9 research outputs found
The Constructive procedures in the spatial transformations of the surface elliptical hyperboloid of one sheet
ΠΠ΅Π΄Π½ΠΎΠ³ΡΠ°Π½ΠΈ Π΅Π»ΠΈΠΏΡΠΈΡΠΊΠΈ Ρ
ΠΈΠΏΠ΅ΡΠ±ΠΎΠ»ΠΎΠΈΠ΄ (ΠΠΠ₯) ΡΠ΅ Π½Π°ΡΠΎΠΏΡΡΠΈΡΠΈ ΡΠ»ΡΡΠ°Ρ ΠΏΠΎΠ²ΡΡΠΈ Π΄Π²ΠΎΡΡΡΡΠΊΠ΅ Π·Π°ΠΊΡΠΈΠ²ΡΠ΅Π½ΠΎΡΡΠΈ, ΠΈΠ· ΠΏΠΎΡΠΎΠ΄ΠΈΡΠ΅ ΠΏΡΠ°Π²ΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΠΈΡ
ΠΏΠΎΠ²ΡΡΠΈ, ΠΊΠΎΡΠ° Π½Π°ΡΡΠ°ΡΠ΅ ΠΊΠ»ΠΈΠ·Π°ΡΠ΅ΠΌ ΡΠ΅Π΄Π½Π΅ ΡΡΠ°Π½ΡΠ²Π΅ΡΠ·Π°Π»Π΅βΠ³Π΅Π½Π΅ΡΠ°ΡΡΠΈΡΠ΅, Π΄ΡΠΆ ΡΡΠΈ Π΄ΠΈΡΠ΅ΠΊΡΡΠΈΡΠ΅ β ΠΌΠΈΠΌΠΎΠΈΠ»Π°Π·Π½Π΅ ΠΏΡΠ°Π²Π΅ ΠΏΡΠΎΡΡΠΎΡΠ°. ΠΠΈΡΠ΅ΡΡΠ°ΡΠΈΡΠ° Π΄Π°ΡΠ΅ ΠΎΠ΄Π³ΠΎΠ²ΠΎΡ Π½Π° Π΄ΡΡΠ³Π°ΡΠΈΡΠΈ ΠΏΡΠΈΠ»Π°Π· Π·Π° ΠΏΠΎΡΡΠ°Π²ΡΠ°ΡΠ΅ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠ²Π½ΠΎβΠ³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΡΠΊΠΎΠ³ ΠΎΠΊΠ²ΠΈΡΠ° ΠΏΠΎΠ²ΡΡΠΈ Ρ ΠΏΡΠΎΡΡΠΎΡ. ΠΠ°Π΄Π°Π²Π°ΡΠ΅ΠΌ ΠΏΡΠΎΡΡΠΎΡΠ½ΠΎΠ³ ΡΠ΅ΡΡΠΎΡΠ΅ΠΌΠ΅Π½ΠΈΠΊΠ° β Π½ΠΎΡΠ°ΡΠ° Π²ΠΎΠ΄ΠΈΡΠ° ΠΏΠΎΠ²ΡΡΠΈ, Ρ ΡΠ°Π·Π»ΠΈΡΠΈΡΠΈΠΌ Π²Π°ΡΠΈΡΠ°Π½ΡΠ°ΠΌΠ° ΠΏΠΎΠ»ΠΎΠΆΠ°ΡΠ°, Π΄Π²Π° ΠΏΡΡΠ° ΠΏΠΎ ΡΡΠΈ ΠΈΠ·Π²ΠΎΠ΄Π½ΠΈΡΠ΅, ΠΈΠ· ΡΠ°Π·Π»ΠΈΡΠΈΡΠΈΡ
ΡΠΈΡΡΠ΅ΠΌΠ° ΠΈΠ·Π²ΠΎΠ΄Π½ΠΈΡΠ°, Ρ Π½ΠΎΠ²ΠΎΠΌ ΠΎΠΊΠ²ΠΈΡΡ, ΡΠ°Π·Π²ΠΈΡΠ΅Π½ ΡΠ΅ Π½ΠΈΠ· ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠ²Π½ΠΈΡ
ΠΏΠΎΡΡΡΠΏΠ°ΠΊΠ°, ΠΊΠΎΡΠΈΠΌΠ° ΡΠ΅ Π³Π΅Π½Π΅ΡΠΈΡΠ΅ ΠΏΠΎΠ²ΡΡ ΠΈ ΠΎΠ΄ΡΠ΅ΡΡΡΡ Π³Π»Π°Π²Π½ΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈ ΠΠΠ₯βΠ°: ΡΡΠ΅Π΄ΠΈΡΡΠ΅, Π³Π»Π°Π²Π½Π΅ ΠΎΡΡΠΎΠ³ΠΎΠ½Π°Π»Π½Π΅ ΠΎΡΠ΅ ΠΈ ΡΠ°Π²Π½ΠΈ ΡΠΈΠΌΠ΅ΡΡΠΈΡΠ΅, ΡΡΡΠΈΠΊΡΠΈΠΎΠ½Π° Π΅Π»ΠΈΠΏΡΠ° ΠΈ ΡΠ΅ΠΌΠ΅Π½Π° ΠΈ ΡΡΠ²ΡΡΡΡΡ ΡΠΈΡ
ΠΎΠ²Π΅ ΠΌΠ΅ΡΡΡΠΎΠ±Π½Π΅ ΡΠ΅Π»Π°ΡΠΈΡΠ΅. ΠΠΎΡΡΡΠΏΡΠΈΠΌΠ° ΠΈ Π½Π°ΡΡΠ½ΠΎ Π·Π°ΡΠ½ΠΎΠ²Π°Π½ΠΈΠΌ ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌΠ° ΠΏΡΠΎΡΠ΅ΠΊΡΠΈΠ²Π½Π΅ ΡΠΈΠ½ΡΠ΅ΡΠΈΡΠΊΠ΅ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅, Π½Π°ΡΡΡΠ½Π΅ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ ΠΈ Π°Π»Π°ΡΠΈΠΌΠ° ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΡΠΊΠ΅ Π³ΡΠ°ΡΠΈΠΊΠ΅, Ρ 