Twisted Hochschild Homology of Quantum Hyperplanes

We calculate the Hochschild dimension of quantum hyperplanes using the twisted Hochschild homology.Comment: 12 pages, LaTe

Quasi-Dirac Operators and Quasi-Fermions

We investigate examples of quasi-spectral triples over two-dimensional commutative sphere, which are obtained by modifying the order-one condition. We find equivariant quasi-Dirac operators and prove that they are in a topologically distinct sector than the standard Dirac operator.Comment: 11 page

The Moyal Sphere

We construct a family of constant curvature metrics on the Moyal plane and compute the Gauss-Bonnet term for each of them. They arise from the conformal rescaling of the metric in the orthonormal frame approach. We find a particular solution, which corresponds to the Fubini-Study metric and which equips the Moyal algebra with the geometry of a noncommutative sphere.Comment: 16 pages, 3 figure

The morphology and application of stem cells in digestive system surgery

Background: Stem cells constitute a group of cells which possess the ability to self-renew as well as the capacity to differentiate into a vast number of different cells within the human organism. Moreover, stem cells are able to undergo a potentially unlimited number of divisions and this characteristic is clinically essential. Specific fields of its application include treatment of diseases mainly in the field of haematology, orthopaedics, surgery, dentistry, and neurology. Materials and methods: In the following work, the current knowledge concerning mechanisms of stem cell treatment in different parts of the digestive system with its diseases as well as adjacent therapy for surgery has been revised. Results: Stem cells therapy may be used in the treatment of various diseases of different parts of the digestive system. This also applies to the end part of the digestive tract (proctological diseases) because stem cells can be used to treat fistulas. Liposuction allows more recovery of mesenchymal stem cells, compared to previous bone marrow harvesting methods. Despite the application of stem cells in the treatment of different diseases used for many years so far, the therapeutic use for the regeneration of the gastrointestinal tract is still rare and unfamiliar. Conclusions: Regenerative medicine seems to be a promising tool in medical research, especially when insulated cells and designed biomaterials are taken into consideration. Major points of discussion include types of stem cells, their origin or differentiation for the treatment of many diseases

Thermal resistance of PCD materials with borides bonding phase

In these studies, one group of PCD materials was prepared using diamond powder and 10 wt % of TiB₂ and the second batch of the PCD material was prepared using a mixture of diamond powder with 5 wt % of TiB₂ and 2 wt % of Co. The materials have been sintered using a Bridgman-type high-pressure apparatus at 8.0±0.2 GPa, at a temperature of 2000±50 °C. Thermogravimetric (TG) measurements and Differential Thermal Analysis (DTA) have been carried out for diamond micropowders, TiB₂ bonding phase, and sintered composites. The coefficients of friction for diamond composites in a sliding contact with an Al₂O₃ ceramic ball have been determined from the room temperature up to 800 °C. Material phase compositions were analyzed for initial samples and after wear tests, at the temperature of 800 °C. Raman spectra of diamond composites with borides bonding phases, observed for the first-order zone centre modes of diamond and graphite during the heating up to 800 °C in air have been presented. Thermal properties have been compared with the commercial diamond-cobalt PCD. It has been found that diamond with TiB₂ and Co is the most resistant to the hardness changes at elevated temperatures and this material maintains the high hardness value up to 800 °C but it has a high coefficient of friction.Досліджено полікристалічні алмазні композити – одну групу матеріалів було приготовано з використанням алмазного порошку і 10 % (за масою) TiB₂, а другу – з алмазного порошку, 5 % (за масою) TiB₂ і 2 % (за масою) Co. Матеріали було спечено в апараті високого тиску типу Бріджмена при тиску 8,0±0,2 ГПа і температурі 2000±50 °С. Термогравіметричні вимірювання та диференційний термічний аналіз було проведено для алмазних мікропорошків, зв’язуючої фази TiB₂ і спечених композітов. Визначено коефіцієнти тертя для алмазних композитів при ковзному контакті з кулькою з кераміки Al₂O₃ при температурі від кімнатної до 800 °С. Фазові склади матеріалів проаналізовано для вихідних зразків і після їх випробування на знос при температурі 800 °С. Представлено спектри комбінаційного розсіювання алмазних композитів зі зв’язуючими фазами боридів, що спостерігаються в центрі зони першого порядку алмазу і графіту в процесі нагрівання до 800 °С на повітрі. Порівнювали термічні властивості отриманих полікристалічних алмазних композитів і промислового композита алмаз–кобальт. Було виявлено, що алмаз з TiB₂ і Co є найбільш стійким до змін твердості при підвищених температурах і зберігає високу твердість до 800 °С, але має високий коефіцієнт тертя.Исследованы поликристаллические алмазных композиты – одна группа материалов была приготовлена с использованием алмазного порошка и 10 % (по массе) TiB₂, а вторая – из алмазного порошка, 5 % (по массе) TiB₂ и 2 % (по массе) Co. Материалы были спечены в аппарате высокого давления типа Бриджмена при давлении 8,0±0,2 ГПа и температуре 2000±50 °С. Термогравиметрические измерения и дифференциальный термический анализ были проведены для алмазных микропорошков, связующей фазы TiB₂ и спеченных композитов. Определены коэффициенты трения для алмазных композитов при скользящем контакте с шариком из керамики Al₂O₃ при температуре от комнатной до 800 °С. Фазовые составы материалов проанализированы для исходных образцов и после их испытания на износ при температуре 800 °С. Представлены спектры комбинационного рассеяния алмазных композитов со связующими фазами боридов, наблюдаемые в центре зоны первого порядка алмаза и графита в процессе нагрева до 800 °С на воздухе. Сравнивали термические свойства полученных поликристаллических алмазных композитов и промышленного поликристаллического композита алмаз–кобальт. Было обнаружено, что алмаз с TiB₂ и Co является наиболее устойчивым к изменениям твердости при повышенных температурах и сохраняет высокую твердость до 800 °С, но имеет высокий коэффициент трения

