The standard method to construct a finite field requires a primitive irreducible polynomial of a given degree. Therefore, it is difficult to apply for the construction of huge finite fields. To avoid this problem, we ...The standard method to construct a finite field requires a primitive irreducible polynomial of a given degree. Therefore, it is difficult to apply for the construction of huge finite fields. To avoid this problem, we propose a new method to construct huge finite fields with the characteristic p = 5 by using an Artin-Schreier tower. Utilizing the recursive basis of the Artin-Schreier tower, we define a nmltiplication algorithm The algorithm can explicitly calculate the multiplication of two elements on the top finite field of this tower, without any primitive element. We also define a linear recurrence equation as an application, which produces a sequence of numbers, and call the new pseudorandom number generator Abstract Syntax Tree （AST） for p = 5. The experircental results show that our new pseudorandom number generator can produce a sequence of numbers with a long period.展开更多
Growth of semi-polar （1-101）GaN has been attempted on a patterned （001） silicon substrate adopting selective area MOVPE. The growth was initiated on （111） facets of the Si, which had been prepared by anisotropy ...Growth of semi-polar （1-101）GaN has been attempted on a patterned （001） silicon substrate adopting selective area MOVPE. The growth was initiated on （111） facets of the Si, which had been prepared by anisotropy etching in a KOH solution. A uni- form semi-polar layer was achieved by coalescence of stripes. Since the growth was performed on facets, the surface was atomically fiat in AFM surface analyses. By using a high temperature grown A1N nucleation layer, we achieved low threading dislocation density at the top most surface. Moreover, by tilting the c-axis of the GaN on the Si substrate, the effect of the thermal expansion coefficient mismatch was much reduced. As the result, we achieved a crack free （1-101）GaN template on （001）Si. On the thus prepared （1-101）GaN, a GalnN/GaN LED was fabricated, which showed excellent performance with weak quantum confined Stark effect.展开更多
基金supported by Overseas Scholars Research Fund of Heilongjiang Provinicial Education Department
文摘The standard method to construct a finite field requires a primitive irreducible polynomial of a given degree. Therefore, it is difficult to apply for the construction of huge finite fields. To avoid this problem, we propose a new method to construct huge finite fields with the characteristic p = 5 by using an Artin-Schreier tower. Utilizing the recursive basis of the Artin-Schreier tower, we define a nmltiplication algorithm The algorithm can explicitly calculate the multiplication of two elements on the top finite field of this tower, without any primitive element. We also define a linear recurrence equation as an application, which produces a sequence of numbers, and call the new pseudorandom number generator Abstract Syntax Tree （AST） for p = 5. The experircental results show that our new pseudorandom number generator can produce a sequence of numbers with a long period.
基金supported by the Grant in Aid for Scientific Research by JSPS and Nagoya University Akasaki Research Center
文摘Growth of semi-polar （1-101）GaN has been attempted on a patterned （001） silicon substrate adopting selective area MOVPE. The growth was initiated on （111） facets of the Si, which had been prepared by anisotropy etching in a KOH solution. A uni- form semi-polar layer was achieved by coalescence of stripes. Since the growth was performed on facets, the surface was atomically fiat in AFM surface analyses. By using a high temperature grown A1N nucleation layer, we achieved low threading dislocation density at the top most surface. Moreover, by tilting the c-axis of the GaN on the Si substrate, the effect of the thermal expansion coefficient mismatch was much reduced. As the result, we achieved a crack free （1-101）GaN template on （001）Si. On the thus prepared （1-101）GaN, a GalnN/GaN LED was fabricated, which showed excellent performance with weak quantum confined Stark effect.
