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Energetic analyses based on homodesmotic reactions show a surprising ability of crowded biphenyls to achieve significant stabilization through intramolecular dispersive interactions, which is underestimated even by state-of-the-art DFT calculations.

An orientation D of a graph G = ( V , E ) is a digraph obtained from G by replacing each edge by exactly one of the two possible arcs with the same end vertices. For each v ∈ V ( G ) , the indegree of v in D, denoted by d D − ( v ) , is the number of arcs with head v in D. An orientation D of G is proper if d D − ( u ) ≠ d D − ( v ) , for all u v ∈ E ( G ) . An orientation with maximum indegree at most k is called a k-orientation. The proper orientation number of G, denoted by χ → ( G ) , is the minimum integer k such that G admits a proper k-orientation. We prove that determining whether χ → ( G ) ≤ k is NP - complete for chordal graphs of bounded diameter, but can be solved in linear-time in the subclass of quasi-threshold graphs. When parameterizing by k, we argue that this problem is FPT for chordal graphs and argue that no polynomial kernel exists, unless NP ⊆ coNP / poly . We present a better kernel to the subclass of split graphs and a linear kernel to the class of cobipartite graphs. Concerning bounds, we first prove that if G is split, then χ → ( G ) ≤ 2 ω ( G ) − 2 and that if G is a k-uniform block graph, then χ → ( G ) ≤ 3 k − 2 . These bounds are tight. We also present new families of trees having proper orientation number at most 2 and at most 3. Actually, we prove a general bound stating that any graph G having no adjacent vertices of degree at least c + 1 has proper orientation number at most c. This implies new classes of (outer)planar graphs with bounded proper orientation number. We also prove that maximal outerplanar graphs G whose weak-dual is a path satisfy χ → ( G ) ≤ 13 . Finally, we present simple bounds to the classes of chordal claw-free graphs and cographs.

A biclique of a graph G is an induced complete bipartite subgraph of G such that neither part is empty. A star is a biclique of G such that one part has exactly one vertex. The star graph of G is the intersection graph of the maximal stars of G . A graph H is star-critical if its star graph is different from the star graph of any of its proper induced subgraphs. We begin by showing that a star-critical pre-image of an n -vertex star graph has at most O n 2 vertices. We then describe a Krausz-type characterization for star graphs. We combine these results to show that the problem of recognizing star graphs is in NP . We also present some properties of the class. In particular, we show that they are biconnected, that every edge belongs to at least one triangle, characterize the structures the pre-image must have in order to generate degree two vertices in its star graph, and bound the diameter of the star graph with respect to the diameter of its pre-image. Finally, we prove a monotonicity theorem, which we apply in order to list every star graph on at most eight vertices.

This paper reports thermodynamic properties of phase transitions of 2,4,6-trichloro and 2,4,6-tribromo anisoles and of 2,4,6-tribromophenol. The vapor pressures of both crystalline and liquid phases (including supercooled liquid) of the three compounds were measured, respectively, in the temperature ranges T = (297.1 to 368.3) K, T = (330.7 to 391.7) K, and T = (336.5 to 401.7) K, using a static method based on capacitance diaphragm manometers. Moreover, the sublimation vapor pressures of 2,4,6-tribromophenol were also measured in the temperature interval (307.2 to 329.2) K, using a Knudsen mass-loss effusion technique. The standard molar enthalpies, entropies, and Gibbs energies of sublimation and of vaporization, at reference temperatures, were derived from the experimental results as well as the (p,T) values of the triple point of each compound. The temperatures and molar enthalpies of fusion of the three benzene derivatives were determined using differential scanning calorimetry and were compared with...

This work aims to provide reliable heat capacities for ethylene glycol and selected oligo(ethylene glycol)s (diethylene glycol, triethylene glycol, tetraethylene glycol, pentaethylene glycol, and h...

Uma orientação $D$ de um grafo simples $G=(V,E)$ é própria se os vértices~$u$ e~$v$ possuem graus de entrada distintos, sempre que~$uv \in E$. O número de orientação de um grafo $G$ é o menor inteiro positivo $k$ tal que $G$ tem uma orientação própria $D$ com maior grau de entrada igual a $k$, denotado por $\po(G)$. Mostramos que decidir se $\po(G) \le k$ é~\FPT, parametrizado por $k$, quando restrito a grafos cordais, apresentamos um kernel exponencial para esta classe de grafos e mostramos que não existe kernel polinomial a menos que $\NP \subseteq \coNP/\poly$. Apresentamos também kernels melhores para grafos split e cobipartidos. Além disto, apresentamos limitantes para subclasses de grafos cordais como grafos blocos, periplanares cordais e para cografos.

We study the discretization of a Dirichlet form on the Koch snowflake domain and its boundary with the property that both the interior and the boundary can support positive energy. We compute eigenvalues and eigenfunctions, and demonstrate the localization of high energy eigenfunctions on the boundary via a modification of an argument of Filoche and Mayboroda. Holder continuity and uniform approximation of eigenfunctions are also discussed.