Reconstruction of the spontaneously broken gauge theory in non-commutative geometry

The scheme previously proposed by the present authors is modified to incorporate the strong interaction by affording the direct product internal symmetry. We do not need to prepare the extra discrete space for the color gauge group responsible for the strong interaction to reconstruct the standard model and the left-right symmetric gauge model(LRSM). The approach based on non-commutative geometry leads us to presents many attractive points such as the unified picture of the gauge and Higgs field as the generalized connection on the discrete space; Minkowski space multipied by N-points discrete space. This approach leads us to unified picture of gauge and Higgs fields as the generalized connection. The standard model needs N=2 discrete space for reconstruction in this formalism. \lr is still alive as a model with the intermediate symmetry of the spontaneously broken SO(10) grand unified theory(GUT). N=3 discrete space is needed for the reconstruction of LRSM to include two Higgs bosons $\phi$ and $\xi$ which are as usual transformed as (2,2*,0)$ and (1,3,-2) under left-handed SU(2)x right-handed SU(2)x U(1), respectively. xi is responsible to make the right handed-neutrino Majorana fermion and so well explains the seesaw mechanism. Up and down quarks have the different masses through the vacuum expectation value of phi.Comment: 21 page

Almost commutative Riemannian geometry: wave operators

Associated to any (pseudo)-Riemannian manifold $M$ of dimension $n$ is an $n+1$-dimensional noncommutative differential structure (\Omega^1,\extd) on the manifold, with the extra dimension encoding the classical Laplacian as a noncommutative `vector field'. We use the classical connection, Ricci tensor and Hodge Laplacian to construct (\Omega^2,\extd) and a natural noncommutative torsion free connection $(\nabla,\sigma)$ on $\Omega^1$. We show that its generalised braiding \sigma:\Omega^1\tens\Omega^1\to \Omega^1\tens\Omega^1 obeys the quantum Yang-Baxter or braid relations only when the original $M$ is flat, i.e their failure is governed by the Riemann curvature, and that \sigma^2=\id only when $M$ is Einstein. We show that if $M$ has a conformal Killing vector field $\tau$ then the cross product algebra $C(M)\rtimes_\tau\R$ viewed as a noncommutative analogue of $M\times\R$ has a natural $n+2$-dimensional calculus extending $\Omega^1$ and a natural spacetime Laplacian now directly defined by the extra dimension. The case $M=\R^3$ recovers the Majid-Ruegg bicrossproduct flat spacetime model and the wave-operator used in its variable speed of light preduction, but now as an example of a general construction. As an application we construct the wave operator on a noncommutative Schwarzschild black hole and take a first look at its features. It appears that the infinite classical redshift/time dilation factor at the event horizon is made finite.Comment: 39 pages, 4 pdf images. Removed previous Sections 5.1-5.2 to a separate paper (now ArXived) to meet referee length requirements. Corresponding slight restructure but no change to remaining conten