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.     

Predicate Abstraction for Dense Real-Time Systems

We propose predicate abstraction as a means for verifying a rich class of safety and liveness properties for dense real-time systems. First, we define a restricted semantics of timed systems which is observationally equivalent to the standard semantics in that it validates the same set of μ-calculus formulas without a next-step operator. Then, we recast the model checking problem S for a timed automaton S and a μ-calculus formula in terms of predicate abstraction. Whenever a set of abstraction predicates forms a so-called basis, the resulting abstraction is strongly preserving in the sense that S validates iff the corresponding finite abstraction validates this formula . Now, the abstracted system can be checked using familiar μ-calculus model checking. Like the region graph construction for timed automata, the predicate abstraction algorithm for timed automata usually is prohibitively expensive. In many cases it suffices to compute an approximation of a finite bisimulation by using only a subset of the basis of abstraction predicates. Starting with some coarse abstraction, we define a finite sequence of refined abstractions that converges to a strongly preserving abstraction. In each step, new abstraction predicates are selected nondeterministically from a finite basis. Counterexamples from failed μ-calculus model checking attempts can be used to heuristically choose a small set of new abstraction predicates for refining the abstraction.     

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.     

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.     

-Admissible control elements for diagonal semigroups on -spaces

For linear systems described by , where A is a diagonal operator on the state space l^r for some 1r<∞ and bl^r, we develop necessary and sufficient conditions for b to be p-admissible. This extends results by Ho, Russell and Weiss to the case r≠2.     

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.     

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.     

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.     

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.     

Ethanol gas sensor based on Al-doped ZnO nanomaterial with many gas diffusing channels

ZnO nanomaterial with multi-microstructures is synthesized by using normal pressure thermal evaporation and then doped with different Al₂O₃ contents by grinding in an agate mortar. The as-prepared Al-doped ZnO nanomaterials are characterized by X-ray diffraction and scanning electron microscopy. The characterization results show that all the compounds are wurtzite with hexagonal structure and are well crystallized. Channels/connecting holes arising from many kinds of ZnO microstructures are abundant. Both annealing and Al₂O₃-doping contributes to an increase in the quasi-one-dimensional and tri-dimensional microstructures. The as-prepared Al-doped ZnO nanomaterials show excellent gas responses to ethanol. The sensing mechanism of the ZnO-based nanomaterials with multi-microstructures is further analyzed by using the Effective Specific Surface Model. Excellent sensitivity (200) companied with short response time (8 s) and recovery time (10 s) to 3000 ppm ethanol is obtained with a ZnO-based sensor with 2 at.% Al₂O₃ at the operating temperature of 290 °C after the sensor is annealed at 500 °C.     

A necessary condition for quantitative exponential stability of linear state-space systems

For an arbitrary n×n constant matrix A the two following facts are well known:

• (1/n)Re(traceA)−max_j=1,…,nRe λ_j(A)0;

• If U is a unitary matrix, one can always find a skew-Hermitian matrix A so that U=e^A.

In this note we present the extension of these two facts to the context of linear time-varying dynamical systemsAs a by-product, this result suggests that, the notion of “slowly varying state-space systems”, commonly used in literature, is mathematically not natural to the problem of exponential stability.     

An Efficient Nelson-Oppen Decision Procedure for Difference Constraints over Rationals

Nelson and Oppen provided a methodology for modularly combining decision procedures for individual theories to construct a decision procedure for a combination of theories. In addition to providing a check for satisfiability, the individual decision procedures need to provide additional functionalities, including equality generation.In this paper, we propose a decision procedure for a conjunction of difference constraints over rationals (where the atomic formulas are of the form xy+c or x<y+c). The procedure extends any negative cycle detection algorithm (like the Bellman-Ford algorithm) to generate (1) equalities between all pair of variables, (2) produce proofs and (3) generates models that can be extended by other theories in a Nelson-Oppen framework. All the operations mentioned above can be performed with only a linear overhead to the cycle detection algorithm, in the average case.     

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.     

VCPSS: A two-in-one two-decoding-options image sharing method combining visual cryptography (VC) and polynomial-style sharing (PSS) approaches

This paper presents a novel method to combine two major branches of image sharing: VC and PSS. n transparencies are created for a given gray-valued secret image. If the decoding computer is temporarily not available at (or, not connected to) the decoding scene, we can still physically stack any t received transparencies (tn is a threshold value) to get a vague black-and-white view of the secret image immediately. On the other hand, when the decoding computer is finally available, then we can get a much finer gray-valued view of the secret image using the information hidden in the transparencies. In summary, each transparency is a two-in-one carrier of the information, and the decoding has two options.     

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].     

A discrete-time dynamic K-winners-take-all neural circuit

A discrete-time mathematical model of K-winners-take-all (KWTA) neural circuit that can quickly identify the K-winning from N neurons, where 1K<N, whose input signals are larger than that of remaining N−K neurons, is given and analyzed. A functional block scheme of the circuit is presented. For N competitors, such circuit is composed of N feedforward and one feedback hard-limiting neurons that are used to determine the dynamic shift of input signals. The circuit has low computational and hardware implementation complexity, high speed of signal processing, can process signals of any finite range, possesses signal order preserving property and does not require resetting and corresponding supervisory circuit that additionally increases a speed of signal processing.     

Interactions Between PVS and Maple in Symbolic Analysis of Control Systems

This paper presents a decision procedure for problems relating polynomial and transcendental functions. The procedure applies to functions that are continuously differentiable with a finite number of points of inflection in a closed convex set. It decides questions of the form ‘is f0?’, where {=,>,<}. An implementation of the procedure in Maple and PVS exploits the existing Maple, PVS and QEPCAD connections. It is at present limited to those twice differentiable functions whose derivatives are rational functions (rationally differentiable). This procedure is particularly applicable to the analysis of control systems in determining important properties such as stability.