Auxiliary Stopping Area Layout Method for High-Speed Maglev considering Multiple Speed Profiles and Bidirectional Operation

Auxiliary stopping area (ASA) is the key guarantee for high-speed maglev train operation safety. Aiming at the layout of the ASA along the track, this article constructs an optimized model of ASA layout and proposes a solving algorithm based on the single target genetic algorithm by analyzing the influence factors of ASA layout. The result of the numerical experiment shows that the proposed method could fulfill the requirements of the maglev train operation safety and efficiency and optimize the cost of the ASA layout while taking the complex line situation, train tracking operation, and bidirectional operation on a single line into account.

A Feynman–Kac formula for magnetic monopoles

We consider the quantum mechanics of a charged particle in the presence of Dirac’s magnetic monopole. Wave functions are sections of a complex line bundle and the magnetic potential is a connection on the bundle. We use a continuum eigenfunction expansion to find an invariant domain of essential self-adjointness for the Hamiltonian. This leads to a proof of the Feynman–Kac formula expressing solutions of the imaginary time Schrödinger equation as stochastic integrals.

Another Proof of Basel Problem

In this paper, we present a new solution to the Basel problem using a complex line integral of log(1+z)/z.

COMPOSITION OF SLICE ENTIRE FUNCTIONS AND BOUNDED L-INDEX IN DIRECTION

We study the following question: "Let $f: \mathbb{C}\to \mathbb{C}$ be an entire function of bounded $l$-index, $\Phi: \mathbb{C}^n\to \mathbb{C}$ be a slice entire function, $n\geq2,$ $l:\mathbb{C}\to \mathbb{R}_+$ be a continuous function.We study the following question: "Let $f: \mathbb{C}\to \mathbb{C}$ be an entire function of bounded $l$-index, $\Phi: \mathbb{C}^n\to \mathbb{C}$ be a slice entire function, $n\geq2,$ $l:\mathbb{C}\to \mathbb{R}_+$ be a continuous function.What is a positive continuous function $L:\mathbb{C}^n\to \mathbb{R}_+$ and a direction $\mathbf{b}\in\mathbb{C}^n\setminus\{\mathbf{0}\}$ such that the composite function $f(\Phi(z))$ has bounded $L$-index in the direction~$\mathbf{b}$?". In the present paper, early known results on boundedness of $L$-index in direction for the composition of entire functions$f(\Phi(z))$ are generalized to the case where $\Phi: \mathbb{C}^n\to \mathbb{C}$ is a slice entire function, i.e.it is an entire function on a complex line $\{z^0+t\mathbf{b}: t\in\mathbb{C}\}$ for any $z^0\in\mathbb{C}^n$ andfor a given direction $\mathbf{b}\in\mathbb{C}^n\setminus\{\mathbf{0}\}$.These slice entire functions are not joint holomorphic in the general case. For~example, it allows consideration of functions which are holomorphic in variable $z_1$ and continuous in variable $z_2.$

The Analogies of Justice and Health inRepublic IV

This paper provides a new interpretation of Plato’s account of justice as psychic health in Republic IV. It argues that what has traditionally been considered to be one single analogy is actually a more complex line of reasoning that contains various medical analogies. These medical analogies are not only different in number but also in kind. I discuss each of them separately, while providing a response to various objections.

Aesthetic Perception of Line Patterns: Effect of Edge-Orientation Entropy and Curvilinear Shape

Curvilinearity is a perceptual feature that robustly predicts preference ratings for a variety of visual stimuli. The predictive effect of curved/angular shape overlaps, to a large degree, with regularities in second-order edge-orientation entropy, which captures how independent edge orientations are distributed across an image. For some complex line patterns, edge-orientation entropy is actually a better predictor for what human observers like than curved/angular shape. The present work was designed to disentangle the role of the two features in artificial patterns that consisted of either curved or angular line elements. We systematically varied these patterns across two more dimensions, edge-orientation entropy and the number of lines. Eighty-three participants rated the stimuli along three aesthetic dimensions ( pleasing, harmonious, and complex). Results showed that curved/angular shape was a stronger predictor for ratings of pleasing and harmonious if the stimuli consisted of a few lines that were clearly discernible. By contrast, edge-orientation entropy was a stronger predictor for the ratings if the stimuli showed many lines, which merged into a texture. No such differences were obtained for complexity ratings. Our findings are in line with results from neurophysiological studies that the processing of shape and texture, respectively, is mediated by different cortical mechanisms.

Lefschetz–Bott Fibrations on Line Bundles Over Symplectic Manifolds

We describe Lefschetz–Bott fibrations on complex line bundles over symplectic manifolds explicitly. As an application, we show that the link of the $A_{k}$-type singularity has more than one strong symplectic filling up to homotopy and blow-up at points when the dimension of the link is greater than or equal to $5$. In the appendix, we show that the total space of a Lefschetz–Bott fibration over the unit disk serves as a strong symplectic filling of a contact manifold compatible with an open book induced by the fibration.