... 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... ... been previously filled; thus there are two possibilities for the added n-p pairs ―either locating at the six open face-sites or in the nucleo. Of t... ... odd outer site. Should we assume, in following calcium, it also has six n-p pairs in its nucleo? No, it is more likely to revert to argon's nucleo, ... ... No, it is more likely to revert to argon's nucleo, with the three added n-p pairs at outer sites, as in accordance with its +3 ion state. Except, wh... ...lds, incident light is absorbed or emitted at element-specific wavelengths (spectral lines). In diffuse molecular fields the more numerous individua...

...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... ..., Cypher, one of the rebels defects. Over a glass of (illusory) rubicund wine and (spectral) juicy steak, he poses the main dilemma of the movie. I... ...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... ... vast majority of humanity, that is), though, they are perceived to be the same. Pairs of events that are each other's cause and effect are accor... ...us problem, to my mind, is the converse: what sets apart causal (cause and effect) pairs of events from other pairs in which both member-events are...

...tor is α x = (t,x,y,z) and it defines a path in space/time called a world line. The 4-velocity is α u = ∂ x dt d and the 4-acceleration is . α ... ...) 00 2 1 g c w − = is gravitational potential, 00 0 g g c v i i − = is the linear velocity of the space rotation, k i ik dx dx h d = 2 σ is the squ... ...ong imaginary world-trajectories σ τ d cd < , having imaginary relativistic\linebreak masses 1 v 2 2 0 − = c im m (tachyons). World- lines of the bo... ...rials, interactions between materials, and metric spaces all depend on the (spectral) geometric shapes which exist in a dimensional hierarchy of met... ...ensional hierarchy of metric spaces. These geometric shapes are the natural spectral structures of metric spaces called space-forms. Space-forms com... ...ween space-form flows. Rotation between these flows is needed to define the spectral shapes, within a Hermitian space setting. These flows (in hyper... ...six faces are each 2-dimensional. 77 Space-forms - By identifying pairs of "opposite" faces of the fundamental domain, a new smooth geomet... ... multi-dimensional system. Metric states - Spectral flows are formed in pairs on space-forms so that each flow is given the opposite state of th... ...lex metric space. This complex structure is needed to take into account the pairs of metric states that are found, as flows on space-forms. The Dira...

... CONTENTS Preface 5 Chapter One INTRODUCTION TO LINEAR ALGEBRA AND S- LINEAR ALGEBRA 1.1 Basic properties of linear al... ...GEBRA 1.1 Basic properties of linear algebra 7 1.2 Introduction to s-linear algebra 15 1.3 Some aapplications of S-linear algebra 30 ... ...Introduction of S-bigroups and S-bivector spaces 46 Chapter Three LINEAR BIALGEBRA, S-LINEAR BIALGEBRA AND THRIR PROPERTIES 3.1 Basic ... ... the new pseudo inner product once again we will have the modified form of spectral theorem. That is, the Smarandache spectral theorem which we wil... ...= c 1 E 1 + c 2 E 2 . c 1 = 4. c 2 = 0. THEOREM (SMARANDACHE SPECTRAL THEOREM FOR S- VECTOR SPACES OVER FINITE RINGS Z N ): Let T i be... ...operties are true on V 1 and V 2 . The primary decomposition theorem and spectral theorem are also true is case of bivector spaces. The only prob... ...of vectors in V = V 1 ∪ V 2 . We say S is a biorthogonal set provided all pairs of distinct vectors in S 1 and all pairs distinct vectors in S 2 ... ...ial to note that neutrosophic roots in general need not occur in conjugate pairs. Now we proceed on to define characteristic neutrosophic polynomia...

...The algebraic structure, linear algebra happens to be one of the subjects which yields itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief economic models and so o...

...In this section we give the definition of linear algebra and just state the few important theorems like Cayley Hamilton theorem, Cyclic Decomposition Theorem, Generalized Cayley Hamilton Theorem and give some properties about linear algebra....

...ints and some edges are common in the directed graphs obtained between those pairs of models. We now proceed on to describe these 24 models for t... ... the vertex v 2 = v' 1 . Now be proceed on to define bigraphs glued by a line / edge. DEFINITION 2.1.4: G = G 1 ∪ G 2 be a bigraph. If the... ... have a common edge then we call the bigraph to be a edge glued bigraph or a line glued bigraph. The following example will show how a line glued... ...∪∪ ⎢⎥ ⎢⎥ ⎢ ⎥ ⎣⎦ ⎢⎥ − ⎢ ⎥ ⎣⎦ ⎣ ⎦ is a mixed square trimatrix. On similar lines we define n-matrix A which is the ‘union’ of n distinct matrices... ...//www.cs.waikato.ac.nz/~mjeff/papers/COSIT2001.p df 248 61. Johnson, T. New spectral theorem for vector spaces over finite fields Z p , Masters D...

