Description Details
... book contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers and functions; and Some irrationality results. Chapter 1 deals essentially with geometric inequalities for the remarkable ele...

Full Text Search Details
...T OF MATHEMATICS BABE Ş-BOLYAI UNIVERSITY 3400 CLUJ-NAPOCA, ROMANIA Geometric Theorems, Diophantine Equations, and Arithmetic Functions ... ... of Geometry and Number theory. The material is divided into ve chapters: Geometric the- orems; Diophantine equations; Arithmetic functions; Divisibi... ...unctions; and Some irrationality results. Chapter 1 deals essentially with geometric inequalities for the remarkable elements of triangles or tetrahed... ...ng of this publication. J ozsef S andor 3 Contents Preface 2 Chapter 1. Geometric theorems 8 1 On Smarandache’s Podaire Theorem . . . . . . . . . .... ...s for the elements of a triangle . . . . . . . . . . . . . . . . 13 4 On a geometric inequality for the medians, bisectors and simedians of an angle o... ...c b 2 +c 2 . Here k +1 2 1= = M (k; 1) is the well-known H older mean of argu- ments k and 1. It is known, that M is a strictly increasing... ... proofs of (1), the given proofs are not illuminating, and the geometrical meanings are hidden. Our aim is to obtain a geometric proof of (1), in an i... ...s and inequalities of type (1)-(3). 2. Inequality (1) is proved usually be means of vectors or complex numbers (or Stew- art’s theorem). For proofs, s... ... 1 :::b x i :::x n the sum of all productsx 1 :::b x i :::x n , whereb x i means that the term x i is missing (e.g. n = 3 this sum is x 1 x 3 +x 2 x 3...

Description Details
...(Author to reader)--Reader, loe here a well-meaning Booke. It doth at the first entrance forewarne thee, that in contriving the same I have proposed unto my selfe no other than a familiar and private end: I have no respect or consideration at all, either to thy servic...

Full Text Search Details
...the curteous Reader Dedicatory Poems The Author to the Reader I. By divers Meanes men come unto a like End II. Of Sadnesse or Sorrowe III. Our Affec... ...nesse, or doing Nothing XXII. Of Running Posts, or Couriers XXIII. Of Bad Meanes emploied to a Good End XXIV. Of the Roman Greatnesse XXV. How a Man ... ... Essays XXXIII. The Historie of Spurina XXXIV. Observations concerning the meanes to warre after the maner of Julius Cæsar XXXV. Of Three Good Women ... ...oever, I hope that may yet save me, which from others strangles others, I meane the coller you have put about my neck with your inscription, Noli me... ...ere they greater in all action. And even as they report of that Syracusan Geometrician, who being taken from his bookish contemplation to shew some p... ...at Disciple about the arts how to frame Syllogismes, or the principles of Geometric, as he endevoured to instruct him with good precepts concerning ... ...ason why Aristotle doth so willingly ascribe that art unto them: then for geometric and arithmetike, they alwaies frame their shole of a cubike figu... ...s not this a quaint imagination, produced by the inevitable necessitie of Geometricall demonstrations? Yet not so unavoidable and beneficiall, but S... ...ce in our beleefe as they need to conclude afterward what they please, as geometricians doe by their graunted questions: the consent and approbation ...

Description Details
... in addition to sample information and analyses their properties. Some estimators are generated from the proposed class and compared with the minimum mean squared error (MMSE) estimator. Numerical computations in terms of percent relative efficiency and absolute relative bias indicate that certain of these estimators substantially improve the MMSE estimator in some guessed...

Full Text Search Details
...estimators are generated from the proposed class and compared with the minimum mean squared error (MMSE) estimator. Numerical computations in terms ... ...gated the impact of measurement errors on a family of estimators of population mean using multiauxiliary information. This error minimization is vit... ...estimators are generated from the proposed class and compared with the minimum mean squared error (MMSE) estimator. Numerical computations in terms o... ...sed interval, Shrinkage estimation technique, Absolute relative bias, Relative mean square error, Percent relative efficiency. 2000 MSC: 62E17 ... ... the class of estimators of the form C β ∧ ; C being a constant for which the mean square error (MSE) of C β ∧ is minimum, is β ∧ = − M h t 4 ,... ... S. and Pattanaik, L.M. (1984): Alternative multivariate ratio estimators using geometric and harmonic means. Jour. Ind. Soc.Agri. Statist., 36, 110-...

Description Details
...ree of charge to a searchable database of articles stretching back to 1998 on its website. The student yearbook is called The Gulielmensian, which means "Williams Thing" in Greek.[52] It was published irregularly in the 1990s, but has been annual for the past several years and dates back to the mid-...

