On the computation of Tricomi's ψ function

Two methods for calculating Tricomi's confluent hypergeometric function are discussed. Both methods are based on recurrence relations. The first method converges like $$\exp ( - \alpha |\lambda |^{1/3} n^{2/3} )for some \alpha > 0$$ and the second like $$\exp ( - \beta |\lambda |^{1/2} n^{1/2} )for some \beta > 0.$$ Several examples are presented.     

On the computation of Bernstein–Sato ideals

In this paper we compare the approach of Briançon and Maisonobe for computing Bernstein–Sato ideals—based on computations in a Poincaré–Birkhoff–Witt algebra—with the readily available method of Oaku and Takayama. We show that it can deal with interesting examples that have proved intractable so far.     

On the fast and fully discretized solution¶of integral and pseudo-differential equations¶on smooth curves

For the fast numerical solution of a fully discrete variant of the trigonometric Galerkin equations associated with periodic integral equations, we consider approximations with small residuals and provide order-optimal estimates for the associated error. The CGNR method is considered as a method with a simple iteration scheme where these approximations can be obtained by a total number of ℳ(N log N ) arithmetical operations, with N denoting the dimension of the space of trigonometric trial polynomials associated with the Galerkin method. Noise in the model of the problem as well as in the right-hand side is admitted. Received: August 1999 / Revised version: July 2000     

On the computation of the 〈3, 4, 5〉 curve skeleton of 3D objects

An algorithm to compute the curve skeleton of 3D objects in voxel images is presented. The skeleton is stable under isometric transformations of the object, since the algorithm is based on the use of the 〈3, 4, 5〉 weighted distance transform, which is a good approximation of the Euclidean distance transform. The 〈3, 4, 5〉 weighted distance transform is used both to identify suitable anchor points, and to efficiently check object voxels according to their distance to the background. The curve skeleton is symmetrically placed within the object, is topologically equivalent to the object, is unit-wide and provides a satisfactory representation of the object. Though the size of the object reconstructed from the curve skeleton via the reverse distance transformation is not as thick as that of the input, shape information is mostly retained by the skeleton, since all regions perceived as significant in the input can still be found in the reconstructed object.     

Control for the synchronization of Chen system via a single nonlinear input

This paper addresses control for the synchronization of Chen chaotic systems via sector nonlinear inputs. Feedback control, adaptive control, fast sliding mode and robust control approaches based on single state feedback controller are investigated. In these cases, sufficient conditions for the synchronization are obtained analytically. Numerical simulations verify the control performances.     

On the convergence of Schröder’s method for the simultaneous computation of polynomial zeros of unknown multiplicity

In this paper, we establish a general theorem for iteration functions in a cone normed space over \({{\mathbb {R}}}^n\). Using this theorem together with a general convergence theorem of Proinov (J Complex 33:118–144, 2016), we obtain a local convergence theorem with a priori and a posteriori error estimates as well as a theorem under computationally verifiable initial conditions for the Schröder’s iterative method considered as a method for simultaneous computation of polynomial zeros of unknown multiplicity. Numerical examples which demonstrate the convergence properties of the proposed method are also provided.     

On the space–time of optimal, approximate and streaming algorithms for synopsis construction problems

Synopses construction algorithms have been found to be of interest in query optimization, approximate query answering and mining, and over the last few years several good synopsis construction algorithms have been proposed. These algorithms have mostly focused on the running time of the synopsis construction vis-a-vis the synopsis quality. However the space complexity of synopsis construction algorithms has not been investigated as thoroughly. Many of the optimum synopsis construction algorithms are expensive in space. For some of these algorithms the space required to construct the synopsis is significantly larger than the space required to store the input. These algorithms rely on the fact that they require a smaller “working space” and most of the data can be resident on disc. The large space complexity of synopsis construction algorithms is a handicap in several scenarios. In the case of streaming algorithms, space is a fundamental constraint. In case of offline optimal or approximate algorithms, a better space complexity often makes these algorithms much more attractive by allowing them to run in main memory and not use disc, or alternately allows us to scale to significantly larger problems without running out of space. In this paper, we propose a simple and general technique that reduces space complexity of synopsis construction algorithms. As a consequence we show that the notion of “working space” proposed in these contexts is redundant. This technique can be easily applied to many existing algorithms for synopsis construction problems. We demonstrate the performance benefits of our proposal through experiments on real-life and synthetic data. We believe that our algorithm also generalizes to a broader range of dynamic programs beyond synopsis construction. Sudipto Guha’s research supported in part by an Alfred P. Sloan Research Fellowship and by NSF Awards CCF-0430376, CCF-0644119.A preliminary version of the paper appeared as “Space efficiency in synopsis construction algorithms”, VLDB Conference 2005, Trondheim, [19].     

