Moisturizing emulsion systems based on the novel long-chain alkyl polyglucoside emulsifier

Mesomorphic behavior of the novel long-chain alkyl polyglucoside emulsifier comprising arachidyl alcohol (C₂₀), behenyl alcohol (C₂₂), and arachidyl glucoside was investigated in order to determine the prevalent stabilization mechanism and moisturizing capacity of emulsion systems based on it. For this to be accomplished thermoanalytical methods (differential scanning calorimetry and thermogravimetric analysis) coupled with microscopy, rheological, X-ray diffraction methods and a short-term in vivo study of skin hydration level were performed. Obtained results have proved that C₂₀/C₂₂ alkyl polyglucoside mixed emulsifier is able to provide the synergism between the two main types of lamellar phases, the liquid-crystalline (Lα), and the gel crystalline (Lβ) one, building the emulsion systems of different stability and performance. Formation of lamellar structures influenced for more than one half of water within the system to be entrapped. Conducted investigation of hydration potential in real-time conditions provided valuable information on the investigated emulsion vehicles’ moisturizing potential as well as their contribution to the skin barrier improvement. Therefore, it could be expected that emulsions based on this alkyl polyglucoside emulsifier could influence the delivery of active ingredients of both the lipophilic and hydrophilic type. The employment of thermoanalytical methods in our work suggests the possibility for thermal methods to be used more frequently in the characterization of both the novel raw materials and the belonging emulsion systems.     

Critical thermodynamics of the two-dimensional +/-J Ising spin glass

We compute the exact partition function of 2d Ising spin glasses with binary couplings. In these systems, the ground state is highly degenerate and is separated from the first excited state by a gap of size 4J. Nevertheless, we find that the low temperature specific heat density scales as exp(-2J/T), corresponding to an "effective" gap of size 2J; in addition, an associated crossover length scale grows as exp(J/T). We justify these scalings via the degeneracy of the low lying excitations and by the way low energy domain walls proliferate in this model.     

Stochastic processes with sample paths in reproducing kernel Hilbert spaces

A theorem of M. F. Driscoll says that, under certain restrictions, the probability that a given Gaussian process has its sample paths almost surely in a given reproducing kernel Hilbert space (RKHS) is either or . Driscoll also found a necessary and sufficient condition for that probability to be .

Doing away with Driscoll's restrictions, R. Fortet generalized his condition and named it nuclear dominance. He stated a theorem claiming nuclear dominance to be necessary and sufficient for the existence of a process (not necessarily Gaussian) having its sample paths in a given RKHS. This theorem - specifically the necessity of the condition - turns out to be incorrect, as we will show via counterexamples. On the other hand, a weaker sufficient condition is available.

Using Fortet's tools along with some new ones, we correct Fortet's theorem and then find the generalization of Driscoll's result. The key idea is that of a random element in a RKHS whose values are sample paths of a stochastic process. As in Fortet's work, we make almost no assumptions about the reproducing kernels we use, and we demonstrate the extent to which one may dispense with the Gaussian assumption.

     

A Class of Schrödinger Operators with Decaying Oscillatory Potentials

We discuss Schrödinger operators on a half-line with decaying oscillatory potentials, such as products of an almost periodic function and a decaying function. We provide sufficient conditions for preservation of absolutely continuous spectrum and give bounds on the Hausdorff dimension of the singular part of the spectral measure. We also discuss the analogs for orthogonal polynomials on the real line and unit circle.     

On Higher-Order Szegő Theorems with a Single Critical Point of Arbitrary Order

We prove the following higher-order Szeg? theorem: If a measure on the unit circle has absolutely continuous part \(w(\theta )\) and Verblunsky coefficients \(\alpha \) with square-summable variation, then for any positive integer m,

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is finite if and only if \(\alpha \in \ell ^{2m+2}\). This is the first known equivalence result of this kind in the regime of very slow decay, i.e., with \(\ell ^p\) conditions with arbitrarily large p. The usual difficulty of controlling higher-order sum rules is avoided by a new test sequence approach.

     

Thermal stability of the amorphous system As-Se-I

The effect of adding iodine to the binary systems As-Se on the thermal stability of the ternary glasses thus formed was investigated by DTA and DDTA. The investigated glasses corresponded to different regions of the phase diagram, i.e. they had different contents of As and I and, consequently, contained different types of structural units.In the investigated ternary systems with iodine, the crystallization effect appears at a lower temperature than in the binary glass As₄₀Se₆₀, and the same holds for the temperatures of softening and melting.For both binary and ternary systems, the activation energies of crystallization were determined. The glass As₄₀Se₆₀ exhibited a somewhat higher activation energy, i.e. a somewhat lower tendency to crystallize than the ternary system.The critical cooling rates of the melts for minimum degree of crystallinity were estimated. The obtained values are approximately equal for the binary (As₂Se₃) and ternary (AsSeI) systems.

