in this study; utilizing the elastic matrix ball has higher processing efficiency and better superficial quality than traditionalgrinding. the diversity of elastic abrasive tool characteristics contact with bend surface results in irregular wear abrasion，and abrasive tool machining status gets complicated. there is no theoretical interpretation of parameters affecting the grinding accuracy. bec...

In vitro, animal cells are mostly cultured on a gel substrate. It was recently shown that substrate stiffness affects cellular behaviors in a significant way, including adhesion, differentiation, and migration. Therefore, an accurate method is needed to characterize the modulus of the substrate. In situ microscopic measurements of the gel substrate modulus are based on Hertz contact mechanics, ...

In the 1920s, Paul Hertz (1881–1940) developed certain calculi based on structural rules only and established normal form results for proofs. It is shown that he anticipated important techniques and results of general proof theory as well as of resolution theory, if the latter is regarded as a part of structural proof theory. Furthermore, it is shown that Gentzen, in his first paper of 1933, wh...

Franck and Hertz described the first observation of quantized excitation in 1914, one year after Bohr published his theory of the hydrogen atom with its concept of quantized energy states. They discovered that electrons moving through mercury vapor with an energy greater than or equal to a critical value near 4.9 eV can excite the 2536 Å line of the mercury spectrum. Electrons with less than th...

The failure of Maxwell's equations to exhibit invariance under the Galilean transformation was corrected by Hertz through a simple, but today largely forgotten, mathematical trick. This involves substituting total (convective) time derivatives for partial time derivatives wherever the latter appear in Maxwell's equations. By this means Hertz derived a formally Galilean-invariant covering theory...