Drag and lift coefficients of inclined finite circular cylinders at moderate Reynolds numbers

The flow around two-dimensional cylinders at moderate Reynolds numbers has been much studied, both for cylinders perpendicular to the flow and for cylinders yawed to the flow. In contrast, yawed finite aspect ratio cylinders have received little attention. In this article we describe computer simulations of cylinders with aspect ratios 2  L/D  20 yawed at angles 0°  α  90° relative to a free stream. The simulations were carried out for Reynolds numbers in the range 1  Re  40. The simulations show that the Independence Principle [Zdravkovich MM. Flow around circular cylinders, vol. 2: applications. New York: Oxford University Press; 2003[1]] is not accurate for α  45°. We have also found that for all aspect ratios, the ratio of the lift to drag force reaches a maximum for 40° < α < 50°. Finally, we present C_L and C_D relationships as best curve fits to computational data.     

Intervals of solutions of the discrete-time algebraic Riccati equation

If two solutions YZ of the DARE are given then the set of solutions X with YXZ can be parametrized by invariant subspaces of the closed loop matrix corresponding to Y. The paper extends the geometric theory of Willems from the continuous-time to the discrete-time ARE making the weakest possible assumptions.     

Long paths in hypercubes with a quadratic number of faults

A path between distinct vertices u and v of the n-dimensional hypercube Q_n avoiding a given set of f faulty vertices is called long if its length is at least 2ⁿ-2f-2. We present a function (n)=Θ(n²) such that if f(n) then there is a long fault-free path between every pair of distinct vertices of the largest fault-free block of Q_n. Moreover, the bound provided by (n) is asymptotically optimal. Furthermore, we show that assuming f(n), the existence of a long fault-free path between an arbitrary pair of vertices may be verified in polynomial time with respect to n and, if the path exists, its construction performed in linear time with respect to its length.     

Inductive Synthesis of Recursive Processes from Logical Properties

This paper proposes an inductive synthesis algorithm for a recursive process. To synthesize a process, facts, which must be satisfied by the target process, are given to the algorithm one by one since such facts are infinitely many in general. When n facts are input to the algorithm, it outputs a process which satisfies the given n facts. And this generating process is repeated infinitely many times. To represent facts of a process, we adopt a subcalculus of μ-calculus. First, we introduce a new preorder _d on recursive processes based on the subcalculus to discuss its properties. p_d q means that pf implies qf, for all formulae f in the subcalculus. Then, its discriminative power and relationship with other preorders are also discussed. Finally, we present the synthesis algorithm. The correctness of the algorithm can be stated that the output sequence of processes by the algorithm converges to a process, which cannot be distinguished from the intended one (if we could know it) by a given enumeration of facts, in the limit. A prototype system based on the algorithm is stated as well.     

A note on path bipancyclicity of hypercubes

In [C.H. Tsai, S.Y. Jiang, Path bipancyclicity of hypercubes, Inform. Process. Lett. 101 (2007) 93–97], the authors showed that any path in an n-cube with length of k, 2k2n−4, lies on a cycle of every even length from 2k to 2ⁿ inclusive. Base on Lemma 5 of that paper, they proved the subcase 2.2.1 of the main theorem of that paper. However, the lemma is false, therefore, we propose a lemma to replace that lemma. Therefore, the main result of [C.H. Tsai, S.Y. Jiang, Path bipancyclicity of hypercubes, Inform. Process. Lett. 101 (2007) 93–97] is still correct.     

To be fair or efficient or a bit of both

Introducing a new concept of (α,β)-fairness, which allows for a bounded fairness compromise, so that a source is allocated a rate neither less than 0α1, nor more than β1, times its fair share, this paper provides a framework to optimize efficiency (utilization, throughput or revenue) subject to fairness constraints in a general telecommunications network for an arbitrary fairness criterion and cost functions. We formulate a non-linear program (NLP) that finds the optimal bandwidth allocation by maximizing efficiency subject to (α,β)-fairness constraints. This leads to what we call an efficiency–fairness function, which shows the benefit in efficiency as a function of the extent to which fairness is compromised. To solve the NLP we use two algorithms. The first is a well-known branch-and-bound-based algorithm called Lipschitz Global Optimization and the second is a recently developed algorithm called Algorithm for Global Optimization Problems (AGOP).We demonstrate the applicability of the framework to a range of examples from sharing a single link to efficiency fairness issues associated with serving customers in remote communities.     

The Undecidability of the First-Order Theories of One Step Rewriting in Linear Canonical Systems

By reduction from the halting problem for Minsky's two-register machines we prove that there is no algorithm capable of deciding the -theory of one step rewriting of an arbitrary finite linear confluent finitely terminating term rewriting system (weak undecidability). We also present a fixed such system with undecidable *-theory of one step rewriting (strong undecidability). This improves over all previously known results of the same kind.     

