Geometrical Frustration: A Study of 4d Hard Spheres

The smallest maximum kissing-number Voronoi polyhedron of 3d spheres is the icosahedron and the tetrahedron is the smallest volume that can show up in Delaunay tessalation. No periodic lattice is consistent with either and hence these dense packings are geometrically frustrated. Because icosahedra can be assembled from almost perfect tetrahedra, the terms "icosahedral" and "polytetrahedral" packing are often used interchangeably, which leaves the true origin of geometric frustration unclear. Here we report a computational study of freezing of 4d hard spheres, where the densest Voronoi cluster is compatible with the symmetry of the densest crystal, while polytetrahedral order is not. We observe that, under otherwise comparable conditions, crystal nucleation in 4d is less facile than in 3d. This suggest that it is the geometrical frustration of polytetrahedral structures that inhibits crystallization.Comment: 4 pages, 3 figures; revised interpretatio

A discrete Laplace-Beltrami operator for simplicial surfaces

We define a discrete Laplace-Beltrami operator for simplicial surfaces. It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian (the so called ``cotan formula'') except that it is based on the intrinsic Delaunay triangulation of the simplicial surface. This leads to new definitions of discrete harmonic functions, discrete mean curvature, and discrete minimal surfaces. The definition of the discrete Laplace-Beltrami operator depends on the existence and uniqueness of Delaunay tessellations in piecewise flat surfaces. While the existence is known, we prove the uniqueness. Using Rippa's Theorem we show that, as claimed, Musin's harmonic index provides an optimality criterion for Delaunay triangulations, and this can be used to prove that the edge flipping algorithm terminates also in the setting of piecewise flat surfaces.Comment: 18 pages, 6 vector graphics figures. v2: Section 2 on Delaunay triangulations of piecewise flat surfaces revised and expanded. References added. Some minor changes, typos corrected. v3: fixed inaccuracies in discussion of flip algorithm, corrected attributions, added references, some minor revision to improve expositio

Unintentional high density p-type modulation doping of a GaAs/AlAs core-multi-shell nanowire

Achieving significant doping in GaAs/AlAs core/shell nanowires (NWs) is of considerable technological importance but remains a challenge due to the amphoteric behavior of the dopant atoms. Here we show that placing a narrow GaAs quantum well in the AlAs shell effectively getters residual carbon acceptors leading to an \emph{unintentional} p-type doping. Magneto-optical studies of such a GaAs/AlAs core multi-shell NW reveal quantum confined emission. Theoretical calculations of NW electronic structure confirm quantum confinement of carriers at the core/shell interface due to the presence of ionized carbon acceptors in the 1~nm GaAs layer in the shell. Micro-photoluminescence in high magnetic field shows a clear signature of avoided crossings of the $n=0$ Landau level emission line with the $n=2$ Landau level TO phonon replica. The coupling is caused by the resonant hole-phonon interaction, which points to a large 2D hole density in the structure.Comment: just published in Nano Letters (http://pubs.acs.org/doi/full/10.1021/nl500818k

The formation of secondary arylphosphines in the reaction of organonickel sigma-complex [NiBr(Mes)(bpy)], where Mes = 2,4,6-trimethylphenyl, bpy = 2,2′-bipyridine, with phenylphosphine

© 2016 Taylor & Francis Group, LLC.The reactivity of organonickel sigma-complex [NiBr(Mes)(bpy)], where Mes = 2,4,6-trimethylphenyl, bpy = 2,2’-bipyridine towards phenylphosphine (PhPH2) has been investigated. It was found that this interaction leads to secondary mesitylphenylphosphine and dimesitylphosphine by formation of new carbon-phosphorus bond involving mesityl fragment of starting organonickel sigma-complex

Study of "racemic compound-like" behavior of diastereomeric mixture of pinanyl sulfoxides by x-ray diffraction, ir spectroscopy, and DFT calculations

