L p − Lq estimates for convolution operators with n-Dimensional singular measures

Let S ⊂ ℜⁿ⁺¹ be the graph of the function ϕ :[−1, 1] ⁿ → ℜ defined by ϕ (x ₁ , …, x_n) = ∑ _j=1 ⁿ |x_j|^αj, with1<α ₁ ≤ … ≤ α_n, let σ the Euclidean area measure on S. In this article we study the L^p − L^q boundedness of convolution operators with the singular Borel measure on Rⁿ⁺¹ given by μ (E)=σ (E ∩ S)     

Zeros of Gegenbauer and Hermite polynomials and connection coefficients

In this paper, sharp upper limit for the zeros of the ultraspherical polynomials are obtained via a result of Obrechkoff and certain explicit connection coefficients for these polynomials. As a consequence, sharp bounds for the zeros of the Hermite polynomials are obtained.

     

Thermotectonic and fault dynamic analysis of Precambrian basement and tectonic constraints with the Parana basin

The Precambrian crystalline basement of southeast Brazil is affected by many Phanerozoic reactivations of shear zones that developed during the end of the Neoproterozoic in the Brasiliano orogeny. These reactivations with specific tectonic events, a multidisciplinary study was done, involving geology, paleostress, and structural analysis of faults, associated with apatite fission track methods along the northeastern border of the Parana basin in southeast Brazil.The results show that the study area consists of three main tectonic domains, which record different episodes of uplift and reactivation of faults. These faults were brittle in character and resulted in multiple generations of fault products as pseudotachylytes and ultracataclasites, foliated cataclasites and fault gouges.Based on geological evidence and fission track data, an uplift of basement rocks and related tectonic subsidence with consequent deposition in the Parana basin were modeled.The reactivations of the basement record successive uplift events during the Phanerozoic dated via corrected fission track ages, at (Ordovician); (Triassic); (Jurassic), (Early Cretaceous); (Late Cretaceous) and (Late Cretaceous). These results indicate differential uplift of tectonic domains of basement units, probably related to Parana basin subsidence. Six major sedimentary units (supersequences) that have been deposited with their bounding unconformities, seem to have a close relationship with the orogenic events during the evolution of southwestern Gondwana.     

Historical sense in the historians of the theory of elasticity

This paper studies the historical and epistemological approaches followed by historians of the theory of elasticity. The authors chosen are Todhunter and Pearson, Love, Timoshenko, and Truesdell, who are perhaps the most important historians in English language since the second half of the nineteenth century. It is shown that the historical purpose has changed from one historian to the next, ranging from history as a compilation of what is known to criticism of the evolution of elasticity. The path of progress is investigated and again there are significant differences between historians although overall they have a sense of confluence towards some form of truth. The relation between history and theory is identified as a recurrent theme. And the epistemology in each author, although not explicitly stated, is seen to change following the main trends in their times or before. Some possible avenues of research are mentioned towards the end.     

Chromo‐Fluorogenic Detection of Nitroaromatic Explosives by Using Silica Mesoporous Supports Gated with Tetrathiafulvalene Derivatives

Three new hybrid gated mesoporous materials ( SN₃‐1 , SNH₂‐2 , and SN₃‐3 ) loaded with the dye [Ru(bipy)₃]²⁺ (bipy=bipyridine) and capped with different tetrathiafulvalene (TTF) derivatives (having different sizes and shapes and incorporating different numbers of sulfur atoms) have been prepared. The materials SN₃‐1 and SN₃‐3 are functionalized on their external surfaces with the TTF derivatives 1 and 3 , respectively, which were attached by employing the “click” chemistry reaction, whereas SNH₂‐2 incorporates the TTF derivative 2 , which was anchored to the solid through an amidation reaction. The final gated materials have been characterized by standard techniques. Suspensions of these solids in acetonitrile showed “zero release”, most likely because of the formation of dense TTF networks around the pore outlets. The release of the entrapped [Ru(bipy)₃]²⁺ dye from SN₃‐1 , SNH₂‐2 , and SN₃‐3 was studied in the presence of selected explosives (Tetryl, TNT, TNB, DNT, RDX, PETN, PA, and TATP). SNH₂‐2 showed a fairly selective response to Tetryl, whereas for SN₃‐1 and SN₃‐3 dye release was found to occur with Tetryl, TNT, and TNB. The uncapping process in the three materials can be ascribed to the formation of charge‐transfer complexes between the electron‐donating TTF units and the electron‐accepting nitroaromatic explosives. Finally, solids SNH₂‐2 and SN₃‐1 have been tested for Tetryl detection in soil with good results, pointing toward a possible use of these or similar hybrid capped materials as probes for the selective chromo‐fluorogenic detection of nitroaromatic explosives.     

