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Parity (mathematics) (X)

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 Book Id: WPLBN0002097036 Subjects: Non Fiction, Education, Mathematics, Mathematics ► Abstract Full Text Search Details...he. In addition, I have edited two others that also deal with the areas of mathematics under the Smarandache Notions umbrella. All of this is a credit... ...nd the second is an even plus an even. Since all powers of B are even, the parity of the numbers will be based on the parity of the last term, which i... ...ng the previous term by a power of B, which is always even. Therefore, the parity of the next term will be based on the parity of the term number, whi... ...s, we have (12 . . . (r-1)) * 3 s + r*3 t + (r-1) . . . 21 which has odd parity. The next element of the sequence is formed by including an addition... ... r*3 w is also odd. Therefore, we have three segments whose sum is of odd parity and we added an additional odd term. This changes the parity to even... ...lement (12 . . . r)*3 s by additional powers of three will not change the parity of the term. Therefore, we have two terms whose combined parity is e... ...arandache is truly a Renaissance man, having produced quality work in art, mathematics and literature. This is my fifth book where I expand on some o...
 Book Id: WPLBN0002097084 Subjects: Non Fiction, Mathematics, Finances, Mathematics ► Abstract Full Text Search Details...els, our approach is predominantly numerate and substantiated by rigorous mathematics rather than being merely normative or speculative. The... ... While countless research papers have been written and published on the mathematics of option pricing formulation, surprisingly little work has be... ... e -r (T-t) ∆s {p U (u) – p U (d)} + (C + Xe -r (T-t) – S)] … put-call parity = – e -r (T-t) ∆s {p U (u) – p U (d)} – C ... ... e -r (T-t) ∆s {p U (u) – p U (d)} + (C + Xe -r (T-t) – S)] … put-call parity = e -r (T-t) ∆s {p D (d) – p D (u)} – C Therefor... ... = (Xe -r (T-t) – S) – {C + (Xe -r (T-t) – S)} … put-call parity = – C Therefore, E (Y put ) = Max [– C, – P] ... .... Numerical Methods and Software. Prentice-Hall Series in Computational Mathematics, New Jersey: Prentice-Hall, 1989. Khoshnevisan, M., S. Bhatt... ...78. Lyuu, Yuh-Dauh. Financial Engineering and Computation – Principles, Mathematics, Algorithms. Cambridge University Press, U.K., 2002. Mark... ...J. The coding of messages subject to chance errors. Illinois Journal of Mathematics 1, 1957: 591-606. Zadeh, L. A. A Theory of Approximate Reaso...
 Book Id: WPLBN0002097105 ► Abstract Full Text Search Details...AND NEUTROSOPHIC RELATIONAL MAPS W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036... ...ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail:... ...cademia Technica Militaria, Bucharest, Romania. Dr. B.S. Kirangi, Department of Mathematics and Computer Science, University of Mysore, Karnataka, I... ... Even more general, of course, is to consider Θ as an operator (of some finite parity) which maps fuzzy sets and relations onto fuzzy sets or fuzzy... ...al, and thus one defines the neutrosophic set. One gives 227 examples from mathematics, physics, philosophy, and applications of the neutrosoph... ... Darwin (biology), Maxwell (electromagnetism), Einstein (mechanics) and Godel (mathematics). Although paradigm shifts vary from one another in thei...
