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... As a new type of poetry with fixed from: The Paradoxist distich is a two-line poem which contains an antithesis. The second line contradicts the f... ...ontains an antithesis. The second line contradicts the first one, but both lines form together a unitary meaning defining the title. Here there are... ...y with fixed from: The Tautological Distich is an apparently redundant two-line poem, but the “redundant” lines together give a deeper meaning to th... ...tion Of the scientific AXIOMATIZATION (II) Geometrization Of the geometry SCHOPENHAUER: “I know That I know” IMITATOR Discovers ... ...s As a new form of poetry with fixed form: The Dualistic Distich is a two-line poem such that the second line is the dualistic of the first and tog... ... reviewed it, something inside of the envelope was opposing. Gerald`s four-line proseful poetry, whose each stanza starts with “and”, was eagerly wa...

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...ess, he actually assumes Greenleaf's identity. Disembarking from a luxurious Cunard liner in his destination, Italy, he "confesses" to a gullible te... ...fortunate state of things and its moral and practical implications. The blurring line between life and its representation in the arts is arguably... ...m "Titanic" is riddled with moral dilemmas. In one of the scenes, the owner of Star Line, the shipping company that owned the now-sinking Unsinkable... ...physical riddles and presses the viewers' intellectual stimulation buttons. A two line bit of dialogue, though, forms the axis of this nightmarish... ...ar questions arise in time travel)? This, precisely, is where the film crosses the line between the intriguing and the macabre. The master puppetee... ...e sense organs that we do (eyes) and may not be acquainted with our mathematics and geometry. Reality can be successfully described and captured by ...

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...quantization. Thus adaptive vector quantization embeds learning in a dynamic geometry, vector quantization may be optimal according to different cr... ...l function S j (y j ). However the competitive learning law can be reduced to linear competitive learning law ij m = S j (y j ) (x – m j ), ... ...3-linked FRMs, 4-linked FRMs and so on in general, an n-linked FRM on similar lines and obtain the hidden relation, which are not explicitly calcul... ...ns membership value in the interval [0, 1]. But very few try to visualize the geometry of fuzzy sets. It is not only of interest but is meaningful t... ...ometry of fuzzy sets. It is not only of interest but is meaningful to see the geometry of fuzzy sets when we discuss fuzziness. Till date researcher... ...sional graphs with the domain X represented as a one-dimensional axis. The geometry of fuzzy sets involves both domain X = (x 1 ,…, x n ) and the... ...main X = (x 1 ,…, x n ) and the range [0, 1] of mappings µ : X → [0, 1]. The geometry of fuzzy sets aids us when we describe fuzziness, define fuzz... ...ple will not make repeated mistakes and become HIV/AIDS victim. This was her line of thinking. Additional Observation: Her husband infected her...

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...s s ds, Anumbertheoreticfunctionanditsmeanvalue 1 21 we move the integral line from s = 3 2 ±iT to s = 1 2 ±iT. This time, the function g(s) = ζ(s) (... ...ar number, because there are close relations between these numbers and the geometry. Now for any positive integern, we definearithmeticalfunctionc(n)as... ...perfectk thpowernumbers 93 To estimate the main term, we move the integral line fromb = 1 k + 1 logx to a = 1 2k + 1 logx Therefore, 1 2πi Z b+iT b−... ...ainterm 1 2πi Z 5 2 +iT 5 2 −iT ζ 2 (s)R(s) x s s ds, we move the integral line from s = 5 2 ±iT to s = 1 2 ±iT. This time, the function ζ 2 (s)R(s) x... ...s s ds, Onthemeanvalueofanewarithmeticalfunction 147 we move the integral line from s = 2±iT to s = 1 2 ±iT. This time, the function f(s) = ζ(s)x s ζ...

