Continued Fraction Expansion
Design of Fractional order Recursive Digital Differentiator using Continued Fraction Expansion
... Abstract- In this paper, new discretized models of fractional order differentiator (FOD) based on different operators are proposed. Specifically in this work, one-third and one-fourth order differentiator models based on ...
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A Wirsing type approach to some continued fraction expansion
... RCF expansion there are many other continued fraction expansions: the continued fraction expansion to the nearest integer, grotesque expansion, Nakada’s α-expansions, ...
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A Fundamental Unit of O_K
... Up to this point we have established strict restrictions on f(x) ∈ Q [x]. We have only considered f as a monic squarefree polynomial of even degree. Further, we have only considered the expansion of √ f when it is ...
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Continued Fraction Evaluation of Jn (X)/Jn-1 (X)
... the continued fraction for evaluating functions are what motivated the present work: to establish computational algorithm for J n (x) / J n − 1 (x) based on its continued fraction ...
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On the length of the period of a real quadratic irrational
... Let D be a positive non-square integer. We shall denote by ω(D) the number of distinct prime divisors of D and h(D) the class number of the quadratic field Q( √ D). In the seventies, there have been several articles on ...
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On the real quadratic fields with certain continued fraction expansions and fundamental units
... the continued fraction expansion of integral basis element for period length is 3 in ...period continued fraction ...special continued fraction expansions of the real ...
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Identification of Patterns of Continued Fractions of √s – [√s] Where is a Square Free Positive Number
... periodic continued fraction represents a quadratic irrational ...the continued fraction expansion of every quadratic irrational is eventually ...periodic continued ...
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Explicit Form of Fundamental Units of Certain Real Quadratic Fields
... the continued fraction expansion of the quadratic irrational number ω d and the fundamental units of certain real quadratic fields can be rapidly determined without using long ...the continued ...
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Continued Fraction Method for Approximation of Heat Conduction Dynamics in a Semi Infinite Slab
... series expansion and the continued fraction expansion in s do not exist at the origin, we consider a continued fraction expansion in the hyperbolic cosine ...
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Algorithm for Fast Calculation of Hirzebruch Jung Continued Fraction Expansions to Coding of Graph Manifolds
... HJ-continued fraction expansion to solve the problems of the coupling constant hierarchy [5] [12] [13] and fine tuning [14] on the base of Kaluza-Klein approach in the multidimensional topological ...
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On the Positive Integer Solutions for a Diophantine Equation
... Abstract. Let P ≔ P(t) be a polynomial in ZX . In this paper, we consider the polynomial solutions of Diophantine equation D: M − 42S − 8M − 252S − 378 = 0 . We also obtain some formulas and recurrence relations on the ...
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The random continued fraction transformation
... Regular continued fractions with bounded digits are very well ...regular continued fraction expansion with digits not exceeding N has Hausdorff dimension strictly between 0 and ...
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Impact of using a broad-based multi-institutional approach to build capacity for non-communicable disease research in Thailand
... research expansion [21]. Our col- laboration provides a framework for continued develop- ment of existing research hubs, expansion to other critical focus areas, institutional capacity ...
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Invariant measures for continued fraction algorithms with finitely many digits
... it gives information about the speed of convergence for a typical point in that system. Entropy as a function of a parameter α is widely studied for Nakada’s α-expansions (see [17, 18, 19, 21, 22]). Also for the (a, ...
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Model reduction and simulation of complex dynamic systems
... Within The three categories are: Optimum curve Dominant fitting mode Continued fraction Continued fraction and tion approaches utilize the greatest number of system parameters therefore [r] ...
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Analysis of Complex Continued Fractions of The Solution of The Equation kx2-nx+n=0 Where n is An Odd Integer And k=[n/2]
... fraction, Periodic complex continued fraction, Gaussian integer, Euclidean algorithm, Quadratic irrational.. KRITHIKA.[r] ...
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Europe pays tribute to late President Kennedy. Bulletin from the European Community. No. 67, November-December 1963
... EEC COMMISSION SEES MORE ECONOMIC EXPANSION IN 1964 ESTIMATES FOR 1964 point to continued economic expansion in the European Economic Community, according to the EEC Commission's third q[r] ...
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An Efficient Continued Fraction Algorithm for Nonlinear Optimization and Its Computer Implementation
... In this paper, we present an iterative algorithm for the problem based on the continued fraction interpolation method. For the general iteration scheme of n points, the algorithm constructs the n + 1th ...
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Some new continued fraction sequence convergent to the Somos quadratic recurrence constant
... Remark It is worth to point out that Lemma provides some continued fraction in- equalities by the multiple-correction method. Similarly, repeating the above approach step by step, we can get more sharp ...
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Absorbing Boundary Conditions For Corner Regions
... even-ordered continued fraction expan- sion of the square-root ...order continued fraction boundary condition is exactly the same as the n-th-order multi-directional boundary conditions with ...
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