The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

Serum protein layers on parylene-C and silicon oxide: effect on cell adhesion

Among the range of materials used in bioengineering, parylene-C has been used in combination with silicon oxide and in presence of the serum proteins, in cell patterning. However, the structural properties of adsorbed serum proteins on these substrates still remain elusive. In this study, we use an optical biosensing technique to decipher the properties of fibronectin (Fn) and serum albumin adsorbed on parylene-C and silicon oxide substrates. Our results show the formation of layers with distinct structural and adhesive properties. Thin, dense layers are formed on parylene-C, whereas thicker, more diffuse layers are formed on silicon oxide. These results suggest that Fn acquires a compact structure on parylene-C and a more extended structure on silicon oxide. Nonetheless, parylene-C and silicon oxide substrates coated with Fn host cell populations that exhibit focal adhesion complexes and good cell attachment. Albumin adopts a deformed structure on parylene-C and a globular structure on silicon oxide, and does not support significant cell attachment on either surface. Interestingly, the co-incubation of Fn and albumin at the ratio found in serum, results in the preferential adsorption of albumin on parylene-C and Fn on silicon oxide. This finding is supported by the exclusive formation of focal adhesion complexes in differentiated mouse embryonic stem cells (CGR8), cultured on Fn/albumin coated silicon oxide, but not on parylene-C. The detailed information provided in this study on the distinct properties of layers of serum proteins on substrates such as parylene-C and silicon oxide is highly significant in developing methods for cell patterning.

Vistas on the C. & M.

Mode of access: Internet.

Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces

2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20.

Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω

Mathematics Subject Classification: 26A16, 26A33, 46E15.

ON SPACES OF COMPACT OPERATORS ON C(K, X) SPACES

This paper concerns the spaces of compact operators kappa(E,F), where E and F are Banach spaces C([1, xi], X) of all continuous X-valued functions defined on the interval of ordinals [1, xi] and equipped with the supremun norm. We provide sufficient conditions on X, Y, alpha, beta, xi and eta, with omega <= alpha <= beta < omega 1 for the following equivalence: (a) kappa(C([1, xi], X), C([1, alpha], Y)) is isomorphic to kappa(C([1,eta], X), C([1, beta], Y)), (b) beta < alpha(omega). In this way, we unify and extend results due to Bessaga and Pelczynski (1960) and C. Samuel (2009). Our result covers the case of the classical spaces X = l(p) and Y = l(q) with 1 < p, q < infinity.

HSU-Robbins and Spitzer's theorems for the variations of fractional Brownian motion

Using recent results on the behavior of multiple Wiener-Itô integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.

On the Schoenberg transformations in data analysis: theory and illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A distance-based discriminant algorithm and a robust multidimensional centroid estimate illustrate the theory, closely connected to the Gaussian kernels of Machine Learning.

Lateral boundary contributions to wave-activity invariants and nonlinear stability theorems for balanced dynamics

The slow advective-timescale dynamics of the atmosphere and oceans is referred to as balanced dynamics. An extensive body of theory for disturbances to basic flows exists for the quasi-geostrophic (QG) model of balanced dynamics, based on wave-activity invariants and nonlinear stability theorems associated with exact symmetry-based conservation laws. In attempting to extend this theory to the semi-geostrophic (SG) model of balanced dynamics, Kushner & Shepherd discovered lateral boundary contributions to the SG wave-activity invariants which are not present in the QG theory, and which affect the stability theorems. However, because of technical difficulties associated with the SG model, the analysis of Kushner & Shepherd was not fully nonlinear. This paper examines the issue of lateral boundary contributions to wave-activity invariants for balanced dynamics in the context of Salmon's nearly geostrophic model of rotating shallow-water flow. Salmon's model has certain similarities with the SG model, but also has important differences that allow the present analysis to be carried to finite amplitude. In the process, the way in which constraints produce boundary contributions to wave-activity invariants, and additional conditions in the associated stability theorems, is clarified. It is shown that Salmon's model possesses two kinds of stability theorems: an analogue of Ripa's small-amplitude stability theorem for shallow-water flow, and a finite-amplitude analogue of Kushner & Shepherd's SG stability theorem in which the ‘subsonic’ condition of Ripa's theorem is replaced by a condition that the flow be cyclonic along lateral boundaries. As with the SG theorem, this last condition has a simple physical interpretation involving the coastal Kelvin waves that exist in both models. Salmon's model has recently emerged as an important prototype for constrained Hamiltonian balanced models. The extent to which the present analysis applies to this general class of models is discussed.

Theorems on the Convergence of Series in Generalized Lommel-Wright Functions

Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20

Mechanisms Predisposing Penile Fracture And Long-term Outcomes On Erectile And Voiding Functions.

