Ab initio calculations of NO2 and SO2 chemisorption onto non-polar ZnO surfaces

The authors present an ab initio study of NO₂ and SO₂ chemisorption onto non-polar ZnO and ZnO surfaces with the aim of providing theoretical hints for further developments in gas sensors. From first principles calculations (DFT-GGA approximation), the most relevant surface reduction scenarios are analyzed and, subsequently, considered in the chemisorption study. First, calculations indicate that NO₂ adsorbs avidly onto Zn surface atoms. This is compatible with the oxidizing character of NO₂. Second, results also explain the sensor poisoning by SO₂ adsorption (since this molecule competes with NO₂ for the same adsorption sites) and indicate that poisoning can only be reverted at typical operation temperatures (T ≤ 700 °C) in the case of stoichiometric ZnO surfaces.     

H2 sensing characteristics of highly textured Pd-doped SnO2 thin films

The effects of the crystallographic orientation on the H₂ gas sensing properties were investigated in highly oriented polycrystalline Pd-doped SnO₂ films, which were obtained using rf magnetron sputtering of a Pd (0.5 wt%)-SnO₂ target on various substrates (a-, m-, r-, and c-cut sapphire and quartz). All the films had a similar thickness (110 nm), root-mean-square (rms) roughness (1.3 nm), surface area, and chemical status (O, Sn, and Pd). However, the orientation of the films was strongly affected by the orientation of the substrates. The (1 0 1), (0 0 2), and (1 0 1) oriented films were grown on (a-cut), (m-cut), and (r-cut) Al₂O₃ substrates, respectively, and rather randomly oriented films were deposited on (0 0 0 1) (c-cut) Al₂O₃ and quartz substrates. In addition, the oriented Pd-doped SnO₂ films were highly textured and had in-plane orientation relationships with the substrates similar to the epitaxial films. The (1 0 1) Pd-doped SnO₂ films on and Al₂O₃ showed a considerably higher H₂ sensitivity, and their gas response decreased with increasing sensing temperature (400–550 °C). The films deposited on and (0 0 0 1) Al₂O₃ showed the maximum sensitivity at 500 °C. The comparison of the H₂ gas response between undoped and Pd-doped SnO₂ films revealed that the Pd-doping shifted the optimum sensing temperature to a lower value instead of improving the gas sensitivity.     

Response time of nanostructured relative humidity sensors

Capacitive relative humidity (RH) sensors were fabricated by coating countersunk interdigitated electrode substrates with nanostructured TiO₂ films produced using glancing angle deposition. Areal capacitance increased from 1 nF cm⁻² to 800 nF cm⁻² as relative humidity was increased from 2% RH and 95% RH. For films deposited at 81° and with a thickness below 4 m, response time was (162±4) ms m⁻¹. Response times increased from 64 ms to 1440 ms as film thickness increased from 280 nm to 8.5 m. The linear dependence of response time with film thickness indicates that device response time is dominated by surface adsorption. Response time decreased with increasing deposition angle, with a slope of (−15.2±1.6) ms degree⁻¹ for the adsorption data, and (−17.3±2.5) ms degree⁻¹ for the desorption data. The optimum operating range of the sensors depends on deposition angle, and can be tuned to different ranges to match application needs.     

Canonical completeness of infinitary μ

This paper presents a new model construction for a natural cut-free infinitary version of the propositional modal μ-calculus. Based on that the completeness of and the related system K_ω(μ) can be established directly – no detour, for example through automata theory, is needed. As a side result we also obtain a finite, cut-free sound and complete system for the propositional modal μ-calculus.     

Positive periodic solutions of second-order nonlinear differential systems with two parameters

By employing the Deimling fixed point index theory, we consider a class of second-order nonlinear differential systems with two parameters . We show that there exist three nonempty subsets of : Γ, Δ₁ and Δ₂ such that and the system has at least two positive periodic solutions for (λ,μ)Δ₁, one positive periodic solution for (λ,μ)Γ and no positive periodic solutions for (λ,μ)Δ₂. Meanwhile, we find two straight lines L₁ and L₂ such that Γ lies between L₁ and L₂.     