Full Text Search Details
...table service to the latter has been the establishment of a news bureau by means of which WilHams news of uniform charac- ter is supplied to some two-... ...he stu dent are lield up for public analy- sis. For tiie aiuiiinus it is a means for presenting a feature of college sentiment which has es- caped the... ...ement in ditferent branches of college activity is attained chietly by the means of fair criticism. The Record in the future, as in the past, will end... ...t attitude on matters of undergraduate discus sion. By independence is not meant aloofness, but a right of im- partially weighing student senti- ment ... ...not assume the qualities of a busybody," ' but rather will continue as the means of pointing out the defects in the college organisn which we think ca... ...hich, besides applying to higher mathematics, illustrate almost all of the geometric theorems encoun- tered in Matliematics 1. Since last October Mr. ...

Excerpt Details
... quantum coding theory. Many good quantum error-correcting codes were constructed from BCH codes, Reed-Muller codes, Reed-Solomon codes and algebraic geometric codes, see [2-6]. So it is natural to construct quantum error-correcting codes from quaternary cyclic codes. It is known that there is a close relation between cyclotomic coset and cyclic codes. Suggested by this re...

Table of Contents Details
...unction 80 W. Zheng and J. Dou : Periodic solutions of impulsive periodic Competitor- Competitor-Mutualist system 86 X. Zhang : On the fourth power mean value of B(Â) 93 Z. Lv : On the F.Smarandache function and its mean value 104 J. Ge : Mean value of F. Smarandache LCM function 109...

Excerpt Details
...In aesthetics, the paradox means the apparent resolution of an enigmatic situation (the result of such a process is the satisfaction of a distention), the emotional moving force being the unforeseen, the unexpected (which generates and also perturbs ...

Full Text Search Details
...nothing! 7 From paradox to paradoxism In aesthetics, the paradox means the apparent resolution of an enigmatic situation (the result of suc... ...an instant, is derived from the appearance of something with a convincing meaning; the second one, that comes immediately, is the perception of some... ...precisely on “disordered” manifestations of language: the amalgamation of meanings produces humour, the “sliding” of meanings assumes an ironical fu... ...proper message-object in the inwardness of his receiving conscience, what means that every receiver may benefit of his “object” of art, autonomous a... ...zation of the literary matter to a multiplicity “without limit” (what may mean, for a rigorous aesthetician, a notional pulverization, including for... ...s of traditional inspiration don’t point out. For instance, in the case of geometrical figures used in paradoxism, there intervenes, in a reader who ... ...ge a relation of relevancy that recognizes the intuitive character of the geometrical evidence (A. Schopenhauer). Or in this Hartmann’s explanation: ... ...anslated from French”, the author remarks with humour), lines, rectangular geometric spaces, zero (the symbol of absence), triangles (translated from... ...rd legislative proposals, remade maxims and, finally, all kind of spatial, geometrical or graffiti arrangements, inventively concentrated on page, le...

Description Details
...The whole paradoxist distich should be as a geometric unitary parabola, hyperbola, ellipse at the borders between art, philosophy, rebus, and mathematics – which exist in complementariness. The School of Paradoxist Literature, which evolved around 1980s, continues thro...

Table of Contents Details
..._____ 86 DEVIL _____________ 86 DOZINESS _________ 86 WINDBAG _________ 86 POETRY ___________ 86 OPPONENT _________ 86 WORTHLESS _______ 86 IT MEANS THAT YOU DON’T DO WHAT HE WANTS __________ 87 PACIFIST __________ 87 NIHILIST ___________ 87 TRANSFORMATION _ 87 VICIOUS CIRCLE ___ 87 DRAWBACK _______ 87 NEGLECT __________ 87 HOPE ______________ 87 SKILLFUL __...

Full Text Search Details
...instein is reported also to have said, “Try and penetrate with our limited means the secrets of nature and you will find that ...there remains some... ... his stay-at-home sibling? Is that what the dilation of time with velocity means? Is that kind of "time travel" an assured, preordained thing? An... ...r the phase velocity to exceed the wavefront velocity, c, but that does not mean that any real energy is traveling faster than c. So, while it is p... ...ive one the idea that, physical systems that are constrained in some way by geometric boundary conditions will have natural structures of energy lev... ...ribe these systems. In these new ideas, these orbital structures depend on geometric shapes, local curvature (the equivalent of a potential), and n... ...ture (the equivalent of a potential), and natural vibrations on the ("new') geometric shapes. These new ideas can account for many properties of wha... ...eractions between materials, and metric spaces all depend on the (spectral) geometric shapes which exist in a dimensional hierarchy of metric spaces... ...etric shapes which exist in a dimensional hierarchy of metric spaces. These geometric shapes are the natural spectral structures of metric spaces ca... ...al properties do not give any organizational structure to the spectra. This means that the function space's relation to the description of physical ...