Purpose. To determine the mechanisms predisposing penile fracture as well as the rate of long-term penile deformity and erectile and voiding functions. Methods. All fractures were repaired on an emergency basis via subcoronal incision and absorbable suture with simultaneous repair of eventual urethral lesion. Patients' status before fracture and voiding and erectile functions at long term were assessed by periodic follow-up and phone call. Detailed history included cause, symptoms, and single-question self-report of erectile and voiding functions. Results. Among the 44 suspicious cases, 42 (95.4%) were confirmed, mean age was 34.5 years (range: 18-60), mean follow-up 59.3 months (range 9-155). Half presented the classical triad of audible crack, detumescence, and pain. Heterosexual intercourse was the most common cause (28 patients, 66.7%), followed by penile manipulation (6 patients, 14.3%), and homosexual intercourse (4 patients, 9.5%). Woman on top was the most common heterosexual position (n = 14, 50%), followed by doggy style (n = 8, 28.6%). Four patients (9.5%) maintained the cause unclear. Six (14.3%) patients had urethral injury and two (4.8%) had erectile dysfunction, treated by penile prosthesis and PDE-5i. No patient showed urethral fistula, voiding deterioration, penile nodule/curve or pain. Conclusions. Woman on top was the potentially riskiest sexual position (50%). Immediate surgical treatment warrants long-term very low morbidity.

Action Of Essential Oils From Brazilian Native And Exotic Medicinal Species On Oral Biofilms.

Essential oils (EO) obtained from twenty medicinal and aromatic plants were evaluated for their antimicrobial activity against the oral pathogens Candida albicans, Fusobacterium nucleatum, Porphyromonas gingivalis, Streptococcus sanguis and Streptococcus mitis. The antimicrobial activity of the EO was evaluates by microdilution method determining Minimal Inhibitory Concentration. Chemical analysis of the oils compounds was performed by Gas chromatography-mass spectrometry (CG-MS). The most active EO were also investigated as to their actions on the biolfilm formation. The most of the essential oils (EO) presented moderate to strong antimicrobial activity against the oral pathogens (MIC--Minimal Inhibitory Concentrations values between 0.007 and 1.00 mg/mL). The essential oil from Coriandrum sativum inhibited all oral species with MIC values from 0.007 to 0.250 mg/mL, and MBC/MFC (Minimal Bactericidal/Fungicidal Concentrations) from 0.015 to 0.500 mg/mL. On the other hand the essential oil of C. articulatus inhibited 63.96% of S. sanguis biofilm formation. Through Scanning Eletronic Microscopy (SEM) images no changes were observed in cell morphology, despite a decrease in biofilm formation and changes on biofilm structure. Chemical analysis by Gas Chromatography-Mass Spectrometry (GC-MS) of the C. sativum essential oil revealed major compounds derivatives from alcohols and aldehydes, while Cyperus articulatus and Aloysia gratissima (EOs) presented mono and sesquiterpenes. In conclusion, the crude oil from C. articulatus exhibited the best results of antimicrobial activity e ability to control biofilm formation. The chemical analysis showed the presence of terpenes and monoterpenes such as a-pinene, a-bulnesene and copaene. The reduction of biofilms formation was confirmed from SEM images. The results of this research shows a great potential from the plants studied as new antimicrobial sources.

Clustering Of Water Bodies In Unpolluted And Polluted Environments Based On Escherichia Coli Phylogroup Abundance Using A Simple Interaction Database.

Different types of water bodies, including lakes, streams, and coastal marine waters, are often susceptible to fecal contamination from a range of point and nonpoint sources, and have been evaluated using fecal indicator microorganisms. The most commonly used fecal indicator is Escherichia coli, but traditional cultivation methods do not allow discrimination of the source of pollution. The use of triplex PCR offers an approach that is fast and inexpensive, and here enabled the identification of phylogroups. The phylogenetic distribution of E. coli subgroups isolated from water samples revealed higher frequencies of subgroups A1 and B23 in rivers impacted by human pollution sources, while subgroups D1 and D2 were associated with pristine sites, and subgroup B1 with domesticated animal sources, suggesting their use as a first screening for pollution source identification. A simple classification is also proposed based on phylogenetic subgroup distribution using the w-clique metric, enabling differentiation of polluted and unpolluted sites.

Contrasting Effects Of Land Use Intensity And Exotic Host Plants On The Specialization Of Interactions In Plant-herbivore Networks.

Human land use tends to decrease the diversity of native plant species and facilitate the invasion and establishment of exotic ones. Such changes in land use and plant community composition usually have negative impacts on the assemblages of native herbivorous insects. Highly specialized herbivores are expected to be especially sensitive to land use intensification and the presence of exotic plant species because they are neither capable of consuming alternative plant species of the native flora nor exotic plant species. Therefore, higher levels of land use intensity might reduce the proportion of highly specialized herbivores, which ultimately would lead to changes in the specialization of interactions in plant-herbivore networks. This study investigates the community-wide effects of land use intensity on the degree of specialization of 72 plant-herbivore networks, including effects mediated by the increase in the proportion of exotic plant species. Contrary to our expectation, the net effect of land use intensity on network specialization was positive. However, this positive effect of land use intensity was partially canceled by an opposite effect of the proportion of exotic plant species on network specialization. When we analyzed networks composed exclusively of endophagous herbivores separately from those composed exclusively of exophagous herbivores, we found that only endophages showed a consistent change in network specialization at higher land use levels. Altogether, these results indicate that land use intensity is an important ecological driver of network specialization, by way of reducing the local host range of herbivore guilds with highly specialized feeding habits. However, because the effect of land use intensity is offset by an opposite effect owing to the proportion of exotic host species, the net effect of land use in a given herbivore assemblage will likely depend on the extent of the replacement of native host species with exotic ones.