Spontaneous formation of vesicles of diblock copolymer EO6BO11 in water: a SANS study

Small angle neutron scattering (SANS) is used to study the structures formed in water by a diblock copolymer EO6BO11 (having 6 ethylene oxide, EO, and 11 butylene oxide, BO, units). The data show that polymer solutions over a broad concentration range (0.05-20 wt %) contain vesicular structures at room temperature. Interestingly, these vesicles could be formed without any external energy input, such as extrusion, which is commonly required for the formation of other block copolymer or lipid vesicles. The EO6BO11 vesicles are predominantly unilamellar at low polymer concentrations, whereas at higher polymer concentrations or temperatures there is a coexisting population of unilamellar and multilamellar vesicles. At a critical concentration and temperature, the vesicular structures fuse into lyotropic arrays of planar lamellar sheets. The findings from this study are in broad agreement with the work of Harris et al. (Langmuir, 2002, 18, 5337), who used electron microscopy to identify the vesicle phase in the same system.     

Comparison of graphs associated to a commutative Artinian ring

Let R be a commutative ring with \(1\ne 0\) and the additive group \(R^+\). Several graphs on R have been introduced by many authors, among zero-divisor graph \(\Gamma _1(R)\), co-maximal graph \(\Gamma _2(R)\), annihilator graph AG(R), total graph \( T(\Gamma (R))\), cozero-divisors graph \(\Gamma _\mathrm{c}(R)\), equivalence classes graph \(\Gamma _\mathrm{E}(R)\) and the Cayley graph \(\mathrm{Cay}(R^+ ,Z^*(R))\). Shekarriz et al. (J. Commun. Algebra, 40 (2012) 2798–2807) gave some conditions under which total graph is isomorphic to \(\mathrm{Cay}(R^+ ,Z^*(R))\). Badawi (J. Commun. Algebra, 42 (2014) 108–121) showed that when R is a reduced ring, the annihilator graph is identical to the zero-divisor graph if and only if R has exactly two minimal prime ideals. The purpose of this paper is comparison of graphs associated to a commutative Artinian ring. Among the results, we prove that for a commutative finite ring R with \(|\mathrm{Max}(R)|=n \ge 3\), \( \Gamma _1(R) \simeq \Gamma _2(R)\) if and only if \(R\simeq \mathbb {Z}^n_2\); if and only if \(\Gamma _1(R) \simeq \Gamma _\mathrm{E}(R)\). Also the annihilator graph is identical to the cozero-divisor graph if and only if R is a Frobenius ring.     

Cyclicity in the Dirichlet space

Let be the Dirichlet space, namely the space of holomorphic functions on the unit disk whose derivative is square-integrable. We give a new sufficient condition, not far from the known necessary condition, for a function f∈ to be cyclic, i.e. for {pf: p is a polynomial} to be dense in . The proof is based on the notion of Bergman–Smirnov exceptional set introduced by Hedenmalm and Shields. Our methods yield the first known examples of such sets that are uncountable. One of the principal ingredients of the proof is a new converse to the strong-type inequality for capacity.     

The de Schipper formula and squares of Riesz spaces

In this paper we introduce and study the square mean and the geometric mean in Riesz spaces. We prove that every geometric mean closed Riesz space is square mean closed and give a counterexample to the converse. We define for positive a, b in a square mean closed Riesz space E an addition via the formulaab=sup {(cos x)a + (sin x)b: 0 x 2π},which goes back to a formula by de Schipper. In case that E is geometric mean closed this turns the mldeflying set of the positive cone of E into a lattice ordered semigroup, which in turn is the positive cone ofa Riesz space E^□. We prove, under the additional condition that E is geometric mean closed, that E^□ is Riesz isomorphic to the square of E as introduced earlier by Buskes and van Rooij.     