...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 ... ...more than n! /m! (n – m)!, n! /m! (n – 1)! non-vanishing terms occurring in pairs in the expansion. The complementary biminor to any bideterminant A... ... a 2 × 2 bideterminant from A B and 2 × 2 determinant from B B . The three pairs of bideterminant which can be formed from A B B B respectively ... ...roperties are true on V 1 and V 2 . The primary decomposition theorem and spectral theorem are also true is case of bivector spaces. The only pro... ...atrix. An m × n bimatrix over the field F is a function A from the sets of pairs of integers (i 1 , j 1 ), (i 2 , j 2 ), 1 ≤ i 1 , i 2 ≤ m and 1 ≤... ...characteristic biroots, latent biroots, eigen bivalues, proper bivalues, or spectral bivalues. We would use in this book either the term charact... ...ublications, 37, American Mathematical Society, 1956. 17. JOHNSON, T., New spectral theorem for vector spaces over finite fields Z p , M.Sc. Disse...

...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...

...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...

... The ghost of Capt. Kidd -- The screaming woman of Marblehead -- Stories about spectral crews -- A ghostly company that come up out of the sea once ev... ...-- The Flying Dutchman -- The crimes for which he suffers -- In pursuit of the spectral ship -- Ghostly ships of extraordinary proportions -- A Monk w... ...in -- English are driven from their designs on Hayti -- Poisoned thorns in the line of march -- An immense fleet -- A conquest without spoils -- Conqu... ...traordinary heroism......................................... 305 Wild Bulls in line of battle............................................ 312 Morgan t... ... drugs, and other merchandise, and to have exchanged with the Indians purples, linens, and other manufactured articles. A city called Arsinoe was at t... ...rs and beds on which they reclined soaked with the briny liquid. STORIES ABOUT SPECTRAL CREWS. Occasionally the spectres come in companies. The Maine ... ...ners close to the head and made a boast that he had cut off over seven hundred pairs of ears without once touching the victims' shoulders; and Matt, t... ...ng their heads to the ground, after which fourteen women of royal rank came in pairs, carrying between them a narrow piece of white cloth, some eight ...

...ngredients, stirring well, and hoping for the best. No one, for instance, offered a linear revenue model of how to translate "eyeballs" - i.e., the ... ...be applied to animals. Law professor Steven Wise, argues in his book, "Drawing the Line: Science and the Case for Animal Rights", for the extension... ...ng and makes us more prone to using violence on humans. Malebranche augmented this line of thinking by "proving" that animals cannot suffer pain be... ...e vast majority of humanity, that is), though, they are perceived to be the same. Pairs of events that are each other's cause and effect are accor... ...us problem, to my mind, is the converse: what sets apart causal (cause and effect) pairs of events from other pairs in which both member-events are... ...there is, it is not finite." In the "Critique of Pure Reason", Kant discovered four pairs of propositions, each comprised of a thesis and an antith... ..., Cypher, one of the rebels defects. Over a glass of (illusory) rubicund wine and (spectral) juicy steak, he poses the main dilemma of the movie. I...

...ngredients, stirring well, and hoping for the best. No one, for instance, offered a linear revenue model of how to translate "eyeballs" - i.e., the ... ...be applied to animals. Law professor Steven Wise, argues in his book, "Drawing the Line: Science and the Case for Animal Rights", for the extension... ...ng and makes us more prone to using violence on humans. Malebranche augmented this line of thinking by "proving" that animals cannot suffer pain be... ...e vast majority of humanity, that is), though, they are perceived to be the same. Pairs of events that are each other's cause and effect are accor... ...us problem, to my mind, is the converse: what sets apart causal (cause and effect) pairs of events from other pairs in which both member-events are... ...there is, it is not finite." In the "Critique of Pure Reason", Kant discovered four pairs of propositions, each comprised of a thesis and an antith... ..., Cypher, one of the rebels defects. Over a glass of (illusory) rubicund wine and (spectral) juicy steak, he poses the main dilemma of the movie. I...

...hematical research into migration has dealt with it on purely statistical lines and studied it on economic terms, while ignoring that migration is ... ...ors C repeatedly through the FCM connection matrix E, thresholding or non-linearly transforming the result after each pass. Independent of the FCMs ... ... networks consists of many simple computing elements generally simple non linear summing junctions connected together by connections of varying stre... ...we see the hidden pattern is a limit cycle fluctuating between the binary pairs {{(0 0 1 0 0 0 0), (0 I 0 0 0 1 0 0 0 0)} and {(0 0 1 0 1 0 0), (0 0... ...erts opinion the neutrosophic directed graph. See that each blocks in the pairs occur only once. Now using the neutrosophic directed graphs we obtai... ...cur only once. Now using the neutrosophic directed graphs we obtain every pairs neutrosophic relational matrices using these matrices we form the n ... ...sis and Application of the Bidirectional Associative Memory to Industrial Spectral Signatures,” Proceedings of the 1989 International Joint Conferen...

