In this paper the application of bounded series theory due to Carathéodory and Toeplitz is explored to study Brune positive real rational function (PRF).
The α-, β- and γ-duals of the sequence space X are respectively defined by. and X γ = { a = ( a k ) ∈ ω : a x = ( a k x k ) ∈ b s for all x = ( x k ) ∈ X }, where cs and bs are the sequence spaces of all convergent and bounded series, respectively [36].
The book is artist Erik Kessels's 12th bound series of found images, which tells an unlikely not-quite story of a stranger, at once bizarre and banal.
Thus it is not surprising that many authors in dealing with the convergence of double sequences should have restricted themselves to the class of bounded sequences or, in dealing with the summability of double series, to the class of series for which the function whose limit is the sum of the series is a bounded function of i and j.
Her 6-0, 6-1 victory, which she finished with an ace, required just 1 hour 3 minutes, and she celebrated with a scream, a series of bounding leaps and even a few dance steps on the grass.
It's one of a spiral-bound series with laminated pages about animal life cycles which gets the point over with a few well-chosen words and bold, warm pictures by Pierre Pratt.
To the east, this region is bounded by a series of long, low ridges, with steep slopes on the west and gentle slopes on the east; the area is 750 miles (1,200 km) long and curves eastward from north to south.
High school juniors and seniors in Girls Write Now have access to Girls College Bound, a series of classes and tutorials meant to help them navigate the application process.
In the remaining "American Identities" galleries the history of metal proceeds by leaps and bounds with a series of isolated standouts.
— In a neighborhood park, Cameron Burrell performed a series of bounding drills as a team of youth basketball players arrived for a hill-climbing workout.
There are cabinets filled with books, including dusty rows of a red-bound series, "Biblioteca Ecuatoriana Mínima" (1960).
