A large deviations principle for stochastic flows of viscous fluids

We study the well-posedness of a stochastic differential equation on the two dimensional torus ${\mathbb{T}}^2$, driven by an infinite dimensional Wiener process with drift in the Sobolev space $L^2(0,T;H^1\left({\mathbb{T}}^2\right))$. The solution corresponds to a stochastic Lagrangian flow in the sense of DiPerna Lions. By taking into account that the motion of a viscous incompressible fluid on the torus can be described through a suitable stochastic differential equation of the previous type, we study the inviscid limit. By establishing a large deviations principle, we show that, as the viscosity goes to zero, the Lagrangian stochastic Navier–Stokes flow approaches the Euler deterministic Lagrangian flow with an exponential rate function.     

Algebraic reflexivity of sets of bounded operators on vector valued Lipschitz functions

In this paper we establish algebraic reflexivity properties of subsets of bounded linear operators acting on spaces of vector valued Lipschitz functions. We also derive a representation for the generalized bi-circular projections on these spaces.     

Differential equations in Schatten classes of operators

We study a system of differential equations in Schatten classes of operators, ${\mathcal{C}_p(\mathcal{H})\,(1 \leq p < \infty}$ ), with ${\mathcal{H}}$ a separable complex Hilbert space. The systems considered are infinite dimensional generalizations of mathematical models of unsupervised learning. In this new setting, we address the usual questions of existence and uniqueness of solutions. Under some restrictions on the spectral properties of the initial conditions, we explicitly solve the system. We also discuss the long-term behavior of solutions.     

Structure of trans-1,4-polybutadiene synthesized with a new catalyst system

Abstract

The structure, phase composition, and temperature behavior of two trans-1,4-polybutadienes (TPBs) were studied by means of x-ray scattering and differential scanning calorimetry (DSC) techniques. The two samples examined were (1) PB synthesized using an immobilized titanium-magnesium catalyst and (2) a random copolymer based on PB prepared with a homogeneous vanadium-containing catalyst used as a reference material. It was found that the nascent structure of the first PB involves three phases: crystalline, mesomorphic (low-temperature form), and amorphous. In the vicinity of 65°C, a first-order phase transition occurs. The system becomes biphasic and contains the high-temperature form of the mesophase, as well as the amorphous phase, component. Above 165°C, the polymer melts to form a single-phase isotropic melt with a structure typical of liquids. The lateral dimension of crystallites reversibly changes at the crystal-mesophase transition. It is suggested that during annealing of the mesophase formed by cooling of the isotropic melt, the chains acquire an extended conformation. Loss of regularity of the structure of macromolecules of TPB causes a reduction of phase transition temperatures, an increase of the imperfection of the crystalline phase, and a contraction of the temperature range of existence of the mesophase.     

Influence of the blend compatibility on the morphology of thin polymer blend films

Thin films of incompatible polymer blends can form a variety of structures on preparation. For the polymer blend system consisting of two poly(styrene-co-para-bromo-styrene)s at different degrees of bromination, PBr_xS/PBr_yS, the compatibility can be tuned through a variation of the difference in the degree of bromination. Within this blend system, two series of samples with different compatibilities were investigated at various blend compositions. The surface morphology of the thin films was investigated by atomic force microscopy (AFM) measurements, while diffuse X-ray scattering provided additional depth sensitivity at a comparable lateral resolution. The results are indicative for phase separation lateral, as well as perpendicular, to the sample surface.     