3D ΠΎΠΊΡΡΠΆΠ΅ΡΡ (ΡΠ· ΡΠΏΠΎΡΡΠ΅Π±Ρ ΡΠΎΡΡΠ²Π΅ΡΠ° Auto CAD), ΡΠ΅Π·Π° Π΄Π°ΡΠ΅ Π½Π°ΡΡΠ½ΠΈ Π΄ΠΎΠΏΡΠΈΠ½ΠΎΡ, ΠΊΡΠΎΠ· ΡΠ΅ΡΠ΅ΡΠ° β ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠ²Π½Π΅ ΠΏΠΎΡΡΡΠΏΠΊΠ΅ ΠΈ ΡΠ΅ΠΎΡΠ΅ΡΡΠΊΠ΅ Π·Π°ΠΊΡΡΡΠΊΠ΅, Ρ ΡΡΠ΅ΡΠΈ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ ΠΏΡΠ°Π²ΠΎΠΈΠ·Π²ΠΎΠ΄Π½Π΅ ΠΏΠΎΠ²ΡΡΠΈ ΠΠΠ₯βΠ° ΠΈ ΡΠ΅Π½ΠΈΡ
ΡΠΈΠΏΠΎΠ²Π°.
Π£ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠ²Π½ΠΈΠΌ ΠΏΠΎΡΡΡΠΏΡΠΈΠΌΠ° ΠΏΡΠΎΡΡΠΎΡΠ½ΠΈΡ
Π°ΡΠΈΠ½ΠΈΡ
ΡΡΠ°Π½ΡΡΠΎΡΠΌΠ°ΡΠΈΡΠ° ΡΠ΅Π΄Π½ΠΎΠ³ΡΠ°Π½ΠΈΡ
Ρ
ΠΈΠΏΠ΅ΡΠ±ΠΎΠ»ΠΎΠΈΠ΄Π°, ΡΠΈΡΠ΅ ΡΡ Π²ΠΎΠ΄ΠΈΡΠ΅ ΡΠΏΠΈΡΠ°Π½Π΅ Ρ ΡΡΠΎΡΡΡΠ°Π½Π΅ ΠΏΡΠΈΠ·ΠΌΠ΅, ΡΡΠ²ΡΡΠ΅Π½Π΅ ΡΡ ΠΈΠ½Π²Π°ΡΠΈΡΠ°Π½ΡΠ΅ ΡΠΈΠΏΠΎΠ²Π° ΡΡΠ°Π½ΡΡΠΎΡΠΌΠ°ΡΠΈΡΠ°. ΠΠ° ΠΏΠΎΡΡΠ°Π²ΡΠ΅Π½ΠΈΠΌ ΠΏΡΠΈΠ½ΡΠΈΠΏΠΈΠΌΠ° ΠΈΠ½ΠΈΡΠΈβΡΠ°Π½Π°.ΡΡ Π΄Π°ΡΠ° ΠΈΡΡΡΠ°ΠΆΠΈΠ²Π°ΡΠ° ΡΠ΅Π»Π°ΡΠΈΡΠ° ΠΎΠΏΡΡΠΈΡ
ΠΈ ΡΠΏΠ΅ΡΠΈΡΠ°Π»Π½ΠΈΡ
ΡΠΈΠΏΠΎΠ²Π° ΠΠ₯, Ρ ΠΎΠΊΠ²ΠΈΡΡ ΠΈΡΡΠ΅ ΡΠ°ΠΌΠΈΠ»ΠΈΡΠ΅ ΠΏΠΎΠ²ΡΡΠΈ. ΠΠ½Π°Π»ΠΈΠ·ΠΎΠΌ ΡΠ²ΠΈΡ
ΡΠΈΠΏΠΎΠ²Π° ΠΏΡΠ΅ΡΠ΅ΠΊΠ° ΠΏΠΎΠ²ΡΡΠΈ ΠΠΠ₯βΠ° ΡΠ° ΡΠ°Π²Π½ΠΈΠΌΠ°, ΡΠ· ΡΡΠΏΠΎΡΡΠ°Π²ΡΠ°ΡΠ΅ ΠΊΠΎΡΠ΅Π»Π°ΡΠΈΡΠ° ΡΠ° ΠΏΠΎΠ»Π°ΡΠ½ΠΈΠΌ ΠΊΠ°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠ°ΠΌΠ° ΠΏΠΎΠ²ΡΡΠΈ, ΡΡΠ²ΠΎΡΠ΅Π½Π° ΡΠ΅ ΡΠ΅ΠΎΡΠΈΡΡΠΊΠ° Π±Π°Π·Π° Π·Π½Π°ΡΠ°, ΠΊΠΎΡΠΈΡΠ½Π° Π·Π° ΠΏΡΠ°ΠΊΡΠΈΡΠ½Ρ ΠΏΡΠΈΠΌΠ΅Π½Ρ ΡΠ΅Π»Π΅ ΠΏΠΎΠ²ΡΡΠΈ, ΠΈΠ»ΠΈ ΡΠ΅Π½ΠΈΡ
ΠΈΡΠ΅ΡΠ°ΠΊΠ°, Ρ ΠΏΠΎΡΡΡΠΏΡΠΈΠΌΠ° Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΡΠΊΠΎΠ³ 3D ΠΌΠΎΠ΄Π΅Π»ΠΎΠ²Π°ΡΠ°. ΠΠΎΠ΄Π΅Π»ΠΈβΡΡΡΡΠΊΡΡΡΠ΅, ΡΠ° Π·Π°Π΄Π°ΡΠΈΠΌ ΠΏΡΠ°Π²ΠΈΠ»Π½ΠΈΠΌ ΠΌΠ°ΡΡΠΈΡΠ°ΠΌΠ°, ΠΊΡΠ΅ΠΈΡΠ°Π½ΠΈ 3D ΠΏΠΎΡΡΡΠΏΡΠΈΠΌΠ°, ΠΎΠ΄ ΠΈΡΠ΅ΡΠ°ΠΊΠ° ΠΏΡΠ°Π²ΠΎΠ³ ΠΈΠ»ΠΈ ΠΊΠΎΡΠΎΠ³ ΡΠΈΠΏΠ° ΠΠΠ₯βΠ°, ΠΏΡΠ΅Π΄ΡΡΠ°Π²ΡΠ°ΡΡ ΠΏΡΠΎΡΠΎΡΠΈΠΏ Π·Π° ΡΠΈΡΠΎΠΊΡ ΠΏΠ°Π»Π΅ΡΡ ΠΌΠΎΠ³ΡΡΠ½ΠΎΡΡΠΈ ΠΏΡΠΈΠΌΠ΅Π½Π΅ Ρ Π°ΡΡ
ΠΈΡΠ΅ΠΊΡΠΎΠ½ΡΠΊΠΎΠΌ ΠΎΠ±Π»ΠΈΠΊΠΎΠ²Π°ΡΡ ΠΊΡΠΎΠ²Π½ΠΈΡ
ΠΏΠΎΠ²ΡΡΠΈΠ½Π° ΠΈΠ»ΠΈ ΡΠ΅Π»ΠΈΡ
ΠΎΠ±ΡΠ΅ΠΊΠ°ΡΠ°. Π‘Π»ΠΈΡΠ°Π½, ΠΏΡΠ°ΠΊΡΠΈΡΠ½ΠΎ ΠΏΡΠΈΠΌΠ΅Π½ΡΠΈΠ², ΡΠ΅Π·ΡΠ»ΡΠ°Ρ Π΄Π°ΠΎ ΡΠ΅ ΠΈ Π΄Π΅ΠΎ ΠΈΡΡΡΠ°ΠΆΠΈΠ²Π°ΡΠ° Π²Π΅Π·Π°Π½ Π·Π° ΠΏΡΠΎΠ΄ΠΎΡΠ΅
