Also, phasor analysis of circuits can include Euler's formula to represent the impedance of a capacitor or an inductor.

During further analysis it should be assumed that the phasor travels times clock-wise along a semicircle of infinite radius.

For phasor analysis, the magnetic permeability and the magnetic capacitivity are complex values2.

For phasor analysis the magnetic inductive reactance is:

At a distance x into the line, there is current phasor I ( x ) traveling through each wire, and there is a voltage difference phasor V ( x ) between the wires ( bottom voltage minus top voltage ).

The quantity measured, such as voltage, is expressed as a sinusoidal phasor.

where is the electric field and is the magnetic field, in phasor representation.

In this diagram, AC power is being transferred from the source, with phasor magnitude voltage ( peak voltage ) and fixed source impedance, to a load with impedance, resulting in a phasor magnitude current.

Here ω = 2πf is the angular frequency ( and f the frequency ), and i = is the imaginary unit, so that I is a phasor.

The phasor diagram is an effective tool for visualizing the relationships between internal voltage, armature current, and terminal voltage.

The analytic representation is a generalization of the phasor concept: while the phasor is restricted to time-invariant amplitude, phase, and frequency, the analytic signal allows for time-variable parameters.

Such a modification implies that the phasor travels along an arc of infinite radius by, where is the multiplicity of the pole on the imaginary axis.

They are phasor solutions, that is they have an implicit time-dependence factor of where is the angular frequency.

As seen above, dielectric complex reluctance is a phasor represented as uppercase Z epsilon where:

As seen above, magnetic complex reluctance is a phasor represented as uppercase Z mu where:

In both cases, nominal power excludes losses in transmission lines between the tower or phasor and the transmitter ; however, it includes losses in a resistor network used to decrease the efficiency of the antenna system.

* Frequency Disturbance Recorder, a type of single phase phasor measurement unit

If the phase quantities are expressed in phasor notation using complex numbers, a vector can be formed for the three phase quantities.

Modern systems use sensors called phasor measurement units ( PMU ) distributed throughout their network to monitor power quality and in some cases respond automatically to them.

Define the operator phasor vector forward by that angle.

In vector analysis of electric circuits, resistance is the real part of complex impedance, while reactance is the imaginary part.

I knew that a conversation with the author would not settle such questions, because a man is not the same as his writing: in the last analysis, the questions had to be settled by the work itself.

Let me quote him even more fully, for his analysis is important to my theme.

It is a weakness of Gabriel's analysis that he never seems to realize that his so-called fundamental law had already been cut loose from its foundations when it was adapted to democracy.

Trevelyan accepts Italian nationalism with little analysis, he is unduly critical of papal and French policy, and he is more than generous in assessing British policy.

The research center of the University's School of Business and Public Administration is prepared to undertake the analysis Dr. Ellis has been talking about.

An analysis of the fiscal tax collection year calendars throughout the state indicates that transition may not be as painful as is commonly thought.

Another important source of evidence only recently receiving much attention is the analysis of atmospheric dust for a meteoritic component.

In the last analysis, religion is the means of inducing, formulating, expressing, enhancing, implementing, and perpetuating man's deepest experience -- the religious.

but the subsequent analysis of characteristics is reported only for the de jure population ( or, in some districts, only the de facto population ).

The criterion score used in the statistical analysis is an index of over- or under-achievement.

Tables 1 and 2 present the results of the statistical analysis of the data when compulsivity is used as the descriptive variable.

Finally, information is retrieved from the dictionary as required by stages of the translation process -- the grammatical description for sentence-structure determination, equivalent-choice information for semantic analysis, and target-language equivalents for output construction.

The first stage of translation after glossary lookup is structural analysis of the input text.

From the point of view of syntactic analysis the head word in the statement is the predicator has broken, and from the point of view of meaning it would seem that the trouble centers in the breaking ; ;

Tone analysis will continue to be difficult and unsatisfactory until a more representative selection of systems is familar to every practicing field linguist.

The great majority of present-day linguists fall into one or more of a number of overlapping types: those who are convinced that tone cannot be analysed, those who are personally scared of tone and tone languages generally, those who are convinced that tone is merely an unnecessary marginal feature in those languages where it occurs, those who have no idea how to proceed with tone analysis, those who take a simplistic view of the whole matter.

One issue that must be faced is the relative difficulty of analysis of different phonologic subsystems.

A third explanation is suggested by Richardson's analysis of Sukuma tone.

The difficulty of analysis of any subsystem in the phonology is an inverse function of the size -- smaller systems are more troublesome -- for any given degree of morphophonemic complexity.

The treatment seems unnecessarily loose-jointed and complex, largely because the method is lax and the analysis seems never to be pushed to a satisfactory or even a consistent stopping-point.

Mr. Alexander H. Wheelan's Study Helps In Point And Figure Technique tells the readers: `` We assure you that the total number of people using this method of market analysis is a very small portion of the sum total of those operating in the securities and commodities markets ''.

The threadbare notion that belief, unlike behaviour, is not subject to objective analysis, has placed intuitive metaphysics squarely against the sociology of knowledge, since it is precisely the job of the sociology of knowledge to treat beliefs as social facts no less viable than social behaviour.

It is rather that introducing them into social analysis reflects not so much a search for truth as for certainty.