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In this paper Mandelbrot discusses self-similar curves that have Hausdorff dimension between 1 and 2.

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## 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**.**0.516 seconds.