Asymptotics of second-order integral matrices lying in a given hyperbolic region and belonging to a given residue class

1982 ◽  
Vol 19 (2) ◽  
pp. 1085-1088 ◽  
Author(s):  
A. M. Istamov
Keyword(s):  
Residue Class ◽  
Second Order ◽  
Hyperbolic Region ◽  
Integral Matrices

Asymptotic distribution of n-th-order integral matrices belonging to a given residue class

1984 ◽  
Vol 25 (2) ◽  
pp. 1030-1051 ◽  
Author(s):  
A. M. Istamov
Keyword(s):  
Asymptotic Distribution ◽  
Residue Class ◽  
Integral Matrices

scholarly journals There are Infinitely Many Fibonacci Primes

2020 ◽  
pp. 1-17
Author(s):  
Fengsui Liu
Keyword(s):  
Residue Class ◽  
Second Order ◽  
Order Topology ◽  
Sieve Method ◽  
Natural Numbers ◽  
Finite Sets ◽  
Index Set ◽  
Infinite Set ◽  
Novel Algorithm

We invent a novel algorithm and solve the Fibonacci prime conjecture by an interaction between proof and algorithm. From the entire set of natural numbers successively deleting the residue class 0 mod a prime, we retain this prime and possibly delete another one prime retained, then we invent a recursive sieve method, a modulo algorithm on finite sets of natural numbers, for indices of Fibonacci primes. The sifting process mechanically yields a sequence of sets of natural numbers, which converges to the index set of all Fibonacci primes. The corresponding cardinal sequence is strictly increasing. The algorithm reveals a structure of particular order topology of the index set of all Fibonacci primes, then we readily prove that the index set of all Fibonacci primes is an infinite set based on the existing theory of the structure. Some mysteries of primes are hidden in second order arithmetics.

Distribution of second-order integral matrices

1992 ◽  
Vol 62 (4) ◽  
pp. 2864-2868
Author(s):  
E. P. Golubeva
Keyword(s):  
Second Order ◽  
Integral Matrices

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

Subsystems of Second Order Arithmetic

2009 ◽  
Author(s):  
Stephen G. Simpson
Keyword(s):  
Second Order ◽  
Second Order Arithmetic ◽  
Order Arithmetic
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