Quasi-Chun-Ching Shih''''s Fractional Fourier Transform with Periodicity of 2,3 and M

Based on Chun-Ching Shih's idea, the basic transform was substituted and the quasi-ChunChing Shih's fractional Fourier transform with periodicity of 2, 3 and M was deduced. The two former transforms and the Chun-Ching Shih's fractional Fourier transform were only the particular cases of quasiChun-Ching Shih's fractional Fourier transform with periodicity of M.     

Covering a string

We consider the problem of finding the repetitive structures of a given stringx. The periodu of the stringx grasps the repetitiveness ofx, sincex is a prefix of a string constructed by concatenations ofu. We generalize the concept of repetitiveness as follows: A stringw covers a stringx if there is a superstring ofx which is constructed by concatenations and superpositions ofw. A substringw ofx is called aseed ofx ifw coversx. We present anO(n logn)-time algorithm for finding all the seeds of a given string of lengthn.Partially supported by SERC Grants GR/F 00898 and GR/J 17844, NATO Grant CRG 900293, ESPRIT BRA Grant 7131 for ALCOMII, and MRC Grant G 9115730.Partially supported by MRC Grant G 9115730 and S.N.U. Posco Research Fund 94-15-1112.     

Transition of the flow in a symmetric channel with periodically expanded grooves

Transition of the flow in a periodically grooved channel is numerically investigated for periodicity indices m=1 up to 6 by assuming the two-dimensional and fully developed flow field, where m is defined as a number of grooves in which the flow repeats periodically. Critical Reynolds numbers for the onset of a self-sustained oscillatory flow from a steady-state flow are evaluated by numerical simulations. It is found that the bifurcations occur at the critical Reynolds numbers as a result of Hopf bifurcation, and a period in the streamwise direction of the oscillatory flow is twice as long as the groove pitch of the channel. In addition, flow visualization with the aluminum dust method is carried out to confirm the results obtained from the numerical simulations. The experimental results are in good agreement with the numerical ones.     

Computing maximal-exponent factors in an overlap-free word

The exponent of a word is the quotient of its length over its smallest period. The exponent and the period of a word can be computed in time proportional to the word length. We design an algorithm to compute the maximal exponent of all factors of an overlap-free word. Our algorithm runs in linear-time on a fixed-size alphabet, while a naive solution of the question would run in cubic time. The solution for non-overlap-free words derives from algorithms to compute all maximal repetitions, also called runs, occurring in the word.We also show there is a linear number of occurrences of maximal-exponent factors in an overlap-free word. Their maximal number lies between 0.66n and 2.25n in a word of length n. The algorithm can additionally locate all of them in linear time.     

Discretization behavior analysis of a switcbing control system from a unified mathematical approach

A useful unified analysis framework is proposed for exploring the intriguing behaviors of a second-order switching control system. Complex discretizafion behaviors of the switching control system are explored in detail, and some intrinsic relationships between the system periodic behaviors and their associated symbolic sequences are studied.     

变化环境下鄱阳湖洪水指标演变特征研究

本文基于鄱阳湖洪水特点,选取特定洪水特征指标,利用数理统计方法分析鄱阳湖洪水特征指标的趋势性、突变性和周期性,并分析演变特征和驱动因素,得到结论如下：1）未来高洪可能性仍然较大,未来6～10a鄱阳湖年最高水位仍处于丰水期;2）洪水在年内分配发生较大改变,变化过程从“矮胖型”向相对“尖瘦型”演变,水量在年内更加集中化;3）高洪持续天数显著增加,19.00m以上的高水位维持时间平均每10a延长2.2d;4）年最高水位及年平均水位周期性变化主要受“五河”入湖周期性变化所控制,同时会受到其他因素影响而改变原有周期性变化规律,年最高水位具有5a为第一主周期,40～49a为第二主周期的变化规律。     

Asymptotic homogenisation in linear elasticity. Part II: Finite element procedures and multiscale applications

The asymptotic expansion homogenisation (AEH) method can be used to solve problems involving physical phenomena on continuous media with periodic microstructures. In particular, the AEH is a useful technique to study of the behaviour of structural components built with composite materials. The main advantages of this approach lie on the fact that (i) it allows a significant reduction of the problem size and (ii) it has the capability to characterise stress and deformation microfields. In fact, specific equations can be developed to define these fields, in a process designated by localisation and not found on typical homogenisation methods. In the AEH methodology, overall material properties can be derived from the mechanical behaviour of selected periodic microscale representative volumes (also known as representative unit-cells, RUC). Nevertheless, unit-cell based modelling requires the control of some parameters, such as reinforcement volume fraction, geometry and distribution within the matrix material. The need for variety and flexibility leads to the development of automatic geometry generation algorithms. Additionally, the unstructured finite element meshes required by these RUC are usually non-periodic and involve the control of specific periodic boundary conditions. This work presents some numerical procedures developed in order to support finite element AEH implementations, rendering them more efficient and less user-dependent. The authors also present a numerical study of the influence of the reinforcement volume fraction on the overall material properties for a metal matrix composite (MMC) reinforced with spherical ceramic particles. A general multiscale application is shown, with both the homogenisation and localisation procedures.