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...ation. But whence had the uneducated man this knowledge? He had never learnt geometry in this world; nor was it born with him; he must therefore have ... ... one of Meno’s slaves, from whom Socrates elic its truths of arithmetic and geometry , which he 18 Meno had never learned in this world. He must the... ... nature; they re main the same as before, though he has drawn the imaginary line by which they are divided at a different point. He has annihilated t... ...TES: And you would speak of a surface and also of a solid, as for example in geometry . MENO: Y es. SOCRATES: Well then, you are now in a condi tion ... ...uare? BOY : I do. SOCRATES: And you know that a square figure has these four lines equal? BOY : Certainly . SOCRATES: And these lines which I have dra... ...there not be another square twice as large as this, and having like this the lines equal? BOY : Y es. SOCRATES: And of how many feet will that be? BOY... ...be? BOY : Of eight feet. SOCRATES: And now try and tell me the length of the line which forms the side of that double square: this is two feet—what wi... ..., but only asking him questions; and now he fancies that he knows how long a line is necessary in order to produce a figure of eight square feet; does... ...edge he could not have ac quired it in this life, unless he has been taught geometry; for he may be made to do the same with all geometry and every o...

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...obling bears A near Resemblance to the Spheres. A Scrap of Parchment hung by Geometry (A great Refinement in Barometry) Can, like the Stars, foretel t... ...is almanacks for this year, merely to find what he said against me; at every line they read, they would lift up their eyes, and cry out, betwixt rage ... ...rstaff Partridge Papers – Swift 29 Explanatory notes. v Seven and Ten. This line describes the year when these events shall happen. Seven and ten mak... ... mean, that he should be overcome or slain. By the green berrys, in the next line, is meant the young Duke of Berry, the Dauphin s third son, who shal... ...y s Pride, perhaps the reader may, as well as the sense of the two following lines. The Bickerstaff Partridge Papers – Swift 30 v Reaums shall, etc. ... ... or other merry gentlemen are pleased to think. As to the tradition of these lines having been writ in the original by Merlin, I confess I lay not muc...

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...reads upon the surface of her rug- ged rocks. The eye can readily mark the line where the soil, warmed by the rays of the sun, bears cultivation and s... ... terrible winter months the women spun and dyed the woollen stuffs and the linen fabrics with which they clothed their families, while the men read, o... ...have attributed to human beings the power to move safely along the slender lines traced beneath the snow by the gran- ite ledges, where yet this coupl... ...back and forth upon the mountain, skimming from terrace to ter- race, from line to line, with the rapidity of a barb, that bird of the desert. Present... .... Here and there from this green ground rose pure white stars edged with a line of gold, and from their throats came crimson anthers but no pistils. A... ...form have given them, and consider them mathematically in the abstract, as geometry treats substances from which it extracts solidity.” 26 Seraphita ... ... here!’ “Let us pass from pure, unmingled Number to corporate Number. Your geometry establishes that a straight line is the shortest way from one poin... ...rror, contradicts it. Who shall decide between rectalinear and curvilinear geometry? between the theory of the straight line and that of the curve? If...

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...ndous Cavorite company ran and ruled the world. And I was in it! I took my line straight away. I knew I was staking every- thing, but I jumped there a... ...arge enough to hold two people and their luggage. It will be made of steel lined with thick glass; it will contain a proper store of solidified air, c... ...n, and off you would fly—” “At a tangent.” “You would go off in a straight line—” I stopped abruptly. “What is to prevent the thing travelling in a st... ...I stopped abruptly. “What is to prevent the thing travelling in a straight line into space for ever?” I asked. “You’re not safe to get any- where, and... ...et at the inside of the sphere, it will fly on through space in a straight line, as you say. But open a window, imagine one of the windows open. Then ... ... mental existences and establish a basis on those. The great principles of geometry, to begin with. He proposed to take some leading proposition of Eu... ... we are on the moon! Make no sudden movements!” “Are you going to try that geometry?” “If I get a chance. But, of course, they may make an ad- vance f... ... of nudging” “They’d better be careful how they nudge me.” “And about that geometry. After all, their way is a way of understanding, too. They begin w...