 Book Id: WPLBN0002097651 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Description Details...zzy Algebra. Originally, the revolutionary theory of Smarandache notions was born as a paradoxist movement that challenged the status quo of existing mathematics. The genesis of Smarandache Notions, a field founded by Florentine Smarandache, is alike to that of Fuzzy Theory: both the fields imperatively questioned the dogmas of classical mathematics.... Full Text Search Details...HE FUZZY ALGEBRA W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology Madras Chennai – 600 036, Indi... ...tarted because of my perception at that time, that the world of classical mathematics – was a little too much of a black and white world, that the p... ...born as a paradoxist movement that challenged the status quo of existing mathematics. The genesis of Smarandache Notions, a field founded by Floren... ...y Theory: both the fields imperatively questioned the dogmas of classical mathematics. Despite the fact that Fuzzy Algebra has been studied for ov... ...1) (0: 0) Figure 7.1.4 404 This automaton is known as the parity check automaton. Now it is important and interesting to note th... ...Normalized fuzzy extension, 150 O Open fuzzy extension, 146 P Parity check automaton, 404 Penultimate, 224 P-fuzzy correspondence, 164 ... ...UTHOR Dr. W. B. Vasantha is an Associate Professor in the Department of Mathematics, Indian Institute of Technology Madras, Chennai, where she liv...
 Book Id: WPLBN0001235224 Subjects: Non Fiction, Education, Economics ► Abstract Full Text Search Details...he software metaphor is correct, the brain must contain the following features: 1. Parity checks through back propagation of signals. The brain's e... ... back (to the origin) and forward, simultaneously, in order to establish a feedback parity loop. 2. The neuron cannot be a binary (two state) mach... ...be no preferred direction, no clustering of mass or of energy, no time, charge, or parity asymmetry in elementary particles. The notion of continuu... ...ractitioners sought to disguise its nature as a social science by applying complex mathematics where common sense and direct experimentation would ... ...ifferently to the same transformation? Arithmetic, formal logic, and, by extension, mathematics and physics deal with proving identities in equation... ...ecognized as an important contribution and applied to problems in geometry, logic, mathematics, computation and physics. One of the first questions... ...t infinite sets are organized in a hierarchy. Russel and Whitehead concluded that mathematics was a branch of the logic of sets and that it is ana... ...ations require an "intuition of mathematical order" without which no creativity in mathematics is possible. He described how some of his creative w...
 Book Id: WPLBN0002097038 Subjects: Non Fiction, Education, Smarandache Collections Collections: Math, Literature, Education, Authors Community, Mathematics ► Abstract Description Details...ting a book, one encounters and overcomes many obstacles. Not the least of which is the occasional case of writer’s block. This is especially true in mathematics where sometimes the answer is currently and may for all time be unknown. There is nothing worse than writing yourself into a corner where your only exit is to build a door by solving unsolved problems. In any case... Full Text Search Details...ctually reached. That statement also holds for some of these problems. In mathematics, one often does not know what the consequences of a statement ... ...nt are. Cnlike a novel however, there are no complete plot resolutions in mathematics as there are no villains to rub out. As the French emphatically... ... divides n'. and associated consequences has spawned many new branches of mathematics. A previous volume in this series[2] introduced the function a... ...For any number of digits k, the number of elements of SEDS depends on the parity ofk. a) Ifk = 2j, then the number of elements of SEDS having m digi... ...ime to stop once again There are still unexplored regions in that area of mathematics loosely defined as the Smarandache notions, but they will be le...
 Book Id: WPLBN0002097108 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...AND NEUTROSOPHIC RELATIONAL MAPS W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036... ...ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail:... ...cademia Technica Militaria, Bucharest, Romania. Dr. B.S. Kirangi, Department of Mathematics and Computer Science, University of Mysore, Karnataka, I... ... Even more general, of course, is to consider Θ as an operator (of some finite parity) which maps fuzzy sets and relations onto fuzzy sets or fuzzy... ...al, and thus one defines the neutrosophic set. One gives 227 examples from mathematics, physics, philosophy, and applications of the neutrosoph... ... Darwin (biology), Maxwell (electromagnetism), Einstein (mechanics) and Godel (mathematics). Although paradigm shifts vary from one another in thei...