Sentences over Integral Domains and Their Computational Complexities

LetRbe a Hilbertian domain and letKbe its fraction field. Letψ(x₁, …, x_n, y) be a quantifier free arithmetical formula overR. We may also takeψ(x₁, …, x_n, y) to be an arithmetical formula overK[x₁, …, x_n] and write it asψ(y). In this paper we show that ifRhas enough non-units and x₁…x_n y ψ(x₁, …, x_n, y), called an ⁿ  sentence, is true inR, then y ψ(y) is true inK[x₁, …, x_n]. Also, ifR=K[T], whereKis an infinite integral domain andx₁…x_n y ψ(x₁, …, x_n, y)is true inR, then y ψ(y) is true inR[x₁, …, x_n]. These results are applied to find the upper and lower bounds of the time complexities of various decision problems on diophantine equations with parameters and arithmetical sentences. Some of the results are: 1. The decision problem of sentences and diophantine equations with parameters over the ring of integers of a global field are co-NP-complete. 2. The decision problem of sentences over the ring of integers of a global field is NP-complete. 3. LetKbe an infinite domain, the time complexities of the decision problems of equations with parameters and sentences over the polynomial ringK[t] are polynomial time reducible to factoring polynomials overK. 4. The decision problem of sentences over all algebraic integer rings is in P. 5. The decision problem of sentences over all integral domains with characteristic 0 is in P. 6. The time complexity of the decision problem of sentences over all integral domains is polynomial time reducible to factoring integers overZand factoring polynomials over finite fields.     

Fully Scalable Fault-Tolerant Simulations for BSP and CGM

In this paper we consider general simulations of algorithms designed for fully operational BSP and CGM machines on machines with faulty processors. The BSP (or CGM) machine is a parallel multicomputer consisting of p processors for which a memory of n words is evenly distributed and each processor can send and receive at most h messages in a superstep. The faults are deterministic (i.e., worst-case distributions of faults are considered) and static (i.e., they do not change in the course of computation). We assume that a constant fraction of processors are faulty.  We present two fault-tolerant simulation techniques for BSP and CGM:  1. A deterministic simulation that achieves O(1) slowdown for local computations and O((log_h p)²) slowdown for communications per superstep, provided that a preprocessing is done that requires O((log_h p)²) supersteps and linear (in h) computation per processor in each superstep.  2. A randomized simulation that achieves O(1) slowdown for local computations and O(log_h p) slowdown for communications per superstep with high probability, after the same (deterministic) preprocessing as above.  Our results are fully scalable over all values of p from Θ(1) to Θ(n). Furthermore, our results imply that if pn for 0<<1 and h=Θ((n/p)^δ) for 0<δ1 (which hold in almost all practical BSP and CGM computations), algorithms can be made resilient to a constant fraction of processor faults without any asymptotic slowdown.     

A Logic for Reasoning about Generic Judgments

This paper presents an extension of a proof system for encoding generic judgments, the logic FOλ^Δ of Miller and Tiu, with an induction principle. The logic FOλ^Δ is itself an extension of intuitionistic logic with fixed points and a “generic quantifier”, , which is used to reason about the dynamics of bindings in object systems encoded in the logic. A previous attempt to extend FOλ^Δ with an induction principle has been unsuccessful in modeling some behaviours of bindings in inductive specifications. It turns out that this problem can be solved by relaxing some restrictions on , in particular by adding the axiom B≡x.B, where x is not free in B. We show that by adopting the equivariance principle, the presentation of the extended logic can be much simplified. Cut-elimination for the extended logic is stated, and some applications in reasoning about an object logic and a simply typed λ-calculus are illustrated.     

Modelling Generic Judgements

We propose a semantics for the -quantifier of Miller and Tiu. First we consider the case for classical first-order logic. In this case, the interpretation is close to standard Tarski-semantics and completeness can be shown using a standard argument. Then we put our semantics into a broader context by giving a general interpretation of in categories with binding structure. Since categories with binding structure also encompass nominal logic, we thus show that both -logic and nominal logic can be modelled using the same definition of binding. As a special case of the general semantics in categories with binding structure, we recover Gabbay & Cheney's translation of FOλ into nominal logic.     

On Some Schützenberger Conjectures

In this paper we consider factorizing codes C over A, i.e., codes verifying the factorization conjecture by Schützenberger. Let n be the positive integer such that aⁿC, we show how we can construct C starting with factorizing codes C′ with a^n′C′ and n′ < n, under the hypothesis that all words aⁱza^j in C, with z(A\a)A*(A\a) (A\a), satisfy i, j, > n. The operation involved, already introduced by Anselmo, is also used to show that all maximal codes C=P(A−1)S+1 with P, SZA and P or S in Za can be constructed by means of this operation starting with prefix and suffix codes. Old conjectures by Schützenberger have been revised.     

