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 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 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.

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.

On the Classification of TI-RADS and Stratification of Signs of Thyroid Cancer According to Ultrasound Data

2017 ◽  
pp. 29-38 ◽  
Author(s):  
E. P. Fisenko ◽  
J. P. Sich ◽  
N. N. Vetsheva
Keyword(s):  
Thyroid Cancer ◽  
Retrospective Analysis ◽  
Thyroid Nodules ◽  
Thyroid Ultrasound ◽  
High Reproducibility ◽  
System 1

Objective:a comparative “blind” assessment of the thyroid nodules identified by ultrasound, according to the TI-RADS scale in various modifications.Materials and methods.Retrospective analysis of 149 echograms  of thyroid nodules by three independent experts was performed (the  experience of ultrasound of thyroid ultrasound for more than 7 years).Results. In solid nodules, high-specific large (more than 94%) and  small (more than 90%) ultrasound signs of thyroid cancer have been identified. The nodes are stratified according to the TI-RADS system: 1 – in the modification J.Y. Kwak et al. (2011), 2 – according to the  proposed system, taking into account small ultrasound signs of  thyroid cancer. High reproducibility of both systems are obtained. In the first system 13.7% of cancer nodes fell into the category of TI- RADS 3 (benign formations), in the second system only 5% of  cancers fell into the category of TI-RADS 3, which is important for  biopsy selection. The sensitivity of the first system was TI-RADS  82.05%, of the second system – 94.87%.Conclusions.Classification of TI-RADS can be used to interpret the  ultrasound results of thyroid nodules, taking into account both the  main large and small ultrasound signs of cancer. For its validation in  our country, it is necessary to further broad discussion of the proposed TI-RADS system.

Interphase distribution of 2-furylethylenes

1985 ◽  
Vol 50 (8) ◽  
pp. 1642-1647 ◽  
Author(s):  
Štefan Baláž ◽  
Anton Kuchár ◽  
Ernest Šturdík ◽  
Michal Rosenberg ◽  
Ladislav Štibrányi ◽  
...  
Keyword(s):  
Partition Coefficient ◽  
Partition Coefficients ◽  
Transport Rate ◽  
Phase System ◽  
Two Phase ◽  
Interphase Distribution ◽  
Distribution Kinetics ◽  
System 1 ◽  
Kinetics Of

The distribution kinetics of 35 2-furylethylene derivatives in two-phase system 1-octanol-water was investigated. The transport rate parameters in direction water-1-octanol (l1) and backwards (l2) are partition coefficient P = l1/l2 dependent according to equations l1 = logP - log(βP + 1) + const., l2 = -log(βP + 1) + const., const. = -5.600, β = 0.261. Importance of this finding for assesment of distribution of compounds under investigation in biosystems and also the suitability of the presented method for determination of partition coefficients are discussed.

Pyrido [2,3-d] thieno [3,2-b] [6H]thiopyran - ein neues heterocyclisches Ringsystem [1] / Pyrido [2,3-d]thieno[3,2-b] [6 H]thiopyran - a New Heterocyclic Ring System [1]

1979 ◽  
Vol 34 (11) ◽  
pp. 1573-1575 ◽  
Author(s):  
Klaus Beelitz ◽  
Klaus Praefcke ◽  
Salo Gronowitz
Keyword(s):  
Uv Irradiation ◽  
Benzene Solution ◽  
Heterocyclic Ring ◽  
Ring System ◽  
Spectroscopic Methods ◽  
System 1

Abstract UV irradiation of S-(3′-thienyl)2-chloro-thionicotinate (1) in benzene solution leads via dehydrohalogenation and cy clization in competition to α-cleavage to formation of thio-lactone 2 besides aldehyde 3 and disulphide 4. 2 contains a new heterocyclic ring system which has been confirmed by spectroscopic methods.

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