Generalized r-matrix structure and algebro-geometric solution for integrable systems

The purpose of this paper is to construct a generalized r-matrix structure of finite dimensional systems and an approach to obtain the algebro-geometric solutions of integrable nonlinear evolution equations (NLEEs). Our starting point is a generalized Lax matrix instead of usual Lax pair. The generalized r-matrix structure and Hamiltonian functions are presented on the basis of fundamental Poisson bracket. It can be clearly seen that various nonlinear constrained (c-) and restricted (r-) systems, such as the c-AKNS, c-MKdV, c-Toda, r-Toda, c-Levi, etc, are derived from the reduction of this structure. All these nonlinear systems have {\it r}-matrices, and are completely integrable in Liouville's sense. Furthermore, our generalized structure is developed to become an approach to obtain the algebro-geometric solutions of integrable NLEEs. Finally, the two typical examples are considered to illustrate this approach: the infinite or periodic Toda lattice equation and the AKNS equation with the condition of decay at infinity or periodic boundary.Comment: 41 pages, 0 figure

Nonlinear computational framework for hybrid ductile glulam joists

This paper starts by presenting a nonlinear algebraic analysis of hybrid glulam sections, including ductile compression-softening constitutive models obtained via regression analysis of material test data, to compute full-range admissible values of moment (M), co-existent curvature (κ) and excluded-area axial force (Fea) for the sections. The (M,κ,Fea) states, double-checked by treating the section alternately as discretised and as a continuum, are clustered into (M,κ) and (M,Fea) data-sets that permit regression-analysis of κ and Fea as polynomial functions of M. For any load on a glulam member the M profile is known, so κ(M) is a more efficient route to calculating deflections than is M(κ). The κ(M) and Fea(M) constitutive functions, which enable assessment of any section state without tedious recalculation, are fused with longitudinal compatibility and equilibrium requirements to predict the joists’ nonlinear responses up to ultimate. Using quartic or Glos compressive constitutive models, spreadsheet-coding of this framework is shown to predict nonlinear local (κ(M)) and global (load–deflection) responses close to test data, also axial and longitudinal-shear stress redistributions mimicking FE predictions for distributed- or point-loaded hybrid glulam joists comprising combinations of poplar, blue-gum, maritime-pine and larch. The results show that post-peak reductions on compressive stress–strain curves cause through-depth reversal of longitudinal-shear at high moments

Tickborne Rickettsial Diseases: Epidemiological studies in China

Rickettsial diseases are vector-borne zoonoses caused by obligate intracellular bacteria within the order Rickettsiales, which was previously described as short, Gram-negative rod bacteria that retained basic fuchsin when stained by the method of Gimenez. As development in molecular technologies, the taxonomy of the fastidious bacterial species in the order Rickettsiales has been modifi ed (Dumler et al. 2001), and certain agents such as Coxiella burnetii, the pathogen of Q fever have recently been removed from this order (Raoult & Roux 1997). Although specialists in the fi eld of rickettsiology frequently disagree over species defi nitions, the taxa as well as names of species or subspecies based on polyphasic taxonomic studies by integrating phenotypic and phylogenetic data (Fournier et al. 2003) are currently accepted and used in this thesis. Three groups of diseases are usually classifi ed as rickettsial diseases. These include (i) rickettsioses caused by the spotted fever group (SFG) and the typhus group rickettsiae of the genus Rickettsia within the family Rickettsiaceae, (ii) ehrlichioses and anaplasmoses due to microorganisms within the family Anaplasmataceae, and (iii) scrub typhus caused by Orientia tsutsugamushi (Raoult & Roux 1997; Dumler et al. 2001; Hechemy et al. 2003; Watt & Parola 2003). Among these rickettsial diseases, scrub typhus is transmitted by trombiculid mites (Watt & Parola 2003), and cat fl ea typhus (also called fl ea-borne spotted fever) due to Rickettsia felis is transmitted by fl ea (Adams et al. 1990; Higgins et al. 1996). Tickborne rickettsial diseases are caused by two groups of intracellular bacteria belonging to the order Rickettsiales, i.e. the SFG of the genus Rickettsia within the family Rickettsiaceae and several genera of Anaplasma and Ehrlichia groups within the family Anaplasmataceae. These pathogens infect and proliferate in the organs of ticks, particularly in the salivary glands, and can be transmitted to animal hosts during feeding (Parola & Raoult 2001). Because each tick species favours particular optimal environmental conditions and biotopes, the geographic distribution of the ticks is usually restricted to a specifi c area (small or large) and tickborne rickettsial diseases are natural focus diseases. This is particularly true for most of the spotted fever rickettsiae, which are maintained in ticks through transstadial (from larvae to nymphs to adults) and transovarial (from one generation to the next through ovaries) transmissions (Raoult & Roux 1997). Ticks are not insects but Arachnids, a class of Arthropods, which also include

Finite dimensional integrable Hamiltonian systems associated with DSI equation by Bargmann constraints

The Davey-Stewartson I equation is a typical integrable equation in 2+1 dimensions. Its Lax system being essentially in 1+1 dimensional form has been found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the present paper, this essentially 1+1 dimensional Lax system is further nonlinearized into 1+0 dimensional Hamiltonian systems by taking the Bargmann constraints. It is shown that the resulting 1+0 dimensional Hamiltonian systems are completely integrable in Liouville sense by finding a full set of integrals of motion and proving their functional independence.Comment: 10 pages, in LaTeX, to be published in J. Phys. Soc. Jpn. 70 (2001

An Efficient Algorithm by Kurtosis Maximization in Reference-Based Framework

This paper deals with the optimization of kurtosis for complex-valued signals in the independent component analysis (ICA) framework, where source signals are linearly and instantaneously mixed. Inspired by the recently proposed reference-based contrast schemes, a similar contrast function is put forward, based on which a new fast fixed-point (FastICA) algorithm is proposed. The new optimization method is similar in spirit to the former classical kurtosis-based FastICA algorithm but differs in the fact that it is much more efficient than the latter in terms of computational speed, which is significantly striking with large number of samples. The performance of this new algorithm is confirmed through computer simulations