Borate‐Driven Gatelike Scaffolding Using Mesoporous Materials Functionalised with Saccharides

We report the development of an MCM‐41 mesoporous support that is functionalised with saccharides at the pore outlets and contains the dye [Ru(bipy)₃]²⁺ in the pores (solid S1 ; bipy=2,2′‐bipyridyl). For this hybrid system, the inhibition of mass transport of the dye from the pore voids to the bulk solution in the presence of borate is demonstrated in water at neutral pH. The formation of the corresponding boroester derivative is related to the selective reaction of borate with the appended saccharides. This control is selective and only anion borate, among several anions and cations, can act as a molecular tap and inhibit the delivery of the entrapped guest. Additionally, the S1 –borate system behaves as pH‐controlled gatelike scaffolding. This pH‐responsive release can be achieved in an acidic pH (due to hydrolysis of the boroester), whereas the system remains closed at neutral pH. Molecular dynamic simulations using force‐field methods have been made to theoretically study the open/close borate‐driven mechanism. A mesoporous silica structure was constructed for this purpose, taking the plane (1?11) of the β‐cristobalite structure as a base on which hexagonal nanopores and anchored saccharide derivatives were included. The final model shows a highly flexible nanopore diameter of approximately 12.5 Å of similar size to the [Ru(bipy)₃]²⁺ complex (ca. 12 Å). However, the anchoring of borate to the appended saccharides results in a remarkable reduction of the pore size (down to ca. 6.4 Å) and a significant constraint in the flexibility and mobility of the saccharides. The theoretical calculations are in agreement with the experimental results and enable visualisation of the functional borate‐driven dye‐delivery‐inhibition outcome.     

Structural identifiability of a model of dialysis

In this paper, structural identifiability from input–output data is considered. A mathematical model to describe a dialysis process based on linear dynamic systems is used and the identifiability of this model is tested. The problem of estimating the parameters and obtaining conditions to assure the uniqueness of the parameters is solved. Some conditions to obtain attractive points for the considered model are given, and finally, the stability problem is analyzed.     

The kinetics and mechanism of the homogeneous,unimolecular gas‐phase elimination of 2‐(4‐substituted‐phenoxy)tetrahydro‐2H‐pyranes

The gas‐phase elimination kinetics of tetrahydropyranyl phenoxy ethers: 2‐phenoxytetrahydro‐2H‐pyran, 2‐(4‐methoxyphenoxy)tetrahydro‐2H‐pyran, and 2‐(4‐tert‐butylphenoxy)tetrahydro‐2H‐pyran were determined in a static system, with the vessels deactivated with allyl bromide, and in the presence of the free radical inhibitor toluene. The working temperature and pressure were 330 to 390°C and 25 to 89 Torr, respectively. The reactions yielded DHP and the corresponding 4‐substituted phenol. The eliminations are homogeneous, unimolecular, and satisfy a first‐order rate law. The Arrhenius equations for decompositions were found as follows:

• 2‐phenoxytetrahydro‐2H‐pyran
• log k₁ (s^?1) = (14.18 ± 0.21) ? (211.6 ± 0.4) kJ mol^?1 (2.303 RT)^?1
• 2‐(4‐methoxyphenoxy)tetrahydro‐2H‐pyran
• log k₁ (s^?1) = (14.11 ± 0.18) ? (203.6 ± 0.3) kJ mol^?1 (2.303 RT)^?1
• 2‐(4‐tert‐butylphenoxy)tetrahydro‐2H‐pyran
• log k₁ (s^?1) = (14.08 ± 0.08) ? (205.9 ± 1.0) kJ mol^?1 (2.303 RT)^?1

The analysis of kinetic and thermodynamic parameters for thermal elimination of 2‐(4‐substituted‐phenoxy)tetrahydro‐2H‐pyranes suggests that the reaction proceeds via 4‐member cyclic transition state. The results obtained confirm a slight increase of rate constant with increasing electron donating ability groups in the phenoxy ring. The pyran hydrogen abstraction by the oxygen of the phenoxy group appears to be the determinant factor in the reaction rate.     

Relativistic perfect fluids in local thermal equilibrium

Every evolution of a fluid is uniquely described by an energy tensor. But the converse is not true: an energy tensor may describe the evolution of different fluids. The problem of determining them is called here the inverse problem. This problem may admit unphysical or non-deterministic solutions. This paper is devoted to solve the inverse problem for perfect energy tensors in the class of perfect fluids evolving in local thermal equilibrium (l.t.e.). The starting point is a previous result (Coll and Ferrando in J Math Phys 30:2918–2922, 1989) showing that thermodynamic fluids evolving in l.t.e. admit a purely hydrodynamic characterization. This characterization allows solving this inverse problem in a very compact form. The paradigmatic case of perfect energy tensors representing the evolution of ideal gases is studied in detail and some applications and examples are outlined.     

Balancing singular discrete-time systems

In this work, we deal with normalizable-balanced singular systems, that is, singular systems where the obtained closed-loop system is balanced by an appropriate feedback. In the invariant case, we use a proportional and derivative feedback to obtain systems without infinite poles. In addition, the existence and construction of state-feedbacks to obtain normalizable-balanced N-periodic singular systems is analyzed.     

Facets of the Graph Coloring Polytope

In this paper we present a study of the polytope associated to a classic linear integer programming formulation of the graph coloring problem. We determine some families of facets. This is the initial step for the development of a branch-and-cut algorithm to solve large instances of the graph coloring problem.     

The effect of polarons on the conductivity of the narrow-band Hubbard chain

We consider a half-filled, narrow band Hubbard chain with Holstein-type electron-phonon coupling to a set of intramolecular vibrational modes. We allow for dispersion in the vibrational spectrum and show, in the limit of zero temperature, that contrary to some recent results the one-electron density of states vanishes at the Fermi energy and the d.c. conductivity does not diverge as the inverse temperature.     

Direct preparation of 3,4-dichloro-2,-dimethyl-3-chromenes from 2,2-dimethyl-4-chromanones

Reaction of 2,2-dimethyl-4-chromanones($\text{1}$) with two equivalents of phosphorus pentachloride affords, 3,4-dichloro-2,2-dimethyl-3-chromenes($\text{2}$) in variable yields depending on the substituents of the aromatic ring. A plausible pathway for this reaction is given.     

Adapted harmonic coordinates

We obtain the necessary and sufficient conditions that a timelike congruence has to satisfy to admit three independent adapted harmonic coordinates of space, proving in the process that if it does then these coordinates are unique up to a linear transformation with constant coefficients. As a particular example we prove that irrotational pure Born (i.e. not Killing) congruences never admit a system of adapted harmonic coordinates of space.     

Synthesis of dienic fluorinated analogs of insect sex pheromones

Synthesis of fluorinated analogs of some dienic insect sex pherormones through a stereocontrolled Wittig reaction of β-fluorinated aldehydes with the appropriate ω-functionalized ylides is reported. Some features of the ¹H and ¹⁹F NMR spectra of these analogs are also discussed.