Students' Verification Strategies for Combinatorial Problems

We focus on a major difficulty in solving combinatorial problems, namely, on the verification of a solution. Our study aimed at identifying undergraduate students' tendencies to verify their solutions, and the verification strategies that they employ when solving these problems. In addition, an attempt was made to evaluate the level of efficiency of the students' various verification strategies in terms of their contribution to reaching a correct solution. 14 undergraduate students, who had taken at least 1 course in combinatorics, participated in the study. None of the students had prior direct learning experience with combinatorial verification strategies. Data were collected through interviews with individual or pairs of participants as they solved, 1 by 1, 10 combinatorial problems. 5 types of verification strategies were identified, 2 of which were more frequent and more helpful than others. Students' verifications proved most efficient in terms of reaching a correct solution when they were informed that their solution was incorrect. Implications for teaching and learning combinatorics are discussed.     

Cannabis-Derived Compounds Cannabichromene and Δ9-Tetrahydrocannabinol Interact and Exhibit Cytotoxic Activity against Urothelial Cell Carcinoma Correlated with Inhibition of Cell Migration and Cytoskeleton Organization

Cannabis sativa contains more than 500 constituents, yet the anticancer properties of the vast majority of cannabis compounds remains unknown. We aimed to identify cannabis compounds and their combinations presenting cytotoxicity against bladder urothelial carcinoma (UC), the most common urinary system cancer. An XTT assay was used to determine cytotoxic activity of C. sativa extracts on T24 and HBT-9 cell lines. Extract chemical content was identified by high-performance liquid chromatography (HPLC). Fluorescence-activated cell sorting (FACS) was used to determine apoptosis and cell cycle, using stained F-actin and nuclei. Scratch and transwell assays were used to determine cell migration and invasion, respectively. Gene expression was determined by quantitative Polymerase chain reaction (PCR). The most active decarboxylated extract fraction (F7) of high-cannabidiol (CBD) C. sativa was found to contain cannabichromene (CBC) and Δ9-tetrahydrocannabinol (THC). Synergistic interaction was demonstrated between CBC + THC whereas cannabinoid receptor (CB) type 1 and type 2 inverse agonists reduced cytotoxic activity. Treatments with CBC + THC or CBD led to cell cycle arrest and cell apoptosis. CBC + THC or CBD treatments inhibited cell migration and affected F-actin integrity. Identification of active plant ingredients (API) from cannabis that induce apoptosis and affect cell migration in UC cell lines forms a basis for pre-clinical trials for UC treatment.     

Migration in an oscillatory flow of a laminar suspension measured by laser anemometry

Oscillatory flow occurs in a wide range of areas of engineering importance. Two-way lateral migration of particles was observed in the flow of a steady, laminar, dilute, neutrally-buoyant suspension of rigid particles in a tube. The equilibrium particle-position was dependent on the dimensionless Womersley parameter. Experiments were performed in which the Womersley parameter was varied between 1.12 and 8.0. For low values of the parameter, two-way radial migration was observed as in steady, laminar flow. For higher values of the parameter, two equilibrium positions were observed, together with three particle free layers across the radius of the tube.     

Emergence of tables as first-graders cope with modelling tasks

In this action research, first-graders were challenged to cope with a sequence of modelling tasks involving an analysis of given situations and choices of mathematical tools. In the course of the sequence, they underwent a change in the nature of their problem-solving processes and developed modelling competencies. Moreover, during the task sequence, the first-graders spontaneously discovered the power of organizing problem data in a table. They did not merely use their existing mathematical knowledge, but also ‘reinvented’ tables as a new mathematical tool. This paper describes the gradual development of this tool as the children moved along the task sequence. Notably, the first-graders exhibited this progress in spite of having relatively little mathematical knowledge.     

Activities to foster training in nuclear and radiochemistry from IACS,IAEA-Vienna

Summary Given the mismatch between supply of and demand for nuclear scientists, education in nuclear and radiochemistry has become a serious concern. The Nuclear and Radiochemistry in Chemistry Education (NRIChEd) Curriculum Project was undertaken to reintroduce the topics normally covered in a one-semester radiochemistry course into the traditional courses of a four-year chemistry major: general chemistry, organic chemistry, quantitative and instrumental analysis, and physical chemistry. NRIChEd uses a three-pronged approach that incorporates radiochemistry topics when related topics in the basic courses are covered, presents special topics of general interest as a vehicle for teaching nuclear and radiochemistry alongside traditional chemistry, and incorporates the use of non-licensed amounts of radioactive substances in demonstrations and student laboratory experiments. This approach seeks not only to reestablish nuclear science in the chemistry curriculum, but to use it as a tool for elucidating fundamental and applied aspects of chemistry as well. Moreover, because of its relevance in many academic areas, nuclear science enriches the chemistry curriculum by encouraging interdisciplinary thinking and problem solving.     

