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The spectral p -norm of r -matrices generalizes the spectral 2-norm of 2-matrices. In 1911 Schur gave an upper bound on the spectral 2-norm of 2-matrices, which was extended in 1934 by Hardy, Littlewood, and Pólya to r -matrices. Recently, Kolotilina, and independently the author, strengthened Schur's bound for 2-matrices. The main result of this paper extends the latter result to r -matrices, thereby improving the result of Hardy, Littlewood, and Pólya. The proof is based on combinatorial concepts like r-partite r-matrix and symmetrant of a matrix, which appear to be instrumental in the study of the spectral p -norm in general. Thus, another application shows that the spectral p -norm and the p -spectral radius of a symmetric nonnegative r -matrix are equal whenever p ≥ r . This result contributes to a classical area of analysis, initiated by Mazur and Orlicz back in 1930. Additionally, a number of bounds are given on the p -spectral radius and the spectral p -norm of r -matrices and r -graphs. [ABSTRACT FROM AUTHOR]

In this note we characterize, within the framework of the theory of finite set, those categories of graphs that are algebraic universal in the sense that every concrete category fully embeds in them. The proof of the characterization is based on the sparse–dense dichotomy and its model theoretic equivalent. [ABSTRACT FROM AUTHOR]

In the Lorentzian product G n × R 1 , we give a comparison theorem between the f -volume of an entire f -maximal graph and the f -volume of the hyperbolic H r + under the condition that the gradient of the function defining the graph is bounded away from 1. This condition comes from an example of non-planar entire f -maximal graph in G n × R 1 and is equivalent to the hyperbolic angle function of the graph being bounded. As a consequence, we obtain a Calabi–Bernstein type theorem for f -maximal graphs in G n × R 1 . [ABSTRACT FROM AUTHOR]

A 1-plane graph is a graph embedded in the plane such that each edge is crossed at most once. A 1-plane graph is optimal if it has maximum edge density. A red–blue edge coloring of an optimal 1-plane graph G partitions the edge set of G into blue edges and red edges such that no two blue edges cross each other and no two red edges cross each other. We prove the following: ( i ) Every optimal 1-plane graph has a red–blue edge coloring such that the blue subgraph is maximal planar while the red subgraph has vertex degree at most four; this bound on the vertex degree is worst-case optimal. ( ii ) A red–blue edge coloring may not always induce a red forest of bounded vertex degree. Applications of these results to graph augmentation and graph drawing are also discussed. [ABSTRACT FROM AUTHOR]

We present a novel approach for optimizing acoustic parameters using sensitivity analysis for computer-aided design and analysis of architectural models. Our approach builds on recent low-dispersion wave-based acoustic solvers that can accurately compute the pressure field in large models. We present an efficient technique to compute the gradient of the pressure field using automatic differentiation and combine that with a quasi-Newtonian optimization method to automatically compute the optimal material properties. We highlight the performance on many complex CAD models to optimize the strength and clarity acoustic parameters, and thereby improve the acoustic characteristics of large models. To the best of our knowledge, this is the first practical and accurate approach for acoustic material optimization of large indoor CAD models. [ABSTRACT FROM AUTHOR]

Abstract: Let denote an -vertex and -edge graph in which is a function mapping each vertex to a positive weight and is a function mapping each edge to a positive length . Given a positive integer , the -Center problem involves finding a set with vertices of to be the locations for building facilities. The objective is to minimize the maximum weighted distance from each vertex in – to its nearest vertex in . This paper considers a practical restriction: the induced subgraph of the selected vertices must be connected. The new variant is called the Connected -Center problem (the problem). For each fixed integer , on block graphs with exactly blocks, we first show that the problem is NP-hard when (1) , for all vertices , and , for all edges , and (2) , for all vertices , and , for all edges , respectively. Second, an -time algorithm for solving the problem on block graphs with unit vertex-weights and unit edge-lengths is proposed. Then, the algorithmic result is extended to handle the situation in which some vertices in cannot be included to form feasible solutions. The complexity of the extended algorithm is also . [Copyright &y& Elsevier]

