12,037 research outputs found
Pot, atom and step economic (PASE) synthesis of highly functionalized piperidines: a five-component condensation
The diastereoselective pot, atom and step economic (PASE) synthesis of highly functionalized piperidines has been realized. The procedure simply involves mixing methyl acetoacetate, 2 equiv of aldehyde and 2 equiv of aniline together in the presence of InCl3. In most cases the piperidine precipitates out of solution. (c) 2007 Elsevier Ltd. All rights reserved
Rational Points on Elliptic Curves y^2=x^3+a^3 in f_{p} where p{\equiv}1(mod6) is Prime
In this work, we consider the rational points on elliptic curves over finite
fields F_{p}. We give results concerning the number of points on the elliptic
curve y^2{\equiv}x^3+a^3(mod p)where p is a prime congruent to 1 modulo 6. Also
some results are given on the sum of abscissae of these points. We give the
number of solutions to y^2{\equiv}x^3+a^3(modp), also given in ([1], p.174),
this time by means of the quadratic residue character, in a different way, by
using the cubic residue character. Using the Weil conjecture, one can
generalize the results concerning the number of points in F_{p} to F_{p^{r}}.Comment: 9 pages; Keywords: Elliptic curves over finite fields, rational
point
Gauge symmetries decrease the number of Dp-brane dimensions
It is known that the presence of antisymmetric background field
leads to noncommutativity of Dp-brane manifold. Addition of the linear dilaton
field in the form , causes the appearance of the
commutative Dp-brane coordinate . In the present article we show
that for some particular choices of the background fields, and $\tilde a^2\equiv [ (G-4BG^{-1}B)^{-1}\
]^{\mu\nu}a_\mu a_\nu=0$, the local gauge symmetries appear in the theory. They
turn some Neuman boundary conditions into the Dirichlet ones, and consequently
decrease the number of the Dp-brane dimensions.Comment: We improve Sec.4. and Conclusion and we added the Appendix in order
to clarify result
On a variant of Giuga numbers
In this paper, we characterize the odd positive integers satisfying the
congruence . We show that
the set of such positive integers has an asymptotic density which turns out to
be slightly larger than 3/8.Comment: 14 page
Cosmological solutions for model with a term
We drive the cosmological solutions of five-dimensional model with
term , where is 4-form field
strength. The behaviors of the scale factors and the scalar potential in
effective theory are examined.As a consequence, we show that the universe
changes from decelerated expansion to accelerated expansion in Einstein frame
of the four-dimensional theory.Comment: 10 pages, 2 figures, version to appear in JCA
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