ΠΎΡΠ½ΠΎΠ²Π½ΠΈΡ
ΠΏΠΎΠ²ΡΡΠΈ Π΄ΡΡΠ³ΠΎΠ³ ΡΡΠ΅ΠΏΠ΅Π½Π° ΠΈ ΠΠΠ₯βΠ°. ΠΠ²Π°ΠΊΠ²Π΅ ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΈΡΠ΅ ΠΏΠΎΠ²ΡΡΠΈ, Ρ ΠΏΠΎΡΡΡΠΏΡΠΈΠΌΠ° ΠΏΡΠΎΡΡΠΎΡΠ½ΠΎΠ³ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΡΠΊΠΎΠ³ ΠΌΠΎΠ΄Π΅Π»ΠΎΠ²Π°ΡΠ° ΡΡ ΡΠΊΡΠΏ ΡΠΌΠ΅ΡΠ½ΠΈΡΠ°, ΠΊΠ°ΠΎ Π΄Π΅ΠΎ ΠΈΠ½ΠΈΡΠΈΡΠ°ΡΠΈΠ²Π΅ ΠΈ ΠΈΠ½ΡΠΏΠΈΡΠ°ΡΠΈΡΠ΅ Π·Π° ΠΏΡΠΎΡΠ΅ΠΊΡΠ°Π½ΡΠ΅ ΠΈ Π³ΡΠ°Π΄ΠΈΡΠ΅ΡΠ΅. Π Π΅Π·ΡΠ»Π°ΡΠ°ΡΠΈ ΠΈΡΡΡΠ°ΠΆΠΈΠ²Π°ΡΠ° ΡΡ ΡΠ΅Π°Π»ΠΈΠ·ΠΎΠ²Π°Π½ΠΈ ΠΈ ΠΊΡΠΎΠ· Π΄Π²Π΅ Π°ΠΏΠ»ΠΈΠΊΠ°ΡΠΈΡΠ΅ Ρ ΡΠΎΡΡΠ²Π΅ΡΡ Auto CAD (ΠΏΠΈΡΠ°Π½Ρ Πutoβlisp ΠΏΡΠΎΠ³ΡΠ°ΠΌΡΠΊΠΈΠΌ ΡΠ΅Π·ΠΈΠΊΠΎΠΌ), ΠΊΠΎΡΠ° ΠΊΠΎΡΠΈΡΡΠΈ ΠΊΡΡΠΆΠ½Π΅ ΠΏΡΠ΅ΡΠ΅ΠΊΠ΅ ΠΠΠ₯βΠ°, Π·Π° Π³Π΅Π½Π΅ΡΠΈΡΠ°ΡΠ΅ ΠΆΠΈΡΠ°Π½ΠΎΠ³ ΠΈ ΠΏΠΎΠ²ΡΡΠΈΠ½ΡΠΊΠΎΠ³ ΠΌΠΎΠ΄Π΅Π»Π° ΠΏΠΎΠ²ΡΡΠΈ, ΡΠ° ΡΡΠΈΠ°Π½Π³ΡΠ»ΠΈΡΠ°Π½ΠΎΠΌ ΠΌΡΠ΅ΠΆΠΎΠΌ. ΠΠΏΠ»ΠΈΠΊΠ°ΡΠΈΠ²Π½ΠΎΡΡ ΠΏΡΠ΅ΡΠ΅ΠΊΠ° ΠΏΠΎΠ²ΡΡΠΈ ΠΏΠΎ ΠΈΠ·Π²ΠΎΠ΄Π½ΠΈΡΠ°ΠΌΠ° ΠΈ ΠΊΡΡΠΆΠ½ΠΈΡΠ°ΠΌΠ°, ΠΎΠ΄ Π·Π½Π°ΡΠ°ΡΠ° ΡΠ΅ Π·Π° ΠΏΡΠ°ΠΊΡΡ Π³ΡΠ°ΡΠ΅ΡΠ°, ΠΊΠΎΡΠ° ΡΠ΅ΠΆΠΈ ΡΠ΅Π΄Π½ΠΎΡΡΠ°Π²Π½ΠΎΡΡΠΈ ΠΈΠ·Π²ΠΎΡΠ΅ΡΠ°, Π° Π΄Π° ΠΏΡΠΈ ΡΠΎΠΌΠ΅ Π½Π΅ ΡΠΌΠ°ΡΡΡΠ΅ Π΅ΡΡΠ΅ΡΡΠΊΡ Π²ΡΠ΅Π΄Π½ΠΎΡΡ ΡΠ΅Π»ΠΎΠΊΡΠΏΠ½Π΅ ΡΠΎΡΠΌΠ΅...Elliptic hyperboloid of one sheet (EHOS) is the general case of a double curved surface, from the family of ruled surfaces, which generates by ruling of a lineβgenerator along three directing skewed lines, in the space. The dissertation gives an answer to a task β finding a new approach in creating constructiveβgeometry "boundaries" for this surface in the space settlement. A wide range of constructive procedures, for the determination and mutual relations of the main parameters of EHOS: center of the surface, orthogonal axes, planes of symmetry, minimal section curve (elliptical "throat") and its vertexes came out from the concept of hexagramic spatial "carrier" of two times three directors β skewed lines, in variety of their positions. The employment of procedures and