Wireless network design via 3-decompositions

We consider some network design problems with applications for wireless networks. The input for these problems is a metric space (X,d) and a finite subset UX of terminals. In the Steiner Tree with Minimum Number of Steiner Points (STMSP) problem, the goal is to find a minimum size set SX−U of points so that the unit-disc graph of S+U is connected. Let Δ be the smallest integer so that for any finite VX for which the unit-disc graph is connected, this graph contains a spanning tree with maximum degree Δ. The best known approximation ratio for STMSP was Δ−1 [I.I. Măndoiu, A.Z. Zelikovsky, A note on the MST heuristic for bounded edge-length Steiner trees with minimum number of Steiner points, Information Processing Letters 75 (4) (2000) 165–167]. We improve this ratio to (Δ+1)/2+1+ε.In the Minimum Power Spanning Tree (MPST) problem, V=X is finite, and the goal is to find a “range assignment” on the nodes so that the edge set contains a spanning tree, and ∑_vVp(v) is minimized. We consider a particular case {0,1}-MPST of MPST when the distances are in {0,1}; here the goal is to find a minimum size set SV of “active” nodes so that the graph (V,E₀+E₁(S)) is connected, where , and E₁(S) is the set the edges in with both endpoints in S. We will show that the (5/3+ε)-approximation scheme for MPST of [E. Althaus, G. Calinescu, I. Măndoiu, S. Prasad, N. Tchervenski, A. Zelikovsky, Power efficient range assignment for symmetric connectivity in static ad hoc wireless networks, Wireless Networks 12 (3) (2006) 287–299] achieves a ratio 3/2 for {0,1}-distances. This answers an open question posed in [E. Lloyd, R. Liu, S. Ravi, Approximating the minimum number of maximum power users in ad hoc networks, Mobile Networks and Applications 11 (2006) 129–142].     

Isolation concepts for efficiently enumerating dense subgraphs

In an undirected graph G=(V,E), a set of k vertices is called c-isolated if it has less than ck outgoing edges. Ito and Iwama [H. Ito, K. Iwama, Enumeration of isolated cliques and pseudo-cliques, ACM Transactions on Algorithms (2008) (in press)] gave an algorithm to enumerate all c-isolated maximal cliques in O(4^cc⁴|E|) time. We extend this to enumerating all maximal c-isolated cliques (which are a superset) and improve the running time bound to O(2.89^cc²|E|), using modifications which also facilitate parallelizing the enumeration. Moreover, we introduce a more restricted and a more general isolation concept and show that both lead to faster enumeration algorithms. Finally, we extend our considerations to s-plexes (a relaxation of the clique notion), providing a W[1]-hardness result when the size of the s-plex is the parameter and a fixed-parameter algorithm for enumerating isolated s-plexes when the parameter describes the degree of isolation.     

Liquid–solid equilibria in quinary system Na,Mg/Cl,SO4,NO3–H2O at 298.15 K

In order to develop the nitrate deposits found close to Lop Nur in the Xinjiang region in China, the solubilities of the system Na⁺,Mg²⁺/Cl⁻,SO₄²⁻, NO₃⁻–H₂O and its subsystems, the quaternary systems Na⁺,Mg²⁺/SO₄²⁻,NO₃⁻–H₂O and Mg²⁺/Cl⁻,SO₄²⁻,NO₃⁻–H₂O, were studied at 298.15 K. The phase diagrams were plotted according to the solubilities achieved. In the equilibrium phase diagram of Mg²⁺/Cl⁻,SO₄²⁻,NO₃⁻–H₂O, there are two invariant points, five univariant curves and four regions of crystallization: Mg(NO₃)₂6H₂O,MgCl₂6H₂O,MgSO₄7H₂O and MgSO₄(1–6)H₂O. In the equilibrium phase diagram of Na⁺,Mg²⁺/SO₄²⁻, NO₃⁻–H₂O, there are five invariant points, eleven univariant curves and seven regions of crystallization: Na₂SO₄,Na₂SO₄10H₂O,NaNO₃,MgSO₄Na₂SO₄4H₂O,NaNO₃Na₂SO₄2H₂O,Mg(NO₃)₂6H₂O and MgSO₄7H₂O. In the equilibrium phase diagram of the Na⁺, Mg²⁺/Cl⁻,SO₄²⁻,NO₃⁻–H₂O system, there are six invariant points, and ten regions of crystallization: NaCl, NaNO₃,Na₂SO₄,Na₂SO₄10H₂O,MgSO₄Na₂SO₄4H₂O, NaNO₃Na₂SO₄2H₂O,MgCl₂6H₂O,Mg(NO₃)₂6H₂O, MgSO₄(1–6)H₂O and MgSO₄7H₂O.     