The oxidation of a β-hydroxysulfide in the pinane series by use of mchloroperbenzoic acid resulted in the formation of the corresponding β-hydroxysulfoxide as a mixture of two diastereomers in 4:5 ratio. According to single-crystal X-ray diffraction (XRD) results, it is established that the diastereomeric mixture of sulfoxides crystallizes in the "racemic compound-like" manner under formation of asymmetric dimers through S=O··H-O interactions. This asymmetric dimer formed from diastereomeric molecules is a structural unit in both crystal modifications, the triclinic and the monoclinic one. The behavior of the diastereomeric mixture of pinane derived sulfoxides in crystals, melts and in tetrachloromethane solutions was studied by IR spectroscopy. The density functional theory (DFT) method with 6-31G (d, p) basis set was used to calculate the optimized geometrical parameters and vibrational frequencies of different associates in solution. The calculated vibrational frequencies are compared with experimental IR spectra. Copyright © 2014 Taylor & Francis Group, LLC

Применение методов фрактальной и вычислительной геометрии для картографической генерализации линейных объектов

We present an algorithm for simplifying linear cartographic objects and results obtained with a computer program implementing this algorithm.Предлагается новый алгоритм генерализации линейных картографических объектов. Основным новшеством алгоритма является автоматическая сегментация – разбиение ломаной на участки с одинаковыми свойствами. Сегментация позволяет подобрать параметры сглаживания индивидуально для каждого участка, за счет чего существенно повышается качество результата

Bis-phosphonium salts of pyridoxine: The relationship between structure and antibacterial activity

A series of 23 novel bis-phosphonium salts based on pyridoxine were synthesized and their antibacterial activities were evaluated in vitro. All compounds were inactive against gram-negative bacteria and exhibited the structure-dependent activity against gram-positive bacteria. The antibacterial activity enhanced with the increase in chain length at acetal carbon atom in the order n-Pr > Et > Me. Further increasing of length and branching of alkyl chain leads to the reduction of antibacterial activity. Replacement of the phenyl substituents at the phosphorus atoms in 5,6- bis(triphenylphosphonio(methyl))-2,2,8-trimethyl-4H-[1,3]-dioxino[4,5-c] pyridine dichloride (compound 1) with n-butyl, m-tolyl or p-tolyl as well as chloride anions in the compound 1 with bromides (compound 14a) increased the activity against Staphylococcus aureus and Staphylococcus epidermidis up to 5 times (MICs = 1-1.25 μg/ml). But in practically all cases chemical modifications of compound 1 led to the increase of its toxicity for HEK-293 cells. The only exception is compound 5,6-bis[tributylphosphonio(methyl)]-2,2,8- trimethyl-4H-[1,3]dioxino[4,5-c]pyridine dichloride (10a) which demonstrated lower MIC values against S. aureus and S. epidermidis (1 μg/ml) and lower cytotoxicity on HEK-293 cells (CC50 = 200 μg/ml). Compound 10a had no significant mutagenic and genotoxic effects and was selected for further evaluation. It should be noted that all bis-phosphonium salt based on pyridoxine were much more toxic than vancomycin. © 2013 Elsevier Ltd. All rights reserved

Surgical stage in sequential therapy of unresectable oral cancer T3-4bN0-3M0: evaluation of treatment results