Abstract: This paper presents a new CCD Bessell VR c I c light curves and photometric analysis of the newly discovered RS CVn type eclipsing binary star V1034 Her. The light curves were obtained at the Çanakkale Onsekiz Mart University Observatory in 2006. Variations of the orbital period of the system were firstly studied. The (O − C) diagram with a low range of observing time of about 20 years shows an upward parabola, which indicates a secular increase in the orbital period of the system. The light curves are generally those of detached eclipsing binaries; however, there are large asymmetries between maxima. The VR c I c light curves were analysed with two different fitting procedures: Wilson–Devinney method supplemented with a Monte Carlo type algorithm and Information Limit Optimization Technique (ILOT). Our general results find V1034 Her. as a well detached system, in which the components are filling ∼65% of their Roche lobes. Light curve asymmetries of the system are explained in terms of large dark starspots on the primary component. The primary star shows a long-lived spot distribution with active longitudes in the same hemisphere. [Copyright &y& Elsevier]

Abstract: The forming limit diagram and its associated analytical and experimental techniques has been widely used for 40 years with the assumption that sheet deformation occurs inplane-stress. Some hydro-forming type processes induce significant normal stress across the workpiece and this has led to a small number of extended formability analyses. However, recent work on the incremental sheet forming process which is known to give higher formability than conventional sheet pressing has shown that the repeated passage of a tool over the sheet leads to significant through-thickness shear strains being induced in the workpiece. Accordingly this paper explores the forming limits of sheet forming processes which induce any possible proportional loading, including all six components of the symmetric stress tensor. Marciniak and Kuczyinski’s famous (1967) analysis is extended to allow such loading, and a new generalised forming limit diagram (GFLD) is proposed to allow visual representation of the resulting forming limit strains. The GFLD demonstrates that forming limits can be increased significantly by both normal compressive stress and through-thickness shear. This increased formability is confirmed by experiments on a specially designed ‘linear paddle testing’ apparatus in which a conventional uniaxial test is augmented by the action of a paddle that ‘strokes’ the sample while also applying a normal force. Tests on the rig show that the paddle action leads to enhanced engineering strains at failure up to 300%. The insight gained in this paper is significant for process analysts, as it may explain existing discrepancies between prediction and experience of forming limits, and is important for designers who may be able to use it to expand process operating windows. [Copyright &y& Elsevier]

Abstract: In the sheet-metal forming industry, forming-limit strains have been a useful tool for quantifying metals formability. However, the experimental measurement of these strains is a difficult, time consuming and expensive process. It would be useful if strains calculated with a theoretical model could replace many of the experimental measurements. In this research, we analyze forming-limit strains of metals using a rate-dependent plasticity, polycrystal, self-consistent (VPSC) model in conjunction with the Marciniak–Kuczynski (M–K) approach. Previous researchers have studied forming limit diagrams (FLDs) based on the full-constraints Taylor model. This is the first time, to the authors’ knowledge, that the self-consistent approach has been introduced to simulate the polycrystal FLD behavior. Numerous microstructural factors characterizing the material have a strong influence on the FLD, so our model includes the effects of slip hardening, strain-rate sensitivity, anisotropy and initial texture. Finally, the calculation of the FLD with a more realistic scale transition successfully predicts some of the experimental tendencies that the Taylor model cannot reproduce for aluminum alloys AA6116-T4 and AA5182-O. [Copyright &y& Elsevier]

Abstract: The Merrifield–Simmons index of a graph is defined as the total number of its independent sets. In this paper, we show that the smallest Merrifield–Simmons index of -graphs is , where is the th Fibonacci number, and characterize the extremal graphs. [Copyright &y& Elsevier]

Abstract: Let be a graph. For , let denote the maximum value of the degree sums of the subsets of of order . In this paper, we prove the following two results. (1) Let be a 2-connected graph. If for every independent set of order , then has a cycle of length at least . (2) Let be a 2-connected graph and a subset of . If for every independent set of order in , then has a cycle that includes every vertex of . This suggests that the degree sum of nonadjacent two vertices is important for guaranteeing the existence of these cycles. [Copyright &y& Elsevier]

Abstract: An edge of a -connected graph is said to be -contractible if its contraction yields a -connected graph. A non-complete -connected graph possessing no -contractible edges is called contraction-critical -connected. Let be a contraction-critical 7-connected graph with vertices, and the set of vertices of degree 7 in . In this paper, we prove that , which improves the result proved by Ando, Kaneko and Kawarabayashi. In the meantime, we obtain that for any vertex in a contraction-critical 7-connected graph there is a vertex such that the distance between and is at most 2, and thus extends a result of Su and Yuan. We present a family of contraction-critical 7-connected graphs in which is independent. [Copyright &y& Elsevier]

Abstract: Let be a simple graph on vertices. In this paper, we prove that if satisfies the condition that for each , then has no nowhere-zero 3-flow if and only if is either one of the five graphs on at most 6 vertices or one of a very special class of graphs on at least 6 vertices. [Copyright &y& Elsevier]

