Module character amenability of Banach algebras

In this paper we introduce the notion of module character amenable Banach algebras and show that they possess module character virtual (approximate) diagonals. As a basic example, we show that for an inverse semigroup S with the set of idempotents E, the semigroup algebra ? ¹(S) is module character amenable as an ? ¹(E)-module if only if S is amenable.     

Module amenability of the second dual and module topological center of semigroup algebras

In this paper we define the module topological center of the second dual $\mathcal{A}^{**}$ of a Banach algebra $\mathcal{A}$ which is a Banach $\mathfrak{A}$ -module with compatible actions on another Banach algebra $\mathfrak{A}$ . We calculate the module topological center of ? ¹(S)^**, as an ? ¹(E)-module, for an inverse semigroup S with an upward directed set of idempotents E. We also prove that ? ¹(S)^** is ? ¹(E)-module amenable if and only if an appropriate group homomorphic image of S is finite.     

On the Stability of Jordan *-Derivation Pairs

In this article, the Hyers–Ulam stability of Jordan *-derivation pairs for the Cauchy additive functional equation and the Cauchy additive functional inequality is proved. A fixed point method to establish of the stability and the superstability for Jordan *-derivation pairs is also employed.     

Nonthermal Atmospheric Argon Plasma Jet Effects on Escherichia coli Biomacromolecules

Nonthermal atmospheric plasma jet, a promising technology based on ionized gas at low temperatures, can be applied for disinfection of contaminated surfaces. In this study, Escherichia coli cells and their macromolecules were exposed to the nonthermal atmospheric argon plasma jet for different time durations. Total protein, genomic DNA, and malondialdehyde (MDA) levels of E. coli were assessed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis and silver staining; agarose gel electrophoresis; and measurement of absorbance at 534 nm, respectively. After exposure, the spectroscopic results of liquid samples indicated that the survival reduction of E. coli can reach to 100 % in an exposure time of 600 s. Moreover, inactivation zones of E. coli, DNA degradation, and MDA levels were significantly increased. Additionally, banding patterns of total protein were changed and amino acid concentrations increased following ninhydrin test. The experimental results suggest that the nonthermal plasma could serve as an effective instrument for both sterilizing E. coli and degrading macromolecules from the surface of the objects being sterilized.     

<Emphasis Type="Italic">E. coli</Emphasis>, <Emphasis Type="Italic">P. aeruginosa</Emphasis>, and <Emphasis Type="Italic">B. cereus</Emphasis> Bacteria Sterilization Using Afterglow of Non-Thermal Plasma at Atmospheric Pressure

We developed and employed a new geometrical structure of dielectric barrier discharge in atmospheric pressure for bacterial broad spectrum sterilization. We utilized a plasma source having an AC power supply at 50 HZ and 5,400 V (rms value). We prepared suspensions of the Gram-negative bacteria species (Escherichia coli, Pseudomonas aeruginosa) and a Gram-positive of Bacillus cereus with Luria–Bertani broth media up to OD_600 nm = 0.25 of McFarland standard. Afterglow of non-thermal atmospheric pressure plasma treated these suspensions. The influence of the atmospheric plasma afterglow on the species was assayed in different time durations 5, 10, and 15 min. The spectroscopic results of this investigation indicated that the survival reduction of the species can reach to 100% for P. aeruginosa in an exposure time of 10 min, E. coli and B. cereus in an exposure time of 15 min.     

Ideal Connes-Amenability of Dual Banach Algebras

Following Runde, we define the concept of ideal Connes-amenability for dual Banach algebras. For an Arens regular dual Banach algebra \({\mathcal {A}}\), we prove that the ideal Connes-amenability of \(\mathcal {A^{**}}\), the second dual of \({\mathcal {A}}\) necessities ideal Connes-amenability of \({{\mathcal {A}}}\). As a typical example, we show that von Neumann algebras are always ideally Connes-amenable. For a locally compact group G, the Fourier–Stieltjes algebra of G is ideally Connes-amenable, but not ideally amenable.     

Character inner amenability for semigroups

Semigroup Forum - Let $$\varphi $$ be a character on a semigroup S. We introduce the notions of $$\varphi $$-inner amenability and character inner amenability for S. We study the relation between...     

The generalized cubic functional equation and the stability of cubic Jordan *-derivations

In the current work, we obtain the general solution of the following generalized cubic functional equation $$\begin{aligned}&f(x+my)+f(x-my)\\&\quad =2\left( 2\cos \left( \frac{m\pi }{2}\right) +m^2-1\right) f(x)-\frac{1}{2}\left( \cos \left( \frac{m\pi }{2}\right) +m^2-1\right) f(2x)\\&\qquad +m^2\{f(x+y)+f(x-y)\} \end{aligned}$$ for an integer $m \ge 1$ . We prove the Hyers–Ulam stability and the superstability for this cubic functional equation by the directed method and a fixed point approach. We also employ the mentioned functional equation to establish the stability of cubic Jordan $*$ -derivations on $C^*$ -algebras and $JC^*$ -algebras.     

On module cohomology of the Fourier algebra of an inverse semigroup

Semigroup Forum - For an inverse semigroup S with the set of idempotents E, we find necessary and sufficient conditions for the Fourier algebra A(S) to be module amenable, module character...