Rigidity theorems for hypersurfaces with constant mean curvature

Let M ⁿ be a compact oriented hypersurface of a unit sphere \(\mathbb{S}^{n + 1} \) (1) with constant mean curvature H. Given an integer k between 2 and n ? 1, we introduce a tensor ? related to H and to the second fundamental form A of M, and show that if |?|² ≤ B _H,k and tr(? ³) ≤ C _n,k |?|³, where B _H,k and C _n,k are numbers depending only on H, n and k, then either |?|² ≡ 0 or |?|² ≡ B _H,k . We characterize all M ⁿ with |?|² ≡ B _H,k . We also prove that if \(\left| A \right|^2 \leqslant 2\sqrt {k(n - k)}\) and tr(? ³) ≤ C _n,k |?|³ then |A|² is constant and characterize all M ⁿ with |A|² in the interval \(\left[ {0,2\sqrt {k\left( {n - k} \right)} } \right] \) . We also study the behavior of |?|², with the condition additional tr(? ³) ≤ C _n,k |?|³, for complete hypersurfaces with constant mean curvature immersed in space forms and show that if sup _M |?|² = B _H,k and this supremum is attained in M ⁿ then M ⁿ is an isoparametric hypersurface with two distinct principal curvatures of multiplicities k y n ? k. Finally, we use rotation hypersurfaces to show that the condition on the trace of ? ³ is necessary in our results; more precisely, for each integer k with 2 ≤ k ≤ n ? 1 and \(H \geqslant 1/\sqrt {2n - 1} \) there is a complete hypersurface M ⁿ in \(\mathbb{S}^{n + 1} \) (1) with constant mean curvature H such that sup _M |?|² = B _H,k , and this supremum is attained in M ⁿ , and which is not a product of spheres.     

On the Conformation of Dimeric Acceptors and Their Polymer Solar Cells with Efficiency over 18 %

The determination of molecular conformations of oligomeric acceptors (OAs) and their impact on molecular packing are crucial for understanding the photovoltaic performance of their resulting polymer solar cells (PSCs) but have not been well studied yet. Herein, we synthesized two dimeric acceptor materials, DIBP3F-Se and DIBP3F-S, which bridged two segments of Y6-derivatives by selenophene and thiophene, respectively. Theoretical simulation and experimental 1D and 2D NMR spectroscopic studies prove that both dimers exhibit O-shaped conformations other than S- or U-shaped counter-ones. Notably, this O-shaped conformation is likely governed by a distinctive “conformational lock” mechanism, arising from the intensified intramolecular π–π interactions among their two terminal groups within the dimers. PSCs based on DIBP3F-Se deliver a maximum efficiency of 18.09 %, outperforming DIBP3F-S-based cells (16.11 %) and ranking among the highest efficiencies for OA-based PSCs. This work demonstrates a facile method to obtain OA conformations and highlights the potential of dimeric acceptors for high-performance PSCs.     

Structural and spectroscopic characterization of epiisopiloturine-metal complexes,and anthelmintic activity vs. S. mansoni

Epiisopiloturine (EPI), extracted from leaves of Pilocarpus microphyllus, a plant originally from the Amazon and Savanna regions in Brazil, was described as a potential drug against Schistosomiasis, a neglected severe disease. Herein, EPI was complexed with copper(II) or zinc(II) salts and the isolated species, [Cu(epi)₄](ClO₄)₂ (1) and [Zn(epi)₂Cl₂] (2), were structurally and spectroscopically characterized. By using X-ray diffraction, the crystal structures of both metal complexes were determined, indicating a square pyramidal geometry for copper for 1 and a tetrahedral environment around zinc for 2. EPR spectra of 1 show a typical tetragonal environment around the central metal ion with some tetrahedral distortion, both in the solid state and in frozen acetonitrile solution, in accordance with crystallographic data. For 2, NMR spectra have bands consistent with a tetrahedral species in solid state or in DMSO-d₆ solution. These spectroscopic characterization data were further supported by Density Functional Theory calculations, showing that these metal complexes are also stable in solution. Those metal complexes were tested against adult worms of Schistosoma mansoni, in comparison to the free alkaloid as anthelmintic agent. Coordination with copper(II) improved the alkaloid schistosomicidal properties, while binding to zinc(II) decreased its activity.     

Numerical estimates of acoustic fields in the ocean generated by moving airborne sources

We investigate the underwater acoustic field in the stratified ocean generated by moving in the air sources. We obtain asymptotic formulas expressed in terms of the retarded time and the Doppler-shifted frequency. The spectral parameter power series method is implemented to find the wave numbers of the propagating modes, their group velocity and an analytic form of the acoustic field in the ocean. Some numerical results are presented.     

