For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in 2021. In works, approaches to formulate this are based either on power one Sonin kernel or convolution with kernels integer-order integrals. To apply calculus, it is useful have wider range operators, for example, using Laplace different types kernels. paper, an extended formulation proposed. Ext...

The probability density function (PDF) and cumulative distribution function of the sum of L independent but not necessarily identically distributed Gamma variates, applicable to the output statistics of maximal ratio combining (MRC) receiver operating over Nakagami-m fading channels or in other words to the statistical analysis of the scenario where the sum of squared Nakagami-m distributions a...

PURPOSE During the last decades, derivatives and integrals of non-integer orders are being more commonly used for the description of constitutive behavior of various viscoelastic materials including soft biological tissues. Compared to integer order constitutive relations, non-integer order viscoelastic material models of soft biological tissues are capable of capturing a wider range of viscoel...

This paper presents the continuous-time fractional linear systems and their main properties. Two particular classes of models are introduced: autoregressive-moving average type tempered system. For both classes, computations impulse response, transfer function, frequency response discussed. It is shown that such can have integer components. From component we deduce stability. The order always s...

The CoI2(PPh3)2/Zn system effectively catalyzes the [2 + 2 + 2] ene-diyne cycloaddition of 1,6-heptadiynes with allenes in a highly regio- and chemoselective fashion to yield substituted benzene derivatives in good to excellent yields.

A new strategy for Rh(I)-catalyzed [2+2+2] cycloadditions of 1,6-diynes with potassium (Z)-(2-bromovinyl)trifluoroborate as the third two-atom unit has been realized, which provides a facile entry to polysubstituented benzene derivatives.

Hexa-substituted benzene derivatives show larger two-photon cross sections than the corresponding dipolar counterparts and the largest values of delta(max) = 2000 GM and delta(max)/MW = 2.25 GM g(-1) have been obtained with a compound having C[triple bond]C and C=C bonds in the conjugation bridge.

We have successfully developed a new synthetic approach to modulate the electrostatic potentials of metallocavitands and thus their selective recognition towards substituted benzene derivatives via integrating two metal cations of different electronegativity into a self-assembled system.