scholarly journals Klein-Beltrami Model. Part I

2018 ◽  
Vol 26 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Roland Coghetto
Keyword(s):  
Hyperbolic Plane ◽  
Disk Model ◽  
Hol Light ◽  
System 2 ◽  
The Absolute ◽  
Further Development ◽  
Klein Model

Summary Tim Makarios (with Isabelle/HOL1) and John Harrison (with HOL-Light2) shown that “the Klein-Beltrami model of the hyperbolic plane satisfy all of Tarski’s axioms except his Euclidean axiom” [3], [4], [14], [5]. With the Mizar system [2], [7] we use some ideas are taken from Tim Makarios’ MSc thesis [13] for the formalization of some definitions (like the absolute) and lemmas necessary for the verification of the independence of the parallel postulate. This work can be also treated as further development of Tarski’s geometry in the formal setting [6]. Note that the model presented here, may also be called “Beltrami-Klein Model”, “Klein disk model”, and the “Cayley-Klein model” [1].

scholarly journals Klein-Beltrami model. Part III

2020 ◽  
Vol 28 (1) ◽  
pp. 1-7
Author(s):  
Roland Coghetto
Keyword(s):  
Equivalence Relation ◽  
Hyperbolic Plane ◽  
Naming Convention ◽  
Hol Light ◽  
Congruence Identity ◽  
The Absolute ◽  
System 1

SummaryTimothy Makarios (with Isabelle/HOL1) and John Harrison (with HOL-Light2) shown that “the Klein-Beltrami model of the hyperbolic plane satisfy all of Tarski’s axioms except his Euclidean axiom” [2],[3],[4],[5].With the Mizar system [1] we use some ideas taken from Tim Makarios’s MSc thesis [10] to formalize some definitions (like the absolute) and lemmas necessary for the verification of the independence of the parallel postulate. In this article we prove that our constructed model (we prefer “Beltrami-Klein” name over “Klein-Beltrami”, which can be seen in the naming convention for Mizar functors, and even MML identifiers) satisfies the congruence symmetry, the congruence equivalence relation, and the congruence identity axioms formulated by Tarski (and formalized in Mizar as described briefly in [8]).

scholarly journals Klein-Beltrami Model. Part II

2018 ◽  
Vol 26 (1) ◽  
pp. 33-48 ◽  
Author(s):  
Roland Coghetto
Keyword(s):  
Hyperbolic Plane ◽  
Hol Light ◽  
System 1 ◽  
Further Development

Summary Tim Makarios (with Isabelle/HOL1) and John Harrison (with HOL-Light2) have shown that “the Klein-Beltrami model of the hyperbolic plane satisfy all of Tarski’s axioms except his Euclidean axiom” [2, 3, 15, 4]. With the Mizar system [1], [10] we use some ideas are taken from Tim Makarios’ MSc thesis [12] for formalized some definitions (like the tangent) and lemmas necessary for the verification of the independence of the parallel postulate. This work can be also treated as a further development of Tarski’s geometry in the formal setting [9].

scholarly journals Pascal’s Theorem in Real Projective Plane

2017 ◽  
Vol 25 (2) ◽  
pp. 107-119
Author(s):  
Roland Coghetto
Keyword(s):  
Projective Plane ◽  
Projective Geometry ◽  
Real Projective Plane ◽  
The Real ◽  
Hol Light ◽  
System 2 ◽  
Special Case

Summary In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines. For proving Pascal’s theorem, we use the techniques developed in the section “Projective Proofs of Pappus’ Theorem” in the chapter “Pappus’ Theorem: Nine proofs and three variations” [11]. We also follow some ideas from Harrison’s work. With HOL Light, he has the proof of Pascal’s theorem2. For a lemma, we use PROVER93 and OTT2MIZ by Josef Urban4 [12, 6, 7]. We note, that we don’t use Skolem/Herbrand functions (see “Skolemization” in [1]).