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...ze of green and crimson lights. The New York Flyer boomed past, and twenty lines of polished steel leaped into the glare. In one of the skyscrapers th... .... His arms were akimbo. His petulant, sleep-swollen face was set in harder lines. He suddenly seemed capable, an official, a man to contrive, to direc... ... her plump neck bagged. But the thing that marked her as having passed the line was that she no longer had reticences before her husband, and no longe... ...ve him a tremendous forehead, arching up two inches beyond the former hair-line. But most wonder-work- ing of all was the donning of his spectacles. T... ... skimpy trousers to the tops of his glaring tan boots, a chorus-man waist- line, pattern of an agitated check, and across the back a belt which belted... ...m, in a corner of the davenport, Ted settled down to his Home Study; plain geometry, Cicero, and the agonizing metaphors of Comus. 68 Babbitt “I don’... ...ipped out the ads of some swell courses.” He snatched from the back of his geometry half a hun- dred advertisements of those home-study courses which ... ...rks on no- body,” Babbitt observed, “not if they stay home and study their geometry and mind their own affairs instead of hang- ing around a lot of po...

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...f his having 5 Henry James married a rich woman made no difference in the line he had traced for himself, and he cultivated his profession with as de... ...anches—as if it were a royal house. Arthur, it appears, is of the reigning line, but poor Lavinia’s young man is not. Beyond this, Arthur’s 33 Henry ... ...erself. She was tasting of the sweets of concealment; she had taken up the line of mystery. “She would be enchanted to be able to prove to herself tha... ...ry another. Only, I should add, he 46 Washington Square should choose his line with discretion.” “Ah, yes, with discretion,” Morris Townsend repeated... ...to render him doubly interesting. “We must settle something—we must take a line,” he declared, passing his hand through his hair and giving a glance a... ...Shall a geometrical proposition relent? I am not so superficial.” “Doesn’t geometry treat of surfaces?” asked Mrs. Al- mond, who, as we know, was clev...

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.... She wore a dress of dark-blue silky stuff, with ruches of blue and green linen lace in the neck and sleeves; and she had emerald-green stockings. He... ...her softness and her fine, exquisite richness of texture and deli- cacy of line. There was a certain playfulness about her too, such a piquancy or iro... ... rows of dwellings, approach- 8 ing curved up the hill-slope, in straight lines along the brow of the hill. They were of darkened red brick, brittle,... ... in spite of the at- tempts that had obviously been made to bring her into line for the day. Her face was pale, yellowish, with a clear, trans- parent... ...ed pattern of dull gold. The high collar, and the inside of the cloak, was lined with dark fur. Beneath she had a dress of fine lavender- coloured clo... ..., masterful, he knew that every problem could be worked out, in life as in geometry. And he would care neither about himself nor about anything but th...

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..., we may take the stories least like poetry as our guide to the truth. The lineage of Theseus, by his father’s side, ascends as high as to Erechtheus ... ... as he added in Homer’s Raising of the Dead, to gratify the Athenians, the line Theseus, Pirithous, mighty sons of gods. Others say Ariadne had sons a... ...ected that famous pillar on the Isthmus, which bears an inscription of two lines, showing the bounds of the two coun- tries that meet there. On the ea... ...iations, but in general outline it runs thus: the kings of Alba reigned in lineal descent from Aeneas and the suc- cession devolved at length upon two... ...n plow- share, and, yoking together a bull and a cow, drove himself a deep line or furrow round the bounds; while the business of those that followed ... ...ives against it as the mere corruption and annihilation of the one good of geometry,—which was thus shamefully turn- ing its back upon the unembodied ... ...pravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as ... ...s of proof, most deserve our admiration. It is not possible to find in all geometry more difficult and intricate questions, or more simple and lucid e...