Abstract: Let be a graph and be a vertex of . We consider the following operation: add a new vertex such that does not distinguish any two vertices which are not distinguished by . We call this operation a one-vertex extension. Adding a true twin, a false twin or a pendant vertex are cases of one-vertex extensions. Here we are interested in graph classes defined by a subset of allowed one-vertex extension. Examples are trees, cographs and distance-hereditary graphs. We give a complete classification of theses classes with respect to their clique-width. We also introduce a new graph parameter called the modular-width, and we give a relation with the clique-width. [Copyright &y& Elsevier]

Abstract: We study 2-dimensional Jacobian maps using so-called Newton–Puiseux charts. These are multi-valued coordinates near divisors of resolutions of indeterminacies at infinity of the Jacobian map in the source space as well as in the target space. The map expressed in these charts takes a very simple form, which allows us to detect a series of new analytical and topological properties. We prove that the Jacobian Conjecture holds true for maps whose topological degree is , for maps with and for maps with. equal to 2 times a prime. [Copyright &y& Elsevier]

Abstract: In this paper, we prove that planar graphs without -cycles and without two 5-cycles sharing exactly one edge are 3-colorable. This improves the result in [O.V. Borodin, A.N. Glebov, A. Raspaud, M.R. Salavatipour, Planar graphs without cycles of length from 4 to 7 are 3-colorable, J. Combin. Theory Ser. B 93 (2005) 303–311]. [Copyright &y& Elsevier]

Abstract: For a simple connected undirected graph , the Wiener index is defined as half the sum of all distances of the form , where the summation is over all possible vertex pairs in . Assuming that has more than one cut-vertex, we obtain an expression for in terms of the Wiener indices of the blocks of and other quantities. [Copyright &y& Elsevier]

Abstract: Simple and combination resonances in coupled oscillators under a random parametric excitation are studied. An efficient numerical method for obtaining the regions of mean square stability is proposed. Based on the method, stability diagrams for different values of the excitation parameter and for four form of the coupling parameters are presented. It is found that the random excitation can have a stabilizing effect under certain conditions. [Copyright &y& Elsevier]

Abstract: In this paper we study representations of permutation groups as automorphism groups of colored graphs and supergraphs. In particular, we consider how such representations for various products of permutation groups can be obtained from representations of factors and how the degree of complexity increases in such constructions. [Copyright &y& Elsevier]

Abstract: Influence diagrams have been widely used as knowledge bases in medical informatics and many applied domains. In conventional influence diagrams, the numerical models of uncertainty are probability distributions associated with chance nodes and value tables for value nodes. However, when incomplete knowledge or linguistic vagueness is involved in the reasoning systems, the suitability of probability distributions is questioned. This study intends to propose an alternative numerical model for influence diagrams, possibility distributions, which extend influence diagrams into fuzzy influence diagrams. In fuzzy influence diagrams, each chance node and value node is associated with a possibility distribution which expresses the uncertain features of the node. This study also develops a simulation algorithm and a fuzzy programming model for diagnosis and optimal decision in medical settings. [Copyright &y& Elsevier]

Abstract: The vertex-distinguishing index of a graph G is the minimum number of colours required to properly colour the edges of G in such a way that any two vertices are incident with different sets of colours. We consider this parameter for some regular graphs. Moreover, we prove that for any graph, the value of this invariant is not changed if the colouring above is, in addition, required to be equitable. [Copyright &y& Elsevier]

Abstract: Current work presents a set of fault models allowing high coverage for sequential cores in systems-on-a-chip. We propose a novel approach combining a hierarchical fault model for functional blocks, a functional fault model for multiplexers and a mixed hierarchical-functional fault model for comparison operators, respectively. The fault models are integrated into a fast high-level decision diagram based test path activation tool. According to the experiments, the proposed method significantly outperforms state-of-the-art test pattern generation tools. The main new contribution of this paper is a formal definition of high-level decision diagram representations and the combination of the three fault models in order to target high gate-level stuck-at fault coverage for sequential cores. [Copyright &y& Elsevier]

Abstract: A distance-colouring relative to distance p of a graph is a mapping of V in a set of colours in such a way that any two vertices of G of distance not greater than p have distinct colours. The purpose of this paper is to give a survey of the results related to the distance-colouring of graphs introduced in 1969. [Copyright &y& Elsevier]

