scholarly journals Triangle conics and cubics

2021 ◽  
Vol 25 (2(36)) ◽  
pp. 58-74
Author(s):  
R. Skuratovskii ◽  
V. Strarodub
Keyword(s):  
Projective Geometry ◽  
Main Task ◽  
Geometrical Object ◽  
Classical Geometry ◽  
Euclidian Space ◽  
Base Curve ◽  
Triangle Centers ◽  
Pass Through

This is a paper about triangle cubics and conics in classical geometry with elements of projective geometry. In recent years, N.J. Wildberger has actively dealt with this topic using an algebraic perspective. Triangle conics were also studied in detail by H.M. Cundy and C.F. Parry recently. The main task of the article was to develop an algorithm for creating curves, which pass through triangle centers. During the research, it was noticed that some different triangle centers in distinct triangles coincide. The simplest example: an incenter in a base triangle is an orthocenter in an excentral triangle. This was the key for creating an algorithm. Indeed, we can match points belonging to one curve (base curve) with other points of another triangle. Therefore, we get a new intersting geometrical object. During the research were derived number of new triangle conics and cubics, were considered their properties in Euclidian space. In addition, was discussed corollaries of the obtained theorems in projective geometry, what proves that all of the descovered results could be transfered to the projeticve plane.

scholarly journals The Russian China in the Last D. A. Prigov’s Novel

2020 ◽  
Vol 15 (1) ◽  
pp. 146-165
Author(s):  
E. V. Kapinos
Keyword(s):  
Far East ◽  
Main Task ◽  
The Novel ◽  
Main Character ◽  
The Far East ◽  
The People ◽  
The Gift ◽  
Pass Through ◽  
John Wilkins

The article relates to the last novel by D. A. Prigov “Katya the Chinese” (published in 2007), based on the memories of the writer’s wife, N. G. Burova from Harbin, who was born and grew up in the Russian China and left it in 1950s. The main task of the article is to show what stylistic techniques, plots, motives, subtexts allow to recreate the atmosphere of the Russian China and the generalized image of the East. The narration synthesizes the memories of the people of Harbin and recognizable storylines of D. A. Prigov’s work (such, for example, as a fantastic bestiary). In the subtext of the novel the following works are found: feuilleton by I. Ilf and E. Petrov “Nikudykin the Commtied”, pro- totyped by the “futurist of life” V. Goltsshmidt, who traveled in 1918–1920s with lectures on Siberia and the Far East, V. Nabokov’s novel “The Gift” with his father’s Asian journey (the plot about his father in “The Gift” influenced the plot about the girl’s father in “Katya the Chinese”), the “Chinese” stories by J. L. Borges “The Garden of Forking Paths” and “The Analytical language of John Wilkins”, etc. In Prigov’s narrative, a particular role is played by an autobiographical excerpt about the Tashkent artist A. N. Volkov and an insertion novel about the “Monastery of Flying Cats”, in- tentionally inaccurately stylized by Prigov as a Chinese legend. Many motifs and subtexts of the novel pass through the prism of the child’s consciousness (the “girl’s”, who is the main character of the novel), which gives the image of the Russian East, along with documentary, fantastic features.

scholarly journals The Three Reflections Theorem Revisited

KoG ◽  
2018 ◽  
pp. 41-48
Author(s):  
Gunter Weiss
Keyword(s):  
Projective Geometry ◽  
Euclidean Plane ◽  
Projective Planes ◽  
Common Point ◽  
Point Of View ◽  
Euclidean Case ◽  
Minkowski Metric ◽  
Point Reflection ◽  
Pass Through ◽  
The Given

It is well-known that, in a Euclidean plane, the product of three reflections is again a reflection, iff their axes pass through a common point. For this ``Three reflections Theorem'' (3RT) also non-Euclidean versions exist, see e.g. [4]. This article presents affine versions of it, considering a triplet of skew reflections with axes through a common point. It turns out that the essence of all those cases of 3RT is that the three pairs (axis, reflection direction) of the given (skew) reflections can be observed as an involutoric projectivity. For the Euclidean case and its non-Euclidean counterparts this property is automatically fulfilled. From the projective geometry point of view a (skew) reflection is nothing but a harmonic homology. In the affine situation a reflection is an indirect involutoric transformation, while ``direct'' or ``indirect'' makes no sense in projective planes. A harmonic homology allows an interpretation both, as an axial reflection and as a point reflection. Nevertheless, one might study products of three harmonic homologies, which result in a harmonic homology again. Some special mutual positions of axes and centres of the given homologies lead to elations or even to the identity, too. A consequence of the presented results are further generalisations of the 3RT, e.g. in planes with Minkowski metric, affine or projective 3-space, or in circle geometries.

