Deciding confluence of certain term rewriting systems in polynomial time

We present a characterization of confluence for term rewriting systems, which is then refined for special classes of rewriting systems. The refined characterization is used to obtain a polynomial time algorithm for deciding the confluence of ground term rewrite systems. The same approach also shows the decidability of confluence for shallow and linear term rewriting systems. The decision procedure has a polynomial time complexity under the assumption that the maximum arity of a function symbol in the signature is a constant.     

High order linear initial-value problems and Schauder bases

In this paper we approximate the solution of a linear initial-value problem, making use of a Schauder basis for certain Banach space associated with such a differential problem. In addition, we apply that results in order to calculate numerically the response from a structure modelled by a three degree-of-freedom mass–damper–spring system.     

Substituted m-phenylene bridges as strong ferromagnetic couplers for Cu(II)-bridge-Cu(II) magnetic interactions: new perspectives

Based on a combined theoretical-experimental study, we propose that substituted m-phenylene ligands (m-N-Phi-N) can act as tuneable strong ferromagnetic couplers connecting Cu(II) ions; a new complex presenting that bridge with J close to +15 cm(-1) has been suggested and synthesized.     

Aggregation of [Cu(II)4] building blocks into [Cu(II)8] clusters or a [Cu(II)4]infinity chain through subtle chemical control

Coordination complexes of the ligand H3L [1,3-bis(3-oxo-3-phenylpropionyl)-2-hydroxy-5-methylbenzene] with Cu(II) are reported. Clusters showing various nuclearities or modes of supramolecular organization have been prepared by slightly changing the reaction conditions and have been crystallographically characterized. The reaction of H3L with one equivalent of Cu(OAc)2 in DMF yields the dinuclear complex [Cu2(HL)2(dmf)2] (1). Reaction in MeOH of H3L with an increased amount of metal, in the form of Cu(NO3)2, and excess strong base (nBu4NOH) affords the cluster [Cu8(L)2(OMe)8(NO3)2] (2). Complex 2 is a dimer of two linear [Cu4] arrays bridged by methoxide ligands, where the polynucleating ligand is fully deprotonated. The [Cu4]2 clusters are linked to each other by NO3- bridges to form one-dimensional coordination polymers. The link between [Cu8] units and their relative spatial positioning can be modified by changing the anion of the Cu(II) salt, as demonstrated by the synthesis of the cluster polymers [Cu8(L)2(OMe)8Cl2] (3) and [Cu8(L)(OMe)7.86Br2.14] (4), where only NO3- has been replaced by Cl- or Br-, respectively. Similarly, when ClO4- is used, compound [Cu8(L)2(OMe)8(ClO4)2(MeOH)4] (5) can be isolated. It contains independent [Cu8] units. A slight change in the stoichiometry of the reaction leading to 2 affords the related complex catena-[Cu4(L)(OMe)3(NO3)2(H2O)0.36] (6). This polymer contains essentially the same [Cu4] moiety as 2, albeit organized in a completely different arrangement. Each [Cu4] unit in 6 is linked by OMe- ligands to two such equivalent groups to form an infinite chain. Magnetic susceptibility measurements reveal weak antiferromagnetic exchange between Cu(II) centers in 1 (J = -0.73 cm(-1)) and strong antiferromagnetic coupling within [Cu4] chains in 2, 5, and 6 (most negative J values of -113.8 and -177.3 cm(-1) for 2 and 6, respectively).     

A solvent-controlled switch of manganese complex assemblies with a beta-diketonate-based ligand

The coordination properties of the new polynucleating ligand H(3)L1 (1,3-bis(3-oxo-3-phenylpropionyl)-2-hydroxy-5-methylbenzene) with Mn(II/III) are described. Depending on the solvent used, the reaction of H(3)L1 with Mn(OAc)(2) yields either of the two new multinuclear assemblies [Mn(2)(HL1)(2)(py)(4)] (1) and [Mn(3)(HL1)(3)] (2), as revealed by X-ray crystallography. The structure of 2 is remarkable in that it shows a unique asymmetric triple-stranded helicate. Complexes 1 and 2 can be interconverted by controlling the solvent of the reaction system, and therefore, this ensemble constitutes an interesting externally addressable switch. In the presence of Mn(III)/pyridine, partial degradation of H(3)L1 occurs via oxidative cleavage, and the new complex [Mn(2)(L2)(2)(py)(4)] (3) is formed. The crystal structure of this complex has shown the fully deprotonated form of the new donor H(3)L2 (3-(3-oxo-3-phenylpropionyl)-5-methylsalicylic acid). From the same reaction, the Mn(II) complex 1 is also obtained. A rational synthesis of H(3)L2 is reported, and this has been used to prepare 3 in high yields, directly from its components. Variable-temperature magnetic susceptibility (chi(m)) measurements were performed on complexes 1-3 under a magnetic field of 1 kG. The data for each complex were fit to the appropriate chi(m) vs T theoretical equation, respectively. In 1, the Mn(II) ions are uncoupled, with g = 2.01. The data from 2 were fit by assuming the presence of an exchange coupled Mn(II)...Mn(II) pair next to a magnetically isolated Mn(II) center. The fit gave J = -2.75 cm(-1), g(12) = 1.97, and g(3) = 1.92, respectively. In 3, two models fit the experimental data. In the most satisfactory, the Mn(III) ions are coupled antiferromagnetically with J = -1.48 cm(-1) and g = 1.98 and a term for weak ferromagnetic intermolecular exchange is included with zJ' = 0.39 cm(-1). The other model contemplates the presence of two uncoupled zero field split Mn(III) ions.     

