Summability of multilinear mappings: Littlewood, Orlicz and beyond

In this paper we prove new results concerning summability properties of multilinear mappings between Banach spaces, such as an extension of Littlewood’s 4/3 Theorem. The role of the Littlewood–Orlicz property in the theory is established, especially in the question of determining when multilinear mappings are (1; 2, . . . , 2)-summing.     

The self-consistent general relativistic solution for a system of degenerate neutrons, protons and electrons in β-equilibrium

We present the self-consistent treatment of the simplest, nontrivial, self-gravitating system of degenerate neutrons, protons and electrons in β-equilibrium within relativistic quantum statistics and the Einstein-Maxwell equations. The impossibility of imposing the condition of local charge neutrality on such systems is proved, consequently overcoming the traditional Tolman-Oppenheimer-Volkoff treatment. We emphasize the crucial role of imposing the constancy of the generalized Fermi energies. A new approach based on the coupled system of the general relativistic Thomas-Fermi-Einstein-Maxwell equations is presented and solved. We obtain an explicit solution fulfilling global and not local charge neutrality by solving a sophisticated eigenvalue problem of the general relativistic Thomas-Fermi equation. The value of the Coulomb potential at the center of the configuration is eV(0)?mπc² and the system is intrinsically stable against Coulomb repulsion in the proton component. This approach is necessary, but not sufficient, when strong interactions are introduced.     

Octahedral norms and convex combination of slices in Banach spaces

We study the relation between octahedral norms, Daugavet property and the size of convex combinations of slices in Banach spaces. We prove that the norm of an arbitrary Banach space is octahedral if, and only if, every convex combination of w^?$w^{?}$-slices in the dual unit ball has diameter 2, which answers an open question. As a consequence we get that the Banach spaces with the Daugavet property and its dual spaces have octahedral norms. Also, we show that for every separable Banach space containing _?1${?}_1$ and for every ε>0$\epsilon >0$ there is an equivalent norm so that every convex combination of w^?$w^{?}$-slices in the dual unit ball has diameter at least 2−ε$2-\epsilon$.     

In situ polymerization and characterization of elastomeric polyurethane-cellulose nanocrystal nanocomposites. Cell response evaluation

Polyurethane/Cellulose nanocrystal (CNC) nanocomposites have been prepared by means of in situ polymerization using CNCs as precursors of polyurethane chains. Thermal, mechanical and morphological characterization has been analyzed to study the effect of CNC on the micro/nanostructure, which consisted of individualized nanocellulose crystallites covalently bonded to hard and soft segments of polyurethane. The incorporation of low CNC content led to a tough material whereas higher amount of CNC provoked an increase in soft and hard segments crystallization phenomenon. Moreover, from the viewpoint of polyurethane and polyurethane nanocomposites applications focused on biomedical devices, biocompatibility studies can be considered necessary to evaluate the influence of CNC on the biological behaviour. SEM micrographs obtained from cells seeded on top of the materials showed that L-929 fibroblasts massively colonized the materials surface giving rise to good substrates for cell adhesion and proliferation and useful as potential materials for biomedical applications.     

Pietsch's factorization theorem for dominated polynomials

We prove that, like in the linear case, there is a canonical prototype of a p-dominated homogeneous polynomial through which every p-dominated polynomial between Banach spaces factors.     

Closure Łukasiewicz algebras

In this paper, the variety of closure n-valued Łukasiewicz algebras, that is, Łukasiewicz algebras of order n endowed with a closure operator, is investigated. The lattice of subvarieties in the particular case in which the open elements form a three-valued Heyting algebra is obtained.     

Hardness of nitric acid treated polyethylene followed by recrystallization

The hardness variation of melt crystallized polyethylene as a consequence of controlled fuming nitric exposure has been investigated using the microindentation technique. This study complements previous results obtained using other reagents (H₂SO₄, ClHSO₃). After HNO₃ exposure the microhardness of polyethylene decreases very rapidly, instead of increasing after the first hours of treatment. The hardness decrease is correlated to the volume fraction of interlamellar microvoids arising through selective acid digestion. For longer treatment times (t>40 h) the fragility of the material increases and the sample collapses under the indenter. The hardening of the degraded material after recrystallization from the melt is followed as a function of treatment time. The results are discussed in the light of the molecular mechanisms involved. Comparison of the experimental data with hardness calculations for ideal PE lamellar structures and chain extended dicarboxylic crystals implies that the major contribution to hardening is due to electron dense groups attachment at the surface of a mixed lamellar structure.     

Domination spaces and factorization of linear and multilinear summing operators

It is well known that not every summability property for multilinear operators leads to a factorization theorem. In this paper we undertake a detailed study of factorization schemes for summing linear and nonlinear operators. Our aim is to integrate under the same theory a wide family of classes of mappings for which a Pietsch type factorization theorem holds. Our construction includes the cases of absolutely p-summing linear operators, (p, σ)-absolutely continuous linear operators, factorable strongly p-summing multilinear operators, (p1,?. . .?, pn)-dominated multilinear operators and dominated (p1,?. . .?, pn; σ)-continuous multilinear operators.     

An ATR-FTIR study of different phosphonic acids in aqueous solution

An ATR-FIR study of the vibrational spectra of 1-hydroxyethane-1,1'-diphosphonic acid (HEDP), nitrilotris(methylenephosphonic acid) (NTMP) and N,N-bis(2-hydroxyethyl)aminomethylphosphonic acid (BHAMP) in aqueous solution is presented. The study was performed in the range of pH from 5 to 9, and bands assignments are given in the 2000-890 cm(-1) range. However, as phosphonates display bands due to the PO stretching vibration mainly in the 900-1200 cm(-1) range, the study is focused in this midinfrared region, which shows important changes as the pH changes, specially the nu(POH) at approximately 925 cm(-1) and nu(PO(3)(2-)) at approximately 970 cm(-1) vibrations. IR analyses give also evidences for the zwitterionic nature of BHAMP and NTMP in solution with a strong indication that the zwitterion in both compounds remains intact throughout the pH range investigated. The successive protonation steps with the decrease of pH were evidenced in the IR spectra of the three studied phosphonates.