A Closer Look at Spontaneous Mirror Symmetry Breaking in Aldol Reactions

The aldol reaction between acetone and 4‐nitrobenzaldehyde run in the nominal absence of any enantioselective catalyst was monitored by chiral HPLC with the aid of an internal standard. The collected data show the presence of a detectable initial enantiomeric excess of the aldol product in the early stages of the reaction in about 50 % of the experiments. Only a small fraction of the reaction contained the non‐racemic aldol product after 24 h. This temporary emergence of natural optical activity could be the signature of a coupled reaction network that leads to a spontaneous mirror‐symmetry‐breaking process, which originates at very low conversions (i.e., strongly depends on events taking place at the very first stages of the process). The reaction is not autocatalytic in the aldol product, which rules out a simple Frank‐type reaction network as the source of the observed symmetry breaking. On the other hand, the isolation and characterisation of a double‐aldol adduct suggested a reaction network that involved both indirect autocatalysis and indirect mutual inhibition between the enantiomers of the reaction product.     

A Sequential Method to Prepare Polymorphs and Solvatomorphs of [Fe(1,3‐bpp)2](ClO4)2⋅nH2O (n=0, 1, 2) with Varying Spin‐Crossover Behaviour

Two polymorphs of the spin crossover (SCO) compound [Fe(1,3‐bpp)₂](ClO₄)₂ ( 1 and 2 ; 1,3‐bpp=2‐(pyrazol‐1‐yl)‐6‐(pyrazol‐3‐yl)pyridine) were prepared using a novel, stepwise procedure. Crystals of 1 deposit from dry solvents, while 2 is obtained from a solid‐state procedure, by sequentially removing lattice H₂O molecules from the solvatomorph [Fe(1,3‐bpp)₂](ClO₄)₂?2 H₂O ( 2 ?2 H₂O), using single‐crystal‐to‐single‐crystal (SCSC) transformations. Hydrate 2 ?2 H₂O is obtained through the same reaction as 1 , now with 2.5 % of water added. Compounds 2 and 2 ?2 H₂O are unstable in the atmosphere and absorb or lose one equivalent of water, respectively, to both yield the stable solvatomorph [Fe(1,3‐bpp)₂](ClO₄)₂?H₂O ( 2 ?H₂O), also following SCSC processes. The four derivatives have been characterised by single‐crystal X‐ray diffraction (SCXRD). Furthermore, the homogeneity of the various compounds as well as their SCSC interconversions have been confirmed by powder X‐ray diffraction (PXRD). Polymorphs 1 and 2 exhibit abrupt SCO behaviour near room temperature with T_1/2↑=279/316 K and T_1/2↓=276/314 K (near 40 K of shift) and different cooperativity.     

Efficient transmission calculations for polydisperse water sprays using spectral scaling

Analytical expressions are developed to scale the extinction, scattering and absorption coefficients as a function of the Sauter mean diameter for polydisperse water sprays in fire suppression systems. A scaling procedure is introduced to avoid prohibitive exact integration of the functions obtained from Mie theory resulting in several orders in magnitude of computational savings. Spectral-based and total transmission of real spray distributions using the scaling procedure are compared to exact results and experimental data. Results show the proposed scaling procedure yields significant computational savings with little loss in accuracy for predictions of spectral and total transmission.     

Structure of triplex DNA in the gas phase

Extensive (more than 90 microseconds) molecular dynamics simulations complemented with ion-mobility mass spectrometry experiments have been used to characterize the conformational ensemble of DNA triplexes in the gas phase. Our results suggest that the ensemble of DNA triplex structures in the gas phase is well-defined over the experimental time scale, with the three strands tightly bound, and for the most abundant charge states it samples conformations only slightly more compact than the solution structure. The degree of structural alteration is however very significant, mimicking that found in duplex and much larger than that suggested for G-quadruplexes. Our data strongly supports that the gas phase triplex maintains an excellent memory of the solution structure, well-preserved helicity, and a significant number of native contacts. Once again, a linear, flexible, and charged polymer as DNA surprises us for its ability to retain three-dimensional structure in the absence of solvent. Results argue against the generally assumed roles of the different physical interactions (solvent screening of phosphate repulsion, hydrophobic effect, and solvation of accessible polar groups) in modulating the stability of DNA structures.