An interpolation problem of positive-real functions (in German)

On positive-real functions (in German)

Positive-real functions, often abbreviated to PR function, are a kind of mathematical function that first arose in electrical network analysis.

With Richard Duffin at Carnegie Mellon, Bott studied existence of electronic filters corresponding to given positive-real functions .

Examples of canonical forms are the realisation of a driving-point impedance by Cauer's canonical ladder network or Foster's canonical form or Brune's realisation of an immittance from his positive-real functions.

A theorem due to Sidney Darlington states that any positive-real function Z(s) can be realised as a lossless two-port terminated in a positive resistor R. No resistors within the network are necessary to realise the specified response.

When a transfer function is specified as a positive-real function (the set of positive real numbers is invariant under the transfer function), then a network of passive components (resistors, inductors, and capacitors) can be designed with that transfer function.

Cauer was interested in finding the necessary and sufficient condition for realisability of a rational one-port network from its polynomial function, a condition now known to be a positive-real function, and the reverse problem of which networks were equivalent, that is, had the same polynomial function.

The integration of the PR function into the organisation is important.

Selecting the right personnel to carry out the PR function.

Fully integrating the PR function into the organisation.

Its goals, programs and outcomes are based on having the PR function provide "bottom line" support to the business units' operating targets.

Please let me know if you would like to discuss Azurix and the PR function further.

About 40 or so people attended the PR function plus several officials, including the Vice Chancellor.

All the poles and zeros of a PR function are in the left half plane or on its boundary the imaginary axis.

The night Miles was arrested, she had successfully evaded his queries about her professional PR functions.

For a rational PR function, the number of poles and number of zeroes differ by at most one.

The composition of two PR functions is PR.

Positive-real functions, often abbreviated to PR function, are a kind of mathematical function that first arose in electrical network analysis.

The PR Function Promoting the Association's welfare facilities and projects to those who need help and the public at large.

These employees were notified by Diane that I was taking over the Azurix PR function and to coordinate their activity through me.

Les was normally upbeat and buoyant, managing to keep up an image that went with his PR function, but today all that had gone out of him.

The Thought Criminals' Doublethink label evolved from a record label to include agency and PR functions.

In addition to this is a Corporate team providing support to the Chief Executive and Board and includes Personnel and PR functions.

A theorem due to Sidney Darlington states that any PR function Z(s) can be realised as a lossless two-port terminated in a positive resistor R.

By itself there was a certain logic to this arrangement. However, what this grouping has done over the years is divorce recruiting promotion almost entirely from the broader, strategic PR function.

A regular flow of press releases is issued by the Public Relations Office and all staff should be aware that interesting developments within their departments can be communicated externally by utilising the PR function.

Bolan had originally guessed the Minister of Cultural Affairs was little more than a PR function given to one of the ruler's favored relatives; now he began to wonder if he should revise his opinion.

It is debatable whether the FSA's leadership in Turkey serves anything more than a PR function — a source for media and western diplomats — without real command of FSA fighters on the ground.

Brune also showed that if the case is limited to scalar PR functions then it is not necessary to allow ideal transformers (a limit to the usefulness of the theory) to be assured of a realisable network solution.

She was instrumental in programs such as the Play Tennis and Girls in Tennis campaigns and directed all aspects of the LTA's PR function, including tournament management and media training for players and coaches.

Making "Working Together" Work The Education and PR function agreed at Basingstoke in 1997 is being managed by Steering Group members Margaret Evans (Campaign Manager) and Brian Mooney (Treasurer) who also covers administrative arrangements.

Presented to a CPRS member whose personal activities and/or leadership have gone beyond the call of duty or responsibility to an employer or client and resulted in a pronounced contribution to the status and acceptance of the PR function as a whole.