Fourier coefficients for Laguerre–Sobolev type orthogonal polynomials

Purpose In this paper, the authors take the first step in the study of constructive methods by using Sobolev polynomials.Design/methodology/approach To do that, the authors use the connection formulas between Sobolev polynomials and classical Laguerre polynomials, as well as the well-known Fourier coefficients for these latter.Findings Then, the authors compute explicit formulas for the Fourier coefficients of some families of Laguerre–Sobolev type orthogonal polynomials over a finite interval. The authors also describe an oscillatory region in each case as a reasonable choice for approximation purposes.Originality/value In order to take the first step in the study of constructive methods by using Sobolev polynomials, this paper deals with Fourier coefficients for certain families of polynomials orthogonal with respect to the Sobolev type inner product. As far as the authors know, this particular problem has not been addressed in the existing literature.

Decentralized Inner-Product Encryption with Constant-Size Ciphertext

With the rise of technology in recent years, more people are studying distributed system architecture, such as the e-government system. The advantage of this architecture is that when a single point of failure occurs, it does not cause the system to be invaded by other attackers, making the entire system more secure. On the other hand, inner product encryption (IPE) provides fine-grained access control, and can be used as a fundamental tool to construct other cryptographic primitives. Lots of studies for IPE have been proposed recently. The first and only existing decentralized IPE was proposed by Michalevsky and Joye in 2018. However, some restrictions in their scheme may make it impractical. First, the ciphertext size is linear to the length of the corresponding attribute vector; second, the number of authorities should be the same as the length of predicate vector. To cope with the aforementioned issues, we design the first decentralized IPE with constant-size ciphertext. The security of our scheme is proven under the ℓ-DBDHE assumption in the random oracle model. Compared with Michalevsky and Joye’s work, ours achieves better efficiency in ciphertext length and encryption/decryption cost.

Metaheuristic Algorithms Applied to Color Image Segmentation on HSV Space

In this research, we propose an unsupervised method for segmentation and edge extraction of color images on the HSV space. This approach is composed of two different phases in which are applied two metaheuristic algorithms, respectively the Firefly (FA) and the Artificial Bee Colony (ABC) algorithms. In the first phase, we performed a pixel-based segmentation on each color channel, applying the FA algorithm and the Gaussian Mixture Model. The FA algorithm automatically detects the number of clusters, given by histogram maxima of each single-band image. The detected maxima define the initial means for the parameter estimation of the GMM. Applying the Bayes’ rule, the posterior probabilities of the GMM can be used for assigning pixels to clusters. After processing each color channel, we recombined the segmented components in the final multichannel image. A further reduction in the resultant cluster colors is obtained using the inner product as a similarity index. In the second phase, once we have assigned all pixels to the corresponding classes of the HSV space, we carry out the second step with a region-based segmentation applied to the corresponding grayscale image. For this purpose, the bioinspired Artificial Bee Colony algorithm is performed for edge extraction.

An algorithmic approach to entanglement-assisted quantum error-correcting codes from the Hermitian curve

<p style='text-indent:20px;'>We study entanglement-assisted quantum error-correcting codes (EAQECCs) arising from classical one-point algebraic geometry codes from the Hermitian curve with respect to the Hermitian inner product. Their only unknown parameter is <inline-formula><tex-math id="M1">\begin{document}$ c $\end{document}</tex-math></inline-formula>, the number of required maximally entangled quantum states since the Hermitian dual of an AG code is unknown. In this article, we present an efficient algorithmic approach for computing <inline-formula><tex-math id="M2">\begin{document}$ c $\end{document}</tex-math></inline-formula> for this family of EAQECCs. As a result, this algorithm allows us to provide EAQECCs with excellent parameters over any field size.</p>

Chebyshev-Steffensen Inequality Involving the Inner Product

In this paper, we prove the Chebyshev-Steffensen inequality involving the inner product on the real m-space. Some upper bounds for the weighted Chebyshev-Steffensen functional, as well as the Jensen-Steffensen functional involving the inner product under various conditions, are also given.