[permalink] [id link]
In this paper Mandelbrot discusses self-similar curves that have Hausdorff dimension between 1 and 2.
Some Related Sentences
paper and Mandelbrot
The essential idea of " fractured " dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoît Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions.
In that paper, Mandelbrot cited previous work by Lewis Fry Richardson describing the counter-intuitive notion that a coastline's measured length changes with the length of the measuring stick used ( see Fig.
Statistical Self-Similarity and Fractional Dimension " is a paper by mathematician Benoît Mandelbrot, first published in Science in 1967.
These curves are examples of fractals, although Mandelbrot does not use this term in the paper, as he did not coin it until 1975.
Near the end of the paper Mandelbrot briefly discusses how one might approach the study of fractal-like objects in nature that look random rather than regular.
paper and discusses
) In a paper dated by editors as circa 1901, he discusses " instinct " and " naturalness ", along with the kind of considerations ( low cost of testing, logical caution, breadth, and incomplexity ) that he later calls methodeutical.
While he did not coin the specific term, Coase indeed discussed " costs of using the price mechanism " in his 1937 paper The Nature of the Firm, where he first discusses the concept of transaction costs, and refers to the " Costs of Market Transactions " in his seminal work, The Problem of Social Cost ( 1960 ).
" An ACM paper discusses Barger and Chris Gulker, along with other early bloggers such as Raphael Carter, as the originators of blogging as a networked practice.
The remainder of Lazarsfeld and Merton ’ s paper discusses structure of ownership and operation of the mass media specific to the U. S .— especially the fact that in the case of magazines, newspapers, and radio advertising ‘ supports the enterprise ’: ‘ Big business finances the production and distribution of mass media … he who pays the piper generally calls the tune ’.
* Lagrange discusses representations of integers by general algebraic forms ; produces a tract on elimination theory ; publishes his first paper on the general process for solving an algebraic equation of any degree via Lagrange resolvents ; and proves Bachet's theorem that every positive integer is the sum of four squares.
The later papers stand in contrast to the Institution's 2000 paper, The Market Place Should Rule on Technology, which discusses Linux as a direct competitor to Microsoft Windows.
A 1992 paper by M. Anthony Lewis and George A. Bekey discusses the possibility of using swarm intelligence to control nanobots within the body for the purpose of killing cancer tumors.
In their paper entitled " When the Enterprise becomes the Prosumerise ", Widality discusses how the very different IT and mobility needs of the prosumer, consumer and enterprise are all now melding into a common set of requirements, driven by the rise of smartphones and downloadable applications that consumers, prosumers and enterprises are consuming in equal numbers.
* Fink, M ( 1984 ), " Meduna and the Origins of Convulsive Therapy ", American Journal of Psychiatry, 141 ( 9 ): 1034-1041 ( This historical and biographical paper discusses the introduction of the shock treatment in psychiatry, the role of a theory of the biological antagonism between epilepsy and schizophrenia, and the contributions of Ladislau von Meduna, Sakel, Ugo Cerletti, and Lucio Bini.
A 2011 ' Black Hat ' paper discusses the real-life security implications of such bit-flips in the internet's DNS system.
The Israeli academic Nitsa Ben-Ari discusses the complex socio-political context of these translations and changes in her paper, The double conversion of Ben-Hur: a case of manipulative translation.
At the 2005 International Joint Conference on Artificial Intelligence, Rubén Sánchez-Pelegrín and Belén Díaz-Agudo presented a paper entitled " An Intelligent Decision Module based on CBR for C-evo " which discusses using C-evo as a platform to perform artificial intelligence research.
However, Kraft's paper discusses only prefix codes, and attributes the analysis leading to the inequality to Raymond Redheffer.
In a 1926 paper, Eoin MacNeill discusses the movements of the Uí Liatháin at considerable length, arguing their leadership in the South Irish conquests and founding of the later dynasty of Brycheiniog, the Welsh genealogies matching Uí Liatháin dynasts in the Irish genealogies.
In this paper Hamilton discusses sex ratios as strategies in a game, and cites Verner as using this language in his 1965 paper which " claims to show that, given factors causing fluctuations of the population's primary sex ratio, a 1: 1 sex-ratio production proves the best overall genotypic strategy ".
