1,720,990 research outputs found
On periodicity of p-adic Browkin continued fractions
No full textThe classical theory of continued fractions has been widely studied for centuries for its important properties of good approximation, and more recently it has been generalized to p-adic numbers where it presents many differences with respect to the real case. In this paper we investigate periodicity for the p-adic continued fractions introduced by Browkin. We give some necessary and sufficient conditions for periodicity in general, although a full characterization of p-adic numbers having purely periodic Browkin continued fraction expansion is still missing. In the second part of the paper, we describe a general procedure to construct square roots of integers having periodic Browkin p-adic continued fraction expansion of prescribed even period length. As a consequence, we prove that, for every n = 1, there exist infinitely many vm ? Q(p) with periodic Browkin expansion of period 2(n), extending a previous result of Bedocchi obtained for n = 1
Some notes on the algebraic structure of linear recurrent sequences
Full text linkSeveral operations can be defined on the set of all linear recurrent sequences, such as the binomial convolution (Hurwitz product) or the multinomial convolution (Newton product). Using elementary techniques, we prove that this set equipped with the termwise sum and the aforementioned products is an R-algebra, given any commutative ring R with identity. Moreover, we provide explicitly a characteristic polynomial of the Hurwitz product and Newton product of any two linear recurrent sequences. Finally, we also investigate whether these R-algebras are isomorphic, considering also the R-algebras obtained using the Hadamard product and the convolution product
Pell hyperbolas in DLP-based cryptosystems
No full textWe present a study on the use of Pell hyperbolas in cryptosystems with security based on the discrete logarithm problem. Specifically, after introducing the group structure over generalized Pell hyperbolas (and also giving the explicit isomorphisms with the classical Pell hyperbolas), we provide a parameterization with both an algebraic and a geometrical approach. The particular parameterization that we propose appears to be useful from a cryptographic point of view because the product that arises over the set of parameters is connected to the Redei rational functions, which can be evaluated in a fast way. Thus, we exploit these constructions for defining three different public key cryptosystems based on the ElGamal scheme. We show that the use of our parameterization allows to obtain schemes more efficient than the classical ones based on finite fields.(c) 2022 Elsevier Inc. All rights reserved
Hot topic: Bisphenol A in cow milk and dietary exposure at the farm level.
No full textChemical hazards may enter the milk chain during primary production. The study, for the first time, investigated the occurrence of bisphenol A (BPA) levels in cow milk samples collected on the farm following manual or mechanical milking and from the cooling tank. We applied a new monitoring model based on the identification of the hazards at each stage of the milk chain to identify potential pathways for contamination along the milk chain. We evaluated exposure to BPA through milk consumption based on detected contamination levels and the temporary tolerable daily intake established by the European Food Safety Authority (EFSA). Milk samples (n = 72) were analyzed using liquid chromatography with fluorescence detection. The mean BPA concentrations were 0.757 μg/L in manually milked samples, 0.580 μg/L in mechanically milked samples, and 0.797 μg/L in milk from the cooling tank. Bisphenol A occurred in the milk chain as a result of different stages of milking, and reached the highest levels at the end of the milk chain. Although the dietary intake of BPA was below the EFSA's temporary tolerable daily intake, exposure to BPA, even at low doses, through milk consumption represents a public health concern. Therefore, to ensure milk safety, new monitoring plans should be applied based on the identification of hazards at each stage of the milk chain
Wild boars as reservoir for Campylobacter and Arcobacter
Full text linkCampylobacteriosis is a significant public health concern with Campylobacter jejuni and Campylobacter coli as main causative agents. Moreover, there is an increasing recognition of other pathogenic Campylobacter species and Campylobacter-like organisms as Arcobacter. However, current knowledge on presence of Arcobacter species in wild boars (Sus scrofa) is lacking, and knowledge on Campylobacter species is based on methods favoring growth of thermotolerant species. In this study, fecal samples originating from 76 wild boars hunted in Campania region (Italy) were examined for the presence of Campylobacter(-like) organisms by a culture dependent approach. Three isolation protocols were performed in parallel: Arcobacter-selective agar plates, mCCDA plates and isolation by passive filtration onto non-selective blood agar plates were used as quantitative isolation methods. Enrichment broths, i.e. Arcobacter selective enrichment broth, Preston broth and CAT broth were used for qualitative detection of low levels or stressed Campylobacter(-like) organisms. The Arcobacter and Campylobacter isolates were identified at species level using matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) and 16S ribosomal RNA (rRNA) sequence analysis. Overall, 41 (53.9%) of the animals excreted Arcobacter or Campylobacter while 38 (50.0%) shed Campylobacter and 8 (10.5%) Arcobacter. Campylobacter lanienae predominated and was isolated from 31 (40.8%) animals. No statistical difference between the age groups or gender with regard to the fecal excretion of Campylobacter(-like) organisms was observed. Thirty animals (39.5%) shed Campylobacter spp. exceeding levels of 10 3 CFU g−1 feces. As samples were obtained from hunted wild boars intended for consumption, a potential contamination of meat with these bacterial pathogens must be considered
