Free-minor closed classes [2] and free-planar graphs [3] are considered. Versions of Kuratowski-like theorem for free-planar graphs and Kuratowski theorem for planar graphs are considered. We are using usual definitions of the graph theory [1]. Considering graph topologically and Kuratowski theorem, we use the notion of minor following the theory of Robertson and Seymour[2]. We say, that a grap...

Let G be a reductive algebraic group and H a closed subgroup of G. Explicit constructions of G-invariant ideals in the algebra K[G/H] are given. This allows to obtain an elementary proof of Matsushima’s criterion: a homogeneous space G/H is an affine variety if and only if H is reductive. 1. Algebraic homogeneous spaces Let G be an affine algebraic group over an algebraically closed field K. A ...

We prove that a riemannian metric on the 2-sphere or the projective plane can be C 2 approximated by a C ∞ metric whose geodesic flow has an elliptic closed geodesic. In this paper we show how to overcome a difficulty presented by Henri Poincaré in the C 2 generic case. In 1905, H. Poincaré [34, p. 259] claimed that any convex surface in R 3 should have an elliptic or degenerate non self-inters...

Abstract. A homogeneous space G/H is said to have a compact Clifford-Klein form if there exists a discrete subgroup Γ of G that acts properly on G/H such that the quotient space Γ\G/H is compact. When n is even, we find every closed connected subgroup H of G = SO(2, n), such that G/H has a compact Clifford-Klein form, but our classification is not quite complete when n is odd. The work reveals ...

In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$  associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $  C^* $-algebra  $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the ...

C. Akemann and G.K. Pedersen [Duke Math. J. 40 (1973), 785– 795.] defined three concepts of semicontinuity for self-adjoint elements of A∗∗, the enveloping von Neumann algebra of a C∗-algebra A. We give the basic properties of the analogous concepts for elements of pA∗∗p, where p is a closed projection in A∗∗. In other words, in place of affine functionals on Q, the quasi–state space of A, we c...

We prove the following three results in Hamiltonian dynamics. • The Weinstein conjecture holds true for every displaceable hypersurface of contact type. • Every magnetic flow on a closed Riemannian manifold has contractible closed orbits for a dense set of small energies. • Every closed Lagrangian submanifold whose fundamental group injects and which admits a Riemannian metric without closed ge...

1. We announce here the following result: Two homotopic diffeomorphisms of a paracompact separable Hubert manifold of infinite dimension are isotopic. (1) In this paper, a hilbert manifold (A-manifold) with or without boundary is always hausdorff, paracompact, separable C°°-differentiable and with the infinite dimensional separable hilbert space H as local model. Let M(M, dM) be an /^-manifold ...

A signed graph is a simple with two types of edges: positive and negative. homomorphism from G to another H mapping \(\varphi : V(G) \rightarrow V(H)\) that preserves vertex adjacencies balance closed walks (the the parity number negative edges). The chromatic \(\chi _s(G)\) order smallest such there H.

For G = SL(3, R) and G = SO(2, n), we give explicit, practical conditions that determine whether or not a closed, connected subgroup H of G has the property that there exists a compact subset C of G with CHC = G. To do this, we fix a Cartan decomposition G = KA + K of G, and then carry out an approximate calculation of (KHK) ∩ A + for each closed, connected subgroup H of G.