Given a graph $G$, a proper $k$-coloring of $G$ is a partition $c = (S_i)_{i\in [1,k]}$ of $V(G)$ into $k$ stable sets $S_1,\ldots, S_{k}$. Given a weight function $w: V(G) \to \mathbb{R}^+$, the weight of a color $S_i$ is defined as $w(i) = \max_{v \in S_i} w(v)$ and the weight of a coloring $c$ as $w(c) = \sum_{i=1}^{k}w(i)$. Guan and Zhu [Inf. Process. Lett., 1997] defined the weighted chromatic number of a pair $(G,w)$, denoted by $\sigma(G,w)$, as the minimum weight of a proper coloring of $G$. The problem of determining $\sigma(G,w)$ has received considerable attention during the last years, and has been proved to be notoriously hard: for instance, it is NP-hard on split graphs, unsolvable on $n$-vertex trees in time $n^{o(\log n)}$ unless the ETH fails, and W[1]-hard on forests parameterized by the size of a largest tree. In this article we provide some positive results for the problem, by considering its so-called dual parameterization: given a vertex-weighted graph $(G,w)$ and an integer $k$, the question is whether $\sigma(G,w) \leq \sum_{v \in V(G)} w(v) - k$. We prove that this problem is FPT by providing an algorithm running in time $9^k \cdot n^{O(1)}$, and it is easy to see that no algorithm in time $2^{o(k)} \cdot n^{O(1)}$ exists under the ETH. On the other hand, we present a kernel with at most $(2^{k-1}+1) (k-1)$ vertices, and we rule out the existence of polynomial kernels unless ${\sf NP} \subseteq {\sf coNP} / {\sf poly}$, even on split graphs with only two different weights. Finally, we identify some classes of graphs on which the problem admits a polynomial kernel, in particular interval graphs and subclasses of split graphs, and in the latter case we present lower bounds on the degrees of the polynomials., Comment: 13 pages

An orientation D of a graph G = (V, E) is a digraph obtained from G by replacing each edge by exactly one of the two possible arcs with the same end vertices. For each v ∈ V(G), the indegree of v in D, denoted by dD−(v), is the number of arcs with head v in D. An orientation D of G is proper if dD−(u) ≠ dD−(v), for all uv ∈ E(G). An orientation with maximum indegree at most k is called a k-orientation. The proper orientation number of G, denoted by χ→(G), is the minimum integer k such that G admits a proper k-orientation. We prove that determining whether χ→(G) ≤ k is NP-complete for chordal graphs of bounded diameter. We also present a tight upper bound for χ→(G) on split graphs and a linear-time algorithm for quasi-threshold graphs.

Oxidative treatment of Multi-Walled Carbon Nanotubes (MWCNT’s) was done by chemical functionalization by using the mixture acid, which is a mixture of sulfuric acid (H2SO4) and nitric acid (HNO3). Functionalization was governed by four parameters namely mixture acid concentration, temperature(T), time of heating(t) and the amount of MWCNTs used. After functionalization, functionalized MWCNT’s were then diluted in dimethylformamide (DMF) to analyse the percentage of soluble MWCNT’s. Also, by increasing the time of functionalization, it was observed that overall yield decreases but the percentage of functionalized product inside the yield quantity remains the same. Material characterization was also carried out at several steps to validate this theory. Chemical functionalization of MWCNT’s is generally significant for the manufacturing of polymer-based nanocomposites. Oxidative treatment enhances the dispersion and interfacial bonding within the epoxy matrix. In this research work, a bio-based epoxy resin was selected for the manufacturing of nanocomposite samples with various concentrations of pristine and functionalized MWCNTs. Mechanical and electrical characterization was finally carried out to increase the knowledge on the interaction of MWCNT’s with the selected green epoxy matrix system and their influence on the original properties of the resin.

An f -reversible process on a graph G = ( V , E ) is a graph dynamical system on V ( G ) defined as follows. Given a function f : V ( G ) → N and an initial vertex labeling c 0 : V ( G ) → { 0 , 1 } , every vertex v changes its label if and only if at least f ( v ) of its neighbors have the opposite state, synchronously in discrete-time. For such processes, we present a new nondecreasing time function similar to the monotonically decreasing energy functions used to study threshold networks, which leads to a periodic behavior after a transient phase. Using this new function, we provide a tight upper bound on the transient length of f -reversible processes. Furthermore, we prove that it is equal to n − 3 for trees with n ≥ 4 vertices and Im ( f ) = { 2 } . Moreover we present an algorithm that generates all the initial configurations attaining this bound and we prove that the number of such configurations is O ( n ) . We also consider the problem of determining the smallest number r f ( G ) of vertices with initial label 1 for which all the vertices eventually reach label 1 after the complete evolution of the dynamics, which models consensus problems on networks. We prove that it is N P -hard to compute r f ( G ) even for bipartite graphs with Δ ( G ) ≤ 3 and Im ( f ) = { 1 , 2 , 3 } . Finally, we prove that β ( G ) ≤ r f ( G ) ≤ β ( G ) + 1 , when f ( v ) = d ( v ) for all v ∈ V ( G ) , where β ( G ) is the size of a minimum vertex cover of G .