Abstract: In this paper the complementary hyperstructure obtained from a multiplicative hyperring is considered. Furthermore a characterization for such hyperstructures obtained starting from a strongly distributive multiplicative hyperring is given. [Copyright &y& Elsevier]

Abstract: A graph is called equipackable if every maximal packing in it is also maximum. This generalizes randomly packable graphs. We survey known results both on randomly packable graphs and on equipackable graphs. As a new result is given a characterization of -equipackable graphs with all valencies at least two. [Copyright &y& Elsevier]

Abstract: It was proved by Fronček, Jerebic, Klavžar, and Kovář that if a complete bipartite graph with a perfect matching removed can be covered by k bicliques, then . We give a slightly simplified proof and we show that the result is tight. Moreover, we use the result to prove analogous bounds for coverings of some other classes of graphs by bicliques. [Copyright &y& Elsevier]

Abstract: In this paper all Veronesean caps of projective spaces of finite dimension over skewfields are classified. More precisely, if , K a skewfield, contains a Veronesean cap X, then K is a field and X is either a Veronese variety or a projection of a Veronese variety. This result extends analogous theorems of Mazzocca and Melone [Caps and Veronese varieties in projective Galois spaces. Discrete Math. 48 (1984) 243–252] and Thas and Van Maldeghem [Classification of finite Veronesean caps, European J. Combin. 25(2) (2004) 275–285] for finite projective spaces. [Copyright &y& Elsevier]

Abstract: We give a simple alternative proof of the representation theorem of all genus two 3-manifolds by a 6-parameter family of integers, due to Casali and Grasselli (see [M.R. Casali, A catalogue of the genus two 3-manifolds, Atti. Sem. Mat. Fis. Univ. Modena 37 (1989) 207–236]; [M.R. Casali, L. Grasselli, 2-Symmetric crystallizations and 2-fold branched coverings of , Discrete Math. 87 (1991) 9–22]). Our approach is different from that of the quoted papers, and it is based on the concept of extended Heegaard diagram. This permits to obtain new topological meanings of the arithmetic conditions which the parameters must satisfy for representing closed manifolds. Some applications and results on some homology spheres of genus 2 complete the paper. [Copyright &y& Elsevier]

Abstract: We present all possible distributions of 3-kings in 3-partite tournaments with at most one transmitter. [Copyright &y& Elsevier]

Abstract: Let denote the graph on a vertices with edges between every pair of vertices. Take p copies of this graph , and join each pair of vertices in different copies with edges. The resulting graph is denoted by , a graph that was of particular interest to Bose and Shimamoto in their study of group divisible designs with two associate classes. The existence of z-cycle decompositions of this graph have been found when . In this paper we consider resolvable decompositions, finding necessary and sufficient conditions for a 4-cycle factorization of (when is even) or of minus a 1-factor (when is odd) whenever a is even. [Copyright &y& Elsevier]

Abstract: The well known correspondence between even cycles of an undirected graph and polynomials in a binomial ideal associated to a graph is extended to odd cycles and polynomials in another binomial ideal. Other binomial ideals associated to an undirected graph are also introduced. The results about them with topics on monomial ideals are used in order to show decision procedures for bipartite graphs, minimal vertex covers, cliques, edge covers and matchings with algebraic tools. All such procedures are implemented in Maple 9.5. [Copyright &y& Elsevier]

Abstract: In this paper we study the elementary properties of double graphs, i.e. of graphs which are the direct product of a simple graph with the graph obtained by the complete graph adding a loop to each vertex. [Copyright &y& Elsevier]

Abstract: In this paper, we define a polynomial invariant of regular isotopy, G L , for oriented knot and link diagrams L. From G L by multiplying it by a normalizing factor, we obtain an ambient isotopy invariant, N L , for oriented knots and links. We compare the polynomial N L with the original Jones polynomial and with the normalized bracket polynomial. We show that the polynomial N L yields the Jones polynomial and the normalized bracket polynomial. As examples, we give the polynomial G L of some knot and link diagrams and compute the polynomial G L for torus links of type (2, n), and applying computer algebra (MAPLE) techniques, we calculate the polynomial G L of torus links of type (2, n). Furthermore we give its applications to alternating links. [Copyright &y& Elsevier]

