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This chapter presents the model of a hybrid system to be used in this volume. The focus is on the data structure and on modeling. The model suggests that the flow set, the flow map, the jump set, and the jump map can be specialized to capture the dynamics of purely continuous-time or discrete-time systems on ℝⁿ. The former corresponds to a flow set equal to ℝⁿ and an empty jump set, while the latter can be captured with an empty flow set and a jump set defined as ℝⁿ. In addition, several examples of hybrid systems are given, including models of hybrid control systems. The model of a hybrid system is then related to other modeling frameworks; such as hybrid automata, impulsive differential equations, and switching systems.

Proximal-to-distal sequencing of limb segments is characteristic of a number of motor behaviors, including throwing, hitting, jumping, and perhaps even reach-to-grasp. Moreover, shoulder- and elbow-related neurons in the primary motor cortex (MI) have been shown to activate earlier than wrist- and finger-related neurons in monkeys performing a button-press task. It was recently discovered that β frequency oscillations in the local field potential (LFP) spontaneously propagate as travelling waves across the surface of the motor cortex along a rostral-to-caudal axis while monkeys perform a variety of visuomotor tasks. This chapter hypothesizes that these propagating LFP waves may promote proximal-to-distal recruitment of motor cortical neurons. This is consistent with a number of intracortical microstimulation experiments in the MI demonstrating a topographic gradient, such that proximal movements of the shoulder and elbow are evoked more rostrally on the precentral gyrus, while wrist and finger movements are elicited more caudally including within the bank of the central sulcus.

This chapter starts out with the 1941 broadcasting ban, which made Ellington record Strayhorn originals such as Take the “A” Train, Chelsea Bridge, and Rain Check. Analysis of these works displays their main characteristics: advanced harmonies, chromatic melodies, a tight structural design, and a clear compositional concept, partly based on classical techniques. The chapter then turns to the first major Ellington-Strayhorn collaboration: Jump for Joy. A study of unused, vanguard 1941-2 works follows, including Blue Star and Pentonsilic. The final section summarizes Strayhorn’s importance in those years: he wrote or co-wrote some of the Ellington band’s stalwarts, he revitalized or fleshed out other pieces, and he arranged most of the band’s pop material. Strayhorn added an entirely new stylistic wing to the Ellington building, of which Ellington was still believed to be the sole architect.

Fritz Haber hired Polanyi to work in the Fiber Chemistry Group of the Kaiser Wilhelm Institute in Berlin. Polanyi helped develop the rotating-crystal method of X-ray crystallography, made solid contributions to understanding the structure of cellulose, pressed forward with his work on adsorption catalysis and electrostatic dipoles, laid the foundation for transition rate theory in reaction kinetics, and investigated the bond strength of crystals; he was also forced to give up a cherished theory about quantum jumps in reaction kinetics, which taught him an important lesson about how scientists work together to distinguish real discoveries from mistaken surmises. Polanyi married Magda Kemeny on February 21, 1921, in a civil ceremony; their first child, George Michael Polanyi, was born on October 1, 1922.

This chapter develops the language of building Turing functionals which is used to characterize promptly simple degrees by low cuppability, and to prove the pseudo-jump inversion theorem of Jockusch and Shore. It provides a new pseudo-jump inversion theorem for Martin–Löf randomness. These results are used to separate highness properties, for instance superhighness from being LR-hard.

This chapter studies lowness properties of sets not necessarily below the halting problem. The main new notions are all related to traceability. It characterizes lowness for Schnorr, and computable randomness. It also studies strong jump traceability and its relationship to the cost function method of Chapter 5. Many research problems are posed.

This chapter starts with a brief history of the science of diffusion. Macroscopically diffusion is characterized by various diffusion coefficients: the self-diffusion coefficient, the tracer diffusion coefficient, the chemical or Fickian diffusion coefficient, and the conductivity diffusion coefficient. Microscopically the gas, liquid-like, and solid state diffusion mechanisms are considered. Solid state diffusion is characterized by the parameters jump rate, jump vector, and coordination number. The stochastic aspects of solid state (jump) diffusion are introduced. Statistical methods (Markov and non-Markov processes) are applied to study the outcome of a sequence of jumps, i.e., the spatial/temporal development of the diffusive process. The nature of the mechanism of a single diffusive event is considered. Topics such as classical jump, phonon-assisted tunnelling, electron-restricted tunnelling, and incoherent tunnelling types, also called hopping, are introduced.

This chapter examines the crucial role of phase fluctuations in two-dimensional (2D) systems. The exponential tail in Josephson current is found close to T_c. The physics of the Berezinskii-Kosterlitz-Thouless transition is discussed. The effect of order parameters and vortex fluctuations of the critical temperature of 2D superconductors are compared. The manifestation of vortex fluctuations above BKT transition is discussed.