Quantitative Analysis of Ti-Si-Ge/Si-Ge/Si Structures by EDS and AES

 A method for quantitative analysis of Ti-Si-Ge/Si-Ge/Si structures with submicron thick layers by energy dispersive spectroscopy (EDS) in transmission electron microscopy (TEM) and Auger electron spectroscopy (AES) was developed. Quantitation of the results of both AES and EDS techniques was performed on the basis of a single reference specimen for the Ti-Si-Ge system comprising a uniform layer of the Ti(Si_0.85Ge_0.15)₂ phase on a silicon substrate. The reference sample was prepared by the same procedure as the samples used in the study, and was thoroughly characterized by X-ray diffractometry, transmission electron microscopy and energy dispersive spectroscopy in scanning electron microscopy. Using this reference sample the elemental sensitivity factors relative to Si were found for both techniques, which enable us to obtain the elemental depth distributions for the studied samples. Good agreement between the results obtained by EDS/TEM, AES and supplementary techniques was found.     

The structure of ions and zwitterionic lipids regulates the charge of dipolar membranes

In pure water, zwitterionic lipids form lamellar phases with an equilibrium water gap on the order of 2 to 3 nm as a result of the dominating van der Waals attraction between dipolar bilayers. Monovalent ions can swell those neutral lamellae by a small amount. Divalent ions can adsorb onto dipolar membranes and charge them. Using solution X-ray scattering, we studied how the structure of ions and zwitterionic lipids regulates the charge of dipolar membranes. We found that unlike monovalent ions that weakly interact with all of the examined dipolar membranes, divalent and trivalent ions adsorb onto membranes containing lipids with saturated tails, with an association constant on the order of ～10 M(-1). One double bond in the lipid tail is sufficient to prevent divalent ion adsorption. We suggest that this behavior is due to the relatively loose packing of lipids with unsaturated tails that increases the area per lipid headgroup, enabling their free rotation. Divalent ion adsorption links two lipids and limits their free rotation. The ion-dipole interaction gained by the adsorption of the ions onto unsaturated membranes is insufficient to compensate for the loss of headgroup free-rotational entropy. The ion-dipole interaction is stronger for cations with a higher valence. Nevertheless, polyamines behave as monovalent ions near dipolar interfaces in the sense that they interact weakly with the membrane surface, whereas in the bulk their behavior is similar to that of multivalent cations. Advanced data analysis and comparison with theory provide insight into the structure and interactions between ion-induced regulated charged interfaces. This study models biologically relevant interactions between cell membranes and various ions and the manner in which the lipid structure governs those interactions. The ability to monitor these interactions creates a tool for probing systems that are more complex and forms the basis for controlling the interactions between dipolar membranes and charged proteins or biopolymers for encapsulation and delivery applications.     

A Counter Example to Cercignani’s Conjecture for the <Emphasis Type="Italic">d</Emphasis> Dimensional Kac Model

Kac’s d dimensional model gives a linear, many particle, binary collision model from which, under suitable conditions, the celebrated Boltzmann equation, in its spatially homogeneous form, arise as a mean field limit. The ergodicity of the evolution equation leads to questions about the relaxation rate, in hope that such a rate would pass on the Boltzmann equation as the number of particles goes to infinity. This program, starting with Kac and his one dimensional ‘Spectral Gap Conjecture’ at 1956, finally reached its conclusion in the Maxwellian case in a series of papers by authors such as Janvresse, Maslen, Carlen, Carvalho, Loss and Geronimo, but the hope to get a limiting relaxation rate for the Boltzmann equation with this linear method was already shown to be unrealistic (although the problem is still important and interesting due to its connection with the linearized Boltzmann operator). A less linear approach, via a many particle version of Cercignani’s conjecture, is the grounds for this paper. In our paper, we extend recent results by the author from the one dimensional Kac model to the d dimensional one, showing that the entropy-entropy production ratio, Γ _N , still yields a very strong dependency in the number of particles of the problem when we consider the general case.     

Large deviations for ℤ d -Actions

We establish large deviations bounds for translation invariant Gibbs measures of multidimensional subshifts of finite type. This generalizes [FO] and partially [C, O, and B], where only full shifts were considered. Our framework includes, in particular, the hard-core lattice gas models which are outside of the scope of [FO, C, O, and B].Partially supported by US-Israel BSF. Partially sponsored by the Edmund Landau Center for research in Mathematical Analysis, supported by the Minerva Foundation (Germany).