On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian Growth

We review applications of theory of classical and quantum integrable systems to the free-boundary problems of fluid mechanics as well as to corresponding problems of statistical mechanics. We also review important exact results obtained in the theory of multi-fractal spectra of the stochastic models related to the Laplacian growth: Schramm-Loewner and Levy-Loewner evolutions

Learning stable weights for data of varying dimension

In this paper we develop a data-driven weight learning method for weighted quasiarithmetic means where the observed data may vary in dimension

The Choquet integral for the aggregation of interval scales in multicriteria decision making

This paper addresses the question of which models fit with information concerning the preferences of the decision maker over each attribute, and his preferences about aggregation of criteria (interacting criteria). We show that the conditions induced by these information plus some intuitive conditions lead to a unique possible aggregation operator: the Choquet integral.

Power-aggregation of pseudometrics and the McShane-Whitney extension theorem for Lipschitz p-convace maps

[EN] Given a countable set of families {Dk:k¿N} of pseudometrics over the same set D, we study the power-aggregations of this class, that are defined as convex combinations of integral averages of powers of the elements of ¿kDk. We prove that a Lipschitz function f is dominated by such a power-aggregation if and only if a certain property of super-additivity involving the powers of the elements of ¿kDk is fulfilled by f. In particular, we show that a pseudo-metric is equivalent to a power-aggregation of other pseudometrics if this kind of domination holds. When the super-additivity property involves a p-power domination, we say that the elements of Dk are p-concave. As an application of our results, we prove under this requirement a new extension result of McShane-Whitney type for Lipschitz p-concave real valued maps.Both authors gratefully acknowledge the support of the Ministerio de Ciencia, Innovación y Universidades, Agencia Estatal de Investigaciones and FEDER under each grants MTM2015-64373-P (MINECO/FEDER, UE) and MTM2016-77054-C2-1-P.Rodríguez López, J.; Sánchez Pérez, EA. (2020). Power-aggregation of pseudometrics and the McShane-Whitney extension theorem for Lipschitz p-convace maps. Acta Applicandae Mathematicae. 170:611-629. https://doi.org/10.1007/s10440-020-00349-3S611629170Dahia, E., Achour, D., Rueda, P., Sánchez Pérez, E.A., Yahi, R.: Factorization of Lipschitz operators on Banach function spaces. Math. Inequal. Appl. 21(4), 1091–1104 (2018)Beliakov, G.: Optimization and aggregation functions. In: Lodwick, W.A., Kacprzyk, J. (eds.) Fuzzy Optimization: Recent Advances and Applications, pp. 77–108. Springer, Berlin (2010)Beliakov, G., Bustince Sola, H., Calvo Sánchez, T.: A Practical Guide to Averaging Functions, vol. 329. Springer, Heidelberg (2016)Botelho, G., Pellegrino, D., Rueda, P.: A unified Pietsch domination theorem. J. Math. Anal. Appl. 365(1), 269–276 (2010)Botelho, G., Pellegrino, D., Rueda, P.: On Pietsch measures for summing operators and dominated polynomials. Linear Multilinear Algebra 62(7), 860–874 (2014)Chávez-Domínguez, J.A.: Duality for Lipschitz p-summing operators. J. Funct. Anal. 261, 387–407 (2011)Chávez-Domínguez, J.A.: Lipschitz $p$-convex and $q$-concave maps (2014). arXiv:1406.6357Defant, A.: Variants of the Maurey-Rosenthal theorem for quasi Köthe function spaces. Positivity 5, 153–175 (2001)Defant, A., Floret, K.: Tensor Norms and Operator Ideals. Elsevier, Amsterdam (1992)Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators. Cambridge University Press, Cambridge (1995)Dugundji, J.: Topology. Allyn and Bacon, Needham Heights (1966)Farmer, J., Johnson, W.: Lipschitz $p$-summing operators. Proc. Am. Math. Soc. 137(9), 2989–2995 (2009)Juutinen, P.: Absolutely minimizing Lipschitz extensions on a metric space. Ann. Acad. Sci. Fenn., Math. 27, 57–67 (2002)Marler, T.R., Arora, J.S.: The weighted sum method for multi-objective optimization: new insights. Struct. Multidiscip. Optim. 41(6), 853–862 (2010)Mustata, C.: Extensions of semi-Lipschitz functions on quasi-metric spaces. Rev. Anal. Numér. Théor. Approx. 30(1), 61–67 (2001)Mustata, C.: On the extremal semi-Lipschitz functions. Rev. Anal. Numér. Théor. Approx. 31(1), 103–108 (2002)Pellegrino, D., Santos, J.: Absolutely summing multilinear operators: a panorama. Quaest. Math. 34(4), 447–478 (2011)Romaguera, S., Sanchis, M.: Semi-Lipschitz functions and best approximation in quasi-metric spaces. J. Approx. Theory 103, 292–301 (2000)Willard, S.: General Topology. Addison-Wesley, Reading (1970)Yahi, R., Achour, D., Rueda, P.: Absolutely summing Lipschitz conjugates. Mediterr. J. Math. 13(4), 1949–1961 (2016

An algebraic multigrid method for Q2−Q1Q_2-Q_1 mixed discretizations of the Navier-Stokes equations

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points. Specifically, we investigate a $Q_2-Q_1$ mixed finite element discretization of the incompressible Navier-Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees-of-freedom (dofs) are defined at spatial locations where there are no corresponding pressure dofs. Thus, AMG approaches leveraging this co-located structure are not applicable. This paper instead proposes an automatic AMG coarsening that mimics certain pressure/velocity dof relationships of the $Q_2-Q_1$ discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity dofs resembles that on the finest grid. To define coefficients within the inter-grid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier-Stokes problems.Comment: Submitted to a journa

Design Your Career - Design Your Life

This research investigates the current plague of unemployment and underemployment that nearly half of qualified individuals in the field of Visual Communications are met with after graduation. Students who major in this field dedicate a tremendous amount of time, money, and energy toward developing a broad skillset that resolves critical matters of communication through visual solutions. Research has demonstrated that despite conditions that are subject to ongoing change of economy, industry, and marketplace there are contributing factors that must be addressed to overcome un/underemployment regardless of circumstances. These include an underdeveloped network of professional contacts, deficiency in recognizing or responding to changing conditions, and a limited ability to customize one’s career around their unique specialization. The purpose of this study is to provide students who major in Visual Communications the information and tools needed to incorporate their ability to adapt and problem solve from their skillset into their search for work. To explore this issue, information was gathered through secondary research that involved data from federal databases, case studies, literature review, and secondary research in general. Return on investment for one’s education is measured in consideration of three primary themes: job satisfaction, income, and quality of life, which may provide hopeful opportunity for professionals in Visual Communications to overcome un/underemployment through career customization