Branes and supersymmetric quantum field theories

Since the discovery of D-branes as non-perturbative, dynamic objects in string theory, various configurations of branes in type IIA/B string theory and M-theory have been considered to study their low-energy dynamics described by supersymmetric quantum field theories.

One example of such a construction is based on the description of Seiberg-Witten curves of four-dimensional N = 2 supersymmetric gauge theories as branes in type IIA string theory and M-theory. This enables us to study the gauge theories in strongly-coupled regimes. Spectral networks are another tool for utilizing branes to study non-perturbative regimes of two- and four-dimensional supersymmetric theories. Using spectral networks of a Seiberg-Witten theory we can find its BPS spectrum, which is protected from quantum corrections by supersymmetry, and also the BPS spectrum of a related two-dimensional N = (2,2) theory whose (twisted) superpotential is determined by the Seiberg-Witten curve. When we don’t know the perturbative description of such a theory, its spectrum obtained via spectral networks is a useful piece of information. In this thesis we illustrate these ideas with examples of the use of Seiberg-Witten curves and spectral networks to understand various two- and four-dimensional supersymmetric theories.

First, we examine how the geometry of a Seiberg-Witten curve serves as a useful tool for identifying various limits of the parameters of the Seiberg-Witten theory, including Argyres-Seiberg duality and Argyres-Douglas fixed points. Next, we consider the low-energy limit of a two-dimensional N = (2, 2) supersymmetric theory from an M-theory brane configuration whose (twisted) superpotential is determined by the geometry of the branes. We show that, when the two-dimensional theory flows to its infra-red fixed point, particular cases realize Kazama-Suzuki coset models. We also study the BPS spectrum of an Argyres-Douglas type superconformal field theory on the Coulomb branch by using its spectral networks. We provide strong evidence of the equivalence of superconformal field theories from different string-theoretic constructions by comparing their BPS spectra.

Random propagation in complex systems : nonlinear matrix recursions and epidemic spread

This dissertation studies long-term behavior of random Riccati recursions and mathematical epidemic model. Riccati recursions are derived from Kalman filtering. The error covariance matrix of Kalman filtering satisfies Riccati recursions. Convergence condition of time-invariant Riccati recursions are well-studied by researchers. We focus on time-varying case, and assume that regressor matrix is random and identical and independently distributed according to given distribution whose probability distribution function is continuous, supported on whole space, and decaying faster than any polynomial. We study the geometric convergence of the probability distribution. We also study the global dynamics of the epidemic spread over complex networks for various models. For instance, in the discrete-time Markov chain model, each node is either healthy or infected at any given time. In this setting, the number of the state increases exponentially as the size of the network increases. The Markov chain has a unique stationary distribution where all the nodes are healthy with probability 1. Since the probability distribution of Markov chain defined on finite state converges to the stationary distribution, this Markov chain model concludes that epidemic disease dies out after long enough time. To analyze the Markov chain model, we study nonlinear epidemic model whose state at any given time is the vector obtained from the marginal probability of infection of each node in the network at that time. Convergence to the origin in the epidemic map implies the extinction of epidemics. The nonlinear model is upper-bounded by linearizing the model at the origin. As a result, the origin is the globally stable unique fixed point of the nonlinear model if the linear upper bound is stable. The nonlinear model has a second fixed point when the linear upper bound is unstable. We work on stability analysis of the second fixed point for both discrete-time and continuous-time models. Returning back to the Markov chain model, we claim that the stability of linear upper bound for nonlinear model is strongly related with the extinction time of the Markov chain. We show that stable linear upper bound is sufficient condition of fast extinction and the probability of survival is bounded by nonlinear epidemic map.

Range of validity of the method of averaging

Sufficient conditions are derived for the validity of approximate periodic solutions of a class of second order ordinary nonlinear differential equations. An approximate solution is defined to be valid if an exact solution exists in a neighborhood of the approximation.

Two classes of validity criteria are developed. Existence is obtained using the contraction mapping principle in one case, and the Schauder-Leray fixed point theorem in the other. Both classes of validity criteria make use of symmetry properties of periodic functions, and both classes yield an upper bound on a norm of the difference between the approximate and exact solution. This bound is used in a procedure which establishes sufficient stability conditions for the approximated solution.

Application to a system with piecewise linear restoring force (bilinear system) reveals that the approximate solution obtained by the method of averaging is valid away from regions where the response exhibits vertical tangents. A narrow instability region is obtained near one-half the natural frequency of the equivalent linear system. Sufficient conditions for the validity of resonant solutions are also derived, and two term harmonic balance approximate solutions which exhibit ultraharmonic and subharmonic resonances are studied.

Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems

This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical

Self-formation of quasiperiodic void structure in CaF2 induced by femtosecond laser irradiation

We report the self-formation of quasiperiodic void structure with the length of several hundred micrometers inside the CaF2 crystal. The quasiperiodical voids along the propagation direction of the laser beam were formed spontaneously after the irradiation of a single femtosecond laser beam which was focused at a fixed point inside the crystal sample. The length of the void array varied with the focal depth beneath the sample surface. The possible mechanism of the self-formed void structure was discussed. (c) 2007 American Institute of Physics.

单束飞秒激光在氧化铝晶体中诱导自组装微米点阵

报道了单束飞秒激光在氧化铝晶体中诱导自组装微米点阵的有关研究进展。当单束飞秒激光被透镜聚焦到氧化铝晶体的内部某固定点， 微米点阵就在聚焦点的下方自动生成。我们发现能否产生自组装点阵和光束的聚焦点距离样品表面的深度有关。通过比较在氧化铝晶体和氟化钙晶体中能够产生点阵的深度，我们发现在氧化铝中较浅的位置即能诱导出点阵，而在氟化钙中则要求深度较深。具体的机理在文中进行了讨论。

Self-organized microvoid array perpendicular to the femtosecond laser beam in CaF2 crystals

Microvoid arrays were self-organized when femtosecond laser beam was tightly focused at a fixed point inside CaF2 crystal sample. Except void array grown below the focal point which had been reported before, we found another void array grown vertical to the laser propagation direction. This result has potential application in the fabrication of integrated micro-optic elements and photonic crystals. The possible mechanism of the phenomenon was proposed and verified experimentally.

Review of NRA tracking projects on salmon, Salmo salar L., and sea trout, Salmo trutta L

The report briefly outlines the programme of the National Rivers Authority (NRA), placing the Fisheries programme in the context of the work of the NRA as a whole, and viewing the tracking work against the broader requirements of the NRA Fisheries research programme. All regions of England and Wales are considered. Two techniques currently exist for studying the detailed timing and extent of movements of adult salmon: tracking of individually identifiable fish, and counting the numbers of fish moving past a fixed point in the river. The development of tracking techniques and the integrated use of tracking and fish counters is briefly reviewed in Section 3. Further details of these techniques are given in Appendices. Section 4 summarises and assesses completed and current NRA tracking studies. Section 5 discusses the scientific content of these studies in relation to similar work carried out elsewhere in the UK. The NRA programme of tracking studies is evaluated in Section 6. Section 7 discusses future fisheries projects and Section 8 details the future development of tracking techniques. Finally, recommendations arising out of this review are summarised in Section 9.

Description of NRA tracking studies: tracking techniques and fish counter technology

The study began on the 7th January 1991 and was completed in June 1991. Two reports have been produced. This report published as R&D Note 33 describes NRA tracking studies, tracking techniques and fish counter technology. The second report published as R&D Note 34 evaluates NRA tracking studies and recommends future research. The latter will be used solely for NRA management purposes. This report briefly outlines the programme of the NRA, placing the Fisheries programme in the context of the work of the NRA as a whole, and viewing the tracking work against the broader requirements of the NRA Fisheries research programme. Two techniques currently exist for studying the detailed timing and extent of movements of adult salmon: tracking of individually identifiable fish, and counting the numbers of fish moving past a fixed point in the river. Further details of these techniques and their development are given in Sections 2 and 3. Section 4 summarises and assesses completed and current NRA tracking Studies. Complete project descriptions for the studies are contained in Appendix A. Section 5 discusses the scientific content of these studies in relation to similar work carried out elsewhere in the UK. Section 6 details the future development of tracking techniques. Tracking work on migratory salmonids has tended to concentrate largely upon the movements of adult salmon. Much of this report will therefore be concerned with salmon tracking studies. NRA studies involving sea trout are referred to where appropriate. The methodological problems of sea trout tracking studies are summarised in Section 2.1.3.

Remodelação alveolar e perfil bacteriano em implantes instalados em diferentes níveis relacionados à crista óssea

