis for Beams and Plates (The Elementary Solution Approach)
Authors: Komkov V. 
Published: June 2007

AbstractWe consider the linear equations modelling the dynamic behavior of vibrating beams and thin plates. We develop the basic equations for the sensitivity function indicating the dynamic structural response to changes in design. Specifically, the properties of the sensitivity function are developed in detail for the vibrating beam equation. We conclude that the knowledge of an elementary solution of the beam equation, and of the sensitivity function for the elementary solution can be used to determine the sensitivity function for a class of admissible loads applied to the beam.
Zur Lösung der Navier‐Stokes‐Gleichung mit Hilfe eines voll impliziten Iterationsverfahrens
Authors: Zwick W. 
Published: June 2007

AbstractWir betrachten die Navier‐Stokes‐Gleichung in der up‐, ωΨ und Ψ‐Formulierung und verwenden zu ihrer Lösung ein voll implizites Iterationsverfahren. In jedem Iterationsschritt wird die linearisierte Navier‐Stokes‐Gleichung gelöst, deren Differentialoperatoren durch verschiedene Differenzenansätze approximiert werden. Zur Lösung der algebraischen Gleichungs‐systeme werden die Matrizen als Produkte aus unteren und oberen Dreiecksmatrizen dargestellt.
Einsatz mathematischer Methoden bei der Hydroenergiegewinnung
Authors: Bauer W. , Buchinger S. , Wacker Hj. 
Published: June 2007

AbstractDer Einsatz mathematischer Methoden im Bereich der Hydroenergieoptimierung wird an Hand von vier konkreten Projekten demonstriert:
Momentanoptimierung
Tagesoptimierung
Höhensteuerung eines Tagesspeicherkraftwerks
Optimierung des Schwellbetriebes.
Im Gegensatz zu (M1), (M2) und (M3) stellt (M4) erst eine Vorstudie dar, die jedoch eine bessere Approximation der Realität liefert als derzeit verwendete Modelle. Der Einsatz bisher bekannter Optimierungstechniken bei der numerischen Lösung speziell von (M1) stieß auf beträchtliche Schwierigkeiten. Aus diesem Grund wurden Optimierungsverfahren auf Einbettungsbasis entwickelt und mit Erfolg eingesetzt.
Instant Optimization
all days optimization
head control for a small storage plant
optimal floating policy for a river section.
Auto‐oscillation Systems with Inertial Self‐excitation
Authors: Babitsky V. I. , Landa P. S. 
Published: June 2007

AbstractA class of dynamical systems is described for which self‐excitation of oscillations is due to inertial interaction between the variables. A number of typical examples are presented for autooscillation systems of this type which are relevant to various fields of science and technology. It is shown that the self‐excited oscillations can be periodical, as well as stochastical, depending on the form of nonlinearities.
On the Choice of Steplength in Path Following Methods
Authors: Schwetlick H. 
Published: June 2007

AbstractA path following method of Newton type widely used in numerical practice is investigated by using a model based on the Kantorovich Theorem. It turns out that within this model a steplength near the maximal steplength accepted by the Kantorovich Theorem is most efficient provided that a uniform accuracy of all points is required. This theoretical result is confirmed by a numerical example taken from nonlinear circuit theory.
On the Convergence of the Higher Order Versions of D. J. Evans' Implicit Matrix Inversion Process
Authors: Alefeld G. 
Published: June 2007

AbstractThe higher order versions of the method introduced by D. J. Evans are investigated. We introduce sufficient conditions for convergence, prove some error estimations and show that under appropriate conditions the iterates are possessing monotonous behaviour. Furthermore we show that these methods can also be used to improve an approximation for the pseudoinverse of a matrix with full column rank.
Nonconvex Problems of Semipermeable Media and Related Topics
Authors: Panagiotopoulos P. D. 
Published: June 2007

AbstractThe present paper deals with B V Ps in the theory of semipermeability potentials. Both the cases of interior and boundary semipermeability problems are studied. After the formulation of the problems in terms of hemivariational inequalities and the definition of the regularised problems an existence result is proved. The proof is constructive and may be used for the approximation of the solution of the problem. Finally, the developed method is applied to certain similar problems arising in the theory of elasticity.
Filmsieden bei der Umströmung der halbunendlichen ebenen Platte und des Keils durch inkompressible Flüssigkeiten
Authors: Schütte V. 
Published: June 2007

