B\"acklund transformations for nonlinear evolution equations: Hilbert space approach

A new method of determining B\"acklund transformations for nonlinear partial differential equations of the evolution type is introduced. Using the Hilbert space approach the problem of finding B\"acklund transformations is brought down to the solution of an abstract equation in Hilbert space.Comment: 15 page

Groups and nonlinear dynamical systems. Chaotic dynamics on the SU(2)xSU(2) group

In our previous paper: K. Kowalski and J. Rembieli\'nski, Groups and nonlinear dynamical systems. Dynamics on the SU(2) group, Physica D 99, 237 (1996), we introduced an abstract Newton-like equation on a general Lie algebra such that submanifolds fixed by the second-order Casimir operator are attracting set. The corresponding group parameters satisfy the nonlinear dynamical system having an attractor coinciding with the submanifold. In this work we discuss the case with the $SU(2)\times SU(2)$ group. The resulting second-order system in $R^6$ is demonstrated to exhibit chaotic behaviour.Comment: 12 pages LaTeX, uses espart.sty and equation.sty; accepted for publication in Chaos, Solitons & Fractal

The europeanization of the cemeteries of World War I in West Galicia : in search of transnational heroism and sacrifice

Focusing primarily on the Łużna-Pustki military cemetery constructed by the Austro-Hungarian army on the Eastern Front after the Battle of Gorlice, also known as the "Little Verdun" (2-5 May 1915), the article deals with the memory of World War I and its use in local, national (Polish) and European contexts. The text shows the history of this lieu de mémoire: its creation, cultural and artistic contexts, and ultimate slide into oblivion during the interwar period and after World War II, before a resurrection in interest in Poland at the turn of the 21st century. Taking into consideration Europeanization processes, the author shows how tangible remnants of World War I are brought into the limelight within European frames of reference and discusses the consequences of this discursive reinterpretation of the Łużna-Pustki military cemetery, awarded a European Heritage Label in 2016

Technology and Properties of Distance Five-layered Double-Weft-Knitted Fabrics with Elastomeric Threads

This paper presents the concept of forming distance weft-knitted fabrics with five knitted layers in their structure. The knitted fabrics developed have a relatively large thickness in relation to the needle pitch and distance between the needle beds of the knitting machine on which they were formed. The effect described was obtained by combining three knitted layers with the use of different reports and the number of monofilament threads knitted-in, and by modifying the knitted layers with elastomer threads. The distance knitted fabrics designed and produced for potential use as preforms for composites and parts protecting against an impact were tested and analysed with respect to their structural parameters

Alternate Solutions Analysis For Transportation Problems

The constraint structure of the transportation problem is so important that the literature is filled with efforts to provide efficient algorithms for solving it.  The intent of this work is to present various rules governing load distribution for alternate optimal solutions in transportation problems, a subject that has not attracted much attention in the current literature, with the result that the load assignment for an alternate optimal solution is left mostly at the discretion of the practitioner.  Using the Shadow Price theory we illustrate the structure of alternate solutions in a transportation problem and provide a systematic analysis for allocating loads to obtain an alternate optimal solution.  Numerical examples are presented to explain the proposed process