Kaluza-Klein dimensional reduction and Gauss-Codazzi-Ricci equations

In this paper we imitate the traditional method which is used customarily in the General Relativity and some mathematical literatures to derive the Gauss-Codazzi-Ricci equations for dimensional reduction. It would be more distinct concerning geometric meaning than the vielbein method. Especially, if the lower dimensional metric is independent of reduced dimensions the counterpart of the symmetric extrinsic curvature is proportional to the antisymmetric Kaluza-Klein gauge field strength. For isometry group of internal space, the SO(n) symmetry and SU(n) symmetry are discussed. And the Kaluza-Klein instanton is also enquired.Comment: 15 page

Prototype of non-genetically modified soybean tracking system using blockchain technology.

Genetically Modified Organisms (GMO) soybean is a soybean whose genetic material has been modified using genetic engineering techniques. GMO defenders say that this technology reduces the cost of food and helps producers deal with pests and diseases more safely. On the opposite consumers and environmental groups argue that transgenic crops drive higher use of pesticides. Because of this, there is a specific market for non-GMO crops. Some companies that export to Asia and Europe markets pay a premium for non-GMO soybean. But this non-GMO soybean must have a certificate indicating their purity, i.e., which there is not a mix with GMO soybean. The aim of this work is the development of a prototype of a system to track non-GMO soybean to guarantee its purity. The prototype developed in this work used blockchain technology. The choice for blockchain was because it is very secure against tampering, and, also is a distributed system proper for applications like this, which will track the non-GMO soybean from cultivation to product delivery

Conformal classes of asymptotically flat, static vacuum data

We show that time-reflection symmetric, asymptotically flat, static vacuum data which admit a non-trivial conformal rescaling which leads again to such data must be axi-symmetric and admit a conformal Killing field. Moreover, it is shown that there exists a 3-parameter family of such data.Comment: 23 page