Fucoxanthin Holds Potential to Become a Drug Adjuvant in Breast Cancer Treatment: Evidence from 2D and 3D Cell Cultures

Fucoxanthin (Fx) is a carotenoid derived from marine organisms that exhibits anticancer activities. However, its role as a potential drug adjuvant in breast cancer (BC) treatment is still poorly explored. Firstly, this study investigated the cytotoxic effects of Fx alone and combined with doxorubicin (Dox) and cisplatin (Cis) on a panel of 2D-cultured BC cell lines (MCF7, SKBR3 and MDA-MB-231) and one non-tumoral cell line (MCF12A). Fucoxanthin induced cytotoxicity against all the cell lines and potentiated Dox cytotoxic effects towards the SKBR3 and MDA-MB-231 cells. The combination triggering the highest cytotoxicity (Fx 10 µM + Dox 1 µM in MDA-MB-231) additionally showed significant induction of cell death and genotoxic effects, relative to control. In sequence, the same combination was tested on 3D cultures using a multi-endpoint approach involving bioactivity assays and microscopy techniques. Similar to 2D cultures, the combination of Fx and Dox showed higher cytotoxic effects on 3D cultures compared to the isolated compounds. Furthermore, this combination increased the number of apoptotic cells, decreased cell proliferation, and caused structural and ultrastructural damages on the 3D models. Overall, our findings suggest Fx has potential to become an adjuvant for Dox chemotherapy regimens in BC treatment.     

Isometries on spaces of vector valued Lipschitz functions

This paper gives a characterization of a class of surjective isometries on spaces of Lipschitz functions with values in a finite dimensional complex Hilbert space.     

Phytochemical Constituents,Antioxidant Activity,and Toxicity Assessment of the Aerial Part Extracts from the Infraspecific Taxa of Matthiola fruticulosa (Brassicaceae) Endemic to Sicily

In a project designed to investigate the specific and infraspecific taxa of Matthiola endemic to Sicily (Italy) as new potential sources of bioactive compounds in this work, the infraspecific taxa of Matthiola fruticulosa were studied, namely, subsp. fruticulosa and subsp. coronopifolia. HPLC–PDA/ESI–MS and SPME–GC/MS analyses of hydroalcoholic extracts obtained from the aerial parts of the two subspecies led to the detection of 51 phenolics and 61 volatile components, highlighting a quite different qualitative–quantitative profile. The antioxidant properties of the extracts were explored through in vitro methods: 1,1-diphenyl-2-picrylhydrazyl (DPPH), reducing power and Fe²⁺ chelating activity assays. The results of the antioxidant tests showed that the extracts possess a different antioxidant ability: particularly, the extract of M. fruticulosa subsp. fruticulosa exhibited higher radical scavenging activity than that of subsp. coronopifolia (IC₅₀ = 1.25 ± 0.02 mg/mL and 2.86 ± 0.05 mg/mL), which in turn displayed better chelating properties (IC₅₀ = 1.49 ± 0.01 mg/mL and 0.63 ± 0.01 mg/mL). Lastly, Artemia salina lethality bioassay was performed for toxicity assessment. The results of the bioassay showed lack of toxicity against brine shrimp larvae for both extracts. The data presented indicate the infraspecific taxa of M. fruticulosa as new and safe sources of antioxidant compounds.     

Transitive A 6-invariant k-arcs in PG(2, q)

For q = p ^r with a prime p ≥ 7 such that ${q \equiv 1}$ or 19 (mod 30), the desarguesian projective plane PG(2, q) of order q has a unique conjugacy class of projectivity groups isomorphic to the alternating group A ₆ of degree 6. For a projectivity group ${\Gamma \cong A_6}$ of PG(2, q), we investigate the geometric properties of the (unique) Γ-orbit ${\mathcal{O}}$ of size 90 such that the 1-point stabilizer of Γ in its action on ${\mathcal O}$ is a cyclic group of order 4. Here ${\mathcal O}$ lies either in PG(2, q) or in PG(2, q ²) according as 3 is a square or a non-square element in GF(q). We show that if q ≥ 349 and q ≠ 421, then ${\mathcal O}$ is a 90-arc, which turns out to be complete for q = 349, 409, 529, 601,661. Interestingly, ${\mathcal O}$ is the smallest known complete arc in PG(2,601) and in PG(2,661). Computations are carried out by MAGMA.