Does there exist for every polyhedron a face-to-face partition into acute tetrahedra (all of whose dihedral angles are acute)?
Does there exist a tetrahedron that can be partitioned into two or more acute tetrahedra?
Is there a face-to-face partition of R4 into acute simplices?
What all are simplicial space-fillers in Rd?
Does there exist for every composite Fermat number Fm = 22^m + 1 a positive integer h such that Fm is divisible by 5h2m+2 + 1?
Given any odd integer k > 2 that is not a Sierpinski number, does there exist a Fermat number Fm having a prime factor of the form k2n + 1?
Is a Fermat number Fm prime if Fm+1 is prime?
Main scientific results
1979 - Construction of an octahedron with non-Lipschitzian boundary
[J4].
1982 - Existence of a strongly regular family of decompositions of
an arbitrary polyhedron into tetrahedra [C1].
1983 - Construction of divergence-free finite element basis
functions with small supports [B1] (for continuous piecewise
linear divergence-free basis functions see [B9]).
1984 - Superconvergence phenomenon in the finite element method
arising from averaging gradients [B3].
1985 - Dual finite element method for the biharmonic problem
[C5].
1986 - Construction of divergence-free finite element functions in three-dimensional
domains [B4].
1987 - A general definition of superconvergence [B6].
1988 - O(h4)-superconvergence of piecewise bilinear
finite element approximations [B7], [B8].
1989 - Finite element solution of time-harmonic Maxwell equations
[C11].
1990 - Preconditioned biconjugate gradient method for a system
of linear algebraic equations in a complex variable [G5],
[B20].
1991 - The maximum angle condition that guarantees optimal
interpolation properties of linear triangular finite elements
[C12].
1992 - The maximum angle condition that guarantees optimal
interpolation properties of linear tetrahedral finite elements
[B11].
1993 - Numerical analysis of finite element variational crimes for a nonlinear
elliptic problem [B14].
1994 - Finite element analysis of a quasilinear nonpotential
elliptic problem of a nonmonotone type [B19].
1995 - Discrete maximum principle on tetrahedral meshes
[B21], [B34], [B35].
1996 - A comparison principle for a quasilinear elliptic problem
[B25].
1997 - Local refinements of unstructured tetrahedral meshes [B26].
1998 - Finite element analysis of a radiation heat transfer problem
[B29].
1999 - Finite speed of gravitational interaction contributes to the expansion
of the universe [B32].
2000 - Numerical analysis of variational crimes for a
quasilinear elliptic problem in 3D [B33].
2001 - A necessary and sufficient condition for the primality
of Fermat numbers [C23].
2002 - Colouring polytopic partitions [C25], in particular,
any tetrahedralization is
four-colourable.
2003 - The nonexistence of a Lobachevsky geometry model of
an isotropic and homogeneous universe [B41] (for the time-lens
principle see [K25]).
2004 - A new relationship between Mersenne and Sophie Germain primes
[B46].
2005 - For a given integer m
there is no face-to-face tetrahedralization of R3
such that each edge is surrounded by m tetrahedra [B50].
2006 - There is no face-to-face partition of R5
into acute simplices
[B54].
2007 - Dissection of the path-simplex in Rn
into n path-simplices [B56].
2008 - Euclidean primes have the minimum number of primitive roots
[B60].
2009 - Gravitational aberration contributes to the dark energy necessary
for the accelerated expansion of the Universe
[B61].
