Admissible orders on fuzzy numbers are total orders which refine a basic and well-known partial order on fuzzy numbers. In this work, we define an admissible order on triangular fuzzy numbers (i.e. TFN's) and study some fundamental properties with its arithmetic and their relation with this admissible order. In addition, we also introduce the concepts of average function on TFN$'s and studies a generalized structure of the vector spaces. In particular we consider the case of TFN's.

The asymptotic structure of three-dimensional Carroll gravity with negative cosmological constant is studied. We formulate a consistent set of boundary conditions preserved by an infinite-dimensional extension of the AdS$_3$ Carroll algebra, which turns out to be isomorphic to a precise generalized BMS$_3$ algebra. This is described by four independent functions of the circle at infinity, generating spatial superrotations, Carroll superboosts, spatial supertranslations and time supertranslations. Remarkably, this asymptotic symmetry algebra contains as subalgebras to BMS$_3$ (generated by spatial superrotations and time supertranslations) and the two-dimensional conformal algebra (spanned by spatial superrotations and spatial supertranslations). We also introduce a new solution - endowed with a Carroll extremal surface - that fulfills this set of asymptotic conditions. By taking advantage of the Chern-Simons formulation of the theory, Carroll thermal properties, obtained from regularity conditions, and entropy of the configuration are also addressed.

In this paper we introduce and analyze, for two and three dimensions, a finite element method to approximate the natural frequencies of a flow system governed by the Stokes-Brinkman equations. Here, the fluid presents the capability of being within a porous media. Taking advantage of the Stokes regularity results for the solution, and considering inf-sup stable families of finite elements, we prove convergence together with a priori and a posteriori error estimates for the eigenvalues and eigenfunctions with the aid of the compact operators theory. We report a series of numerical tests in order to confirm the developed theory.

We introduce a family of discontinuous Galerkin methods to approximate the eigenvalues and eigenfunctions of a Stokes-Brinkman type of problem based in the interior penalty strategy. Under the standard assumptions on the meshes and a suitable norm, we prove the stability of the discrete scheme. Due to the non-conforming nature of the method, we use the well-known non-compact operators theory to derive convergence and error estimates for the method. We present an exhaustive computational analysis where we compute the spectrum with different stabilization parameters with the aim of study its influence when the spectrum is approximated.

In this article the pursuit problem of objects that moves with different accelerations and initial speeds is studied. Initially, the situation in which the escaping object moves in a straight line is considered. Under this condition, and if both objects starts from rest, it is shown that the trajectory of the chasing object match those obtain for the case of uniform motions. When both objects have different initial speeds and accelerations, we first note that if the escaping object starts its motion with a speed which is function of the acceleration and initial speed of the chasing object, then the pursuit curve is the same obtained for no initial speeds. Latter solution is used to solve the chase problem when both objects have different accelerations and initial speeds. Finally, making use of the preceding results, a numerical procedure is proposed for obtaining the pursuit curve when the escaping object moves in an arbitrary path.

Self-Adaptive Systems (SASs) are increasingly deployed in critical domains such as healthcare, finance, autonomous vehicles, and smart cities. Ensuring their architectural trustworthiness is essential for maintaining system stability and quality attributes over time. Since SAS architectures are inherently complex, reference models such as MAPE-K have been proposed to guide their design, emphasizing the Feedback Loop as a central component. MAPE-K prescribes abstractions and communication rules that, when preserved, enhance system maintainability, comprehensibility, and conformance. However, maintenance activities often introduce deviations, leading to architectural erosion and loss of compliance with the reference model. Architectural Conformance Checking (ACC) addresses this issue by verifying whether a system's implementation aligns with its Planned Architecture (PA) or a reference model like MAPE-K. In this paper, we introduce REMEDY, a tailored ACC approach for SASs that consists of three key components: (i) A domain-specific language (DSL) for specifying planned architectures based on MAPE-K abstractions; (ii) A tool for recovering the system's current architecture (CA); (iii) A conformance checking process that detects and visualizes architectural deviations. We evaluate REMEDY by comparing its SAS-specific DSL with a general-purpose DSL, demonstrating higher productivity and precision in architectural specification. Additionally, REMEDY effectively identifies and facilitates the correction of non-conformance issues, thereby improving the maintainability and architectural trustworthiness of adaptive systems.