A substituição clínica de dentes naturais perdidos por implantes osteointegrados tem representado uma das primeiras opções terapêuticas para a reabilitação de pacientes total ou parcialmente edêntulos. Apesar dos excelentes índices de sucesso demonstrados pelas restaurações implanto-suportadas, alguns fatores permanecem não esclarecidos, principalmente no que diz respeito à remodelação óssea ao redor dos implantes osteointegrados. Desta forma, o objetivo deste estudo foi avaliar a relação do nível de instalação dos implantes dentários com os parâmetros clínicos, com a remodelação óssea peri-implantar e com a colonização bacteriana, em implantes de plataforma regular, submetidos à carga imediata. Implantes de plataforma regular foram instalados em dois diferentes níveis em relação à crista óssea ao nível ósseo e supra ósseo (1 mm). No total, trinta e cinco implantes em 9 pacientes (idade média de 62,4 11,2 anos) foram avaliados radiograficamente no momento da instalação dos implantes (T1) e 6 meses após (T2), momento no qual também foram feitas análises clínicas e coleta de amostras para o teste microbiológico. Nos exames radiográficos foram analisadas a perda óssea, a partir de mensurações lineares da distância entre um ponto fixo do componente protético e o ponto mais coronário do contato osso-implante, e a densidade óptica alveolar obtida a partir de regiões ósseas de interesse (ROIs). As análises clínicas consistiram na avaliação da profundidade de sondagem e na mensuração do volume do fluido gengival peri-implantar. O perfil bacteriano dos sítios avaliados foi caracterizado por meio do método de análise de checkerboard DNA-DNA hybridization. Os testes estatísticos realizados mostraram não haver relação entre o nível de instalação dos implantes em relação à crista óssea e a remodelação óssea alveolar, tanto com relação à perda óssea (p = 0,725), como com relação à densidade óptica alveolar (p = 0,975). Também não foi possível estabelecer uma correlação entre a remodelação óssea e parâmetros clínicos como profundidade de sondagem e volume do fluido gengival peri-implantar. Com relação ao perfil bacteriano, não foram encontradas diferenças estatisticamente significativas entre os grupos avaliados para nenhuma das 40 bactérias analisadas.

Trace theory

The concept of traces has been introduced for describing non-sequential behaviour of concurrent systems via its sequential observations. Traces represent concurrent processes in the same way as strings represent sequential ones. The theory of traces can be used as a tool for reasoning about nets and it is hoped that applying this theory one can get a calculus of the concurrent processes anologous to that available for sequential systems. The following topics will be discussed: algebraic properties of traces, trace models of some concurrency phenomena, fixed-point calculus for finding the behaviour of nets, modularity, and some applications of the presented theory.

The Category-Theoretic Solution of Recursive Domain Equations

Recursive specifications of domains plays a crucial role in denotational semantics as developed by Scott and Strachey and their followers. The purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place. The idea is to follow the well-known analogy between partial orders and categories, generalizing from least fixed-points of continuous functions over cpos to initial ones of continuous functors over $\omega $-categories. To apply these general ideas we introduce Wand's ${\bf O}$-categories where the morphism-sets have a partial order structure and which include almost all the categories occurring in semantics. The idea is to find solutions in a derived category of embeddings and we give order-theoretic conditions which are easy to verify and which imply the needed categorical ones. The main tool is a very general form of the limit-colimit coincidence remarked by Scott. In the concluding section we outline how compatibility considerations are to be included in the framework. A future paper will show how Scott's universal domain method can be included too.

谓词μ演算和模态图的语义一致性

模态图是谓词μ演算的一种有效的图形表示形式。证明了谓词μ演算和模态图的语义一致性，详细讨论了谓词μ演算公式、嵌套谓词等式系和模态图之间的关系，并给出了一种优化的从线性公式到嵌套谓词等式系的转换算法。

