On Power-Associative Nilalgebras of Dimension N and Nilindex N-1

Whether or not a finite-dimensional, commutative, power-associative nilalgebra is solvable is a well-known open problem. In this paper, we describe commutative, power-associative nilalgebras of dimension n ≥ 6 and nilindex n ? 1 based on the condition that n ? 4 ≤ dim 𝔄³ ≤ n ? 3. This paper is a continuation of [10 Fernadez , J. C. G. , Garcia , C. I. , Montoya , M. L. R. ( 2013 ). On power-associative nilalgebras of nilindex and dimension n . Revista Colombiana de Matemáticas 47 : 1 – 11 . [Google Scholar]], where we describe commutative power-associative nilalgebras of dimension and nilindex n. We observe that the Jordan case was obtained by L. Elgueta and A. Suazo in [2 Elgueta , L. , Suazo , A. ( 2002 ). Jordan nilalgebras of nilindex n and dimension n + 1 . Comm. Algebra 30 : 5547 – 5561 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]].     

On Jordan-Nilalgebras of Index 3

We study commutative algebras that satisfy the Jacobi identity. Such algebras are Jordan algebras. We describe some of their properties and give a new bound of the index of nilpotency. We prove that every commutative nilalgebra of nilindex 3 generated by k elements over a field of characteristic ≠ 2, 3 is nilpotent of index less than or equal to k + 5.     

Dynamic Capacity Acquisition and Assignment under Uncertainty

Given a set of m resources and n tasks, the dynamic capacity acquisition and assignment problem seeks a minimum cost schedule of capacity acquisitions for the resources and the assignment of resources to tasks, over a given planning horizon of T periods. This problem arises, for example, in the integrated planning of locations and capacities of distribution centers (DCs), and the assignment of customers to the DCs, in supply chain applications. We consider the dynamic capacity acquisition and assignment problem in an environment where the assignment costs and the processing requirements for the tasks are uncertain. Using a scenario based approach, we develop a stochastic integer programming model for this problem. The highly non-convex nature of this model prevents the application of standard stochastic programming decomposition algorithms. We use a recently developed decomposition based branch-and-bound strategy for the problem. Encouraging preliminary computational results are provided.     

The pressure dependence of the néel temperature in FeF2

A Mössbauer measurement of the pressure dependence of the Néel temperature in FeF₂ is reported. Up to the maximum pressure of 50 kbar T_N increases at the rate of 0.27 ± 0.03°K/kbar. When this pressure dependence is converted to volume dependence, the result, d In T_N/d In V = 3.2 ± 0.3, is found to obey the $\text{“10}\text{3}$ rule” established by Bloch for a wide variety of antiferromagnetic insulators.     

Nanostructured lipid carriers for triamcinolone acetonide delivery to the posterior segment of the eye

Triamcinolone acetonide (TA) is a corticosteroid drug currently administered by intravitreal injection for a broad spectrum of inflammatory, edematous and angiogenic ocular diseases. To increase the drug's bioavailability by ocular instillation, TA was encapsulated in nanostructured lipid carriers (NLC), previously optimized by our group using a factorial design approach. In the present paper, nanometric (∼200 nm), unimodal and negatively charged NLC loaded with the fluorescent lipid marker Nile red (NR-NLC) and drug (TA-NLC) were produced by high pressure homogenization. Based on the selected formulations, in vivo tests were carried out by eye-drop instillation of NR-NLC in mice, revealing the systems’ ability of delivering lipophilic actives to the posterior segment of the eye via the corneal and non-corneal pathways. Short and long-term stability of TA-NLC was assessed by high performance stability analysis using the Turbiscan^®. The results showed a backscattering of less than 1.5% and during a period of 6 months, anticipated the low tendency of these particles for aggregation during shelf life when stored at room temperature.     

Amplification of the linear and nonlinear optical response of a chiral molecular crystal

We have observed large second-order nonlinear optical and vibrational circular dichroism (VCD) responses in a charge-transfer-type L-Histidinium salt. Using X-ray Diffraction, VCD spectroscopy, and time-dependent density functional theory to characterize the compound, we employ a two-level model to explain and quantify the strongly enhanced optical signals. We find that both linear and nonlinear optical responses are greatly enhanced by a single low-lying charge-transfer state.     

