On the solutions of universal differential equation by noncommutative Picard-Vessiot theory

Basing on Picard-Vessiot theory of noncommutative differential equations and algebraic combinatorics on noncommutative formal series with holomorphic coefficients, various recursive constructions of sequences of grouplike series converging to solutions of universal differential equation are proposed. Basing on monoidal factorizations, these constructions intensively use diagonal series and various pairs of bases in duality, in concatenation-shuffle bialgebra and in a Loday's generalized bialgebra. As applications, the unique solution, satisfying asymptotic conditions, of Knizhnik-Zamolodchikov equations is provided by d\'evissage

Families of eulerian functions involved in regularization of divergent polyzetas

Extending the Eulerian functions, we study their relationship with zeta function of several variables. In particular, starting with Weierstrass factorization theorem (and Newton-Girard identity) for the complex Gamma function, we are interested in the ratios of $\zeta(2k)/\pi^{2k}$ and their multiindexed generalization, we will obtain an analogue situation and draw some consequences about a structure of the algebra of polyzetas values, by means of some combinatorics of noncommutative rational series. The same combinatorial frameworks also allow to study the independence of a family of eulerian functions.Comment: preprin

On The Global Renormalization and Regularization of Several Complex Variable Zeta Functions by Computer

This review concerns the resolution of a special case of Knizhnik-Zamolodchikov equations ($KZ_3$) using our recent results on combinatorial aspects of zeta functions on several variables and software on noncommutative symbolic computations. In particular, we describe the actual solution of $(KZ_3)$ leading to the unique noncommutative series, $\Phi_{KZ}$, so-called Drinfel'd associator (or Drinfel'd series). Non-trivial expressions for series with rational coefficients, satisfying the same properties with $\Phi_{KZ}$, are also explicitly provided due to the algebraic structure and the singularity analysis of the polylogarithms and harmonic sums

Visible light emission from reverse-biased silicon nanometer-scale diode-antifuses

Silicon nanometer-scale diodes have been fabricated to emit light in the visible range at low power consumption. Such structures are candidates for emitter elements in Si-based optical interconnect schemes. Spectral measurements of Electroluminescence (EL) on the reverse-biased nanometer-scale diodes brought into breakdown have been carried out over the photon energy range of 1.4-2.8 eV. Previously proposed mechanisms for avalanche emission from conventional silicon p-n junctions are discussed in order to understand the origin of the emission. Also the stability of the diodes has been tested. Results indicate that our nanometer-scale diodes are basically high quality devices. Furthermore due to the nanometer-scale dimensions, very high electrical fields and current densities are possible at low power consumption. This makes these diodes an excellent candidate to be utilized as a light source in Si-based sensors and actuator application

Remark on the Entropy Production of Adaptive Run-and-Tumble Chemotaxis

Chemotactic active particles, such as bacteria and cells, exhibit an adaptive run-and-tumble motion, giving rise to complex emergent behaviors in response to external chemical fields. This motion is generated by the conversion of internal chemical energy into self-propulsion, allowing each agent to sustain a steady-state far from thermal equilibrium and perform works. The rate of entropy production serves as an indicates of how extensive these agents operate away from thermal equilibrium, providing a measure for estimating maximum obtainable power. Here we present the general framework for calculating the entropy production rate created by such population of agents from the first principle, using the minimal model of bacterial adaptive chemotaxis, as they execute the most basic collective action -- the mass transport

Ultrasound-assisted extraction of GAC peel : an optimization of extraction conditions for recovering carotenoids and antioxidant capacity

The peel of Gac fruit (Momordica cochinchinensis Spreng.), which is considered as waste of Gac processing, has been found to possess high levels of carotenoids and other antioxidants. This study aimed at determining the optimal conditions of an ultrasound-assisted extraction for recovering carotenoids and antioxidant capacity from Gac peel. A response surface methodology using the Box–Behnken design was employed to investigate the impact of extraction time, temperature and ultrasonic power on the recovery of total carotenoid and antioxidant capacity. The results showed that an extraction time of 76 min, temperature of 50 °C and ultrasonic power of 250 W were the optimal conditions for the extraction. The experimental carotenoid yield and antioxidant capacity obtained under the optimal extraction conditions were validated as 269 mg/100 g DW (dry weight) and 822 µM TE (Trolox equivalent)/100 g DW, respectively. These values were not significantly different from the values predicted by the models. The HPLC analysis for carotenoid composition showed that β-carotene, lycopene and lutein were the principal carotenoids of the extract, which constitute 86% of the total carotenoid content. Based on the obtained results, the ultrasound-assisted extraction using ethyl acetate under the above optimal conditions is suggested for the simultaneous recovery of carotenoids and antioxidant capacity from Gac peel