Abstract: The aim of this study is the evaluation of the maximum slope angle of frustums of pyramid and cone carried out by incremental forming and the validation of a FE code in order to have an instrument able to evaluate the limits of the process as regards to the geometry of the manufacturing product. In the specific case, afterwards the mechanical characterization and the evaluation of the sheets formability, frustums of pyramid and cone, with different slope angles, have been carried out, up to the appearance of fractures in the sheet. A FE analysis of the process has allowed to highlight the sheet zones characterized by different strains and to locate the critical points by the interpretation of the forming limit diagrams. [Copyright &y& Elsevier]

Abstract: Gavril [F. Gavril, Maximum weight independent sets and cliques in intersection graphs of filaments, Inform. Process. Lett. 73 (2000) 181–188] defined two new families of intersection graphs: the interval-filament graphs and the subtree-filament graphs. The complements of interval-filament graphs are the cointerval mixed graphs and the complements of subtree-filament graphs are the cochordal mixed graphs. The family of interval-filament graphs contains the families of cocomparability, polygon-circle, circle and chordal graphs. In the present paper we introduce a generalization of the subtree-filament graphs, namely, the -interval-filament graphs. We prove that the family of 3D-interval-filament graphs, the family of complements of co(interval-filament) mixed graphs and the family of overlap graphs of interval-filaments are the same, and show that every -interval-filament graph has an intersection representation by a family of piecewise linear filaments. We use the properties of these graphs to describe an algorithm for maximum weight holes of a given parity in -interval-filament graphs and an algorithm for antiholes of a given parity in interval-filament and subtree-filament graphs. We define various subfamilies of -interval-filament graphs and characterize them as overlap graphs and as complements of -mixed graphs. [Copyright &y& Elsevier]

Abstract: The -total labelling number of a graph G is the width of the smallest range of integers that suffices to label the vertices and the edges of G such that no two adjacent vertices have the same label, no two adjacent edges have the same label and the difference between the labels of a vertex and its incident edges is at least 2. In this paper we prove that if G is an outerplanar graph with maximum degree , then if , or and G is 2-connected, or and G contains no intersecting triangles. [Copyright &y& Elsevier]

Abstract: The Grundy (or First-Fit) chromatic number of a graph is the maximum number of colors used by the First-Fit coloring of the graph . In this paper we give upper bounds for the Grundy number of graphs in terms of vertex degrees, girth, clique partition number and for the line graphs. Next we show that if the Grundy number of a graph is large enough then the graph contains a subgraph of prescribed large girth and Grundy number. [Copyright &y& Elsevier]

Abstract: Let be a simple undirected graph with a set V of vertices and a set E of edges. Each vertex has an integer valued demand . The source location problem with vertex-connectivity requirements in a given graph G asks to find a set S of vertices with the minimum cardinality such that there are at least vertex-disjoint paths between S and each vertex . In this paper, we show that the problem with , can be solved in linear time. Moreover, we show that in the case where for some vertex , the problem is NP-hard. [Copyright &y& Elsevier]

Abstract: Let denote the number of odd components of a graph G. The deficiency of G is defined as , and this equals the number of vertices unmatched by any maximum matching of G. A subset is called a Tutte set (or barrier set) of G if , and an extreme set if . Recently a graph operator, called the D-graph , was defined that has proven very useful in examining Tutte sets and extreme sets of graphs which contain a perfect matching. In this paper we give two natural and related generalizations of the D-graph operator to all simple graphs, both of which have analogues for many of the interesting and useful properties of the original. [Copyright &y& Elsevier]

Abstract: By Petersen''s theorem, a bridgeless cubic multigraph has a 2-factor. Fleischner generalised this result to bridgeless multigraphs of minimum degree at least three by showing that every such multigraph has a spanning even subgraph. Our main result is that every bridgeless simple graph with minimum degree at least three has a spanning even subgraph in which every component has at least four vertices. We deduce that if G is a simple bridgeless graph with n vertices and minimum degree at least three, then its line graph has a 2-factor with at most components. This upper bound is best possible. [Copyright &y& Elsevier]

Abstract: In this paper, we study the crossing number of the circulant graph and prove that for . [Copyright &y& Elsevier]

Abstract: For a connected graph , an edge set is a k-restricted-edge-cut if is disconnected and every component of has at least k vertices. The cardinality of a minimum k-restricted-edge-cut is the k-restricted-edge-connectivity of G, denoted by . In this paper, we study sufficient conditions for to be optimal, especially when and 3. [Copyright &y& Elsevier]

Abstract: We show that a set of graphs has bounded tree-width or bounded path-width if and only if the corresponding set of line graphs has bounded clique-width or bounded linear clique-width, respectively. This relationship implies some interesting algorithmic properties and re-proves already known results in a very simple way. It also shows that the minimization problem for NLC-width is NP-complete. [Copyright &y& Elsevier]