Herein, we present experimental evidence that protic ionic liquids (PILs), derived from 1 : 1 liquid mixtures of the organic superbases 1,5-diazabicyclo[4.3.0]non-5-ene (DBN) and 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) with carboxylic acids, form azeotropic mixtures with acid/base molar fractions different from 1 : 1. The ability of the carboxylic acids to form strong hydrogen bonds with the PIL ion pair leads to an azeotropic composition richer in the acid component. The results show that the azeotropic composition is ruled by the extent of acid-base equilibrium and the relative volatility of the neutral species in the PIL medium. The PILs show marked negative deviations from Raoult's Law with the stronger superbase (DBU) leading to an azeotropic composition closer to the equimolar 1 : 1 ratio.

Deadlock prevention techniques are essential in the design of robust distributed systems. However, despite the large number of different algorithmic approaches to detect and solve deadlock situations, yet there remains quite a wide field to be explored in the study of deadlock-related combinatorial properties. In this work we consider a simplified AND-OR model, where the processes and their communication are given as a graph G. Each vertex of G is labelled AND or OR, in such a way that an AND-vertex (resp., OR-vertex) depends on the computation of all (resp., at least one) of its neighbors. We define a graph convexity based on this model, such that a set $$S \subseteq V(G)$$ is convex if and only if every AND-vertex (resp., OR-vertex) $$v \in V(G){\setminus }S$$ has at least one (resp., all) of its neighbors in $$V(G) {\setminus } S$$ . We relate some classical convexity parameters to blocking sets that cause deadlock. In particular, we show that those parameters in a graph represent the sizes of minimum or maximum blocking sets, and also the computation time until system stability is reached. Finally, a study on the complexity of combinatorial problems related to such graph convexity is provided.

We consider an iterative irreversible process on graphs. Starting with some initial set S of vertices of a given graph G, this process iteratively adds to S all vertices u of G outside of S for which the intersection of the current set S with the neighborhood NG(u) of u in G belongs to a collection (u) of subsets of NG(u) given for each vertex u.Inspired by discrete convexity notions, we study the corresponding interval number, where only one iteration is executed, and the hull number, where the number of iterations is unbounded. Special choices of the function allow to include several well studied graph processes and parameters within this framework.Our contributions comprise hardness results for very restricted cases, linear time algorithms for trees, and a probabilistic upper bound.

As a natural variant of the many decycling notions studied in graphs, we consider the problem to decide whether a given graph G has a matching M such that G − M is a forest. We establish NP-completeness of this problem for 2-connected planar subcubic graphs, and describe polynomial time algorithms that also determine such a matching if it exists for graphs that are claw- and paw-free, P 5 -free, chordal, and C 4 -free distance hereditary.

A comprehensive thermodynamic study of the whole ortho-polyphenylbenzenes series from biphenyl (n = 1) to hexaphenylbenzene (n = 6) is presented. Combustion calorimetry and phase equilibria measurements for 1,2,3,4-tetraphenylbenzene (n = 4) and pentaphenylbenzene (n = 5) together with literature data were used to understand and quantify the constraint effect of ortho-substitution on the molecular energetics and phase stability of polyaromatic compounds. All of the derived thermodynamic properties (enthalpy of sublimation, entropy of sublimation, and gas phase molecular energetics) show a marked trend shift at n = 4 to 5, which is related to the change of the degree of molecular flexibility after 1,2,3,4-tetraphenylbenzene (n = 4). The greater intramolecular constraint in the more crowded members of the series (n = 5 and 6) leads to a significant change in the molecular properties and cohesive energy. The trend shift in the molecular properties is related with the decrease in molecular flexibility, which leads to lower molecular entropy and destabilization of the intramolecular interaction potential due to the increased hindrance in a confined molecular space.

The molecular and supramolecular structure and energetics of tetracene and rubrene were investigated by a combined experimental and theoretical study. Accurate equilibrium vapour pressures at various temperatures were measured for both compounds. For rubrene the energetic analysis evidences lower crystal packing efficiency, strong molecular destabilization and confirms the non-planar twisted equilibrium structure in the gas phase. The results also indicate that phenyl internal rotation in rubrene is highly hindered. The intra- and intermolecular interactions in crystal tetracene and rubrene were evaluated by computational methods. The representative stacked dimer of the tetracene...tetracene interaction in rubrene has lower ionization energy than the one modelling the same interaction in tetracene, due to stronger cation...pi interactions in the cation-radical of rubrene. Charge distribution in the cation dimer is symmetrical in rubrene, whereas in tetracene it is largely localized on the C-H center dot center dot center dot pi donor partner of the herringbone dimer. These findings highlight the impact of cation...pi interactions on the semiconducting properties of OSCs.

The synthesis and reactivity of 2-[(1E,3E)-4-arylbuta-1,3-dien-1-yl]-4H-chromen-4-ones as dienes in Diels–Alder (DA) reactions with several electron-poor and electron-rich dienophiles under microwave irradiation was studied. The optimized reaction conditions were achieved with N-methylmaleimide as the dienophile and Sc(OTf)3 (OTf = triflate) as a Lewis acid under microwave-assisted and solvent-free conditions. The Lewis acid improved the reaction yields as it prevented the adducts obtained from undergoing a second DA reaction; thus, the formation of a bisadduct was avoided. The α,β:γ,δ-diene of the starting chromones was the most reactive, and the computational results confirmed the experimental findings. Theoretical calculations also provided a rationale for the unexpected lack of reactivity shown by some dienophiles. The adducts prepared were dehydrogenated with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ); however, the aza adducts were sensitive to the highly energetic reaction conditions necessary for the aromatization.

