Invariant Subspaces for Semigroups of Algebraic Operators

T. Laffey showed (Linear and Multilinear Algebra6(1978), 269–305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of Hthis result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair {A, B} of arbitrary bounded operators satisfying rank (AB−BA)=1 and several related conditions. In addition, it is shown that a semigroup of algebraically unipotent operators of bounded degree is triangularizable.     

Study of flame-retardant finishing of cellulose fibres: Organic–inorganic hybrid versus conventional organophosphonate

The aim of this study was to introduce a non-formaldehyde inorganic–organic hybrid sol–gel flame-retardant precursor (SiOP) containing phosphorous, nitrogen, and silicon and to compare its functional properties with those of the conventional formaldehyde-containing organic flame-retardant agent, organophosphonate (OP). SiOP was used at concentrations of 2%, 4%, and 8%, and OP was used at a concentration of 200 g/dm³. Both agents were applied to 100% cotton (CO) woven fabric by the pad-dry-cure method under the appropriate conditions. The presence of the SiOP and OP coatings on the CO fabric was confirmed by scanning electron microscopy, energy dispersive X-ray spectroscopy and Fourier-transform infrared spectroscopy. The results of the vertical tests of flammability and the thermogravimetric analyses showed that the presence of the SiOP coating changed the thermal degradation pathway of the CO fabric and resulted in an increase in the thermo-oxidative stability of the cellulose fibres. The thermo-oxidative stability was enhanced by the addition of higher amount of dry solids. At comparable dry solids contents, OP preserved significantly greater flame retardancy and thermo-oxidative stability than did SiOP. These results indicated that the SiOP precursor could not act as an effective alternative to the OP agent in the flame-retardant protection of CO fabric.     

Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos

We apply the recently improved version of the 0–1 test for chaos to real experimental time series of laser droplet generation process. In particular two marginal regimes of dripping are considered: spontaneous and forced dripping. The outcomes of the test reveal that both spontaneous and forced dripping time series can be characterized as chaotic, which coincides with the previous analysis based on nonlinear time series analysis.     

Antimicrobial properties of viscose yarns ring-spun with integrated amino-functionalized nanocellulose

Cellulose - Bio-based, renewable and biodegradable products with multifunctional properties are also becoming basic trends in the textile sector. In this frame, cellulose nanofibrils (CNFs) have...     

Moral Dilemmas and Vagueness

In this paper we point out some interesting structural similarities between vagueness and moral dilemmas as well as between some of the proposed solutions to both problems. Moral dilemma involves a situation with opposed obligations that cannot all be satisfied. Transvaluationism as an approach to vagueness makes three claims concerning the nature of vagueness: (1) it involves incompatibility between mutually unsatisfiable requirements, (2) the underlying requirements retain their normative power even when they happen to be overruled, and (3) this incompatibility turns out to be rather benign in practice. Given that transvaluationism is inspired by moral dilemmas, these claims are assessed in respect to them. Transvaluationism provides a smooth account of the mentioned claims concerning vagueness. Following a brief discussion of Sorensen’s views on moral dilemmas and conflict vagueness, we offer a model of moral pluralism accommodating structurally similar claims about the nature of moral conflict and moral dilemmas.     

Cellulose liquefaction in acidified ethylene glycol

Wood pulp cellulose was used in a study of its catalyzed liquefaction in the presence of ethylene glycol, p-toluene sulfonic acid monohydrate or sulphuric acid being the catalysts. For this study, microcrystalline cellulose, Whatman filter paper no. 1 and cotton linters with molar masses of 76,000, 699,000 and 1,910,000 g mol⁻¹, respectively were used. This liquefaction was studied by gravimetric determinations, by X-ray diffraction analysis of the residual cellulose and by monitoring of the molar mass decrease over different time intervals, using size-exclusion chromatography. The disordered regions, even of cellulose with the highest molar mass degraded in the initial minute of liquefaction. However, the highly ordered cellulose regions remained relatively stable for a longer time. None the less, partial degradation of the highly ordered regions of the cellulose was achieved.     

Maximal dominated operator semigroups

Maximal operator semigroups, bounded in a certain sense, on real or complex vector spaces are studied. For any maximal semigroup \MM dominated by a certain pair of homogeneous functions there is an operator quasinorm for which \MM is exactly the semigroup of contractions in this quasinorm. Applications to Riesz spaces are given. In particular, maximal semigroups of matrices dominated by a given positive matrix are characterized. We thus answer the question implicitly posed in [2]. November 20, 1998