Thermal Wave Measurements with a Mirage Detection for Investigation of Thermal Diffusivity of GdCa4O(BO3)3 Single Crystals

Single crystals of GdCa4O(BO3)3 were examined to determine their thermal properties. Samples were grown by the Czochralski pulling technique. There were three types of samples: a pure crystal, the crystal doped with neodymium (4 at.% of Nd), and the third one doped with ytterbium (7 at.% of Yb). All samples were rectangular prisms with edges parallel to the axes of the optical indicatrix X, Y , Z (principal axes). The thermal diffusivity was determined by means of the thermal wave method with the optical detection of the temperature disturbance based on a mirage effect. Experimental results showed anisotropy of the thermal diffusivity. The thermal diffusivity along Y direction has the highest value while values obtained in X and Z axes are much lower. Dopants cause decrease in the thermal diffusivity for all investigated directions

Studying Algebraic Structures Using Prover9 and Mace4

In this chapter we present a case study, drawn from our research work, on the application of a fully automated theorem prover together with an automatic counter-example generator in the investigation of a class of algebraic structures. We will see that these tools, when combined with human insight and traditional algebraic methods, help us to explore the problem space quickly and effectively. The counter-example generator rapidly rules out many false conjectures, while the theorem prover is often much more efficient than a human being at verifying algebraic identities. The specific tools in our case study are Prover9 and Mace4; the algebraic structures are generalisations of Heyting algebras known as hoops. We will see how this approach helped us to discover new theorems and to find new or improved proofs of known results. We also make some suggestions for how one might deploy these tools to supplement a more conventional approach to teaching algebra.Comment: 21 pages, to appear as Chapter 5 in "Proof Technology in Mathematics Research and Teaching", Mathematics Education in the Digital Era 14, edited by G. Hanna et al. (eds.), published by Springe

Evidence for the Gompertz Curve in the Income Distribution of Brazil 1978-2005

This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form $G(x)=\exp [\exp (A-Bx)]$, where $x$ is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution $P(x)= \beta x^{-\alpha}$. This result means that similarly to other countries, Brazil's income distribution is characterized by a well defined two class system. The parameters $A$, $B$, $\alpha$, $\beta$ were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil's economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.Comment: 22 pages, 15 figures, 4 tables. LaTeX. Accepted for publication in "The European Physical Journal B

A method for finding new sets of axioms for classes of semigroups

We introduce a general technique for finding sets of axioms for a given class of semigroups. To illustrate the technique, we provide new sets of defining axioms for groups of exponent n, bands, and semilattices

A Facile Electrochemical Preparation of Reduced Graphene Oxide@Polydopamine Composite: A Novel Electrochemical Sensing Platform for Amperometric Detection of Chlorpromazine

© 2016 The Author(s). We report a novel and sensitive amperometric sensor for chlorpromazine (CPZ) based on reduced graphene oxide (RGO) and polydopamine (PDA) composite modified glassy carbon electrode. The RGO@PDA composite was prepared by electrochemical reduction of graphene oxide (GO) with PDA. The RGO@PDA composite modified electrode shows an excellent electro-oxidation behavior to CPZ when compared with other modified electrodes such as GO, RGO and GO@PDA. Amperometric i-t method was used for the determination of CPZ. Amperometry result shows that the RGO@PDA composite detects CPZ in a linear range from 0.03 to 967.6 μM. The sensor exhibits a low detection limit of 0.0018 μM with the analytical sensitivity of 3.63 ± 0.3 μAμM-1 cm-2. The RGO@PDA composite shows its high selectivity towards CPZ in the presence of potentially interfering drugs such as metronidazole, phenobarbital, chlorpheniramine maleate, pyridoxine and riboflavin. In addition, the fabricated RGO@PDA modified electrode showed an appropriate recovery towards CPZ in the pharmaceutical tablets