33,332 research outputs found
On Generalized Lucas Pseudoprimality of Level k
No full textWe investigate the Fibonacci pseudoprimes of level k, and we disprove a statement concerning the relationship between the sets of different levels, and also discuss a counterpart of this result for the Lucas pseudoprimes of level k. We then use some recent arithmetic properties of the generalized Lucas, and generalized Pell–Lucas sequences, to define some new types of pseudoprimes of levels k+ and k− and parameter a. For these novel pseudoprime sequences we investigate some basic properties and calculate numerous associated integer sequences which we have added to the Online Encyclopedia of Integer Sequences
Soil erodibility in Europe: a high-resolution dataset based on LUCAS
No full textThe greatest obstacle to soil erosion modelling at larger spatial scales is the lack of data on soil characteristics. One key parameter for modelling soil erosion is the soil erodibility, expressed as the K-factor in the widely used soil erosion model, the Universal Soil Loss Equation (USLE) and its revised version (RUSLE). The K-factor, which expresses the susceptibility of a soil to erode, is related to soil properties such as organic matter content, soil texture, soil structure and permeability. With the Land Use/Cover Area frame Survey (LUCAS) soil survey in 2009 a pan-European soil dataset is available for the first time, consisting of around 20,000 points across 25 Member States of the European Union. The aim of this study is the generation of a harmonized high-resolution soil erodibility map (with a grid cell size of 500 m) for the 25 EU member states. Soil erodibility was calculated for the LUCAS survey points using the nomograph of Wischmeier and Smith (1978). A Cubist regression model was applied to correlate spatial data such as latitude, longitude, remotely sensed and terrain features in order to develop a high-resolution soil erodibility map. The mean K-factor for Europe was estimated at 0.032 t ha h ha-1 MJ-1 mm-1 with a standard deviation of 0.009 t ha h ha-1 MJ-1 mm-1. The yielded soil erodibility dataset compared well with the published local and regional soil erodibility data. However, the incorporation of the protective effect of surface stone cover, which is usually not considered for the soil erodibility calculations, resulted in an on average 15% decrease of the K-factor. The exclusion of this effect in K-factor calculations is likely to result in an overestimation of soil erosion, particularly for the Mediterranean countries, where highest percentages of surface stone cover were observed
K. I. Berlekamp, Lucas County, Ohio, 1969
No full textTerms associated with the photograph are: Lucas County Sheriffs Department | portrait | posse | Berlekamp, K. I
Myrtle K. Jung, Lucas County, Ohio, 1969
No full textTerms associated with the photograph are: Lucas County Sheriffs Department | portrait | cook | Jung, Myrtle K
Penerapan metode snake oil pada bilangan fibonacci, K-Fibonacci, Pell, K-Lucas, Lucas, dan K-Lucas, untuk membuktikan identitas kombinatorial
No full textINDONESIA:
Pada skripsi ini, akan ditunjukkan metode snake oil dapat diterapkan pada bilangan Fibonacci, k-Fibonacci, Pell, k-Pell, Lucas, dan k-Lucas untuk membuktikan identitas kombinatorial. Diketahui, barisan Fibonacci, k-Fibonacci, Pell. k-Pell, Lucas dan k-Lucas yang didefinisikan secara rekursif akan dibentuk menjadi fungsi pembangkit, setelah itu dengan menerapkan metode snake oil pada bilangan Fibonacci, k-Fibonacci, Pell, k-Pell, Lucas, dan k-Lucas, maka dapat membuktikan identitas kombinatorial.
ENGLISH:
For this literature, showed that snake oil method can be applied on a number Fibonacci, k-Fibonacci, Pell, k-Pell, Lucas, and K-Lucas to prove the identity of the kombinatorial. Known, the Fibonacci sequence, k-Fibonacci, Pell, k-Pell, Lucas, and k-Lucas is defined recursively formed into generation functionology. Show by Applying the method of snake oil in a number Fibonacci, k-Fibonacci, Pell, k-Pell, Lucas, and k-Lucas, then can be proved the identity combinatorial
Fermat -Fibonacci and -Lucas numbers
No full textsummary:Using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and Pethő, we find all -Fibonacci and -Lucas numbers which are Fermat numbers. Some more general results are given
On some links between the generalised Lucas pseudoprimes of level k
No full textPseudoprimes are composite integers sharing behaviours of the prime numbers, often used in practical applications like public-key cryptography. Many pseudoprimality notions known in the literature are defined by recurrent sequences. In this paper we first establish new arithmetic properties of the generalized Lucas and Pell-Lucas sequences. Then we study the recent notion of generalized Pell and Pell-Lucas pseudoprimes of level k, and find inclusions between the sets of pseudoprimes on different levels. In this process we extend several results concerning Fibonacci, Lucas, Pell, and Pell-Lucas sequences
The Generalized k-Fibonacci and k-Lucas Numbers
No full textIn this paper we give the generalization {G(k,n)}(n is an element of N) of k-Fibonacci and k-Lucas numbers. After that, by using this generalization, it has been obtained some new algebraic properties on these numbers
Properties and applications of k-Fibonacci, k-Lucas numbers
No full textBu çalışmada ilk olarak, Falco'n ve Plaza tarafından Fibonacci sayılarının yeni bir genelleştirilmesi olan k-Fibonacci sayıları tanımlandı ve bu tanımdan yararlanılarak Lucas sayılarının bir genelleştirilmesi olan k-Lucas sayıları elde edildi. Binet formülü ve matris cebirinden yararlanılarak, k-Fibonacci ve k-Lucas sayıları için bazı önemli özellikler bulundu. Ardından k-Fibonacci ve k-Lucas sayıları için üreten fonksiyonları içeren özdeşlikler elde edildi. Son olarak da bu sayıların sürekli kesirler cinsinden yazılabileceği gösterildi.In this study, first the k-Fibonacci numbers were defined as a new generalization of the Fibonacci numbers by Falco?n and Plaza. Using this definition, k-Lucas numbers were obtained as a generalization of Lucas numbers. We have found some important properties of k-Fibonacci and k-Lucas numbers. The generating functions including identities for k-Fibonacci and k-Lucas numbers were obtained by Binet formula and matrix algebra. Finally, it was shown that these numbers can the written in the form of a continued fraction
On matrices with the pell, pell-lucas, k−pell and k−pell-lucas quaternions
No full textIn this paper, for any positive real number k, we introduce the k−Pell and k−Pell-Lucas quaternions and we consider certain matrices whose entries are Pell, PellLucas, k−Pell and k−Pell-Lucas quaternions. We investigate the g−circulant, right circulant, left circulant and a special kind of a tridiagonal matrices whose entries are elements of these sequences. We present the determinant of these matrices and with the tridiagonal matrices we show that the determinant is equal to the nth term of the Pell, Pell-Lucas, k−Pell and k−Pell-Lucas quaternion sequences
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