Kinetical Study of the Catalytic Hydrogenation of Catechol by Metals

In this paper, the kinetical study of catalytic hydrogenation of catechol over platinum metal catalysts in liquid phase under room temperature and one atmospheric pressure was investigated. Simple models “straight line” model 1 together with “triangle” model 2 were used to interpret for the change of compositions of samples traced during the reaction process, and the interpretation was found to be satisfactory. These models are as following: Model 1: consecutive reaction path catechol→2-hydroxycyclohexanone→cyclohexane-1,2-diol Model 2: catechol→cyclohexane-1, 2-diol directly was added to reaction path of model 1. The relative reaction rates during hydrogenation processes over ruthenium, rhodium, palladium and platinum were calculated too. It was also found that the strength of oxygen affinity with catalysts was the factor influenced the selectivity of reaction path and the stereoselectivity of cis and trans diol products.     

The structure of di-μ-pentafluorobenzoatobis[bis(pentafluorophenyl)(triphenylphosphine oxide)thallium(iii)]

An X-ray crystallographic study has shown that the complex (C₆H₅)₂TlO₂CC₆F₅(OPPh₃) has a dimeric structure with unsymmetrical pentafluorobenzoate bridging (TlO 2.531 and 2.789 Å) but an exact crystallographic centre of symmetry. The pentafluorobenzoate groups are also unsymmetrically chelated to thallium (TlO 2.389 and 2.531 Å.), which overall has irregular six coordination.     

Differentiation of teaching and learning mathematics: an action research study in tertiary education

Diversity and differentiation within our classrooms, at all levels of education, is nowadays a fact. It has been one of the biggest challenges for educators to respond to the needs of all students in such a mixed-ability classroom. Teachers’ inability to deal with students with different levels of readiness in a different way leads to school failure and all the negative outcomes that come with it. Differentiation of teaching and learning helps addressing this problem by respecting the different levels that exist in the classroom, and by responding to the needs of each learner. This article presents an action research study where a team of mathematics instructors and an expert in curriculum development developed and implemented a differentiated instruction learning environment in a first-year engineering calculus class at a university in Cyprus. This study provides evidence that differentiated instruction has a positive effect on student engagement and motivation and improves students’ understanding of difficult calculus concepts.     

Fibonacci Numbers and an Area Puzzle: Connecting Geometry and Algebra in the Mathematics Classroom

A mathematical puzzle that asks about “missing” area leads to an exploration of the Fibonacci sequence as well as genuine inquiry in plane geometry connected to algebra. This article discusses the inquiry, the concepts, the solution, and an extension that deepens all students’ understanding of connections between algebra and geometry.     

Cultural influences on sex differentials in mathematics aptitude and achievement

Results of mathematics testing of 14‐year‐olds and college freshmen in the West Bank indicate more substantial variation on the basis of cultural factors than on the basis of gender. In particular, no significant difference in the mathematical abilities of men and women appeared in the college group.     

Fastest mixing Markov chain problem for the union of two cliques

A symmetric, random walk on a graph G can be defined by prescribing weights to the edges in such a way that for each vertex the sum of the weights of the edges incident to the vertex is at most one. The fastest mixing, Markov chain (FMMC) problem for G is to determine the weighting that yields the fastest mixing random walk. We solve the FMMC problem in the case that G is the union of two complete graphs.     

Reverse Order Law for the Group Inverse in Semigroups and Rings

In this paper, we provide equivalent conditions for the two-sided reverse order law for the group inverse (ab)^# = b ^# a ^# and (ba)^# = a ^# b ^#, in semigroups and rings. Moreover, we prove that, under finiteness conditions, these conditions are also equivalent with the one-sided reverse order law (ab)^# = b ^# a ^#.