Complex homomorphisms on self-conjugate algebras of functions

Let X be a non-void set and A be a subalgebra of \({\mathbb{C}^{X}}\) . We call a \({\mathbb{C}}\) -linear functional \({\varphi}\) on A a 1-evaluation if \({\varphi(f) \in f(X) }\) for all \({f\in A}\) . From the classical Gleason–Kahane–?elazko theorem, it follows that if X in addition is a compact Hausdorff space then a mapping \({\varphi}\) of \({C_{\mathbb{C}}(X) }\) into \({\mathbb{C}}\) is a 1-evaluation if and only if \({\varphi}\) is a \({\mathbb{C}}\) -homomorphism. In this paper, we aim to investigate the extent to which this equivalence between 1-evaluations and \({\mathbb{C}}\) -homomorphisms can be generalized to a wider class of self-conjugate subalgebras of \({\mathbb{C}^{X}}\) . In this regards, we prove that a \({\mathbb{C}}\) -linear functional on a self-conjugate subalgebra A of \({\mathbb{C}^{X}}\) is a positive \({\mathbb{C}}\) -homomorphism if and only if \({\varphi}\) is a \({\overline{1}}\) -evaluation, that is, \({\varphi(f) \in\overline{f\left(X\right)}}\) for all \({f\in A}\) . As consequences of our general study, we prove that 1-evaluations and \({\mathbb{C}}\) -homomorphisms on \({C_{\mathbb{C}}\left( X\right)}\) coincide for any topological space X and we get a new characterization of realcompact topological spaces.     

A note on the Holst action, the time gauge, and the Barbero–Immirzi parameter

In this note, we review the canonical analysis of the Holst action in the time gauge, with a special emphasis on the Hamiltonian equations of motion and the fixation of the Lagrange multipliers. This enables us to identify at the Hamiltonian level the various components of the covariant torsion tensor, which have to be vanishing in order for the classical theory not to depend upon the Barbero–Immirzi parameter. We also introduce a formulation of three-dimensional gravity with an explicit phase space dependency on the Barbero–Immirzi parameter as a potential way to investigate its fate and relevance in the quantum theory.     

Zero-Dimensional Imbeddability

In this article, we try to understand which generically complete intersection monomial ideals with fixed radical are Cohen–Macaulay. We are able to give a complete characterization for a special class of simplicial complexes, namely the Cohen–Macaulay complexes without cycles in codimension 1. Moreover, we give sufficient conditions when the square-free monomial ideal has minimal multiplicity.     

Cytoplasmic RNA and nuclear changes detected cytochemically during the degeneration of salivary glands of the tick Rhipicephalus sanguineus (Latreille, 1806) (Acari, Ixodidae)

The present study reports cytochemistry data about salivary glands of females (unfed, engorged, and at day three post-engorgement) and males (unfed, at day seven post-attachment, and at days three and seven post-detachment from the host) of the tick Rhipicephalus sanguineus. The results revealed nuclear changes in engorged females and at day three post-engorgement, and in males in all stages (except unfed). These changes were more prominent in females. Cytoplasmic changes were also observed in cells of all acini of males and females. In types II and III acini of engorged females, nuclear changes were observed in the shape (irregular, with blebs, fragmenting or fragmented), size (enlarged or reduced), and arrangement and condensation level of chromatin (marginal or as blebs). Changes were also detected in nucleoli, regarding their shape (fragmenting or fragmented), size (enlarged), and location (central, marginal or as blebs). Some nucleoli were also compacted or disorganized. In females at day three pos-engorgement, all acini exhibited similar changes to those observed in engorged females. RNA staining was stronger in cells of engorged females than those at day three post-engorgement. In males at day seven post-attachment, cells of types II, III, IV acini presented changes in the size of the nucleus and condensation level of chromatin similar to those of females. The shape of the nucleus was round, irregular or undergoing fragmentation, and the chromatin was located at the margin or throughout the nucleus. The changes in the nucleolus were similar to those of females, regarding size and organization, although round-shaped and in the central location. In males at day three post-detachment, cells of all acini exhibited nuclear changes similar to those of males at day seven post-attachment, in addition to the fragmentation of the nucleolus. At day seven post-detachment, changes were detected in all acini similar to the observed in males at day seven post-attachment. Regarding cytoplasmic RNA, staining was prominent in males at day seven post-attachment and weak in those at day seven post-detachment from the host. In females as well as males, different RNA staining patterns in the cytoplasm and nuclear changes characterized apoptotic cell death.     

Lattice norms on the unitization of a truncated normed Riesz space

Positivity - Truncated Riesz spaces was first introduced by Fremlin in the context of real-valued functions. An appropriate axiomatization of the concept was given by Ball. Keeping only the first...