UV–Vis can be used as an easy and forthright technique to accurately estimate the band gap energy of organic π-conjugated materials, widely used as thin films/composites in organic and hybrid electronic devices such as OLEDs, OPVs and OFETs. The electronic and optical properties, including HOMO–LUMO energy gaps of π-conjugated systems were evaluated by UV–Vis spectroscopy in CHCl3 solution for a large number of relevant π-conjugated systems: tris-8-hydroxyquinolinatos (Alq3, Gaq3, Inq3, Al(qNO2)3, Al(qCl)3, Al(qBr)3, In(qNO2)3, In(qCl)3 and In(qBr)3); triphenylamine derivatives (DDP, p-TTP, TPB, TPD, TDAB, m-MTDAB, NPB, α-NPD); oligoacenes (naphthalene, anthracene, tetracene and rubrene); oligothiophenes (α-2T, β-2T, α-3T, β-3T, α-4T and α-5T). Additionally, some electronic properties were also explored by quantum chemical calculations. The experimental UV–Vis data are in accordance with the DFT predictions and indicate that the band gap energies of the OSCs dissolved in CHCl3 solution are consistent with the values presented for thin films.

6 pags., 2 figs., 3 tabs., 2 schs., We report a study on the energetics and structural properties of gallic (1) and ellagic (2) acids. The experimental values of standard enthalpy of formation in solid state at 298.15 K, ΔH (cd) of 1 as (−985.0 ± 2.9 kJ·mol) and 2 as (−1377.9 ± 4.7 kJ·mol) have been determined. The vapour pressure of 1 have been measure by Knudsen effusion methodology and the derived enthalpy of sublimation, Δ H , was combined with the ΔH (cd) in order to derive its gas-phase enthalpy of formation, ΔH (1,g) = −835.7 ± 4.0 kJ·mol. Quantum chemical calculations, at DFT (M05-2X) and composite ab initio Gn (n = 3, 4) levels of theory, provided the consistency of the experimental results and a plausible estimation of ΔH (g) of 2 as (−1128.6 ± 6.4 kJ·mol), which was deduced from the isodesmic-reactions methodology., J.Z.D acknowledges the support funding to IQFR-CSIC (Spain) andperuvian CONCYTEC (INNÓVATE PERÚ, ECIP-1-P-030-14 Grant). Wewish to thank Fundação para a Ciência e Tecnologia (FCT), Lisbon,Portugal, and the European Social Fund (ESF) for their financial supportto CIQUP, University of Porto (Projects:PEst-C/QUI/UI0081/2011,FCUP-CIQ-UP-NORTE-07-0124-FEDER-000065). Carlos F.R.A.C.L.thanks for is Research Grant SFRH/BPD/77972/2011.

In this work, rearrangement reactions subsequent to the oxidation of tertiary amines were studied in 2-(cyanoethyl)-2-azanorbornane/ene systems. [1,2]- and [2,3]-Meisenheimer rearrangements, as well as the Cope elimination reaction, were observed with virtually complete selectivity. It was found that 2-(cyanoethyl)-2-azanorbornanes afford N-hydroxylamines through Cope elimination reactions and 2-(cyanoethyl)-2-azanorbornenes are prone to Meisenheimer rearrangements. In addition, the endo/exo configuration of 2-azanorbornenes plays a key role in the Meisenheimer rearrangement outcome. All the synthesized compounds were fully characterized by NMR spectroscopy and HRMS.

Given a graph G and a function f : V ( G ) → N we study the iterative process on G such that, given an initial vertex labelling c 0 : V ( G ) → { 0 , 1 } , each vertex v changes its label if and only if at least f ( v ) of its neighbors have the different label. It is known that these processes reach periodic behavior after a phase called transient. We give a tight upper bound for transient length and we show that the period is at most two, for all c 0 . We also study the problem of finding the minimum number r f ( G ) of vertices with initial label 1, such that all vertices reach label 1. Given a constant k ≥ 1 , we show that is NP-complete to determine if r f ( G ) ≤ k , even if G is a bipartite graph with Δ ( G ) ≤ 3 and f : V ( G ) → { 1 , 2 , 3 } . We also prove that this problem is NP-complete for planar cubic graphs and f : V ( G ) → { 3 } , through relationship between r f ( G ) and the size of a minimum vertex cover of G , in the case in which f ( v ) = d ( v ) , for all vertex v .

A b-coloring of the vertices of a graph is a proper coloring where each color class contains a vertex which is adjacent to at least one vertex in each other color class. The b-chromatic number of G is the maximum integer b ( G ) for which G has a b-coloring with b ( G ) colors. This problem was introduced by Irving and Manlove (1999), where they showed that computing b ( G ) is NP -hard in general and polynomial-time solvable for trees. A natural question that arises is whether the edge version of this problem is also NP -hard or not. Here, we prove that computing the b-chromatic index of a graph G is NP -hard, even if G is either a comparability graph or a C k -free graph, and give partial results on the complexity of the problem restricted to trees, more specifically, we solve the problem for caterpillars graphs. Although solving problems on caterpillar graphs is usually quite simple, this problem revealed itself to be unusually hard. The presented algorithm uses a dynamic programming approach that combines partial solutions which are proved to exist if, and only if, a particular polyhedron is non-empty.

