In an attempt to classify all of the overlap-free morphisms constructively using the Latin-square morphism, we came across an interesting counterexample, the Leech square-free morphism. We generalize the combinatorial properties of the Leech square-free morphism to gain insights on a larger class of both overlap-free morphisms and square-free morphisms.

Let X be any variety in characteristic zero. V?X an open subset that has toroidal singularities. We show the existence of a canonical desingularization except for V. It is morphism f:Y?X, which does not modify V and transforms into embedding Y, with singularities extending those on Moreover, exceptional divisor simple normal crossings Y. The theorem naturally generalizes Hironaka desingularizat...

We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo $p^2$ - we expect that such varieties, after finite \'etale cover, admit toric fibration over an ordinary abelian variety. prove this assertion implies of Occhetta and Wi\'sniewski, which states zero image variety is To end analyse the behaviour families ...

The existence and the construction of a specification morphism between two algebraic specifications is a crucial step in modular system design and in the reusability of software. The problem of determining the existence of a signature morphism between two algebraic signatures is analyzed and proved to be NP-complete by reducing the well known 3SAT problem. As a consequence, the problem of findi...

INTRODUCTION Huxley, Mayr, Osmond, and Hoffer (1964) presented a hypothesis that schizophrenia is a genetic morphism (see Huxley, 1955). This is in general agreement with the proposition that all genetic characteristics which exist in a population at a frequency higher than can be maintained by mutation alone must be a morphism. The frequency of the morphic gene is the result of a balance betwe...

A nonerasing morphism σ is said to be weakly unambiguous with respect to a word s if σ is the only nonerasing morphism that can map s to σ(s), i. e., there does not exist any other nonerasing morphism τ satisfying τ(s) = σ(s). In the present paper, we wish to characterise those words with respect to which there exists such a morphism. This question is nontrivial if we consider so-called length-...

Polar spaces are presented from the point of view of paraprojective spaces. Morphisms are introduced and some immediate categorical aspects are reviewed. The morphisms of polar spaces are then studied in more details and are shown to preserve the spaces’ structure. Finally, it is shown that a morphism of polar spaces can be split into a morphism of nondegenerate polar spaces and a morphism of p...