Synthesis of aminopyridines and aminopyridones by cobalt-catalyzed [2+2+2] cycloadditions involving yne-ynamides: scope, limitations, and mechanistic insights

An in-depth study of the cobalt-catalyzed [2+2+2] cycloaddition between yne-ynamides and nitriles to afford aminopyridines has been carried out. About 30 nitriles exhibiting a broad range of steric demand and electronic properties have been evaluated, some of which open new perspectives in metal-catalyzed arene formation. In particular, the use of [CpCo(CO)(dmfu)] (dmfu=dimethyl fumarate) as a precatalyst made possible the incorporation of electron-deficient nitriles into the pyridine core. Modification of the substitution pattern at the yne-ynamide allows the regioselectivity to be switched toward 3- or 4-aminopyridines. Application of this synthetic methodology to the construction of the aminopyridone framework using a yne-ynamide and an isocyanate was also briefly examined. DFT computations suggest that 3-aminopyridines are formed by formal [4+2] cycloaddition between the nitrile and the intermediate cobaltacyclopentadiene, whereas 4-aminopyridines arise from an insertion pathway.     

Calixarene‐Based Surfactants: Conformational‐Dependent Solvation Shells for the Alkyl Chains

Thermodynamic parameters obtained from studying the micellization of amphiphilic p‐sulfonatocalix[n]arenes were correlated with the alkyl chain length and with the number of monomeric units (n) in the calix[n]arene structure. The micellization Gibbs free energy (Δ${G{{{\rm o}\hfill \atop {\rm M}\hfill}}}$ ) becomes more negative upon increasing the alkyl chain length of the p‐sulfonatocalix[4]arene. This is in agreement with the trend generally observed for other surfactants. However, the Δ${G{{{\rm o}\hfill \atop {\rm M}\hfill}}}$ value for transferring one CH₂ group from the bulk aqueous medium to the micelle [Δ${G{{{\rm o}\hfill \atop {\rm M}\hfill}}}$ (CH₂)] is lower than the value generally observed for single‐chain surfactants, suggesting the existence of intramolecular interactions between the alkyl chains of the free unimers. On the other hand, the critical micelle concentration (cmc; per alkyl chain unit) increased with the increasing number of monomeric units. These results are explained on the basis of the conformation adopted by the calixarene in the bulk solution. The calix[4]arene derivatives are preorganized into the cone conformation, which is favorable for the formation of globular aggregates. The calix[6]arene and calix[8]arene derivatives do not adopt cone conformations. Changing these conformations to the more favorable cone conformer in the aggregates implies an energetic cost that contributes to making Δ${G{{{\rm o}\hfill \atop {\rm M}\hfill}}}$ less efficient. In the case of the calix[6]arene derivative this energetic cost is enthalpic, whereas in the case of the octamer it is both enthalpic and entropic. Both the Δ${G{{{\rm o}\hfill \atop {\rm M}\hfill}}}$ (CH₂) value and the change in heat capacity (ΔC${{\rm p}{{{\rm o}\hfill \atop {\rm M}\hfill}}}$ ) seem to indicate that for the cone calix[4]arene derivatives all alkyl chains are solvated by the same hydration shell, whereas in the case of the highly flexible calix[8]arene derivative each alkyl chain is individually hydrated.     

Using Calixarenes To Model Polyelectrolyte Surfactant Nucleation Sites

The formation of mixed micelles composed of dodecyltrimethylammonium bromide (C₁₂TAB) and a hexamethylated p‐sulfonatocalix[6]arene (SC6HM) was studied by several techniques. It was found that above the critical aggregation concentration the concentrations of free and micellized surfactant are strongly related to that of SC6HM. When there is free SC6HM in solution, the addition of C₁₂TAB mainly results in an increase in the concentration of micellized surfactant, but when all SC6HM has been aggregated, the addition of C₁₂TAB results in a substantial increase in the concentration of free surfactant in solution. When the concentration of free surfactant is equal to the critical micelle concentration of the pure system, a second independent aggregation process is observed. This aggregation behavior has many features that are similar to those of more complex systems that involve surfactants in the presence of oppositely charged polyelectrolytes. In this way, calixarenes can serve as simple models to mimic polyelectrolytes and to gain insight into the complex behavior displayed by these macromolecules.     

“Clickable” Hydrosoluble PEGylated Cryptophane as a Universal Platform for 129Xe Magnetic Resonance Imaging Biosensors

We describe the synthesis of a highly water‐soluble cryptophane 1 that can be seen as a universal platform for the construction of ¹²⁹Xe magnetic resonance imaging (MRI)‐based biosensors. Compound 1 is easily functionalized by Huisgen cycloaddition and exhibits excellent xenon‐encapsulation properties. In addition, 1 is nontoxic at the concentrations typically used for hyperpolarized ¹²⁹Xe MRI.