Aryl derivatives of ferrocene are used for the modification of graphitic surfaces. Stronger adsorption is utilized as a route to enable the electrochemically tagging of new carbon materials. Model experiments are reported on an EPPG electrode where the adsorption of 1-(biphen-4-yl)ferrocene is found to be a factor of ca. 5 times more thermodynamically favorable than the underivatised form. Two further derivatives were also studied and the voltammetric responses of this class of ferrocenes are found to be significantly influenced by ion-pairing. Finally, the successful use of these new materials for the modification and redox tagging of graphene nanoplatelets is demonstrated. © 2016 WILEY-VCH Verlag GmbH and Co.

A b-coloring of a graph is a proper coloring of its vertices such that every color class contains a vertex that has neighbors in all other color classes. The b-chromatic number of a graph is the largest integer b ( G ) such that the graph has a b-coloring with b ( G ) colors. This metric is upper bounded by the largest integer m ( G ) for which G has at least m ( G ) vertices with degree at least m ( G ) - 1 . There are a number of results reporting that graphs with high girth have high b-chromatic number when compared to m ( G ) . Here, we prove that every graph with girth at least 7 has b-chromatic number at least m ( G ) - 1 . Our proof also yields a polynomial algorithm that produces an optimal b-coloring of these graphs.

The self-association equilibrium, i.e. formation of noncovalent dimers, in two triphenylamine derivatives, TPD (N,N'-bis(3-methylphenyl)-N,N'-diphenylbenzidine) and mMTDAB (1,3,5-tris[(3-methylphenyl)phenylamino]benzene), in solution was evaluated by (1)H NMR spectroscopy. The gas-phase energetics of the respective dimerization processes was explored by computational quantum chemistry. The results indicate that self-association is significantly more extensive in TPB than in TDAB. It is proposed that this fact helps to explain why TPB presents a stability higher than expected in the liquid phase, which is reflected in a lower melting temperature, a less volatile liquid, and possibly a higher tendency to form a glass. These results highlight the influence of self-association on the phase equilibria and thermodynamic properties of pure organic substances.

We study the problem of determining whether a given graph \(G=(V,E)\) admits a matching M whose removal destroys all odd cycles of G (or equivalently whether \(G-M\) is bipartite). This problem is equivalent to determine whether G admits a (2, 1)-coloring, which is a 2-coloring of V(G) in which each color class induces a graph of maximum degree at most 1. We determine a dichotomy related to the NP-completeness of such a decision problem, where it is NP-complete even for 3-colorable planar graphs of maximum degree 4, while it is linear-time solvable for graphs of maximum degree at most 3. In addition, we present polynomial-time algorithms for many graph classes including those in which every odd-cycle subgraph is a triangle, graphs having bounded dominating sets, and \(P_5\)-free graphs. Additionally, we show that this problem is fixed-parameter tractable when parameterized by the clique-width, which implies that it is polynomial-time solvable for many interesting graph classes, such as distance-hereditary, outerplanar, and chordal graphs.

In this work, we describe the reactivity of chlorodiphenylphosphine and its oxide, as well as diphenylphosphine, with some glyoxylate derivative systems: methyl glyoxylate, methyl or 8-phenylneomenthyl glyoxylate oximes, and methyl cyanoformate. By analyzing the reactions outcomes and with the aid of computational chemistry, we propose some reaction mechanisms and molecular rearrangements.

The host-guest chemistry of ferrocene derivatives was explored by a combined experimental and theoretical study. Several 1-arylferrocenes and 1,1'-diarylferrocenes were synthesized by the Suzuki-Miyaura cross-coupling reaction. The ability of these compounds to bind small cations in the gas phase was investigated experimentally by electrospray ionization mass spectrometry (ESI-MS). The results evidenced a noticeable ability of all 1,1'-diarylferrocenes studied to bind cations, while the same was not observed for the corresponding 1-arylferrocenes nor ferrocene. The 1,1'-diarylferrocenecation relative interaction energies were evaluated by ESI-MS and quantum chemical calculations and showed that cation binding in these systems follows electrostatic trends. It was found that, due to their unique molecular shape and smooth torsional potentials, 1,1'-diarylferrocenes can act as molecular tweezers of small-sized cations in the gas phase.

The measure techniques based on function points are used as reference to measure effort and costs of a software development project, which is applied by private and public companies in several areas. In the current scenario in Court of Justice of Paraiba, the effort estimates of development are performed in all products, and function points analysis are used to conduct these estimates. Recently, the software testing team raised in court of justice of Paraiba and improved the product quality and the process itself. This paper aims an analysis, presentation and implementation of effort estimation by using function points, describing the collected outcomes and then ensuring a greater accuracy in the estimation of time and effort to achieve the test process activities keeping the quality of the results.

