CIMA: Financiamento base 2020-2023

 

1.                    Differential Equations and Optimization (DEO)

 

 

1.1.               Boundary value problems for ordinary differential equations

 

· - Nonlinear periodic Ambrosetti-Prodi type problems: sufficient conditions on the nonlinearities to obtain the Ambrosetti-Prodi alternative.

· - Coupled systems with two parameters: discussion of the Ambrosetti-Prodi alternative on both parameters.

· - First-and second-order nonlinear periodic impulsive coupled systems with generalized impulsive effects: It was proved a necessary condition for the existence of solutions: the sum of the impulses must be null. Moreover, several local monotone conditions were established for the nonlinearities and the impulsive functions.

· - Solvability of impulsive coupled systems with phi-Laplacian differential equations.

· - Sufficient conditions for the solvability of third-order functional Ambrosetti-Prodi-type problems.

 

1.2.               Calculus of Variations and Optimal Control

 

· Decomposition of L^1(a,b) functions through a convenient convergent series.

· Determination of the sign of the Lebesgue integral of a product of two functions.

· A geometric approach to the Liapunov theorem on convexity of the range of vector measures under constraints.

· Calculus of variations and applications to material sciences. Namely, nonlocal and local supremal functionals, integral representation and homogenization and partial differential equations.

· Integral representation in the context of Structured Deformations and measures. In particular, applications to thin structures.

 

1.3.           Non-smooth Analysis

 

·        Geometric (local) properties of compact convex sets in Rn, which are given (locally) through an implicit equation.

·        Relationships between positive directional curvatures (in the set) and the existence of second-order derivatives (in the polar set).

 

1.4.      Numerical methods for partial differential equations and fluid mechanics

 

· Research activities in the area of mathematics of fluid mechanics and its applications to hemodynamics. In particular, studies were carried out on Ambrosetti-Prodi-type differential equations.

· Research activities on Ulam Stabilities for a Class of Higher Order Integro-Differential Equations

 

1.5.           Multiobjective optimization

 

Development of multi-objective optimization methods for a forestry management problems in Portugal based on constraint programming.

 

 

2.                   Dynamical Systems (DS)

 

●                       Study of the human behaviors subjected to couplings and strategies of suppressing chaotic behavior using couplings.

●                       New approaches to obtain necessary and/or sufficient conditions for quasiconvexity, in the planar case. Study of general variational problems and the numerical treatment of the problems under study.

●                       Theoretical models that can simulate fractures and/or lack of homogeneity in ornamental rocks, such as marble.

●                       Existence of trapped modes around freely-floating bodies in a multi-layer flui

●                        .Velocity and energy of periodic travelling interfacial waves.

●                         Discrete dynamical systems in two dimensions with chaotic behavior and limit cycles, in particular the Lozi maps and Lozi-type maps. The models obtained are based on a prototype of a suspended load device consisting of a drive system for a cart moving horizontally with a pendulum attached, when the model is subjected to piecewise linear control driven by a cart speed control signal

 

●                       Development of tools associated with symbolic dynamics that will allow us to characterize qualitatively the complexity of systems, such as the calculation of topological entropy and the Lyapunov exponent.

 

●                       Development of forest management scheduling models that address wildfire risk, both at stand and landscape levels, with the incorporation of concerns about regularity of volume, wildfire resistance or adjacency constraints. This research is applied to the Zona de Intervenção Florestal (ZIF) de Paiva and de Entre-Douro e Sousa (ZIF_VS) that is in northwestern Portugal.

 

●                       Non-autonomous attractors in non-autonomous dynamical systems generated by the introduction of simple limiters, according to a temporal sequence, in the iteration of tent maps.

 

●                       Representations of Cuntz-Krieger algebras. Classification of the Cuntz-Krieger sub algebras. Branching systems and representations of graph algebras

 

●                       Cellular automata and genetic algorithms. Evolutionary dynamics of networks of automata.

 

●                       Development of composite materials, using clay, celulosis and other raw materials, for bio-climatization of buildings.

 

●                       Mini ecosystems – Experimental setup. New systems will be established, arising from previous ones.

●                       Study of robotic motion using the dynamical model introduced in previous year. Development of the interaction model between robots. Codification of tasks and strategies. Experimental, computational and theoretical work.

