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The first one is a conjecture of Ian Hughes which states that iff1, ..., fn are primary invariants of a finite linear groupG, then the least common multiple of the degrees of thefi is a multiple of the exponent ofG.
      
The condition, which is expressed in terms of the intertwining operators of each primary summand of the quasi-regular representation, is then interpreted in the case of the compact Heisenberg manifolds.
      
A method of algebraic operation of special matrices involved in the problem is given in this paper for obtaining a new solution for the m + 1 experiments based upon the old solution for the primary m experiments.
      
Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival.
      
The resulting average value of the Avrami exponent at n = 3.34 suggests that primary crystallization may correspond to a three-dimensional spherulitic growth.
      
Finally, some primary conclusions are given by comparing the simulation results with experimental observation.
      
Water proved to be the primary factor affecting δ13C under water stress.
      
According to the international methods of pest risk analysis and urban forestry characteristics in Beijing, a quantitative risk assessment system in Beijing for three primary non-indigenous pests was proposed.
      
Soil NH4+/NO3- nitrogen characteristics in primary forests and the adaptability of some coniferous species
      
A large number of studies show that the "nutrition habitats" associated with primary forest soils are typically dominated by NH4+ rather than NO3-, generally with NO3- content much lower than NH4+.
      
Results also showed that the number of species of primary concern is two; of secondary concern, nine; of the third level, 23; and of least concern, 330 species.
      
The results showed that the tested poplar can be classified into five groups, and indicated the clear separation of varieties of different sections of poplar and the primary distinction between native and exotic poplar varieties.
      
Under such stress conditions, air temperature was the primary factor to affect Tr in July and August and photosynthetically active radiation (PAR) was the primary factor in October.
      
Reverse driving character plays an important role in evaluating the performance of a haptic device, and it is the primary rule in the mechanical design.
      
Enabling quality managers to utilize and manage quality data efficiently under modern quality management circumstances is a primary issue for improving enterprise quality management.
      
The reliability performance of the control system can be considerably improved by adopting a control strategy combined with the hot spared redundancy of the primary system and the cold spared redundancy of the emergent one.
      
They both were greatest at the climax, moderate at the intermediate and smallest at the primary succession stage.
      
Maintenance of ecosystem health is the primary focus of a sound ecological restoration.
      
As a proxy of the vegetation growing process, NDVI difference represents net primary productivity of vegetation at a certain time interval under an environment controlled by certain climatic conditions and other factors.
      
The key characteristic of the new model is that it can predict directly the protein-protein interaction from the primary sequence, and the MRRM is more suitable than the RRM for this prediction.
      
 

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