Summary Subacute necrotizing myelopathy (SNM) or Foix-Alajouanine syndrome is a rare disease characterized by progressive neurological dysfunction caused by a spinal dural arteriovenous fistula (AVF). Radiological diagnosis is usually suspected when there is intramedullary nonspecific enhancement and perimedullary flow voids. Ring-enhancement is rarely reported in the scope of AVF, which poses a diagnostic challenge and raises the suspicion of a spinal cord tumor. In such situations, biopsy can be required and delay proper diagnosis. We report the case of a patient with SNM, who underwent biopsy on the assumption of it being a spinal cord tumor. Resumo Mielopatia necrotizante subaguda (MNS) ou síndrome de Foix-Alajouanine é uma doença rara que se caracteriza por disfunção neurológica progressiva causada por uma fístula arteriovenosa espinal dural. O diagnóstico radiológico é comumente suspeitado quando aparece captação não específica de contraste e de artefatos de fluxo (flow voids) perimedulares. Raramente, a captação de contraste exibe o aspecto em anel, constituindo um grande desafio diagnóstico. Nesses casos, o principal diagnóstico diferencial é um tumor intramedular, e os pacientes são encaminhados para biópsia da lesão, atrasando o diagnóstico definitivo. Relatamos o caso de uma paciente com MNS, a qual foi submetida à biópsia da lesão em virtude de suspeita de tumor intramedular.

This work presents a comprehensive evaluation of the phase behaviour and cohesive enthalpy of protic ionic liquids (PILs) composed of 1,5-diazabicyclo[4.3.0]non-5-ene (DBN) or 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) organic superbases with short-chain length (acetic, propionic and butyric) carboxylic acids. Glass transition temperatures, Tg, and enthalpies of vaporization, ΔHvap, were measured for six [BH][A] (1 : 1) PILs (B = DBN, DBU; A = MeCOO, EtCOO, nPrCOO), revealing more significant changes upon increasing the number of –CH2– groups in the base than in the acid. The magnitude of ΔHvap evidences that liquid PILs have a high proportion of ions, although the results also indicate that in DBN PILs the concentration of neutral species is not negligible. In the gas phase, these PILs exist as a distribution of ion pairs and isolated neutral species, with speciation being dependent on the temperature and pressure conditions – at high temperatures and low pressures the separated neutral species dominate. The higher Tg and ΔHvap of the DBU PILs are explained by the stronger basicity of DBU (as supported by NMR and computational calculations), which increases the extent of proton exchange and the ionic character of the corresponding PILs, resulting in stronger intermolecular interactions in condensed phases.

An experimental and theoretical study on the phase and molecular stability of Mq3 (M = Al, Ga, and In; q = 8-hydroxyquinoline) is presented. The results suggest that the energy difference between the meridional and facial isomers of Mq3 shall be significantly lower than previously though and provide an explanation for the reported mer–fac solid–solid transition. The first accurate vapor pressure measurements for Alq3, Gaq3, and Inq3 are presented, which are of great relevance for the manufacturing of thin films by vacuum deposition. Phase transition thermodynamics indicates higher cohesive energies of the mer-isomers and an entropic differentiation that can be associated with the different molecular symmetry of the mer- and fac-isomers.

The self-association equilibrium constants, Kass, for the dimerization of some small oligothiophenes in acetone, acetonitrile and chloroform were measured by (1)H NMR spectroscopy. The gas phase interaction energies for some oligothiophene dimers were determined by computational quantum chemistry. The (1)H NMR results indicate that Kass generally increases with the chain length (the number of thienyl rings, n) and solvent polarity; however, Kass for thiophene (n = 1) was found to be higher than for the bithiophenes (n = 2). The linear oligothiophenes 2,2'-bithiophene and 2,2',5',2''-terthiophene were found to self-associate less than their corresponding nonlinear isomers 3,3'-bithiophene and 3,2',5',3''-terthiophene in solution and in the gas phase. For α-quaterthiophene (n = 4) Kass in solution was found to be smaller than expected. The non-linear dependence of the standard molar Gibbs energy of self-association, ΔassG, on the chain length in solution could be nicely reproduced and related to the conformational entropy change of dimerization. It was observed that the melting properties of oligothiophenes correlate well with their tendency to self-associate, with more self-association leading to increased liquid stability, and thus lower melting temperatures. These results highlight the relevance of self-association in isotropic systems for the correct molecular interpretation of phase equilibria.

A b-coloring of the vertices of a graph is a proper coloring where each color class contains a vertex which is adjacent to a vertex in each other color class. The b-chromatic number of G is the maximum integer χ b ( G ) for which G has a b-coloring with χ b ( G ) colors. This problem was introduced by Irving and Manlove in 1999, where they showed that computing χ b ( G ) is NP -hard in general and polynomial-time solvable for trees. A natural question that arises is whether the edge version of this problem is also NP -hard or not. Here, we prove that computing the b-chromatic index of a graph G is NP -hard, even if G is either a comparability graph or a C k -free graph, and give some partial results on the complexity of the problem restricted to trees.