牦牛粪便对青藏高原东部高寒草甸土壤养分系统的影响

川西北高寒草甸位于青藏高原东部地区，是我国四大牧区之一，也是长江和黄河等江河源区的重要水源涵养功能区。近几十年来，大量牦牛粪便被牧民作为生物能源、肥料或者食用菌产业的原料而利用，为草原生态系统的养分平衡增加了生态风险。鉴于在青藏高原地区针对牦牛粪便的相关研究尚未见报道，本文从粪便和土壤养分相互变化趋势的角度出发，研究了粪便在夏秋两季的分解状况和粪便其下及其周围土壤的养分变化。通过此研究，将有助于了解牦牛粪便在自然状态下的分解速率以及粪便对土壤养分及土壤微生物生物量的影响，为粪便对草地土壤生态系统的贡献提供概念性认识，同时也为高寒草甸草地这种脆弱生态系统的可持续管理提供理论依据。 针对牦牛粪便自身养分释放及其对土壤在时间和空间尺度上的影响，本文通过模拟牛粪堆积，在不同时间和固定区域内对牛粪和土壤进行了夏秋两季的采样测定，分析了牛粪及土壤NO3--N、NH4+-N、速效K、无机P、有机C、全N 和全P 含量随时间的变化趋势。得到如下结果： 1. 在研究区域内，牛粪对草地生态系统具有较强的养分（N、P）贡献能力。据初步统计，其估值大致为氮素699~932 kg ha-1，P 素为110~147 kg ha-1。牛粪（湿重、干重）在夏秋季节的分解速率具有较大差异，夏季显著快于秋季。夏季牛粪湿重、干重在2 个月左右之后分别降为初期的14%和24%，而秋季同期分别降为35%和52%。牛粪养分（NO3--N、NH4+-N、速效K、无机P、有机C、全N 和全P）的分解速率在夏季也要显著快于秋季。秋季经过2 个月左右的分解之后，牛粪以上含量分别降至初始态的32%、60%、36%、64%、58%、63%和43%，远高于夏季的同期水平。 2. 在不同季节，牛粪周围的土壤养分（NO3--N、NH4+-N、速效K 和无机P）含量变化随时间改变呈现相同的趋势。但是，牛粪周围不同远近下土壤养分随时间的动态变化幅度略有不同。粪下土壤养分含量随时间变化波动较大，距粪便越远，随时间变化的变幅越为平缓。总体来说，在夏季由于粪便分解较快，对土壤养分的持续作用时间不及秋季，秋季粪便分解变慢，表现出养分的缓释特征。其次，牛粪对粪下土壤影响的持续时间也长于对周围土壤的作用时间。 3. 粪便对土壤养分（NO3--N、NH4+-N、速效K、无机P）影响的范围在不同季节具有差异。夏季要高于秋季，但对周围土壤养分影响的持续时间低于秋季。在夏季短期内，牛粪对土壤NO3--N 和速效K 含量的影响范围能够超过30cm，而对NH4+-N 和无机P 的影响范围则介于10cm 和30cm 之间。在2 个月左右之后，牛粪对周围土壤养分的影响能力基本消失。在秋季，牛粪对周围土壤养分影响范围难以达到30cm 处。粪便在夏季对其下土壤和周围土壤的有机C、全N 和全P 含量并无显著影响，但在秋季能显著增加其下土壤有机C、全N 和全P 含量。 4. 牛粪在秋季对土壤SMB-C、SMB-N 和SMB-P 含量的影响能够持续2 个月以上，由于秋冬季节牛粪分解缓慢，因此推断这种效应持续时间至少能够1 年左右。另一方面，牛粪在秋季对土壤SMB-C、SMB-N 和SMB-P 含量的影响范围主要集中在其下土壤，而周围的影响效应并不明显。 The grassland on the eastern fringe of Qinghai-Tibetan Plateau was one of the four greatest pasture zones in our country and the main water conservation function zones in the hesastream of Yangtse River and Huanghe river. Rencent years, lots of dung in this area was used as biological energy, fertilizer or material of fungoid growing, leading to high risk of nutrient banlance in grassland ecosystem. In view of the researches on the impact of yak dung in this area are relatively rare, the present study focused on the relationship of dung and soil nutrient transformation in sunmer and autumn, which could profoundly illuminate the mechanism of dung decomposition and the effect of dung on soil chemical properties and soil microbe biomass. The present study also contributed to a basic understand and provided scientific management in the high-frigid ecosystem. Decomposition of yak dung and its effect on soil chemical properties in eastern grassland of Qinghai-Tibetan Plateau were determined. The study simulated the real dung pats, took dung and soil samples at different time and fixed-point in summer and autumn. The samples were analysed for NO3--N, NH4+-N, available K, inorganic P, total organic C (TOC), total N (TN), total P (TP). It was concluded that: 1. In study area, the yak dung supplied to ecosystem substantial nutrient. It is estimated that the N contribution of dung was approximately 699~932 kg ha-1, P contribution was approximately 110~147 kg ha-1. The rate of yak decomposition was more rapid in summer than autumn, the wet and dry weight of yak decreased to 14% and 24% respectively after 2 months when dung excreted in summer, with 35% and 52% in autumn. The content of NO3--N、NH4+-N、available K、inorganic P、TOC、TN and TP in dung decomposed more rapid in summer too. After 2 months when dung excreted in autumn, the content of above nutrient decreased to 32%、60%、36%、64%、58%、63% and 43% respectively，which were significantly higher than summer. 2. The content of NO3--N、NH4+-N、available K and inorganic P in soil around dung had the same transformation trend in each season, whereas it was distinguishing at different gradient of distance from dung, the nutrient in soil below dung had the most significant change while the more far from dung, the less change in soil. It was concluded that the yak dung had prolong impacts on soil in autumn compared with summer, besides, it aslo showed that the yak dung had protract effect on soil below dung compared with soil around dung. 3. The yak dung had expansive impact on soil around dung in summer whereas had relatively short effect compared with autumn. In short-term at summer, there was a significant increase about the content of NO3--N and available K around 30cm radius from dung pat while the content of NH4+-N and inorganic P between 10cm to 30cm. After 2 months, the impact almost disappeared. In autumn, the effect was hard to reach 30cm. The yak dung had no significant effects on the content of TOC、TN and TP in soil below or around dung in summer whereas there was a obvious increase in soil below dung pat in autumn. 4. The duration of effect of yak dung on soil microbial biomass(SMB) C、N and P was at least 2 months, maybe even more than 1 year. On the other hand, the impact of dung on SMB-C、SMB-N and SMB-P mainly acted on soil below dung while no obious effect on soil around dung.