Approximate Homomorphisms of Ternary Semigroups

A mapping $f:(G_1,[ ]_1)\to (G_2,[ ]_2)$ between ternary semigroups will be called a ternary homomorphism if $f([xyz]_1)=[f(x)f(y)f(z)]_2$. In this paper, we prove the generalized Hyers--Ulam--Rassias stability of mappings of commutative semigroups into Banach spaces. In addition, we establish the superstability of ternary homomorphisms into Banach algebras endowed with multiplicative norms.Comment: 10 page

Asymptotic stability of the Cauchy and Jensen functional equations

The aim of this note is to investigate the asymptotic stability behaviour of the Cauchy and Jensen functional equations. Our main results show that if these equations hold for large arguments with small error, then they are also valid everywhere with a new error term which is a constant multiple of the original error term. As consequences, we also obtain results of hyperstability character for these two functional equations

Regulation and localization of endogenous human tristetraprolin

Tumor necrosis factor (TNF) has been implicated in the development and pathogenicity of infectious diseases and autoimmune disorders, such as septic shock and arthritis. The zinc-finger protein tristetraprolin (TTP) has been identified as a major regulator of TNF biosynthesis. To define its intracellular location and examine its regulation of TNF, a quantitive intracellular staining assay specific for TTP was developed. We establish for the first time that in peripheral blood leukocytes, expression of endogenous TTP is confined to the cytoplasm. Baseline expression of TTP was higher in monocytes than in lymphocytes or neutrophils. After in vitro incubation with lipopolysaccharide (LPS), leukocyte TTP levels increased rapidly, peaking after approximately 2 hours. Monocytes showed the greatest response to LPS stimulation and lymphocytes the least. TTP levels were also studied in leukocytes isolated from healthy volunteers infused with a bolus dose of LPS. TTP expression and initial upregulation in response to LPS infusion were consistent with the in vitro data. Neutrophil TTP levels responded first, reaching an initial peak within 1 hour, monocyte levels peaked next at 2 hours, followed by lymphocytes at 4 hours. This response paralleled plasma TNF levels, which peaked 2 hours after infusion and were no longer detectable after 12 hours. A second rise in intracellular TTP levels, which did not parallel plasma TNF levels, was observed in all leukocyte populations, starting 12 hours after infusion. These data establish the cytoplasmic location of TTP, supporting a major role for this protein in regulating TNF production, and suggest that TTP levels are not regulated solely by TNF

Approximately Ternary Homomorphisms and Derivations on C

We investigate the stability and superstability of ternary homomorphisms between C*-ternary algebras and derivations on C*-ternary algebras, associated with the following functional equation f((x2-x1)/3)+f((x1-3x3)/3)+f((3x1+3x3-x2)/3)=f(x1)

An Introduction to Hyperbolic Barycentric Coordinates and their Applications

Barycentric coordinates are commonly used in Euclidean geometry. The adaptation of barycentric coordinates for use in hyperbolic geometry gives rise to hyperbolic barycentric coordinates, known as gyrobarycentric coordinates. The aim of this article is to present the road from Einstein's velocity addition law of relativistically admissible velocities to hyperbolic barycentric coordinates along with applications.Comment: 66 pages, 3 figure

Gyrations: The Missing Link Between Classical Mechanics with its Underlying Euclidean Geometry and Relativistic Mechanics with its Underlying Hyperbolic Geometry

Being neither commutative nor associative, Einstein velocity addition of relativistically admissible velocities gives rise to gyrations. Gyrations, in turn, measure the extent to which Einstein addition deviates from commutativity and from associativity. Gyrations are geometric automorphisms abstracted from the relativistic mechanical effect known as Thomas precession