NEWTON'S THEOREM WITH RESPECT TO A LOT OFCENTERS AND THEIR APPLICATIONS

In this paper we shall extend the paper [1] to a separate Taylor's Theorem with respect to a lot of centers, namely Newton's Theorem Of a lot of centers. From it we obtain the analogous results in the paper [2]. namely an interpolation formula of the difference of higher order. Finally we give their applications.

A Comparative Study on Two Techniques of Reducing the Dimension of Text Feature Space

With the development of large scale text processing, the dimension of text feature space has become larger and larger, which has added a lot of difficulties to natural language processing. How to reduce the dimension has become a practical problem in the field. Here we present two clustering methods, i.e. concept association and concept abstract, to achieve the goal. The first refers to the keyword clustering based on the co occurrence of

Effects of walk-off on cross-phase modulation induced modulation instability in an optical fibre with high-order dispersion

This paper investigates the effects of walk-off among optical pulses on cross-phase modulation induced modulation instability in the normal dispersion region of an optical fibre with high-order dispersion. The results indicate that, in the case of high-order dispersion, the walk-off effect takes on new characteristics and will influence considerably the shape, position and especially the number of the spectral regions of the gain spectra of modulation instability. Not only the group-velocity mismatch, but also the difference of the third-order dispersion of two optical waves will alter the gain spectra of modulation instability but in different ways. Depending on the values of the walk-off parameters, the number of the spectral regions may increase from two to at most four, and the spectral shape and position may change too.

The Difference in Cognition Consistency Between the Sciences and Humanities

It is reasonable that the strict sciences represented by mathematics, physics and chemistry have nearly been a kind of substitutional belief of humans after "the Death of God". To conclude theoretically, the significant attraction or the extremely great power of science is, in a word, the validity of thinking and action. From the viewpoint of human action or prac-

What is the Difference Between a Five-star and a Six or Sevenstar Hotel?

In 2006 I outlined the new national star- rating system for UK Hotels,which ranges from one-star basic to five-star plush.In another article I quoted an hotel owner in the south of England,who said that the new system was a waste of time,because it did not align itself with the international system.So,she increased facilities

Time Quanta Present in Simple Quantum Systems

Differences of the time periods in two independent quantum systems are examined on a semiclassical level. The systems are the electron in the hydrogen atom and a free-electron particle moving in a one-dimensional potential box, respectively. It is demonstrated that in both systems the relativistic correction to the time interval can be expressed as a multiple of the same quantum of time. The size of the quantum is proportional to the ratio of the Planck’s constant and the rest energy of the electron particle.

Sequential First-Price Auction with Randomly Arriving Buyers

In this paper we reanalyze Said’s(2011) work by retaining all his assumptions except that we use the first-price auction to sell differentiated goods to buyers in dynamic markets instead of the second-price auction. We conclude that except for the expression of the equilibrium bidding strategy, all the results for the first-price auction are exactly the same as the corresponding ones for the second-price auction established by Said(2011). This implies that the well-known "revenue equivalence theorem"holds true for Said’s(2011) dynamic model setting.