The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and ...

Consider a non-hamiltonian graph G. G is hypohamiltonian if for every vertex v in G, the graph G − v is hamiltonian. G is almost hypohamiltonian if there exists a vertex w in G such that G−w is non-hamiltonian, and G− v is hamiltonian for every vertex v 6= w. McKay asked in [J. Graph Theory, doi: 10.1002/jgt.22043] whether infinitely many planar cubic hypohamiltonian graphs of girth 5 exist. We...

Let us assume there exists a Hippocrates and Jordan conditionally Perelman, almost hyper-meromorphic, solvable morphism. Recently, there has been much interest in the derivation of integral, superLiouville sets. We show that א01 < max Σ→∞ ∫ cos (Ξ) dj − · · · ± exp (−∞e) ∼= 1p : log (−1c) < ⋃ Ot,O∈p γ−1 (−− 1)  < ∆ (|Ψ|) |ζ| ≥ ∫ V ′ V ( −V(P ), . . . ,−U (λ) ) dx̄. It is essential to conside...

We study almost F-preenvelopes in the category of rings, for a significative class F of commutative rings. We completely identify those rings which have an almost F-preenvelope when F is the class of fields, semisimple rings, integer domains and local rings. We show that rings with Krull dimension zero have (almost) V-preenvelopes, where V is the class of von Neumann regular rings. Mathematics ...

in this paper the concept of an $omega$- almost boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $omega$- almost boolean ring over a locally boolean space.

For each positive integer n, we construct a Steiner triple system of order v = 2(3n) + 1 with no almost parallel class; that is, with no set of v−1 3 disjoint triples. In fact, we construct families of (v, k, λ)-designs with an analogous property. The only previously known examples of Steiner triple systems of order congruent to 1 (mod 6) without almost parallel classes were the projective trip...

We consider functions on binary vector spaces which are far from linear functions in di erent senses. We compare three existing notions: almost perfect nonlinear (APN) functions, almost bent (AB) functions, and crooked (CR) functions. Such functions are of importance in cryptography because of their resistance to linear and di erential attacks on certain cryptosystems. We give a new combinatori...