Color Symmetry, Semigroups, Fractals

We discuss within one common context topics of color symmetry, using semigroups for generalization of symmetry, fractals, and some naturally occurring interrelations thereof. This free essay is emotionally inspired by the impressive scientific work of Prof. Douglas Jay Klein and his numerous collaborators, who contributed into diverse fields of chemistry, physics, and mathematics. (doi: 10.5562/cca2303

Traversing Every Edge in Each Direction Once, But Not at Once: Cubic (Polyhedral) Graphs

A {\em retracting-free bidirectional circuit} in a graph $G$ is a closed walk which traverses every edge exactly once in each direction and such that no edge is succeeded by the same edge in the opposite direction. Such a circuit revisits each vertex only in a number of steps. Studying the class $\mathit{\Omega}$ of all graphs admitting at least one retracting-free bidirectional circuit was proposed by Ore (1951) and is by now of practical use to nanotechnology. The latter needs in various molecular polyhedra that are constructed from a single chain molecule in the retracting-free way. Some earlier results for simple graphs, obtained by Thomassen and, then, by other authors, are specially refined by us for a cubic graph $Q$. Most of such refinements depend only on the number $n$ of vertices of $Q$

Forcing, Freedom, & Uniqueness in Graph Theory & Chemistry

Harary’s & Randić’s ideas of “forcing” & “freedom” involve subsets of double bonds of Kekule structure such as to be unique to that Kekule structure. Such forcing sets are argued to be greatly generalizable to deal with various other coverings, and thence forcing seems to be fundamental, and of notable potential utility. Various forcing invariants associated to (molecular) graphs ensue, with illustrative (chemical) ex-amples and some mathematical consequences being provided. A complementary “uniqueness” idea is not-ed, and the general characteristic of “derivativity” of “forcing” is established (as is relevant for QSPR fit-tings). Different ways in which different sorts of forcings arise in chemistry are briefly indicated.(doi: 10.5562/cca2000

Characterisation of a cobalt-60 small-beam animal irradiator using a realtime silicon pixelated detector

The paper presents a study performed by the Centre for Medical Radiation Physics (CMRP) using a high spatial and temporal resolution silicon pixelated detector named MagicPlate- 512. The study focuses on the characterisation of three pencil beams from a low-dose rate, 6 TBq, cobalt-60 source, in terms of percentage depth dose, beam profiles, output factor and shutter timing. Where applicable, the findings were verified against radiochromic EBT3 film and ionization chambers. It was found that the results of the MagicPlate-512 and film agreed within 0.9 mm for penumbra and full-width at half-maximum measurements of the beam profiles, and within 0.75% for percentage depth dose study. The dose rate of the cobalt-60 source was determined to be (10.65±0.03) cGy/min at 1.5 cm depth in Solid Water. A significant asymmetry of the small pencil beam profile was found, which is due to the irregular machining of the small collimator. The average source shutter speed was calculated to be 26 cm/s. The study demonstrates that the MagicPlate-512 dosimetry system, developed at CMRP, is capable of beam characterisation even in cases of very low dose rate sources

In vivo real-time rectal wall dosimetry for prostate radiotherapy

Rectal balloons are used in external beam prostate radiotherapy to provide reproducible anatomy and rectal dose reductions. This is an investigation into the combination of a MOSFET radiation detector with a rectal balloon for realtime in vivo rectal wall dosimetry. The MOSFET used in the study is a radiation detector that provides a water equivalent depth of measurement of 70 μm. Two MOSFETs were combined in a face-to-face orientation. The reproducibility, sensitivity and angular dependence were measured for the dual MOSFET in a 6 MV photon beam. The dual MOSFET was combined with a rectal balloon and irradiated with hypothetical prostate treatments in a phantom. The anterior rectal wall dose was measured in real time and compared with the planning system calculated dose. The dual MOSFET showed angular dependence within ±2.5% in the azimuth and +2.5%/−4% in the polar axes. When compared with an ion chamber measurement in a phantom, the dual MOSFET agreed within 2.5% for a range of radiation path lengths and incident angles. The dual MOSFET had reproducible sensitivity for fraction sizes of 2–10 Gy. For the hypothetical prostate treatments the measured anterior rectal wall dose was 2.6 and 3.2% lower than the calculated dose for 3DCRT and IMRT plans. This was expected due to limitations of the dose calculation method used at the balloon cavity interface. A dual MOSFET combined with a commercial rectal balloon was shown to provide reproducible measurements of the anterior rectal wall dose in real time. The measured anterior rectal wall dose agreed with the expected dose from the treatment plan for 3DCRT and IMRT plans. The dual MOSFET could be read out in real time during the irradiation, providing the capability for real-time dose monitoring of the rectal wall dose during treatment

