What is so mysterious about the electronic states of SCI?

The 15 lowest lying doublet electronic states of the molecule SCI have been investigated theoretically at a high level of correlation treatment (MRCI). For the ground state (X ²II), spectroscopic constants were obtained from a set of eight vibrational intervals. This result extends our knowledge about this state beyond the experimentally known data that presently were derived from only two bands. Spin-orbit constants, transition probabilities and radiative lifetimes complement its spectroscopic characterization. For the excited electronic states, a global view of the doublet states is presented that can help us understand the scarcity of experimental data on electronic transitions for this system and also the difficulty of assigning the only two transitions so far recorded. Most of these states are repulsive, and for the few high lying bound ones, of Rydberg character, avoided crossings restrict the number of accessible vibrational states. Crossing by repulsive states and predissociation is also a factor that can prevent further emissions. Two new bound excited states, ²δ and ²Σ, predicted in this study, are of direct relevance to an interpretation of the limited experimental data available on electronic transitions.     

What is in a pebble shape?

We propose to characterize the shapes of flat pebbles in terms of the statistical distribution of curvatures measured along the pebble contour. This is demonstrated for the erosion of clay pebbles in a controlled laboratory apparatus. Photographs at various stages of erosion are analyzed, and compared with two models. We find that the curvature distribution complements the usual measurement of aspect ratio, and connects naturally to erosion processes that are typically faster at protruding regions of high curvature.     

Why is super-resolution so inefficient?

Many optical imaging systems have been designed to achieve spatial resolution exceeding the limit proposed by Abbe theory, namely lambda/2NA. These systems invariably use light inefficiently. We discuss the application of information theory to this problem, in an effort to find an upper limit to the theoretical efficiency of a super-resolving system, as a function of the degree to which its capabilities exceed the Abbe limit.     

What is the problem in the locality problem?

In connection with my previous paper Locality, Reflection, and Wave-Particle Duality [Found. Phys. 17, 813 (1987)], in this paper I distinguish explicitly, in the locality problem, between assertions, deductively established results, interpretations, intuitions, and facts. This clarifies the structure of the problem.     

Truncating expansions in bi-orthogonal bases: What is preserved?

In this work, we test the survival of topological information of an attractor under the truncations of a bi-orthogonal decomposition. We generate synthetic patterns which evolve dynamically in a desired way, and investigate the number of modes which should be kept in a truncation in order to be able to recover the information which we provided to the system. We show that a premature truncation of this kind of decomposition, based on existing energy criteria, leads to orbits that do not preserve the topological properties of the original signal.     

Nanometer Calibration Particles: What is Available and What is Needed?

Information on available polystyrene calibration spheres is presented regarding the particle diameter, uncertainty in the size, and the width of the size distribution for particles in a size range between 20 and 100nm. The use of differential mobility analysis for measuring the single primary calibration standard in this size range, 100nm NIST Standard Reference Material®1963, is described along with the key factors in the uncertainty assessment. The issues of differences between international standards and traceability to the NIST Standard are presented. The lack of suitable polystyrene spheres in the 20–40nm size range will be discussed in terms of measurement uncertainty and width of the size distributions. Results on characterizing a new class of molecular particles known as dendrimers will be described and the possibilities of using these as size calibration standards for the size range from 3 to 15nm will be discussed.     

A multiple production study of neutral strange particles in νμ CC interactions in the NOMAD experiment

A multiple production study of neutral strange particles in ν_μ charged current interactions has been performed using the full data sample from the NOMAD experiment. This analysis allows one to investigate the mechanisms of strange particle production in neutrino interactions. In this study we have tried to build a model for the production of strange particles, which would allow us to describe our measured rates of neutral strange particles, as well as the rates of the single-, double-and triple-V ⁰ production: Λ, K ⁰, , K ⁰ K ⁰, ΛK ⁰, Λ , K ⁰ , ΛΛ, and K ⁰ K ⁰ K ⁰. The text was submitted by the authors in English.     

What is a complex graph?

Many papers published in recent years show that real-world graphs G(n,m) (n nodes, m edges) are more or less “complex” in the sense that different topological features deviate from random graphs. Here we narrow the definition of graph complexity and argue that a complex graph contains many different subgraphs. We present different measures that quantify this complexity, for instance C_1e, the relative number of non-isomorphic one-edge-deleted subgraphs (i.e. DECK size). However, because these different subgraph measures are computationally demanding, we also study simpler complexity measures focussing on slightly different aspects of graph complexity. We consider heuristically defined “product measures”, the products of two quantities which are zero in the extreme cases of a path and clique, and “entropy measures” quantifying the diversity of different topological features. The previously defined network/graph complexity measures Medium Articulation and Offdiagonal complexity (OdC) belong to these two classes. We study OdC measures in some detail and compare it with our new measures. For all measures, the most complex graph has a medium number of edges, between the edge numbers of the minimum and the maximum connected graph . Interestingly, for some measures this number scales exactly with the geometric mean of the extremes: . All graph complexity measures are characterized with the help of different example graphs. For all measures the corresponding time complexity is given.Finally, we discuss the complexity of 33 real-world graphs of different biological, social and economic systems with the six computationally most simple measures (including OdC). The complexities of the real graphs are compared with average complexities of two different random graph versions: complete random graphs (just fixed n,m) and rewired graphs with fixed node degrees.     

