Minimal simple closed 18-surfaces and a topological preservation of 3D surfaces

The aim of this paper is to investigate a map which preserves digital topological properties of a digital 3D surface, such as the topological number, digital k-contractibility and so on. Furthermore, the two types of minimal simple closed 18-surfaces MSS₁₈ and are established in Z³ in relation with 18-contractibility, which are shown to be different from each other up to digital 18-homotopy. Moreover, it is proved that MSS₁₈ is the minimal simple closed 18-surface without 18-contractibility and is the minimal Malgouyres’ simple closed 18-surface with 18-contractibility. Finally, we show that a digital (k₀,k₁)-homeomorphism preserves a simple k₀-surface to a simple k₁-surface and vice versa.     

The <Emphasis Type="Italic">k</Emphasis>-Homotopic Thinning and a Torus-Like Digital Image in <Emphasis Type="Bold">Z</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

In order to discuss digital topological properties of a digital image (X,k), many recent papers have used the digital fundamental group and several digital topological invariants such as the k-linking number, the k-topological number, and so forth. Owing to some difficulties of an establishment of the multiplicative property of the digital fundamental group, a k-homotopic thinning method can be essentially used in calculating the digital fundamental group of a digital product with k-adjacency. More precisely, let be a simple closed k _i -curve with l _i elements in . For some k-adjacency of the digital product which is a torus-like set, proceeding with the k-homotopic thinning of , we obtain its k-homotopic thinning set denoted by DT _k . Writing an algorithm for calculating the digital fundamental group of , we investigate the k-fundamental group of by the use of various properties of a digital covering (Z×Z,p ₁×p ₂,DT _k ), a strong k-deformation retract, and algebraic topological tools. Finally, we find the pseudo-multiplicative property (contrary to the multiplicative property) of the digital fundamental group. This property can be used in classifying digital images from the view points of both digital k-homotopy theory and mathematical morphology.

Supporting early pruning in top-k query processing on massive data

This paper analyzes the execution behavior of “No Random Accesses” (NRA) and determines the depths to which each sorted file is scanned in growing phase and shrinking phase of NRA respectively. The analysis shows that NRA needs to maintain a large quantity of candidate tuples in growing phase on massive data. Based on the analysis, this paper proposes a novel top-k algorithm Top-K with Early Pruning (TKEP) which performs early pruning in growing phase. General rule and mathematical analysis for early pruning are presented in this paper. The theoretical analysis shows that early pruning can prune most of the candidate tuples. Although TKEP is an approximate method to obtain the top-k result, the probability for correctness is extremely high. Extensive experiments show that TKEP has a significant advantage over NRA.     

Augmented k-ary n-cubes

We define an interconnection network AQ_n,k which we call the augmented k-ary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube AQ_n,k has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n-cube AQ_n,k: is a Cayley graph, and so is vertex-symmetric, but not edge-symmetric unless n = 2; has connectivity 4n − 2 and wide-diameter at most max{(n − 1)k − (n − 2), k + 7}; has diameter , when n = 2; and has diameter at most , for n ? 3 and k even, and at most , for n ? 3 and k odd.     

Performance evaluation for a transportation system in stochastic case

In a single-commodity multistate flow network, the arc capacity is stochastic and thus the system capacity (i.e. the maximum flow from the source to the sink) is not a fixed number. This paper constructs a multicommodity multistate flow network with weighted capacity allocation to model a transportation system. Each arc with cost attribute has several possible capacities. The capacity weight, the consumed amount of arc capacity by per commodity, varies with the arcs and types of commodity. We define the system capacity as a demand vector d if the system fulfills at most d. The addressed problem in this work is to measure the service quality of a transportation system. We propose a performance index, the probability that the upper bound of the system capacity equals a demand vector d subject to the budget constraint. A simple algorithm based on minimal cuts is presented to generate all (d,B)-MC that are the maximal capacity vectors meeting exactly the demand d under the budget B. The proposed performance index can be subsequently evaluated in terms of such (d,B)-MC.     

