Gnomonic Projections on two planes

1906 ◽  
Vol 14 (65) ◽  
pp. 149-156 ◽  
Author(s):  
John W. Evans
Keyword(s):  
Fixed Point ◽  
Horizontal Plane ◽  
Vertical Plane ◽  
The Other ◽  
Unit Distance ◽  
Simultaneous Use

The gnomonic projection in which the faces of crystals are represented by the points where their normals through a fixed point–the centre of projection–meet a plane–the plane of projection–is already widely used by crystallographers. I propose in the following pages to show the advantages of the simultaneous use of two such planes of projection.It is in most cases convenient for the two planes to be at right angles, and for the centre of projection to be at an equal (unit) distance from each. Circumstances, however, in some cases render it desirable to vary these conditions. When the planes are at right angles, one may conveniently be described as the horizontal plane, and the other as the vertical plane.

Two Egyptian Construction Tools

1993 ◽  
Vol 86 (2) ◽  
pp. 166-167
Author(s):  
John F. Lamb
Keyword(s):  
Horizontal Plane ◽  
Vertical Plane ◽  
The Other

Among the objects in the Ramses II exhibition at Fair Park in Dallas in 1989 were two tools from the tomb of Sen-nedjem, one of Ramses II's workmen. One was a level for determining the horizontal plane, the other was a plumb level for determining the vertical plane.

scholarly journals 3. On the Combined Motions of the Magnetic Needle, and on the Aurora Borealis.

1851 ◽  
Vol 2 ◽  
pp. 334-350
Author(s):  
J. A. Broun
Keyword(s):  
Horizontal Plane ◽  
Magnetic Force ◽  
Vertical Plane ◽  
The Other ◽  
Aurora Borealis ◽  
Centre Of Gravity ◽  
True Position ◽  
Magnetic Needle ◽  
The Way

When a steel needle or rod is so constructed that its centre of gravity is in a finely-turned axle at right angles to its length, it will rest in any position when the axle is placed upon polished planes; when, however, we magnetize the needle, it assumes a position which is that of the direction of the magnetic force at the place: in this way we obtain the ordinary dipping-needle. The dipping-needle can obviously move only in one plane, that to which the axle is at right angles; were it possible to suspend it freely, so that it could move in every plane with every variation of the direction of the magnetic force, we should then be able, by observing the variations of its position, to determine at once the laws which a magnet in its true position obeys; this, however, we have not been able to do; even the small variations in the vertical plane, which we might expect to obtain from the ordinary dipping-needle, are nearly or altogether destroyed by the friction of the axle upon its supports; and there are many mechanical difficulties in the way of the other methods of suspension. It has been found convenient, then, to make use of the simplest methods of suspending magnets in a horizontal plane; and to endeavour to deduce, from the composition of their motions, the laws both of the variation of the force with which a truly suspended magnet is directed, and of the direction of that force itself.

The Horizontal-Vertical Illusion: Transfer of Illusion Decrement

1993 ◽  
Vol 77 (1) ◽  
pp. 339-347 ◽  
Author(s):  
Eleana Kubi ◽  
Burton M. Slotnick
Keyword(s):  
Horizontal Plane ◽  
Vertical Plane ◽  
Practice Effect ◽  
The Other ◽  
Horizontal Line ◽  
Not Given ◽  
Production Task ◽  
Alternate Form ◽  
Potential Factors ◽  
And Performance

Subjects first adjusted 20 vertical lines to be equal in length to the horizontal line in small or large inverted-T figures and were then given 10 additional trials on the other size figure. Vertical lines were made significantly shorter than the horizontal line but accuracy gradually improved and performance was not disrupted by the switch in figure size. By Trial 30, adjusted vertical lines did not differ from the length of the horizontal line. Other subjects were first tested on the small inverted-T figure and then asked to produce 1-in. lines in the vertical plane and in the horizontal plane. These subjects also improved on the adjustment task but, on the production task, were no more accurate than control subjects who were not given practice on the adjustment task. Thus, the magnitude of the Horizontal-Vertical Illusion decreases with practice alone and this practice effect readily transfers to figures of other sizes but not to an alternate form of the illusion. The potential factors responsible for the improvement and transfer are discussed.

scholarly journals Dielectric anisotropy as indicator of crystal orientation fabric in Dome Fuji ice core: method and initial results

