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Subalgebras and finitistic dimensions of Artin algebras
Artin algebras representation dimension finitistic dimension
2011/9/16
Abstract: Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
Representation dimensions of triangular matrix algebras
Representation dimension tilting module finite type
2011/9/15
Abstract: Let $A$ be a finite dimensional hereditary algebra over an algebraically closed field $k$, $T_2(A)=(\begin{array}{cc}A&0 A&A\end{array})$ be the triangular matrix algebra and $A^{(1)}=(\begi...
Hausdorff and packing dimensions of the images of random fields
Hausdorff packing dimensions the images of random fields
2010/11/24
Let $X=\{X(t),t\in\mathbb{R}^N\}$ be a random field with values in $\mathbb{R}^d$. For any finite Borel measure $\mu$ and analytic set $E\subset\mathbb{R}^N$, the Hausdorff and packing dimensions of t...
Symmetry analysis and exact solutions of semilinear heat flow in multi-dimensions
Symmetry analysis exact solutions semilinear heat flow in multi-dimensions
2010/11/24
A symmetry group method is used to obtain exact solutions for a semilinear radial heat equation in $n>1$ dimensions with a general power nonlinearity. The method involves an ansatz technique to solve...
Optimal dispersive estimates for the wave equation with $C^{(n-3)/2}$ potentials in dimensions $4\le n\le 7$
the wave equation math
2010/11/22
We prove optimal dispersive estimates for the wave group $e^{it\sqrt{-\Delta+V}}$ for a class of real-valued potentials $V\in C^{(n-3)/2}({\bf R}^n)$, $4\le n\le 7$, such that $\partial_x^\alpha V(x)=...
On duality and negative dimensions in the theory of Lie groups and symmetric spaces
duality negative dimensions theory Lie groups symmetric spaces
2010/11/8
We give one more interpretation of the symbolic formulae $U(-N)=U(N)$ and $Sp(-2N)=SO(2N)$ by comparing the values of certain Casimir operators in the corresponding tensor representations. We show al...
Homogenization of the G-equation with incompressible random drift in two dimensions
the G-equation incompressible dimensions
2010/11/8
We study the homogenization limit of solutions to the G-equation with random drift. This Hamilton-Jacobi equation is a model for flame propagation in a turbulent fluid in the regime of thin flames. F...
Closed nodal surfaces for simply connected domains in higher dimensions
Laplacian eigenfunction nodal domain
2010/12/1
We give an example of a domain in dimension N 3, homeomorphic to a ball and with analytic boundary, for which the second eigenvalue of the Dirichlet Laplacian has an eigenfunction with a closed noda...