There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition

THE difficulty of reconciling line spectra with the kinetic theory of gases, has been referred to by Prof. Fitzgerald (NATURE, January 3, p. 221). The following considerations show that it is possible under certain suppositions to have a number of spectral rays with a very restricted number of degrees of freedom. Most of us, I believe, now accept a definite atomic charge of electricity, and if each charge is imagined to be capable of moving along the surface of an atom, it would represent two degrees of freedom. If a molecule is capable of sending out a homogeneous vibration, it means that there must be a definite position of equilibrium of the “electron.” If there are several such positions, the vibrations may take place in several periods. Any one molecule may perform for a certain time a simple periodic oscillation about one position of equilibrium, and owing to some impact the electron may be knocked over into a new position. The vibrations under these circumstances would not be quite homogeneous, but if the electron oscillates about any one position sufficiently long to perform a few thousand oscillations, we should hardly notice the want of homogeneity. Each electron at a given time would only send out vibrations which in our instruments would appear as homogeneous. Each molecule could thus successively give rise to a number of spectral rays, and at any one time the electron in the different molecules would, by the laws of probability, be distributed over all possible positions of equilibrium, so that we should always see all the vibrations which any one molecule of the gas is capable of sending out. The probability of an electron oscillating about one of its positions of equilibrium need not be the same in all cases. Hence a line may be weak not because the vibration has a smaller amplitude, but because fewer molecules give rise to it. The fact that the vibrations of a gas are not quite homogeneous, is borne out by experiment. If impacts become more frequent by increased pressure, we should expect from the above views that the time during which an electron performs a certain oscillation is shortened; hence the line should widen, which is the case. I have spoken, for the sake of simplicity, as if an electron vibrating about one position of equilibrium could only do so in one period. If the forces called into play, by a displacement, depend on the direction of the displacement, there would be two possible frequencies. If the surface is nearly symmetrical, we should have double lines.

/pdf/the-kinetic-theory-of-gases-13lklkm24y.pdf

The Kinetic Theory of Gases

https://www.win.tue.nl/~atijssel/pdf_files/Bergant-Simpson-Tijsseling_2006.pdf

Water hammer with column separation: A historical review

Aim: To develop classification criteria for Chinese pulse diagnosis and to objectify the ancient diagnostic technique. Methods: Chinese pulse curves are treated as wave signals. Multidimensional variable analysis is performed to provide the best curve fit between the recorded Chinese pulse waveforms and the collective Gamma density functions. Results: Chinese pulses can be recognized quantitatively by the newly-developed four classification indices, that is, the wave length, the relative phase difference, the rate parameter, and the peak ratio. The new quantitative classification not only reduces the dependency of pulse diagnosis on Chinese physician's experience, but also is able to interpret pathological wrist-pulse waveforms more precisely. Conclusions: Traditionally, Chinese physicians use fingertips to feel the wrist-pulses of patients in order to determine their health conditions. The qualitative theory of the Chinese pulse diagnosis is based on the experience of Chinese physicians for thousands of years. However, there are no quantitative theories to relate these different wrist-pulse waveforms to the health conditions of patients. In this paper, new quantified classification indices have been introduced to interpret the Chinese pulse waveform patterns objectively.

Developing classification indices for Chinese pulse diagnosis

https://www3.ntu.edu.sg/home/mjjshu/CTM07.pdf

Developing classification indices for Chinese pulse diagnosis.

A comprehensive review of current analytical models, experimental techniques, and influencing factors is carried out to highlight the current challenges in this area. The study of fluid-solid boundary conditions has been ongoing for more than a century, starting from gas-solid interfaces and progressing to that of the more complex liquid-solid case. Breakthroughs have been made on the theoretical and experimental fronts but the mechanism behind the phenomena remains a puzzle. This paper provides a review of the theoretical models, and numerical and experimental investigations that have been carried out till date. Probable mechanisms and factors that affect the interfacial discontinuity are also documented.

/pdf/fluid-velocity-slip-and-temperature-jump-at-a-solid-surface-2jcvsne0so.pdf

Fluid velocity slip and temperature jump at a solid surface

A comprehensive study of the problem of modelling vaporous cavitation in transmission lines is presented. The two-phase homogeneous equilibrium vaporous cavitation model which has been developed is compared with the conventional column separation model. The latter predicts unrealistically high pressure spikes because of a conflict arising from the prediction of negative cavity sizes if the pressure is not permitted to fall below the vapour pressure, or the prediction of negative absolute pressures if the cavity size remains positive. This is verified by a comparison of predictions with previously published experimental results on upstream, midstream and downstream cavitation. The new model has been extended to include frequency-dependent friction. The characteristics predicted by the frequency-dependent friction model show close correspondence with experimental data.

Modelling vaporous cavitation on fluid transients

https://www3.ntu.edu.sg/home/MJJShu/IJPVP03.pdf

Jian-Jun Shu

Papers

Developing classification indices for Chinese pulse diagnosis

Developing classification indices for Chinese pulse diagnosis.

Fluid velocity slip and temperature jump at a solid surface

Modelling vaporous cavitation on fluid transients

Modelling vaporous cavitation on fluid transients