1,720,969 research outputs found
A note on cyclotomic polynomials and Linear Feedback Shift Registers
No full textLinear Feedback Shift Registers (LFSR) are tools commonly used in cryptography in many contexts, for example as pseudo-random numbers generators. In this paper we characterize LFSR with certain symmetry properties. Related to this question we also classify polynomials f satisfying the property that if α is a root of f then f (α deg f) = 0. The classification heavily depends on the choice of the fields of coefficients of the polynomial; we consider the cases (Figure presented.) and K = Q
A note on the determinant 308 in Proskuryakov's linear algebra book
Full text linkWe put in evidence and correct a mistake in the formula for the determinant 308 in Proskuryakov’s linear algebra book. We apply this formula to reprove
the well-known fact that the Fubini-Study metric on the complex projective space
is Einstein
Kaehler maps of Hermitian symmetric spaces into complex space forms
No full textIn this paper, we give a complete description of the Kähler immersions of Hermitian symmetric spaces into finite or infinite dimensional complex space forms
Parallel Kaehler submanifolds of quaternionic Kaehler symmetric spaces
No full textAbstract. The non totally geodesic parallel 2n-dimensional Kähler submanifolds of the n-dimensional quaternionic projective space were classified by K. Tsukada. Here we give the complete classification of non totally geodesic immersions of parallel 2m-dimensional Kähler submanifolds in a quaternionic Kähler symmetric space of non zero scalar curvature, i.e., in a Wolf space or in its non compact dual. They are exhausted by parallel Kähler submanifolds of a totally geodesic submanifold which is either an Hermitian symmetric space or a quaternionic projective space
Group law on affine conics and applications to cryptography
Full text linkIn this paper, we highlight that the point group structure of elliptic curves, over finite or infinite fields, may be also observed on reducible cubics with an irreducible quadratic component. Starting from this, we introduce in a very general way a group's structure over any kind of conic. In the case of conics over finite fields, we see that the point group is cyclic and lies on the quadratic component. Thanks to this, some applications to cryptography are described, considering convenient parametrizations of the conics. We perform an evaluation of the complexity of the operations involved in the parametric groups and consequently in the cryptographic applications. In the case of the hyperbolas, the Rédei rational functions can be used for performing the operations of encryption and decryption, and the More's algorithm can be exploited for improving the time costs of computation. Finally, we provide also an improvement of the More's algorithm
HOMOGENEOUS RIEMANNIAN MANIFOLDS WITH NON-TRIVIAL NULLITY
Full text linkWe develop a general theory for irreducible homogeneous spaces M = G/H, in relation to the nullity distribution ν of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that give a deep insight of such spaces. In particular, there must exist an order-two transvection, not in the nullity, with null Jacobi operator. This fact was very important for finding out the first homogeneous examples with non-trivial nullity, i.e., where the nullity distribution is not parallel. Moreover, we construct irreducible examples of conullity k = 3, the smallest possible, in any dimension. None of our examples admit a quotient of finite volume. We also proved that H is trivial and G is solvable if k = 3. Another of our main results is that the leaves, i.e., the integral manifolds, of the nullity are closed (we used a rather delicate argument). This implies that M is a Euclidean affine bundle over the quotient by the leaves of ν. Moreover, we prove that ν⊥ defines a metric connection on this bundle with transitive holonomy or, equivalently, ν⊥ is completely non-integrable (this is not in general true for an arbitrary autoparallel and at invariant distribution). We also found some general obstruction for the existence of non-trivial nullity: e.g., if G is reductive (in particular, if M is compact), or if G is two-step nilpotent
Cones and Cartan geometry
Full text linkWe show that the extended principal bundle of a Cartan geometry of type (A(m,R),GL(m,R)), endowed with its extended connection ωˆ, is isomorphic to the principal A(m,R)-bundle of affine frames endowed with the affine connection as defined in classical Kobayashi-Nomizu volume I. Then we classify the local holonomy groups of the Cartan geometry canonically associated to a Riemannian manifold. It follows that if the holonomy group of the Cartan geometry canonically associated to a Riemannian manifold is compact then the Riemannian manifold is locally a product of cones.Fil: Di Scala, Antonio Jose'. Politecnico di Torino; ItaliaFil: Olmos, Carlos Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática. Grupo de Geometria Diferencial; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Vittone, Francisco. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentin
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