Wave equation for generalized Zener model containing complex order fractional derivatives

We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from the Second Law of Thermodynamics are derived. The initial boundary value problem for such materials is formulated and solution is presented in the form of convolution. Two specific examples are analyzed.     

Generalized group actions in a global setting

We study generalized group actions on differentiable manifolds in the Colombeau framework, extending previous work on flows of generalized vector fields and symmetry group analysis of generalized solutions. As an application, we analyze group invariant generalized functions in this setting.     

Global Controllability for Quasilinear Nonnegative Definite System of ODEs and SDEs

Journal of Optimization Theory and Applications - We consider exact and averaged control problem for a system of quasilinear ODEs and SDEs with a nonnegative definite symmetric matrix of the...     

Identification of the Key Enzyme of Roseoflavin Biosynthesis

The bacteria Streptomyces davawensis and Streptomyces cinnabarinus produce roseoflavin, the only known natural riboflavin (vitamin B₂) analogue with antibiotic activity. Roseoflavin can be considered a natural antimetabolite and has been postulated to be biosynthesized from riboflavin via the key intermediate 8‐demethyl‐8‐aminoriboflavin (AF). The required site‐specific substitution of one of the methyl groups on the dimethylbenzene ring of riboflavin by an amino group (to give AF) is challenging. The pathway from riboflavin to AF has remained elusive, and the corresponding enzyme/s was/were unknown. Herein, we show by systematic gene deletion, heterologous gene expression, and biochemical studies that the enzyme specified by the gene BN159_7989 from S. davawensis is able to carry out a whole set of chemical reactions starting from riboflavin‐5′‐phosphate to give the final product 8‐demethyl‐8‐aminoriboflavin‐5′‐phosphate (AFP).     

The Cattaneo type space-time fractional heat conduction equation

The classical heat conduction equation is generalized using a generalized heat conduction law. In particular, we use the space-time Cattaneo heat conduction law that contains the Caputo symmetrized fractional derivative instead of gradient ${{\partial_x}}$ and fractional time derivative instead of the first order partial time derivative ${{\partial_t}}$ . The existence of the unique solution to the initial-boundary value problem corresponding to the generalized model is established in the space of distributions. We also obtain explicit form of the solution and compare it numerically with some limiting cases.