Criteria for the solubility of finite groups by their centralizers

For any group G, let C(G){\mathcal{C}(G)} denote the set of centralizers of G. We say that a group G has n centralizers (G is a C_n{\mathcal{C}_n}-group) if |C(G)| = n{|\mathcal{C}(G)| = n}. In this note, we show that the derived length of a soluble C_n{\mathcal{C}_n}-group (not necessarily finite) is bounded by a function of n.     

A note on quasi-permutation representations of groups with two character degrees

In Behravesh (J. Lond. Math. Soc. (2) 55:251–260, 1997), we gave algorithms to calculate c(G), q(G) and p(G) for a finite group G. In this paper we will show that in groups with two character degrees we may have c(G)=q(G)≠p(G).     

Students’ ways of understanding a proof

We present a model for describing the growth of students’ understandings when reading a proof. The model is composed of two main paths. One is focused on becoming aware of the deductive structure of the proof, in other words, understanding the proof at a semantic level. Generalization, abstraction, and formalization are the most important transitions in this path. The other path focuses on the surface-level form of the proof, and the use of symbolic representations. At the end of this path, students understand how and why symbolic computations formally establish a claim, at a syntactic level. We make distinctions between states in the model and illustrate them with examples from early secondary students’ mathematical activity. We then apply the model to one student’s developing understanding in order to show how the model works in practice. We close with some suggestions for further research.     

Students' attitude towards computer algebra systems (CAS) and their choice of using CAS in problem-solving

We explore students choice of using computer algebra systems (CAS) in problem-solving relative to their self-reported attitude towards learning mathematics with CAS. Our research design is a case study of nine Norwegian upper-secondary mathematics students with a wide range of attitude towards CAS. Our findings on routine problems indicate that (1) students use CAS whenever students perceive the problem as time-consuming regardless of their attitude towards CAS, and (2) students attitude affects their use of CAS whenever students perceive the problem as non-time-consuming. Norway, among other countries, has implemented CAS as an essential digital resource towards learning mathematics in upper-secondary school. Our discussion focuses on the implications of our findings have on local mathematics educators and national policy-makers.     

Queues with Simultaneous Arrival of Customers and the Dependence Structure of the Waiting Times

Methodology and Computing in Applied Probability - We consider a queueing system where some customers decide to simultaneously wait in two queues, rather than in a single queue, to receive their...     

The Effect of Wettability on Waterflood Oil Recovery in Carbonate Rock Samples: A Systematic Multi-scale Experimental Investigation

Transport in Porous Media - On the basis of a well-based model (Model I) developed in a previous work (Liu and Valkó in SPE J 2019. https://doi.org/10.2118/197049-PA ), in which a fractional...     

Nonlinear vibration mitigation of a flexible rotor shaft carrying a longitudinally dispositioned unbalanced rigid disc

Nonlinear Dynamics - This study is dedicated to investigate the nonlinear dynamics of a system composed of a flexible rotor shaft carrying a longitudinally dispositioned unbalanced rigid disc. The...     

CD47 in the Brain and Neurodegeneration: An Update on the Role in Neuroinflammatory Pathways

CD47 is a receptor belonging to the immunoglobulin (Ig) superfamily and broadly expressed on cell membranes. Through interactions with ligands such as SIRPα, TSP-1, integrins, and SH2-domain bearing protein tyrosine phosphatase substrate-1 (SHPS-1), CD47 regulates numerous functions like cell adhesion, proliferation, apoptosis, migration, homeostasis, and the immune system. In this aspect, previous research has shown that CD47 modulates phagocytosis via macrophages, the transmigration of neutrophils, and the activation of T-cells, dendritic cells, and B-cells. Moreover, several studies have reported the increased expression of the CD47 receptor in a variety of diseases, including acute lymphoblastic leukemia (ALL), chronic myeloid leukemia, non-Hodgkin’s lymphoma (NHL), multiple myeloma (MM), bladder cancer, acute myeloid leukemia (AML), Gaucher disease, Multiple Sclerosis and stroke among others. The ubiquitous expression of the CD47 cell receptor on most resident cells of the CNS has previously been established through different methodologies. However, there is little information concerning its precise functions in the development of different neurodegenerative pathologies in the CNS. Consequently, further research pertaining to the specific functions and roles of CD47 and SIRP is required prior to its exploitation as a druggable approach for the targeting of various neurodegenerative diseases that affect the human population. The present review attempts to summarize the role of both CD47 and SIRP and their therapeutic potential in neurodegenerative disorders.     

Molecular dynamics simulations of hydrogen adsorption/desorption by palladium decorated single-walled carbon nanotube bundle

Utilising molecular dynamics simulations, the hydrogen molecules adsorption isotherms of the (8,?0) palladium decorated single-walled carbon nanotube (SWNT) were obtained. The hydrogen adsorption was studied on the external, interstial and internal surfaces of the SWNT bundle at several temperatures ranging from 77 to 400?K. The results were compared with the bare single-walled carbon nanotube bundle under the same conditions. The decorated carbon nanotube bundle hydrogen adsorption was significantly higher than that of the bare one. The hydrogen desorption and readsorption were studied using temperature as the readsorption/desorption variable. The rate constants were calculated for the hydrogen desorption at different temperatures. The calculated decorated SWNT bundle hydrogen desorption activation energy was higher than that for the bare SWNT bundle. The calculated activation energies for the hydrogen desorption in both nanotube bundles specified the temperature dependency of hydrogen desorption.