MAURER-CARTAN EQUATION OF A_∞-ALGEBRAS

The axioms of A ∞ algebras can be written as Maurer Cartan equation.Infi nitesimal multiplication of a graded associative algebra is defined and the integrability of infinitesimal multiplication is discussed through the Massey F product.

Invariance of specific mass increment in the case of non-equilibrium growth

The invariance of specific mass increments of crystalline structures that co-exist in the case of non-equilibrium growth is grounded for the first time by using the maximum entropy production principle. Based on the hypothesis of the existence of a universal growth equation, and through the dimensional analysis, an explicit form of the time-dependent specific mass increment is proposed. The applicability of the obtained results for describing growth in animate nature is discussed.

Comparison of Temperature Field Distribution between Cement Preclinkering Technology and Cement Precalcining Technology

Through the comparison of calcination conditions between cement preclinkering technology and cement precalcining technology,we studied the characteristics of temperature field distribution of cement preclinkering technology systems including cyclone preheater,preclinkering furnace,and rotary kiln.We used numericalsimulation method to obtain data of temperature field distribution.Some results are found by system study.The ratio of tailcoalof cement preclinkering technology is about 70%,and raw mealtemperature can reach 1070 ℃.Shorter L/D kiln type of preclinkering technology can obtain more stable calcining zone temperature.The highest solid temperature of cement preclinkering technology is higher than 80 ℃,and high temperature region（〉1450 ℃）length is 2 times,which is beneficialfor calcining clinker and higher clinker quality.So cement preclinkering technology can obtain more performance temperature filed,which improves both the solid-phase reaction and liquid-phase reaction.

The Prime Sequence: Demonstrably Highly Organized While Also Opaque and Incomputable-With Remarks on Riemann’s Hypothesis, Partition, Goldbach’s Conjecture, Euclid on Primes, Euclid’s Fifth Postulate, Wilson’s Theorem along with Lagrange’s Proof of It and Pascal’s Triangle, and Rational Human Intelligence

The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The main conclusion revolves entirely around two points. First, on the one hand, it is shown that the prime sequence exhibits an extremely high level of organization. But second, on the other hand, it is also shown that the clearly detectable organization of the primes is ultimately beyond human comprehension. This conclusion runs radically counter and opposite—in regard to both points—to what may well be the default view held widely, if not universally, in current theoretical mathematics about the prime sequence, namely the following. First, on the one hand, the prime sequence is deemed by all appearance to be entirely random, not organized at all. Second, on the other hand, all hope has not been abandoned that the sequence may perhaps at some point be grasped by human cognition, even if no progress at all has been made in this regard. Current mathematical research seems to be entirely predicated on keeping this hope alive. In the present paper, it is proposed that there is no reason to hope, as it were. According to this point of view, theoretical mathematics needs to take a drastic 180-degree turn. The manner of demonstration that will be used is direct and empirical. Two key observations are adduced showing, 1), how the prime sequence is highly organized and, 2), how this organization transcends human intelligence because it plays out in the dimension of infinity and in relation to π. The present paper is part of a larger project whose design it is to present a complete and final mathematical and physical theory of rational human intelligence. Nothing seems more self-evident than that rational human intelligence is subject to absolute limitations. The brain is a material and physically finite tool. Everyone will therefore readily agree that, as far as reasoning is concerned, there are things that the brain can do and things that it cannot do. The search is therefore for the line that separates the two, or the limits beyond which rational human intelligence cannot go. It is proposed that the structure of the prime sequence lies beyond those limits. The contemplation of the prime sequence teaches us something deeply fundamental about the human condition. It is part of the quest to Know Thyself.