Attracting ellipsoids and synthesis of oscillatory regimes

An approach to stabilization of nonlinear oscillations in multidimensional spaces is proposed on the basis of the V.I. Zubov’s stability theory for invariant sets. As a special case, the derived controls make it possible to excite self-oscillating regimes in specified state subspaces R ^2k ? R ²ⁿ with simultaneous oscillation damping on Cartesian products R ^2n?2k .     

Tilings of nonorientable surfaces by Steiner triple systems

A Steiner triple system of order n (for short, STS(n)) is a system of three-element blocks (triples) of elements of an n-set such that each unordered pair of elements occurs in precisely one triple. Assign to each triple (i,j,k) ? STS(n) a topological triangle with vertices i, j, and k. Gluing together like sides of the triangles that correspond to a pair of disjoint STS(n) of a special form yields a black-and-white tiling of some closed surface. For each n ≡ 3 (mod 6) we prove that there exist nonisomorphic tilings of nonorientable surfaces by pairs of Steiner triple systems of order n. We also show that for half of the values n ≡ 1 (mod 6) there are nonisomorphic tilings of nonorientable closed surfaces.     

Novel carbazole/anthracene hybrids for efficient blue organic light-emitting diodes

Two novel carbazole/anthracene hybrided molecules, namely 2-(anthracen-9-yl)-9-ethyl-9H-carbazole (AnCz) and 2,7-di(anthracen-9-yl)-9-ethyl-9H-carbazole (2AnCz), were designed and synthesized via palladium catalyzed coupling reaction. The anthracene was attached either at the 2-site (AnCz) or at both 2,7-sites (2AnCz) of the central carbazole core to tune the conjugation state and the optoelectronic properties of the resultant molecules. Both of them show good solubility in common organic solvents. They also possess relatively high HOMO levels (−5.39 eV, −5.40 eV) that would facilitate efficient hole injection and be favorable for high power efficiencies when used in organic light-emitting devices (OLEDs). AnCz and 2AnCz were used as non-doped emitter to fabricate OLEDs by vacuum evaporation. Good performance was achieved with maximum luminance efficiency of 2.61 cd A⁻¹ and CIE coordinates of (0.15, 0.12) for AnCz, and 9.52 cd A⁻¹ and (0.22, 0.37) for 2AnCz.     

Embedding hamiltonian paths in hypercubes with a required vertex in a fixed position

Assume that n is a positive integer with n?2. It is proved that between any two different vertices x and y of Qn there exists a path Pl(x,y) of length l for any l with h(x,y)?l?n²−1 and 2|(l−h(x,y)). We expect such path Pl(x,y) can be further extended by including the vertices not in Pl(x,y) into a hamiltonian path from x to a fixed vertex z or a hamiltonian cycle. In this paper, we prove that for any two vertices x and z from different partite set of n-dimensional hypercube Qn, for any vertex y∈V(Qn)−{x,z}, and for any integer l with h(x,y)?l?n²−1−h(y,z) and 2|(l−h(x,y)), there exists a hamiltonian path R(x,y,z;l) from x to z such that dR(x,y,z;l)(x,y)=l. Moreover, for any two distinct vertices x and y of Qn and for any integer l with h(x,y)?l?²n−1 and 2|(l−h(x,y)), there exists a hamiltonian cycle S(x,y;l) such that dS(x,y;l)(x,y)=l.     

New complexity results for the k-covers problem

The k-covers problem (kCP) asks us to compute a minimum cardinality set of strings of given length k > 1 that covers a given string. It was shown in a recent paper, by reduction to 3-SAT, that the k-covers problem is NP-complete. In this paper we introduce a new problem, that we call the k-bounded relaxed vertex cover problem (RVCP_k), which we show is equivalent to k-bounded set cover (SCP_k). We show further that kCP is a special case of RVCP_k restricted to certain classes G_x,k of graphs that represent all strings x. Thus a minimum k-cover can be approximated to within a factor k in polynomial time. We discuss approximate solutions of kCP, and we state a number of conjectures and open problems related to kCP and G_x,k.     