AbstractIm Rahmen der Grenzschichttheorie werden mit Hilfe der Methode der Integralsätze Aufgaben der Umströmung der halbunendlichen ebenen Platte durch eine Flüssigkeit, deren Temperatur außerhalb des Siedebereiches liegt, und der Umströmung des Keils durch eine siedende Flüssigkeit gelöst. Für kleine Werte des Parameters R = (ϱvμv/ϱLμL)0,5 werden analytische Näherungslösungen angegeben, insbesondere Formeln zur Bestimmung der Reibungs‐ und Wärmeübertragungskoeffizienten.
Die automatische Gleichungsgenerierung beliebig strukturierter mechanischer Systeme unter besonderer Berücksichtigung der Anforderungen der Anforderungen aus dem Schienenfahrzeugbau
Authors: Krettek O. , Ofierzyński M. 
Published: June 2007

AbstractDer Bau von spurgebundenen aber auch spurungebundenen Verkehrsmitteln ist an die strenge Einhaltung geometrischer, kinematischer, Statischer und dynamischer Restriktionen gebunden. Wird nur eine dieser Vorgaben verletzt, kann die Einsetzbarkeit des Fahrzeugs in Frage gestellt sein. Obwohl die entsprechenden Nachweise zum Teil äußerst aufwendig sind, fehlt es bis heute an einem EDV‐Programmsystem, das für sich in Anspruch nehmen kann, die Beziehungen für sämtliche erforderlichen Rechnungsgänge vollautomatisch und modellgetreu auch für verwickelte Mechanismen, wie sie etwa bei Schienenfahrzeuglaufwerken vorkommen, zu generieren und zu lösen. Diese Lücke soll das hier dargestellte graphentheoretisch aufgebaute vorerst allerdings lediglich in Teilen fertiggestellte System schließen. Einzugeben bleiben als einziges die rechnungsbedeutsamen Strukturpunkte sowie die Parameter des Fahrzeugs wie Massen, Längen, Federkennungen u. drgl. m.
A Curved Finite Element of Revolution Shells after Timoshenko's Shear Model
Authors: Rikards R. B. , Goldmanis M. V. 
Published: June 2007

AbstractThis paper discusses solutions of the problems associated with bending and stability of shells of revolution by means of the finite‐element method and using the principle of minimum potential energy and the theory of Timoshenko‐type shells. A curved finite element of third order is proposed to calculate shells of revolution under axisymmetric loads. The convergence properties of the proposed element are examined in the bending and stability problems. As examples are given the problems of bending of a cylindrical shell, deformation of a toroidal shell, stability analysis of a toroidal shell under external pressure and stability analysis of a shall of meridianally variable shape under external pressure.
Complex Swirling Radial Jets
Authors: Filip P. , Kolář V. , Curev A. G. 
Published: June 2007

Similarity solutions of single, multiple and antisymmetrical swirling radial jets are presented using a proposed 3‐D formulation of Reichardt's Hypothesis. The derivation of mean velocity field description of the multiple and antisymmetrical swirling radial jets is based on the superposition principle of single swirling radial jet solutions obtained from the linear equations of motion (derived in the frame of Reichardt's procedure). Hence, the method used provides — in contrast to other ones — a means flow analytical description of complex turbulent jets.Es werden die Ähnlichkeitslösungen des einfachen, mehrfachen und antisymmetrischen Radialstrahles mit Rotation vorgelegt, ausgehend von einer in Vorschlag gebrachten dreidimensionalen Formulierung der Reichardtschen Hypothese. Die Beschreibung des Feldes der gemittelten Geschwindigkeit des mehrfachen und des antisymmetrischen Radialstrahles mit Rotation basiert auf dem Superpositionsprinzip von Lösungen für den einfachen Radialstrahl mit Rotation, die sich aus den linearen Bewegungsgleichungen ergeben, die im Rahmen des Reichardtschen Verfahren erhalten wurden. Die in Vorschlag gebrachte Lösung liefert — zum Unterschied von anderen Methoden — eine analytische Bewschreibung des gemittelten Stromes der komplexen turbulenten Freistrahlen.
Ein objektives Stoffgesetz des plastischen Materialverhaltens
Authors: Backhaus G. 
Published: June 2007

AbstractDie in früheren Arbeiten des Verfassers entwickelte Spannungs‐Deformations‐Beziehung für beliebige plastische Verformungsvorgänge wird in die Form einer objektiven (bezugssystemindifferenten) Stoffgleichung gebracht. Am Beispiel einer großen Verformung wird gezeigt, daß die Unterschiede zwischen den Rechnungsergebnissen bei Benutzung der ersteren Beziehung (vereinfachte Stoffgleichung) und den Ergebnissen bei Verwendung der objektiven Stoffgleichung vernachlässigbar sind. Die vereinfachte Stoffgleichung kann zur Ermittlung von Größe und Richtung des Spannungs‐Vektors längs Verformungswegen großer Krümmung dienen. Rechnungen unter Verwendung experimentell ermittelbar Materialwerte zeigen, daß für Krümmungswerte unterhalb von 100 bis 10 — abhängig vom Material — die einfache Fließtheorie anwendbar ist.
Über simultane Eigenwertalgorithmen beim Schwingungsproblem
Authors: Meyer A , Döhler B. 
Published: June 2007

