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 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 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.

scholarly journals Gauge Integral

2017 ◽  
Vol 25 (3) ◽  
pp. 217-225
Author(s):  
Roland Coghetto
Keyword(s):  
Real Interval ◽  
Proof Assistants ◽  
Lebesgue Integral ◽  
Riemann Integral ◽  
Hol Light ◽  
Mizar Mathematical Library ◽  
System 1

Summary Some authors have formalized the integral in the Mizar Mathematical Library (MML). The first article in a series on the Darboux/Riemann integral was written by Noboru Endou and Artur Korniłowicz: [6]. The Lebesgue integral was formalized a little later [13] and recently the integral of Riemann-Stieltjes was introduced in the MML by Keiko Narita, Kazuhisa Nakasho and Yasunari Shidama [12]. A presentation of definitions of integrals in other proof assistants or proof checkers (ACL2, COQ, Isabelle/HOL, HOL4, HOL Light, PVS, ProofPower) may be found in [10] and [4]. Using the Mizar system [1], we define the Gauge integral (Henstock-Kurzweil) of a real-valued function on a real interval [a, b] (see [2], [3], [15], [14], [11]). In the next section we formalize that the Henstock-Kurzweil integral is linear. In the last section, we verified that a real-valued bounded integrable (in sense Darboux/Riemann [6, 7, 8]) function over a interval a, b is Gauge integrable. Note that, in accordance with the possibilities of the MML [9], we reuse a large part of demonstrations already present in another article. Instead of rewriting the proof already contained in [7] (MML Version: 5.42.1290), we slightly modified this article in order to use directly the expected results.

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.

Polarity Determination in Sphalerite and Wurtzite Structures

1990 ◽  
Vol 48 (2) ◽  
pp. 500-501
Author(s):  
Stuart McKernan ◽  
C. Barry Carter
Keyword(s):  
Opposite Polarity ◽  
Single Domain ◽  
Polar Material ◽  
Electron Microscopic ◽  
Dynamical Interaction ◽  
X Ray ◽  
Polarity Determination ◽  
The Absolute ◽  
Microscopic Techniques

The determination of the absolute polarity of a polar material is often crucial to the understanding of the defects which occur in such materials. Several methods exist by which this determination may be performed. In bulk, single-domain specimens, macroscopic techniques may be used, such as the different etching behavior, using the appropriate etchant, of surfaces with opposite polarity. X-ray measurements under conditions where Friedel’s law (which means that the intensity of reflections from planes of opposite polarity are indistinguishable) breaks down can also be used to determine the absolute polarity of bulk, single-domain specimens. On the microscopic scale, and particularly where antiphase boundaries (APBs), which separate regions of opposite polarity exist, electron microscopic techniques must be employed. Two techniques are commonly practised; the first [1], involves the dynamical interaction of hoLz lines which interfere constructively or destructively with the zero order reflection, depending on the crystal polarity. The crystal polarity can therefore be directly deduced from the relative intensity of these interactions.

Studies of Vegetative Plant Tissue Compatibility/Incompatibility: The Role of Acid Phosphatase in Lethal Cell Senescence in an Incompatible Heterograft

1980 ◽  
Vol 38 ◽  
pp. 530-531
Author(s):  
Randy Moore
Keyword(s):  
Acid Phosphatase ◽  
Thick Layer ◽  
Cell Necrosis ◽  
Enzyme Localization ◽  
Vegetative Plant ◽  
Cell Autolysis ◽  
Graft Interface ◽  
System 1 ◽  
Thin Fibril

Previous work has indicated that the graft incompatihility between Sedrmi telephoides and Solanum pennellil involves cell necrosis that results In a thick layer of collapsed cells at the graft Interface. This necrotic layer insulates the stock from the scion, which results in abscission of the Sedum scion after 4-6 weeks due to desiccation and starvation. Thus, cell autolysis (which is restricted to Sedum) characterizes the Incompatibility response in this system (1). In order to elucidate the events that lead to cell autolysis, and thus better understand the cellular site and mode of action of cellular incompatibility, the appearance and fate of the hydrolytlc enzyme acid phosphatase (AP) was followed in both the compatible Sedum autograft and the incompatible Sedum/Solanum heterograft. Acid phosphatase was localized by a modified Gomori-type reaction; positive (i.e., including NaF inhibitor) and negative (lacking substrate) controls showed no enzymatic precipitate. Following an initial association with the endoplasmic reticulum (ER) and dictyosomes at 6-10 hours after grafting, AP activity in the compatible Sedum autograft is associated primarily with the plasmalemma (Fig. 1). By 18-24 hours after grafting, the AP activity is restricted to the tono-plast and vacuole (Fig. 2). This strict compartmentation and absence of enzyme from the cytosol is maintained throughout the development of the compatible graft. While AP activity in the incompatible Sedum/Solanum heterograft is Initially similar to the compatible Sedum autograft (i.e., initially found on the ER and dictyosomes), there is a marked difference in enzyme localization in the two graft partners as the incompatibility response develops. As in the compatible autograft, Solanum cells at the graft interface show an Increase in AP activity that Is restricted to the vacuole and tonoplast, with little or no enzyme activity in the cytosol (Fig. 3). In comparable Sedum cells, however, there is a dramatic Increase In AP activity in the cytosol (Fig. h); this cytosollc AP activity is associated with thin fibril-like structures (Fig. 5) measuring approximately 60 A in diameter. This high cytoplasmic AP activity In Sedum cells results in cell autolysis, death, and eventual cell collapse to form the characteristic necrotic layer separating the two graft partners.

516: A Simplified Method to Estimate the Absolute Renal Uptake of 99MTC-DMSA: Evaluation with a New Model using the Radioactivity of Nephrectomy Specimens as Reference

2005 ◽  
Vol 173 (4S) ◽  
pp. 140-141
Author(s):  
Mariana Lima ◽  
Celso D. Ramos ◽  
Sérgio Q. Brunetto ◽  
Marcelo Lopes de Lima ◽  
Carla R.M. Sansana ◽  
...  
Keyword(s):  
New Model ◽  
Renal Uptake ◽  
Simplified Method ◽  
The Absolute

Translocation Relative to Range

Methodology ◽  
2008 ◽  
Vol 4 (3) ◽  
pp. 132-138 ◽  
Author(s):  
Michael Höfler
Keyword(s):  
Risk Difference ◽  
Binary Outcomes ◽  
Number Needed To Treat ◽  
Likert Scales ◽  
Psychological Science ◽  
The Absolute ◽  
The Difference ◽  
Variance Parameters ◽  
Standardized Index ◽  
Maximum Possible Magnitude

A standardized index for effect intensity, the translocation relative to range (TRR), is discussed. TRR is defined as the difference between the expectations of an outcome under two conditions (the absolute increment) divided by the maximum possible amount for that difference. TRR measures the shift caused by a factor relative to the maximum possible magnitude of that shift. For binary outcomes, TRR simply equals the risk difference, also known as the inverse number needed to treat. TRR ranges from –1 to 1 but is – unlike a correlation coefficient – a measure for effect intensity, because it does not rely on variance parameters in a certain population as do effect size measures (e.g., correlations, Cohen’s d). However, the use of TRR is restricted on outcomes with fixed and meaningful endpoints given, for instance, for meaningful psychological questionnaires or Likert scales. The use of TRR vs. Cohen’s d is illustrated with three examples from Psychological Science 2006 (issues 5 through 8). It is argued that, whenever TRR applies, it should complement Cohen’s d to avoid the problems related to the latter. In any case, the absolute increment should complement d.

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