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.     

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.     

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.     

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.     

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.     

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 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.     

-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.     

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.     

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.     

Fast periodic graph exploration with constant memory

We consider the problem of periodic exploration of all nodes in undirected graphs by using a finite state automaton called later a robot. The robot, using a constant number of states (memory bits), must be able to explore any unknown anonymous graph. The nodes in the graph are neither labelled nor coloured. However, while visiting a node v the robot can distinguish between edges incident to it. The edges are ordered and labelled by consecutive integers 1,…,d(v) called port numbers, where d(v) is the degree of v. Periodic graph exploration requires that the automaton has to visit every node infinitely many times in a periodic manner. In this paper, we are interested in minimisation of the length of the exploration period. In other words, we want to minimise the maximum number of edge traversals performed by the robot between two consecutive visits of a generic node, in the same state and entering the node by the same port. Note that the problem is unsolvable if the local port numbers are set arbitrarily, see [L. Budach, Automata and labyrinths, Math. Nachr. 86 (1978) 195–282]. In this context, we are looking for the minimum function π(n), such that, there exists an efficient deterministic algorithm for setting the local port numbers allowing the robot to explore all graphs of size n along a traversal route with the period π(n). Dobrev et al. proved in [S. Dobrev, J. Jansson, K. Sadakane, W.-K. Sung, Finding short right-hand-on-the-wall walks in graphs, in: Proc. 12th Colloquium on Structural Information and Communication Complexity, SIROCCO 2005, in: Lecture Notes in Comput. Sci., vol. 3499, Springer, Berlin, 2005, pp. 127–139] that for oblivious robots π(n)10n. Recently Ilcinkas proposed another port labelling algorithm for robots equipped with two extra memory bits, see [D. Ilcinkas, Setting port numbers for fast graph exploration, in: Proc. 13th Colloquium on Structural Information and Communication Complexity, SIROCCO 2006, in: Lecture Notes in Comput. Sci., vol. 4056, Springer, Berlin, 2006, pp. 59–69], where the exploration period π(n)4n−2. In the same paper, it is conjectured that the bound 4n−O(1) is tight even if the use of larger memory is allowed. In this paper, we disprove this conjecture presenting an efficient deterministic algorithm arranging the port numbers, such that, the robot equipped with a constant number of bits is able to complete the traversal period in π(n)<3.75n−2 steps hence decreasing the existing upper bound. This reduces the gap with the lower bound of π(n)2n−2 holding for any robot.     

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.     

Approximate fixed point sequence for a finite family of asymptotically pseudocontractive mappings

Let E be a real Banach space and K be a nonempty, closed, convex, and bounded subset of E. Let T_i:K→K, i=1,2,…,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε_n}, and asymptotically pseudocontractive mappings with sequences , where {ε_n} and , i=1,2,…,N, satisfy certain mild conditions. Let a sequence {x_n} be generated from x₁K by

for all integers n1, where T_n=T_n(modN), {u_n} be a sequence in K, and {λ_n}, {θ_n} and {μ_n} are three real sequences in [0,1] satisfying appropriate conditions; then x_n−T_lx_n→0 as n→∞ for each l{1,2,…,N}.     

Fast linear expected-time algorithms for computing maxima and convex hulls

This paper examines the expected complexity of boundary problems on a set ofN points inK-space. We assume that the points are chosen from a probability distribution in which each component of a point is chosen independently of all other components. We present an algorithm to find the maximal points usingKN + O (N^1–1/K log^1/K N) expected scalar comparisons, for fixedK 2. A lower bound shows that the algorithm is optimal in the leading term. We describe a simple maxima algorithm that is easy to code, and present experimental evidence that it has similar running time. For fixedK 2, an algorithm computes the convex hull of the set in 2KN + O(N^1–1/K log^1/KN) expected scalar comparisons. The history of the algorithms exhibits interesting interactions among consulting, algorithm design, data analysis, and mathematical analysis of algorithms.This work was performed while this author was visiting AT&T Bell Laboratories.     

Limited width parallel prefix circuits

In this paper, we present lower and upper bounds on the size of limited width, bounded and unbounded fan-out parallel prefix circuits. The lower bounds on the sizes of such circuits are a function of the depth, width, and number of inputs. The size requirement of an N input bounded fan-out parallel prefix circuit having limited width W and extra depth k (the difference between allowed and minimum possible depth) is shown to be (N log₂ W/2 ^k + N) for k log₂ W. This implies that insisting on minimum depth causes the circuit size to be nonlinear, while as little as log₂log₂ W of extra depth can possibly reduce the size to linear. Also, we show that there is a clear difference between the two cases of bounded and unbounded fan-out by proving the size of a limited width, unbounded fan-out parallel prefix circuit lies between a lower bound of ((2 + 2^1–k /3)N) and an upper bound of O((2 + 2^1–k )N).Uniform, systolic constructions of limited width parallel prefix circuits are provided here and shown to be asymptotically optimal. By associating the width of the circuit with the number of processors and the fan-out capabilities of the circuit with the interconnection structure of a multiprocessor, time- and processor-efficient algorithms may be developed.     

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].     

Strongly Hamiltonian laceability of the even k-ary n-cube

The interconnection network considered in this paper is the k-ary n-cube that is an attractive variance of the well-known hypercube. Many interconnection networks can be viewed as the subclasses of the k-ary n-cubes include the cycle, the torus and the hypercube. A bipartite graph is Hamiltonian laceable if there exists a Hamiltonian path joining every two vertices which are in distinct partite sets. A bipartite graph G is strongly Hamiltonian laceable if it is Hamiltonian laceable and there exists a path of length N − 2 joining each pair of vertices in the same partite set, where N = |V(G)|. We prove that the k-ary n-cube is strongly Hamiltonian laceable for k is even and n  2.     

On a Method of Paired Representation: Enhancement and Decomposition by Series Direction Images

In the paired representation, a two-dimensional (2-D) image is represented uniquely by a complete set of 1-D signals, so-called splitting-signals, that carry the spectral information of the image at frequency-points of specific subsets that divide the whole domain of frequencies. Image processing can thus be reduced to processing of splitting-signals and such process requires a modification of only a few spectral components of the image, for each signal. For instance, the α-rooting method of image enhancement can be fulfilled through processing one or a few splitting-signals. Such process can even be accomplished without computing the 2-D Fourier transforms of the original and enhanced images. To show that, we present an effective formula for inverse 2-D N×N-point paired transform, where N is a power of 2. The representation of the image and 2-D DFT by paired splitting-signals leads to the new concepts of direction and series images, that define the resolution and periodic structures of the image components, which can be packed in the form of the “resolution map” of the size of the image. Simple method of image enhancement by series images is described.