Analysis and design of photobioreactors for microalgae production II: experimental validation of a radiation field simulator based on a Monte Carlo algorithm

In a previous study, we developed a methodology to assess the intrinsic optical properties governing the radiation field in algae suspensions. With these properties at our disposal, a Monte Carlo simulation program is developed and used in this study as a predictive autonomous program applied to the simulation of experiments that reproduce the common illumination conditions that are found in processes of large scale production of microalgae, especially when using open ponds such as raceway ponds. The simulation module is validated by comparing the results of experimental measurements made on artificially illuminated algal suspension with those predicted by the Monte Carlo program. This experiment deals with a situation that resembles that of an open pond or that of a raceway pond, except for the fact that for convenience, the experimental arrangement appears as if those reactors were turned upside down. It serves the purpose of assessing to what extent the scattering phenomena are important for the prediction of the spatial distribution of the radiant energy density. The simulation module developed can be applied to compute the local energy density inside photobioreactors with the goal to optimize its design and their operating conditions.     

Topological structures of complex belief systems

The concepts of substantive beliefs and derived beliefs are defined, a set of substantive beliefs S like open set and the neighborhood of an element substantive belief. A semantic operation of conjunction is defined with a structure of an Abelian group. Mathematical structures exist such as poset beliefs and join‐semilattttice beliefs. A metric space of beliefs and the distance of belief depending on the believer are defined. The concepts of closed and opened ball are defined. S′ is defined as subgroup of the metric space of beliefs Σ and S′ is a totally limited set. The term s is defined (substantive belief) in terms of closing of S′. It is deduced that Σ is paracompact due to Stone's Theorem. The pseudometric space of beliefs is defined to show how the metric of the nonbelieving subject has a topological space like a nonmaterial abstract ideal space formed in the mind of the believing subject, fulfilling the conditions of Kuratowski axioms of closure. To establish patterns of materialization of beliefs we are going to consider that these have defined mathematical structures. This will allow us to understand better cultural processes of text, architecture, norms, and education that are forms or the materialization of an ideology. This materialization is the conversion by means of certain mathematical correspondences, of an abstract set whose elements are beliefs or ideas, in an impure set whose elements are material or energetic. Text is a materialization of ideology. © 2013 Wiley Periodicals, Inc. Complexity 19: 46–62, 2013     

Human serum albumin unfolding pathway upon drug binding: A thermodynamic and spectroscopic description

The interest on phenothiazine drugs has been increased during last years due to their proved utility in the treatment of several diseases and biomolecular processes. In the present work, the binding of the amphiphilic phenothiazines promazine and thioridazine hydrochlorides to the carrier protein human serum albumin (HSA) has been examined by ζ-potential, isothermal titration calorimetry (ITC), fluorescence and circular dichorism (CD) spectroscopies, and dynamic light scattering (DLS) at physiological pH with the aim of analyzing the role of the different interactions in the drug complexation process with this protein. The ζ-potential results were used to check the existence of complexation. This is confirmed by a progressive screening of the protein charge up to a reversal point as a consequence of drug binding. On the other hand, binding causes alterations on the tertiary and secondary structures of the protein, which were observed by fluorescence and CD spectroscopies, involving a two-step, three-state transition. The thermodynamics of the binding process was derived from ITC results. The binding enthalpies were negative, which reveal the existence of electrostatic interactions between protein and drug molecules. In addition, increases in entropy are consistent with the predominance of hydrophobic interactions. Two different classes of binding sites were detected, viz. Binding to the first class of binding sites is dominated by an enthalpic contribution due to electrostatic interactions whereas binding to a second class of binding sites is dominated by hydrophobic bonding. In the light of these results, protein conformational change resembles the acid-induced denaturation of HSA with accumulation of an intermediate state. Binding isotherms were derived from microcalorimetric results by using a theoretical model based on the Langmuir isotherm. On the other hand, the population distribution of the different species in solution and their sizes were determined through dynamic light scattering (DLS). Aggregation of drug/protein complexes was found as a result of a possible expansion of protein structure induced at high drug concentrations. In addition, the presence of free drug aggregates at concentrations below the drug critical micelle concentration was also detected.     

TTF-based bent-core liquid crystals

The synthesis and characterization of bent-core liquid crystals which incorporate TTF groups is reported; different bent-core mesophases are induced depending on the molecular structure and properties derived from their compact packing have been studied.     

Deep eutectic solvents as both active fillers and monomers for frontal polymerization

The deep eutectic solvents (DESs) based on the mixtures of a variety of ammonium salts and hydrogen bond donors containing acrylic acids and acrylamides are capable of sustaining frontal polymerization (FP). The selection of ammonium salt affects the reactivity and allows FP at relatively low temperature but with full conversion. Also, full conversion allows us to use these polymers for biomedical applications (e.g., drug delivery systems) as the unreactive ammonium salts can be released from the resulting polymer without by‐products. We call these components “active fillers,” which can be ammonium salts with biological or pharmaceutical importance. For instance, we prepared poly(acrylic acid) loaded with lidocaine hydrochloride (a common anesthetic), the release of which was found to occur in a controlled fashion. The ammonium salts also create a sufficiently high viscosity to suppress buoyancy‐driven convection without additional materials. The DES here described played an all‐in‐one role, providing the monomer, the active filler, and the polymerization medium for FPs. © 2013 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013