It is shown that for the one-dimensional quantum anharmonic oscillator with potential $V(x)= x^2+g^2 x^4$ Perturbation Theory (PT) in powers of $g^2$ (weak coupling regime) and semiclassical expansion $\hbar$ energies coincide. related to fact dynamics $x$-space $(gx)$-space corresponds same energy spectrum effective constant $\hbar g^2$. Two equations, which govern those two spaces, Riccati-Bl...

It is a classical theorem of Sarason that an analytic function bounded mean oscillation (BMOA) vanishing if and only its rotations converge in norm to the original as angle rotation tends zero. In series two papers, Blasco et al. have raised problem characterizing all semigroups holomorphic functions $(\varphi\_{t})$ can replace semigroup Sarason’s theorem. We give complete answer this question...

Novelty is an important psychological construct that affects both perceptual and behavioral processes. Here, we propose a lexical novelty score (LNS) for a song’s lyric, based on the statistical properties of a corpus of 275,905 lyrics (available at www.smcnus.org/lyrics/). A lyric-level LNS was derived as a function of the inverse document frequencies of its unique words. An artist-level LNS w...

and Applied Analysis 3 2. Main Results and Proofs In this section, we give our main results and their proofs. Before stating these results, we need some auxiliary results, which are incorporated in the lemmas which follows. Lemma 2.1. Assume that g ∈ H Bn and μ : Bn → 0,∞ are normal. Then Tg : H∞ log → Bμ is compact if and only if Tg : H∞ log → Bμ is bounded and for any bounded sequence fk k∈N ...

Our aim is to explain instances in which the value of the logarithmic Mahler measure m(P ) of a polynomial P ∈ Z[x, y] can be written in an unexpectedly neat manner. To this end we examine polynomials defining rational curves, which allows their zero-locus to be parametrized via x = f(t), y = g(t) for f, g ∈ C(t). As an illustration of this phenomenon, we prove the equality πm(y2 + y(x+ 1) + x2...

A Bloch point singularity can form a metastable state in a magnetic nanosphere. We classify possible types of Bloch points and analytically derive the shape of the magnetization distribution for different Bloch points. We show that an external gradient field can stabilize the Bloch point: The shape of the Bloch point becomes radially dependent. We compute the magnetization structure of the nano...

The Multi-Dimensional Logarithmic Number System (MDLNS), with similar properties to the Logarithmic Number System (LNS), provides more degrees of freedom than the LNS by virtue of having two orthogonal bases and the ability to use multiple digits. Unlike the LNS, there is no direct functional relationship between binary/floating point representation and the MDLNS representation. Traditionally l...

In order to meet the users’ demand, bike sharing systems must be regularly rebalanced. The problem of balancing bike sharing systems (BBSS) is concerned with designing optimal tours and operating instructions for relocating bikes among stations to maximally comply with the expected future bike demands. In this paper, we tackle the BBSS by means of Constraint Programming: first, we introduce two...