 

●                       Study of cryptographic systems using cellular automata and chaotic discrete dynamical systems

 

●                        Study of oscillations on non-homogeneous materials. Coupling of harmonic oscillators

 

 

 

3.              Logic, Algebra and Geometry (LAG)

 

3.1.            Numerical semigroups

 

· Frobenius number and genus.

· Invariants of numerical semigroups : the multiplicity, embedding dimension, degree of singularity, conductor, Apery sets, pseudo-Frobenius number and type.

 

3.2.                Logic

 

· Definition of generalizations of the Levi and Harper Identities, which are suitable to the context of non-prioritized operators of belief change defined on belief bases (i.e. sets of formulas not necessarily closed under deduction).

 

· Revision of our logic for contrary-to-duty conditionals, showing how to adjust our logical models in such a way as to avoid the counterintuitive results pointed out by Bjørn Kjos-Hanssen, but keep the main results that support our logical analysis of contrary-to-duty (CTD) scenarios.

 

· Equality in the context of Non-standard Analysis.

 

· Apply techniques from Proof Mining, information to obtain the strong convergence of the Halpern-Mann algorithm in the context of CAT(0) spaces.

 

· Theory of scales and the semantics of vague adjectives. The models of this theory are necessarily Non-standard leading to denominate our philosophical conception as non-standard primitivism, since in our theory vague quantities are not reducible to precise degrees.

 

· A realisability with states that takes advantage of the Robinson-Lightstone construction, allowing to obtain computational content of some principles of non-standard arithmetic

 

· Characterization of definable Skolem functions and its relationship with trichotomy in the context of o-minimal structures was obtained.

 

· Development of a hybrid logic with varying domains, extending earlier works in hybrid logic by Martins, Manzano and Blackburn.

 

· Analysis of the finite content of Dykstra's algorithm through the logic tools commonly used in the Proof Mining program

 

 

 

3.3.                Neutrices and external numbers

 

·      Polynomials with external numbers: Influence of errors in the coefficients on the roots of polynomials. A complete account on the shape of these errors could be given, both in the real and the complex setting.

 

·      Flexible systems of linear equations or inclusions. This studies the influence of errors in the coefficients and the right-hand member (modelled by external numbers) on the solution.

 

3.4.                Flexible linear algebra and optimization

 

·             Flexible linear algebra and near optimization under general conditions

 

3.5.                Active learning in teaching of Mathematics in higher education

 

3.6.                Artinian Jordan Algebras and Algebras of Gorenstein of codimension 4

 

·      Generalisation of results on bounds for the Jordan type of Artinian algebras, to the cases of non-graded algebras, and algebras with a non-standard grading, and free extensions.

 

·      Study of new invariants of Artinian algebras derived from the Jordan type, and their relation to deformations.

 

·       Study of Gorenstein homogeneous ideals

 

·      Study of the Hodge-Riemann relations (HRR) for graded Artinian Gorenstein (AG) algebras, and classification of those AG algebras in codimension two satisfying the HRR in terms of their Macaulay dual generators

 

3.7.                Monads on smooth projective varieties

 

Monads on smooth projective varieties whose bounded derived category of coherent sheaves has a semi-orthogonal decomposition.

 

3.8.                Vector bundles on the 3-dimensional projective space

 

Existence of vector bundles E on the 3-dimensional projective space defined by a linear resolution and homological dimension 2, and such that the Euler characteristic of the bundle End(E) is one.

 

 

4.                     Statistics, Stochastic Processes and Applications

(SSPA)

 

4.1. Stochastic currents of Brownian motion. 

Study of the stochastic currents of Brownian motion and its relation to Hida distributions.

 

4.2. Feynman integrals.

 

Construction of the Feynman integral for the Schrödinger propagator with combinations of exponentially growing and harmonic oscillator potentials as well-defined white noise functionals.

 

4.3. Random potentials for Markov processes.

Integral functionals of Markov processes in the  case , and applications to  compound Poisson processes, Brownian motion and diffusions.

 

4.4. Hydrodynamic limits for the free Kawasaki dynamics of continuous particle systems.

 

An infinite particle system of independent jumping particles was studied.

Their construction is recalled, further properties are derived, the relation with hierarchical equations, Poissonian analysis, and second quantization are discussed. The hydrodynamic limit for a general initial distribution satisfying a mixing condition is derived. The large time asymptotic is computed under an extra assumption.

 

4.5. Compound Poisson processes: potentials Green measures and random times.

 

Existence of Green measures for Markov processes with a nonlocal jump generator. The non-singular jump kernel has no second moment and satisfies a suitable condition on its Fourier transform. We also study the same problem for certain classes of random time changes Markov processes with jump generators.

