Unimodular lattices with long shadow

Let L be an odd unimodular lattice of dimension n with shadow n−16. If min(L)?3 then dim(L)?46 and there is a unique such lattice in dimension 46 and no lattices in dimensions 44 and 45. To prove this, a shadow theory for theta series with spherical coefficients is developed.     

On the origin of electron stimulated desorption of H+ from metal surface

The emission of hydrogen ESD ions from polycrystalline Nb is studied experimentally. The results demonstrate clearly that no ESD emission of H⁺ occurs from a pure H adsorbate. However, adsorption of H₂O, present as an impurity in H₂, and H₂ adsorption on Nb preceded by O adsorption, produce strong H⁺ ESD emission. It is shown that Auger ionization of O can account for the increased H⁺ yield and it is postulated that similar effects also occur on other metal surfaces.     

Electronic structure of Si(111) surfaces

We report on new angle-resolved photoemission studies of Si(111) 2 × 1 and 7 × 7 surfaces. The emission from the 2 × 1 surface shows much structure. For normal emission the energy positions are insensitive to the photon energy in the range 19–27 eV. The emission has been interpreted as a probe of the surface density of states, SDOS, including both surface states, resonances and bulk-like states. The SDOS was also calculated as a function of parallel momentum k_∥ for a model of the Si(111) 2 × 1 surface obtained from energy minimization considerations. We identify emission from the dangling bond band, which has a positive dispersion of 0.6 eV, and also emission from surface resonances which have some character of the compressed and stretched back bonds. There are also other predicted surface resonances that correspond to experimental peaks which have not been identified in previous work. Except for the dangling bond band, the surface resonances are limited in k_∥ space, so that it is not possible to follow these resonance bands over all angles. Maximum intensity for the normal emission from the dangling bond is obtained at 23 eV, while the emission from the lowest s-like states monotonically increases towards 30 eV photon energy. When annealing the cleaved 2 × 1 surface to the 7 × 7 reconstructed surface, the spectra broaden significantly. The intensity of the dangling bond decreases and we see a very small metallic edge.     

Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

Fractional integrals and weakly singular integral equations of the first kind in then-dimensional ball

The purpose of the paper is to introduce and to investigate a new class of fractional integrals connected with balls in ?ⁿ. A Riesz potentialI _Ω ^α ρ over a ball Ω is represented by a composition of such integrals. Using this representation we obtain necessary and sufficient solvability conditions for the equationI _Ω ^α ρ =f in the space L_p(Ωw) with a power weight w(x) and solve the equation in a closed form. The investigation is based on a special Fourier analysis adopted for operators commuting with rotations and dilations in ?ⁿ.     

Mach's principle. Part 1. Initial state of the universe the universe

The integral formulation of equations of general relativity proposed earlier as a mathematical tool for Mach's principle forbids the conventional singular cosmologies but is compatible with the de Sitter initial space.     

Voice responses to changes in pitch of voice or tone auditory feedback

The present study was undertaken to examine if a subject's voice F0 responded not only to perturbations in pitch of voice feedback but also to changes in pitch of a side tone presented congruent with voice feedback. Small magnitude brief duration perturbations in pitch of voice or tone auditory feedback were randomly introduced during sustained vowel phonations. Results demonstrated a higher rate and larger magnitude of voice F0 responses to changes in pitch of the voice compared with a triangular-shaped tone (experiment 1) or a pure tone (experiment 2). However, response latencies did not differ across voice or tone conditions. Data suggest that subjects responded to the change in F0 rather than harmonic frequencies of auditory feedback because voice F0 response prevalence, magnitude, or latency did not statistically differ across triangular-shaped tone or pure-tone feedback. Results indicate the audio-vocal system is sensitive to the change in pitch of a variety of sounds, which may represent a flexible system capable of adapting to changes in the subject's voice. However, lower prevalence and smaller responses to tone pitch-shifted signals suggest that the audio-vocal system may resist changes to the pitch of other environmental sounds when voice feedback is present.     

On the Structure of Eigenfunctions Corresponding to Embedded Eigenvalues of Locally Perturbed Periodic Graph Operators

The article is devoted to the following question. Consider a periodic self-adjoint difference (differential) operator on a graph (quantum graph) G with a co- compact free action of the integer lattice $\mathbb{Z}^{n}The article is devoted to the following question. Consider a periodic self-adjoint difference (differential) operator on a graph (quantum graph) G with a co- compact free action of the integer lattice . It is known that a local perturbation of the operator might embed an eigenvalue into the continuous spectrum (a feature uncommon for periodic elliptic operators of second order). In all known constructions of such examples, the corresponding eigenfunction is compactly supported. One wonders whether this must always be the case. The paper answers this question affirmatively. What is more surprising, one can estimate that the eigenmode must be localized not far away from the perturbation (in a neighborhood of the perturbation’s support, the width of the neighborhood dependent upon the unperturbed operator only). The validity of this result requires the condition of irreducibility of the Fermi (Floquet) surface of the periodic operator, which is known in some cases and is expected to be satisfied for periodic Schr?dinger operators.     

Self-organized minimum-energy structures for dielectric elastomer actuators

When a stretched elastomer is laminated to a flat plastic frame, a complex shape is formed, which is termed a minimum-energy structure. It is shown how self-organized structures can be applied in the development of actuators with complex, out-of-plane actuationmodes. This unusual concept is then demonstrated in the case of dielectric elastomer actuators. Among advantages of this approach are the simplicity in manufacturing, the potential complexity and sophistication of the manufactured structures, and the general benefits of the concept when applied to other electro-mechanically active materials. PACS 46.32.+x; 77.65.-j; 83.80.Va