We give a characterization theorem for non-degenerate plane foliations of degree different from 1 having a rational first integral. Moreover, we prove that the degree r of a non-degenerate foliation as above provides the minimum number, r+ 1, of points in the projective plane through which pass infinitely many algebraic leaves of the foliation.

It is shown that associated with each metric space (X, d) there is a compactification udX of X that can be characterized as the smallest compactification of X to which each bounded uniformly continuous real-valued continuous function with domain X can be extended. Other characterizations of udX are presented, and a detailed study of the structure of udX is undertaken. This culminates in a topol...

Let S ⊂ R3 be a C4-smooth relatively compact orientable surface with a sufficiently regular boundary. For β ∈ R+, let Ej(β) denote the jth negative eigenvalue of the operator associated with the quadratic form H(R) ∋ u 7→ ∫∫∫

The usual ordering “≤" on R is a total ordering, that is, for any two real numbers in R, we can determine their order without difficulty. However, for any two closed intervals in R, there is not a natural ordering among the set of all closed intervals in R. Several methods have been developed to compare two intervals. In this paper, we define the μ-ordering which is a new method for ordering cl...

We prove that affine configurations of 4 lines in R3 are topologically and combinatorially homeomorphic to affine configurations of 6 points in R4.

Quadratic theory of gravity is a complicated constraint system. We investigate some consequences of treating quadratic terms perturbatively (higher derivative version of backre-action effects), which is consistent with the way existence of quadratic terms was originally established (radiative loop effects and renormalization procedures which induced quadratic terms). We show that this approach ...

Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp. R⊂R[[X]]). By using this extension we will present some of the faithfulness conditions of local cohomology modules, and show that if the Lynch's conjecture, i...