Mappings of Domains in Rn and Their Metric Tensors

We consider quasi-isometric mappings of domains in multidimensional Euclidean spaces. We establish that a mapping depends continuously in the sense of the topology of Sobolev classes on its metric tensor to within isometry of the space. In the space of metric tensors we take the topology determined by means of almost everywhere convergence. We show that if the metric tensor of a mapping is continuous then the length of the image of a rectifiable curve is determined by the same formula as in the case of mappings with continuous derivatives. (Continuity of the metric tensor of a mapping does not imply continuity of its derivatives.)     

A series of exact solutions for (2 + 1)-dimensional Wick-type stochastic generalized Broer-Kaup system via a modified variable-coefficient projective Riccati equation mapping method

A modified variable-coefficient projective Riccati equation mapping method is applied to (2 + 1)-dimensional Wick-type stochastic generalized Broer-Kaup system. With the help of Hermit transformation, we obtain a series of new exact stochastic solutions to the stochastic Broer-Kaup system in the white noise environment.     

Concepts of probabilistic sets

In the field of pattern recognition or decision making theory, the important subjects are as follows: (1) ambiguity of property of objects, (2) variety of character of objects, (3) subjectivity of observers, (4) evolution of knowledge of observers (i.e. learning). Considering these points, the concept of probabilistic set is proposed. It is based on both probability theory and fuzzy concepts. A probabilistic set on a total space is defined by a point wise measurable function from a parameter space (which is a probability space) to a characteristic space (which is a measurable space). It is shown that the family of all probabilistic sets constitutes a complete pseudo-Boolean algebra. Moment analysis is possible by using a probability measure of the parameter space. Other useful concepts are also mentioned such as probabilistic mappings and expected cardinal numbers.     

Another generalization of weighted Ostrowski type inequality for mappings of bounded variation

A new generalization of weighted Ostrowski type inequality for mappings of bounded variation with a unified sharp bound is established.     

In-bone protein digestion followed by LC-MS/MS peptide analysis as a new way towards the routine proteomic characterization of human maxillary and mandibular bone tissue in oral surgery

Proteomic characterization of alveolar bones in oral surgery represents an analytical challenge due to their insoluble character. The implementation of a straightforward technique could lead to the routine use of proteomics in this field. This work thus developed a simple technique for the characterization of bone tissue for human maxillary and mandibular bones. It is based on the direct in-bone tryptic digestion of proteins in both healthy and pathological human maxillary and mandibular bone samples. The released peptides were then identified by the LC-MS/MS. Using this approach, a total of 1120 proteins were identified in the maxillary bone and 1151 proteins in the mandibular bone. The subsequent partial least squares–discrimination analysis (PLS-DA) of protein data made it possible to reach 100% discrimination between the samples of healthy alveolar bones and those of the bone tissue surrounding the inflammatory focus. These results indicate that the in-bone protein digestion followed by the LC-MS/MS and subsequent statistical analysis can provide a deeper insight into the field of oral surgery at the molecular level. Furthermore, it could also have a diagnostic potential in the differentiation between the proteomic patterns of healthy and pathological alveolar bone tissue. Data are available via ProteomeXchange with the identifier PXD026775.     

冠心病微量元素谱的计算机模式识别

用计算机多元分析研究冠心病微量元素谱，识别冠心病患者与健康者；非线性映射法判别率男性８６．６％，女性９６．２％；ＳＩＭＣＡ差别法正确回判率男性８５．０％，女性８８．３％。     

Characterization of sugar juice heat exchanger tube deposit

Fouling of heat exchanger surfaces during sugar manufacture reduces productivity and increases energy demand. This study characterizes a deposit (including its internal structure) formed in a sugar factory's evaporator unit using a variety of X‐ray diffraction and scanning electron microscopy techniques (including X‐ray powder diffraction, X‐ray fluorescence, elemental mapping with energy dispersive spectroscopy and backscattered electron imaging). Calcium sulfate dihydrate, calcium oxalate mono‐ and dihydrate, hydroxyapatite, amorphous silica and organic matter are present in the deposit. The composition of the deposit (which contains three layers) varies along the height of the tube. There are noticeable differences in the composition and porosity among the layers in the deposit. A porous structure consisting of a mixture of amorphous silica, calcium oxalate dihydrate and organic matter is attached to the surface of the deposit in contact with sugar juice, while a denser morphology of amorphous silica and hydroxyapatite is attached to the tube wall. Elemental mapping identifies an association between Si, Al, Mg, Fe and O, suggesting the presence of a silicate compound as a minor component in the deposit. An attempt is made to rationalize the formation of the observed phases. Copyright © 2010 John Wiley & Sons, Ltd.     

