The fractional supersymmetry chiral algebras, A(K), in two-dimensional conformal field theory are extended Virasoro algebras with fractional spin currents J (K). We show that associativity and closure of A(K) determines its structure constants in the case that the Virasoro algebra is extended by precisely one current. We compute the structure constants of the A(K) algebras explicitly and we sho...

This work presents a lossy partial differential acoustic wave equation including fractional derivative terms. It is derived from first principles of physics (mass and momentum conservation) and an equation of state given by the fractional Zener stress-strain constitutive relation. For a derivative order α in the fractional Zener relation, the resulting absorption α(k) obeys frequency power-laws...

We prove that fractional k-factors can be transformed among themselves by using a new adjusting operation repeatedly. We introduce, analogous to Berge’s augmenting path method in matching theory, the technique of increasing walk and derive a characterization of maximum fractional k-factors in graphs. As applications of this characterization, several results about connected fractional 1-factors ...

In this paper, we present an impulsive version of Filippov’s Theorem for fractional differential inclusions of the form: D ∗ y(t) ∈ F (t, y(t)), a.e. t ∈ J\{t1, . . . , tm}, α ∈ (1, 2], y(t+k )− y(t − k ) = Ik(y(t − k )), k = 1, . . . ,m, y(t+k )− y (t−k ) = Ik(y (t−k )), k = 1, . . . ,m, y(0) = a, y′(0) = c, where J = [0, b], D ∗ denotes the Caputo fractional derivative and F is a setvalued ma...

k , 0 ≤ k ≤ [α i ], 1 ≤ i ≤ n, where Dα ∗ denote Caputo fractional derivative. The RVIM, for differential equations of integer order is extended to derive approximate analytical solutions for systems of fractional differential equations. Advantage of the RVIM, is simplicity of the computations and convergent successive approximations without any restrictive assumptions or transform functions. S...

Finally, we wrap-up this lecture with our new result which achieves a competitive factor of Õ(log k log n) for the k-server problem on n nodes1. This is joint work with Nikhil Bansal, Niv Buchbinder, and Aleksander Madry. Our basic approach is based on the framework of [CMP08]. The key idea in our work is that instead of using the allocation problem (as suggested by [CMP08]), we use the fractio...

We discuss relationships among T-colorings of graphs and chromatic numbers, fractional chromatic numbers, and circular chromatic numbers of distance graphs. We first prove that for any finite integral set T that contains 0, the asymptotic T-coloring ratio R(T ) is equal to the fractional chromatic number of the distance graph G(Z, D), where D=T&[0]. This fact is then used to study the distance ...

Objective(s): Development of a nanobiosystem by using plant essential oils with green synthesized silver nanoparticles that present synergistic antibacterial activity for overcoming antibiotic resistance in pathogenic bacteria. Material and Methods: Essential oils (EOs) of Kelussia odoratissima and Teucrium polium extracted by hydrodistillation were analyzed by gas chromatography-mass spectrome...

We calculate the transverse velocity fluctuations correlation function of a linear and homogeneous viscoelastic liquid by using a generalized Langevin equation (GLE) approach. We consider a long-ranged (power-law) viscoelastic memory and a noise with a long-range (power-law) auto-correlation. We first evaluate the transverse velocity fluctuations correlation function for conventional time deriv...