Full Text Search Details
...heory and Experiments. . . . . . . . . . . . . . . . . . . 30 C. Castro On Geometric Probability, Holography, Shilov Boundaries and the Four Physical ... ...located at the point R p (r 0 )≡0. The mapping ψ must be obtained from the geometrical properties of the metric tensor of the solution to the vacuum f... ...M g ,g g ) directly. Only in Minkowski space does r have a direct physical meaning, as mapping (B) indicates, where it is a radial coordinate. Hencefo... .... Henceforth, when I refer to the radial coordinate orr-parameter I always meanr∈(M s ,g s ). The solution for the gravitational feld of the simple co... ...ature singularity at r=0 in terms of f, and with legerdemain reaches it by means of an ad hoc extension in the ludicrous Kruskal-Szekeres formulation.... ...A,B,C>0, whereA,B,C are analytic functions. I emphatically remark that the geometric relations between the components of the metric tensor of (2a) are... ...2a). The physical features of(M g ,g g ) must be determined exclusively by means of the resulting g μμ ∈(M g ,g g ), not by foisting upon (M g ,g g ) ... ...of the Point-Mass July, 2005 PROGRESS IN PHYSICS Volume 2 this elementary geometrical fact. Consequently, they have managed to attribute tor 0 =0 mir... ...nd (2a) are not suffciently general and so their forms suppress their true geometrical characteristics. Consider two pointsP 1 andP 2 on a radial line...

Full Text Search Details
... the Platonic theory of ″reminiscence″ is not a mere speculation, and the meaning of the spirit of science and philosophy is in fact the expression ... ...efånescu stated in his ″Christian Philosophy″: < To be realistic does not mean to be materialistic or less idealistic; it means to be idealistic and ... ...ialistic or less idealistic; it means to be idealistic and vice versa, it means to spiritualize matter. We should not be mistaken by being idealistic... ...e same length. If, for example, the intellectual activity prevails, which means several events in a shorter time interval, this can be graphically re... ...he same system of co-ordinates, in order to compare the results. The geometrical drawing above is indicative of the fact that under the stated c... ... the consequence is the shortening of the vectors′ resultant, which would mean the lengthening of the duration of the material existence – a possibil... ...an objectification, the appearance of Möbius strip − that closed, curved, geometric surface with the defining feature to be the only single-face – a... ...sistent with the usual terminology. The Möbius strip, that sort of curved geometrical surface with the paradoxical feature of being the sole ″unifac...

Full Text Search Details
...spherical), it is now most likely to be associated with a class of differential geometric spaces called Riemannian manifolds. Here, geometry is stud... ...ity, so we require it in a very general way. A Smarandache geometry (1969) is a geometric space (i.e., one with points and lines) such that some “ax... ...achevski, and Riemann sought to contradict. In fact, Riemann began the study of geometric spaces that are non-uniform with respect to the parallel p... ...stars. In any s-manifold, s-lines extend indefinitely in this way. By this we mean that we can follow an s-line for any distance in either directi... ...s ∠AOB have measure 150º. Geometry in an s-manifold Two things determine the geometric structure in a particular s-manifold, the configuration of... ...Hilbert’s axioms will be S-deniable, however, and we will see a wide variety of geometric structures in intuitively manageable spaces. Hilbert sep... ...t regions will overlap if the picture is extended upwards, but these regions are meant to be disjoint except for the boundaries, which are identified... ...er reasonably from Euclidean geometry. By the measure of a given angle, we will mean the smallest non-negative one. For example, in the plane, we ca... ...have seen that there can be pairs of points that are remote, or 0- aligned. This means that there are pairs of points that do not lie on the same s-li...

Full Text Search Details
...ory. Therefore it is concluded that quadrupole mass detectors would be the means by to discovery of waves of the metric. However, the experiment is on... ...utA>. Then, in physics, NON- MATTER is what is not matter, i. e. nonmatter means anti- matter together with unmatter. 2 Classifcation A. Matter is mad... ...umber of antiprotons, and thus the antimatter atom is neutral. C. Unmatter means neither matter nor antimatter, but in between, an entity which has co... ...es, while the ion and un-ion of type 2 have opposite charges. D. Nonmatter means what is not matter, therefore non- matter actually comprises antimatt... ...is is precisely due to the existence of the additional potential energy of geometric origin. Let us prove this statement. From equation (16) we know t... ... of the well-known phenomenon of photon teleportation, given by the purely geometrical methods of Einstein’s theory. As it is known, the basic space-t... ...anation of virtual par- ticles and virtual interaction given by the purely geometrical methods of Einstein’s theory. It is possible that this method w... ...ll. It turned out that Clifford algebras contained the appropriate algebro-geometric features to im- plement this principle of polydimensional transfo... ...becomes theng 2 /A 2 max , and the phase space interval coincides with the geometric interval discussed by [61], [54], [67], [22]. The transformations...