...ys who starve to death are the true winners because they get to the finish line first. Yes, a party for losing jobs and visas. Games too. My favorite ... ..., however, he assumed that the officer who was in charge of the removal of linen and the return of the bottom bunks into seats was asleep. Being forty... ...s well dally until one of the officers of the train returned to remove the linen and readjust the seats or he would have to lie in the tenebrous tomb ... ...hting back parts of the disheveled hair that obstructed the process, was a spectral and indistinct image of his wife. He judged that she was no differ... ... to the stupa posing for pictures at its base. They seemed to come only in pairs to compound the quasi-reality of the experience of foreign travel int... ...lity of the experience of foreign travel into something more solid, for as pairs the dopamine was doubled for these mundane presences, leaving him alo...

...conomic and physical state variables come in intensive/extensive variable pairs and the one such pair that is receiving much current intellectual at... ...ncy to filter out the dissonance-causing information. (Bem, 1967). The non-linear feedback process could in effect be the force which keeps blowing u... ...perts. That reasoning that we advance has two basic components – a linear feedback process containing no looping and a non-linear feedback pr... ...motional factors. Festinger’s dissonance theory began by postulating that pairs of cognitions (elements of knowledge), given that they are relevant ... ...tion to reality and on the extent to which the particular cognition is in line with various other cognitions. Resistance to change of cognition depe... ...the coefficients a j provides an indirect but highly efficient method of spectral estimation. In a full nonlinear autoregressive model, quadratic (...

...fferent from the bistructures using category theory of Girard's classical linear logic. We do not approach the bialgebraic structures using category... ...c. We do not approach the bialgebraic structures using category theory or linear logic. We can broadly classify the study under four heads : ... ...ndache strong Moufang groupoid (S-strong Moufang groupoid). On similar lines we define Smarandache Bol groupoid, Smarandache strong Bol groupoid,... ...8: Let (L, +, ) be a biloop, i.e. L = L 1 ∪ L 2 . For any pre- determined pairs a 1 , b 1 ∈ L 1 and a 2 , b 2 ∈ L 2 in the biloop L, a principal ... ...commutative pair. But we see on the contrary that all S-pseudo commutative pairs in general need not be a pseudo commutative pair). If in a S-sub... ...eft for the reader to prove. DEFINITION 9.1.2: Let X be a set if on X, pairs of binary operations can be defined so that (X, ∗, ∗'), (X, o, o') i... ...erties are true on V 1 and V 2 . The primary decomposition theorem and spectral theorem are also true is case of bivector spaces. The only proble... ...R[x] a bivector space over R? Substantiate your claim. 7. State and prove spectral theorem for bivector space. 8. Illustrate spectral theorem by an ...

... concept of bialgebraic structures which we define and study are slightly different from the bistructures using category theory of Girard's classical linear logic. We do not approach the bialgebraic structures using category theory or linear logic....

...discussion. The youth took no part in them. As he walked along in careless line he was engaged with his own eternal debate. He could not hin-der himse... ...over the grass and in among the tree trunks, he could see knots and waving lines of skirmishers who were running hither and thither and firing at the ... ...were running hither and thither and firing at the landscape. A dark battle line lay upon a sunstruck clearing that gleamed orange color. A flag flutte... ...d. The shoulder of one of the tramping bearers knocked heavily against the spectral soldier who was staring into the unknown. The youth joined this cr... ...ly happy. He wished that he, too, had a wound, a red badge of courage. The spectral soldier was at his side like a stalking reproach. The man’s eyes w... ...ther soldiers, snoring and heaving, or lying death- like in slumber. A few pairs of legs were stuck forth, rigid and straight. The shoes displayed the... ...he sol-diers were bended and stooped like sprinters be-fore a signal. Many pairs of glinting eyes peered from the grimy faces toward the curtains of t...

...t succeeded in getting one through a London book- seller. This I compared, line by line, with the Edinburgh edi- 4 The Lady of the Lake tion of 1821 ... ... poem) has been changed to “bound” in all editions since 1821 ; and, eight lines below, the old word “ barded “ has become “ barbed.” Scores of simila... ...little skiff shot to the bay, That round the promontory steep Led its deep line in graceful sweep, Eddying, in almost viewless wave, The weeping willo... ...tion’s artful aid,” as here, and in the next two lines; most frequently in pairs of words. 124 The Lady of the Lake 38. As Chief, etc. Note here, as ... ...uch occasions, is evident from the stories of armies in the air, and other spectral phenomena with which history abounds. Such an apparition is said t... ... herself to be at those times endowed with a faculty of seeing visions and spectral appearances which shun the common ken. ‘In the year before the gre...