AbstractEs werden Verfahren zur simultanen Berechung einiger Eigenwerte und Eigenvektoren dargelegt, die besonders für großdimensionierte, schwach besetzte Matrizen geeignet sind, und es wird auf die Anwendung bei gedämpften und ungedämpften Schwingungsproblemen eingegangen.
Zur Berechnung der stochastisch erregten Schaufelradbaggernickschwingungen bei Berücksichtigung der Rückkopplung in der Schwingungserregung
Authors: Mohr H. , Renger A. 
Published: June 2007

AbstractEine Differentialgleichung, die die stochastischen und selbsterregten Nickschwingungen von Schaufelradbaggern beschreibt, wird unter Berücksichtigung der Rückkopplungseffekte am Schaufelrad hergeleitet und gelöst. Zur Bestimmung analytischer Näherungslösungen sowie zur Stabilitätsuntersuchung wird die Mittelungsmethode für stochastische Schwingungen nach Stratonowitch verwendet. Es wird eine ingenieurmäßige Darstellung dieser Methode gegeben, deren Anwendbarkeit auf die Baggerschwingungen durch numerische Integration der Differentialgleichung unter Verwendung eines Simulationsansatzes für die stochastischen Erregungen bestätigt wird.
Analysis of an Amplitude Equation for Autovibrational Flow Regimes at Resonance External Forces
Authors: Levina G. V. , Nepomnyaschiy A. A. 
Published: June 2007

AbstractResonance effects in viscous flows produced by unsteady external forces are studied. With the help of a small parameter method the amplitude equation for a resonance case is derived. It is shown that the amplitude of the secondary regime is proportional to the cubic root amplitude of external force. Possible transitions between supercritical motions are investigated. The map of secondary regimes in dependence on the amplitude equation coefficients is given.
Determination of Optimal Upstream Weighting Parameter for the Finite Element Solution of Transient Transport Equation
Authors: Honma S. , Karadi G. 
Published: June 2007

AbstractIn this study the results of a numerical experiment involving the finite element solution of the convection‐dominated transport equation are presented. It is shown that, for large Peclet numbers, the standard Galerkin approach produces unacceptable oscillations. Although the upstream weighting residual method eliminates this problem for steady state problems, its application to transient flow problems has received considerable criticism, because false dispersion and/or the smearing of steep gradients are observed. The numerical experiments performed for transient problems revealed that the upstream weighting residual method can be improved considerably if the upstream weighting parameter is selected as a function of the Courant number. Based on the results of these numerical experiments, a relationship between the optimal weighting parameter and the Courant number is proposed so that oscillations are eliminated and false dispersion is reduced to an acceptable level.
Zur optimalen Steuerung in Neumannschen Randbedingungen bei Evolutionsgleichungen
Authors: Kampowsky W. 
Published: June 2007

AbstractDie Arbeit beschäftigt sich mit Problemen optimaler Steuerung, die durch nichtlineare Rand‐Anfangswertprobleme für parabolische Differentialgleichungen zweiter Ordnung beschrieben werden. Es werden Randsteuerungen mit Randbedingungen vom Neumannschen Typ betrachtet. Das Rand‐Anfangswertproblem wird funktionalanalytisch verallgemeinert und als Anfangswertaufgabe für eine Evolutionsgleichung im Rahmen der Theorie monotoner Operatoren untersucht. Im wesentlichen werden notwendige Optimalitätsbedingungen hergeleitet, die aus einer allgemeinen Variationsungleichung und einer adjungierten Evolutionsgleichung bestehen. Die Arbeit ergänzt die Untersuchungen von Randsteuerungen in Dirichletschen Randbedingungen in [5].
A Mixed Finite Element Method for Fourth Order Partial Differential Equations
Authors: Balasundaram S. , Bhattacharyya P. K. 
Published: June 2007

AbstractThis paper deals with a new mixed finite element solution of the Dirichlet problem of fourth order elliptic linear partial differential operators with variable coefficients. As examples, bending problems of elastic plates having variable thickness have been considered, for which the algorithm of this method allows a simultaneous determination of the deflection, the curvature components and the „actual”︁ bending and twisting moments of the plate, the „actual”︁ bending and twisting moments being the components of the Lagrange multiplier of this method. Suitable error estimates are obtained under necessary regularity assumptions on the solution.
On Superlinear Convergence of Some Stable Variants of the Secant Method
Authors: Burdakov O. P. 
Published: June 2007

AbstractIn a recent author's paper four classes of methods of the secant type for solving systems of nonlinear equations were proposed. They are stable with respect to linear dependence of the search directions. If the Jacobian matrix is symmetric, then two of them take into account this property. It is proved here that some four special methods from the classes converge superlinearly.