Multiple capture in Pontryagin’s recurrent example

This paper considers Pontryagin’s generalized nonstationary example [1, p. 478] with several participants under equal dynamic and inertia capabilities of the players. Multiple capture occurs when a given number of pursuers catch one evader. We obtain sufficient conditions for the multiple capture of the evader by a group of pursuers.     

Multiple capture in Pontryagin’s almost periodic example

This paper considers Pontryagin’s generalized nonstationary example with several participants under the same dynamic and inertial capabilities of the players, in which the set of admissible control actions is a convex compact set and the terminal sets are convex compact sets. We obtain sufficient conditions for the multiple capture of one evader by a group of pursuers under the assumption that some functions associated with the initial data and game parameters are almost periodic. Each pursuer cannot make a capture more than once before being eliminated from the game. Such a situation may happen when the evader must be “terminated” but contact between the pursuer and the evader does not guarantee termination.     

Solving Kirkman’s Schoolgirl Problem in a Few Seconds

The Social Golfer Problem has been extensively used by the constraint community in recent years as an example of a highly symmetric problem. It is an excellent problem for benchmarking symmetry breaking mechanisms such as SBDS or SBDD and for demonstrating the importance of the choice of the right model for one problem. We address in this paper a specific instance of the Golfer Problem well known as Kirkmans Schoolgirl Problem and list a collection of techniques and tricks to find efficiently all its unique solutions. In particular, we propose SBDD+, a generic improvement over SBDD which allows a deep pruning when a symmetry is detected during the search. Our implementation of the presented techniques improves previously published results by an order of magnitude for CPU time as well as for number of backtracks. It computes the seven unique solutions of Kirkmans problem in a few seconds.     

Solution to Euler’s elastic problem

Euler’s problem on stationary configurations of elastic rod with fixed endpoints and tangents at the endpoints is considered. The corresponding optimal control problem is reduced to several systems of algebraic equations in Jacobi’s functions. An algorithm and software for solving the optimal control problem are constructed.     

Goal-oriented error control in adaptive mixed FEM for Signorini’s Problem

This paper outlines goal-oriented finite element error control for Signorini’s problem. The discretization is based on a mixed formulation proposed by Hlavacek et al. which is extended to higher-order polynomials. A duality argument based on a variational inequality is applied, which allows for the estimates in h- as well as hp-adaptivity. Numerical results confirm the applicability of the theoretical findings.     

A Closed-Form Solution to Stollery’s Problem with Damage in Utility

Stollery (Can J Econ 31(3):730–742, 1998) studied a polluting oil-extracting economy governed by a constant utility criterion. The pollution, resulted from oil use, negatively affected production and utility. Stollery provided a closed-form solution for the case where only the production function was affected by the damage. This paper offers a closed-form solution to a non-trivial example of this economy with damage in the utility function. The solution is used for the analysis of uncertainties in resource policy caused by uncertainties in reserve estimate and in the intensity of the damage.     

Image Segmentation Using Euler’s Elastica as the Regularization

The active contour segmentation model of Chan and Vese has been widely used and generalized in different contexts in the literature. One possible modification is to employ Euler’s elastica as the regularization of active contour. In this paper, we study the new effects of this modification and validate them numerically using the augmented Lagrangian method.     

From Boltzmann to Euler: Hilbert’s 6th problem revisited

This article addresses the hydrodynamic limit of the Boltzmann equation, namely the compressible Euler equations of gas dynamics. An exact summation of the Chapman–Enskog expansion originally given by Gorban and Karlin is the key to the analysis. An appraisal of the role of viscosity and capillarity in the limiting process is then given where the analogy is drawn to the limit of the Korteweg–de Vries–Burgers equations as a small parameter tends to zero.     

An analysis of a firm’s capacity in Mazda’s Keiretsu

Capacity is defined as the power resulting from the specific position of a company in a network organization. This article extends the theory of network organizations to examine Mazda’s Yokokai Keiretsu, and proposes a new approach to calculating a firm’s capacity in a network. Capacity is divided into two categories, take-in capacity and take-out capacity, and the gap between them is called the capacity difference. We analyze the impact of capacity difference as a determinant of corporate performance in network organizations, thus providing a new perspective for successful corporate management.     

Three tokens in Herman’s algorithm

Herman’s algorithm is a synchronous randomized protocol for achieving self-stabilization in a token ring consisting of N processes. The interaction of tokens makes the dynamics of the protocol very difficult to analyze. In this paper we study the distribution of the time to stabilization, assuming that there are three tokens in the initial configuration. We show for arbitrary N and for an arbitrary timeout t that the probability of stabilization within time t is minimized by choosing as the initial three-token configuration the configuration in which the tokens are placed equidistantly on the ring. Our result strengthens a corollary of a theorem of McIver and Morgan (Inf. Process Lett. 94(2): 79–84, 2005), which states that the expected stabilization time is minimized by the equidistant configuration.     