 Book Id: WPLBN0002097043 Subjects: Non Fiction, Algebra, Smarandache Collections ► Abstract Full Text Search Details...TION TO LINEAR BIALGEBRA W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036, Ind... ... web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: smar... ...ica Militaria, Bucharest, Romania, Prof. Dr. B. S. Kirangi, Department of Mathematics and Computer Science, University of Mysore, Karnataka, India.... ... dimension (6, 4). Now the bicodes are generated by bimatrices and we have parity check bimatrices to play a role in finding the check symbols. Thus... ...k 2 × n 2 ) with entries from the same field Z q , H = H 1 ∪ H 2 is the parity check bimatrix of the bicode C. The standard form of H is (A 1 , ... ... n 2 – k 2 identity matrices respectively. The bimatrix H is called the parity check bimatrix of the bicode C = C 1 ∪ C 2 . C is also called the... ..., k) = C (6 ∪ 7, 3 ∪ 4) = C 1 (6, 3) ∪ C 2 (7, 4) be a bicode got by the parity check bimatrix, H = H 1 ∪ H 2 where H = 011100 1110100 1010... ...x 2 is a sent message and y = y 1 ∪ y 2 is a received message using the parity check bimatrix H = H 1 ∪ H 2 one can easily verify whether the ... ...d many times since it may quite properly be regarded as an area of applied mathematics. The subject finds its place in the work of Euler. Subsequent...
 Book Id: WPLBN0002097643 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details... A 2 B 1 B 2 4 0 1 2 3 1 W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology Madras, Chennai – 600036, ... ...e Smarandache Semigroup, International Conference on Combinatorial Methods in Mathematics, II Meeting of the project 'Algebra, Geometria e Combinato... ...i ) z 0 z 1 (0,0) (1;1) (1;1) (0,0) This automaton is know as the parity check automaton. Now it is important and interesting to not... ...7 Next state function, 93, 97 Output alphabet, 94 Output function, 94 Parity Check Automaton, 96 Semi automaton, 93-94, 96, 102 Semigroup... ...he Author Dr. W. B. Vasantha is an Associate Professor in the Department of Mathematics, Indian Institute of Technology Madras, Chennai, where she...
 Book Id: WPLBN0002097117 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...re more interested to attract all types of reader we have not used very high mathematics. DEFINITION 1.1.1: An FCM is a directed graph with conc... ...sacred thread? Do all the non-Brahmins who 122 wear the sacred thread, have parity with the Brahmins? Now, in our country the Singurao, Chettiar, ... ...ics, Masters Dissertation, Guide: Dr. W. B. Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, (2001). 7. Bechtel, J.H... ...es, Masters Dissertation, Guide: Dr. W. B. Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, (2000). 22. Kananaikal, ... ...oblem, Masters Dissertation, Guide: Dr.W.B.Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, Chennai, (1999). 26. Ko... ...dents, Masters Dissertation, Guide: Dr.W.B.Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, Chennai, (2001). 32. Ma...
 Book Id: WPLBN0002097093 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...erican Research Press Rehoboth 2002 József Sándor DEPARTMENT OF MATHEMATICS BABE Ş-BOLYAI UNIVERSITY 3400 CLUJ-NAPOCA, ROMANIA Geome... ...n its inexhaustible wealth, wherein it so greatly surpasses other parts of mathematics..." (K.F. Gauss, Disquisitiones arithmeticae, G ottingen, 1801... ...uable advice or support in the preparation of this material. These are the Mathematics Department of the Babe s-Bolyai University, the Domus Hun- gar... ...ntimate correlation between the Theory of numbers and other departments of Mathematics, not excluding geometry..." (Felix Klein, Evanston Colloquium L... ...b =d(v 2 u 2 ) c = 2duv (1) where (u;v) = 1, v > u and u;v have distinct parity; d is arbitrary (or b! c, c! b). The area of ABC is A = bc 2 =d 2 uv... ...be written as (m 2 + n 2 )j2 mn (m 2 n 2 ). Since (m;n) = 1, of di erent parity, it is immediate that ( m 2 + n 2 ; 2mn(m 2 n 2 )) = 1, giving (m ... ...m 2 +n 2 ) (18) where k 1 is arbitrary and (m;n) = 1, m>n are of di erent parity. In the same manner, by r a = p a = uq b u in case i) b u = (... ...v 2 ) 2uv; (5) where u>v, (u;v) = 1 are positive integers of the di erent parity, and t 1 is arbitrary positive integer, (and x!y, y!x, z!z). Proof.... ... 2 u 4 + 4dv 2 = 3T 2 and z = T du 2 2 . ThereforeT anddu 2 have the same parity. Now, by solving the equationd 2 u 4 4dv 2 +3T = 0 one obtains d =...