Local aromaticity of [n]acenes, [n]phenacenes, and [n]helicenes (n = 1-9)

The local aromaticity of the six-membered rings in three series of benzenoid compounds, namely, the [n]acenes, [n]phenacenes, and [n]helicenes for n = 1-9, has been assessed by means of three probes of local aromaticity based on structural, magnetic, and electron delocalization properties. For [n]acenes our analysis shows that the more reactive inner rings are more aromatic than the outer rings. For [n]phenacenes, all indicators of aromaticity show that the external rings are the most aromatic. From the external to the central ring, the local aromaticity varies in a damped alternate way. The trends for the [n]helicene series are the same as those found for [n]phenacenes. Despite the departure from planarity in [n]helicenes, only a very slight loss of aromaticity is detected in [n]helicenes as compared to the corresponding [n]phenacenes. Finally, because of magnetic couplings between superimposed six-membered rings in the higher members of the [n]helicenes series, we have demonstrated that the NICS indicator of aromaticity artificially increases the local aromaticity of their most external rings.     

Engineering strategy to improve peptide analogs: from structure-based computational design to tumor homing

We present a chemical strategy to engineer analogs of the tumor-homing peptide CREKA (Cys-Arg-Glu-Lys-Ala), which binds to fibrin and fibrin-associated clotted plasma proteins in tumor vessels (Simberg et al. in Proc Natl Acad Sci USA 104:932–936, 2007) with improved ability to inhibit tumor growth. Computer modeling using a combination of simulated annealing and molecular dynamics were carried out to design targeted replacements aimed at enhancing the stability of the bioactive conformation of CREKA. Because this conformation presents a pocket-like shape with the charged groups of Arg, Glu and Lys pointing outward, non-proteinogenic amino acids α-methyl and N-methyl derivatives of Arg, Glu and Lys were selected, rationally designed and incorporated into CREKA analogs. The stabilization of the bioactive conformation predicted by the modeling for the different CREKA analogs matched the tumor fluorescence results, with tumor accumulation increasing with stabilization. Here we report the modeling, synthetic procedures, and new biological assays used to test the efficacy and utility of the analogs. Combined, our results show how studies based on multi-disciplinary collaboration can converge and lead to useful biomedical advances.     

Can A Denaturant Stabilize DNA? Pyridine Reverses DNA Denaturation in Acidic pH

The stability of DNA is highly dependent on the properties of the surrounding solvent, such as ionic strength, pH, and the presence of denaturants and osmolytes. Addition of pyridine is known to unfold DNA by replacing π–π stacking interactions between bases, stabilizing conformations in which the nucleotides are solvent exposed. We show here experimental and theoretical evidences that pyridine can change its role and in fact stabilize the DNA under acidic conditions. NMR spectroscopy and MD simulations demonstrate that the reversal in the denaturing role of pyridine is specific, and is related to its character as pseudo groove binder. The present study sheds light on the nature of DNA stability and on the relationship between DNA and solvent, with clear biotechnological implications.     

UV assisted photo reactive polyether-polyesteramide resin for future applications in 3D printing

Among additive manufacturing, photocuring 3D printing technologies are very relevant because of its high printing speed and high precision. However, the limited performance of photosensitive thermoset polymers is the bottleneck for the application of photocuring 3D printing in some fields, particularly in the biomedical sector. Thus, the development of biodegradable and biocompatible materials is highly desirable and of utmost importance. In this work, a biodegradable and non-cytotoxic thermoset polymer for photocuring 3D printing is reported. It consists of an unsaturated polyesteramide bearing phenylalanine, 2-butene-1,4-diol and fumarate building blocks, which is photocured under UV irradiation using a low molecular weight poly(ethylene glycol) diacrylate as crosslinker. The main characteristics of the new thermoset are: (1) very high volumetric and mechanical integrity stabilities, comparable to that of photocured epoxides; (2) very high degradation temperature; (3) very low water absorption capacity; (4) relatively fast enzymatic degradation, reaching 16.5% after 3 months; and (5) non-cytotoxic response in presence of epithelial cells, even when soluble molecular fragments coming from biodegradation are considered. These properties favor the future utilization of the new polyether-polyesteramide resin in the manufacturing of more sustainable products via 3D printing methods, such as stereolithography, that uses UV sources.