2021 ◽  
pp. 1-12
Author(s):  
Tomotaka Saruya ◽  
Shuji Fujita ◽  
Ryo Inoue
Keyword(s):  
Crystal Orientation ◽  
Horizontal Plane ◽  
Ice Core ◽  
Vertical Plane ◽  
Vertical Direction ◽  
Core Sample ◽  
Dielectric Anisotropy ◽  
Principal Axes ◽  
Polycrystalline Ice ◽  
Initial Results

Abstract Polycrystalline ice is known to exhibit macroscopic anisotropy in relative permittivity (ɛ) depending on the crystal orientation fabric (COF). Using a new system designed to measure the tensorial components of ɛ, we investigated the dielectric anisotropy (Δɛ) of a deep ice core sample obtained from Dome Fuji, East Antarctica. This technique permits the continuous nondestructive assessment of the COF in thick ice sections. Measurements of vertical prism sections along the core showed that the Δɛ values in the vertical direction increased with increasing depth, supporting previous findings of c-axis clustering around the vertical direction. Analyses of horizontal disk sections demonstrated that the magnitude of Δɛ in the horizontal plane was 10–15% of that in the vertical plane. In addition, the directions of the principal axes of tensorial ɛ in the horizontal plane corresponded to the long or short axis of the elliptically elongated single-pole maximum COF. The data confirmed that Δɛ in the vertical and horizontal planes adequately indicated the preferred orientations of the c-axes, and that Δɛ can be considered to represent a direct substitute for the normalized COF eigenvalues. This new method could be extremely useful as a means of investigating continuous and depth-dependent variations in COF.

scholarly journals Well-definedness and observational equivalence for inductive–coinductive programs

2019 ◽  
Vol 29 (4) ◽  
pp. 419-468
Author(s):  
Henning Basold ◽  
Helle Hvid Hansen
Keyword(s):  
Fixed Point ◽  
Modal Logic ◽  
The Other ◽  
Observational Equivalence ◽  
Other Hand ◽  
Inductive Types ◽  
Point Types ◽  
Usual Topology

Abstract We define notions of well-definedness and observational equivalence for programs of mixed inductive and coinductive types. These notions are defined by means of tests formulas which combine structural congruence for inductive types and modal logic for coinductive types. Tests also correspond to certain evaluation contexts. We define a program to be well-defined if it is strongly normalizing under all tests, and two programs are observationally equivalent if they satisfy the same tests. We show that observational equivalence is sufficiently coarse to ensure that least and greatest fixed point types are initial algebras and final coalgebras, respectively. This yields inductive and coinductive proof principles for reasoning about program behaviour. On the other hand, we argue that observational equivalence does not identify too many terms, by showing that tests induce a topology that, on streams, coincides with usual topology induced by the prefix metric. As one would expect, observational equivalence is, in general, undecidable, but in order to develop some practically useful heuristics we provide coinductive techniques for establishing observational normalization and observational equivalence, along with up-to techniques for enhancing these methods.

Correction to a definition of negation

1984 ◽  
Vol 49 (1) ◽  
pp. 47-50 ◽  
Author(s):  
Frederic B. Fitch
Keyword(s):  
Fixed Point ◽  
Personal Communication ◽  
The Other ◽  
Transfinite Induction ◽  
Original Form ◽  
Basic Logic ◽  
Double Negation ◽  
Original Letter ◽  
The Law ◽  
Definition Of

In [3] a definition of negation was presented for the system K′ of extended basic logic [1], but it has since been shown by Peter Päppinghaus (personal communication) that this definition fails to give rise to the law of double negation as I claimed it did. The purpose of this note is to revise this defective definition in such a way that it clearly does give rise to the law of double negation, as well as to the other negation rules of K′.Although Päppinghaus's original letter to me was dated September 19, 1972, the matter has remained unresolved all this time. Only recently have I seen that there is a simple way to correct the definition. I am of course very grateful to Päppinghaus for pointing out my error in claiming to be able to derive the rule of double negation from the original form of the definition.The corrected definition will, as before, use fixed-point operators to give the effect of the required kind of transfinite induction, but this time a double transfinite induction will be used, somewhat like the double transfinite induction used in [5] to define simultaneously the theorems and antitheorems of system CΓ.

