Nonlinear vibration of beams and rectangular plates

Zusammenfassung Der Einfluss von Vorspannungen auf die freien und erzwungenen nichtlinearen Schwingungen von Balken und rechteckigen Platten wird mittels einer einfachen Erweiterung der Lösungen für Fälle ohne Vorspannung untersucht. Es wird eine einzige Koordinatenfunktion benützt; es werden einfach aufgelegte und eingespannte Fälle betrachtet; und die Diskussion wird auch auf den überkritischen Bereich ausgedehnt.     

An Extremal Problem on Contractible Edges in 3-Connected Graphs

An edge e in a 3-connected graph G is contractible if the contraction G/e is still 3-connected. The existence of contractible edges is a very useful induction tool. Let G be a simple 3-connected graph with at least five vertices. Wu [7] proved that G has at most vertices that are not incident to contractible edges. In this paper, we characterize all simple 3-connected graphs with exactly vertices that are not incident to contractible edges. We show that all such graphs can be constructed from either a single vertex or a 3-edge-connected graph (multiple edges are allowed, but loops are not allowed) by a simple graph operation. Research partially supported by an ONR grant under grant number N00014-01-1-0917     

Frequency discrimination of complex tones; assessing the role of component resolvability and temporal fine structure

Thresholds for discriminating the fundamental frequency (FO) of a complex tone, FODLs, are small when low harmonics are present, but increase when the number of the lowest harmonic, N, is above eight. To assess whether the relatively small FODLs for N in the range 8-10 are based on (partly) resolved harmonics or on temporal fine structure information, FODLs were measured as a function of N for tones with three successive harmonics which were added either in cosine or alternating phase. The center frequency was 2000 Hz, and N was varied by changing the mean FO. A background noise was used to mask combination tones. The value of FO was roved across trials to force subjects to make within-trial comparisons. N was roved by +/- 1 for every stimulus, to prevent subjects from using excitation pattern cues. FODLs were not influenced by component phase for N= 6 or 7, but were smaller for cosine than for alternating phase once N exceeded 7, suggesting that temporal fine structure plays a role in this range. When the center frequency was increased to 5000 Hz, performance was much worse for low N, suggesting that phase locking is important for obtaining low FODLs with resolved harmonics.     

Stimulus variability and the phonetic relevance hypothesis: effects of variability in speaking style, fundamental frequency, and speaking rate on spoken word identification

Three experiments were conducted to examine the effects of trial-to-trial variations in speaking style, fundamental frequency, and speaking rate on identification of spoken words. In addition, the experiments investigated whether any effects of stimulus variability would be modulated by phonetic confusability (i.e., lexical difficulty). In Experiment 1, trial-to-trial variations in speaking style reduced the overall identification performance compared with conditions containing no speaking-style variability. In addition, the effects of variability were greater for phonetically confusable words than for phonetically distinct words. In Experiment 2, variations in fundamental frequency were found to have no significant effects on spoken word identification and did not interact with lexical difficulty. In Experiment 3, two different methods for varying speaking rate were found to have equivalent negative effects on spoken word recognition and similar interactions with lexical difficulty. Overall, the findings are consistent with a phonetic-relevance hypothesis, in which accommodating sources of acoustic-phonetic variability that affect phonetically relevant properties of speech signals can impair spoken word identification. In contrast, variability in parameters of the speech signal that do not affect phonetically relevant properties are not expected to affect overall identification performance. Implications of these findings for the nature and development of lexical representations are discussed.     