Enhanced chemosensing of ammonia based on the novel molecular semiconductor-doped insulator (MSDI) heterojunctions

A series of new molecular semiconductor-doped insulator (MSDI) heterojunctions as conductimetric transducers to NH₃ sensing were fabricated based on a novel semiconducting molecular material, an amphiphilic tris(phthalocyaninato) rare earth triple-decker complex, Eu₂[Pc(15C5)₄]₂[Pc(OC₁₀H₂₁)₈], quasi-Langmuir-Shäfer (QLS) film, as a top-layer, and vacuum-deposited and cast film of CuPc as well as copper tetra-tert-butyl phthalocyanine (CuTTBPc) QLS film as a sub-layer, named as MSDIs 1, 2 and 3, respectively. MSDIs 1-3 and respective sub-layers prepared from three different methods were characterized by X-ray diffraction, electronic absorption spectra and current-voltage (I-V) measurements. Depending on the sub-layer film-forming method used, α-phase CuPc film structure, β-phase CuPc crystallites and H-type aggregates of CuTTBPc have been obtained, respectively. An increasing sensitivity to NH₃ at varied concentrations in the range of 15-800 ppm, follows the order MSDI 2 < MSDI 3 < MSDI 1, revealing the effect of sub-layer film structures on sensing performance of the MSDIs. In particular, the time-dependent current plot of the MSDI 1, with α-phase CuPc film as a sub-layer, clearly shows an excellent separation of the different ammonia concentration levels and nearly complete reversibility and reproducibility even at room temperature, which is unique among the phthalocyanine-based ammonia sensors thus far reported in the literature. This provides a general method to improve sensor response of organic heterojunctions by controlling and tuning the film structure of sub-layer with appropriate fabrication techniques. On the other hand, the enhanced sensitivity, stability and reproducible response of the MSDI 1 heterostructure in comparison with the respective single-layer films have also been obtained. A judicious combination of materials and molecular architectures has led to enhanced sensing properties of the MSDI 1, in which control at the molecular level can be achieved.     

On polymorphic types of untyped terms

Let S be a finite set of β normal closed terms and M and N a pair of β normal, η   distinct, closed terms. Then there exist polymorphic types a,b$a,b$ such that every member of S can be typed as a, and M and N have η expansions which can be typed as b; where, in the resulting typings, the members of S can be simultaneously consistently identified, and the η expansions of M and N are βη inconsistent (no model with more than one element of any type). A similar result holds in the presence of surjective pairing.     

A dual K-Na selective Prussian blue nanotubes sensor

A strategy for dual sensing of Na⁺ and K⁺ ions using Prussian blue nanotubes via selective inter/deintercalation of K⁺ ion and competitive inhibition by Na⁺ ion, is reported. The analytical signal is derived from the cyclic voltammetry cathodic peak position E_pc of Prussian blue nanotubes. Na⁺ and K⁺ levels in a sample solution can be determined conveniently using one Prussian blue nanotubes sensor. In addition, this versatile method can be applied for the analysis of single type of either Na⁺ or K⁺ ions. The dual-ion sensor response towards Na⁺ and K⁺ can be described using a model based on the competitive inhibition effects of Na⁺ on K⁺ inter/deintercalation in Prussian blue nanotubes. Successful application of the Prussian blue nanotubes sensor for Na⁺ and K⁺ determination is demonstrated in artificial saliva.     

