Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by Lp-modulus of smoothness

We prove a sharp estimate for the k-modulus of smoothness, modelled upon a $L^p$-Lebesgue space, of a function f in $W^k{L}^{\frac{pn}{n+kp},p}(\mathrm{\Omega })$, where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, $k,n\in \mathbb{N}$, $k<n$ and $\frac{n}{n?k}<p<+\infty$. This sharp estimate is used to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces into generalized Hölder spaces defined by means of the k-modulus of smoothness. General results are illustrated with examples. In particular, we obtain a generalization of the classical Jawerth embeddings.     

Scanning electron microscopy of Ancylostoma spp. dog infective larvae captured and destroyed by the nematophagous fungus Duddingtonia flagrans

The interaction between the nematode-trapping fungus Duddingtonia flagrans (isolate CG768) against Ancylostoma spp. dog infective larvae (L₃) was evaluated by means of scanning electron microscopy. Adhesive network trap formation was observed 6 h after the beginning of the interaction, and the capture of Ancylostoma spp. L₃ was observed 8 h after the inoculation these larvae on the cellulose membranes colonized by the fungus. Scanning electron micrographs were taken at 0, 12, 24, 36 and 48 h, where 0 is the time when Ancylostoma spp. L₃ was first captured by the fungus. Details of the capture structure formed by the fungus were described. Nematophagous Fungus Helper Bacteria (NHB) were found at interactions points between the D. flagrans and Ancylostoma spp. L₃. The cuticle penetration by the differentiated fungal hyphae with the exit of nematode internal contents was observed 36 h after the capture. Ancylostoma spp. L₃ were completely destroyed after 48 h of interaction with the fungus. The scanning electron microscopy technique was efficient on the study of this interaction, showing that the nematode-trapping fungus D. flagrans (isolate CG768) is a potential exterminator of Ancylostoma spp. L₃.     

Temperature dependence of the Ho L2‐edge XMCD spectra of Ho6Fe23

An X‐ray magnetic circular dichroism (XMCD) study performed at the Ho L_2,3‐edges in Ho₆Fe₂₃ as a function of temperature is presented. It is demonstrated that the anomalous temperature dependence of the Ho L₂‐edge XMCD signal is due to the magnetic contribution of Fe atoms. By contrast, the Ho L₃‐edge XMCD directly reflects the temperature dependence of the Ho magnetic moment. By combining the XMCD at both Ho L₂‐ and L₃‐edges, the possibility of determining the temperature dependence of the Fe magnetic moment is demonstrated. Then, both μ_Ho(T) and μ_Fe(T) have been determined by tuning only the absorption L‐edges of Ho. This result opens new possibilities of applying XMCD at these absorption edges to obtain quantitative element‐specific magnetic information that is not directly obtained by other experimental tools.     

The Extremal Truncated Moment Problem

For a degree 2n real d-dimensional multisequence to have a representing measure μ, it is necessary for the associated moment matrix to be positive semidefinite and for the algebraic variety associated to β, , to satisfy rank card as well as the following consistency condition: if a polynomial vanishes on , then . We prove that for the extremal case , positivity of and consistency are sufficient for the existence of a (unique, rank -atomic) representing measure. We also show that in the preceding result, consistency cannot always be replaced by recursiveness of . The first-named author’s research was partially supported by NSF Research Grants DMS-0099357 and DMS-0400741. The second-named author’s research was partially supported by NSF Research Grant DMS-0201430 and DMS-0457138.     

Radium equivalent and annual effective dose from geological samples from Pedra – Pernambuco – Brazil

The natural radioactivity of an uranium-anomalous area utilized for agricultural activities in Pedra, Brazil, was monitored. For this, samples from the granite and calcium-silicate amphibole rocks underlying this area and also from samples of the soil derived from these rocks were collected and analyzed by high-resolution gamma spectrometry. The equivalent radium (Ra_eq) was used as a reference for estimating the rate of the effective equivalent dose. The average, minimum and maximum values for the samples were of 319.2 Bq kg^?1 (91.1–758.5 Bq kg^?1) for soil; 327.5 Bq kg^?1 (36.3–1624.0 Bq kg^?1) for granitic rocks and 70,124.5 Bq kg^?1 (16,979.6–147,159.0 Bq kg^?1) for the calcium-silicate amphibole rocks. An estimation of the external exposition was carried out based on the calculation of the parameters obtained.     

A strict topology on Orlicz spaces

Let φ be a Young function, Ω be a locally compact space, and μ be a positive Radon measure on Ω. We consider a strict topology (in the sense of Sentilles‐Taylor) on the Orlicz function space and investigate various properties of this locally convex topology. We also study the Orlicz space of a locally compact group G with a left Haar measure under the strict topology and certain other natural locally convex topologies. Finally we present some results on various continuity properties of convolution operators on under the topology and other natural ones.     

Joins of 1-planar graphs

A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once.In this paper,we study 1-planar graph joins.We prove that the join G + H is 1-planar if and only if the pair [G,H] is subgraph-majorized by one of pairs [C3 ∪ C3,C3],[C4,C4],[C4,C3],[K2,1,1,P3] in the case when both elements of the graph join have at least three vertices.If one element has at most two vertices,then we give several necessary/sufficient conditions for the bigger element.