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...iently fuzzify the δ rule. However a fuzzy system cannot guarantee the previous derivatives to exist. In order to obtain the derivatives, some ideas... ...lanco [6] limited the fuzzy operator to o = (∨, ∧). His main idea was to define derivatives at those points where they do not exist originally, and ... ...se points where they do not exist originally, and he called his method “smooth derivative”. Although he succeeded in getting a fuzzy δ rule, there ... ...1 M M ~ (d) – M ~ (d) + Figure 1.22.3 135 The introduction of the smooth derivative by the authors have improved the effectiveness of the tra... ... ij j j ij w O O E w E ∂ ∂ ∂ ∂ = ∂ ∂ * ( 1 ) in any interval where the derivatives are defined. Let us expand the second factor of (1): ... ...p), Max (y, p) are derivable into the open intervals y < p and y > p but their derivative is not defined in y = p (see Figure 1.23.2). ⎩ ⎨ ⎧ > < ... ...usual we will assign in any case the value in y = p equal to the left or right derivative, respectively, that is, finally we will assume ⎩ ⎨ ⎧ >... ...To improve this behavior we will develop a new procedure, the so-called “smooth derivative” which is based on the following idea. ⎩ ⎨ ⎧ > ≤ = ∂ ∂ ,... ...63 Rough set, 226 S Sagittal diagram, 14 Similarity relation, 17 Smooth derivative, 88 Solution matrix, 40 Solvability degree, 154 Special...

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...terms of physical observable quantities [1, 2], where we formulate regular derivatives through chronometrically invariant (physical observable) der...

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...polynomial near-ring. For any polynomial p(x) ∈ R [x [0, 1] ] define the derivative of p(x) as follows. n 1 s n s 1 0 x p ... x p p ) x ( p If +... ... ) x ( dp then ] x [ R ) x ( p ] 1 , 0 [ ] 1 , 0 [ ∈ ∈ Likewise successive derivatives are also defined i.e. product of s i p i ∈ R as s i ∈ [0, 1...

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...d [3]. 1. Let us consider the function f(x) = x sinx (0<x< ) and its rst derivative f 0 (x) = 1 sinx (sinx x cosx)> 0: Hence the functionf is monot... ... 2 lnx x + ln p 2 + 1 12(x 1) (3) Proof. Suppose f has a second order derivative on (a;b). Using the "trapezoidal formula" ([3]), we can write: Z... ... (1 ;1)nA, and since lim x&k! S (x) S (k!) x k! = 0, it has a right- derivative in A[f1g. 171 4 S is Riemann integrable in [a;b] R for all... ...(log logn) n(logn) . The function f(x) = (log logx) =x(logx) has a derivative given by x 2 (logx) 2 f 0 (x) = (log logx) 1 (logx) 1 [... ...where G(x) and H(x) are polynomials with integer coe cients. By taking the derivative of the right side of (1), one obtains the equality e x G(x) H(x...

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... considers the paradoxism as an “instrumentalization of the postmodernism”, a derivative of that one, attaining now a level of emancipation, of auton...

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...Contents Tangent Space and Derivative Mapping on Time Scale BY EMIN ¨OZYILMAZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 Basic Properties Of Second Smarandache Bol Loops BY T.G.JA´IY´E O. L´A . . . . . . . . . . . . . . . . ....

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...∂F n ∂x m −Δ n km ∂F i ∂x n =0. Calling upon the formulae for chr.inv.-derivatives, we transform the frst term in the chr.inv.-d’Alembert vector e... ...rvature derived from the Riemann-Christoffel curvature tensor. If the frst derivatives of the metric (the space deformations) are zero, then its secon... ...rivatives of the metric (the space deformations) are zero, then its second derivatives D. Rabounski. A New Method to Measure the Speed of Gravitation ... ...was introduced, after considering non-commutativity of the chr.inv.-second derivatives of a vector ∇ i ∇ k Q l − − ∇ k ∇ i Q l = 2A ik c 2 ∂... ...s general relativity concepts in the new context (in particular, covariant derivative and geodesics equations). We refer the reader to Refs. [1, 2, 3,... ...om the nondifferentiability [1]. Then one builds a complex covariant total derivative that reads in the simplest case (spinless particle, nonrelativis... ...nstruction in which the full velocity feld V+W intervenes in the covariant derivative [6]. In the same way as in general relativity, the geodesics equ... ...ity, the geodesics equation can therefore be written, using this covariant derivative, in terms of a free, inertial motion-like equation, dV dt =0. (2... ...iU)=0. (3) We see in this expression that the real part of the covar- iant derivative, d R /dt=∂/∂t+V.∇, is the standard total derivative expressed in...

