Circle Diagram Research Articles

Finding maximum cliques in circle graphs

AbstractA circle diagram consists of a circle C and a set of n chords. This diagram defines a graph with n vertices where each vertex corresponds to a chord, and two vertices are adjacent if their corresponding chords intersect in C. A graph G is called a circle graph if it is defined by some circle diagram. An algorithm which requires O(n2) steps to generate one maximum clique is presented. The algorithm can also be used to generate all maximum cliques where the number of steps need to generate each additional maximum clique is linear in its size. This compares favourably with Gavril's algorithm [4] which works in O(n3) steps.

TEM00-THERMO-INSENSITIVE CAVITY IN THE PRESENCE OF SEVERAL THERMO-PERTURBATIONS

The general solution of TEM00-thermo-insensitive cavity in the presence of several thermo-perturbation centers has been obtained by means of the transformation circle diagram. In this cavity the circles π in the places of thermo-perturbation centers are tangent successively; one of the circles π1 is tangent to the circle σ1 of the mirror R1 of the cavity; and the spot sizes of the fundamental mode determined by the circles π satisfy the requirement selecting fundamental mode by self-diaphragm. At the same time, the simple designing process and calculating formulas of such cavity, particularly a frequency doubled cavity, has been established according to this solution.

Circle diagram for a compensated linear induction motor

Circle diagram for a compensated linear induction motor

The Angle-Scanned Interferometer

Angle-scanned interferometers are a class of ac interferometers in which the optical path difference is varied as a function of time by varying the incidence angle. The resulting interferogram has the properties of a hologram of a point source and may be used to determine the input energy wavelength and incidence angle. A new category of interferometer type is suggested, beam symmetry, which determines the output fringe pattern behavior as a function of input angle. An interference circle diagram is presented as an aid to understanding the characteristic response of symmetrical interferometers and angle-scanned interferometers. A number of angle-scanned interferometer examples are described in terms of the interference circle diagram.

Use of Frequency Scanning Techniques for Subsynchronous Resonance Analysis

Frequency scanning employs an approximate technique which is efficient, and cost effective for the analysis of Subsynchronous Resonance (SSR). This technique is particularly suited to screening type studies to sort out the critical system conditions from the multitude of system conditions which can exist. Following is a description of the frequency scanning technique, its use in analysis of SSR problems, correlation with field test results, and an example of data preparation and program application. In addition, a new analysis technique using circle diagrams is presented.

Circle diagram for d.c. dynamic braking of linear induction motors

A circle diagram is described for the d.c. braking of an idealised linear induction motor with an iron-backed or air-backed conducting secondary. Braking thrust and normal force can be easily predicted from the diagram. Experimental confirmation of the method is described.

THE ELIMINATION AND REGULATION OF ASTIGMATISM IN SPHERICAL MIRROR FOLDED CAVITIES

By selecting appropriate cavity configurations, the astigmatism of optical mode in spherical mirror folded cavities can be partially eliminated and regulated. The codi-tion of anastigmatism elimination for output branch of spherical mirror folded cavities is calculated by means of the transformation circle diagram.

Power Fluidics—Amplifying Properties of Specially Designed Junctions

Specially designed 3-terminal elements called flow-junctions (FJs) and ‘reverse flow diverters' (RFDs) are shown to have useful amplifying properties which are often unrecognised. These are described by relating the devices to ideal network elements using an indefinite circle diagram. The FJ is useful between two transformer-like states and at the mid-point of this range its utility is described by its impedance matrix. A circuit using an RFD is shown to give a large-signal power gain which compares favourably with an equivalent circuit using a vortex device.

Influence of temperature on the anisotropy of the yield point of fredeformed carbon steel

1. The test temperature has a marked influence on the anisotropy of plastic deformation of steel. Regardless of the degree of preliminary deformation, the greatest anisotropy is observed between 100 and 300°C. On cooling, the anisotropy of the yield points decreases. 2. At room temperature and elevated temperatures, the directions in which the yield points are maximal coincide with the direction of the predeformation. At low temperatures these directions do not coincide; the degree of disorientation depends on the temperature, and is 45° at t=−196°C. 3. The circle diagrams characterizing the anisotropy of steel at various temperatures are closely approximated by Eq. (1), which involves three anisotropy parameters which depend practically linearly on the degree of plastic deformation.