 Book Id: WPLBN0001235286 Subjects: Non Fiction, Philosophy, Science ► Abstract Full Text Search Details...nd no amount of interactions with us, humans, is ever going to change this. Why is Mathematics so Successful? In earlier epochs, people used myths ... ...es, the encroachment of mathematical modeling and statistics notwithstanding. Yet, mathematics reigns supreme and unchallenged in the natural scien... ...supreme and unchallenged in the natural sciences. Why is that? What has catapulted mathematics (as distinct from traditional logic) to this august ... ...stinct from traditional logic) to this august position within three centuries? Mathematics is a language like no other. Still, it suffers from ... ...evelop constantly (consider slang, or the emergence of infinite numbers theories in mathematics). But, they evolve within a formal grammar and synta... ...be no preferred direction, no clustering of mass or of energy, no time, charge, or parity asymmetry in elementary particles. The notion of continuu...
 Book Id: WPLBN0001235233 Subjects: Non Fiction, Psychology, Education ► Abstract Full Text Search Details...he software metaphor is correct, the brain must contain the following features: 1. Parity checks through back propagation of signals. The brain's e... ... back (to the origin) and forward, simultaneously, in order to establish a feedback parity loop. 2. The neuron cannot be a binary (two state) machi... ...measurement and by organizing the results and presenting them using the language of mathematics. This does not atone for its primordial sin: that it... ...d measurement and organizes the results, often presenting them in the language of mathematics. In some quarters, these practices lends it an air o... ...measurement and by organizing its results and presenting them using the language of mathematics. This does not atone for its primordial sin: that it...
 Book Id: WPLBN0001235225 Subjects: Non Fiction, Religion, Philosophy ► Abstract Full Text Search Details...he software metaphor is correct, the brain must contain the following features: 1. Parity checks through back propagation of signals. The brain's e... ... back (to the origin) and forward, simultaneously, in order to establish a feedback parity loop. 2. The neuron cannot be a binary (two state) mach... ...be no preferred direction, no clustering of mass or of energy, no time, charge, or parity asymmetry in elementary particles. The notion of continuu... ...ractitioners sought to disguise its nature as a social science by applying complex mathematics where common sense and direct experimentation would ... ...ifferently to the same transformation? Arithmetic, formal logic, and, by extension, mathematics and physics deal with proving identities in equation... ...ecognized as an important contribution and applied to problems in geometry, logic, mathematics, computation and physics. One of the first questions... ...t infinite sets are organized in a hierarchy. Russel and Whitehead concluded that mathematics was a branch of the logic of sets and that it is ana... ...ations require an "intuition of mathematical order" without which no creativity in mathematics is possible. He described how some of his creative w...
 Book Id: WPLBN0001235228 Subjects: Non Fiction, Education, Security ► Abstract Full Text Search Details...ions Deregulation and Monetary Control Act of 1980 forced S&L's to achieve interest parity with commercial banks, thus eliminating the interest ceil... ...LE - p16} 7. VARIANCE and STANDARD DEVIATION as measures of the difference between mathematics and reality. They are the measures of the frustrat...