A structural study of three synthesized stereoisomeric oximes, (−)-8-phenylmenthyl glyoxylate oxime (8-PMGO), (+)-8-phenylneomenthyl glyoxylate oxime (8-PnMGO), and (−)-8-phenylisoneomenthyl glyoxylate oxime (8-PinMGO), was performed by means of variable temperature 1H NMR spectroscopy, X-ray crystallography, and ab initio calculations. It was found that in 8-PMGO a conformation where the phenyl and oxime moieties are stacked is significantly favored, whereas in the other stereoisomers this preference was not so evident. The conformational differences found between the isomers were used to rationalize the outcome of the reaction (simultaneous 1,3-cycloaddition and aza-Diels–Alder reaction) between the referred oximes and cyclopentadiene, in which the stereoselectivity was evaluated and found to be nicely reproduced by a simple conformational analysis. The global results indicate that the stereoselectivity of the studied oximes, a bit higher for 8-PMGO, originates from their particular conformational distribution, in which the phenyl∙oxime aromatic interaction plays a decisive role.

Methylation at the C2 position of 1,3-disubstituted imidazolium-based ionic liquids (ILs) is one of the structural features that has gained attention due to its drastic impact on thermophysical and transport properties. Several hypotheses have been proposed to explain this effect but there is still much discrepancy. Aiming for the rationalization of the effects of these structural features on the properties of imidazolium ILs, we present a thermodynamic and computational study of two methylated ILs at the C2 position of imidazolium, [1C42C13C1im][NTf2] and [1C32C13C1im][NTf2]. The phase behaviour (glass transition and vaporization equilibrium) and computational studies of the anion rotation around the cation and ion pair interaction energies for both ILs were explored. The results have shown that C2-methylation has no impact on the enthalpy of vaporization. However, it decreases the entropy of vaporization, which is a consequence of the change in the ion pair dynamics that affects both the liquid and gas phases. In addition, the more hindered dynamics of the ion pair are also reflected in the increase in the glass transition temperature, Tg. The entropic contribution of anion-around-cation rotation in the imidazolium [NTf2] ILs was quantified experimentally by the comparative analysis of the entropy of vaporization, and computationally by the calculation of the entropies of hindered internal rotation. The global results exclude the existence of significant H-bonding in the C2-protonated (non-methylated) ILs and explain the C2-methylation effect in terms of reduced entropy of the ion pair in the liquid and gas phases. In light of these results, the C2-methylation effect is intrinsically entropic and originates from the more hindered anion-around-cation rotation as a consequence of the substitution of the -H with a bulkier -CH3 group.

Herein a core scaffold of 1-phenylnaphthalenes and 1,8-diphenylnaphthalenes with different substituents on the phenyl rings was used to study substituent effects on parallel-displaced aromatic π⋅⋅⋅π interactions. The energetics of the interaction was evaluated in gas phase based on the standard molar enthalpies of formation, at T=298.15 K, for the compounds studied; these values were derived from the combination of the results obtained by combustion calorimetry and Knudsen/Quartz crystal effusion. A homodesmotic gas-phase reaction scheme was used to quantify and compare the intramolecular interaction enthalpies in various substituted 1,8-diphenylnaphthalenes. The application of this methodology allowed a direct evaluation of aromatic interactions, and showed that substituent effects on the interaction enthalpy cannot be rationalized solely on classical electrostatic grounds, because no correlation with the σ(meta) or σ(para) Hammett constants was observed. Moreover, the results obtained indicate that aromatic π⋅⋅⋅π interactions are significantly enhanced by substitution, in a way that correlates with the ability of the interacting aryl rings to establish dispersive interactions. A combined experimental and computational approach for calculation of the true aromatic π⋅⋅⋅π interaction energies in these systems, free of secondary effects, was employed, and corroborates the rationale derived from the experimental results. These findings clearly emphasize the role of dispersion and dilute the importance of electrostatic forces on this type of interactions.

In this work, the interplay between structure and energetics in some representative phenylnaphthalenes is discussed from an experimental and theoretical perspective. For the compounds studied, the standard molar enthalpies, entropies and Gibbs energies of sublimation, at T = 298.15 K, were determined by the measurement of the vapor pressures as a function of T, using a Knudsen/quartz crystal effusion apparatus. The standard molar enthalpies of formation in the crystalline state were determined by static bomb combustion calorimetry. From these results, the standard molar enthalpies of formation in the gaseous phase were derived and, altogether with computational chemistry at the B3LYP/6-311++G(d,p) and MP2/cc-pVDZ levels of theory, used to deduce the relative molecular stabilities in various phenylnaphthalenes. X-ray crystallographic structures were obtained for some selected compounds in order to provide structural insights, and relate them to energetics. The thermodynamic quantities for sublimation suggest that molecular symmetry and torsional freedom are major factors affecting entropic differentiation in these molecules, and that cohesive forces are significantly influenced by molecular surface area. The global results obtained support the lack of significant conjugation between aromatic moieties in the α position of naphthalene but indicate the existence of significant electron delocalization when the aromatic groups are in the β position. Evidence for the existence of a quasi T-shaped intramolecular aromatic interaction between the two outer phenyl rings in 1,8-di([1,1'-biphenyl]-4-yl)naphthalene was found, and the enthalpy of this interaction quantified on pure experimental grounds as -(11.9 ± 4.8) kJ·mol(-1), in excellent agreement with the literature CCSD(T) theoretical results for the benzene dimer.