CD-Spectroscopic Investigations for the Determination of the Absolute Configuration of α-Alkylated 1,4-CycIohexanedione Derivatives

2000 ◽  
Vol 55 (11) ◽  
pp. 1011-1014 ◽  
Author(s):  
Jörg Fleischhauer ◽  
Sven Gabriel ◽  
Dieter Ender ◽  
Anja Nühring ◽  
Axel Wollmer
Keyword(s):  
Absolute Configuration ◽  
Membered Ring ◽  
Cd Spectra ◽  
Pure Material ◽  
Enantiomerically Pure ◽  
System 2 ◽  
The Absolute ◽  
Stereogenic Center ◽  
Rotational Strengths

The absolute configuration of the conformationally flexible six membered ring system 2-methyl- and 2,6-dimethyl-l,4-cyclohexanedione monoethylene acetal was determined by comparison of measured and calculated CD spectra. The rotational strengths were calculated by means of the CNDO/S-method assuming R at the stereogenic center. The results were compared with the predictions made by the octant rule. The enantiomerically pure material was synthesized via the corresponding SAMP- and RAMP-hydrazones.

scholarly journals Smooth or Stepped? Laboratory Comparison of Enhanced Sonifications for Monitoring Patient Oxygen Saturation

2019 ◽  
Vol 62 (1) ◽  
pp. 124-137
Author(s):  
Renae Collett ◽  
Isaac Salisbury ◽  
Robert G. Loeb ◽  
Penelope M. Sanderson
Keyword(s):  
Oxygen Saturation ◽  
Pulse Oximeter ◽  
Primary Outcome ◽  
Auditory Information ◽  
Threshold Values ◽  
Auditory Cues ◽  
Pulse Tone ◽  
Smooth Effects ◽  
The Absolute ◽  
Further Development

Background: The pulse oximeter (PO) provides anesthesiologists with continuous visual and auditory information about a patient’s oxygen saturation (SpO2). However, anesthesiologists’ attention is often diverted from visual displays, and clinicians may inaccurately judge SpO2 values when relying on conventional PO auditory tones. We tested whether participants could identify SpO2 value (e.g., “97%”) better with acoustic enhancements that identified three discrete clinical ranges by either changing abruptly at two threshold values (stepped-effects) or changing incrementally with each percentage value of SpO2 (smooth-effects). Method: In all, 79 nonclinicians participated in a between-subjects experiment that compared performance of participants using the stepped-effects display with those who used the smooth-effects display. In both conditions, participants heard sequences of 72 tones whose pitch directly correlated to SpO2 value, and whose value could change incrementally. Primary outcome was percentage of responses that correctly identified the absolute SpO2 percentage, ±1, of the last pulse tone in each sequence. Results: Participants using the stepped-effects auditory tones identified absolute SpO2 percentage more accurately ( M = 53.7%) than participants using the smooth-effects tones ( M = 47.9%, p = .038). Identification of range and detection of transitions between ranges showed even stronger advantages for the stepped-effects display ( p < .005). Conclusion: The stepped-effects display has more pronounced auditory cues at SpO2 range transitions, from which participants can better infer absolute SpO2 values. Further development of a smooth-effects display for this purpose is not necessary.

THE MARKOV SPECTRA FOR COCOMPACT FUCHSIAN GROUPS

2009 ◽  
Vol 05 (04) ◽  
pp. 679-718 ◽  
Author(s):  
L. YA. VULAKH
Keyword(s):  
Projective Plane ◽  
Hyperbolic Plane ◽  
Quadratic Field ◽  
Imaginary Quadratic Field ◽  
Fuchsian Groups ◽  
Markov Spectrum ◽  
Discrete Part ◽  
Klein Model

Applying the Klein model D2 of the hyperbolic plane and identifying the geodesics in D2 with their poles in the projective plane, the author has developed a method for finding the discrete part of the Markov spectrum for Fuchsian groups. It is applicable mostly to non-cocompact groups. In the present paper, this method is extended to cocompact Fuchsian groups. For a group with signature (0;2,2,2,3), the complete description of the discrete part of the Markov spectrum is obtained. The result obtained leads to the complete description of the Markov and Lagrange spectra for the imaginary quadratic field with discriminant -20.

scholarly journals Klein-Beltrami model. Part IV

2020 ◽  
Vol 28 (1) ◽  
pp. 9-21
Author(s):  
Roland Coghetto
Keyword(s):  
Hyperbolic Plane ◽  
Hol Light ◽  
System 1

SummaryTimothy Makarios (with Isabelle/HOL1) and John Harrison (with HOL-Light2) shown that “the Klein-Beltrami model of the hyperbolic plane satisfy all of Tarski’s axioms except his Euclidean axiom” [2],[3],[4, 5].With the Mizar system [1] we use some ideas taken from Tim Makarios’s MSc thesis [10] to formalize some definitions and lemmas necessary for the verification of the independence of the parallel postulate. In this article, which is the continuation of [8], we prove that our constructed model satisfies the axioms of segment construction, the axiom of betweenness identity, and the axiom of Pasch due to Tarski, as formalized in [11] and related Mizar articles.