Full Text Search Details
...ing a finite probability of complete financial ruin for the trader but no meaningful mathematical expression can model this case under the assumptio... ...umption of normality, it does not necessarily rule out the possibility of mean reversion as M itself undergoes transition over time implying a proba... ...e in the foreseeable future. The temporal drift rate may be viewed as the mean reversion parameter k such that k j M t tends to M t+j . In partic... ... coherent market information. If the process driving volatility is indeed mean reverting then a low implied volatility on an option with a shorter ti... ... This theorizes that volatility is rationally expected to gravitate geometrically back towards its long-term mean level of σ M. That is, whe... ...sumed to evolve over time following the stochastic diffusion process of a geometric Brownian motion. The risk-free return S 0 is continuously compo... ...l the important aspects of Demand theory could be analyzed ordinally using geometric devices, which later came to be known as “indifference curves”. ... ...ed on the underlying assumption that asset prices evolve according to the geometric diffusion process of a Brownian motion. The Brownian motion mode... ...holes type expected utility functions A. Formal definitions: A geometric Brownian motion is assumed to be the ubiquitous stochastic diffus...

Full Text Search Details
...s firm be this quarter. He winks, he grins - this is interpreted by Wall Street to mean that profits will go up. The share price surges: no one wan... ...ibution (how many shareowners are there) and, as a result, its liquidity. Liquidity means how freely can one buy and sell it and at which quantities... ...ed MINUS Capital Expenditures MINUS Changes in Working Capital A sound debt ratio means: FCFE = Net Income MINUS (1 - Debt Ratio)*(Capital Expend... ...gence. "Due Diligence" is a legal term (borrowed from the securities industry). It means, essentially, to make sure that all the facts regarding th... ... the entrepreneurs. They feel that they are losing their creation to cold-hearted, mean spirited, corporate predators. They rebel and prefer to rem... ...n obstacles is the highly subjective nature of technical analysis - the presence of geometric shapes in historical price charts is often in the eyes... ...t forth complex "wave theories". Technical analysts now regularly employ dozens of geometric configurations in their divinations. Technical analysi... ...lume, and other market statistics exhibit regularities - often ... in the form of geometric patterns ... that can be profitably exploited to extra... ...ssociated with only one value of implied volatility. The model assumes a certain - geometric Brownian - distribution of stock prices that has been ...

Full Text Search Details
...eation. Also, to experiment." 2.2. Etymology: Paradoxism = paradox+ism, means the theory and school of using paradoxes in literary, artistic, phi... ...lorentin Smarandache) # Basic Thesis of Paradoxism: 4 everything has a meaning and a non-meaning in a harmony with each other. # Essence of Parad... ...h! - style of the non-style; - poems without verse (because poems don't mean words)- dumb poems with loud voice; - poems without poems (because th... ...ten at all! Enjoy them. Only after nuisance you really know what pleasure means. They provide a mirror of everybody's infinite soul. Art, generally... ...Hence don't wonder about this anti-book! If you don't understand it, that means you understand all. That is the goal of the manifesto. Because Art i... ...nce we have k different structures on M. For example we can construct a geometric multi-space formed by the union of three distinct subspaces: an...

Full Text Search Details
...…… 192 3.16 Smarandache Route Sequences …………………. 198 3.17 Smarandache Geometrical Partitions and Sequences …………………. 200 3.18 Smarandache Luck... ...teger Part π n Sequence [ π 1 ], [ π 2 ], [ π 3 ], . . . where [ ] means the integer part of the expression. The first few terms of the sequen... ...e proved that for n = 10 r -1 , T n is the sum of the r terms of the Geometric progression with the first term as 25 and the common ratio a... ...be proven that for n = 10 r -1 , T n is the sum of the r terms of the Geometric progression with the first term as 20 and the common ratio a... .... . ) (1/m 2 + 1/m 2 2 +1/m 2 3 + . . . ). We have the sums of the geometric series with common ratio < 1 P = { (1/m 1 )/ ( 1 – 1/m 1 ) ... ...al Symmetric functions give us another way of generalizing the Arithmetic-Geometric Mean Inequality. One can easily prove that: (x 1 x 2 x 3 x 4 ... ...ic functions give us another way of generalizing the Arithmetic-Geometric Mean Inequality. One can easily prove that: (x 1 x 2 x 3 x 4 ) 1/4 ≤ [... ...s relatively prime to N is given by (N φ(N))/2. Therefore, the arithmetic mean (A. M.) of the numbers in the sum is N/2. Their geometric mean is giv... ... 1/ φ(N) G. M. = {FI(N)} Using the relationship between these means when the numbers are not all equal (A. M. > G. M.), we have ...

