Intersection of ultrafilters may have measure zero

We show that it is consistent with ZFC that the intersection of some family of less than ultrafilters have measure zero. This answers a question of D. Fremlin.The author thanks the Lady Davis Fellowship Trust for full supportPartially supported by Basic Research Fund, Israel Academy of Sciences, publication 436     

The essential nonlinearity ofN-level quantum thermodynamics

This paper explores the possibility that linear dynamical maps might be used to describe the energy-conserving, entropy-increasing motions which occur in closed thermodynamic systems as they approach canonical thermal equilibrium. ForN-level quantum systems withN>2, we prove that no such maps exist which are independent of the initial state.     

An investigation of the laryngeal system as the resonance source of the singer''s formant

Since its introduction, the Sundberg model of the laryngeal system as the resonance source of the singer's formant has gained wide acceptance. However, no studies directly testing this hypothesis in vivo have previously been reported. Thus, the present study was undertaken to test this hypothesis on three classically trained professional male singers. The vocal behaviors of the singer-subjects were evaluated during modal and pulse register phonation via magnetic resonance imaging, strobolaryngoscopy, and acoustic analysis. Results indicated the subjects did not achieve the laryngopharyngeal/laryngeal outlet cross-sectional area ratio requisite to the model and that the formant remained robust in pulse register phonation. It was concluded that these subjects' behaviors were not consistent with Sundberg's model and that the model was inadequate to account for the generation of the singer's formant in these three subjects.     

Cavity resonant mode in a metal film perforated with two-dimensional triangular lattice hole arrays

The transmission property of metallic films with two-dimensional hole arrays is studied experimentally and numerically. For a triangular lattice subwavelength hole array in a 150 nm thick Ag film, both cavity resonance and planar surface modes are identified as the sources of enhanced optical transmissions. Semi-analytical models are developed for calculating the dispersion relation of the cavity resonant mode. They agree well with the experimental results and full-wave numerical calculations. Strong interaction between the cavity resonant mode and surface modes is also observed.     

How do they know it is a parallelogram? Analysing geometric discourse at van Hiele Level 3

In this article, we introduce Sfard's discursive framework and use it to investigate prospective teachers' geometric discourse in the context of quadrilaterals. In particular, we focus on describing and analysing two participants' use of mathematical words and substantiation routines related to parallelograms and their properties at van Hiele level 3 thinking. Our findings suggest that a single van Hiele level of thinking encompasses a range of complexity of reasoning and differences in discourse and thus a deeper investigation of students' mathematical thinking within assigned van Hiele levels is warranted.     

Numerical simulations for tumor and cellular immune system interactions in lung cancer treatment

We investigate a new mathematical model that describes lung cancer regression in patients treated by chemotherapy and radiotherapy. The model is composed of nonlinear integro-differential equations derived from the so-called kinetic theory for active particles and a new sink function is investigated according to clinical data from carcinoma planoepitheliale. The model equations are solved numerically and the data are utilized in order to find their unknown parameters. The results of the numerical experiments show a good correlation between the predicted and clinical data and illustrate that the mathematical model has potential to describe lung cancer regression.     

Comment on “Role of the velocity frame of reference in thermodiffusion in liquid mixtures” by M. Eslamian,C.G. Jiang and M.Z. Saghir

We analyze the material transport equations (MTE) derived by Eslamian and co-authors and address the criticism expressed regarding the approach formulated in our previous work. In doing so, we show that the MTE formulated by Eslamian and co-authors are valid only in closed stationary non-isothermal systems in combination with the restrictions on the Onsager coefficients formulated in our work which is criticized, and that for non-stationary systems the approach we took can be used.