A relation between Г-convergence of functionals and their associated gradient flows

Giorgi conjectured in 1979 that if a sequence of functionals converges in the sense of Г-convergence to a limiting functional, then the corresponding gradient flows will converge as well after changing timescale appropriately. It is shown that this conjecture holds true for a rather wide kind of functionals. Project supported by the National Natural Science Foundation of China (Grant No. 19701018).     

Dimensions of cusp forms for Γ0(p) in degree two and small weights

We investigate degree two Siegel cusp forms of small weight for Γ₀(p). Using the Restriction Technique we compute some dimensions and verify the conjectures ofHashimoto in some examples of weights three and four. For weight two we determine the dimension for primesp ≤ 41 and find only lifts. We explain in general how to compute spaces of Siegel cusp forms for subgroups of finite index in Γ _n .     

The Poincaré series of the algebras of simultaneous invariants and covariants of two binary forms

Let ? _{d 1, d 2} and 𝒞 _{d 1, d 2} be the algebras of simultaneous invariants and simultaneous covariants of the two binary forms of degrees d ₁ and d ₂. Formulas for computation of the Poincaré series 𝒫? _{d 1, d 2} (z), 𝒫𝒞 _{d 1, d 2} (z) of the algebras are found. By using these formulas, we have computed the series for d ₁, d ₂ ≤ 20.     

The representations of two types of functionals on L~∞(Ω,F) and L~∞(Ω,F,P)

This article gives the representations of two types of real functionals on Z∞(Ω,F) or L∞(Ω,F,P) in terms of Choquet integrals. These functionals are comonotonically subadditive and comonotonically convex, respectively.     

The connection between the zeros of the ζ-function and sequences(g(p)), p prime,mod 1

In this paper we give the connection between the zeros of the -function and sequences(g(p)), p prime, mod 1 ifg(x)=x for 0, >0 or ifg(X) is a polynomial in .     

The representation theorem of onto isometric mappings between two unit spheres of l∞-type spaces and the application on isometric extension problem

In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of real l∞-type spaces, then we conclude that such mappings can be extended to the whole space as (real) linear isometries.