Matrix representations for toric parametrizations

In this paper we show that a surface in parametrized over a 2-dimensional toric variety can be represented by a matrix of linear syzygies if the base points are finite in number and form locally a complete intersection. This constitutes a direct generalization of the corresponding result over established in [Busé, L., Jouanolou, J.-P., 2003. J. Algebra 265 (1), 312–357] and [Busé, L., Chardin, M.J., 2005. Symbolic Comput. 40 (4–5), 1150–1168]. Exploiting the sparse structure of the parametrization, we obtain significantly smaller matrices than in the homogeneous case and the method becomes applicable to parametrizations for which it previously failed. We also treat the important case in detail and give numerous examples.     

Elementary approximation algorithms for prize collecting Steiner tree problems

This paper deals with approximation algorithms for the prize collecting generalized Steiner forest problem, defined as follows. The input is an undirected graph G=(V,E), a collection T={T₁,…,T_k}, each a subset of V of size at least 2, a weight function , and a penalty function . The goal is to find a forest F that minimizes the cost of the edges of F plus the penalties paid for subsets T_i whose vertices are not all connected by F. Our main result is a -approximation for the prize collecting generalized Steiner forest problem, where n2 is the number of vertices in the graph. This obviously implies the same approximation for the special case called the prize collecting Steiner forest problem (all subsets T_i are of size 2). The approximation algorithm is obtained by applying the local ratio method, and is much simpler than the best known combinatorial algorithm for this problem.Our approach gives a -approximation for the prize collecting Steiner tree problem (all subsets T_i are of size 2 and there is some root vertex r that belongs to all of them). This latter algorithm is in fact the local ratio version of the primal-dual algorithm of Goemans and Williamson [M.X. Goemans, D.P. Williamson, A general approximation technique for constrained forest problems, SIAM Journal on Computing 24 (2) (April 1995) 296–317]. Another special case of our main algorithm is Bar-Yehuda's local ratio -approximation for the generalized Steiner forest problem (all the penalties are infinity) [R. Bar-Yehuda, One for the price of two: a unified approach for approximating covering problems, Algorithmica 27 (2) (June 2000) 131–144]. Thus, an important contribution of this paper is in providing a natural generalization of the framework presented by Goemans and Williamson, and later by Bar-Yehuda.     

Martingale families and dimension in P

We introduce a new measure notion on small complexity classes (called F-measure), based on martingale families, that gets rid of some drawbacks of previous measure notions: it can be used to define dimension because martingale families can make money on all strings, and it yields random sequences with an equal frequency of 0’s and 1’s. On larger complexity classes ( and above), F-measure is equivalent to Lutz resource-bounded measure. As applications to F-measure, we answer a question raised in [E. Allender, M. Strauss, Measure on small complexity classes, with application for BPP, in: Proc. of the 35th Ann. IEEE Symp. on Found. of Comp. Sci., 1994, pp. 807–818] by improving their result to: for almost every language A decidable in subexponential time, . We show that almost all languages in  do not have small non-uniform complexity. We compare F-measure to previous notions and prove that martingale families are strictly stronger than Γ-measure [E. Allender, M. Strauss, Measure on small complexity classes, with application for BPP, in: Proc. of the 35th Ann. IEEE Symp. on Found. of Comp. Sci., 1994, pp. 807–818], we also discuss the limitations of martingale families concerning finite unions. We observe that all classes closed under polynomial many-one reductions have measure zero in  iff they have measure zero in . We use martingale families to introduce a natural generalization of Lutz resource-bounded dimension [J.H. Lutz, Dimension in complexity classes, in: Proceedings of the 15th Annual IEEE Conference on Computational Complexity, 2000, pp. 158–169] on , which meets the intuition behind Lutz’s notion. We show that -dimension lies between finite-state dimension and dimension on . We prove an analogue of a Theorem of Eggleston in , i.e. the class of languages whose characteristic sequence contains 1’s with frequency α, has dimension the Shannon entropy of α in .     

First-principles study of ground-state properties and phase stability of vanadium nitrides

