Quadratic--quartic functional equations in RN--spaces

In this paper, we obtain the general solution and the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary $t$-norms $$f(2x+y)+f(2x-y)=4[f(x+y)+f(x-y)]+2[f(2x)-4f(x)]-6f(y).$$Comment: 11 page

Thermal delay of drop coalescence

We present the results of a combined experimental and theoretical study of drop coalescence in the presence of an initial temperature difference T[subscript 0] between a drop and a bath of the same liquid. We characterize experimentally the dependence of the residence time before coalescence on T[subscript 0] for silicone oils with different viscosities. Delayed coalescence arises above a critical temperature difference T[subscript c] that depends on the fluid viscosity: for T[subscript 0] > T[subscript c], the delay time increases T[subscript 0] [superscript 2/3] as for all liquids examined. This observed dependence is rationalized theoretically through consideration of the thermocapillary flows generated within the drop, the bath and the intervening air layer.National Science Foundation (U.S.) (Grant CMMI-1727565)National Science Foundation (U.S.) (Grant DMS-1614043

On Approximate Cubic Homomorphisms

We investigate the generalized Hyers-Ulam-Rassias stability of the system of functional equations: f(xy)=f(x)f(y), f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x), on Banach algebras. Indeed we establish the superstability of this system by suitable control functions

Stability of Ternary Cubic Derivations on Ternary Frèchet Algebras

Abstract: In this paper, we prove the generalized Hyers-Ulam-Rassias stability and superstability of ternary cubic derivations on ternary Frèchet algebras

Surpass streamline flow-diverter embolization device for treatment of iatrogenic and traumatic internal carotid artery injuries

Iatrogenic and traumatic cerebral internal carotid artery injuries are uncommon but potentially lethal complications. Direct surgical repair of ICA injuries may be difficult in an acute setting. However, endovascular treatment with a flow-diverter embolization device is a feasible alternative technique that we experienced. In this clinical report, we describe demographic data, radiographic images, lesion characteristics, endovascular procedure notes, postprocedural hospital course, and follow-up digital subtraction angiography of 5 patients. At least 6-month follow-up was available in all patients without occurrence of rebleeding and other complications