Bacteria and cancer cell pearl chain under dielectrophoresis

In this work, we aim to observe and study the physics of bacteria and cancer cells pearl chain formation under dielectrophoresis (DEP). Experimentally, we visualized the formation of Bacillus subtilis bacterial pearl chain and human breast cancer cell (MCF-7) chain under positive and negative dielectrophoretic force, respectively. Through a simple simulation with creeping flow, AC/DC electric fields, and particle tracing modules in COMSOL, we examined the mechanism by which bacteria self-organize into a pearl chain across the gap between two electrodes via DEP. Our simulation results reveal that the region of greatest positive DEP force shifts from the electrode edge to the leading edge of the pearl chain, thus guiding the trajectories of free-flowing particles toward the leading edge via positive DEP. Our findings additionally highlight the mechanism why the free-flowing particles are more likely to join the existing pearl chain rather than starting a new pearl chain. This phenomenon is primarily due to the increase in magnitude of electric field gradient, and hence DEP force exerted, with the shortening gap between the pearl chain leading edge and the adjacent electrode. The findings shed light on the observed behavior of preferential pearl chain formation across electrode gaps.     

Physical and electrochemical characterizations of LiFePO4-incorporated Ag nanoparticles

Olivine-type LiFePO₄ composite materials for cathode material of the lithium-ion batteries were synthesized by using a sol-gel method and were coated by a chemical deposition of silver particles. As-obtained LiFePO₄/C-Ag (2.1 wt.%) composites were characterized by transmission electron microscopy (TEM), powder X-ray diffraction (XRD), conductivity measurements, cyclic voltammetry, as well as galvanostatic measurements. The results revealed that the discharge capacity of the LiFePO₄/C-Ag electrode is 136.6 mAh/g, which is 7.6% higher than that of uncoated LiFePO₄/C electrode (126.9 mAh/g). The LiFePO₄/C coated by silver nanoparticles enhances the electrode conductivity and specific capacity at high discharge rates. The improved capacity at high discharge rates may be attributed to increased electrode conductivity and the synergistic effect on electron and Li⁺ transport after silver incorporation.     

Teacher preparation for a problem-solving curriculum in Singapore

Problem solving is at the heart of the Singapore Mathematics curriculum. However, it remains a challenge for teachers to realise this curricular goal in practice. Here, we review the efforts of Singapore mathematics teacher educators in incorporating problem-solving (teaching) competency in teacher education and PD programmes. We discuss conceptual and practical issues, actions taken and changes made in building teachers?? capacity to enact a problem-solving curriculum in a school-based design experiment project. In the project, teachers learnt problem solving, observed and then carried out lessons, using the ??Mathematics Practical????akin to the science practical??as key to instruction and assessment.     

Regiospecific Formation and Unusual Optical Properties of 2,5‐Bis(arylethynyl)rhodacyclopentadienes: A New Class of Luminescent Organometallics

A series of 2,5‐bis(arylethynyl)rhodacyclopentadienes has been prepared by a rare example of regiospecific reductive coupling of 1,4‐(p‐R‐phenyl)‐1,3‐butadiynes (R?H, Me, OMe, SMe, NMe₂, CF₃, CO₂Me, CN, NO₂, ?C?C‐(p‐C₆H₄?NHex₂), ?C?C?(p‐C₆H₄?CO₂Oct)) at [RhX(PMe₃)₄] ( 1 ) (X=?C?C?SiMe₃ ( a ), ?C?C‐(p‐C₆H₄?NMe₂) ( b ), ?C?C?C?C?(p‐C₆H₄?NPh₂) ( c ) or ?C?C?{p‐C₆H₄‐C?C?(p‐C₆H₄‐N(C₆H₁₃)₂)} ( d ) or Me ( e )), giving the 2,5‐bis(arylethynyl) isomer exclusively. The rhodacyclopentadienes bearing a methyl ligand in the equatorial plane (compound 1 e ) have been converted into their chloro analogues by reaction with HCl etherate. The rhodacycles thus obtained are stable to air and moisture in the solid state and the acceptor‐substituted compounds are even stable to air and moisture in solution. The photophysical properties of the rhodacyclopentadienes are highly unusual in that they exhibit, exclusively, fluorescence between 500–800 nm from the S₁ state, with quantum yields of Φ=0.01–0.18 and short lifetimes (τ=0.45–8.20 ns). The triplet state formation (Φ_ISC=0.57 for 2 a ) is exceptionally slow, occurring on the nanosecond timescale. This is unexpected, because the Rh atom should normally facilitate intersystem crossing within femto‐ to picoseconds, leading to phosphorescence from the T₁ state. This work therefore highlights that in some transition‐metal complexes, the heavy atom can play a more subtle role in controlling the photophysical behavior than is commonly appreciated.     

