GENERALIZED CANONICAL TRANSFORMATION AND SYMPLECTIC ALGORITHM OF THE AUTONOMOUS BIRKHOFFIAN SYSTEMS

The Birkhoff systems are the generalization of the Hamiltonian systems. Generalized canonical transformations are studied. The symplectic algorithm of the Hamiltonian systems is extended into that of the Birkhoffian systems . Symplectic differential scheme of autonomous Birkhoffian systems was structured and discussed by introducing the Kailey Transformation .     

1/3 PURE SUB-HARMONIC SOLUTION AND FRACTAL CHARACTERISTIC OF TRANSIENT PROCESS FOR DUFFING＇S EQUATION

The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.     

WAVELET APPROXIMATE INERTIAL MANIFOLD AND NUMERICAL SOLUTION OF BURGERS'''' EQUATION

ＩｎｔｒｏｄｕｃｔｉｏｎＢｕｒｇｅｒｓ’ｅｑｕａｔｉｏｎｉｓｏｎｅｏｆｖｅｒｙｉｍｐｏｒｔａｎｔｆｌｕｉｄｅｑｕａｔｉｏｎｓ.Ｉｔｓｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｉｓｒａｔｈｅｒｔｈａｎｃｏｍｐｌｅｘｉｔｙｏｗｉｎｇｔｏｔｈｅｎｏｎｌｉｎｅａｒｔｅｒｍ .Ｔｅｍａｎｅｔａｌ.[1] ｓｔｕｄｉｅｄｔｈｅｅｘｉｓｔｅｎｃｅｏｆａｇｌｏｂａｌａｔｔｒａｃｔｏｒ,ｉｎｅｒｔｉａｌｍａｎｉｆｏｌｄａｎｄａｐｐｒｏｘｉｍａｔｅｉｎｅｒｔｉａｌｍａｎｉｆｏｌｄａｓｓｏｃｉａｔｅｄｗｉｔｈｄｙｎａｍｉｃａｌｓｙｓ…     

An electronic, aptamer-based small-molecule sensor for the rapid, label-free detection of cocaine in adulterated samples and biological fluids

Whereas spectroscopic and chromatographic techniques for the detection of small organic molecules have achieved impressive results, these methods are generally slow and cumbersome, and thus the development of a general means for the real-time, electronic detection of such targets remains a compelling goal. Here we demonstrate a potentially general, label-free electronic method for the detection of small-molecule targets by building a rapid, reagentless biosensor for the detection of cocaine. The sensor, based on the electrochemical interrogation of a structure-switching aptamer, specifically detects micromolar cocaine in seconds. Because signal generation is based on binding-induced folding, the sensor is highly selective and works directly in blood serum and in the presence of commonly employed interferents and cutting agents, and because all of the sensor components are covalently attached to the electrode surface, the sensor is also reusable: we achieve >99% signal regeneration upon a brief, room temperature aqueous wash. Given recent advances in the generation of highly specific aptamers, this detection platform may be readily adapted for the detection of other small molecules of a wide range of clinically and environmentally relevant small molecules.     

Substoichiometric determination of rhenium in copper ores and molybdenum concentrates by neutron activation analysis

A simple and rapid substoichiometric method is described for the estimation of rhenium in copper ores and molybdenum concentrates by neutron activation analysis. 2 μg of Re can be determined with an accuracy of 4%. The variation of the mean at 95% confidence limit does not exceed 2%. The time required for processing three samples is less than 60 min.     

Spline collocation approach to boundary value problems

A well-known Stokes problem is discussed by a cubic spline collocation method. Two consecutive cubic splines are obtained for the problem. The results by this method are compared with those of an orthogonal collocation method. The selection of the length of the subintervals of the range of the boundary value problem is also justified. The results obtained by these two methods are compared with the analytic solution. The methods involve simple algebra, and hence the calculations do not require the help of a computer. Necessary error analysis has been carried out.     

NUMERICAL INVESTIGATION OF EVOLUTION OF DISTURBANCES IN SUPERSONIC SHARP CONE BOUNDARY LAYERS

The spatial evolution of 2-D disturbances in supersonic sharp cone boundary layers was investigated by direct numerical simulation (DNS) in high order compact difference scheme. The results suggested that, although the normal velocity in the sharp cone boundary layer was not small, the evolution of amplitude and phase for small amplitude disturbances would be well in accordance with the results obtained by the linear stability theory (LST) which supposes the flow was parallel. The evolution of some finite amplitude disturbances was also investigated, and the characteristic of the evolution was shown. Shocklets were also found when the amplitude of disturbances increased over some value.     

A FORM INVARIANCE OF CONSTRAINED BIRKHOFFIAN SYSTEM

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔｕｄｙｏｆｔｈｅｄｙｎａｍｉｃｓｏｆＢｉｒｋｈｏｆｆｉａｎｓｙｓｔｅｍｉｓａｎａｃｔｉｖｅｂｒａｎｃｈｉｎｔｈｅｍｏｄｅｒｎｃｌａｓｓｉｃａｌｍａｔｈｅｍａｔｉｃｓａｎｄａｍｏｄｅｒｎｄｅｖｅｌｏｐｉｎｇｄｉｒｅｃｔｉｏｎｉｎｍａｔｈｅｍａｔｉｃｐｈｙｓｉｃｓ ,ａｎｄｃａｎｂｅａｐｐｌｉｅｄｔｏｑｕａｎｔｕｍｍｅｃｈａｎｉｃｓ,ｓｔａｔｉｓｔｉｃａｌｍｅｃｈａｎｉｃｓ ,ｂｉｏｌｏｇｉｃｐｈｙｓｉｃｓ,ｍｅｃｈａｎｉｃｓｏｆｓｐａｃｅｆｌｉｇｈｔａｎｄｓｏｍｅｆｉｅ…