Previous research has shown a significant percentage of dropouts in university studies, particularly in the first years. Furthermore, evidence links higher motivation and curricular improvement in students when they enhance their self-regulated learning (SRL). A systematic review was conducted using the PRISMA method to identify and analyze interventions to improve SRL in first-year undergraduate students. The interventions analyzed addressed student learning, classroom management by teachers, evaluation processes, and administrative management. Additionally, the need for a holistic and continuous approach was identified, covering cognitive, metacognitive, motivational, behavioral, and affective dimensions. The combination of self-perception questionnaires and academic grades was the most used strategy to measure intervention effectiveness. These findings emphasize the importance of adapting interventions to specific contexts and ensuring their continuity to maximize the impact on the development of students’ self-regulated learning. The results reveal a high heterogeneity in the approaches applied, highlighting the most effective techniques as follows: specialized workshops, the use of virtual tools, and group and individual tutoring. Intracurricular interventions, integrated within course content and led by the faculty, demonstrated greater success by embedding SRL strategies into the teaching–learning process. In contrast, extracurricular interventions, conducted by tutors or academic advisors, faced challenges related to student motivation and participation.

The mixed boundary value problem for a compressible Stokes system of partial differential equations in a bounded domain is reduced to two different systems of segregated direct Boundary-Domain Integral Equations (BDIEs) expressed in terms of surface and volume parametrix-based potential type operators. Equivalence of the BDIE systems to the mixed BVP and invertibility of the matrix operators associated with the BDIE systems are proved in appropriate Sobolev spaces.

The deep neural network (DNN) was applied for estimating a set of unknown parameters of a dynamical system whose measured data are given for a set of discrete time points. We developed a new vectorized algorithm that takes the number of unknowns (state variables) and number of parameters into consideration. The algorithm, first, trains the network to determine weights and biases. Next, the algorithm solves the systems of algebraic equations to estimate the parameters of the system. If the right hand side function of the system is smooth and the system have equal numbers of unknowns and parameters, the algorithm solves the algebraic equation at the discrete point where absolute error between the neural network solutions and the measured data is minimum. This improves the accuracy and reduces computational time. Several tests were carried out in linear and non-linear dynamical systems. Last, we showed that the DNN approach is more successful in terms of computational time as the number of hidden layers increases.

A mixed boundary value problem (BVP) for the diffusion equation in non-homogeneous media partial differential equation is reduced to a system of direct segregated parametrix-based boundary-domain integral equations (BDIEs). We use a parametrix different from the one employed by Mikhailov [Localized boundary-domain integral formulations for problems with variable coefficients. Eng Anal Bound Elem. 2002;26:681–690], Mikhailov and Portillo [A new family of boundary-domain integral equations for a mixed elliptic BVP with variable coefficient. In: Paul Harris, editor. Proceedings of the 10th UK conference on boundary integral methods. Brighton: Brighton University Press; 2015. p. 76–84] and Chkadua, Mikhailov, Natroshvili [Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient. I: equivalence and invertibility. J Integral Eqs Appl. 2009;21:499–543]. We prove the equivalence between the original BVP and the corresponding BDIE system. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed.

The interior Dirichlet boundary value problem for the diffusion equation in nonhomogeneous media is reduced to a system of boundary‐domain integral equations (BDIEs) employing the parametrix obtained in Portillo (2019). We further extend the results obtained in Portillo (2019) for the mixed problem in a smooth domain with L²(Ω) right‐hand side to Lipschitz domains and partial differential equation (PDE) right‐hand side in the Sobolev space H⁻¹(Ω), where neither the classical nor the canonical conormal derivatives are well‐defined. Equivalence between the system of BDIEs and the original BVP is proved along with their solvability and solution uniqueness in appropriate Sobolev spaces.

A system of boundary-domain integral equations is derived from the bidimensional Dirichlet problem for the diffusion equation with variable coefficient using a novel parametrix different from the one widely used in the literature by the authors Chkadua, Mikhailov and Natroshvili. Mapping properties of the surface and volume parametrix-based potential-type operators are analysed. Invertibility of the single layer potential is also studied in detail in appropriate Sobolev spaces. We show that the system of boundary-domain integral equations derived is equivalent to the Dirichlet problem prescribed and we prove the existence and uniqueness of solution in suitable Sobolev spaces of the system obtained by using arguments of compactness and Fredholm Alternative theory. A discussion of the possible applications of this new parametrix is included.