In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{...

In this paper, we investigate the Hyers-Ulam stability of the orthogonally  cubic equation and  Pexiderized cubic equation [f(kx+y)+f(kx-y)=g(x+y)+g(x-y)+frac{2}{k}g(kx)-2g(x),]in multi-normed spaces by the direct method and the fixed point method. Moreover, we prove the Hyers-Ulam stability of the  $2$-variables cubic  equation [ f(2x+y,2z+t)+f(2x-y,2z-t) =2...

We present an in situ beam characterization technique to analyze femtosecond optical beams in a folded version of a 2f-2f setup. This technique makes use of a two-dimensional spatial light modulator (SLM) to holographically redirect radiation between different diffraction orders. This manipulation of light between diffraction orders is carried out locally within the beam. Because SLMs can withs...

The PdCl(2)-promoted reactions of methylenecyclopropanes (MCPs) 1 bearing diaryl substituents on the terminal double bond were carefully investigated. The solvents employed significantly affected the reaction outcomes. It was found that dimeric allylpalladium(ii) complexes 2a-2f can be obtained as the sole products in acceptable to good yields under mild reaction conditions with THF as the solv...

In this paper, the 2f/1f tunable diode laser wavelength modulation spectroscopy is used for the simultaneous measurement of concentration and temperature of CO2 in the exhaust plume of an aero engine. The suitability of the R48 spectral feature of CO2 at 1997.2 nm is discussed for this project and for further application of CO2 tomographic imaging on large-scale aero-engines. To ensure accurate...

We propose a new hybrid fault model for clock synchronization and single-round (approximate) agreement in synchronous distributed systems1, which accurately captures both node and link faults. Unlike conventional “global” fault models, which rest upon the total number of faulty nodes in the system, it solely relies upon the number of faults in any two non-faulty nodes’ “perceptions” —conveyed b...

We report the design and synthesis of a series of new cyclometalated iridium hydrides derived from the C-H bond activation of aromatic nitrones and the biological evaluation of these iridium hydrides as antitumor agents. The nitrone ligands are based on the structure of a popular antioxidant, α-phenyl-N-tert-butylnitrone (PBN). Compared to cisplatin, the iridium hydrides exhibit excellent antit...

Up conversion is an Anti-Stokes luminescent process by which photons of low energy are piled up to generate light at a higher energy. Here we show that the addition of fluoride anions to a D2O solution of a macrocyclic erbium complex leads to the formation of a supramolecular [(ErL)2F](+) assembly in which fluoride is sandwiched between two complexes, held together by the synergistic interactio...

A novel series of meta-substituted ethanediamide and 2-butenediamide derivatives were synthesized and tested for their ability to inhibit electric eel acetylcholinesterase (AChE) and equine serum butyrylcholinesterase (BuChE). The synthesized compounds were evaluated against ChE enzymes using the colorimetric method described by Ellman et al. (Biochem. Pharmacol., 7, 1961). It was revealed that...