Some Bounds for the Number of Components of Real Zero Sets of Sparse Polynomials

We prove that the zero set of a 4-nomial in n variables in the positive orthant has at most three connected components. This bound, which does not depend on the degree of the polynomial, not only improves the best previously known bound (which was 10) but is optimal as well. In the general case, we prove that the number of connected components of the zero set of an m-nomial in n variables in the positive orthant is lower than or equal to (n+1)^{m-1}2^{1 + (m - 1)(m - 2)/2}, improving slightly the known bounds. Finally, we show that for generic exponents, the number of non-compact connected components of the zero set of a 5-nomial in three variables in the positive octant is at most 12. This strongly improves the best previously known bound, which was 10384. All the bounds obtained in this paper continue to hold for real exponents.Comment: 24 pages, 6 figures. Corrected typos, added reference

Economic Strain, Family Structure and Problems With Children Among Displaced Workers

For a small sample of Indiana families that had recently experienced unemployment due to a plant closing, perceived economic strain was related to a larger number of academic and interpersonal problems for their oldest child at home, average age thirteen. The relationship between parental economic strain and children\u27s difficulties lessened with the introduction into the analysis of selected parental psychological resources and coping strategies. Family structure was also related to children\u27s problems, despite parental resources and coping strategies

High Performance & Smart Manufacturing

Additive Manufacturing can be considered as one of the key factors for sustainable economic growth, increasing competitiveness and innovative technology with the potential to transform global manufacturing industry, to influence the environmental impact and to change the European economies. In recent years, 3D printing has grown rapidly and has shown great potential in various application fields: from bioengineering, to microfluidics and electronics. There is a growing interest for 3D printing focused on the production of functional structures. The possibility to obtain functional elements by 3D printing, such as batteries, antennas, membranes, sensors etc. is one of the key points of the evolution of this technology. Research on new kinds of printable materials and the ability to control and predict their performance are essential to achieve broader use of 3-D printing. Engineered materials, specifically studied for being 3D printable and exhibiting optimized properties and multifunctionality, will provide intense potential and opportunities in a myriad of applications, resulting in better functionality of the manufactured device (e.g, biocompatibility, electrical conductivity, optical response, chemical sensitivity, mechanical behaviour...) coupled with improved printability. The main approaches in the evolution of 3D printable materials consist in working with multiple materials or nanocomposites to create new combinations that have unique properties expanding the range of 3D printable objects. This Ph.D research activity on High Performance & Smart Manufacturing has been held in Materials and Micro Systems Laboratory of Politecnico di Torino (ChiLab) and in collaboration with Microla Optoelectronics S.r.l. First, a study of Additive Manufacturing techniques, already on the market, was performed. Then the optimization of a stereolithographic printing machine was carried out. One part of the PhD research was based on the study of new smart materials, with intrinsic features that can give to the printed objects a concrete function. For this purpose, functionalized photosensitive polymers, realized by Politecnico di Torino, were used to build 3D structures. Also aromatic polymers were laser processed with the aim to make them conductive and, in the future, reliable for additive manufacturing processes. A further and important task during the PhD activity was the integration of stereolithographic processes both at micro and nanoscale. This important task was possible thanks to the fruitful collaboration with the Laser Zentrum of Hannover (LZH - Germany). At LZH laboratories, a two-photon polymerization (2PP) set-up allowed the fabrication of different nano-structures for microfluidic application. The first attempt was the fabrication of a nano-filter printed directly inside a micro-channel outlet as published in “3D printed suspended micro-filter integrated in a printed microfluidic channel”. This work, once established the process feasibility, may lead to an interesting application in Bioanalytics for the sieving of extracellular vesicles of endocytic origin