Computer-assisted optimization of reversed-phase HPLC isocratic separation of neutral compounds

An appropriate optimization strategy should be used to find a desired resolution or selectivity with a minimum number of experiments in a limited time, which could assure the baseline separation of all target compounds. It was usually realized by means of a specialized computer program. In this paper, mapping optimization method and overlapping resolution mapping were compared for the optimization of a reversed-phase high-performance liquid chromatography (HPLC) isocratic separation of neutral compounds. The calculated resolutions and separation time of 7 to 10 experiments are fitted by different equations, which were used to build a contour plot with a minimum effective resolution and maximum retention time as a function of a mobile phase composition. The balance between resolution and analysis time could be easily realized by the overlapping of the final overlapping resolution mapping and analysis time mapping. The validity of the two methods was confirmed by some typical experiments. The models are simple, visual, and common without theoretical arithmetic.     

Controlled enzyme-immobilisation on capillaries for microreactors for peptide mapping

In the present paper, the covalent immobilisation of the digesting enzyme trypsin has been achieved through photo-immobilisation on a portion of a silica capillary, thus leading to the construction of a capillary electrophoretic (CE)-microreactor for peptide mapping. The CE-microreactor is characterised by being a single piece, thus ensuring no fluidic or electrical leakage. The enzyme was immobilised with a surface density of 15.8 g/cm², the stability was high (80% after 38 days) and the rate of conversion was 0.2 ng/s. On-line protein mapping was tested with proteins of different dimensions, showing competitiveness in terms of time (completed map within 15 min) and exhaustive maps of small proteins. The results of the CE-microreactor and the potential to immobilise biocomponents easily on a desired portion of the capillary indicate further developments towards the construction of a variety of miniaturised enzymatic screening devices for high-throughput screening analysis.     

Characterisation of botulinum toxins type C, D, E, and F by matrix-assisted laser desorption ionisation and electrospray mass spectrometry

In a follow-up of the earlier characterisation of botulinum toxins type A and B (BTxA and BTxB) by mass spectrometry (MS), types C, D, E, and F (BTxC, BTxD, BTxE, BTxF) were now investigated. Botulinum toxins are extremely neurotoxic bacterial toxins, likely to be used as biological warfare agent. Biologically active BTxC, BTxD, BTxE, and BTxF are comprised of a protein complex of the respective neurotoxins with non-toxic non-haemagglutinin (NTNH) and, sometimes, specific haemagglutinins (HA). These protein complexes were observed in mass spectrometric identification. The BTxC complex, from Clostridium botulinum strain 003-9, consisted of a 'type C1 and D mosaic' toxin similar to that of type C strain 6813, a non-toxic non-hemagglutinating and a 33 kDa hemagglutinating (HA-33) component similar to those of strain C-Stockholm, and an exoenzyme C3 of which the sequence was in full agreement with the known genetic sequence of strain 003-9. The BTxD complex, from C. botulinum strain CB-16, consisted of a neurotoxin with the observed sequence identical with that of type D strain BVD/-3 and of an NTNH with the observed sequence identical with that of type C strain C-Yoichi. Remarkably, the observed protein sequence of CB-16 NTNH differed by one amino acid from the known gene sequence: L859 instead of F859. The BTxE complex, from a C. botulinum isolated from herring sprats, consisted of the neurotoxin with an observed sequence identical with that from strain NCTC 11219 and an NTNH similar to that from type E strain Mashike (1 amino acid difference with observed sequence). BTxF, from C. botulinum strain Langeland (NCTC 10281), consisted of the neurotoxin and an NTNH; observed sequences from both proteins were in agreement with the gene sequence known from strain Langeland. As with BTxA and BTxB, matrix-assisted laser desorption/ionisation (MALDI) MS provided provisional identification from trypsin digest peptide maps and liquid chromatography-electrospray (tandem) mass spectrometry (LC-ES MS) afforded unequivocal identification from amino acid sequence information of digest peptides obtained in trypsin digestion.