 

4.6. A Biorthogonal Approach to Infinite Dimensional Fractional Poisson Measure.

 

The biorthogonal approach to the analysis of the infinite dimensional fractional Poisson measure on the dual of Schwartz test function space.

The kernels of the monomials may be expressed in terms of the Stirling operators of the first and second kind as well as the falling factorials in infinite dimensions. The test and generalized function spaces associated to an adequate measure are completely characterized using an integral transform as entire functions.

 

4.7. Stochastic differential equation

 

· Mixed stochastic differential equation models for individual growth, with generalization to parameter dependence on the individual genetic values: properties of the models, parameter estimation, testing significance of genetic values, and study of new approximate delta method of parameters’ estimation and its comparison with previous approximate methods; application to bovine growth data.

· General stochastic differential equation growth and fishing models with Allee effects: conditions for extinction and for existence of a stationary distribution with general autonomous natural growth with Allee effects and general autonomous harvesting efforts. Cases where density-dependent intensity effects of environmental noise.

 

4.8. Machine learning

 

Application of machine learning in the detection procedure to estimate the water level of stream channels from images acquired by low-cost cameras.

 

4.9. Metrology

 

Study and evaluation of measurement uncertainty and of new theoretical and applied metrological capabilities, in several areas of physical metrology, namely those related to volume, flow and density with applications in health. Use of Monte Carlo and Bayesian methods to evaluate uncertainties in complex problems. Statistics applied to interlaboratory comparison studies.

 

4.10. Statistics

 

· Type I error and power of the alternative approaches to two-way ANOVA in the presence of heteroscedastic errors and discrete data.

· Relationship between the nursing work environment and the quality of pressure ulcer care in integrated continuing care units in Alentejo.

●                       Identification of sensory and emotional profiles and customer segmentation of three different types of Seaweed bonbons, to find sensory drivers of liking.

 

· Characterization of the sleep and physical activity and sports habits of Portuguese elementary school children and identification of factors related to the child's sleep disturbance index and respective subscales.

· A predictive model for the occurrence of Road Traffic Accidents (RTA) on a road with a high RTA rate (the prediction is obtained for each road segment for a given time and day and combines results from statistical methods, spatial analysis, and artificial intelligence models).

· GIS tools were combining with machine learning and artificial intelligence, developing spatial intelligence (departing from a heatmap analysis, and applying kernel density estimation, new spatial approaches were used, namely DBSCAN and Getis-Ord).

· Several determinants for the type of RTA collision, crash, pedestrian running-over were identified.

· Statistical modelling of attendance at Emergency Service of the Hospital do Espírito Santo (HESE) de Évora; Profile of the hyper user of the emergency service.

· A Generalized Linear Mixed-Effects analysis was conducted to study if co-laughter, laughter rate, and the percentage of voiced frames in laughs are influenced by such factors.

· Analysis and evaluation of faults at tide gauge stations based on the Crow-AMSAA model and survival models.

· Determination of how correction with dolomitic limestone and continuous or deferred grazing affect ingesting behaviour and the use of space in natural pastures when the pasture growth rate is maximum.

· Analysis of factors associated with depression and anxiety symptoms among university students in Portugal, Sweden and Germany.

· Validation of the Medication Management Ability Assessment and determination of the level of functional ability of older adults to manage a simulated therapeutic regimen, understand their main limitations when facing changes and relationship between the functional ability to manage medication and cognitive functions.

· Assessment of the impact of implementing a “Geriatric Proximity” intervention on the functioning, satisfaction with social support, affective experience, and feelings of loneliness of institutionalized older adults in the times of the pandemic

· similarity/dissimilarity measures in time series, considering different structures of dependence between observations - for example, stationary series, non-stationary series (with trend and/or seasonality), with structural change -, exploring the difference between raw or with certain transformations.

· Evaluation, through simulation studies, of methods for testing (retrospectively) breaks or changes in structure in time series, at unknown moments of time, including determining the number of these breaks as well as the confidence intervals of break dates.

· Study of the recreational fishing to gather socioeconomic and biological information on shore angling fisheries in the Natural Marine Park of the Algarve Reef – Pedra do Valado (MPA).

 

· Study of differences in knowledge about sexuality depending on sexual orientation, within the scope of the study “Sexual Education of Portuguese Young People - Knowledge and Sources”