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...ure 1b.] S’ S a 1 θ r a 2 v Figure 1. GDT Projective and Elliptic Geometry Theorems a.) Right conic projection in G determining S’ ellipse... ... ,b 2 } are the corresponding minor axial radii as determined from elliptic geometry. We only require reference to one of the ellipse's two focal po... ... to be determined: the elliptic length (σ e ) defined as: the length of the line from any point P on the elliptic surface to the positive focus. Th... ... Graph 2. Relative Doppler Frequency (ν ν ν ν) Equations (7.2): solid line, and (7.3): dashed line : ( v = 0.9c). (ν ν ν ν) Freq 16 The d... ...cs obey the laws of special relativity. [44] VSE was seen to be a dividing line separating general relativity (GRT) from gravitational models, whic... ... be heterogeneous with electron well loci determined by intranuclear proton geometry. It is obvious that proton charge repulsion, interior to a spher... ... (cubic) surface. Coupled with proton repulsion, the logical result of this geometry is eight proton potential wells, (octet sites) with lowest pot... ... however, the eight ionizations of the 2p and 2s orbitals proceed in a near linear progression, so that there is no clear way to differentiate betwe... ...t progression supports the primary hypothesis of charge projection. Thus, a line drawn from the nucleo through a filled outer site defines a line of...

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... As a new type of poetry with fixed from: The Paradoxist distich is a two-line poem which contains an antithesis. The second line contradicts the f... ...ontains an antithesis. The second line contradicts the first one, but both lines form together a unitary meaning defining the title. Here there are... ...y with fixed from: The Tautological Distich is an apparently redundant two-line poem, but the “redundant” lines together give a deeper meaning to th... ...tion Of the scientific AXIOMATIZATION (II) Geometrization Of the geometry SCHOPENHAUER: “I know That I know” IMITATOR Discovers ... ...s As a new form of poetry with fixed form: The Dualistic Distich is a two-line poem such that the second line is the dualistic of the first and tog... ... reviewed it, something inside of the envelope was opposing. Gerald`s four-line proseful poetry, whose each stanza starts with “and”, was eagerly wa...

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...i, ness, too. I deal in love, and so must you. Since, for me, the bottom line in life and in business is people, it is important that they are nou... ..., it is gone for, ever. "Yesterday is a page turned; you cannot add one line to it or erase one word from it. It is closed forever and can affect ... ...first begin." The fastest runner in the world will never cross the finish line unless he or she first begins the race. The great inventions of the ... ...f a great mind that has gone before. In every case, people are the bottom line. Governments, educa~ tional institutions and corporations all exist t... ...d Game, the Dymaxion Airocean World Map, his develop, ment of Synergetic Geometry and his most famous invention, the Geodesic Dome. I was stationed... ...e are one in truth Q orne people live life as if it were a o horizontal line with all of us stand, ing in it single file, fighting desperately to ...

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... the work of feelings combined with intellect. It uses, for beginning students, geometry, matrices and diagrams. When studying Kabbalah, they recogn... ...s the case here. Kabbalah utilizes many mathematical concepts such as matrices, geometry, numbers, graphs, characters and letters, etc. These approa... ...s called Mouth (Peh). The part where the Light enters is called Body (Guf). The line exerting a restriction, inside the Guf , is called Navel (Tabu... ...t’s pressure by twenty percent below the Peh into the Guf, until it reaches the line of the Tabur. When the Light is expelled from the Guf, the Scree... ...hen the turn of the last Partzuf arrives, its lower part crosses the separating line, the Barrier (Machsom) between the spiritual world and our worl... ...making comparisons between spiritual and material laws. He even wrote a book on geometry. Perceiving one of the highest spiritual worlds, he was abl... ...riction. A new border for the spreading of the Light is being formed along this line: the Parsa. This border was located before in the Sium of Galga... ...elfish properties; immediately Malchut, ascending upward, covers it and forms a line, called Parsa, to limit the downward spreading of the Light. Th...

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...rosophic vector space over the neutrosophic field K(I ). By basis we mean a linearly independent set which spans the neutrosophic space. Now we ill... ...developed the theory of trees, in order to solve the system of simultaneous linear equations, which give the current in each branch and each circuit... ... single connected region and adjacent countries are those having a boundary line (not merely a single point) in common. The conjecture has acted a... ...ph in which people are represented by points and interpersonal relations by lines. Such relations include love, hate, communication and power. In fa... ...oposed the diagram in which the points represent physical particles and the lines represent paths of the particles after collisions. The study of M... ...bus. In mathematics his research papers are in number theory, non-Euclidean geometry, synthetic geometry, algebraic structures, statistics, and mult...

