Fixed point theorems for the sum of two weakly sequentially continuous mappings

In the present paper, we prove some Krasnosel’skii-Leray-Schauder type fixed point theorems for weak topology. Some fixed point theorems for the sum of two weakly sequentially continuous mappings are also presented. Our results extend and improve on ones from several earlier works.     

The antipodal mapping theorem and difference equations in Banach spaces†

We employ the Borsuk–Krasnoselskii antipodal theorem to prove a new fixed point theorem in ordered Banach spaces. Then, the applicability of the result is shown by presenting sufficient conditions for the existence of solutions to initial value problems for first-order difference equations in Banach spaces. To prove that result we shall employ set valued analysis techniques.     

Biocatalytic anode for glucose oxidation utilizing carbon nanotubes for direct electron transfer with glucose oxidase

Covalently linked layers of glucose oxidase, single-wall carbon nanotubes and poly-l-lysine on pyrolytic graphite resulted in a stable biofuel cell anode featuring direct electron transfer from the enzyme. Catalytic response observed upon addition of glucose was due to electrochemical oxidation of FADH₂ under aerobic conditions. The electrode potential depended on glucose concentration. This system has essential attributes of an anode in a mediator-free biocatalytic fuel cell.     

Cucurbit[7]uril mediates the stereoselective [4+4] photodimerization of 2-aminopyridine hydrochloride in aqueous solution

The 2:1 guest-host complex of 2-aminopyridine hydrochloride with cucurbit[7]uril (CB[7]) undergoes a stereoselective [4+4] photodimerization reaction in aqueous solution to yield exclusively the anti-trans isomer of 4,8-diamino-3,7-diazatricyclo[4.2.2.2(2,5)]dodeca-3,7,9,11-tetraene, and in the absence of CB[7], the photochemical reaction produces the anti-trans and syn-trans photodimers in a 4:1 ratio. In addition, encapsulation of the photodimer product in the CB[7] cavity stabilizes it with respect to the otherwise observed rearomatization to the 2-aminopyridine monomer at room temperature.     

Inhibition of C(2)-H/D exchange of a bis(imidazolium) dication upon complexation with cucubit[7]uril

Inclusion of the alpha,alpha'-bis(3-(1-methylimidazolium))-p-xylene dication in cucurbit[7]uril (CB[7], K(CB[7]) = (4.3 x 10(9) M(-1)), with C-H...O=C hydrogen bonding between the guest C(2)-protons and the carbonyl oxygens of the host portals, inhibits the H/D exchange for the C(2)-proton with k(OD) (25 degrees C, D2O) decreasing from 1.2 x 10(3) M(-1) s(-1) (pKa = 22.3) in the absence of CB[7] to 0.9 M(-1) s(-1) (pKa = 25.4) in the presence of 1.1 equiv. CB[7].     

Impact of a conformationally restricted receptor on the BF2 chelated azadipyrromethene fluorosensing platform

Conformational control of the receptor-fluorophore orientation of BF2 chelated azadipyrromethene sensors reveals two photophysically different modes of analyte triggered fluorescence switching both of which exhibit large off-on fluorescence intensity responses to the light input-output of the sensors in the visible red spectral region.     

Infinitely many solutions for fractional Schrodinger-Maxwell equations

In this paper using fountain theorems we study the existence of infinitely many solutions for fractional Schr\"{o}dinger-Maxwell equations \[\begin{cases} (-\Delta)^\alpha u+\lambda V(x)u+\phi u=f(x,u)-\mu g(x)|u|^{q-2}u, \text{ in } \mathbb R^3,\(-\Delta)^\alpha \phi=K_\alpha u^2, \text{ in } \mathbb R^3, \end{cases}\] where $\lambda,\mu >0$ are two parameters, $\alpha\in (0,1]$, $K_\alpha=\frac{\pi^{-\alpha}\Gamma(\alpha)}{\pi^{-(3-2\alpha)/2}\Gamma((3-2\alpha)/2)}$ and $(-\Delta)^\alpha$ is the fractional Laplacian. Under appropriate assumptions on $f$ and $g$ we obtain an existence theorem for this system.     

Positive solutions for a nonlinear discrete fractional boundary value problem with a $p$-Laplacian operator

In this paper using the monotone iterative technique we establish the existence and uniqueness of positive solutions for a nonlinear discrete fractional boundary value problem with a $p$-Laplacian operator. Also we discuss an iterative sequence which yields the approximate solution for this problem.