Generalized Hyers-Ulam-Rassias Theorem in Menger Probabilistic Normed Spaces

We introduce two reasonable versions of approximately additive functions in a Šerstnev probabilistic normed space endowed with Π triangle function. More precisely, we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in above mentioned spaces

Pattern formation of reaction-diffusion system having self-determined flow in the amoeboid organism of Physarum plasmodium

The amoeboid organism, the plasmodium of Physarum polycephalum, behaves on the basis of spatio-temporal pattern formation by local contraction-oscillators. This biological system can be regarded as a reaction-diffusion system which has spatial interaction by active flow of protoplasmic sol in the cell. Paying attention to the physiological evidence that the flow is determined by contraction pattern in the plasmodium, a reaction-diffusion system having self-determined flow arises. Such a coupling of reaction-diffusion-advection is a characteristic of the biological system, and is expected to relate with control mechanism of amoeboid behaviours. Hence, we have studied effects of the self-determined flow on pattern formation of simple reaction-diffusion systems. By weakly nonlinear analysis near a trivial solution, the envelope dynamics follows the complex Ginzburg-Landau type equation just after bifurcation occurs at finite wave number. The flow term affects the nonlinear term of the equation through the critical wave number squared. Contrary to this, wave number isn't explicitly effective with lack of flow or constant flow. Thus, spatial size of pattern is especially important for regulating pattern formation in the plasmodium. On the other hand, the flow term is negligible in the vicinity of bifurcation at infinitely small wave number, and therefore the pattern formation by simple reaction-diffusion will also hold. A physiological role of pattern formation as above is discussed.Comment: REVTeX, one column, 7 pages, no figur

Anti-cancer effects and mechanism of actions of aspirin analogues in the treatment of glioma cancer

INTRODUCTION: In the past 25 years only modest advancements in glioma treatment have been made, with patient prognosis and median survival time following diagnosis only increasing from 3 to 7 months. A substantial body of clinical and preclinical evidence has suggested a role for aspirin in the treatment of cancer with multiple mechanisms of action proposed including COX 2 inhibition, down regulation of EGFR expression, and NF-κB signaling affecting Bcl-2 expression. However, with serious side effects such as stroke and gastrointestinal bleeding, aspirin analogues with improved potency and side effect profiles are being developed. METHOD: Effects on cell viability following 24 hr incubation of four aspirin derivatives (PN508, 517, 526 and 529) were compared to cisplatin, aspirin and di-aspirin in four glioma cell lines (U87 MG, SVG P12, GOS – 3, and 1321N1), using the PrestoBlue assay, establishing IC50 and examining the time course of drug effects. RESULTS: All compounds were found to decrease cell viability in a concentration and time dependant manner. Significantly, the analogue PN517 (IC50 2mM) showed approximately a twofold increase in potency when compared to aspirin (3.7mM) and cisplatin (4.3mM) in U87 cells, with similar increased potency in SVG P12 cells. Other analogues demonstrated similar potency to aspirin and cisplatin. CONCLUSION: These results support the further development and characterization of novel NSAID derivatives for the treatment of glioma

Generalized Ulam-Hyers Stability of Jensen Functional Equation in Šerstnev PN Spaces

We establish a generalized Ulam-Hyers stability theorem in a &#352;erstnev probabilistic normed space (briefly, &#352;erstnev PN-space) endowed with . In particular, we introduce the notion of approximate Jensen mapping in PN-spaces and prove that if an approximate Jensen mapping in a &#352;erstnev PN-space is continuous at a point then we can approximate it by an everywhere continuous Jensen mapping. As a version of a theorem of Schwaiger, we also show that if every approximate Jensen type mapping from the natural numbers into a &#352;erstnev PN-space can be approximated by an additive mapping, then the norm of &#352;erstnev PN-space is complete.</p

General System of Cubic Functional Equations in non{Archimedean Spaces

[[abstract]]In this paper, we introduce Menger probabilistic non-Archimedean normed spaces. we prove the generalized Hyers{Ulam{Rassias stability for a general system of cubic functional equations in non{Archimedean normed spaces and Menger probabilistic non{Archimedean normed spaces

Generalized Ulam-Hyers Stability of Jensen Functional Equation in &#352;erstnev PN Spaces

We establish a generalized Ulam-Hyers stability theorem in a &#352;erstnev probabilistic normed space (briefly, &#352;erstnev PN-space) endowed with &#x03A0;M. In particular, we introduce the notion of approximate Jensen mapping in PN-spaces and prove that if an approximate Jensen mapping in a &#352;erstnev PN-space is continuous at a point then we can approximate it by an everywhere continuous Jensen mapping. As a version of a theorem of Schwaiger, we also show that if every approximate Jensen type mapping from the natural numbers into a &#352;erstnev PN-space can be approximated by an additive mapping, then the norm of &#352;erstnev PN-space is complete