 Book Id: WPLBN0000678547 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...ums of money, I laid them out in learning navigation, and other parts of the mathematics, useful Gulliver’ s Travels – Swift 8 to those who intend t... ...is dominions, had been educated in the study of philosophy, and particularly mathematics; yet when he observed my shape exactly, and saw me walk erect... ...eople is very defective, consist ing only in morality, history, poetry, and mathematics, wherein they must be allowed to excel. But the last of these... ... victuals from below, which were drawn up by pulleys. The knowledge I had in mathematics, gave me great assistance in acquiring their phraseology, whi... ... – Swift 143 in their conceptions upon all other subjects, except those of mathematics and music. They are very bad reasoners, and vehemently given ... ...Yahoos of that country and those in ours; for he only meant to observe what parity there was in our natures. He had heard, indeed, some curious Houy...
 Book Id: WPLBN0000662188 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...iolent act, a fortiori approves all lesser acts. But the establishment, by parity of reason, retained upon its rolls all the degrees, all the modi- fi... ...hand, Charlemagne, even in that early age, was familiar with the intricate mathematics and 92 Theological Essays and Other Papers – V olume Two the e...
 Book Id: WPLBN0000677128 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details... to under- 61 Balzac stand their full bearing. “‘Monsieur,’ he said, ‘the parity of these three substances, in appearance so distinct, led me to thin... ...Emmanuel, trembling with pleasure, “Gabriel is at the head of his class in mathematics; if he would like to enter the Ecole Polytechnique, he could th...
 Book Id: WPLBN0000677986 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...cret of vegetable nature; he watches the slow life of plants; he notes the parity of motion among all the species, and the parity of their nutrition; ... ..., one of the demigods of hu- manity. His doctrine of re-incarnation is the mathematics of materialism, the vital law of its phases. T o each of the di...
 Book Id: WPLBN0000660982 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...h the full volume of sound correspond- ing to the full volume of water, on parity of principles, no- body will doubt that the current of blood pouring... ...f schools dedicated to liberal objects, is opposed to schools for teaching mathematics, or, more widely , to schools for teaching science. 2 “Class,”... ...falling under hyper-physi- cal or cata-physical laws, loses its shadow, by parity of argu- ment, an audible object, in the same circumstances, should ...
 Book Id: WPLBN0000677390 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details... never before heard of, has left in London, in the days of steam and gas and photographs of thieves and electric telegraphs, the sanctuaries and stews... ... certain auxiliaries which in most countries and all ages have been bestowed upon man for his use, but it is undeniable that other mem- bers of the pr...
 Book Id: WPLBN0000661761 ► Abstract Full Text Search Details...obvious that England pays for the car- riage of the linen, and Germany, by parity of reason, for that of the cloth. But if we apply to these questions... ...t and unsettled of all branches of knowledge. If we open any book, even of mathematics or natural philosophy, it is impossible not to be struck with t... ...con- 110 Essays on Some Unsettled Questions of Political Economy fined to mathematics, but is of the essence of all science which admits of general r... ...duced from these assumptions, would be as true in the abstract as those of mathematics; and would be as near an approxima- tion as abstract truth can ...
 Book Id: WPLBN0000675604 ► Abstract Full Text Search Details... other logical forms, a mere figure of speech transferred from the sphere of mathematics, may be doubted. That Plato and the most subtle philosopher o... ...t extend to the gods, nor our knowledge know anything which is divine, so by parity of reason they , being gods, are not our masters, neither do they ...
 Book Id: WPLBN0000662125 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...nst the errors into which his own inexperience had been insnared. The dis- parity of years between himself and his wife he notices in a beautiful scen... ...in England. NO NO NO NO NOTE 23. TE 23. TE 23. TE 23. TE 23. And hence, by parity of reason, under the opposite circum- stances, under the circumstanc... ...er, Lam- bert, and Immanuel Kant,—had vindicated the preeminence of German mathematics. Already, in 1755, had the same Immanuel Kant, whilst yet a pro...