This paper discusses the quality framework in relation to active process models and suggests a revised framework based on this.
paper and self-similar
The idea of self-similar curves was taken further by Paul Pierre Lévy, who, in his 1938 paper Plane or Space Curves and Surfaces Consisting of Parts Similar to the Whole described a new fractal curve, the Lévy C curve.
paper and curves
In a 1990 paper by Novikov and several others, Cauchy problem in spacetimes with closed timelike curves, the authors state:
Among the coauthors of this 1990 paper were Kip Thorne, Mike Morris, and Ulvi Yurtsever, who in 1988 had stirred up renewed interest in the subject of time travel in general relativity with their paper Wormholes, Time Machines, and the Weak Energy Condition, which showed that a new general relativity solution known as a traversable wormhole could lead to closed timelike curves, and unlike previous CTC-containing solutions it did not require unrealistic conditions for the universe as a whole.
For instance, bending without stretching or tearing a page of paper gives an isometric embedding of the page into Euclidean space because curves drawn on the page retain the same arclength however the page is bent.
Monge's paper gives the ordinary differential equation of the curves of curvature, and establishes the general theory in a very satisfactory manner ; the application to the interesting particular case of the ellipsoid was first made by him in a later paper in 1795.
To make this graph paper, one places a grid of parallels and meridians on the hemisphere, and then stereographically projects these curves to the disk.
The most important are those relating to algebraic curves and surfaces, especially the short paper Allgemeine Eigenschaften algebraischer Curven.
Stephen Hawking in his 1992 paper on the chronology protection conjecture posited that closed timelike curves cannot be created, and thus cannot be used for time travel.
His 1952 paper introduced, inter alia the basic geostatistical concepts of ‘ support ’, ‘ spatial structure ’,’ selective mining units ’ and ‘ grade-tonnage curves ’.
They were introduced by in his work on Heegner points on modular elliptic curves, which was motivated by his earlier paper and the work of.
The Fletcher – Munson curves are one of many sets of equal-loudness contours for the human ear, determined experimentally by Harvey Fletcher and Wilden A. Munson, and reported in a 1933 paper entitled " Loudness, its definition, measurement and calculation " in the Journal of the Acoustic Society of America.
Although it is also used for womenswear, the drafting method is more commonly employed in menswear and involves drafting a pattern directly onto pattern paper using a variety of straightedges and curves.
In this paper, van Stockum was apparently the first to notice the possibility of closed timelike curves, one of the strangest and most disconcerting phenomena in general relativity.
paper and have
He was aware of her as a frightfully good-looking American WAC, a second lieutenant assigned to do the paper work, ( regardless of how important she might have thought she was ) in the Command offices, but that was all.
Steinberg seems to have gone directly back to the score, discounting tradition, and has built his performance on the intention to reproduce as faithfully as possible exactly what Brahms set down on paper.
A group of researchers at the University of Washington have given a paper which briefly outlines some of these techniques.
There have been many extremely competent men who have been converted into very incompetent managers or submerged in paper work, to their own and the public's dissatisfaction and loss.
Instead of isolating the literal flatness by specifying and circumscribing it, the pasted paper or cloth releases and spreads it, and the artist seems to have nothing left but this undepicted flatness with which to finish as well as start his picture.
and the broad, opaque shapes of pasted paper would have been isolated in such a way as to make them jump out of plane.
It is only fairly recently, however, that linguists have developed a systematic way of charting voices on paper in a way that tells even more about the speakers and about the success or failure of human communication between two people.
The congressman who, in Paris, may have stuffed his wallet with enough franc notes to paper the roof of Notre-Dame will systematically scream that a $200 increase in entertainment allowance for a second secretary is tantamount to debauchery of the Treasury.
By the time Felix turned up it was early afternoon, which, one would think, would be late enough so that by then, except for small children and a few hardy souls who had not yet sobered up, it could have been expected that people would no longer be having any sort of active interest in the previous night's noisemakers and paper hats.
You still have your paper hat and you're wearing it, but then, it is an extraordinary paper hat and, in addition to anything else you may be, you are also the sculptor who created that most peculiar dame out in the back yard.
It's not too much to assume that you will have a more lasting interest in paper hats than will Mr. Average Citizen.
You have your paper horn clutched in your big, craggy fist, and for your entrance you have planned a noisy, colorful and exuberant greeting to your friends and tenants.
Some are so filled with gratitude, for the gift of life and the love of God, that their joy spills out on the paper and brightens the lives of thousands whom they have never known, and will never see.
Two days before he was taken sick, Cousin Elec was out worrying about what too much rain might do to his sweetpeas, and Cousin Elec had always preserved in the top drawer of his secretary a mother-of-pearl paper knife which Theresa had coveted as a child and which he had promised she could have when he died.
The representations of a line and a curve as marks on a piece of paper or as pixels on a computer screen have a positive width.
Also, according to Disraeli's biographer, Lord Blake, the paper was " atrociously edited ", and would have failed regardless.