An efficient algorithm for constructing a connected dominating set in mobile ad hoc networks

The connected dominating set (CDS) is widely used as a virtual backbone in mobile ad hoc networks. Although many distributed algorithms for constructing the CDS have been proposed, nearly all of them require two or more separated phases, which may cause problems such as long delay in the later phases when the network size is large. This paper proposes a Distributed Single-Phase algorithm for constructing a connected dominating set, DSP-CDS, in ad hoc networks. The DSP-CDS is an asynchronous distributed algorithm and converges quickly in a single phase. Each node uses one-hop neighborhood information and makes a local decision on whether to join the dominating set. Each node bases its decision on a key variable, strength, which guarantees that the dominating set is connected when the algorithm converges. The rules for computing strength can be changed to accommodate different application needs. The DSP-CDS adapts well to dynamic network topologies, upon which the algorithm makes only necessary local updates to maintain the CDS of the network. The performance of the DSP-CDS can be tuned by adjusting two main parameters. Extensive simulations have demonstrated that those parameters can affect the CDS size, the CDS diameter, and number of rounds for the algorithm to converge. Comparisons with other multiple-phase CDS algorithms have shown that the DSP-CDS converges fast and generates a CDS of comparable size.     

Upper bounds on the queuenumber of k-ary n-cubes

A queue layout of a graph consists of a linear order of its vertices, and a partition of its edges into queues, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph G, denoted by qn(G), is called the queuenumber of G. Heath and Rosenberg [SIAM J. Comput. 21 (1992) 927-958] showed that boolean n-cube (i.e., the n-dimensional hypercube) can be laid out using at most n−1 queues. Heath et al. [SIAM J. Discrete Math. 5 (1992) 398-412] showed that the ternary n-cube can be laid out using at most 2n−2 queues. Recently, Hasunuma and Hirota [Inform. Process. Lett. 104 (2007) 41-44] improved the upper bound on queuenumber to n−2 for hypercubes. In this paper, we deal with the upper bound on queuenumber of a wider class of graphs called k-ary n-cubes, which contains hypercubes and ternary n-cubes as subclasses. Our result improves the previous bound in the case of ternary n-cubes. Let denote the n-dimensional k-ary cube. This paper contributes three main results as follows:

(1)

if n?3.

(2)

if n?2 and 4?k?8.

(3)

if n?1 and k?9.

     

Non-contractible non-edges in 2-connected graphs

Any pair of non-adjacent vertices forms a non-edge in a graph. Contraction of a non-edge merges two non-adjacent vertices into a single vertex such that the edges incident on the non-adjacent vertices are now incident on the merged vertex. In this paper, we consider simple connected graphs, hence parallel edges are removed after contraction. The minimum number of nodes whose removal disconnects the graph is the connectivity of the graph. We say a graph is k-connected, if its connectivity is k. A non-edge in a k-connected graph is contractible if its contraction does not result in a graph of lower connectivity. Otherwise the non-edge is non-contractible. We focus our study on non-contractible non-edges in 2-connected graphs. We show that cycles are the only 2-connected graphs in which every non-edge is non-contractible.     

A simple band ratio technique to quantify the colored dissolved and detrital organic material from ocean color remotely sensed data

