On the Hörmander Classes of Bilinear Pseudodifferential Operators

Bilinear pseudodifferential operators with symbols in the bilinear analog of all the Hörmander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise results about which classes are closed under transposition and can be characterized in terms of asymptotic expansions are presented. This work extends the results for more limited classes studied before in the literature and, hence, allows the use of the symbolic calculus (when it exists) as an alternative way to recover the boundedness on products of Lebesgue spaces for the classes that yield operators with bilinear Calderón–Zygmund kernels. Some boundedness properties for other classes with estimates in the form of Leibniz’ rule are presented as well.     

Compact complete null curves in complex 3-space

We prove that for any open orientable surface S of finite topology, there exist a Riemann surface M, a relatively compact domain M ? M and a continuous map X: $\overline M $ → ?³ such that:

• M and M are homeomorphic to S, M-M and M ? $\overline M $ contain no relatively compact components in M
• X| _M is a complete null holomorphic curve, $X{|_{\overline M - M}}:\overline M - M \to {{\Bbb C}^3}$ is an embedding and the Hausdorff dimension of X( $\overline M $ ?M) is 1.

Moreover, for any ε > 0 and compact null holomorphic curve Y:N→?³ with non-empty boundary Y (?N), there exist Riemann surfaces M and M homeomorphic to N ^○ and a map X: $\overline M $ → ?³ in the above conditions such that δ ^H (Y(?N),X( $\overline M $ ? M)) < ε, where δ ^H (·,·) means Hausdorff distance in ?³.     

The obrechkoff integral transform: properties and relation to a generalized fractional calculus

This survey is devoted to one of the most general Laplace-type integral transforms, the so-called Obrechkoff integral transform, introduced and studied for the first time by Obrechkoff[25]. It has been modified by Dimovski [5],[6] and used as a basis of a Mikusinski-type operational calculus for the hyper-Bessel differential operators of arbitrary order. Later, in a series of papers Dimovski and Kiryakova [8],[9],[10] have found operational properties, complex and real inversion formulas, Abel-type theorems for the Obrechkoff transform. This theory has been further developed by Kiryakova [16],[17],[18] using the tools of the Meijer's G-functions and of the fractional calculus. Namely, a new definition as a G-transform has been given for the Obrechkoff transform. The hyper-Bessel operators themselves, have given rise to a new generalized fractional calculus and further extensive use of the G-functions. Many other generalized differentiation and integration operators happen to be special cases in this calculus, too. Special cases of the Obrechkoff transform have been "rediscovered" later by many authors. We give examples how their results could be derived from the general ones surveyed here.     

Gutmann's Donor Numbers Correctly Assess the Effect of the Solvent on the Kinetics of SNAr Reactions in Ionic Liquids

We report an experimental study on the effect of solvents on the model S_NAr reaction between 1‐chloro‐2,4‐dinitrobenzene and morpholine in a series of pure ionic liquids (IL). A significant catalytic effect is observed with reference to the same reaction run in water, acetonitrile, and other conventional solvents. The series of IL considered include the anions, NTf₂^?, DCN^?, SCN^?, CF₃SO₃^?, PF₆^?, and FAP^? with the series of cations 1‐butyl‐3‐methyl‐imidazolium ([BMIM]⁺), 1‐ethyl‐3‐methyl‐imidazolium ([EMIM]⁺), 1‐butyl‐2,3‐dimethyl‐imidazolium ([BM₂IM]⁺), and 1‐butyl‐1‐methyl‐pyrrolidinium ([BMPyr]⁺). The observed solvent effects can be attributed to an “anion effect”. The anion effect appears related to the anion size (polarizability) and their hydrogen‐bonding (HB) abilities to the substrate. These results have been confirmed by performing a comparison of the rate constants with Gutmann's donicity numbers (DNs). The good correlation between rate constants and DN emphasizes the major role of charge transfer from the anion to the substrate.     

Incompatible elements in bottom sediments of the Itaipú Dam Reservoir by EDXRF

Journal of Radioanalytical and Nuclear Chemistry - Sediments play an important role in the distribution of trace elements in the aquatic system and act as a sink for metals. Incompatible elements...     

Studies towards the synthesis of ertugliflozin from l-Arabinose

A new method for the diastereoselective synthesis of enantiomerically pure ertugliflozin was developed. The crucial step involves an aldol condensation between 1-(4-chloro-3-(4-ethoxybenzyl)phenyl)ethanone and (4R,5R)-5-(((tert-butyldimethylsilyl)oxy)methyl)-2,2-dimethyl-5-((trityloxy)methyl)-1,3-dioxolane-4-carbaldehyde, which was prepared from known 2-C-trityloxymethyl-2,3-O-isopropylidene-l-erythrose (easily accessible in three steps from l-arabinose) by standard reduction/oxidation and protection/deprotection manipulations. Dihydroxylation of the aldol condensation product and further global deprotection led to the formation of the target molecule.     

Limit sets for complete minimal immersions

In this paper we study the behaviour of the limit set of complete proper compact minimal immersions in a domain with the boundary We prove that the second fundamental form of the surface ∂G is nonnegatively defined at every point of the limit set of such immersions. A. Alarcón’s research is partially supported by MEC-FEDER Grant no. MTM2004-00160.     

Photosensitizer-Mesoporous Silica Nanoparticles Combination for Enhanced Photodynamic Therapy†

Mesoporous silica nanoparticles (MSNs) are widely known for their versatile applications. One of the most extended is as drug delivery systems for the treatment of cancer and other diseases. This review compiles the most representative examples in the last years of functionalized MSNs as photosensitizer carriers for photodynamic therapy (PDT) against cancer. Several commercially available photosensitizers (PSs) demonstrated poor solubility in an aqueous medium and insufficient selectivity for cancer tissues. The tumor specificity of PSs is a key factor for enhancing the PDT effect and at the same time reducing side effects. The use of nanoparticles and particularly MSNs, in which PS is covalently anchored or physically embedded, can overcome these limitations. For that, PS-MSNs can be externally decorated with compounds of interest in order to act as an active target for certain cancer cells, demonstrating enhanced phototoxicity in vitro and in vivo. The objective of this review is to collect and compare different nanosystems based on PS-MSNs pointing out their advantages in PDT against diverse types of cancers.