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 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 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.

The Game Performance Assessment Instrument (GPAI): Some Concerns and Solutions for Further Development

2008 ◽  
Vol 27 (2) ◽  
pp. 220-240 ◽  
Author(s):  
Daniel Memmert ◽  
Stephen Harvey
Keyword(s):  
Performance Assessment ◽  
Performance Index ◽  
Assessment Instrument ◽  
Coding System ◽  
Performance Indices ◽  
Observer Reliability ◽  
System 1 ◽  
Further Development ◽  
Game Performance

The purpose of this article is to discuss some concerns with the Game Performance Assessment Instrument (GPAI). This review of the GPAI includes five perceived problems with the GPAI scoring and coding system: (1) calculation of individual and overall game performance indices, (2) use of game involvement versus game performance index to analyze game performance, (3) observer reliability, (4) nonlinearity, and (5) usefulness of action. In this article, we suggest a reexamination of the GPAI scoring and coding system that will lead to more efficient use of this game performance instrument. Some of the suggested modifications can be implemented quickly, whereas others need further research.

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.

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.

The stability of dislocation networks under various oxygen-doping conditions in superconducting Bi2Sr2CaCu2Oy single crystals and their influence on the flux pinning properties

1994 ◽  
Vol 52 ◽  
pp. 802-803
Author(s):  
Y. Feng ◽  
X. Y. Cai ◽  
R. J. Kelley ◽  
D. C. Larbalestier
Keyword(s):  
Single Crystals ◽  
Oxygen Content ◽  
Basal Plane ◽  
Flux Pinning ◽  
Pinning Centers ◽  
Before And After ◽  
Anomalous Peak ◽  
Basal Plane Dislocation ◽  
The Stability ◽  
Further Development

The issue of strong flux pinning is crucial to the further development of high critical current density Bi-Sr-Ca-Cu-O (BSCCO) superconductors in conductor-like applications, yet the pinning mechanisms are still much debated. Anomalous peaks in the M-H (magnetization vs. magnetic field) loops are commonly observed in Bi2Sr2CaCu2Oy (Bi-2212) single crystals. Oxygen vacancies may be effective flux pinning centers in BSCCO, as has been found in YBCO. However, it has also been proposed that basal-plane dislocation networks also act as effective pinning centers. Yang et al. proposed that the characteristic scale of the basal-plane dislocation networksmay strongly depend on oxygen content and the anomalous peak in the M-H loop at ˜20-30K may be due tothe flux pinning of decoupled two-dimensional pancake vortices by the dislocation networks. In light of this, we have performed an insitu observation on the dislocation networks precisely at the same region before and after annealing in air, vacuumand oxygen, in order to verify whether the dislocation networks change with varying oxygen content Inall cases, we have not found any noticeable changes in dislocation structure, regardless of the drastic changes in Tc and the anomalous magnetization. Therefore, it does not appear that the anomalous peak in the M-H loops is controlled by the basal-plane dislocation networks.

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.

Perceived Burden of Informal Caregivers of a Chronically Ill Older Family Member

GeroPsych ◽  
2011 ◽  
Vol 24 (3) ◽  
pp. 143-154 ◽  
Author(s):  
Elmar Gräßel ◽  
Raffaela Adabbo
Keyword(s):  
Family Member ◽  
Informal Caregiver ◽  
Chronically Ill ◽  
Stress Model ◽  
The Past ◽  
Perceived Burden ◽  
Hypothetical Construct ◽  
Care Situation ◽  
The Impact ◽  
Further Development

The burden of caregivers has been intensively researched for the past 30 years and has resulted in a multitude of individual findings. This review illustrates the significance of the hypothetical construct of perceived burden for the further development and design of the homecare situation. Following explanations regarding the term informal caregiver, we derive the construct burden from its conceptual association with the transactional stress model of Lazarus and Folkman. Once the extent and characteristics of burden have been set forth, we then present the impact of perceived burden as the care situation. The question of predictors of burden will lead into the last section from which implications can be derived for homecare and relief of caregivers.

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