The geometry of manifolds and the perception of space

This essay discusses the development of key geometric ideas in the 19th century which led to the formulation of the concept of an abstract manifold (which was not necessarily tied to an ambient Euclidean space) by Hermann Weyl in 1913. This notion of manifold and the geometric ideas which could be formulated and utilized in such a setting (measuring a distance between points, curvature and other geometric concepts) was an essential ingredient in Einstein's gravitational theory of space-time from 1916 and has played important roles in numerous other theories of nature ever since.Comment: arXiv admin note: substantial text overlap with arXiv:1301.064

On Recognizing Transparent Objects in Domestic Environments Using Fusion of Multiple Sensor Modalities

Current object recognition methods fail on object sets that include both diffuse, reflective and transparent materials, although they are very common in domestic scenarios. We show that a combination of cues from multiple sensor modalities, including specular reflectance and unavailable depth information, allows us to capture a larger subset of household objects by extending a state of the art object recognition method. This leads to a significant increase in robustness of recognition over a larger set of commonly used objects.Comment: 12 page

Парсическая роль интеллигенции в истории

In 1661, Borelli and Ecchellensis published a Latin translation of a text which they called the Ltmmas of Archimedes. The first fifteen propositions of this translation correspond to the contents of the Arabic Book of Assumptions, which the Arabic tradition attributes to Archimedes. The work is not found in Greek and the attribution is uncertain at best. Nevertheless, the Latin translation of the fifteen propositions was adopted as a work of Archimedes in the standard editions and translations by Heiberg, Heath, Ver Eecke and others. Our paper concerns the remaining two propositions, 16 and 17, in the Latin translation by Borelli and Ecchellensis, which are not found in the Arabic Book of Assumptions. Borelli and Ecchellensis believed that the Arabic Book of Assumptions is a mutilated version of a lost "old book" by Archimedes which is mentioned by Eutodus (ca. A.D. 500) in his commentary to Proposition 4 of Book 2 of Archimedes' On the Sphere and Cylinder. This proposition is about cutting a sphere by a plane in such a way that the volumes of the segments have a given ratio. Because the fifteen propositions in the Arabic Book of Assumptions have no connection whatsoever to this problem, Borelli and Ecchellensis "restored" two more propositions, their 16 and 17. Propositions 16 and 17 concern the problem of cutting a given line segment AG at a point X in such a way that the product AX· XG2 is equal to a given volume K. This problem is mentioned by Archimedes, and although he promised a solution, the solution is not found in On the Sphere and Cylinder. In his commentary, Eutodus presents a solution which he adapted from the "old book" of Archimedes which he had found. Proposition 17 is the synthesis of the problem by means of two conic sections, as adapted by Eutodus. Proposition 16 presents the diorismos: the problem can be solved only if K::::;;; AB · BG2, where point B is defined on AG such that AB = 1/zBG. We will show that Borelli and Ecchellensis adapted their Proposition 16 not from the commentary by Eutocius but from the Arabic text On Filling the Gaps in Archimedes' Sphere and Cylinder which was written by Abu Sahl al-Kuru in the tenth century, and which was published by Len Berggren. Borelli preferred al-Kiihi's diorismos (by elementary means) to the diorismos by means of conic sections in the commentary of Eutocius, even though Eutocius says that he had adapted it from the "old book." Just as some geometers in later Greek antiquity, Borelli and Ecchellensis bdieved that it is a "sin" to use conic sections in the solution of geometrical problems if elementary Euclidean means are possible. They (incorrectly) assumed that Archimedes also subscribed to this opinion, and thus they included their adaptation of al-Kuru's proposition in their restoration of the "old book" of Archimedes. Our paper includes the Latin text and an English translation of Propositions 16 and 17 of Borelli and Ecchellensis

Rethinking the discovery function of proof within the context of proofs and refutations

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth graders engaged in proofs and refutations, we demonstrate that facing a counterexample of a primitive statement can become a starting point of students’ activity for discovery, and that a proof of the primitive statement can function as a useful tool for inventing a new conjecture that holds for the counterexample. An implication for developing tasks by which students can experience this discovery function is mentioned.ArticleInternational Journal of Mathematical Education in Science and Technology. 45(7):1053-1067 (2014)journal articl

Исследование микроструктуры безобжиговых периклазоуглеродистых огнеупоров при использовании в качестве заполнителя различного вида периклаза

У статті представлено результати досліджень мікроструктури периклазовуглецевих зразків, у яких в якості наповнювача використовували різні види периклазу. Петрографічні дослідження показали, що зразки щільні та міцні, як на плавленому, так і на спеченому периклазі.In clause the results of researches of microstructure magnesia-carbon refractors are submitted, at which in quality filler used different kind magnesia. Microstructures of samples strong and dense, both on melted, and on sintered periclase have shown, that

Development and validation of a visual grading scale for assessing image quality of AP pelvis radiographic images

