the theory of fuzzy linear regression models

... that G0(x) = 0 for all x in[a; b], then G(x) remains constant there Trang 5Theorems I, II and III form the Fundamental Theorem of Calculus Theproof depends on the then remarkable results about partition ... volume 4 of Encyclop´edie suggested that the theory of limits be put on a firm foundation He was one ofthe first to understand the importance of functions and, in this article, he defined the derivative ... number of discontinuities (Cauchysense) He obtains convergence to the midpoint of jumps He neededthe continuity to gain the existence of the integral His proof requires a monotonicity of f. 15

Ngày tải lên: 27/03/2014, 11:51

... fraction of the human race As good an instance of this phase of culture as may be had is afforded by the tribes of the Andamans, or by the Todas of the Nilgiri Hills The scheme of life of these ... of the owner with the other members of the group Property is still of the nature of trophy, but, with the cultural advance, it becomes more and more a trophy of successes scored in the game of ... time there is the knowledge of the dead languages and the occult sciences; of correct spelling; of syntax and prosody; of the various forms of domestic music and other household art; of the latest

Ngày tải lên: 29/03/2014, 12:20

... doubt the theory of numbers was Gauss' fa~ourite sub- ject, Indeed, in a much quoted dictum, he asserted that Mathe- matics is the Queen of the Sciences and the Theory of Numbers is the ... and this led to the celebrated studies of Furtwangler, Artin and others in the context of class field theory. Gauss and number theory xiii By far the largest section of the Disquisitiones ... fact there is now a rich and fertile theory relating to the transcendence and algebraic independence of values assumed... in the theory of numbers, known since the time of

Ngày tải lên: 31/03/2014, 16:20

... the other hand, it is well known that in number theory,more than in any other branch of mathematics, it is easy to reach the frontiers of knowledge It is easy to propound problems in number theory ... many of these problems; but the trouble with thenatural problems of number theory is that they are either too easy or muchtoo difficult I shall therefore try to expose some problems that are of ... Trang 7These lectures are intended as an introduction to the elementary theory ofnumbers I use the word “elementary” both in the technical sense—complexvariable theory is to be avoided—and in the

Ngày tải lên: 31/03/2014, 16:21

... and other concepts are not included in the book The bibliography gives a survey of books in the area of nonlinear optimization and related areas like approximation theory and optimal control theory ... Consequently the functional / is convex D In general the convexity of the level sets Sa does not imply the convexity of the functional / : this fact motivates the definition of the concept of quasiconvexity ... textbook Of course, the question of the solvability of a concrete nonlinear optimization problem is of primary interest and, therefore, existence theorems are presented in Chapter 2 Sub-sequently the

Ngày tải lên: 01/04/2014, 11:34

... application of Theorem 2.1 to (73) yields the desired inequality Remark 3.1: In the proof for Theorem 3.1, if we apply Theorem 2.2 instead of Theorem 2.1 to (73), then we obtain another bound ... many authors have expounded on various aspects of the theory of dynamic equa- tions on time scales. For example [2-10], and the references therein. In these investiga- tions, integral inequalities ... universal symbols for further use. Throughout this paper, R denotes the set of real numbers and R + =[0,∞), while Z denotes the set of integers. For two given sets G, H,wedenotethesetofmaps from G to

Ngày tải lên: 21/06/2014, 01:20

... g(m, n)≡ 0, q = 1, p≥ 1, then Theorem 2.1 reduces to [[13], Theorem 1] Following a similar process as the proof of Theorem 2.1, we have the following three theorems Theorem 2.2 Suppose u, a, ... in the first variable, while decreasing in the second variable” in Theorem 2.1, which is unnecessary for the proof since a(m) = m, b (n) = n, then Theorem 2.1 reduces to [[14], Theorem 3] Furthermore, ... is decreasing in the second variable” in Theorem 2.5, then Theorem 2.5 reduces to [[14], Theorem 7] Furthermore, if g(m, n) ≡ 0, q = 1, p ≥ 1, then Theorem 2.5 reduces to [[13], Theorem 3] Following

Ngày tải lên: 21/06/2014, 02:20

... introduced the concept of “theory of a metric fixed point theorem” and used this theory for the case of multivalued contractionsee 4 For the singlevalued case, see5 The purpose of this paper ... Proceedings of the 9th International Conference on Fixed Point Theory and Its Applications, Yokohama Publishing, to appear Trang 95 I A Rus, “The theory of a metrical fixed point theoremml: theoretical ... semicontinuous, then TY ∈ P cp X, for every Y ∈ P cp X; b the continuity of T implies the continuity of T : P cp X → P cp X. The set of all nonempty invariant subsets of T is denoted

Ngày tải lên: 21/06/2014, 11:20

... applications of IFSs in image processing theory, in the theory of stochastic growth models, and in the theory of random dynamical systems, one can consult3 5 There is a current effort to extend Hutchinson’s ... pagesdoi:10.1155/2008/312876 Research Article Applications of Fixed Point Theorems in the Theory of Generalized IFS Alexandru Mihail and Radu Miculescu Department of Mathematics, Bucharest University, Bucharest, ... denotes the set PX \ {∅}. For a subset A of PX, by A∗we mean A\ {∅} Given a metric spaceX, d, KX denotes the set of compact subsets of X and BX denotes the set of closed bounded subsets of

Ngày tải lên: 21/06/2014, 23:20

... initialis- ing them, we calculated the distances between the probability density functions (pdfs) of the HMM states of the retrained syllable models and the pdfs of the corresponding states of the initialised ... what one would expect. There were two possible reasons for the larger impact of the further training on the TIMIT models. Either the bound- aries of the syllable models with the largest KLDs had ... ing higher in the case of TIMIT. This implies that the fur- ther training affected the TIMIT models more than the CGN models. Given the greater impact of the longer-length mod- els on the recognition