 Book Id: WPLBN0000675583 ► Abstract Full Text Search Details...to disprove them.” Undoubtedly: and such teaching suffices on a subject like mathematics, where there is nothing at all to be said on the wrong side o... ...eelings, by persisting in their abominable worship or creed. But there is no parity between the feeling of a person for his own opinion, and the feeli...
 Book Id: WPLBN0000675585 ► Abstract Full Text Search Details...uperiority in women over men, must certainly make them, with anything like parity of quali fications in other respects, more apt than men in that cho... ...such pro cess ? Mrs. Somerville, alone perhaps of women, knows as much of mathematics as is now needful for making any considerable mathematical disc...
 Book Id: WPLBN0000662419 ► Abstract Full Text Search Details...natural ob- jects, as fitted for poetic purposes, there is no immense dis- parity, and that both are capable of poetic treatment. Both, accordingly, h... ...The Poetical Works of Alexander Pope: V ol. 2 his enemies. However, as the parity is so remarkable, I hope it will continue to the last; and if ever h... ...physic begs defence, And Metaphysic calls for aid on Sense! See Mystery to Mathematics fly! In vain! they gaze, turn giddy, rave, and die. Religion, b...
 Book Id: WPLBN0000661675 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...uld not suffer the Arabic to benefit by its own obscurity to the injury of mathematics. And the book remains a monument to this day, that a system of ... ... allis, Savilian professor of geometry at Oxford, the improver of analytic mathematics, and the great historian of algebra. Algebra it was that sugges... ...e his act either murder, or manslaughter, or justifiable homi- cide; so by parity of reason, suicide is open to distinctions of the same or correspond...
 Book Id: WPLBN0000660962 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...ep wine in the vat. They conjectured of old at Athens, an aptitude for the mathematics in him they saw ingeniously bavin up a burthen of brushwood. In... ...ave got by fight- ing, you may make use of them without reproach. The dis- parity and inequality are only weighed and considered from the condition of... ... with Phocion, for in this couple there would have been a more likely dis- parity, to the Roman’s advantage. As to Marcellus, Sylla, and Pompey, I ver...
 Book Id: WPLBN0000662362 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...s of Jupiter? And, as no such discoveries were there, why did they not, by parity of logic, and for mere consis- tency, deny the telescope as a fact, ... ...men on the art of fortification. In 1770, he was appointed to the Chair of Mathematics, which he exchanged soon after for that of Logic and Metaphysic... ...nd also the fact that D’Alembert, whose philosophy was miserably below his mathematics, many years afterwards still continued to represent the dispute...
 Book Id: WPLBN0000660978 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...ed, is the small- est State in the Union. I may perhaps best show its dis- parity to other States by saying that New York extends about two hundred an... ...n intended that it should be given. But there are axioms in politics as in mathematics, which recommend themselves to the mind at once, and require no...
 Book Id: WPLBN0000649872 ► Abstract Full Text Search Details...s himself always occupied: writing his memoirs, solving problems in higher mathematics, turning snuffboxes on a lathe, working in the garden, or super... ... closed the exercise book with the next day’s lesson, was about to leave: “Mathematics are most important, madam! I don’t want to have you like our si... ...re of his weaknesses. “The hours are the same, and the lathe, and also the mathematics and my geometry lessons,” said Princess Mary gleefully, as if h... ...the minutest details himself. Prin- cess Mary had ceased taking lessons in mathematics from her father, and when the old prince was at home went to hi... ...ion to infinity, do we reach a solution of the problem. A modern branch of mathematics having achieved the art of dealing with the infinitely small ca... ...enisov had two hundred, and Dolokhov might have as many more, but the dis- parity of numbers did not deter Denisov. All that he now wanted to know was...
 Book Id: WPLBN0000661392 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...still greater number. There is not, however, a more certain proposition in mathematics, than that the more tickets you adventure upon, the more likely... ..., which every province af- fords to the public in time of war, ought, from parity of reason, to bear the same proportion to the extraordinary revenue ...
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