IN SEARCH OF IDEAL KNOTS

A concise introduction to the mathematical theory of knots is presented. Definitions of basic notionsare explained. Then, knots are considered as material objects and the question concerning their optimalconformations is posed. A numerical algorithm searching for the ideal knots is described. A few resultsobtained with its help are presented.Pozna

Conformal lattice of magnetic bubble domains in garnet film

We report experimental observations of magnetic bubble domain arrays with no apparent translational symmetry. Additionally the results of comparative numerical studies are discussed. Our goal is to present experimental evidence for natural occurence of conformal structures.Comment: 7 pages, 2 figures, LaTeX2e, accepted as paper E090 at JEMS'01 (Joint European Magnetic Symposia, formerly EMMA + MRM), August 28th to September 1st, 2001, Grenoble, Franc

The wine market - an empicrical examination of in-store consumer behaviour

Business success in the current highly competitive environment determines primarily the ability to understand the customer and his needs and identify the factors that influence consumer behavior. Therefore, the examination of consumer behavior and obtaining feedback on the development and state of the market as well as identifying current trends is an essential part of any successful business. Producers and traders are increasingly forced to adapt to the rapid development and changes in the market. This is especially important with food products, given the wide range of assortment, substitutability of particular groceries and strengthening competitive pressure of manufacturers and retailers. In general, consumer decision-making related to food is influenced by a number of different factors that are changing under the influence of new trends (greater emphasis on quality, country of origin etc.). Even more specific category is the wine market, which is subject to specific criteria of consumer choice, since from a consumer perspective, it is not a product of daily consumption. The world wine market is increasing; new producers as well as new groups of customers are emerging on the market. The distribution channels are becoming more diversified and wine is offered in both specialty stores and self-service outlets; hypermarkets, supermarkets and discount stores. Due to this trend the investigation of in-store consumer behavior becomes crucial. The aim of the paper is to discuss the usefulness of eye tracking based research for examining perceptions of people shelf displays. The research integrates measurements with a mobile eye camera (Eye tracker glasses) in real conditions of a wine shop in order to reveal the impact of merchandising (display of domestic and foreign wines) on the visual attention of the consumer. The results of qualitative research carried out in March 2015 will be presented

Riddled-like Basin in Two-Dimensional Map for Bouncing Motion of an Inelastic Particle on a Vibrating Board

Motivated by bouncing motion of an inelastic particle on a vibrating board, a simple two-dimensional map is constructed and its behavior is studied numerically. In addition to the typical route to chaos through a periodic doubling bifurcation, we found peculiar behavior in the parameter region where two stable periodic attractors coexist. A typical orbit in the region goes through chaotic motion for an extended transient period before it converges into one of the two periodic attractors. The basin structure in this parameter region is almost riddling and the fractal dimension of the basin boundary is close to two, {\it i.e.}, the dimension of the phase space.Comment: 4 pages, 5 figures. to be published in J. Phys. Soc. Jpn. (2002

Quadrisecants give new lower bounds for the ropelength of a knot

Using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is at least 15.66. This improves the previously known lower bound of 12. Numerical experiments have found a trefoil with ropelength less than 16.372, so our new bounds are quite sharp.Comment: v3 is the version published by Geometry & Topology on 25 February 200

On non-measurable sets and invariant tori

The question: "How many different trajectories are there on a single invariant torus within the phase space of an integrable Hamiltonian system?" is posed. A rigorous answer to the question is found both for the rational and the irrational tori. The relevant notion of non-measurable sets is discussed.Comment: 8 pages, 1 figur

Stiff knots

We report on the geometry and mechanics of knotted stiff strings. We discuss both closed and open knots. Our two main results are: (i) Their equilibrium energy as well as the equilibrium tension for open knots depend on the type of knot as the square of the bridge number; (ii) Braid localization is found to be a general feature of stiff strings entanglements, while angles and knot localization are forbidden. Moreover, we identify a family of knots for which the equilibrium shape is a circular braid. Two other equilibrium shapes are found from Monte Carlo simulations. These three shapes are confirmed by rudimentary experiments. Our approach is also extended to the problem of the minimization of the length of a knotted string with a maximum allowed curvature.Comment: Submitted to Phys. Rev.

Layer dynamics of a freely standing smectic-A film

We study the hydrodynamics of a freely-standing smectic-A film in the isothermal, incompressible limit theoretically by analyzing the linearized hydrodynamic equations of motion with proper boundary conditions. The dynamic properties for the system can be obtained from the response functions for the free surfaces. Permeation is included and its importance near the free surfaces is discussed. The hydrodynamic mode structure for the dynamics of the system is compared with that of bulk systems. We show that to describe the dynamic correlation functions for the system, in general, it is necessary to consider the smectic layer displacement $u$ and the velocity normal to the layers, $v_z$, together. Finally, our analysis also provides a basis for the theoretical study of the off-equilibrium dynamics of freely-standing smectic-A films.Comment: 22 pages, 4 figure

Time resolved particle dynamics in granular convection

We present an experimental study of the movement of individual particles in a layer of vertically shaken granular material. High-speed imaging allows us to investigate the motion of beads within one vibration period. This motion consists mainly of vertical jumps, and a global ordered drift. The analysis of the system movement as a whole reveals that the observed bifurcation in the flight time is not adequately described by the Inelastic Bouncing Ball Model. Near the bifurcation point, friction plays and important role, and the branches of the bifurcation do not diverge as the control parameter is increased. We quantify the friction of the beads against the walls, showing that this interaction is the underlying mechanism responsible for the dynamics of the flow observed near the lateral wall

Koncepcja jakości usługi handlowej

In the process of providing a trade service, an important role is played by tangible elements. Their role is visible both in the process of providing thereof and in the fact that an effect of the process is also tangible goods. The features of the very trade service, such as heterogeneity, simultaneousness of service consumption with provision thereof, lack of possibility to store and, first of all, intangible nature, cause that the main burden of assessment of quality of the service should be left to purchasers thereof. Therefore, in case of services, there are often used the concept of perceived quality. This quality is defined as customer’s feelings connected with quality of a definite service or as a customer’s opinion on or attitude towards the service.В процессе предоставления торговой услуги существенное значение имеют материальные элементы. Их роль заметна как в процессе предоставления услуги, так и в факте, что эффектом того процесса являются также материальные блага. Свойства самой торговой услуги, такие как гетерогенность, одновременность потребления с предоставлением, отсутствие возможности складировать и, прежде всего, нематериальный характер, приводят к тому, что основное бремя оценки качества услуги должно быть оставлено за покупателями услуг. И потому в случае услуг часто используют концепцию воспринимаемого качества. Это качество определяют как ощущения клиента, связанные с качеством определенной услуги, или как мнение клиента об услуге или отношение к ней