Form of circle diagram for the linear induction motor

A circle diagram is described for an idealised linear induction motor operating under constant-current conditions, with an iron-backed or air-backed conducting-sheet rotor. The diagram yields a great deal of information about the performance of the machine, including normal force. Simplified expressions are derived relating complex input power, thrust and normal force. The theory is compared with the experimental results obtained from static-impedance tests on a linear induction motor.

Circle diagram of induction machines from practical test results

An easy method of calculating the coordinates of the centre of the circle of admittance for an induction machine is presented. The formulae derived are very simple and obtainable from direct laboratory tests. The performances predicted by this circle diagram are compared to the IEEE test procedure and prove the circle diagram at least as good as a computer model.

Base resistance measurements on bipolar junction transistors via low temperature bridge techniques

Accurate measurements of ohmic base resistance for bipolar junction transistors at low frequencies and for medium to low-bias conditions are somewhat difficult to obtain. Presented herein is a technique involving measurement of the input common-emitter h ie parameter at cryogenic temperatures (where the intrinsic input resistance parameter is quite small) using conventional low-frequency bridge techniques. Comparison of results obtained by this procedure are made with results obtained by the input impedance circle diagram method and the noise figure method.

静止クレーマ方式の円線図による定常特性の解析

静止クレーマ方式の円線図による定常特性の解析

Characterization and measurement of the base and emitter resistances of bipolar transistors

Most previously published methods of measuring transistor base resistance are surveyed and compared. The input impedance circle diagram method is examined in detail and correction factors due to parasitic capacitances are derived. Emitter series resistance is also estimated from this data. A new method of measuring base resistance requiring much less measurement effort is introduced and shown to give good agreement with the circle diagram method. This method is called the phase cancellation method and gives an estimate of base resistance from the common base input impedance at the collector current where its imaginary part is zero. Also an estimate of series emitter resistance is obtained from this measurement and shown to agree well with other methods.

Graphics in Optical Coating Design

Graphical displays of complex reflectance for nonabsorbing multilayer optical coatings based upon circle diagrams are presented. Similar displays are then developed for absorbing films. The two types of display are used to analyze several common multilayers, and a repetitive structure with period characteristics is introduced.

Extensions of the Circle Diagram

The representation of the normalized point impedance of a uniform transmission line by means of a bipolar coordinate system is extended to propagation in nonuniform transmission lines and stratified media (even with a turning point, provided certain asymptotic approximations are also made). The normalized impedance is the solution of a generalized Riccati equation. It is solved approximately by applying the circle diagram to a set of homogeneous lines such that the stepwise varying wavenumber approximates the continuously varying one. The technique is applied to obtain the reflection from and transmission through layers, the eigenvalues and eigenfunctions, and Green's functions. Some further applications will be discussed. [This research is supported by the ONR Acoustics Program.]

A Modified Form of the Combined Power Circle Diagram for Transmission Line Calculations

A Modified Form of the Combined Power Circle Diagram for Transmission Line Calculations

Steady-State Performance of Reluctance Machines

Polyphase reluctance machine performance is analyzed by direct-and quadrature-axis components, by circle diagrams, and by machine admittance. Specific equations are deduced for pull-out out torque, maximum power factor, no-load current, and pull-out current. A method is given by which the entire motor performance may be calculated through knowledge of machine admittance. Comparisons are made between calculated and measured results.

Techniques for the Measurement of Complex Microwave Conductivity and the Associated Errors

Complex microwave conductivity of 9 /spl Omega/ /spl dot/ cm p-type silicon samples has been measured using conventional reflection and transmission bridges to examine their relative advantages and disadvantages. An attempt has been made to improve the reflection results from an analysis of the parameters of a circle diagram for reflection coefficient obtained on using a variable reactive termination after the semiconductor-filled waveguide section. In conformity with the calculated accuracy attainable from different types of measurement under the actual experimental condition, using commercial standards, the dielectric constant for the sample was found to be scattered over a region of /spl plusmn/0.4. It has been concluded that because of lack of accuracy in commercial standards for attenuation and phase shift, the potential accuracy of the conventional microwave methods falls too short of its mark to make any detinite conclusion about the effective mass of carriers in semiconductors at room temperatures.

The Measurement of the Synchronous Reactances of a Salient Pole Machine with Reference to its Circle Diagram

The Measurement of the Synchronous Reactances of a Salient Pole Machine with Reference to its Circle Diagram