On graphs determining links with maximal number of components via medial construction

Let G be a connected plane graph, D(G) be the corresponding link diagram via medial construction, and μ(D(G)) be the number of components of the link diagram D(G). In this paper, we first provide an elementary proof that μ(D(G))≤n(G)+1, where n(G) is the nullity of G. Then we lay emphasis on the extremal graphs, i.e. the graphs with μ(D(G))=n(G)+1. An algorithm is given firstly to judge whether a graph is extremal or not, then we prove that all extremal graphs can be obtained from K₁ by applying two graph operations repeatedly. We also present a dual characterization of extremal graphs and finally we provide a simple criterion on structures of bridgeless extremal graphs.     

Optical color image encryption based on Arnold transform and interference method

In this paper, we propose a novel method to encrypt a color image based on Arnold transform (ART) and interference method. A color image is decomposed into three independent channels, i.e., red, green and blue, and each channel is then encrypted into two random phase masks based on the ART and interference method. Light sources with corresponding wavelengths are used to illuminate the retrieved phase-only masks during image decryption. The influence of security parameters on decrypted images is also analyzed. Numerical simulation results are presented to illustrate the feasibility and effectiveness of the proposed method.     

Non-contact evaluation of the resonant frequency of a microstructure using ultrasonic wave

This paper presents a novel non-contact method for evaluating the resonant frequency of a microstructure, Firstly, the microstructure under test is excited by ultrasonic waves. This excitation method does not impose any undefined load on the specimen like the electrostatic excitation and also this is the first actual use of ultrasonic wave for exciting a microstructure in the literature. Secondly, the amplitudes of the microstructure are determined by image edge detection using a Mexican hat wavelet transform on the vibrating images of the microstructure. The vibrating images are captured by a CCD camera when the microstructure is vibrated by ultrasonic waves at a series of discrete high frequencies （〉30 kHz）. Upon processing the vibrating images, the amplitudes at various excitation frequencies are obtained and an amplitude-frequency spectrum is obtained from which the resonant frequency is subsequently evaluated. A micro silicon structure consisting of a perforated plate （192 × 192 μm） and two cantilever beams （76 × 43 μm） which is about 4 μm thickness is tested. Since laser interferometry is not required, thermal effects on a test object can be avoided. Hence, the setup is relatively simple. Results show that the proposed method is a simple and effective approach for evaluating the dynamic characteristics of microstructures.     

Reviving Pólya's “Look Back” in a Singapore school

This study is based on the stance that Pólya's “Look Back,” though understudied, remains relevant to Mathematics curricula that place emphasis on problem solving. Although the Singapore Mathematics curriculum adopts the goal of teaching Look Back, research about how it is carried out in actual classroom practice is rare. In our project, we focus on a redesign of a teacher development programme that is targeted to help teachers realize Pólya's original vision of Look Back in the classroom. We report the cases of two teachers who have participated in the teacher development programme: their thinking about Look Back (through interview records) and their interpretation of Look Back in their classroom practice (through video records). By bringing these two spheres of data together, we discuss their degree of ‘buy-in’ to Look Back in the overall problem solving enterprise.