A sufficient condition for a graph to be hamiltonian

Those non-hamiltonian graphsG withn vertices are characterized, which satisfy the Ore-type degree-conditiond(x)+d(y)n–2 for each pairx,yM of different nonadjacent vertices whereM consists of two vertices ofG. As an application a theorem on hamiltonian connectivity of graphs is given. Furthermore, a condition is presented which is sufficient for the existence of a covering of a graph by two disjoint paths with prescribed set of startpoints and prescribed set of endpoints. A class of graphs is described which have no covering of this kind.     

Über Mittelwerte multiplikativer zahlentheoretischer Funktionen mehrerer Variablen

In [8] the author extended the concept of neighbouring functions (cp. [9]) to the case of several variables. Using these results it is shown that under some weak conditions a multiplicative functionf in two variables has a mean-value different from zero if and only if the two multiplicative functionsf ₁(n)=f(n, 1) andf ₂(n)=f(1,n) have mean-values different from zero. Applications to theorems ofDelange [3],Elliott [6] andDaboussi [1] are given.     

The median procedure in cluster analysis and social choice theory

Classical approachs for fitting and aggregation problems, specially in cluster analysis, social choice theory and paired comparisons methods, consist in the minimization of a remoteness function between relational data and a relational model. The notion of median, with its algebraic, metric, geometrical and statistical aspects, allow a unified treatment of many of base problems. Properties of median procedures are organized according to four directions: stabilities and axiomatic characterizations; Arrow-like properties; combinatorial properties; effective computational possibilities. Finally, interesting mathematical problems, related to the notion of median are surveyed.     

On vertex symmetric digraphs

The problem of how “near” we can come to a n-coloring of a given graph is investigated. I.e., what is the minimum possible number of edges joining equicolored vertices if we color the vertices of a given graph with n colors. In its generality the problem of finding such an optimal color assignment to the vertices (given the graph and the number of colors) is NP-complete. For each graph G, however, colors can be assigned to the vertices in such a way that the number of offending edges is less than the total number of edges divided by the number of colors. Furthermore, an Ω(epn) deterministic algorithm for finding such an n-color assignment is exhibited where e is the number of edges and p is the number of vertices of the graph (e?p?n). A priori solutions for the minimal number of offending edges are given for complete graphs; similarly for equicolored K_m in K_p and equicolored graphs in K_p.     

Genetics of Vocal Quality Characteristics in Monozygotic Twins: A Multiparameter Approach

The main purpose of this study was to determine the vocal quality characteristics among the 45 monozygotic cotwins (MT). As the performance of the voice is related to several genetically determined anatomical and physiological factors, the authors hypothesized that the vocal characteristics and the overall vocal quality by means of the Dysphonia Severity Index (DSI) will be identical in MT. An additional objective of this study was to determine whether sex and age influence vocal similarities in MT and to compare the voice characteristics of MT with the normative data of unrelated peers. As more environmental factors influence the aging of the voice, age-related differences were expected. No sex-related differences were expected. Subjective and objective assessment techniques determined the vocal quality. No significant differences were obtained, and most comparisons resulted in significant correlation coefficients. For the acoustic parameters jitter and shimmer only, no significant correlation coefficients could be obtained. It is clear that the perceptual voice characteristics, the laryngeal aerodynamic measurements of maximum phonation time (MPT), the vocal performances, and the overall vocal quality by means of the DSI are similar in MT. These vocal characteristics are not influenced either by the subjects' age or sex and are situated within the normative range of unrelated peers. To what extent other aspects (environment, anxiety, tension, etc) might play a role in the acoustical dimensions regarding frequency and amplitude perturbation, which were in the normal range, is a subject of further research.     

Effects of Field Orientation on the Driven Lattice Gas

Steady states of the driven lattice gas (DLG) on triangular, hexagonal and square lattices with the field at several fixed orientations to the principal lattice vectors were studied by Monte Carlo simulation. In most cases a strong field suppressed change to a low-temperature ordered phase. On each lattice, one field orientation that caused nonequilibrium ordering was identified. On triangular and hexagonal lattices, dependence of energy and anisotropy on field strength was studied at those orientations. Anisotropic ordering along the field developed at intermediate temperatures under weak fields. Partial ordering along the field persisted to low temperature under strong fields.     

Nonlinear spin current and magnetoresistance of molecular tunnel junctions

We report on a theoretical study of spin-polarized quantum transport through a Ni-bezenedithiol(BDT)-Ni molecular magnetic tunnel junction (MTJ). Our study is based on carrying out density functional theory within the Keldysh nonequilibrium Green's function formalism, so that microscopic details of the molecular MTJ are taken into account from first principles. A magnetoresistance ratio of approximately 27% is found for the Ni-BDT-Ni MTJ which declines toward zero as bias voltage is increased. The spin currents are nonlinear functions of bias voltage, even changing sign at certain voltages due to specific features of the coupling between molecular states and magnetic leads.     

Simultaneous demodulation technique for a multiplexed fiber Fizeau interferometer and fiber Bragg grating sensor system

We propose a demodulation technique for a multiplexed fiber Fizeau interferometer (FFI) and fiber Bragg grating (FBG) sensor system using the discrete wavelet transform with signal processing enhancements. This simple and flexible demodulation technique determines the cavity length of FFI and the Bragg wavelength of FBG simultaneously and is especially suited for quasi-static measurements. We demonstrate this demodulation technique by performing some strain measurements, and a strain resolution of 1.0 microepsilon and an accuracy of 2.6 microepsilon are obtained. The maximum cross-talk of the sensor system is 6% of the applied strains.