scientifically based methods of Projective Synthetic Geometry, Descriptive Geometry and tools of computer graphics, in 3D surroundings (using Auto CAD software for engineers), are of importance for the scientific contributions of this dissertation, achieved solutions β constructive procedures and theoretical conclusions, in the sphere of geometry of ruled surface EHOS and its types.
In the constructive procedures of spatial affine transformations of hyperboloids of one sheet, whose directing lines are "inscribed" in three sided prisms, the invariants of all the types of transformations are determined. Further investigations, concerning relations of general and special types of HOS, inside the same family of surfaces, are initiated by settled principles. The analysis of all the types of sections of EHOS, including the correlation to the polar properties of the surface, resulted with theoretical base, as an input for the practical application of "whole" surface or its fragments, in the procedures of 3D geometrical modeling. The models β structures, above regular patterns (polygons) are created by 3D procedures and tools, using fragments of straight or inclined EHOS. They represent the prototypes for the creative palette of possible architectural shapes of roofs or buildings. Very similar results came out of the part of research, concerning intersections of EHOS and basic second order surfaces (primitives): cone, cylinder and sphere. The "combinations" of such surfaces, in 3D
geometrical modeling procedures, offered just some directions, like an initiation and inspiration for the architects and civil engineers..
Review of Particle Physics