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... resolution based on Archimedean triangular norms 40 1.6 Solving non-linear optimization problem with FRE constraints 48 1.7 Method... ...8 4 1.19 A FRE in dynamic fuzzy systems 113 1.20 Solving FRE with a linear objective function 117 1.21 Some properties of minimal sol... ...h deneutrofication algorithm for largest solution 268 4.9 Solving NRE with a linear objective function 269 4.10 Some properties of minimal soluti... ... Y with non-zero membership grades in R(X, Y) are represented in the diagram by lines connecting the respective nodes. 11 We illustrate the sa... ...ments of X are comparable by the ordering such an ordering is usually called a linear ordering, some alternative names used in the literature are t... ..., rebus. In mathematics his research papers are in number theory, non-Euclidean geometry, synthetic geometry, algebraic structures, statistics, and ...

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...Matrix theory has been one of the most utilised concepts in fuzzy models and neutrosophic models. From solving equations to characterising linear transformations or linear operators, matrices are used. Matrices find their applications in several real models. In fact it is not an exaggeration if one says that matrix theory and linear algebra (i.e. vector space...

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...Matrices provide a very powerful tool for dealing with linear models. Bimatrices which we are going to define in this chapter are still a powerful and an advanced tool which can handle over one linear model at a time. Bimatrices will be useful when time bound comparisons are ne...

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...EIR PROPERTIES 2.1 Introduction to Bivector Spaces 79 2.2. Systems of linear biequations 87 2.3 Bitransformation in bivector spaces 96 2.4 ... ...paces 105 2.5 Bieigen values and Bieigen vectors 117 2.6 Bidiagonalizable linear bioperator and its properties 124 4 Chapter Three ... ...zy models and neutrosophic models. From solving equations to characterising linear transformations or linear operators, matrices are used. Matrices ... ...odels. In fact it is not an exaggeration if one says that matrix theory and linear algebra (i.e. vector spaces) form an inseparable component of eac... ...vention of new notions like birings, Smarandache birings, bivector spaces, linear bialgebra, bigroupoids, bisemigroups, etc. But most of these are ... ... Princeton, 1960. 20. KOSTRIKIN, A.I, and MANIN, Y. I., Linear Algebra and Geometry, Gordon and Breach Science Publishers, 1989. 21. LANG, S., Alg... ...bus. In mathematics his research papers are in number theory, non-Euclidean geometry, synthetic geometry, algebraic structures, statistics, and mult...

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...to the particular commodity of my kinsfolk and friends: to the end, that losing me (which they are likely to do ere long), they may therein find some lineaments of my conditions and humours, and by that meanes reserve more whole, and more lively foster the knowledge and acquaintance they have had of me. Had my intention beene to forestal and purchase the world's opinion a...

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...ng me (which they are likely to do ere long), they may therein find some lineaments of my conditions and humours, and by that meanes reserve more w... ...Deus simul atque volam, me solvet opinor, Hoc sentit, moriar. Mors ultima linea rerum est. -- HOR. 1. i. Ep. xvi. 76. In gyves and fetters I will ha... ...e to bee in painting, for sometimes the Painters hand shall draw certaine lines or draughts, so farre exceeding his conception or skill, that himsel... ...h rich and poore, Kings and groomes, Greekes and Barbarians. And were you lineally descended in the fiftieth degree from Hercules, they deeme it a v... .... Nor is there any one art whereof I am able so much as to draw the first lineaments. And there is no scholler (be he of the lowest forme) that may ... ...ter and wiser, he shall be entertained with Logicke, naturall Philosophy. Geometry, and Rhetoricke, then having setled his judgement, looke what sci... ...ause they were wont to bestow more time about astrology, law, logike, and geometry, than such arts could deserve; and diverted them from the devoirs... ... the use. So are all things spent and vented like. Physike is received as Geometry: and jugling tricks, enchantments, bonds, the commerce of decease... ... are things that often shock together: and it hath beene told mee that in geometry (which supposeth to have gained the high point of certainty among...