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The 2-group of symmetries of a split chain complex      2-group of symmetries  split chain complex        font style='font-size:12px;'> 2011/1/19
We explicitly compute the 2-group of self-equivalences and (homotopy classes of) chain homotopies between them for any split chain complex A• in an arbitrary K-linear abelian category (K any com...
The Past and the Future in the Present      The Past  the Future  Present        font style='font-size:12px;'> 2011/3/1
We show how the shared information between the past and future|the excess entropy|derives from the components of directional information stored in the present|the predictive and retrodictive causal s...
This paper studies the valuation of a class of credit default swaps (CDSs) with the embedded option to switch to a different premium and notional principal anytime prior to a credit event.
Fano symmetric varieties with low rank     Symmetric varieties  Fano varieties       font style='font-size:12px;'> 2011/2/22
The symmetric projective varieties of rank one are all smooth and Fano by a classic result of Akhiezer. We classify the locally factorial (respectively smooth) projective symmetric G-varieties of rank...
This paper proves some results on negative gradient dynamics of Morse functions on Hilbert manifolds. It contains the compactness of ow lines, manifold structures of certain compacti- ed moduli spa...
A note on the border of an exponential family     Algebraic Statistics  Convex Support  Extended Exponential Family       font style='font-size:12px;'> 2011/1/17
Limits of densities belonging to an exponential family appear in many applications, e.g. Gibbs models in Statistical Physics, relaxed combinatorial optimization,coding theory, critical likelihood comp...
A Note on the Jordan Canonical Form      Note  Jordan Canonical Form        font style='font-size:12px;'> 2011/1/20
A proof of the Jordan canonical form, suitable for a first course in linear algebra, is given. The proof includes the uniqueness of the number and sizes of the Jordan blocks. The value of the customar...
When every principal ideal is flat      PF-ring  direct product  localization  Dedekind domain       font style='font-size:12px;'> 2011/1/20
This paper deals with well-known notion of PF-rings, that is, rings in which principal ideals are flat. We give a new characterization of PF-rings. Also, we provide a necessary and sufficient conditio...
A class of non-Hermitian quadratic su(2) Hamiltonians that ful l an anti-linear symmetry is constructed. If unbroken this anti-linear symmetry leads to a purely real spectrum and the Hamiltonian can b...
Motivated by the study of billiards in polygons, we prove fine results for the distribution of gaps of directions of saddle connections on translation surfaces.
Mutation and instanton knot homology      Mutation  instanton knot homology        font style='font-size:12px;'> 2011/1/18
If K is a knot or link in R3 and S  R3 is a smoothly embedded 2-sphere meeting K transversely in 4-points, then one can form a new knot or link K′ as follows. One cuts R3 along S and then glues the t...
Evaporation of 2-Dimensional Black Holes     Evaporation  2-Dimensional Black Holes       font style='font-size:12px;'> 2011/3/1
We present a detailed analysis of results from a new study of the quantum evaporation of Callan-Giddings-Harvey-Strominger (CGHS) black holes within the mean field approximation. This semi-classical t...
LDPC Codes for Compressed Sensing      LDPC Codes  Compressed Sensing        font style='font-size:12px;'> 2011/1/17
We present a mathematical connection between channel coding and compressed sensing.
In this paper we have discusses 􀀀-left, 􀀀-right, 􀀀-bi-, 􀀀-quasi-, 􀀀-interior and 􀀀-ideals in 􀀀-AG-groupoids and regular 􀀀-AG...
Considering a non-constant smooth solution f of the Tanno equation on a closed,connected K¨ahler manifold (M, g, J) with positively definite metric g, Tanno showed that the manifold can be finitely co...

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