In this correspondence, for every periodic p−ary sequence satisfying ideal two-level autocorrelation property the existence of an element of the field GF(p) which appears one time less than all the rest that are equally distributed in a period of that sequence, is proved by algebraic method. In addition, it is shown that such a special element might not be only the zero element but as well arbi...

Segmental mechanics consists of multiple wire cross-sections in different segments of the arch. The advantages of segmental mechanics in comparison with continuous mechanics are a statically determinate force system, relatively constant force, minimal side-effects on the anchorage unit, minimal arch wire fabrication, decreased treatment duration and enhanced esthetics. Individual retraction of ...

Let (P,≺) be a finite poset and let G be its comparability graph. If cl(G) is the clutter of maximal cliques of G, we prove that cl(G) satisfies the maxflow min-cut property and that its edge ideal is normally torsion free. We prove that edge ideals of complete admissible uniform clutters are normally torsion free. The normality of a monomial ideal is expressed in terms of blocking polyhedra an...

We prove a strong version of a theorem of Balcerzak-RoslanowskiShelah by showing, in ZFC, that there exists a simply definable Borel σ-ideal for which both the ccc and property (M) fail. The proof involves Polish group actions. Definition. A Borel ideal is an ideal I on a Polish space X with the following property: for all A ∈ I, there exists a Borel subset B of X such that A ⊂ B and B ∈ I. We ...

in this work, different types of chaotic 1-manifolds which lie on the chaotic spheres or on a torus are introduced. some types of retractions of the chaotic spheres affect on the 1-chaotic systems, and other types of retractions occur to the geometric manifold but make the 1-chaotic manifold invariant. the existed retractions are discussed through new proved theorems. also we construct diffe...

In this paper, we introduce a notion of adjoint ideal sheaves along closed subvarieties of higher codimension and prove a restriction property of our adjoint ideal sheaves using characteristic p methods.

We prove that the existence of a $1$-Lipschitz retraction (a contraction) from space $X$ onto its subspace $A$ implies persistence diagram embeds into $X$. As tool we introduce tight injections modules as maps inducing said embeddings. show contractions always exist shortest loops in metric graphs and conjecture on planar all homology basis. Of primary interest are geodesic spaces. These act id...

A conjugation-invariant ideal I ⊆ C[zj , zj : j = 1, . . . , n] has the Quillen property if every real valued, strictly positive polynomial on the real zero set VR(I) ⊆ C n is a sum of hermitian squares modulo I . We first relate the Quillen property to the archimedean property from real algebra. Using hereditary calculus, we then quantize and show that the Quillen property implies the subnorma...

The basal plane cleavage energy (CE) of graphite is a key material parameter for understanding many of the unusual properties of graphite, graphene and carbon nanotubes. Nonetheless, a wide range of values for the CE has been reported and no consensus has yet emerged. Here we report the first direct, accurate experimental measurement of the CE of graphite using a novel method based on the self-...

We consider the fuzzification of the notion of an n-fold implicative ideal, an n-fold (weak) commutative ideal. We give characterizations of an n-fold fuzzy implicative ideal. We establish an extension property for n-fold fuzzy commutative ideals. 2000 Mathematics Subject Classification. 06F35, 03G25, 03E72.