Application of TEM to Deformation, Wear, and Fracture of Ceramics

1974 ◽  
Vol 32 ◽  
pp. 472-473
Author(s):  
B. J. Hockey
Keyword(s):  
Wear Resistance ◽  
High Temperature ◽  
Mechanical Behavior ◽  
Brittle Materials ◽  
High Temperature Strength ◽  
Wide Range ◽  
Corrosive Environments ◽  
Further Development

Ceramics, such as Al2O3 and SiC have numerous current and potential uses in applications where high temperature strength, hardness, and wear resistance are required often in corrosive environments. These materials are, however, highly anisotropic and brittle, so that their mechanical behavior is often unpredictable. The further development of these materials will require a better understanding of the basic mechanisms controlling deformation, wear, and fracture.The purpose of this talk is to describe applications of TEM to the study of the deformation, wear, and fracture of Al2O3. Similar studies are currently being conducted on SiC and the techniques involved should be applicable to a wide range of hard, brittle materials.

Bulk standards for low-temperature biological x-ray microanalysis

1984 ◽  
Vol 42 ◽  
pp. 282-283
Author(s):  
P. Echlin ◽  
M. McKoon ◽  
E.S. Taylor ◽  
C.E. Thomas ◽  
K.L. Maloney ◽  
...  
Keyword(s):  
Phase Separation ◽  
Low Temperature ◽  
Analytical Method ◽  
Salt Solutions ◽  
Absolute Concentration ◽  
Cooling Process ◽  
X Ray ◽  
The Absolute ◽  
Analytical Procedures ◽  
Electrical Conductors

Although sections of frozen salt solutions have been used as standards for x-ray microanalysis, such solutions are less useful when analysed in the bulk form. They are poor thermal and electrical conductors and severe phase separation occurs during the cooling process. Following a suggestion by Whitecross et al we have made up a series of salt solutions containing a small amount of graphite to improve the sample conductivity. In addition, we have incorporated a polymer to ensure the formation of microcrystalline ice and a consequent homogenity of salt dispersion within the frozen matrix. The mixtures have been used to standardize the analytical procedures applied to frozen hydrated bulk specimens based on the peak/background analytical method and to measure the absolute concentration of elements in developing roots.

A Quantitative Ultrastructural Study of Peripheral Blood Lymphocytes Containing Parallel Tubular Arrays in Epstein-Barr Virus and Cytomegalo-Virus Mononucleosis

1981 ◽  
Vol 39 ◽  
pp. 454-455
Author(s):  
C. M. Payne ◽  
P. M. Tennican
Keyword(s):  
Peripheral Blood ◽  
Lymphocyte Count ◽  
Epstein Barr Virus ◽  
Absolute Lymphocyte Count ◽  
Peripheral Blood Lymphocytes ◽  
Clinical State ◽  
Barr Virus ◽  
The Absolute ◽  
Epstein Barr ◽  
Tubular Arrays

In the normal peripheral circulation there exists a sub-population of lymphocytes which is ultrastructurally distinct. This lymphocyte is identified under the electron microscope by the presence of cytoplasmic microtubular-like inclusions called parallel tubular arrays (PTA) (Figure 1), and contains Fc-receptors for cytophilic antibody. In this study, lymphocytes containing PTA (PTA-lymphocytes) were quantitated from serial peripheral blood specimens obtained from two patients with Epstein -Barr Virus mononucleosis and two patients with cytomegalovirus mononucleosis. This data was then correlated with the clinical state of the patient.It was determined that both the percentage and absolute number of PTA- lymphocytes was highest during the acute phase of the illness. In follow-up specimens, three of the four patients' absolute lymphocyte count fell to within normal limits before the absolute PTA-lymphocyte count.In one patient who was followed for almost a year, the absolute PTA- lymphocyte count was consistently elevated (Figure 2). The estimation of absolute PTA-lymphocyte counts was determined to be valid after a morphometric analysis of the cellular areas occupied by PTA during the acute and convalescent phases of the disease revealed no statistical differences.

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