摘要 :
We give an algebraic proof of a class number formula for dihedral extensions of number fields of degree 2q, where q is any odd integer. Our formula expresses the ratio of class numbers as a ratio of orders of cohomology groups of ...
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We give an algebraic proof of a class number formula for dihedral extensions of number fields of degree 2q, where q is any odd integer. Our formula expresses the ratio of class numbers as a ratio of orders of cohomology groups of units and allows one to recover similar formulas which have appeared in the literature. As a corollary of our main result, we obtain explicit bounds on the (finitely many) possible values which can occur as ratio of class numbers in dihedral extensions. Such bounds are obtained by arithmetic means, without resorting to deep integral representation theory.
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Due to the entry into force in 2014 of the European F-Gas Regulation n 517/2014 and the subsequent Kigali amendment, the phase-out of the medium and high-GWP refrigerants has speeded up in all refrigeration fields. The effect on t...
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Due to the entry into force in 2014 of the European F-Gas Regulation n 517/2014 and the subsequent Kigali amendment, the phase-out of the medium and high-GWP refrigerants has speeded up in all refrigeration fields. The effect on the plug-in or stand-alone systems has meant that other environmentally friendly refrigerants must replace the R134a with low or ultra-low GWP maintaining the same operating conditions and reducing the energy consumption. Extended examples of these fluids are the hydrocarbons R600a and R290 and the inorganic fluid R744 (CO2). However, there are other alternatives to the HFCs R152a and R1234yf or the hydrocarbon R1270 that have hardly been analysed and can make a positive contribution to this sector. Accordingly, this work aims to evaluate the behaviour of a commercial beverage cooler experimentally when it is optimised with six alternatives to the HFC R134a: R152a, R1234yf, R290, R1270, R600a and R744. Results demonstrated that fluids R290, R1270, R152a, R744 and R600a reduce the energy of R134a in 27.5%, 26.3%, 13.7%, 3.9% and 1.2%, respectively, while the use of R1234yf increases the energy usage to 4.1%.
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In this article, we study some variants of the Bombieri-Vinogradov theorem for number fields. We refine the level of distribution in the previous work of Murty-Petersen. When investigating the short interval version, we give a new...
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In this article, we study some variants of the Bombieri-Vinogradov theorem for number fields. We refine the level of distribution in the previous work of Murty-Petersen. When investigating the short interval version, we give a new zero density estimate of large sieve type, unlike the result of Hinz which is directly used in Thorner's work. Further, we strengthen the result of Thorner for the Bombieri-Vinogradov theorem in short intervals. As applications, we improve some numerical results on the bounded gaps of primes in Chebotarev sets and the Euclidean algorithm for S-integers.
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This work analyses the influence of the Internal Heat Exchan ger (IHX) on the energy performance of a vapor compression cycle associated with a freezing cabinet using different R404A low-GWP alternatives. Among them, the refrigera...
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This work analyses the influence of the Internal Heat Exchan ger (IHX) on the energy performance of a vapor compression cycle associated with a freezing cabinet using different R404A low-GWP alternatives. Among them, the refrigerants R454C (GPW100=146), R455A (GPW100=146), R468A (GPW100=146), R290 (GPW100=5) and R1270 (GPW100=1.8) have been tested in a horizontal freezing cabinet maintaining a product target temperature of -20°C at the heat rejection temperatures of 20, 30 and 40°C. The results from tests show that the use of the IHX reduces energy consumption in all scenarios without significantly increasing the compressor's discharge temperature. For a test period of 16 h, the refrigerants that offer better reductions are R404A and R1270, followed by R455A, R290, R454C and R468A. The maximum energy saving is rated to 9.2% at the heat rejection temperature of 40°C, demonstrating that the enhancement of the IHX is better as higher the heat rejection conditions are.
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This paper shows that a positive proportion of the imaginary quadratic fields with 2-class rank equal to 3 have 4-class rank equal to zero and infinite Hilbert 2-class field towers.
摘要 :
Let
p
≡
3
...
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Let
p
≡
3
(
mod
4
)
{p\equiv 3\pmod{4}}
and
l
≡
5
(
mod
8
)
{l\equiv 5\pmod{8}}
be different primes such that
p
l
=
1
{\frac{p}{l}=1}
and
2
p
=
p
l
4
{\frac{2}{p}=\frac{p}{l}_{4}}
. Put
k
=
?
?
(
l
)
{k=\mathbb{Q}(\sqrt{l})}
, and denote by ? its fundamental unit. Set
K
=
k
?
(
-
2
?
p
?
?
?
l
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摘要 :
Приведены результаты изучения ритма сезонного развития (2002—2013 гг.) 10 видов рода Rosa L., интродуцированных в парк Ботанического с...
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Приведены результаты изучения ритма сезонного развития (2002—2013 гг.) 10 видов рода Rosa L., интродуцированных в парк Ботанического сада Ботанического института. Степень зимостойкости видов зависит от степени синхронности окончания вегетации с окончанием вегетации местными древесными породами. В озеленении Санкт-Петербурга можно широко использовать зимостойкие виды R. altaica, R. amblyotis, R. davurica, R. myriacantha, R. glauca, R. rugosa, R. spinosissima и сравнительно зимостойкие R. gallica и R. sweginzowii.
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摘要 :
Let X be an affine surface admitting a unique affine ruling and a $\mathbb{C}^*$ -action. Assume that the ruling has a unique degenerate fibre and that this fibre is irreducible. In this paper we give a short proof of the followin...
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Let X be an affine surface admitting a unique affine ruling and a $\mathbb{C}^*$ -action. Assume that the ruling has a unique degenerate fibre and that this fibre is irreducible. In this paper we give a short proof of the following result of Miyanishi and Masuda: the universal covering of X is a hypersurface in the affine 3-space given by the equation x m y = z d − 1, where m > 1.
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摘要 :
Let Gamma g,1mbe the mapping class group of the orientable surface sigma g,1mof genusgwith one parametrized boundary curve andmpermutable punctures; whenm=0we omit it from the notation. Let beta m(sigma g,1)be the braid group onms...
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Let Gamma g,1mbe the mapping class group of the orientable surface sigma g,1mof genusgwith one parametrized boundary curve andmpermutable punctures; whenm=0we omit it from the notation. Let beta m(sigma g,1)be the braid group onmstrands of the surface sigma g,1. We prove thatH*(Gamma g,1m;Z2) approximately equal to H*(Gamma g,1;H*(beta m(sigma g,1);Z2)). The main ingredient is the computation ofH*(beta m(sigma g,1);Z2)as a symplectic representation of Gamma g,1.
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