What’s in a Name?

It was a cold winter’s night in 1991. After a long, difficult day in work I decided to have an early night. ‘Yep’, I said to my husband Brian at about 9 pm, ‘I’m going to bed with Clifford Stoll.’ Only being a few months’ married I was quick to clarify this by adding, ‘His Cuckoo’s Egg, that is.’ Hence the fascination began. I wanted to catch Markus Hess just as badly as Clifford Stoll did. I became Clifford Stoll’s doppelganger. I was with him every step of the way, checking those printouts and examining those logs. I was on call, waiting for that bleeper to go off. (This temporary aberration only lasted whilst reading the book)! The interesting thing is that I never once thought of Markus Hess as being ingenious let alone clever. I was more enthralled by the ingenuity of the pursuer rather than the dogged persistence of the pursued.     

The Octagon in Leonardo’s Drawings

Mark Reynolds presents a study on Leonardo’s abundant use of the octagon in his drawings and architectural renderings. Specifically, he focuses on Leonardo’s applications of the octagon: in his studies and sketches of the centralized church, and for which we can find influences specifically from Brunelleschi, as well as from other fifteenth-century architects working with this type of religious structure; in his almost obsessive and frequently repetitious drawing of octagonal shapes and forms in his notebooks throughout his career; in his project for a pavilion while with the Sforzas in the last part of his period in Milan. Also examined are ways to develop the modules to accommodate and the θ rectangles. The application of the modular units, so far, have been within the square and its gridwork, but as the octagon has traditionally been used in the development of both the circle and the square, this shape is an interesting challenge in terms of linking the two-dimensional surface to the three-dimensional forms we are planning to generate. The object is to provide us with more insight as to why the octagon held so much fascination for Leonardo as one of the ultimate geometric expressions of grandeur and practicality in spatial organization, design, and development. Often in Leonardo’s drawings of octagons, precise geometric constructions were lacking; the master’s approach was freehand. The author seeks to learn if Leonardo’s sketches can be put to the rigors of strict geometric construction, and still be viable as accurate renderings of octagonal geometric spaces with his own geometric constructions of those same spaces.     

Euler’s predictor–corrector technique for solving the depth-integrated shallow water equations

Euler’s predictor–corrector technique combined with finite analysis method is applied to solve 2D advection–diffusion shallow water equations. In this algorithm the momentum equations are calculated by the finite analysis method based on a single mesh, while the continuity equation is solved by Euler’s predictor–corrector technique. To verify the performance of this approach, the simulation of tidal flow in the Huangpu estuary is carried out. The numerical results are found to be consistent with the field results, implying that this proposed method is effective and applicable.     

The machine’s role in human’s service automation and knowledge sharing

The possibility of interacting with remote services in natural language opens up new opportunities for sharing knowledge and for automating services. Easy-to-use, text-based interfaces might provide more democratic access to legal information, government services, and everyday knowledge as well. However, the methodology of engineering robust natural language interfaces is very diverse, and widely deployed solutions are still yet to come. The main contribution is a detailed problem analysis on the theoretical level, which reveals that a text-based interface is best understood as an artificial agent that represents the interests of the remote party who is separated in time and space from the client. A possible ethical issue about the development of such an agent is also discussed.     

Circularity or Lacunae in Tarski’s Truth-Schemata

Tarski avoids the liar paradox by relativizing truth and falsehood to particular languages and forbidding the predication to sentences in a language of truth or falsehood by any sentences belonging to the same language. The Tarski truth-schemata stratify an object-language and indefinitely ascending hierarchy of meta-languages in which the truth or falsehood of sentences in a language can only be asserted or denied in a higher-order meta-language. However, Tarski’s statement of the truth-schemata themselves involve general truth functions, and in particular the biconditional, defined in terms of truth conditions involving truth values standardly displayed in a truth table. Consistently with his semantic program, all such truth values should also be relativized to particular languages for Tarski. The objection thus points toward the more interesting problem of Tarski’s concept of the exact status of truth predications in a general logic of sentential connectives. Tarski’s three-part solution to the circularity objection which he anticipates is discussed and refuted in detail.     

Application of Denisyuk’s holograms in advertising

In this article described application of holograms of Denisyuk executed in special technology, for advertizing. High advertizing influence is noted at a simultaneous combination of two factors—high diffraction efficiency and taken out before the hologram orthoscopic, or pseudoscopic images.