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Content available remote Remarks on *-(σ, τ)-Lie ideals of *-prime rings with derivation
Let R be a *- prime ring with characteristic not 2, U a nonzero *- (σ, τ)-Lie ideal of R, d a nonzero derivation of R. Suppose σ, τ be two automorphisms of R such that σd = dσ, τd = dτ and * commutes with σ, τ, d. In the present paper it is shown that if d(U) ⊆ Z or d2 (U) ⊆ Z, then U ⊆ Z.
Content available remote Approximate property of a functional equation with a general involution
In this paper, we prove the Hyers-Ulam stability of the functional equation f(x + y, z + w) + f(x + σ (y), z + τ(w)) = 2f(x, z) + 2f(y, w), where σ, τ are involutions.
W zachodniej części piaskowni Łubienica-Superunki, położonej na Wysoczyźnie Ciechanowskiej (północne Mazowsze), stwierdzono występowanie struktur peryglacjalnych, takich jak: inwolucje, bruk peryglacjalny oraz pseudomorfozy po dużych epigenetycznych klinach mrozowych z wypełnieniem lodowo-piaszczystym (ang. composite wegdes). Struktury te wykształcone są w większości bezpośrednio pod współczesną glebą i warstwą piasków pokrywowych o małej miąższości poza jednym z klinów, który występuje w obrębie osadów fluwioglacjalnych w transgresji młodszego stadiału zlodowacenia warty.
In the western part of the Łubienica-Superunki sand pit, located on the Ciechanowska Upland (northern Mazovia), periglacial structures were observed such as: involutions, periglacial pavement and large epigenetic composite wegde psuedomorphs. The structures occur usually below contemporary topsoil and thin layer of cover sands, besides one frost wedge, which is developed in fluvioglacial sediments from transgression of younger Saalian ice sheet.
Content available remote Involutory BE-algebras
This paper is devoted to the study of some structural properties of bounded and involutory BE-algebras and investigate the relationship between them. We construct a commutative monoid by definition of proper operation in an involutory BE-algebra. Some rules of calculus for BE-algebras with a semi-lattice structure are provided. Many results related to the natural order of a BE-algebras were found. Finally, we show that an involutory bounded BE-algebra X is semi-simple.
Content available remote On Jordan triple α-* centralizers of semiprime rings
Let R be a 2-torsion free semiprime ring equipped with an involution *. An additive mapping T : R → R is called a left (resp. right) Jordan α-* centralizer associated with a function α : R → R if T(x2) = T(x)α(x*) (resp. T(x2) = α(x*)T(x)) holds for all x (…) R. If T is both left and right Jordan α-* centralizer of R, then it is called Jordan α-* centralizer of R. In the present paper it is shown that if α is an automorphism of R, and T : R → R is an additive mapping such that 2T(xyx) = T(x)α(y*x*) + α(x*y*)T(x) holds for all x; y (…) R, then T is a Jordan α-* centralizer of R.
Content available remote Finite directly indecomposable monogenic entropic quasigroups with quasi-identity
In this paper we characterize finite directly indecomposable monogenic entropic quasigroups with quasi-identity.
Content available remote Finite simple monogenic entropic quasigroups with quasi-identity
In this paper we describe finite simple monogenic entropic quasigroups with quasi-identity.
Content available remote Quantifiers on lattices with an antitone involution
Quantifiers on lattices with an antitone involution are considered and it is proved that the poset of existential quantifiers is antiisomorphic to the poset of relatively complete sublattices.
We propose a scalable block cipher which is an involutional SPN. We use one S-box which is an involution and a bit permutation which also is an involution. As a result we received a totally involutional cipher. It means that we use the same network, and especially the same S-box and the same permutation P in the encryption and decryption data processing. PP-1 is a symmetric block cipher designed for platforms with very limited resources, especially with restricted amount of memory needed to store its components
Content available remote About Various Methods of Calculating the Sum [formula]
Pupils of secondary school as well as students often have problems with calculating the sums of the mth powers of successive natural numbers. In this paper we present certain methods of finding such sums.
Content available remote A Formal Language Analysis of DNA Hairpin Structures
The concept of hairpin structures in formal languages is motivated from the biocomputing and bioinformatics fields. Hairpin (-free) DNA structures have numerous applications to DNA computing and molecular genetics in general. A word is called hairpin-free if it cannot be written in the form xvyq(v)z, with certain additional conditions, for an involution q (a function q with the property that q2 equals the identity function). A particular involution, the so-called Watson-Crick involution, can characterize binding of two DNA strands. We study algebraic and decision properties, finiteness and descriptional complexity of hairpin (-free) languages. We show an existence of polynomial-time algorithms deciding hairpin-freeness of regular and context-free sets. Two related DNA secondary structures are considered, taking into the account imperfect bonds (bulges, mismatches) and multiple hairpins. Finally, effective methods for design of long hairpin-free DNA words are given.
Content available remote Free actions of semiprime rings with involution induced a derivation
Let R be an associative ring. An element a is an element of R is said to be dependent of a mapping F : R -> R in case F (x) a = ax holds for all x is an element of R. A mapping F : R -> R is called a free action in case zero is the only dependent element of F. In this paper free actions of semiprime *- rings induced by a derivation are considered. We prove, for example, that in case we have a derivation D : R -> R, where R is a semiprime *-ring, then the mapping F defined by F(x) = D(x*) + D(x)*,x is an element of R, is a free action. It is also proved that any Jordan *-derivation on a 2-torsion free semiprime *-ring is a free action.
Content available remote A non-standard version of the Borsuk-Ulam theorem
E. Pannwitz showed in 1952 that for any n≥2, there exist continuous maps φ : Sn → Sn and f : Sn → R2 such that f(x) ≠ f(φ(x)) for any x ∈ Sn. We prove that, under certain conditions, given continuous maps ψ,φ : X → X and f : X → R2, although the existence of a point x ∈ X such that f(ψ(x)) = f(φ(x)) cannot always be assured, it is possible to establish an interesting relation between the points f(φψ(x)), f(φ2(x)) and f(ψ2(x)) when f(φ(x)) ≠ f(ψ(x)) for any x ∈ X, and a non-standard version of the Borsuk–Ulam theorem is obtained.
In an n-dimensional complex projective space there are considered pairs of (anti)involutions generating cyclic collineations of arbitrary order. There are obtained canonical matrix representations of such involutions and tbere is proved the theorem on decomposition of any cyclic collineation into two antiinvolutions.
Content available remote Set-valued iterative square roots of bijections
There are different ideas how to generalize the notion of an iterative root, especially when a function does not have a "real" root. We consider a multifunction as a substitute for this notion.
Content available remote Noncontinuous linear operators and independent linear topologies
We establish the existence of badly noncontinuous injective linear operators, isomorphisms and involutions between topological linear spaces. As an application, a metrizable linear topology independent of a given one is exhibited.
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