.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 60 The Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 61 Stu... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 125 The Log and Line . . . . . . . . . . . . . . . . . . . . . . . . . 492 126 The Life Buo... ...hale, As it floundered in the sea.” Elizabeth Oakes Smith. “The quantity of line withdrawn from the different boats engaged in the capture of this one ... ... all latitudes and longitudes, does the name of the White Sea exert such a spectralness over the fancy, while that of the Yellow Sea lulls us with mor... ... bleached like the skeleton of a stranded walrus. All down her sides, this spectral appearance was traced with long channels of reddened rust, while a... ...noses on the Pequod’s deck proved more vigilant discoverers than the three pairs of eyes aloft. A peculiar and not very pleasant smell was smelt in th... ...s upwardly projected from their faces like so many jib booms. Now and then pairs of them would drop their work, and run up to the mast head to get som... ...lantern, a space has been left clear for the workmen. They generally go in pairs, — a pike and gaff man and a spade man. The whaling pike is similar t... ...ep but the Parsee; who crouching in the bow, sat watching the sharks, that spectrally played round the whale, and tapped the light cedar planks with t...

...ly amidships, for I saw nothing, the strange steamboat having passed beyond my line of vision. The Martinez heeled over, sharply, and there was a cras... ... his feet. The man who had spoken to him was clearly a Cockney, with the clean lines and weakly pretty, almost effeminate, face of the man who has abs... ... Chapter II 11 on his face. Out of my experience with stewards on the Atlantic liners at the end of the voyage, I could have sworn he was waiting for ... ...hould have been asleep, of lying on the forecastle head and gazing down at the spectral ripple of foam thrust aside by the Ghost’s forefoot. It sounde... ... were rowing as well as sailing. Even the hunters were pulling, and with three pairs of oars in the water they rapidly overhauled what I may appropria... ... Furling the sail and lashing it securely about the mast, boom, sprit, and two pairs of spare oars, I threw it overboard. A line connected it with the...

...le, As it floundered in the sea.” —Elizabeth Oakes Smith. “The quantity of line withdrawn from the boats engaged in the capture of this one whale, amo... ...matra than here? Would he not far rather lay him down lengthwise along the line of the equator; yea, ye gods! go down to the fiery pit itself, in orde... ... hovering in the centre of the picture over three blue, dim, perpendicular lines floating in a nameless yeast. A boggy, soggy, squitchy picture truly,... ...ll lati- tudes and longitudes, does the name of the White Sea exert such a spectralness over the fancy, while that of the Y ellow Sea lulls us with mo... ... bleached like the skeleton of a stranded walrus. All down her sides, this spectral appearance was traced with long channels of red- dened rust, while... ...noses on the Pequod’s deck proved more vigilant discoverers than the three pairs of eyes aloft. A peculiar and not very pleasant smell was smelt in th... ... upwardly projected from their faces like so many jib- booms. Now and then pairs of them would drop their work, and run up to the mast-head to get som... ...lantern, a space has been left clear for the workmen. They generally go in pairs,— a pike-and-gaffman and a spade-man. The whaling-pike is similar to ...

......................................................................... 169 LINES TO A FRIEND VISITING AMERICA............................................ ...........................................................508 Index of First Line ....................................508 14 The Poems of George Meredi... ...ls close, Thick brambles and dark brushwood tufts, And briared brakes that line the dells With shaggy beetling brows, had sung Shrill music, while the... .... Yet here, Like the pause to things hunted, in doubt, The stillness bred spectral fear Of the awfulness ranging without, And imminent. Downward the... ...now they dream like sunlight on a sea, And deem you hold the half of happy pairs. He who’s for us, for him are we! V —Ladies, I listened to a ring of ... ...e dazzling wizard who would have her bleed On fruitless marsh and snows of spectral gloom For victory that was victory scarce in name. Husky his clari... ... dark was it endowed; Stood day before a vision shooting wide. Whereat the spectral enemy lost form; The traversed wilderness exposed its track. He fe...

...d them from the neck to the knees, and trou- sers of white and very coarse linen, the ill-woven texture of which betrayed the slovenly industrial habi... ...over his shoulder a heavy stick of knotted oak, at the end of which hung a linen bag with little in it. Some wore, over the red cap, a coarse felt hat... ...rs which was fastened round it. Others were clothed entirely in the coarse linen of which the trousers and wallets of all were made, and showed nothin... ...nd tawny schists, must have been seen in order to understand how vividly a spectral image was suggested by the empty and gloomy carcass of the buildin... ...racticable that the small- est vehicles can only be drawn over them by two pairs of oxen or Breton horses, which are small but usually vigorous. These...