History and internal picture of the disease

1934 ◽  
Vol 30 (2) ◽  
pp. 151-161
Author(s):  
R. A. Luria
Keyword(s):  
General Practitioner ◽  
Outpatient Clinics ◽  
Main Task ◽  
Socialist Society ◽  
Ability To Work ◽  
Internal Organs ◽  
Pass Through

The main task of the general practitioner, especially in our era of building a new socialist society, is to recognize diseases of the internal organs as early as possible, when one can practically count on recovery and full restoration of a person's ability to work. If we exclude acute illnesses, the majority of patients with early forms of disease are those millions of workers who pass through outpatient clinics, polyclinics and dispensaries and who are relatively rarely admitted to hospitals not only for treatment but, most importantly, for the timely establishment of correct disease recognition.

scholarly journals Policy of Inflation Targeting in the Presence of Fiscal Deficit and External Debt: Opt or Not to Opt.

2011 ◽  
Vol 50 (4II) ◽  
pp. 841-852
Author(s):  
Muhammad Ali Kemal
Keyword(s):  
Exchange Rate ◽  
Interest Rate ◽  
Real Exchange Rate ◽  
Real Interest Rate ◽  
Foreign Exchange Market ◽  
Inflation Targeting ◽  
Main Task ◽  
Short Run ◽  
Pass Through ◽  
Exchange Rate Pass Through

The main task of the macroeconomic policy-makers is to control unemployment and inflation at the minimum possible level. Different policies have been tried to control inflation at its minimum possible level and inflation targeting is the most popular among them. It is the commitment to maintain inflation at the announced level and use interest rate as an instrument to control it if it is expected to diverge from the announced level. However in a higher \dollar denominated debt. country Central Bank is reluctant to increase interest rate because it pressurises the foreign exchange market, which leads to exchange rate depreciation. If there is exchange rate pass through effect to prices, depreciation leads to increase in prices. Thus increase in interest rate does not decrease prices instead results in increase in prices. The two important linkages were tested in this study are (i) increase in real interest rate depreciates the currency, and (ii) depreciation in real exchange rate leads to increase in prices. Using VAR model we concluded that real exchange rate is not significantly associated to the real interest rate in the short run and exchange rate pass through effect to prices is not present in Pakistan.

Hybrid Twist and Wrench Control for a Robotic Manipulator

1988 ◽  
Vol 110 (2) ◽  
pp. 138-144 ◽  
Author(s):  
H. Lipkin ◽  
J. Duffy
Keyword(s):  
Projective Geometry ◽  
Euclidean Geometry ◽  
Hybrid Control ◽  
Necessary Conditions ◽  
Screw Theory ◽  
Unit Length ◽  
Rigid Bodies ◽  
Classical Geometry ◽  
Invariant Formulation ◽  
Elliptic Geometry

Three necessary conditions derived from classical geometry are proposed to evaluate formulations for the simultaneous twist and wrench control of rigid bodies, and for any theory to be meaningful it must be invariant with respect to (1) Euclidean collineations, (2) change of (Euclidean) unit length, and (3) change of basis. It is demonstrated in this paper that a previously established theory of hybrid control for robot manipulators is in fact based on the metric of elliptic geometry and is thus noninvariant with respect to (1) and (2). A new alternative invariant formulation based on the metric of Euclidean geometry and an induced metric of projective geometry is presented in terms of screw theory. An example of insertion illustrates both the invariant and noninvariant methods.

Instrumentation for detecting channelling radiation in the high-voltage electron microscope

1983 ◽  
Vol 41 ◽  
pp. 318-319
Author(s):  
J. H. Butler ◽  
C. J. Humphreys
Keyword(s):  
Monochromatic Light ◽  
Incident Beam ◽  
Laboratory Frame ◽  
Relativistic Electrons ◽  
Voltage Electron ◽  
Dipole Emission ◽  
Sinusoidal Oscillations ◽  
Pass Through ◽  
Incident Beam Energy ◽  
Increasing Function

Electromagnetic radiation is emitted when fast (relativistic) electrons pass through crystal targets which are oriented in a preferential (channelling) direction with respect to the incident beam. In the classical sense, the electrons perform sinusoidal oscillations as they propagate through the crystal (as illustrated in Fig. 1 for the case of planar channelling). When viewed in the electron rest frame, this motion, a result of successive Bragg reflections, gives rise to familiar dipole emission. In the laboratory frame, the radiation is seen to be of a higher energy (because of the Doppler shift) and is also compressed into a narrower cone of emission (due to the relativistic “searchlight” effect). The energy and yield of this monochromatic light is a continuously increasing function of the incident beam energy and, for beam energies of 1 MeV and higher, it occurs in the x-ray and γ-ray regions of the spectrum. Consequently, much interest has been expressed in regard to the use of this phenomenon as the basis for fabricating a coherent, tunable radiation source.