Geant4 simulation model of electromagnetic processes in oriented crystals for the accelerator physics

Electromagnetic processes of charged particles interaction with oriented crystals provide a wide variety of innovative applications such as beam steering, crystal-based extraction/collimation of leptons and hadrons in an accelerator, a fixed-target experiment on magnetic and electric dipole moment measurement, X-ray and gamma radiation source for radiotherapy and nuclear physics and a positron source for lepton and muon colliders, a compact crystalline calorimeter as well as plasma acceleration in the crystal media. One of the main challenges is to develop an up-to-date, universal and fast simulation tool to simulate these applications. We present a new simulation model of electromagnetic processes in oriented crystals implemented into Geant4, which is a toolkit for the simulation of the passage of particles through matter. We validate the model with the experimental data as well as discuss the advantages and perspectives of this model for the applications of oriented crystals mentioned above.Comment: 18 pages, 9 figure

Borane Polyhedra as Building Blocks for Unknown but Potentially Isolatable New Molecules – Extensions based on Computations of the Known B18H22 Isomers

Known borane polyhedral cluster characteristics can be used for predicting new architectural constructs. We propose additional structures derived from B18H22 : three positional isomers different from the well-known anti-B18H22 and syn-B18H22 boranes. We have also derived two new cyclic structures based on the condensation of borane pentagonal pyramids and bipyramids. The concatenation of polyhedral borane molecules is also considered from a mathematical point of view. (doi: 10.5562/cca2304

Modular proteins from the Drosophila sallimus (sls) gene and their expression in muscles with different extensibility

The passive elasticity of the sarcomere in striated muscle is determined by large modular proteins, such as titin in vertebrates. In insects, the function of titin is divided between two shorter proteins, projectin and sallimus (Sls), which are the products of different genes. The Drosophila sallimus (sls) gene codes for a protein of 2 MDa. The N-terminal half of the protein is largely made up of immunoglobulin domains and unique sequence; the C-terminal half has two stretches of sequence similar to the elastic PEVK region of titin, and at the end of the molecule there is a region of tandem Ig and fibronectin domains. We have investigated splicing pathways of the sls gene and identified isoforms expressed in different muscle types, and at different stages of Drosophila development. The 5’ half of sls codes for zormin and kettin; both proteins contain Ig domains and can be expressed as separate isoforms, or as larger proteins linked to sequence downstream. There are multiple splicing pathways between the kettin region of sls and sequence coding for the two PEVK regions. All the resulting protein isoforms have sequence derived from the 3’ end of the sls gene. Splicing of exons varies at different stages of development. Kettin RNA is predominant in the embryo, and longer transcripts are expressed in larva, pupa and adult. Sls isoforms in the indirect flight muscle (IFM) are zormin, kettin and Sls(700), in which sequence derived from the end of the gene is spliced to kettin RNA. Zormin is in both M-line and Z-disc. Kettin and Sls(700) extend from the Z-disc to the ends of the thick filaments, though, Sls(700) is only in the myofibril core. These shorter isoforms would contribute to the high stiffness of IFM. Other muscles in the thorax and legs have longer Sls isoforms with varying amounts of PEVK sequence; all span the I-band to the ends of the thick filaments. In muscles with longer Ibands, the proportion of PEVK sequence would determine the extensibility of the sarcomere. Alternative Sls isoforms could regulate the stiffness of the many fibre types in Droso phila muscles