The tame dimension vectors for trees

We consider representations of quivers over an algebraically closed field K. A dimension vector of a quiver is called hypercritical, if there is an m-parameter family of indecomposable representations for the dimension vector with m?2, but every family of representations for all smaller dimension vectors depends on a single parameter. We characterise the hypercritical dimension vectors for trees via their Tits forms and those of their decompositions and present the complete list of the hypercritical dimension vectors.Finally, this leads to a combinatorial classification of the tame dimension vectors for trees which is also given by the Tits forms.     

The effect of linear perturbations on the Yamabe problem

In conformal geometry, the Compactness Conjecture asserts that the set of Yamabe metrics on a smooth, compact, aspherical Riemannian manifold $\left( M,g\right) $ is compact. Established in the locally conformally flat case by Schoen (Lecture Notes in Mathematics, vol. 1365, pp. 120–154. Springer, Berlin 1989, Surveys Pure Application and Mathematics, 52 Longman Science, Technology, pp. 311–320. Harlow 1991) and for $n\le 24$ by Khuri–Marques–Schoen (J Differ Geom 81(1):143–196, 2009), it has revealed to be generally false for $n\ge 25$ as shown by Brendle (J Am Math Soc 21(4):951–979, 2008) and Brendle–Marques (J Differ Geom 81(2):225–250, 2009). A stronger version of it, the compactness under perturbations of the Yamabe equation, is addressed here with respect to the linear geometric potential $\frac{n-2}{4(n-1)} {{\mathrm{Scal}}}_g,\, {{\mathrm{Scal}}}_g$ being the Scalar curvature of $\left( M,g\right) $ . We show that a-priori $L^\infty $ –bounds fail for linear perturbations on all manifolds with $n\ge 4$ as well as a-priori gradient $L^2$ –bounds fail for non-locally conformally flat manifolds with $n\ge 6$ and for locally conformally flat manifolds with $n\ge 7$ . In several situations, the results are optimal. Our proof combines a finite dimensional reduction and the construction of a suitable ansatz for the solutions generated by a family of varying metrics in the conformal class of $g$ .     

Effective location models for sorting recyclables in public management

The recycling of urban solid wastes is a critical point for the “closing supply chains” of many products, mainly when their value cannot be completely recovered after use. In addition to environmental aspects, the process of recycling involves technical, economic, social and political challenges for public management. For most of the urban solid waste, the management of the end-of-life depends on selective collection to start the recycling process. For this reason, an efficient selective collection has become a mainstream tool in the Brazilian National Solid Waste Policy. In this paper, we study effective models that might support the location planning of sorting centers in a medium-sized Brazilian city that has been discussing waste management policies over the past few years. The main goal of this work is to provide an optimal location planning design for recycling urban solid wastes that fall within the financial budget agreed between the municipal government and the National Bank for Economic and Social Development. Moreover, facility planning involves deciding on the best sites for locating sorting centers along the four-year period as well as finding ways to meet the demand for collecting recyclable materials, given that economic factors, consumer behavior and environmental awareness are inherently uncertain future outcomes. To deal with these issues, we propose a deterministic version of the classical capacity facility location problem, and both a two-stage recourse formulation and risk-averse models to reduce the variability of the second-stage costs. Numerical results suggest that it is possible to improve the current selective collection, as well as hedge against data uncertainty by using stochastic and risk-averse optimization models.     

Null-Lagrangians and the indeterminate couple stress model

The aims of this note is to present a new model based on a new representation of the curvature energy in the indeterminate couple stress model and to discuss some related choices from the literature. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fixed Point Theorems Under Combined Topological and Variational Conditions

The new idea is to replace part of the conditions on the operator involved in the classical fixed point theorems of Schauder, Krasnoselskii, Darbo and Sadovskii, by assumptions upon the associated functional, in case that the fixed point equation has a variational form. Fixed points minimizing the associated functionals are obtained via Ekeland’s variational principle and the Palais–Smale compactness condition guaranteed by the topological properties of the nonlinear operators.     

Existence and multiplicity results to Neumann problems for elliptic equations involving the p-Laplacian

In this paper, existence results of positive solutions to a Neumann problem involving the p-Laplacian are established. Multiplicity results are also pointed out. The approach is based on variational methods.     

An examination of tissue engineered scaffolds in a bioreactor

Replacement tissues, designed to fill in articular cartilage defects, should exhibit the same properties as the native material. The aim of this study is to foster the understanding of, firstly, the mechanical behavior of the material itself and, secondly, the influence of cultivation parameters on cell seeded implants as well as on cell migration into acellular implants. In this study, acellular cartilage replacement material is theoretically, numerically and experimentally investigated regarding its viscoelastic properties, where a phenomenological model for practical applications is developed. Furthermore, remodeling and cell migration are investigated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dissipative operators and additive perturbations in locally convex spaces

Let be a densely defined operator on a Banach space X. Characterizations of when generates a C₀‐semigroup on X are known. The famous result of Lumer and Phillips states that it is so if and only if is dissipative and is dense in X for some . There exists also a rich amount of Banach space results concerning perturbations of dissipative operators. In a recent paper Tyran–Kamińska provides perturbation criteria of dissipative operators in terms of ergodic properties. These results, and others, are shown to remain valid in the setting of general non–normable locally convex spaces. Applications of the results to concrete examples of operators on function spaces are also presented.