Local well-posedness for the nonlinear Schr\"odinger equation in the intersection of modulation spaces Mp,qs(Rd)∩M∞,1(Rd)M_{p, q}^s(\mathbb{R}^d) \cap M_{\infty, 1}(\mathbb{R}^d)

We introduce a Littlewood-Paley characterization of modulation spaces and use it to give an alternative proof of the algebra property, somehow implicitly contained in Sugimoto (2011), of the intersection $M^s_{p,q}(\mathbb{R}^d) \cap M_{\infty, 1}(\mathbb{R}^d)$ for $d \in \mathbb{N}$, $p, q \in [1, \infty]$ and $s \geq 0$. We employ this algebra property to show the local well-posedness of the Cauchy problem for the cubic nonlinear Schr\"odinger equation in the above intersection. This improves Theorem 1.1 by B\'enyi and Okoudjou (2009), where only the case $q = 1$ is considered, and closes a gap in the literature. If $q > 1$ and $s > d \left(1 - \frac{1}{q}\right)$ or if $q = 1$ and $s \geq 0$ then $M^s_{p,q}(\mathbb{R}^d) \hookrightarrow M_{\infty, 1}(\mathbb{R}^d)$ and the above intersection is superfluous. For this case we also reobtain a H\"older-type inequality for modulation spaces.Comment: 14 page

A Guide to Localized Frames and Applications to Galerkin-like Representations of Operators

This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We investigate the representation of operators using localized frames in a Galerkin-type scheme. We show how the boundedness and the invertibility of matrices and operators are linked and give some sufficient and necessary conditions for the boundedness of operators between the associated Banach spaces.Comment: 32 page

Linear perturbations of the Wigner transform and the Weyl quantization

We study a class of quadratic time-frequency representations that, roughly speaking, are obtained by linear perturbations of the Wigner transform. They satisfy Moyal's formula by default and share many other properties with the Wigner transform, but in general they do not belong to Cohen's class. We provide a characterization of the intersection of the two classes. To any such time-frequency representation, we associate a pseudodifferential calculus. We investigate the related quantization procedure, study the properties of the pseudodifferential operators, and compare the formalism with that of the Weyl calculus.Comment: 38 pages. Contributed chapter for volume on the occasion of Luigi Rodino's 70th birthda

An optimally concentrated Gabor transform for localized time-frequency components

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on $l^p$-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples

Understanding Terrorist Organizations with a Dynamic Model

Terrorist organizations change over time because of processes such as recruitment and training as well as counter-terrorism (CT) measures, but the effects of these processes are typically studied qualitatively and in separation from each other. Seeking a more quantitative and integrated understanding, we constructed a simple dynamic model where equations describe how these processes change an organization's membership. Analysis of the model yields a number of intuitive as well as novel findings. Most importantly it becomes possible to predict whether counter-terrorism measures would be sufficient to defeat the organization. Furthermore, we can prove in general that an organization would collapse if its strength and its pool of foot soldiers decline simultaneously. In contrast, a simultaneous decline in its strength and its pool of leaders is often insufficient and short-termed. These results and other like them demonstrate the great potential of dynamic models for informing terrorism scholarship and counter-terrorism policy making.Comment: To appear as Springer Lecture Notes in Computer Science v2: vectorized 4 figures, fixed two typos, more detailed bibliograph

An Analysis on the Impact of Export Rebate to Export Structure in China

实践经验证明，出口退税政策的实施对促进一国对外贸易，尤其是出口贸易的发展具有重要的作用。而在坚持“应退尽退”的税收中性原则下，相机的实施差别退税率的出口退税政策则在优化出口商品结构、优化产业结构等方面具有积极的作用。我国现行的出口退税政策自1985年正式实施以来，国家曾根据经济形势的变化多次对出口退税率进行调整，对不同行业的出口退税率的调整力度不尽相同，因而出口退税政策在实施的过程中对不同行业的影响也迥然不同。 本文中，笔者首先介绍了出口退税政策在国外的发展情况以及在我国的演变过程，尤其是1994年税制改革后我国对出口退税率的调整经过，并结合我国出口商品结构的变动情况进行定性分析；然后再根据...It has been proved that export rebate policy plays an important role in promoting the international trade of a country,particularly the development of the export. Under the principle of tax neutrality, adopting different export rebate rate in different conditions makes positive effect on optimization of export structure and industry structure. Since 1985, China has repeatedly adjusted the export r...学位：经济学硕士院系专业：经济学院财政系_财政学(含税收学)学号：1552007115009

Determinants of legacy effects in pine trees – implications from an irrigation-stop experiment

Tree responses to altered water availability range from immediate (e.g. stomatal regulation) to delayed (e.g. crown size adjustment). The interplay of the different response times and processes, and their effects on long-term whole-tree performance, however, is hardly understood. Here we investigated legacy effects on structures and functions of mature Scots pine in a dry inner-Alpine Swiss valley after stopping an 11-yr lasting irrigation treatment. Measured ecophysiological time series were analysed and interpreted with a system-analytic tree model. We found that the irrigation stop led to a cascade of downregulations of physiological and morphological processes with different response times. Biophysical processes responded within days, whereas needle and shoot lengths, crown transparency, and radial stem growth reached control levels after up to 4 yr only. Modelling suggested that organ and carbon reserve turnover rates play a key role for a tree’s responsiveness to environmental changes. Needle turnover rate was found to be most important to accurately model stem growth dynamics. We conclude that leaf area and its adjustment time to new conditions is the main determinant for radial stem growth of pine trees as the transpiring area needs to be supported by a proportional amount of sapwood, despite the growth-inhibiting environmental conditions

Cornerstones of Sampling of Operator Theory

This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of the subject back to the original work of the third-named author in the late 1950s and early 1960s, and to the innovations in spread-spectrum communications that preceded that work. We give a brief overview of the NOMAC (Noise Modulation and Correlation) and Rake receivers, which were early implementations of spread-spectrum multi-path wireless communication systems. We examine in detail the original proof of the third-named author characterizing identifiability of channels in terms of the maximum time and Doppler spread of the channel, and do the same for the subsequent generalization of that work by Bello. The mathematical limitations inherent in the proofs of Bello and the third author are removed by using mathematical tools unavailable at the time. We survey more recent advances in sampling of operators and discuss the implications of the use of periodically-weighted delta-trains as identifiers for operator classes that satisfy Bello's criterion for identifiability, leading to new insights into the theory of finite-dimensional Gabor systems. We present novel results on operator sampling in higher dimensions, and review implications and generalizations of the results to stochastic operators, MIMO systems, and operators with unknown spreading domains