Ngày tải lên: 22/06/2014, 19:20

... prove the following theorem: IV The sum of the hth powers of the divisors of m is 1 Find numbers x such that the sum of the divisors of x is a perfect square 2 Show that the sum of the divisors of ... chapter is intendedto give the reader some indication of the direction of further study with a briefaccount of the nature of the material in each of the topics suggested Thetreatment throughout ... that the number of terms in the expansion is (α1+ 1)(α2+ 1) (αn+ 1) Hence we have thetheorem: II The number of divisors of m is (α1+ 1)(α2+ 1) (αn+ 1) III The sum of the divisors of m is

Ngày tải lên: 28/06/2014, 19:20

... respectively the gre atest number of the first class or the least of the second. In every case the separation of the system R into the two classes A 1 , A 2 is such that every number of the first class ... separation of the same into two portions such that every point of one portion lies to the left of every point of the other. I find the essence of continuity in the converse, i. e., in the following ... hypothesis A 3 L, L 3 L, then by (10) is the other condition... parts of a system S, then is M(A, B, C, ) 3 S The proof follows from (8), (3) 11 Theorem If P is part of one of the

Ngày tải lên: 28/06/2014, 19:20

... the modulus of the product of two complex numbers is equal to the uct of their moduli, while the amplitude of the product is equal to the sum oftheir amplitudes prod-For example, the square of ... , αn are the roots of equation(7), the sum of the roots is equal to −c1/c0, the sum of the products of the roots taken two at a time is equal to c2/c0, the sum of the products of the roots taken ... an equation in x of degree n, in which the coefficient of xn is unity, the sum of then roots is equal to the negative of the coefficient of xn−1, the sum of the products of the roots two at a

Ngày tải lên: 28/06/2014, 19:20

... Time of the Ether Theory 11 Rise of the Ether Theory 11 Idea of a Stationary Ether 12 Ether in the Neighborhood of Moving Bodies 12 Ether Entrained in Dielectrics 13 The Lorentz Theory ... attention tothe ease with which we may handle the optics of moving media by themethods of the theory of relativity as compared with the difficulty oftreatment on the basis of the ether theory In ... Einstein Theory of Relativity 21 The First Postulate of Relativity 21 The Second Postulate of the Einstein Theory of Relativity 22 Suggested Alternative to the Postulate of the Independence of the

Ngày tải lên: 28/06/2014, 19:20

... and de la Vall´e-Poussin, in the theory of primes, as one of the lande marks in the modern history of the theory of numbers But there is an enormous amount which remains ... the sense in which, for example, the classical proofs in the theory of the distribution of primes are transcendental, for it does not make use of the machinery of the ... in the history of the problem It is of exceptional interest not only in itself but also on account of the method.. .THE THEORY OF NUMBERS 7 of solutions of the equation

Ngày tải lên: 28/06/2014, 19:20

... called an invariant of f under thetransformations of the set The most extensive subdivision of the theory of invariants in its presentstate of development is the theory of invariants of algebraical ... Invarianten-theorie” in the “Jahresbericht der deutschen Mathematiker-Vereinigung” for 1890-1891 The first draft of the manuscript of the book was in the form of notes for a course of lectures on the theory of invariants, ... a definite kind of atransformation, like the transformation of the points in a plane by a lineartransformation of their co¨ordinates Invariant theory treats of the properties ofthe system which

Ngày tải lên: 28/06/2014, 19:20

... rolled against one, only the bigger of the results of the throw of the two dice counts If the defender’s throw is at least as high as the attacker’s then defender wins In other words, for attacker ... where the payoffs are given for the player whose strategies are recorded in the first column of the matrix (The other player’s strategies are recorded in the first row of the matrix.) Sometimes the ... equilibrium point then the pay-offs for the players at each of those have to agree That allows us to speak of the (unique) value of the game, namely the entry in the matrix defined by the equilibrium...

Ngày tải lên: 08/04/2014, 12:17

... agency theory and the transaction costs theory as a theory of economic organization rather than as a theory of entrepreneurship A separate line of thinking in the theory of the firm is the dynamic ... not the focus of that theory The theory of the firm is preoccupied with the functioning of the corporate enterprise in the context of market structures and competition processes In the wake of ... framework of the agency theory and the theory of asymmetric information The question goes into the heart of the present theory, into the paradigm on which it is based This paradigm is the famous...

Ngày tải lên: 24/10/2012, 09:11

... and proves the consistency of the resulting NL2S estimator by a modification of the proof of Amemiya (1974) 5.1.4 Tests of hypotheses I will consider the test of the hypothesis of the form h(a) ... considered the estimation of the parameters of a single equation in the system of simultaneous equations Now, I will consider the estimation of all the parameters of the system The equations of the ... exactly holds in the linear case The practical consequence of the approximation (2.24) is that all the results for the linear regression model are asymptotically valid for the non -linear regression...

Ngày tải lên: 23/10/2013, 10:15

... k e ) PO = the current price of the stock DIV1 = the dividend paid at the end of year ke = the required return on investment in equity P1 = the sale price of the stock at the end of the first ... Pt + C Pt R = the rate of return on the security Pt+1 = price of the security at time t+1, the end of the holding period Pt = price of the security at time t, the beginning of the holding period ... expectations for the efficient market condition to hold Rationale Behind the Theory Rof > R* ⇒ Pt ↑ ⇒ Rof ↓ Rof < R* ⇒ Pt ↓ ⇒ Rof ↑ until Rof = R* In an efficient market all unexploited profit opportunities...

Ngày tải lên: 05/01/2014, 16:56