This paper is devoted to the completeness issue of RMLCI | the relative modal logic with composition and intersection | a restriction of the propositional dynamic logic with intersection. The trouble with RMLCI is that the operation of intersection is not modally deenable. Using the notion of mosaics, we give a new proof of a theorem considered in a previous paper \Complete axiomatization of a ...

Then C∼(X) df = ⊕sC ∼(X) becomes a graded Q-algebra under the intersection product, and we define D∼(X) to be the Q-subalgebra of C∼(X) generated by the divisor classes: D∼(X) = Q[C ∼(X)]. The elements of D∼(X) will be called the Lefschetz classes on X (for the relation ∼). They are the algebraic classes on X expressible as linear combinations of intersections of divisor classes (including the ...

A vanishing theorem is proved for`-adic cohomology with compact support on a singular aane complete intersection. As an application, it is shown that for an aane complete intersection deened over a nite eld of q elements, the reciprocal \poles" of the zeta function are always divisible by q as algebraic integers. A p-adic proof is also given, which leads to further q-divisibility of the poles o...

A theorem of Picard type is proved for entire holomorphic mappings into projective varieties. This theorem has local nature in the sense that the existence of Julia directions can be proved under natural additional assumptions. An example is given which shows that Borel’s theorem on holomorphic curves omitting hyperplanes has no such local counterpart. Let P be complex projective space of dimen...

The creation and propagation of jump discontinuities in the solutions of semilinear strictly hyperbolic systems is studied in the case where the initial data has a discrete set, {xi}~= 1, of jump discontinuities. Let S be the smallest closed set which satisfies: (i) S is a union of forward characteristics. (ii) S contains all the forward characteristics from the points {xi}~= 1" (iii) if two fo...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

Introduction In this note I show how very general and powerful results about the union and intersection of matroids due to J. Edmonds [19] may be deduced from a matroid generalisation of Hall's theorem by R. Rado [13]. Throughout, S, T, will denote finite sets, |X| will denote the cardinality of the set X and {xt: iel} denotes the set whose distinct elements are the elements x{. A matroid (S, M...

(1) f~(n) < exp [(log n) 1 /2 ]E Recently, I observed that using a combinatorial theorem due to Rado and myself (1) can be considerably improved and it might, in fact, be possible to obtain the correct order of magnitude for f 1 (n) . The combinatorial theorem in question states as follows [2] : Let g(k, t) be the smallest integer so that if A 1 , • • • , A 8 , s = g(k, t), are sets each having...

We study nonsingular minimal surfaces of general type with pg = 6 and K2 = 13 whose canonical image is contained in a single nonsingular quadric. We show that under these assumptions, such surfaces are regular and their canonical ideal has codimension 3. Led by Buchsbaum–Eisenbud’s structure theorem, we define a map of S into a weighted Grassmannian, which factors through an embedding of the ca...