On the mass and momentum transport in the Navier–Stokes slip layer

The Navier–Stokes slip boundary conditions are considered as conditions following from the mass and momentum balances within a thin, shell-like moving boundary layer. A problem of consistency between different models, that describes the internal and external friction in a viscous fluid, is stated within the framework of a proper form of the layer momentum balance. Appropriate constitutive equations for friction forces are formulated. The common features of the Navier, Stokes, Reynolds, and Maxwell concepts of a boundary slip layer are revalorized and discussed. Different mobility mechanisms connected with the transpiration phenomena, important for flows in micro- and nanochannels, are classified as a part of equations for the external friction.     

On the Verge of a Building

By the theory of Christopher Alexander, the famous architecture theorist, function of the verge of building and the pattern of its realization are illustrated. The selectable pattern for architecture design and drawing is discussed.     

On the Equivalence of Some Models of Computation

In[1],a definition of computation was given.In[3],we have clarified the necessity of thedefinition.Here we prove the equivalence between the definition and some models ofcomputation.Hence the sufficiency of the definition is clear abundantly.     

Which city is the greenest? A multi-dimensional deconstruction of city rankings

The question “which city is the greenest” sounds trivial, but in reality, this question contains statistical ambiguities. In this study, we approach this issue by ranking cities by green space shares. However, we do not base our ranking only on one green parameter and the commonly used administrative boundaries. Instead, we broaden access to rankings through several approaches: First, we calculate two parameters, i.e. green space shares and green space per capita. Second, we apply these parameters for two cases: for all green areas as well as for green areas with a minimum size of one hectare. The latter are considered to have an impact on near-home recreation and the local climate. Third, we relate these parameters on the one hand to administrative spatial units constituting the entity ‘city’, but juxtapose these on the other hand with two alternative spatial reference units: a morphological spatial unit that closely encompasses the built-up pattern of the city, and a standardized buffer unit around the city centers. The variability of these manifold rankings obtained by this study makes clear: the rank of one city in a relational system to other cities depends strongly on these parameters and spatial units applied. In our experiments we rank and compare the 80 major cities in Germany. The diversity of results allows to discuss the susceptibility of spatial statistics to ambiguities that may arise from the use of different concepts. By integrating these multidimensional concepts into one final ranking, we propose a strategy for a more holistic and robust approach while revealing uncertainties.     

Filtering of the pressure spurious modes in PN–PN spectral approximations of the Stokes system

In the framework of Jacobi polynomials based spectral methods, the $\text{P}{}_{\mathrm{N}}$–$\text{P}{}_{\mathrm{N}}$ approximation of the Stokes system generally shows the drawback that the pressure kernel does not reduce to the constant field. However, this drawback goes together with the advantage that the velocity field may be perfectly solenoı̈dal, i.e. the divergence of the velocity is the null polynomial. In this paper we suggest a filtering algorithm to recover the pressure in an efficient way.     

On the stability of interconnected systems†

This paper investigates the stability of systems which can be regarded as composed of interconnected subsystems. A sufficient condition for inputs-output L ^p stability, in terms of the L ^p gains of the subsystems and their interconnections is derived. For the case of L ² stability, it is compared with other criteria for asymptotic stability, obtained by Lyapunov techniques, and shown to give better results for a certain class of systems.     

On the cost–effectiveness of PRAMs

We introduce a formalism which allows to treat computer architecture as a formal optimization problem. We apply this to the design of shared memory parallel machines. While present parallel computers of this type only support the programming model of a shared memory but often process simultaneous access by several processors to the shared memory sequentially, theoretical computer science offers solutions for this problem that are provably fast and asymptotically optimal. But the constants in these constructions seemed to be too large to let them be competitive. We modify these constructions under engineering aspects and improve the price/performance ratio by roughly a factor of 6. The resulting machine has surprisingly good price/performance ratio even if compared with distributed memory machines. For almost all access patterns of all processors into the shared memory, access is as fast as the access of only a single processor. Received: 29 June 1993 / 22 June 1999     

On the Expressive Power of F-Logic Language

F-logic language is a logic database language based on frame logic.It is powerful in expressing object-oriented features.However,there was little work discussing its capability of manipulating complex objects.In this paper,the authors compare the capability of F-logic with that of logic database languages represented by COL.Through two pairs of semantic-preserving transformations,F-logic progams and their corresponding Herbrand interpretations,and vice versa.Also,the effects of negation are discussed.The results of this paper indicate that,without consideration of the effects of OID generating,F-logic language has the same power in manipulatin complex objects as COL,LDL1,and ELPS.     

On the Development of Applications of Logic in Programming

1.Preliminary RemarksBy Logic we mean the discipline which includes proof theory,model theory,recur-sion thoery and axiomatic set theory.In recent years there is a growing recognition of therelevance of logic to computer programming.The close relationship between these twofields seems to be aptly capsuled in the formula proposed by Patrick Hayes among others