What is “Twang”?

A single female professional vocal artist and pedagogue sang examples of “twang” and neutral voice quality, which a panel of experts classified, in almost complete agreement with the singer's intentions. Subglottal pressure was measured as the oral pressure during the occlusion during the syllable /pae/. This pressure tended to be higher in “twang,” whereas the sound pressure level (SPL) was invariably higher. Voice source properties and formant frequencies were analyzed by inverse filtering. In “twang,” as compared with neutral, the closed quotient was greater, the pulse amplitude and the fundamental were weaker, and the normalized amplitude tended to be lower, whereas formants 1 and 2 were higher and 3 and 5 were lower. The formant differences, which appeared to be the main cause of the SPL differences, were more important than the source differences for the perception of “twanginess.” As resonatory effects occur independently of the voice source, the formant frequencies in “twang” may reflect a vocal strategy that is advantageous from the point of view of vocal hygiene.     

What is double parton scattering?

Processes such as double Drell–Yan and same-sign WW   production have contributions from double parton scattering, which are not well-defined because of a δ⁽²⁾(_z⊥=0)${\delta }^{(2)}({\mathbf{z}}_{\perp }=0)$ singularity that is generated by QCD evolution. We study the single and double parton contributions to these processes, and show how to handle the singularity using factorization and operator renormalization. We compute the QCD evolution of double parton distribution functions (PDFs) due to mixing with single PDFs. The modified evolution of dPDFs at _z⊥=0${\mathbf{z}}_{\perp }=0$, including generalized dPDFs for the non-forward case, is given in Appendix A. We include a brief discussion of the experimental interpretation of dPDFs and how they can probe flavor, spin and color correlations of partons in hadrons.     

What is the role of chaotic scattering in irreversible processes?

We study kinetic properties of simple mechanical models of deterministic diffusion like the scattering of a point particle in a billiard of Lorentz type and the multibaker area-preserving map. We show how dynamical chaos and, in particular, chaotic scattering are related to the transport property of diffusion. Moreover, we show that the Liouvillian dynamics of the multibaker map can be decomposed into the eigenmodes of diffusive relaxation associated with the Ruelle resonances of the Perron-Frobenius operator.     

Quantum mechanics in a two-dimensional spacetime: What is a wavefunction?

Conventional quantum mechanics specifies the mathematical properties of wavefunctions and relates them to physical experiments by invoking the Born postulate. There is no known direct connection between wavefunctions and any external physical object. However, in the case of a two-dimensional spacetime there is a completely classical context for wavefunctions where the connection with an external reality is transparent and unambiguous. By examining this case, we show how a classical stochastic process assembles a Dirac wavefunction based solely on the detailed counting of reversible paths. A direct comparison of how a related process assembles a Probability Density Function reveals both how and why PDFs and wavefunctions differ, including the ubiquitous implication of complex numbers for the latter. The appearance of wavefunctions in a context that is free of the complexities of quantum mechanics suggests the study of such models may shed some light on interpretive issues.     

What is the Relativistic Volterra Lattice?

We develop a systematic procedure of finding integrable 6ldquo;relativistic” (regular one-parameter) deformations for integrable lattice systems. Our procedure is based on the integrable time discretizations and consists of three steps. First, for a given system one finds a local discretization living in the same hierarchy. Second, one considers this discretization as a particular Cauchy problem for a certain 2-dimensional lattice equation, and then looks for another meaningful Cauchy problem, which can be, in turn, interpreted as a new discrete time system. Third, one has to identify integrable hierarchies to which these new discrete time systems belong. These novel hierarchies are called then “relativistic”, the small time step $h$ playing the role of inverse speed of light. We apply this procedure to the Toda lattice (and recover the well-known relativistic Toda lattice), as well as to the Volterra lattice and a certain Bogoyavlensky lattice, for which the “relativistic” deformations were not known previously. Received: 1 April 1998 / Accepted: 21 July 1998     

What is spin-magnetic moment of electron?

We investigate the problem about what the spin-magnetic moment is. The magnetic moment of the Dirac electron in the frame along z-axis is evaluated. This is identified with the spin-magnetic moment of the electron, because there is not any z-component of magnetic moment caused by orbital angular momentum in our frame. The correct value of the spin-magnetic moment and the correct ratio of the spin-magnetic moment to the spin (i.e. g=2) are obtained explicitly. In deriving them, the negative energy solutions of the Dirac equation perform essential roles. We find that the transition current from a positive energy state to a negative energy state causes spin-magnetic moment of the electrons in vacuum. This fact implies that the ratio of the spin-magnetic moment to the spin may change depending on the environments. For example, it may have different values in materials.