Full Text Search Details
...al (UPI) It is impossible to describe any human action if one does not refer to the meaning the actor sees in the stimulus as well as in the end his... ...er welfare and utility (i.e., the idea of progress). They render our chaotic world meaningful and make us feel part of a larger whole. Economics st... ...ting much-feared scarcity encourages hoarding which engenders the very evil it was meant to fend off. Ideas and knowledge - inputs as important as ... ... and a conveyor or conduit of the price signal - as well as a store of value and a means of exchange. Markets and scarcity are intimately related.... ...ous times. The very distinction between "original" and "copy" becomes obsolete and meaningless. Knowledge products are "non- rival goods" (i.e., can... ...ssociated with only one value of implied volatility. The model assumes a certain - geometric Brownian - distribution of stock prices that has been ... ...n obstacles is the highly subjective nature of technical analysis - the presence of geometric shapes in historical price charts is often in the eyes... ...t forth complex "wave theories". Technical analysts now regularly employ dozens of geometric configurations in their divinations. Technical analys... ...olume, and other market statistics exhibit regularities - often ... in the form of geometric patterns ... that can be profitably exploited to extra...

Full Text Search Details
...an or Jewish, but for many people these terms have come to lose nearly all meaning except to identify them with a set of traditional festivals and a g... ... they seemed to be. I realized that to become a minister of religion would mean to live a lie, for I could not really believe in what I would be expec... ... Jung’s ideas. Symbols of Transformation is devoted to a discussion of the meaning and feeling-value of symbols in personal life, as well as in cultur... ...te truths. 6 Even so, it took Plato most of his lifetime to understand the meaning of the motto Socrates had adopted from the Oracle at Delphi, “Know ... ...eved without help. Despair had swept over me, making life intolerable. The meaninglessness of my personal life and my career led me to analysis as a w... ...itual power in their bark and body painting. A bark painting begins with a geometric de- sign of several colors. Onto this background is carefully mar...

Full Text Search Details
...theory of relativity (STR) is indeed a kinematical perspective. By that I mean to say that STR simply deals with velocities, which are kinematical q... ...oo-sweeping generalization. Physics books tell us that time has physical meaning only in its measurement in the form of uniformly repeated or perio... ...iven to conclude that c is an absolute speed limit (...Not sure what that means any more?) is that no energy from a light signal would be returned to... ...earances and that lightspeed presents no physical barrier, then that would mean speeds in excess of 300 megameters per second away from Earth can pro... ... the maximum speed. As it happens that we have never been able to observe meaningful speed greater than that of light, and because light appears to ... ...een relativistic distortions of space & time in the Minkowski diagram and geometric rotation (a transformation of visual perception) of a spacetime ...

Full Text Search Details
... Tool Pg 155 The Effects of Using Fire Pg 156 Pyramidal Focus Pg 160 The Geometric Structure of Self-Awareness Pg 163 The Geometric Structure ... ... Pg 1676 Reptilian Snake Undead Pg 1676 The Gordian Knot Ph 1685 The Meaning of the Gordian Knot Pg 1689 Summation Pg 1703 The Unseen Un... ...before the Big Bang happened. Actual Infinity The definition of Infinite means something is without limits, without bounds, without any end to ... ...it to their smallness The Path of Splitness Chapter One: The Universe 4 means that the smallest finite energy particles would all have to be ex... ...en them. Because if there were any dissimilarity between them, it would then mean that they are made up of even smaller things that cause these dis... ...sense. They make mathematical sense. They make mechanical sense. They make geometric sense. They make physical sense. Trying to take The Path ... ... unconnected bits of knowledge called scientific data. Separating scientific geometric knowledge from scientific mathematical knowledge and the sci... ...isappear and not return? The east side of Africa: the African Veldt. The Geometric Structure of Self-Awareness One crucial difference between... ... with tools, with something dead between their hands and in their hands. The geometric difference between a four-sided, and a five-sided feedback sy...