Induced segmental reorganization in sabellid worms

Development ◽  
1978 ◽  
Vol 47 (1) ◽  
pp. 85-96
Author(s):  
N. J Berrill
Keyword(s):  
Unique Feature ◽  
Vertical Plane ◽  
Main Axis ◽  
The Other ◽  
Basal Portion ◽  
Thoracic Stomach ◽  
The Right ◽  
Number Of Segments ◽  
Head Regeneration ◽  
Complete Inversion

Processes of regeneration and reorganization are analyzed in two sabellid polychaetes. Abdominal pieces of Branchiomma nigromaculata, during head regeneration, ordinarily reorganize only a fraction of the number of segments typical of the thorax. In pieces transected in the vertical plane, but obliquely with regard to the main axis of the worm, the extent of reorganization is greatly enhanced. The same number of segments transform on the right and left sides, the surviving damaged segments transforming on one side and a corresponding number of more posterior, undamaged segments transforming on the other. Reorganization is shown, in abdominal pieces of Sabella melanostigma, to involve destruction and inversed dorso-ventral reconstitution of all parapodial structures in the segments affected, the conversion of intestine to thoracic stomach, and the invasion of previously abdominal segments by a pair of large nephridia which grow posteriorly after being formed in the basal portion of the head blastema. All three events exhibit a time-graded character, starting soonest at the anterior end and progressively later posteriorly, and apparently independently of one another. Abdominal type segments are formed only from the anterior region of the caudal, prepygidial zone of growth, successively, never by transformation. The dorso-ventrality of abdominal segments is the inverse of the thoracic, with the antero-posterior polarity unchanged, in all circumstances. Only during posterior regeneration from thoracic segments are thoracic segments produced from the posterior zone of growth, but only two or three are thus formed, the zone of growth then changing to the production of abdominal segments. It is concluded that the unique feature of sabellid-serpulid organization is the complete inversion of the dorso-ventrality of the posterior zone of growth as the result of emancipation from the generally dominating dorsal field emanating from the anterior end.

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

scholarly journals 4. On a Thermomagnetic Thermoscope

1880 ◽  
Vol 10 ◽  
pp. 538-539
Author(s):  
W. Thomson
Keyword(s):  
Magnetic Moment ◽  
Horizontal Plane ◽  
Hardened Steel ◽  
The Other ◽  
Silk Fibre ◽  
Steel Wires ◽  
The One

This thermoscope is founded on the change produced in the magnetic moment of a steel magnet by change of temperature. Several different forms suggest themselves: the one which seems best adapted to give good results is to be made as follows:—(1.) Prepare an approximately astatic system of two thin, hardened steel wires, r b, r′ b′, each 1 cm. long, one of them, r, b, hung by a single silk fibre, and the other hung bifilarly from it, by fibres about 3 cms. long, so attached that the projections of the two, on a horizontal plane, shall be inclined at an angle of about ·01 of a radian (or ·57°) to one another.

scholarly journals A New Method for the Calculation of Energy and Power Requirements of Bucket Wheel Excavators

2019 ◽  
Vol 10 (1) ◽  
pp. 15-20
Author(s):  
József András ◽  
József Kovács ◽  
Endre András ◽  
Ildikó Kertész ◽  
Ovidiu Bogdan Tomus
Keyword(s):  
Energy Consumption ◽  
Numerical Method ◽  
Horizontal Plane ◽  
Vertical Plane ◽  
New Method ◽  
Energy Requirements ◽  
Belt Conveyor ◽  
Analytical Formulas ◽  
Power And Energy ◽  
Continuous Working

Abstract The bucket wheel excavator (BWE) is a continuous working rock harvesting device which removes the rock by means of buckets armoured with teeth, mounted on the wheel and which transfers rock on a main hauling system (generally a belt conveyor). The wheel rotates in a vertical plane and swings in the horizontal plane and raised / descended in the vertical plane by a boom. In this paper we propose a graphical-numerical method in order to calculate the power and energy requirements of the main harvesting structure (the bucket wheel) of the BWE. This approach - based on virtual models of the main working units of bucket wheel excavators and their working processes - is more convenient than those based on analytical formulas and simplification hypotheses, and leads to improved operation, reduced energy consumption, increased productivity and optimal use of available actuating power.

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