This chapter describes the basics of spin injection and spin transport in magnetic nanohybrid structures. Particular emphasis is placed on the nonlocal spin transport in a spin injection and detection device of F1/N/F2 structure, where F1 is a spin injector, N is a nonmagnetic metal or semiconductor, and F2 is a spin detector. The spin-dependent transport equations for the electrochemical potentials of up and down spins are solved, and the efficient spin injection, spin accumulation, spin current, spin transfer, and spin detection are examined in the structure of arbitrary junction resistance, its source ranging from a metallic contact to a tunneling regime. It is demonstrated that discussion concerning the nonlocal spin-injection devices provide opportunities to relate novel phenomena, such as pure spin-current injection and manipulation, spin injection into superconductors or semiconductors, and spin Hall effect in nanohybrid stuctures.

This chapter examines how the jumping spider's eight eyes are structured, how they function, and how they might have evolved. It also reviews the intricate vision-based predatory strategies for which jumping spiders are justly renowned. The last part of the chapter combines what is known about variation in salticid eye design and behavior with what is known from traditional taxonomic and modern phylogenetic data in order to reconsider the hypothesis that araneophagy has been a driving force in the evolution of the salticid principal eye.

This chapter presents techniques for jumps, covering the glissade, glissade précipité, glissade from fourth position for big traveling jumps, assemblé, assemblé porté, jeté, grand jeté, sissonne, posé, brisé, and entrechat six.

This chapter presents the epidemiological profile of suicide in Singapore. The suicide rate in Singapore has remained steady between 1993–2003, ranging from 8–12 per 100,000. The male:female suicide ratio is approximately 1.7:1 with jumping from a height being the most common method of suicide. Marriage has been shown to be a protective factor (especially in males) with the widowed or divorced being at higher risk. In the young, relationships and social factors, such as study stresses, are major risk factors; in mid-age adults, job/financial problems and mental illness are important, and in the older age group, physical illness is most significant. Those with mental illness (especially with schizophrenia and depressive disorders) are also at particular risk, especially if they have been recently hospitalized.

This chapter argues that the Aristophanic plot-line often provides an impression of realist continuity because there are innumerable moments, or miniature sequences, of consequential action. It explains that the apparent ‘jumps’ associated with Aristophanes' characters and plots are not only related in kind: they may be the same thing. It notes that Aristophanic Old Comedy is best seen as a sequence of relational states between one interest party — often but not always, one focal individual — and the world at large. It adds that the pattern involves a series of five states or stages: dissatisfaction, quest, conflict, victory, celebration.

This chapter presents incoherent QENS studies performed on Li⁺, Na⁺, H^-, and Cl^- ions. Purely coherent QENS concerns F^- and O^2- conductors, whereas for Ag⁺ a mixture of coherent and incoherent QENS prohibits quantitative data evaluation. On the other hand, AgI is one of the best solid ionic conductors, and QENS studies are performed and combined with impedance spectroscopy at high frequencies. For this system, the well-known jump relaxation model is derived. Na⁺ motion in β-Al₂O₃ is investigated by QENS in detail. Much effort has been spent on Li⁺ diffusion motivated by applications of Li in batteries. For anionic conductors, the system best investigated by means of QENS is Cl^- diffusion in SrCl₂.

In the case of spatially limited jump diffusion, the incoherent scattering function consists of an elastic and a quasielastic part, and the fraction of elastic intensity is called the incoherent structure factor, EISF. This chapter evaluates different scenarios and the corresponding EISFs. Long range translational diffusion gives rise to quasielastic scattering consisting of a single Lorentzian with a linewidth proportional to Q². The Chudley–Elliott model for lattice gases describes translational jump diffusion in Bravais lattices. QENS from translational jump diffusion on lattices with all sites equivalent consists of a set of Lorentzians. Even more complex is QENS from diffusion over energetically different sites. The system of rate equation is expressed in terms of a jump matrix, but this matrix is not hermitean. The resulting eigenvalues are the linewidths of the Lorentzians, whereas from the eigenvectors the intensity of the Lorentzians can be calculated. This full power of QENS can only be realized on the basis of direction-dependent measurements on single-crystalline samples. A completely different approach is the so-called two-state model which applies for disordered systems and which is also derived in full detail.

This chapter considers some questions which only make sense in a multivariate setting. It deals with two problems: one is about a multidimensional underlying process X, and we want to decide whether two particular components of X jump at the same time: this can happen always, or never, or for some but not all jump times. The second problem is again about a one-dimensional underlying process X, but we study the pair (X, σ‎), with the second component being the volatility of the first component X. Again, we want to decide whether X and σ‎ jump at the same times, always, or never, or sometimes. The process X is observed at the regularly spaced observation times iΔ‎₀, within a finite time interval [0, T].

This chapter deals with jumping. Jumping, as it has evolved in competition recently, rarely has direct practical application, but the educational value of the sport is tremendous. Jumping fosters bravery, dexterity, courage, and a strong spirit, all of which results in a ski jumper's acquisition of self-confidence, composure, and resourcefulness—traits that are crucial while skiing over varied terrain. In addition, the skier experiences enjoyment and pleasure after the completion of a successful jump. To that end, the chapter takes a look at jumping exclusively from an athletic point of view. Here, it illustrates the proper techniques for a beautiful and successful jump and takes note of any possible mistakes which might be incurred.