The role of a form of vector potential - normalization of the antisymmetric gauge

Results obtained for the antisymmetric gauge A=[Hy,-Hx]/2 by Brown and Zak are compared with those based on pure group-theoretical considerations and corresponding to the Landau gauge A=[0,Hx]. Imposing the periodic boundary conditions one has to be very careful since the first gauge leads to a factor system which is not normalized. A period N introduced in Brown's and Zak's papers should be considered as a magnetic one, whereas the crystal period is in fact 2N. The `normalization' procedure proposed here shows the equivalence of Brown's, Zak's, and other approaches. It also indicates the importance of the concept of magnetic cells. Moreover, it is shown that factor systems (of projective representations and central extensions) are gauge-dependent, whereas a commutator of two magnetic translations is gauge-independent. This result indicates that a form of the vector potential (a gauge) is also important in physical investigations.Comment: RevTEX, 9 pages, to be published in J. Math. Phy

Development of novel laser processes for ophthalmology and dentistry

This thesis is focused on the development of novel laser processes for ophthalmology and dentistry. Firstly an in-depth investigation into the possibility of using 10.6 μm CO2 laser radiation for removal of hard dental tissue is presented. Different processing regimes are investigated to find optimal processing parameters that allow precise tissue removal without introducing any unwanted damage. Moreover the temperature increase during laser processing is measured to ensure process safety at the early stage research. When using a water spray the maximum recorded temperature increase in the pulpal chamber was ~3 oC (for a repetition rate of 250 Hz) which is below the critical level of 5.5 oC which would cause tissue necrosis. The application of picosecond plasma mediated ablation of porcine sclera to create cavities which could form portals of entry to enhance drug delivery to the posterior eye is also investigated. To ensure that the process would not present a risk of unwanted damage to the eye both the temperature rise in the tissue and power transmission through the tissue is investigated during laser processing. The feasibility of this tissue modification as a means to improve drug permeation through the sclera is investigated with a Franz cell setup. It was found that if a drug (fluorescein dextran was used to simulate drug diffusion) is placed in a 5 mm by 5 mm by 100 μm cavity its permeation through the tissue increases by 11 – 12 times in first 5 hours compared to unmodified tissue. To support experimental work and provide insight to the physical mechanism of the tissue removal process two theoretical computational models are developed. First an ALE moving boundary model is applied to investigate single pulse removal of hard dental tissue. For single line plasma mediated scanning ablation of porcine sclera a 2D finite element blow-off model is which confirms the presence of a heat accumulation phenomenon that can influence the depth of the cavity formed. Consequently in this thesis the viability of two laser processes for application to modification of hard dental and soft scleral tissue has been demonstrated which opens up the possibility for developing novel procedures for surgery and dieses treatment

Dynamic analysis of the gantry crane used for transporting BOP

In the paper the dynamic analysis of a gantry crane used for transporting of BOP (BlowOut Preventer) is presented. The crane is placed on a drilling platform. Sea waves cause motion of the platform and the load. Description of such systems can be used in the design process of control systems which allows us to compensate waving. Homogenous transformations and joint coordinates are used to describe behavior of the system. Equations of motion are derived using the Lagrange equations of the second order. In the paper the results of numerical calculations are presented as well

Badanie zużycia płytek skrawającychc z węglików spiekanych w gatunku GC4325 z powłoką Inveio i GC4215

Artykuł pochodzi z VIII Konferencji Szkoły Obróbki Skrawaniem na temat "Synergia nauki z przemysłem" 17-19 września 2014, Międzyzdroje-Szczecin (Artykuł zamieszczony na płycie CD

Analysis of compounds activity concept learned by SVM using robust Jaccard based low-dimensional embedding

Support Vector Machines (SVM) with RBF kernel is one of the most successful models in machine learning based compounds biological activity prediction. Unfortunately, existing datasets are highly skewed and hard to analyze. During our research we try to answer the question how deep is activity concept modeled by SVM. We perform analysis using a model which embeds compounds' representations in a low-dimensional real space using near neigh- bour search with Jaccard similarity. As a result we show that concepts learned by SVM is not much more complex than slightly richer nearest neighbours search. As an additional result, we propose a classi cation technique, based on locally sensitive hashing approximating the Jaccard similarity through minhashing technique, which performs well on 80 tested datasets (consisting of 10 proteins with 8 di erent representations) while in the same time allows fast classi cation and ecient online training

Linearized 9-Bit Hybrid LBDD PWM Modulator for Digital Class-BD Amplifier

The paper presents an original architecture andimplementation of 9-bit Linearized Pulse Width Modulator(LPWM) for Class-BD amplifier, based on the hybrid methodusing STM32 microcontroller and Programmable Tapped DelayLine (PTDL). The analog input signals are converted into 12-bitPCM signals, then are directly transformed into 32-bit LBDDDPWM data of the pulse-edge locations within n-th period of theswitching frequency, next requantized to the 9-bit digitaloutputs, and finally converted into the two physical trains of 1-bitPWM signals, to control the output stage of the Class-BD audioamplifier. The hybrid 9-bit quantizer converts 6 MSB bits usingcounter method, based on the peripherals of STM32microcontroller, while the remaining 3 LSB bits - using a methodbased on the PTDL. In the paper extensive verification ofalgorithm and circuit operation as well as simulation inMATLAB and experimental results of the proposed 9-bit hybridLBDD DPWM circuit have been performed. It allows to attainSNR of 80 dB and THD about 0,3% within the audio baseband

The Optimal Sample Size in Crosswise Model for Sensitive Questions

The problem is in the estimation of the fraction of population with a stigmatizing characteristic. In the paper the nonrandomized response model proposed by Tian, Yu, Tang, and Geng (2007) is considered. The exact confidence interval for this fraction is constructed. Also the optimal sample size for obtaining the confidence interval of a given length is derived