This work reports a thermodynamic study and structural analysis of a series of linear α-oligothiophenes to explore the effect of the successive increase of the number of thiophene rings on the thermodynamic properties related to solid–liquid and solid–gas equilibria. The compounds studied were α-quaterthiophene (α-4T), α-quinquethiophene (α-5T), and α-sexithiophene (α-6T). For each compound, the vapor pressures at different temperatures were measured using the Knudsen effusion method combined with a quartz crystal microbalance (KMBQ). From the obtained results, the standard molar enthalpies, entropies and Gibbs energies of sublimation were determined. For α-4T and α-5T (α-6T decomposes), the fusion temperatures and the standard molar enthalpies of fusion were determined in a power compensated differential scanning calorimeter (DSC). Standard molar entropies of fusion were derived accordingly. The obtained results for sublimation and fusion were compared with available data for the analogous thiophene (T),...

A new Knudsen effusion apparatus, enabling simultaneous gravimetric and quartz crystal microbalance mass loss detection, is described. This device allows the measurement of vapour pressures of small sample mass (50 to 100) mg over a wide temperature range (350 to 650) K using very short effusion time intervals. The performance of the apparatus was checked by measuring the vapour pressures of anthracene, benzanthrone, and 1,3,5-triphenylbenzene, between (0.1 and 1) Pa, over temperature intervals of 20 K. The derived standard molar enthalpies of sublimation and vapour pressures are in excellent agreement with the mean of the available literature values and with the recommended values. The new working methodology and design of this apparatus allows the measurement of high quality vapour pressure data due to: accurate temperature measurement and control; improvement in vacuum thermal contact between the effusion cell and the oven metal block; optimisation of the quartz crystal sensor head microbalance position; efficient temperature control of the quartz crystal microbalance head; accurate measurement of the resonance crystal frequency using an impedance circuit analyser methodology.

A series of 1-arylnaphthalenes and 1,8-diarylnaphthalenes were synthesized by the Suzuki–Miyaura cross-coupling methodology showing significant differentiation in the yields and selectivity between aryl rings with electron donating (higher yields), and electron withdrawing substituents (lower yields). These results strongly support the relation between the nucleophilicity of the boronate complex and its reactivity, and emphasize the importance of the transmetalation step in the overall efficiency of this cross-coupling reaction. The results obtained with non-symmetric 1,8-diarylnaphthalenes indicate preference for arylation of an already arylated species (the 1-aryl-8-bromonaphthalene intermediate) over mono-arylation of 1,8-dibromonaphthalene. Evidences for the existence of intramolecular Pd⋯π and aromatic interactions in some Pd(II) complexes were found.

The thermodynamic study of the phase transition (fusion and sublimation) of 2,2′:5′,2″-terthiophene and 3,2′:5′,3″-terthiophene is presented. The obtained data is used to evaluate the (solid + liquid) and (solid + gas) phase equilibrium, and draw the phase diagrams of the pure compounds near the triple point coordinates. For each compound the vapour pressures at different temperatures were measured by a combined Knudsen effusion method with a vacuum quartz crystal microbalance. Based on the previous results, the standard molar enthalpies, entropies and Gibbs energies of sublimation were derived at T = 298.15 K. For the two terthiophenes and for 3,3′-bithiophene, the temperature, and the molar enthalpies of fusion were measured in a power compensated differential scanning calorimetry. The relationship between structure and energetics is discussed based on the experimental results, ab initio calculations and previous literature data for 2,2′-bithiophene and 3,3′-bithiophene. The 3,2′:5′,3″-terthiophene shows a higher solid phase stability than the 2,2′:5′,2″-terthiophene isomer arising from the higher cohesive energy due to positioning of the sulphur atom in the thiophene ring. The higher phase stability of 3,3′-bithiophene relative to 2,2′-bithiophene isomer is also related to its higher absolute entropy in the solid phase associated with the ring positional degeneracy observed in the crystal structure of this isomer. A significant differentiation in the crystal phase stability between isomers was found.

The thermodynamic and structural study of a series of polyphenylbenzenes, from benzene, n(Ph) = 0, to hexaphenylbenzene, n(Ph) = 6, is presented. The available literature data for this group of compounds was extended by the determination of the relevant thermodynamic properties for 1,2,4-triphenylbenzene, 1,2,4,5-tetraphenylbenzene, and hexaphenylbenzene, as well as structural determination by X-ray crystallography for some of the studied compounds. Gas phase energetics in this class of compounds was analyzed from the derived standard molar enthalpies of formation in the gaseous phase. The torsional profiles relative to the phenyl-phenyl hindered rotations in some selected polyphenylbenzenes, as well as the gas phase structures and energetics, were derived from quantum chemical calculations. In the ideal gas phase, a significant enthalpic destabilization was observed in hexaphenylbenzene relative to the other polyphenylbenzenes, due to steric crowding between the six phenyl substituents. A relatively low enthalpy of sublimation was observed for hexaphenylbenzene, in agreement with the decreased surface area able to establish intermolecular interactions. The apparently anomalous low entropy of sublimation observed for hexaphenylbenzene is explained by its high molecular symmetry and the six highly hindered phenyl internal rotations. For the series of polyphenylbenzenes considered, it was shown that the differentiation in the entropy of sublimation can be chiefly ascribed to the torsional freedom of the phenyl substituents in the gas phase and the entropy terms related with molecular symmetry.