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...n the log of a negative number if f(X) > X. Speculative trading in derivative securities like stock index futures with a highly leveraged pos... ...y function. The core idea was to define a utility density function as the derivative of some utility function that is normalized to yield values bet... ...ucture. Denoted by σ’ t (t), (where the symbol ’ indicates first derivative) the implied volatility at time t of an option expiring at time... ...havior where acquiring portfolio insurance through the usage of financial derivatives could reduce or remove investment risk. 38 In this s... ...e exact nature of investor utility structures that underlie investment in derivative financial assets. This is an area we deem to be of tremendous in... ...eric perspective of behavioral economics. 2.1 Brief Review of Financial Derivatives Basically, a derivative financial asset is a legal cont... ...d that claim, in exchange for a mutually agreed consideration. While many derivative securities are traded on the floors of exchanges just like ordi... ...are traded on the floors of exchanges just like ordinary securities, some derivatives are not exchange-traded at all. These are called OTC (Over-the... ...s are not exchange-traded at all. These are called OTC (Over-the-Counter) derivatives, which are contracts not traded on organized exchanges but rat...

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...e the fundamental metric tensor can be considered constant, while the frst derivatives of the metric (the Christoffel sym- bols) are zero. As a matter... ...s satisfy the condition DU α ∂v = DV α ∂s , (2.2) (where D is the absolute derivative operator) that can be easy verifed by checking the calculation. ... ...damard break only if the functions g αβ (x σ ) permit breaks in their frst derivatives. In accordance with Hadamard himself [20], the second derivativ... ...ffel tensor was built, proceeding from the non-commutativity of the second derivatives of an arbitrary vector taken in the given space. Taking the sec... ...f an arbitrary vector taken in the given space. Taking the second chr.inv.-derivatives of an arbitrary vector ∇ i ∇ k Q l − ∇ k ∇ i Q l = 2A i... ...rame the fundamental metric tensor can betaken as constant, while the frst derivatives of the metric (the Christoffel symbols) are zero. As a matter o... ...ts contravariant (upper- index) form, ∇ i is the symbol for the chr.inv.-derivative (the chr.inv.-analogue to the covariant derivative symbol∇ σ ), ... ...which attraction of gravity spreads, ∂ ∂t is the symbol for the chr.inv.-derivative with respect to time. A chronometrically invariant criterion for... ...n of four-dimensional world-coordinates, which has no more than frst order derivatives of thef. The Zelmanov chr.inv.-criterion (5.3) was applied in a...

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...ties as an extension of dialectics; b) and its derivative “neutrosophic”, such as “neutrosophic logic”, “neutrosophic set”... ...othing! The poet is not a prince of ducks! The notion of "poetry" and its derivatives have become old-fashioned in this century, and people laugh at ... ...features and substantive conditions of an entity <E> - but the whole <E'> derivative spectrum in connection with <Neut-E>. Epistemology studies phi... ...fferent people, schools, cultures; <A/Neut-A> = spectrum of <A> derivatives/deviations, because <A> partially mixes/melts fi... ...erent people, schools, cultures; <Anti-A/Neut-A> = spectrum of <Anti-A> derivatives/deviations, which means partial <Anti-A> ... ...ial <Neut-A> combined in various percentage; <A'/Anti-A'> = spectrum of derivatives/deviations after mixing <A'> and <Anti-A'> s... ... We mean, a very dynamic system by rapid small changes, characterized by a derivative. The static system is dead. Leon Walras was right: monopolie... ...what's <Neut-A>, afterwards focus on <Anti-A>, and don't forget all their derivatives. Let's question any and all. Let's be skeptical versus any "... ...n demeanor functions upon the laws of differential equations with partial derivatives with respect to more or less adverse-to-each-other parameters. ...

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... is obtained for the optimal value such that and . The annulation of the first derivative is obtained by the solution of the equation or equivalentl... ...und using classical numerical methods. It is also easy to check that the second derivative is always negative and therefore reaches its maximal value ... ...ty and correlation: methods and applications, in risk management and financial derivatives: Aguide to mathematics (S.Das,ED) 337-354. [4] Bailer-J...