A modular integer GCD algorithm

This paper describes the first algorithm to compute the greatest common divisor (GCD) of two n-bit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A generalization of the binary GCD algorithm, in: ISSAC '93: International Symposium on Symbolic and Algebraic Computation, Kiev, Ukraine, 1993, pp. 111–116; K. Weber, The accelerated integer GCD algorithm, ACM Trans. Math. Softw. 21 (1995) 111–122] when U and V are close to the same size, that replaces U by (U−bV)/p, where p is one of the prime moduli and b is the unique integer in the interval (−p/2,p/2) such that . When the algorithm is executed on a bit common CRCW PRAM with O(nlognlogloglogn) processors, it takes O(n) time in the worst case. A heuristic model of the average case yields O(n/logn) time on the same number of processors.     

R-Matrices for Leibniz Algebras

Leibniz agebras are a generalization of Lie algebras, where no symmetry properties of the bracket are required. In this Letter we introduce a notion of R-matrices for this structure and the related Yang–Baxter equations, and discuss some of their basic properties.     

Modeling Language Evolution

We describe a model for the evolution of the languages used by the agents of a society. Our main result proves convergence of these languages to a common one under certain conditions. A few special cases are elaborated in more depth.     

Evaluation of the Use of Elicitors for the Production of Antioxidant Compounds in Liquid Cultures of Ganoderma curtisii from Costa Rica

The use of substances or conditions as elicitors can significantly increase the production of secondary metabolites. In this research, the effects of different elicitors on the production of antioxidant secondary metabolites were evaluated in a strain of Ganoderma sp. The elicitors tested were pH changes in different growth phases of the fungus (pH 3, 5.5 and 8), different concentrations of peptone as a nitrogen source (1 g/L and 10 g/L), and the addition of chemical agents to the culture medium (ethanol, growth regulators, and salts). The alkaline pH during the stationary phase and the high availability of nitrogen were effective elicitors, producing cultures with higher antioxidant activity (37.87 g/L and 43.13 g/L dry biomass) although there were no significant differences with other treatments.     

Fermion family recurrences in the Dyson–Schwinger formalism

We study the multiple solutions of the truncated propagator Dyson–Schwinger equation for a simple fermion theory with Yukawa coupling to a scalar field. Upon increasing the coupling constant g, other parameters being fixed, more than one non-perturbative solution breaking chiral symmetry becomes possible and we find these numerically. These “recurrences” appear as a mechanism to generate different fermion generations as quanta of the same fundamental field in an interacting field theory, without assuming any composite structure. The number of recurrences or flavors is reduced to the question of the value of the Yukawa coupling, and it has no special profound significance in the standard model. The resulting mass function can have one or more nodes and the measurement that potentially detects them can be thought of as a collider-based test of the virtual dispersion relation for the charged lepton member of each family. This requires the three independent measurements of the charged lepton’s energy, three-momentum and off-shellness. We illustrate how this can be achieved for the (more difficult) case of the tau lepton. PACS 12.15.Ff; 11.30.Rd     

Multi‐responses Methodology Applied in the Electroanalytical Determination of Hair Dye by Using Printed Carbon Electrode Modified with Graphene

This paper describes a rapid and sensitive method for determination of the hair dye Basic Blue 41 in wastewater samples using screen‐printed carbon electrodes modified with graphene (SPCE/Gr). The method is based on the reversible reduction of azo groups of the dye at potential of ?0.23 V/?0.26 V, where both the anodic and cathodic currents increased 1,300 % when compared to screen‐printed carbon (SPCE) and glassy carbon electrodes (GCE). The optimization of a square wave voltammetric method was performed by means of 2³ factorial design, Doehlert matrix and multi‐response assays, and the best parameters were: frequency (54.8 Hz), step potential (6 mV), pulse amplitude (43.7 mV) and pH 4.5. The analytical curve was constructed from 3.00×10^?8 to 2.01×10^?6 mol L^?1, with detection and quantification limits of 5.00×10^?9 and 1.70×10^?8 mol L^?1, respectively. The repeatability of the method evaluated for 10 consecutive measurements at concentrations of 1.70×10^?7 mol L^?1 and 1.70×10^?6 mol L^?1, showed relative standard deviation of 3.56 and 0.57 %, respectively. The sensor based in SPCE/Gr was successfully applied in wastewater samples collected from a drinking water treatment plant and validated by comparison with HPLC‐DAD method with good accuracy.     

Development and application of electrochemical sensor of boron-doped diamond (BDD) modified by drop casting with tin hexacyanoferrate

Journal of Solid State Electrochemistry - This work presents the development and characterization of an electrochemical sensor of tin hexacyanoferrate (SnHCF), produced from the modification by...     

The Cayley–Dickson process for dialgebras

We adapt the algorithm of Kolesnikov and Pozhidaev, which converts a polynomial identity for algebras into the corresponding identities for dialgebras, to the Cayley–Dickson doubling process. We obtain a generalization of this process to the setting of dialgebras, establish some of its basic properties, and construct dialgebra analogues of the quaternions and octonions.