Periodic representations for cubic irrationalities
No full textIn this paper we present some results related to the problem of finding periodic representations for algebraic numbers. In particular, we analyze the problem for cubic irrationalities. We show an interesting relationship between the convergents of bifurcating continued fractions related to a couple of cubic irrationalities, and a particular generalization of the Rédei polynomials. Moreover, we give a method to construct a periodic bifurcating continued fraction for any cubic root paired with another determined cubic root
BTLE: Atomic swaps with time-lock puzzles
Full text linkWe present BTLE (Broadcast Time-Lock Exchange Protocol), a two-step protocol that aims to decentralize exchange of funds between two blockchains in scenarios similar to online exchanges. BTLE leverages time-lock puzzles to achieve that. In the first phase, the BTLE-MA protocol allows for a matching between a market maker and one of the competing market takers. In the second phase, the BTLE-AS algorithm allows the exchange between the market maker and the winning market taker. It is not necessary to use both the BTLE-MA and BTLE-AS algorithms in a decentralized-exchange scenario: existing atomic swaps based on hashed time-lock contract (HTLC) can benefit from BTLE-MA and can be adapted to an exchange where there are multiple possible participants. Moreover, BTLE computations are off-chain, so BTLE can be used in those blockchain pairs where at least one of the two does not have a scripting language or where the pair do not have the same hash function in common. This solves a limitation of HTLC-based atomic swaps. We also propose a new time-lock puzzle based on Pell conic calculations as an alternative to the classical time-lock puzzle of Rivest et al. BTLE has been implemented and tested. Experiments demonstrate that this new time-lock puzzle based on the Pell conic is superior for the intended goal. With an N N -bit modulus of 2,000 bits, the RSW-TL approach resolves the puzzle in approximately 100 s, whereas our BM-TL method requires over 4,000 s, significantly reducing the number of squaring operations needed
Group law on affine conics and applications to cryptography
Full text linkIn this paper, we highlight that the point group structure of elliptic curves, over finite or infinite fields, may be also observed on reducible cubics with an irreducible quadratic component. Starting from this, we introduce in a very general way a group's structure over any kind of conic. In the case of conics over finite fields, we see that the point group is cyclic and lies on the quadratic component. Thanks to this, some applications to cryptography are described, considering convenient parametrizations of the conics. We perform an evaluation of the complexity of the operations involved in the parametric groups and consequently in the cryptographic applications. In the case of the hyperbolas, the Rédei rational functions can be used for performing the operations of encryption and decryption, and the More's algorithm can be exploited for improving the time costs of computation. Finally, we provide also an improvement of the More's algorithm
Writing π as sum of arctangents with linear recurrent sequences, Golden mean and Lucas numbers
No full textIn this paper, we study the representation of π as sum of arctangents. In particular, we highlight the role of linear recurrent sequences obtaining new identities. Moreover, we provide a method in order to express π as sum of arctangents involving the Golden mean, the Lucas numbers, and more in general any quadratic irrationality. © World Scientific Publishing Company
Colored compositions, Invert operator and elegant compositions with the "black tie"
No full textThis paper shows how the study of colored compositions of integers reveals some unexpected and original connection with the Invert operator. The Invert operator becomes an important tool to solve the problem of directly counting the number of colored compositions for any coloration. The interesting consequences arising from this relationship also give an immediate and simple criterion to determine whether a sequence of integers counts the number of some colored compositions. Applications to Catalan and Fibonacci numbers naturally emerge, allowing to clearly answer to some open questions. Moreover, the definition of colored compositions with the "black tie" provides straightforward combinatorial proofs to a new identity involving multinomial coefficients and to a new closed formula for the Invert operator. Finally, colored compositions with the "black tie" give rise to a new combinatorial interpretation for the convolution operator, and to a new and easy method to count the number of parts of colored compositions. © 2014 Elsevier B.V. All rights reserved
- …