Introduction. Unresectable oral cancer is an urgent and complex problem in modern oncology. Annually, the proportion of patients with stage III–IV is 35 %, and the one-year mortality rate for this pathology reaches 32 %. Patients with advanced oral tumors usually have a negative prognosis and treatment tactics are limited to radiation therapy (RT), chemoradiation therapy, or sequential therapy, including induction chemotherapy (CT). Polymodal therapy for oral cancer is of particular interest in the treatment of pathology in this area.The study objective – to analyze the results of sequential treatment, including induction CT followed by RT and induction CT followed by surgery and RT in patients with unresectable oral cancer (T3–4bN0–3M0).Materials and methods. This retrospective study included 30 patients (11 women and 19 men) with primary non-resectable squamous cell carcinoma of the oral cavity (T3–4bN0–3M0) who received 2–3 courses of induction chemotherapy (CT) with DCF (docetaxel, cisplatin, 5-fluorouracil). Mean patients’ age was 61.2 years. The first treatment stage included induction CT according to the following scheme: docetaxel (75 mg/m2 /day on day 1) + cisplatin (75 mg/m2 /day on day 1) + 5-fluorouracil (1000 mg/m2 /day on days 1–4) repeated every 21 days. Study participants were divided into 2 groups according to their objective response to CT. Patients with resectable residual tumors have undergone surgery (after induction CT) followed by radical radiation therapy (RT) (induction CT + surgery + RT). Patients with non-resectable residual tumors/no objective response/no complete response after induction CT have undergone radical RT (induction CT + RT).Results. The objective response rate (ORR) to induction CT was 66.6 % (20 / 30). Five out of thirty patients (16.7 %) received no subsequent therapy: 3 individuals developed grade III–IV adverse events, while 2 individuals had progressive disease. One-third of patients (10 / 30; 33.3 %) had surgery followed by RT. Half of patients (15 / 30; 50 %) received RT after induction CT. The two-year relapse-free survival rates in the groups of induction CT + surgery + RT and induction CT + RT was 14 and 16 %, respectively (p = 0.49). The two-year overall survival rates in the same groups were 44 and 38 %, respectively (р = 0.74).Conclusion. Resectability was achieved in 33.3 % (10 / 30) of patients with initially unresectable oral cancer after induction CT. A sequential therapy regimen, including a surgical stage after induction CT, did not demonstrate a statistically significant increase in overall and disease-free survival rates. Sequential multimodal treatment of common oral cancers has some potential, but requires further study to assess its significance

Comparative analysis of resection boundaries depending on the defect elimination method in oral mucosal cancer

Introduction. Surgical intervention remains the main method for treatment of the oral mucosa cancer. The generally accepted standard of the resection boundary that provides optimal local control is 5 mm. Adequate boundaries of indentation and choice of the reconstruction method are important issues facing specialists in head and neck tumors.   Aim. To evaluate parameters of the resection edge in the surgical treatment of malignant neoplasms of the oral mucosa depending on the method of eliminating of the post-resection defect and its effect on the frequency of local relapse.   Materials and methods. A retrospective analysis included 168 primary patients (50 % men and 50 % women) who received surgical treatment in the head and neck tumor department of the Republican Clinical Oncology Dispensary of the ministry of Health of the Republic of Bashkortostan (ufa) from 2019 to 2023. The median age of patients was 63 years (interquartile range (IQR) 55–69 years). most often, the primary tumor was located in the tongue – in 59.5 % (100/168) of cases. According to the method of post-resection defect removal, the patients were divided into 3 groups. In group 1, reconstruction was performed with local tissues (n = 71), in group 2 – with pedicle flaps (n = 41), and in group 3 – with revascularized flaps (n = 56). The median follow-up period was 18 months (IQR 8–28 months).   Results. Resection boundaries in group 1 were 7.0 mm (IQR 5.0–12.5 mm), in group 2 – 6.5 mm (IQR 5–13 mm), and in group 3 – 12.5 mm (IQR 7.5–15.0 mm). The overall frequency of near/positive resection boundaries was 14.8 % (25/168). In group 1, it was 15.5 % (11/71), in group 2 – 19.5 % (8/41), in group 3 – 10.7 % (6/56). According to the analysis, relapse of the disease after radical treatment was noted in 32 % (55/168) of patients, of which 14.8 % (25/168) had a local relapse, 12.5 % (21/168) had a regional relapse, and 5.4 % (9/168) developed distant metastases. The frequency of local relapse in group 1 was 18.3 % (13/71), in group 2 – 23.8 % (10/41), in group 3 – 5.5 % (3/56). According to the analysis data, statistically significant differences in the boundary of indentation in the groups were revealed depending on the reconstruction method (p = 0.005).   Conclusion. Based on the results of the present retrospective analysis, the choice of reconstruction method affects the resection boundary in real clinical practice. Limitations in the surgical indentation that surgeon faces when choosing a method for eliminating a post-resection defect are demonstrated