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Arc index of pretzel knots of type $(-p,q,r)$
knot pretzel knot arc presentation arc index Kauffman polynomial
2012/4/18
We computed the arc index for the pretzel knots $K=P(-p,q,r)$ with $p,q,r\ge2$, $r\geq q$ and at most one of $p,q,r$ is even. If $q=2$, then the arc index $\alpha(K)$ equals the minimal crossing numbe...
A New Extension of Hilbert-type Integral Inequality with Two Pairs of Conjugate Exponents
mathematical analysis Hilbert's type integral inequality conjugate exponent Holder inequality equivalent form
2011/9/29
In the paper, by introducing two pairs of conjugate exponents(p，q) and (r，s), we establish a new generalizations of the Hilbert-type ineqaulity with a best constant. As application, the reverse and it...
A Giambelli formula for the $S^1$-equivariant cohomology of type A Peterson varieties
Giambelli formula $S^1$-equivariant cohomology of type Peterson varieties
2011/2/22
The main result of this note is a Giambelli formula for the Peterson Schubert classes in the S1-equivariant cohomology ring of a type A Peterson variety. Our results depend on the Monk formula for the...
Sequences of Nilsson type appear in abundance in Algebraic Geometry, Enumerative Combinatorics,
Mathematical Physics and Quantum Topology. We give an elementary introduction on this subject,
includi...
A Furstenberg-Katznelson-Weiss type theorem on (d + 1)-point configurations in sets of positive density in finite field geometries
positive density finite field geometries
2010/12/9
We show that if E ⊂ Fdq , the d-dimensional vector space over the finite field with q elements,and |E| ≥ qd, where q−1 2 ≪ ≤ 1, then E contains an isometric copy of at least cd&#...
The Gauss image of entire graphs of higher codimension and Bernstein type theorems
Gauss image entire graphs of higher codimension Bernstein type theorems
2010/12/9
Under suitable conditions on the range of the Gauss map of a complete submanifold of Euclidean space with parallel mean curvature, we construct a strongly subharmonic function and derive a-priori esti...
Criteria of Le page Type in Involutive Banach Algebras
Banach algebra Commutativity C\star-algebra antilinear map Spectral radius Numerical radius
2010/3/3
The Le Page inequality in Banach algebras is \parallel xy \parallel\leqa\parallel yx\parallel. We consider inequalities where a linear involution appears and has consequences on the involution itself ...