Using a series of density functional electronic structure total energy calculations, we have systematically studied the ground-state properties and phase stability of vanadium nitrides. Comparison of enthalpy of formation shows that V ₂N is equally stable (polymorphic) in , and Fe₂C phases within a few meV. Formation enthalpy of the various phases considered for perfect stoichiometric V N_1.0 shows that it has enhanced stability in hexagonal WC and NiAs structures in relation to NaCl-type δ-phase. The TiAs phase of VN has nearly same energy as NaCl structure. Comparison of energetics of -type , for x=0 and 0.3333 and of , for x=0, 0.0625, 0.125 and 0.25 shows that vacancies on the nitrogen sublattice lowers the formation enthalpy in relation to respective stoichiometric phases which is in agreement with experiments, as bulk vanadium nitrides are known to be generally non-stoichiometric. The calculated dilute heat of solution for the interstitial nitrogen is found to be in good agreement with experimental values and shows that nitrogen prefers to occupy the octahedral sites in bcc vanadium. The α^′-FeN and martensite structures, considered for the metastable phases of vanadium nitrides, have higher formation enthalpy in relation to equilibrium phases. Analysis of electronic density of states of V ₂N shows that the low energy , and Fe₂C phases are characterized by broad V 3d-N 2p and V 3d bonding bands. Density of states of VN shows that in the low energy WC and NiAs phases some of the antibonding states are made empty, leading to a minimum near the Fermi level. For and , density of states shows that vacancies on the nitrogen sublattice introduce additional filled states in the 3d band below Fermi level enabling enhanced bonding. Comparison between bulk moduli and atomic volumes for the various phases of vanadium nitrides shows that higher bulk moduli are dominated by increased V–N bonds combined with low atomic volumes.     

Directional dynamics for cellular automata: A sensitivity to initial condition approach

A cellular automaton is a continuous function F defined on a full-shift which commutes with the shift σ. Often, to study the dynamics of F one only considers implicitly σ. However, it is possible to emphasize the spatio-temporal structure produced by considering the dynamics of the -action induced by (σ,F).In this purpose we study the notion of directional dynamics. In particular, we are interested in directions of equicontinuity and expansivity, which generalize the concepts introduced by Gilman [Robert H. Gilman, Classes of linear automata, Ergodic Theory Dynam. Systems 7 (1) (1987) 105–118] and P. Kůrka [Petr Kůrka, Languages, equicontinuity and attractors in cellular automata, Ergodic Theory Dynam. Systems 17 (2) (1997) 417–433]. We study the sets of directions which exhibit this special kind of dynamics showing that they induce a discrete geometry in space-time diagrams.     

Nonnegative matrices with prescribed extremal singular values

We consider the problem of constructing nonnegative matrices with prescribed extremal singular values. In particular, given 2n−1 real numbers and , we construct an n×n nonnegative bidiagonal matrix B and an n×n nonnegative semi-bordered diagonal matrix C, such that and are, respectively, the minimal and the maximal singular values of certain submatrices B_j and C_j of B and C, respectively. By using a singular value perturbation result, we also construct an n×n nonnegative matrix with prescribed singular values σ₁≥≥σ_n.     

Computation of bases of free modules over the Weyl algebras

A well-known result due to J.T. Stafford asserts that a stably free left module M over the Weyl algebras D=A_n(k) or B_n(k)–where k is a field of characteristic 0–with is free. The purpose of this paper is to present a new constructive proof of this result as well as an effective algorithm for the computation of bases of M. This algorithm, based on the new constructive proofs [Hillebrand, A., Schmale, W., 2001. Towards an effective version of a theorem of Stafford. J. Symbolic Comput. 32, 699–716; Leykin, A., 2004. Algorithmic proofs of two theorems of Stafford. J. Symbolic Comput. 38, 1535–1550] of J.T. Stafford’s result on the number of generators of left ideals of D, performs Gaussian elimination on the formal adjoint of the presentation matrix of M. We show that J.T. Stafford’s result is a particular case of a more general one asserting that a stably free left D-module M with is free, where denotes the stable rank of a ring D. This result is constructive if the stability of unimodular vectors with entries in D can be tested. Finally, an algorithm which computes the left projective dimension of a general left D-module M defined by means of a finite free resolution is presented. It allows us to check whether or not the left D-module M is stably free.     

Bounded cost algorithms for multivalued consensus using binary consensus instances

In this paper, we present two bounded cost algorithms that solve multivalued consensus using binary consensus instances. Our first algorithm uses log₂n number of binary consensus instances where n is the number of processes, while our second algorithm uses at most binary consensus instances, where is the maximum length of the binary representation of all proposed values in the run. Both algorithms are significant improvements over the previous algorithm in [A. Mostefaoui, M. Raynal, F. Tronel, From binary consensus to multivalued consensus in asynchronous message-passing systems, Information Processing Letters 73 (5–6) (2000) 207–212], where the number of binary consensus instances needed to solve one multivalued consensus is unbounded.