Finite gain stabilization requires analog control

A causal feedback map, taking sequences of measurements and producing sequences of controls, is denoted as finite set if, within any finite time horizon, its range is in a finite set. Bit-rate constrained or digital control are particular cases of finite-set feedback. In this paper, we show that the finite gain (FG) l_p stabilization, with 1p∞, of a discrete-time, linear and time-invariant unstable plant is impossible by finite-set feedback. In addition, we show that, under finite-set feedback, weaker (local) versions of FG l_p stability are also impossible. These facts are not obvious, since recent results have shown that input to state stabilization is viable by bit-rate constrained control. In view of such existing work, this paper leads to two conclusions: (1) even when input to state stability is attainable by finite-set feedback, small changes in the amplitude of the external excitation may cause, in relative terms, a large increase in the amplitude of the state (2) FG l_p stabilization requires logarithmic precision around zero. Since our conclusions hold with no assumption on the feedback structure, they cannot be derived from existing results. We adopt an information theoretic viewpoint, which also brings new insights into the problem of stabilization.     

Approximating the Minimum Chain Completion problem

A bipartite graph G=(U,V,E) is a chain graph [M. Yannakakis, Computing the minimum fill-in is NP-complete, SIAM J. Algebraic Discrete Methods 2 (1) (1981) 77–79] if there is a bijection such that Γ(π(1))Γ(π(2))Γ(π(|U|)), where Γ is a function that maps a node to its neighbors.We give approximation algorithms for two variants of the Minimum Chain Completion problem, where we are given a bipartite graph G(U,V,E), and the goal is find the minimum set of edges F that need to be added to G such that the bipartite graph G^′=(U,V,E^′) (E^′=EF) is a chain graph.     

Interfaces as functors, programs as coalgebras—A final coalgebra theorem in intensional type theory

In [P. Hancock, A. Setzer, Interactive programs in dependent type theory, in: P. Clote, H. Schwichtenberg (Eds.), Proc. 14th Annu. Conf. of EACSL, CSL’00, Fischbau, Germany, 21–26 August 2000, Vol. 1862, Springer, Berlin, 2000, pp. 317–331, URL citeseer.ist.psu.edu/article/hancock00interactive.html; P. Hancock, A. Setzer, Interactive programs and weakly final coalgebras in dependent type theory, in: L. Crosilla, P. Schuster (Eds.), From Sets and Types to Topology and Analysis. Towards Practicable Foundations for Constructive Mathematics, Oxford Logic Guides, Clarendon Press, 2005, URL www.cs.swan.ac.uk/csetzer/] Hancock and Setzer introduced rules to extend Martin-Löf's type theory in order to represent interactive programming. The rules essentially reflect the existence of weakly final coalgebras for a general form of polynomial functor. The standard rules of dependent type theory allow the definition of inductive types, which correspond to initial algebras. Coalgebraic types are not represented in a direct way. In this article we show the existence of final coalgebras in intensional type theory for these kind of functors, where we require uniqueness of identity proofs () for the set of states and the set of commands which determine the functor. We obtain the result by identifying programs which have essentially the same behaviour, viz. are bisimular. This proves the rules of Setzer and Hancock admissible in ordinary type theory, if we replace definitional equality by bisimulation. All proofs [M. Michelbrink, Verifications of final coalgebra theorem in: Interfaces as Functors, Programs as Coalgebras—A Final Coalgebra Theorem in Intensional Type Theory, 2005, URL www.cs.swan.ac.uk/csmichel/] are verified in the theorem prover agda [C. Coquand, Agda, Internet, URL www.cs.chalmers.se/catarina/agda/; K. Peterson, A programming system for type theory, Technical Report, S-412 96, Chalmers University of Technology, Göteborg, 1982], which is based on intensional Martin-Löf type theory.     

Thermostable tensoresistors of Co doped GaSb–FeGa1.3 eutectic composites

The microstructure and tensoresistive properties of GaSb–FeGa_1.3 eutectic composites doped with 0.1% Co have been investigated. It was found that the Co impurity atoms mainly accumulate in the metallic inclusions. The length of the inclusions in GaSb–FeGa_1.3Co was measured to be about half of those in undoped GaSb–FeGa_1.3 eutectics. The tensometric characteristics of gauges based on GaSb–FeGa_1.3Co have been found to be more thermostable than undoped samples.