OBJECTIVE: Apply psychometric theory to develop and validate a visual grading scale for assessing visual perception of AP pelvis digital image quality. METHODS: Psychometric theory was used to guide scale development. Seven phantom and 7 cadaver images of visually and objectively predetermined quality were used to help assess scale reliability and validity. 151 volunteers scored phantom images; 184 volunteers scored cadaver images. Factor analysis and Cronbach’s alpha were used to assess scale validity and reliability. RESULTS: A 24 item scale was produced. Aggregated mean volunteer scores for each image correlated with the rank order of the visually and objectively predetermined image qualities. Scale items had good inter-item correlation (≥0.2) and high factor loadings (≥0.3). Cronbach's alpha (reliability) revealed that the scale has acceptable levels of internal reliability for both phantom and cadaver images (α= 0.8 and 0.9, respectively). Factor analysis suggested the scale is multidimensional (assessing multiple quality themes). CONCLUSION: This study represents the first full development and validation of a visual image quality scale using psychometric theory. It is likely that this scale will have clinical, training and research applications. ADVANCES IN KNOWLEDGE: This article presents data to create and validate visual grading scales for radiographic examinations. The visual grading scale, for AP pelvis examinations, can act as a validated tool for future research, teaching and clinical evaluations of image quality

Activation of the SMU.1882 Transcription by CovR in Streptococcus mutans

In Streptococcus mutans, the global response regulator CovR plays an important role in biofilm formation, stress-tolerance response, and caries production. We have previously shown that CovR acts as a transcriptional repressor by binding to the upstream promoter regions of its target genes. Here, we report that in vivo, CovR activates the transcription of SMU.1882, which encodes a small peptide containing a double-glycine motif. We also show that SMU.1882 is transcriptionally linked to comA that encodes a putative ABC transporter protein. Several genes from man gene clusters that encode mannose phosphotranferase system flank SMU.1882 -comA genes. Genomic comparison with other streptococci indicates that SMU.1882 is uniquely present in S. mutans, while the man operon is conserved among all streptococci, suggesting that a genetic rearrangement might have taken place at this locus. With the use of a transcriptional reporter system and semi-quantitative RT-PCR, we demonstrated the transcriptional regulation of SMU.1882 by CovR. In vitro gel shift and DNase I foot-printing analyses with purified CovR suggest that CovR binds to a large region surrounding the -10 region of the P1882. Using this information and comparing with other CovR regulated promoters, we have developed a putative consensus binding sequence for CovR. Although CovR binds to P1882, in vitro experiments using purified S. mutans RpoD, E. coli RNA polymerase, and CovR did not activate transcription from this promoter. Thus, we speculate that in vivo, CovR may interfere with the binding of a repressor or requires a cofactor

Organic-Inorganic Nanostructure Architecture via Directly Capping Fullerenes onto Quantum Dots

A new form of fullerene-capped CdSe nanoparticles (PCBA-capped CdSe NPs), using carboxylate ligands with [60] fullerene capping groups that provides an effective synthetic methodology to attach fullerenes noncovalently to CdSe, is presented for usage in nanotechnology and photoelectric fields. Interestingly, either the internal charge transfer or the energy transfer in the hybrid material contributes to photoluminescence (PL) quenching of the CdSe moieties.open2

Familial hypercholesterolemia in St.-Petersburg: the known and novel mutations found in the low density lipoprotein receptor gene in Russia

BACKGROUND: Familial hypercholesterolemia is a human monogenic disease caused by population-specific mutations in the low density lipoprotein (LDL) receptor gene. Despite thirteen different mutations of the LDL receptor gene were reported from Russia prior to 2003, the whole spectrum of disease-causing gene alterations in this country is poorly known and requires further investigation provided by the current study. METHODS: Forty-five patients with clinical diagnosis of FH were tested for the apolipoprotein B (apoB) mutation R3500Q by restriction fragment length analysis. After exclusion of R3500Q mutation high-sensitive fluorescent single-strand conformation polymorphism (SSCP) analysis and automatic DNA sequencing were used to search for mutations in the LDL receptor gene. RESULTS: We found twenty one rare sequence variations of the LDL receptor gene. Nineteen were probably pathogenic mutations, and two (P518P, T705I) were considered as neutral ones. Among the mutations likely to be pathogenic, eight were novel (c.670-671insG, C249X, c.936-940del5, c.1291-1331del41, W422X, c.1855-1856insA, D601N, C646S), and eleven (Q12X, IVS3+1G>A, c.651-653del3, E207X, c.925-931del7, C308Y, L380H, c.1302delG, IVS9+1G>A, V776M, V806I) have already been described in other populations. None of the patients had the R3500Q mutation in the apoB gene. CONCLUSIONS: Nineteen pathogenic mutations in the LDL receptor gene in 23 probands were identified. Two mutations c.925-931del7 and L380H are shared by St.-Petersburg population with neighbouring Finland and several other mutations with Norway, Sweden or Denmark, i.e. countries from the Baltic Sea region. Only four mutations (c.313+1G>A, c.651-653del3, C308Y and W422X) were recurrent as all those were found in two unrelated families. By this study the number of known mutations in the LDL receptor gene in St.-Petersburg area was increased nearly threefold. Analysis of all 34 low density lipoprotein receptor gene mutations found in St.-Petersburg argues against strong founder effect in Russian familial hypercholesterolemia