The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,873 new measurements from 758 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 118 reviews are many that are new or heavily revised, including a new review on Neutrinos in Cosmology.Starting with this edition, the Review is divided into two volumes. Volume 1 includes the Summary Tables and all review articles. Volume 2 consists of the Particle Listings. Review articles that were previously part of the Listings are now included in volume 1.The complete Review (both volumes) is published online on the website of the Particle Data Group (http://pdg.lbl.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is also available.The 2018 edition of the Review of Particle Physics should be cited as: M. Tanabashi (Particle Data Group), Phys. Rev. D 98, 030001 (2018)
Review of Particle Physics: Particle Data Group
The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,873
new measurements from 758 papers, we list, evaluate, and average measured properties of gauge bosons and the
recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical
particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search
limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs
Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology,
Particle Detectors, Colliders, Probability and Statistics. Among the 118 reviews are many that are new or heavily
revised, including a new review on Neutrinos in Cosmology.
Starting with this edition, the Review is divided into two volumes. Volume 1 includes the Summary Tables
and all review articles. Volume 2 consists of the Particle Listings. Review articles that were previously part of the
Listings are now included in volume 1.
The complete Review (both volumes) is published online on the website of the Particle Data Group
(http://pdg.lbl.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet
with the Summary Tables and essential tables, figures, and equations from selected review articles is also available