Radiation Damage, Contrast and Statistics in High Resolution Biological Electron Microscopy

1970 ◽  
Vol 28 ◽  
pp. 260-261
Author(s):  
Robert M. Glaeser
Keyword(s):  
High Resolution ◽  
Particle Flux ◽  
Unit Area ◽  
Signal To Noise ◽  
Resolution Image ◽  
High Resolution Image ◽  
Pass Through ◽  
Counting Statistics ◽  
The Relationship ◽  
Picture Element

It is well known that a large flux of electrons must pass through a specimen in order to obtain a high resolution image while a smaller particle flux is satisfactory for a low resolution image. The minimum particle flux that is required depends upon the contrast in the image and the signal-to-noise (S/N) ratio at which the data are considered acceptable. For a given S/N associated with statistical fluxtuations, the relationship between contrast and “counting statistics” is s131_eqn1, where C = contrast; r2 is the area of a picture element corresponding to the resolution, r; N is the number of electrons incident per unit area of the specimen; f is the fraction of electrons that contribute to formation of the image, relative to the total number of electrons incident upon the object.

A New High Intensity Grid Cap for RCA-EMU-3 Electron Microscopes

1968 ◽  
Vol 26 ◽  
pp. 316-317
Author(s):  
George Christov ◽  
Bolivar J. Lloyd
Keyword(s):  
Electron Beam ◽  
Electron Microscope ◽  
High Voltage ◽  
High Intensity ◽  
Electron Gun ◽  
Tungsten Filament ◽  
Fluorescent Screen ◽  
Electron Microscopes ◽  
Pass Through ◽  
Ground Potential

A new high intensity grid cap has been designed for the RCA-EMU-3 electron microscope. Various parameters of the new grid cap were investigated to determine its characteristics. The increase in illumination produced provides ease of focusing on the fluorescent screen at magnifications from 1500 to 50,000 times using an accelerating voltage of 50 KV.The EMU-3 type electron gun assembly consists of a V-shaped tungsten filament for a cathode with a thin metal threaded cathode shield and an anode with a central aperture to permit the beam to course the length of the column. The cathode shield is negatively biased at a potential of several hundred volts with respect to the filament. The electron beam is formed by electrons emitted from the tip of the filament which pass through an aperture of 0.1 inch diameter in the cap and then it is accelerated by the negative high voltage through a 0.625 inch diameter aperture in the anode which is at ground potential.

Immunocytochemical localization of p65 with one-nanometer gold particles following silver development

1989 ◽  
Vol 47 ◽  
pp. 1042-1043
Author(s):  
Richard W. Burry ◽  
Diane M. Hayes
Keyword(s):  
Plasma Membrane ◽  
Bovine Serum Albumin ◽  
Calf Serum ◽  
Specific Protein ◽  
Immunocytochemical Localization ◽  
Electron Microscopic ◽  
Gold Particles ◽  
Pass Through ◽  
Label Distribution ◽  
Phosphate Buffered Saline

Electron microscopic (EM) immunocytochemistry localization of the neuron specific protein p65 could show which organelles contain this antigen. Antibodies (Ab) labeled with horseradish peroxidase (HRP) followed by chromogen development show a broad diffuse label distribution within cells and restricting identification of organelles. Particulate label (e.g. 10 nm colloidal gold) is highly desirable but not practical because penetration into cells requires destroying the plasma membrane. We report pre-embedding immunocytochemistry with a particulate marker, 1 nm gold, that will pass through membranes treated with saponin, a mild detergent.Cell cultures of the rat cerebellum were fixed in buffered 4% paraformaldehyde and 0.1% glutaraldehyde (Glut.). The buffer for all incubations and rinses was phosphate buffered saline with: 1% calf serum, 0.2% saponin, 0.1% gelatin, 50 mM glycine 1 mg/ml bovine serum albumin, and (not in the HRP labeled cultures) 0.02% sodium azide. The monoclonal #48 to p65 was used with three label systems: HRP, 1 nm avidin gold with IntenSE M development, and 1 nm avidin gold with Danscher development.

Is there an electron wind?

1990 ◽  
Vol 48 (4) ◽  
pp. 798-799
Author(s):  
L. D. Marks ◽  
J. P. Zhang
Keyword(s):  
Electron Microscopy ◽  
High Resolution Electron Microscopy ◽  
Zone Axis ◽  
Electron Holography ◽  
Electron Wave ◽  
Small Particles ◽  
Resolution Electron ◽  
Pass Through ◽  
Electron Wind ◽  
Inelastic Scatter

A not uncommon question in electron microscopy is what happens to the momentum transferred by the electron beam to a crystal. If the beam passes through a crystal and is preferentially diffracted in one direction, is the momentum ’lost’ by the beam transferred to the crystal? Newton’s third law implies that this must be the case. Some experimental observations also indicate that this is the case; for instance, with small particles if the particles are supported on the top surface of a film they often do not line up on the zone axis, but if they are on the bottom they do. However, if momentum is transferred to the crystal, then surely we are dealing with inelastic scattering, not elastic scattering and is not the scattering probability different? In addition, normally we consider inelastic scatter as incoherent, and therefore the part of the electron wave that is inelastically scattered will not coherently interfere with the part of the wave that is scattered; but, electron holography and high resolution electron microscopy work so the wave passing through a specimen must be coherent with the wave that does not pass through the specimen.

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