Probing the formation mechanism and chemical states of carbon-supported Pt-Ru nanoparticles by in situ X-ray absorption spectroscopy

The understanding of the formation mechanism of nanoparticles is essential for the successful particle design and scaling-up process. This paper reports findings of an X-ray absorption spectroscopy (XAS) investigation, comprised of X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) regions, to understand the mechanism of the carbon-supported Pt-Ru nanoparticles (NPs) formation process. We have utilized Watanabe's colloidal reduction method to synthesize Pt-Ru/C NPs. We slightly modified the Watanabe method by introducing a mixing and heat treatment step of Pt and Ru oxidic species at 100 degrees C for 8 h with a view to enhance the mixing efficiency of the precursor species, thereby one can achieve improved homogeneity and atomic distribution in the resultant Pt-Ru/C NPs. During the reduction process, in situ XAS measurements allowed us to follow the evolution of Pt and Ru environments and their chemical states. The Pt LIII-edge XAS indicates that when H2PtCl6 is treated with NaHSO3, the platinum compound is found to be reduced to a Pt(II) form corresponding to the anionic complex [Pt(SO3)4]6-. Further oxidation of this anionic complex with hydrogen peroxide forms dispersed [Pt(OH)6]2- species. Analysis of Ru K-edge XAS results confirms the reduction of RuIIICl3 to [RuII(OH)4]2- species upon addition of NaHSO3. Addition of hydrogen peroxide to [RuII(OH)4]2- causes dehydrogenation and forms RuOx species. Mixing of [Pt(OH)6]2- and RuOx species and heat treatment at 100 degrees C for 8 h produced a colloidal sol containing both Pt and Ru metallic as well as ionic contributions. The reduction of this colloidal mixture at 300 degrees C in hydrogen atmosphere for 2 h forms Pt-Ru nanoparticles as indicated by the presence of Pt and Ru atoms in the first coordination shell. Determination of the alloying extent or atomic distribution of Pt and Ru atoms in the resulting Pt-Ru/C NPs reveals that the alloying extent of Ru (JRu) is greater than that of the alloying extent of Pt (JPt). The XAS results support the Pt-rich core and Ru-rich shell structure with a considerable amount of segregation in the Pt region and with less segregation in the Ru region for the obtained Pt-Ru/C NPs.     

A framework for constructing de Bruijn sequences via simple successor rules

We present a simple framework for constructing de Bruijn sequences, and more generally, universal cycles, via successor rules. The framework is based on the often used method of joining disjoint cycles. It generalizes four previously known de Bruijn sequence constructions and is applied to derive three new and simple de Bruijn sequence constructions. Four of the constructions apply the pure cycling register and three apply the complemented cycling register. The correctness of each new construction is easily proved using the new framework. Each of the three new de Bruijn sequence constructions can be generated in $O\left(n\right)$-time per bit using $O\left(n\right)$-space.     

Multivariate extreme value copulas with factor and tree dependence structures

Parsimonious extreme value copula models with O(d) parameters for d observed variables of extrema are presented. These models utilize the dependence characteristics, including factor and tree structures, assumed on the underlying variables that give rise to the data of extremes. For factor structures, a class of parametric models is obtained by taking the extreme value limit of factor copulas with non-zero tail dependence. An alternative model suitable for both factor and tree structures imposes constraints on the parametric Hüsler-Reiss copula to get representations in terms of O(d) other parameters. Dependence properties are discussed. As the full density is often intractable, the method of composite (pairwise) likelihood is used for model inference. Procedures to improve the stability of bivariate density evaluation are also developed. The proposed models are applied to two data examples — one for annual extreme river flows and one for bimonthly extremes of daily stock returns.     

Dependence Properties of Conditional Distributions of some Copula Models

For multivariate data from an observational study, inferences of interest can include conditional probabilities or quantiles for one variable given other variables. For statistical modeling, one could fit a parametric multivariate model, such as a vine copula, to the data and then use the model-based conditional distributions for further inference. Some results are derived for properties of conditional distributions under different positive dependence assumptions for some copula-based models. The multivariate version of the stochastically increasing ordering of conditional distributions is introduced for this purpose. Results are explained in the context of multivariate Gaussian distributions, as properties for Gaussian distributions can help to understand the properties of copula extensions based on vines.     

Eulogy for Professor Mirka Miller (1949–2016)

The CIMPA Research School on Mathematical Models for Security Applications was dedicated to the memory of Emeritus Professor Mirka Miller, who suggested that it be held in Havana. Mirka Miller, member of the editorial board of Mathematics in Computer Science, devoted her research to Graph Theory and Data Security, fields where she made important and beautiful contributions.