Abstract: We determine the graphs with maximal spectral radius among the ones on n nodes with diameter D. [Copyright &y& Elsevier]

Abstract: In this report, micromagnetic simulations of magnetization dynamics driven by spin-polarized currents (SPCs) on magnetic nanopillars of permalloy/Cu/permalloy with different rectangular cross-sections are presented. Complete dynamical stability diagrams from initial parallel and antiparallel states have been computed for 100ns. The effects of a space-dependent polarization function together with the presence of magnetostatic coupling from the fixed layer and classical Ampere field have been taken into account. [Copyright &y& Elsevier]

Abstract: The Lower Palaeozoic rocks of the west of Ireland Caledonides provide a novel way to test the reliability of discrimination diagrams in sedimentary rocks. A comparison between the geochemical signature of the tuff bands and the signature from the adjacent sedimentary rocks reveals that a combination of multi-element diagrams and discrimination diagrams is best suited to identify the tectonic environment of deposition. The tuff bands from the Ordovician and Silurian formations all carry an active continental margin signature. Only three of the sedimentary discrimination diagrams assigned more than 50% of the samples to this setting. The results from the discrimination diagrams indicate an active margin setting for the Ordovician Mweelrea and Rosroe Formations and the Silurian formations, whilst the Derrylea and Sheeffry sedimentary samples have a passive margin signature. Overall the results show that in the case where felsic volcanism occurred on a quartz-rich source region the active continental margin field on many established discrimination diagrams is not reliable in identifying this setting. However, the study highlights one of the key strengths of discrimination diagrams in their ability to be used as a lever to reveal significant information about the sediment source, as in this case to identify sediment that has been transported from different tectonic settings and deposited in one sedimentary basin. [Copyright &y& Elsevier]

Abstract: We solve a conjecture of Roditty, Shoham and Yuster [P.J. Cameron (Ed.), Problems from the 17th British Combinatorial Conference, Discrete Math., 231 (2001) 469–478; Y. Roditty, B. Shoham, R. Yuster, Monotone paths in edge-ordered sparse graphs, Discrete Math. 226 (2001) 411–417] on the caterpillar arboricity of planar graphs. We prove that for every planar graph , the edge set E can be partitioned into four subsets in such a way that , for , is a forest of caterpillars. We also provide a linear-time algorithm which constructs for a given planar graph G, four forests of caterpillars covering the edges of G. [Copyright &y& Elsevier]

Abstract: In this paper, we combine qualitative analysis with numerical exploration to study traveling waves of a generalized Camassa–Holm equation. Two new types of bounded traveling waves are found. One of them is called compacton-like wave because it is of some properties of compacton. Similarly, the other is called kink-like wave since it possesses some properties of kink. Their implicit expressions are obtained. For some concrete data, the diagrams of the implicit functions are displayed, and the numerical simulation is made. The results imply that our theoretical analysis is agreeable with the numerical simulation. [Copyright &y& Elsevier]

Abstract: Earlier concepts of ultrahigh-cycle fatigue (UHCF) of both ductile single-phase type I materials that do not contain inclusions and type II materials, e.g., high-strength steels containing non-metallic inclusions as (internal) crack initiation sites, are extended. In particular, the multi-stage fatigue life diagrams with a conventional high-cycle fatigue (HCF) limit and a possible lower fatigue limit in the UHCF range are discussed for both classes of materials in terms of the relevant fatigue cracking mechanisms. In this context, it is emphasized that it is important to consider in both cases details of fatigue crack initiation as a life-determining factor in the HCF and, even more so, in the UHCF regime. Different factors such as the density, size, location and distribution of non-metallic inclusions and details of specimen geometry and surface quality in the case of type II materials are discussed with respect to their influence on the transition stress separating the ranges of surface and internal fatigue cracking and with regard to fatigue lives. [Copyright &y& Elsevier]

Abstract: We study the traffic states and jams induced by a slowdown of vehicles in a single-lane highway. The two-stage optimal velocity model is used in which the optimal velocity function has two turning points. The fundamental (flow-density) diagrams are calculated. At low density, the flow (current) increases linearly with density, while it saturates at some values of intermediate density. When the flow saturates, the discontinuous front (stationary shock wave) appears before or within the section of slowdown. The values of saturated flow are determined by the extreme values of theoretical current curves. The relationship between the densities is derived before and after the discontinuity. [Copyright &y& Elsevier]