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Zusammenfassung Mittels DTA und DDTA wurde untersucht, wie die Zugabe von Jod zu dem binären System As-Se die thermische Stabilität der so gebildeten ternären Gläser beeinflußt. Die untersuchten Gläser entsprechen verschiedenen Regionen des Phasendiagrammes, d.h. sie besitzen einen unterschiedlichen As- bzw. I-Gehalt und enthielten unterschiedlich geartete Struktureinheiten.Bei den untersuchten jodhaltigen ternären Systemen tritt der Kristallisationseffekt bei niedrigeren Temperaturen auf als bei den binären Gläsern As₄₀Se₆₀, das gleiche gilt für die Schmelz- als auch für die Erweichungstemperatur.Sowohl bei den binären als auch bei den ternären Systemen wurde die Aktivierungs energie für den Kristallisationsprozeß ermittelt. Das Glas As₄₀Se₆₀ zeigte eine etwas höhere Aktivierungsenergie, d.h. eine etwas geringere Neigung zur Kristallisation als das ternäre System.Für die kritische Abkühlgeschwindigkeit der Schmelzen zum Erreichen eines minimalen Kristallinitätsgrades wurden bei den binären (As₂Se₃) und ternären (AsSeI) Systemen annähernd gleiche Werte bestimmt.

     

Orthogonal Polynomials with Recursion Coefficients of Generalized Bounded Variation

We consider probability measures on the real line or unit circle with Jacobi or Verblunsky coefficients satisfying an ? ^p condition and a generalized bounded variation condition. This latter condition requires that a sequence can be expressed as a sum of sequences ?? ^(l), each of which has rotated bounded variation, i.e., $$\sum_{n=0}^\infty \vert e^{i\phi_l}\beta_{n+1}^{(l)} -\beta_n^{(l)}\vert < \infty$$ for some ${\phi_l}$ . This includes a large class of discrete Schr?dinger operators with almost periodic potentials modulated by ? ^p decay, i.e. linear combinations of ${\lambda_n {\rm cos}(2\pi\alpha n + \phi)}$ with ${\lambda \in \ell^p}$ of bounded variation and any ??. In all cases, we prove absence of singular continuous spectrum, preservation of absolutely continuous spectrum from the corresponding free case, and that pure points embedded in the continuous spectrum can only occur in an explicit finite set.     

Role of galectin-3 in tumour metastasis

We used metastatic variant of B16 melanoma (B16F1) to study lung colonization galectin-3-deficient (gal-3^−/−) C57BL/6 mice. In vivo study showed that compared with gal-3^+/+ mice, gal-3^−/−mice exhibited resistance to lung colonization of B16F1 melanoma cells (p < 0.03). In vitro assays showed higher number of attached malignant cells in the tissue section derived from gal-3^+/+ mice (p < 0.001) and tumor specific cytotoxicity of lymphoid cells of tumour inoculated gal-3^−/− suggesting that galectin-3 is considered as therapeutic target.     

An alkyl polyglucoside-mixed emulsifier as stabilizer of emulsion systems: the influence of colloidal structure on emulsions skin hydration potential

To be considered as a suitable vehicle for drugs/cosmetic actives, an emulsion system should have a number of desirable properties mainly dependent on surfactant used for its stabilization. In the current study, C(12-14) alkyl polyglucoside (APG)-mixed emulsifier of natural origin has been investigated in a series of binary (emulsifier concentration 10-25% (w/w)) and ternary systems with fixed emulsifier content (15% (w/w)) with or without glycerol. To elucidate the systems' colloidal structure the following physicochemical techniques were employed: polarization and transmission electron microscopy, X-ray diffraction (WAXD and SAXD), thermal analysis (DSC and TGA), complex rheological, pH, and conductivity measurements. Additionally, the emulsion vehicles' skin hydration potential was tested in vivo, on human skin under occlusion. In a series of binary systems with fixed emulsifier/water ratios ranging from 10/90 to 25/75 the predominance of a lamellar mesophase was found, changing its character from a liquid crystalline to a gel crystalline type. The same was observed in gel emulsions containing equal amounts of emulsifier and oil (15% (w/w)), but varying in glycerol content (0-25%). Different emulsion samples exhibited different water distribution modes in the structure, reflecting their rheological behavior and also their skin hydration capacity.