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On Toric Symmetry of P1×P2
, 2013
"... Toric varieties are a class of geometric objects with a combinatorial structure encoded in polytopes. P1×P2 is a well known variety and its polytope is the triangular prism. Studying the symmetries of the triangular prism and its truncations can lead to symmetries of the variety. Many of these sym ..."
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Toric varieties are a class of geometric objects with a combinatorial structure encoded in polytopes. P1×P2 is a well known variety and its polytope is the triangular prism. Studying the symmetries of the triangular prism and its truncations can lead to symmetries of the variety. Many
Distributions of r1·r2 and p1·p2 in Atoms
"... ABSTRACT: We consider the twoelectron position and momentum dot products, α = r1·r2 and β = p1·p2, and present a method for extracting their distributions, A(α) and B(β), from molecular wave functions built on Gaussian basis functions. The characteristics of the Hartree−Fock AHF(α) and BHF(β) for H ..."
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ABSTRACT: We consider the twoelectron position and momentum dot products, α = r1·r2 and β = p1·p2, and present a method for extracting their distributions, A(α) and B(β), from molecular wave functions built on Gaussian basis functions. The characteristics of the Hartree−Fock AHF(α) and BHF
� Punktpaar: P1^P2 Kugel: P1^P2^P3^P4
"... beschreibt den Schnitt von S1 und S2, den SchnittKreis C ..."
The effect of elliptic shape on the period ratio P 1 /P 2 of emerging coronal loops
, 2009
"... ABSTRACT Aims. We determine the effect of an elliptical shape on the period ratio for the standing transversal oscillations of a longitudinally stratified coronal loop throughout its emergence from the low solar atmosphere into the ubiquitously magnetised corona. Methods. Under the assumption that ..."
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mode to the first harmonic (P 1 /P 2 ) at various stages of emergence is determined, assuming that the oscillation periods are much shorter than the characteristic time scale of loop emergence. Results. We find that there are two separate cases of elliptical shape that occur, the minor ellipse
How to Factor N1 and N2 When p1 = p2 mod 2 t
"... Abstract. Let N1 = p1q1 and N2 = p2q2 be two different RSA moduli. Suppose that p1 = p2 mod 2 t for some t, and q1 and q2 are α bit primes. Then May and Ritzenhofen showed that N1 and N2 can be factored in quadratic time if t ≥ 2α + 3. In this paper, we improve this lower bound on t. Namely we prove ..."
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Abstract. Let N1 = p1q1 and N2 = p2q2 be two different RSA moduli. Suppose that p1 = p2 mod 2 t for some t, and q1 and q2 are α bit primes. Then May and Ritzenhofen showed that N1 and N2 can be factored in quadratic time if t ≥ 2α + 3. In this paper, we improve this lower bound on t. Namely we
P = (p1, p2,..., pn) ∣ pi> 0,
, 2005
"... Abstract. In this paper we have considered a difference of Jensen’s inequality for convex functions and proved some of its properties. In particular, we have obtained results for Csiszár [5] f−divergence. A result is established that allow us to compare two measures under certain conditions. By the ..."
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Abstract. In this paper we have considered a difference of Jensen’s inequality for convex functions and proved some of its properties. In particular, we have obtained results for Csiszár [5] f−divergence. A result is established that allow us to compare two measures under certain conditions. By the application of this result we have obtained a new inequality for the well known means such as arithmetic, geometric and harmonic. Some divergence measures based on these means are also defined.
The fundamental properties of natural numbers
 Journal of Formalized Mathematics
, 1989
"... Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1.h ..."
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Cited by 688 (73 self)
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number k holdsP[k] provided the following conditions are satisfied: • P[0], and • For every natural number k such thatP[k] holdsP[k+1]. Let n, k be natural numbers. Then n · k is a natural number. Let n, k be natural numbers. Observe that n · k is natural. Next we state several propositions: (18) 2 0 ≤ i
Ktheory for operator algebras
 Mathematical Sciences Research Institute Publications
, 1998
"... p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b] is a ..."
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Cited by 558 (0 self)
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p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b
Results 1  10
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165,262