We define an isomorphism between the group of points of a conic and the set of integers modulo a prime equipped with a non-standard product. This product can be efficiently evaluated through the use of Rédei rational functions. We then exploit the isomorphism to construct a novel RSA-like scheme. We compare our scheme with classic RSA and with RSA-like schemes based on the cubic or conic equation. The decryption operation of the proposed scheme turns to be two times faster than RSA, and involves the lowest number of modular inversions with respect to other RSA-like schemes based on curves. Our solution offers the same security as RSA in a one-to-one communication and more security in broadcast applications.

Multidimensional continued fractions (MCFs) were introduced by Jacobi and Perron in order to generalize the classical continued fractions. In this paper, we propose an introductive fundamental study about MCFs in the field of the p-adic numbers Qp. First, we introduce them from a formal point of view, i.e., without considering a specific algorithm that produces the partial quotients of a MCF, and we perform a general study about their convergence in Qp.In particular, we derive some conditions about their convergence and we prove that convergent MCFs always strongly converge in Qp contrarily to the real case where strong convergence is not ever guaranteed. Then, we focus on a specific algorithm that, starting from a m-tuple of numbers in Qp, produces the partial quotients of the corresponding MCF. We see that this algorithm is derived from a generalized p-adic Euclidean algorithm and we prove that it always terminates in a finite number of steps when it processes rational numbers.

This 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.

Robustness against the possible occurrence of outlying observations is critical to the performance of a measurement process. Open questions relevant to statistical testing for candidate outliers are reviewed. A novel fuzzy logic approach is developed and exemplified in a metrology context. A simulation procedure is presented and discussed by comparing fuzzy versus probabilistic models.