Search results for "fractions"
showing 10 items of 114 documents
Selmer's Multiplicative Algorithm
2011
Abstract.The behavior of the multiplicative acceleration of Selmer's algorithm is widely unknown and no general result on convergence has been detected yet. Solely for its 2-dimensional, periodic expansions, there exist some results on convergence and approximation due to Fritz Schweiger. In this paper we show that periodic expansions of any dimension do in fact converge and that the coordinates of the limit points are rational functions of the largest eigenvalue of the periodicity matrix.
On Sturmian Graphs
2007
AbstractIn this paper we define Sturmian graphs and we prove that all of them have a certain “counting” property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of compact directed acyclic word graphs of central Sturmian words. In order to prove this result, we give a characterization of the maximal repeats of central Sturmian words. We show also that, in analogy with the case of Sturmian words, these graphs converge to infinite ones.
On lazy representations and Sturmian graphs
2011
In this paper we establish a strong relationship between the set of lazy representations and the set of paths in a Sturmian graph associated with a real number α. We prove that for any non-negative integer i the unique path weighted i in the Sturmian graph associated with α represents the lazy representation of i in the Ostrowski numeration system associated with α. Moreover, we provide several properties of the representations of the natural integers in this numeration system.
Sturmian graphs and integer representations over numeration systems
2012
AbstractIn this paper we consider a numeration system, originally due to Ostrowski, based on the continued fraction expansion of a real number α. We prove that this system has deep connections with the Sturmian graph associated with α. We provide several properties of the representations of the natural integers in this system. In particular, we prove that the set of lazy representations of the natural integers in this numeration system is regular if and only if the continued fraction expansion of α is eventually periodic. The main result of the paper is that for any number i the unique path weighted i in the Sturmian graph associated with α represents the lazy representation of i in the Ost…
LDL and HDL subfractions, dysfunctional HDL: treatment options.
2014
Low-density lipoproteins (LDL) are considered as important risk factors for cardiovascular diseases (CVD), while highdensity lipoproteins (HDL) are well recognized for their putative role in reverse cholesterol transport and other atheroprotective functions. Both LDL and HDL are heterogeneous in nature, including various subfractions depending on the method of isolation (≥ 7 LDL and 10 HDL subspecies, respectively). While it is established that small, dense LDL (sdLDL) have atherogenic potential, the role of different HDL subfractions is still largely unclear. The majority of clinical studies suggest an atheroprotective role of larger HDL particles, although recent work has highlighted the…
Эмануэль Гринберг - выдающиеся достижения в прикладной математике: радио-фильтры, корпуса танкеров, графы и интегральные схемы Emanuels Grinbergs - i…
2018
The paper is dedicated to the 50th anniversary of the Grinberg theorem. The main works of Emanuel Grinberg (1911-1982) in applied mathematics are described, following the stages of his life path, namely: the design of radio receivers and the calculation of radio filters (1949-1959), hull of tanker calculations (1962-1964), the study of graph theory and the proof of the Grinberg theorem (1968), designing of integrated circuits (1968-1980). Calculations of radio filters are associated with the expansion of the use of continued fractions for the analysis of linear electric circuits (the Kauer model) and the developing of new tools – the Grinberg brackets (as an extension of the Euler brackets)…
Subcellular fractionation of tissue culture cells.
2003
Cell fractionation techniques include some of the most important and widely used analytical tools in cell and molecular biology, and are essential for the development of cell-free assays that reconstitute complicated cellular processes. In addition to simple gradient systems, this unit discusses the immuno-purification of organelles, in particular endosomes. As antigens, purification can be achieved using endogenous or ectopically expressed proteins, provided that appropriate antibodies are available. Alternatively, tagged proteins can be used, when combined with anti-tag antibodies. Now that sequencing of the genomes of several organisms has been completed, biochemical strategies, and in p…
Characterization of the cleavage site and function of resulting cleavage fragments after limited proteolysis of Clostridium difficile toxin B (TcdB) …
2005
Clostridium difficiletoxin B (TcdB) is a single-stranded protein consisting of a C-terminal domain responsible for binding to the host cell membrane, a middle part involved in internalization, and the N-terminal catalytic (toxic) part. This study shows that TcdB is processed by a single proteolytic step which cleaves TcdB10463between Leu543and Gly544and the naturally occurring variant TcdB8864between Leu544and Gly545. The cleavage occurs at neutral pH and is catalysed by a pepstatin-sensitive protease localized in the cytoplasm and on the cytoplasmic face of intracellular membranes. The smaller N-terminal cleavage products [63 121 Da (TcdB10463) and 62 761 Da (TcdB8864)] harbour the cytotox…
Differential subcellular localization of endogenous and transfected soluble epoxide hydrolase in mammalian cells: evidence for isozyme variants
1999
AbstractEndogenous, constitutive soluble epoxide hydrolase in mice 3T3 cells was localized via immunofluorescence microscopy exclusively in peroxisomes, whereas transiently expressed mouse soluble epoxide hydrolase (from clofibrate-treated liver) accumulated only in the cytosol of 3T3 and HeLa cells. When the C-terminal Ile of mouse soluble epoxide hydrolase was mutated to generate a prototypic putative type 1 PTS (-SKI to -SKL), the enzyme targeted to peroxisomes. The possibility that soluble epoxide hydrolase-SKI was sorted slowly to peroxiosmes from the cytosol was examined by stably expressing rat soluble epoxide hydrolase-SKI appended to the green fluorescent protein. Green fluorescent…
The role of crystalline, mobile amorphous and rigid amorphous fractions in the performance of recycled poly (ethylene terephthalate) (PET)
2012
[EN] The action of thermo-mechanical degradation induced by mechanical recycling of poly(ethylene terephthalate) was simulated by successive injection moulding cycles. Degradation reactions provoked chain scissions and a reduction in molar mass mainly driven by the reduction of diethyleneglycol to ethylene glycol units in the flexible domain of the PET backbone, and the formation of -OH terminated species with shorter chain length. The consequent microstructural changes were quantified taking into account a three-fraction model involving crystalline, mobile amorphous (MAF) and rigid amorphous fractions (RAF). A remarkable increase of RAF, to a detriment of MAF was observed, while the percen…