Spectral reflectances of the ocean, R, as derived from ocean color remote sensing data at four wavelengths (412, 443, 490, and 555 nm), can be used to form two ratios of spectral reflectance, namely R(412)/R(443), and R(490)/R(555), thereafter denoted R₄₄₃⁴¹² and R₅₅₅⁴⁹⁰. The former is mainly sensitive to the colored dissolved organic material (CDOM), albeit influenced by the algal content as depicted by the chlorophyll concentration, ([Chl]); in contrast, the latter is essentially depending on [Chl], although it is also influenced by CDOM. Therefore the signatures of CDOM and [Chl] which are not truly separable, can nevertheless be identified by considering simultaneously the two ratios. The concomitant variations in these ratios can be established via a bio-optical model developed for Case 1 waters. This model implicitly includes a “mean” relationship between CDOM and [Chl], and thus produces a unique curve relating R₄₄₃⁴¹² to R₅₅₅⁴⁹⁰. Deviations with respect to this mean relationship can be introduced through a factor Φ, with Φ > 1 (excess) or < 1 (deficit), applied to the CDOM-[Chl] ratio. A family of R₄₄₃⁴¹²-R₅₅₅⁴⁹⁰ curves is thus generated, in correspondence with the discrete values given to Φ; this “grid” (or numerically, a 2-D lookup table) allows the Φ-[Chl] couple to be unambiguously derived for any R₄₄₃⁴¹²-R₅₅₅⁴⁹⁰ couple. By applying this straightforward algorithm to actual reflectance ratios derived from ocean color imagery, the relative anomalies in CDOM with respect to its standard (Chl-related) values can be efficiently assessed. Within the global ocean (discarding the coastal zones), the Φ factor is widely varying, between at least ? and 3, and is roughly log-normally distributed around ~ 1 (no anomaly). The spatial distributions of the Φ factor in the whole ocean are strongly featured according to latitude, season, and hydrographic regimes, and these features are regularly reproducible, from year to year (2002-2007). This simple method is also validated against available in situ data, and its results compare favorably, for instance, to those of the GSM (Garver-Siegel-Maritorena) inversion method, in terms of retrieved CDOM concentrations and distribution patterns.     

Feynman graph generation and calculations in the Hopf algebra of Feynman graphs

Two programs for the computation of perturbative expansions of quantum field theory amplitudes are provided. feyngen can be used to generate Feynman graphs for Yang–Mills, QED and φ^k${\phi }^k$ theories. Using dedicated graph theoretic tools feyngen can generate graphs of comparatively high loop orders. feyncop implements the Hopf algebra of those Feynman graphs which incorporates the renormalization procedure necessary to calculate finite results in perturbation theory of the underlying quantum field theory. feyngen is validated by comparison to explicit calculations of zero dimensional quantum field theories and feyncop is validated using a combinatorial identity on the Hopf algebra of graphs.     

Geometry-based semantic ID for persistent and interoperable reference in feature-based parametric modeling

In current feature-based parametric design systems, the reusability principle is not fully supported as it was expected. Unpredictability and ambiguity of models often happen during design modification within one system as well as among different systems. This reference deficiency significantly reduces the power of feature-based parametric modeling, where geometry re-evaluation generates unexpected shapes. In this paper, a sufficient condition of B-Rep variance based on geometry continuity in parametric complex Euclidean (P^pC³) space is proposed. Shape and relation parameters are differentiated in P^pC³, thus parametric family can be defined. A semantic id scheme based on continuity of geometry is developed to solve the problem of naming persistency and to improve interoperability of CAD feature modeling. Hierarchical namespaces localize entity creation and identification. All geometric and topological entities are referred uniformly based on surface ids, and topology semantics is retained in id itself.     

Iterations for solving linear variational inequalities on domains with nonlinear boundaries

This paper deals with numerical methods for solving linear variational inequalities on an arbitrary closed convex subsetC of ? ⁿ . Although there were numerous iterations studied for the caseC=? ₊ ⁿ , few were proposed for the case whenC is a closed convex subset. The essential difficulty in this case is the nonlinearities ofC's boundaries. In this paper iteration processes are designed for solving linear variational inequalities on an arbitrary closed convex subsetC. In our algorithms the computation of a linear variational inequality is decomposed into a sequence of problems of projecting a vector to the closed convex subsetC, which are computable as long as the equations describing the boundaries are given. In particular, using our iterations one can easily compute a solution whenC is one of the common closed convex subsets such as cube, ball, ellipsoid, etc. The non-accurate iteration, the estimate of the solutions on unbounded domains and the theory of approximating the boundaries are also established. Moreover, a necessary and sufficient condition is given for a vector to be an approximate solution. Finally, some numerical examples are presented, which show that the designed algorithms are effective and efficient. The exposition of this paper is self-contained.