Thermal Decomposition Kinetics of Some Metal Complexes of 2,3-Hydroxyimino-4-phenyl-6-phenyazo-1-thia-4,5-diazacyclohexa-5-diene

The Ni(II), Cu(II) Co(II) and Zn(II) complexes of 2,3‐hydroxyimino‐4‐phenyl‐6‐phenyazo‐1‐thia‐4,5‐diaza‐ cyclohexa‐5‐diene (H₂L) were synthesized. Thermal behavior of these complexes was studied in dynamic nitrogen atmosphere by TA (thermogravimetric analysis), DTA (differential thermal analysis) and DTG (differential thermal gravimetry) techniques. The reaction order, the activation energies, the entropies, the enthalpies, the free energies, and the pre‐exponential factors of the thermal decomposition reactions were calculated from the thermogravimetric curves. The kinetic analysis of the thermogravimetric data was performed by using several methods such as MacCallum‐Tanner (MT), van Krevelen (vK), Madhusudanan‐Krishnan‐Ninan (MKN), Wanjun‐Yuwen‐Hen‐Cunxin (WYHC), Horowitz‐Metzger (HM) and Coats‐Redfern method (CR) based on the single heating rate. Most appropriate methods were determined for each decomposition step according to the least‐square linear regression. The Ni(II), Cu(II) Co(II) and Zn(II) complexes displayed one‐ or two‐stage decomposition pattern when heating in a dynamic nitrogen atmosphere and metal oxides remained as end products of the complexes. The characterization of the end products of the decomposition was performed by X‐ray diffraction.     

Hydrogenated Graphene and Hydrogenated Silicene: Computational Insights

Density functional calculations are performed to study the energetic, structural, and electronic properties of graphene and silicene functionalized with hydrogen. Our calculations predict that H atoms bind much more strongly to silicene than to graphene. The adsorbed H atoms tend to cooperatively stabilize each other leading to a two‐dimensional nucleation and growth mechanism. The different structural and electronic modifications induced by H in fully functionalized graphene and silicene (known as graphane and silicane) are also explained. Finally, the electronic properties of defective graphane with multiple hydrogen vacancies are investigated. Engineering the vacancies in graphane offers a way to modify the electronic properties of this material.     

Hermite interpolation with symmetric polynomials

We study the Hermite interpolation problem on the spaces of symmetric bivariate polynomials. We show that the multipoint Berzolari-Radon sets solve the problem. We also give a Newton formula for the interpolation polynomial and use it to prove a continuity property of the interpolation polynomial with respect to the interpolation points.     

Analysis of the mean squared derivative cost function

In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by‐product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory. Copyright © 2017 John Wiley & Sons, Ltd.     

Common Core State Standards in the Middle Grades: What's New in the Geometry Domain and How Can Teachers Support Student Learning?

The Common Core State Standards for Mathematics (CCSSM) is a primary focus of attention for many stakeholders' (e.g., teachers, district mathematics leaders, and curriculum developers) intent on improving mathematics education. This article reports on specific content shifts related to the geometry domain in the middle grades (6–8) mathematics curriculum. The methodology employed allows for comparisons of content across multiple standards documents. We report on some dramatic changes with regards to the geometry content taught in the middle grades. We found 52% of the middle grades geometry CCSSM learning expectations will be new to the respective grade level at which they are taught in at least six of the eight states analyzed in this study (57% in grade 6, 50% in grade 7, and 50% in grade 8). We also highlight three areas that represent “new” geometry content at the middle grades based on our analysis of CCSSM and pre‐CCSSM state standards.     

Twostep-by-twostep continuous PIRKN-type PC methods for nonstiff IVPs

In this paper, we start with the consideration of direct collocation-based Runge-Kutta-Nyström (RKN) methods with continuous output formulas for solving nonstiff initial-value problems (IVPs) for systems of special second-order differential equations y″(t) = f(t, y(t)). At nth step, the continuous output formulas can be used for calculating the step values at (n + 2)th step and the integration processes can be proceeded twostep-by-twostep. In this case, we obtain twostep-by-twostep RKN methods with continuous output formulas (continuous TBTRKN methods). Furthermore, we consider a parallel predictor-corrector (PC) iteration scheme using the continuous TBTRKN methods as corrector methods with predictor methods defined by the continuous output formulas. The resulting twostep-by-twostep parallel-iterated RKN-type PC methods with continuous output formulas (twostep-by-twostep continuous PIRKN-type PC methods or TBTCPIRKN methods) give us a faster integration processes. Numerical comparisons based on the solution of a few widely-used test problems show that the new TBTCPIRKN methods are much more efficient than the well-known PIRKN methods, the famous nonstiff sequential ODEX2, DOP853 codes and comparable with the CPIRKN methods.