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1

On the existence of complex Hadamard submatrices of the Fourier matrices

Bond Bailey Madison, Glickfield R. Alexander, Herr John E.

Demonstratio Mathematica

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2019

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Vol. 52, nr 1

1--9

EN

We use a theorem of Lam and Leung to prove that a submatrix of a Fourier matrix cannot be Hadamard for particular cases when the dimension of the submatrix does not divide the dimension of the Fourier matrix. We also make some observations on the trace-spectrum relationship of dephased Hadamard matrices of low dimension.

2

From Branching to Linear Time, Coalgebraically

Cîrstea C.

Fundamenta Informaticae

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2017

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Vol. 150, nr 3/4

379--406

EN

We consider state-based systems modelled as coalgebras whose type incorporates branching, and show that suitably adapting the definition of coalgebraic bisimulation yields a general and uniform account of the linear-time behaviour of a state in such a coalgebra. By moving away from a boolean universe of truth values, our approach can measure the extent to which a state in a system with branching is able to exhibit a particular linear-time behaviour. This instantiates to measuring the probability of a specific behaviour occurring in a probabilistic system, or measuring the minimal cost of exhibiting a given behaviour in the case of weighted computations.

3

The use of the terms trace, mark and structure

Vallon L. H., Rindsberg A. K., Martin A. J.

Annales Societatis Geologorum Poloniae

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2015

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Vol. 85, No. 3

527--528

EN

Mark, trace and structure have been in consistently used in ichnology for many years; we wish to clarify the origins and to prescribe correct usage of these terms. The origins of the words are ancient and complex; in the twentieth century they were given clear definitions as ichnologic terms. Seilacher (1953) defined a mark (German Marke) as a physical (abiogenic) sedimentary structure, as in the common terms sole mark, flute mark, but not bite mark or scratch mark. Trace has been defined many times; we recommend the consensus definition of Bertling et al. (2006) as “a morphologically recurrent structure resulting from the life activity of an individual organism (or homotypic or ganisms) modifying the substrate”; this in cludes dwelling trace, feeding trace, bite trace. Structure, as implied in another consensus paper (Frey, 1973), is a neutral term for geologic patterns resulting from either biogenic or abiogenic processes. Use of the three terms in a clear consistent manner will aid communication both among ichnologists and between ichnologists and their colleagues in other fields.

4

Infinite Traces and Symbolic Dynamics - the Minimal Shift Case

Foryś W., Oprocha P.

Fundamenta Informaticae

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2011

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Vol. 111, nr 2

147-161

EN

We study interrelations between symbolic descriptions of concurrently evolving systems and underlying sequential dynamics. The basic framework for this research is formulated on the background of the theory of traces. We focus our interests on minimal shifts and t-shifts generated by them, that is shifts defined in the space of infinite real traces. We show that sets of infinite real traces generated by minimal shifts are always closed and, under some conditions, are also tshifts. Additional discussion for the case of small alphabets (containing at most four letters) is also provided.

5

A Kleene-Schützenberger Theorem for Trace Series over Bounded Lattices

Huschenbett M.

Fundamenta Informaticae

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2011

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Vol. 112, nr 2/3

171-191

EN

We study weighted trace automata with weights in strong bimonoids. Traces form a generalization of words that allow to model concurrency; strong bimonoids are algebraic structures that can be regarded as "semirings without distributivity". A very important example for the latter are bounded lattices, especially non-distributive ones. We show that if both operations of the bimonoid are locally finite, then the classes of recognizable and mc-rational trace series coincide and, in general, are properly contained in the class of c-rational series. Moreover, if, in addition, in the bimonoid the addition is idempotent and the multiplication is commutative, then all three classes coincide.

6

Architektura wczoraj fragmentem współczesności

Kobylarczyk J.

Czasopismo Techniczne. Architektura

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2011

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R. 108, z. 4-A/2

182--187

PL

W artykule zaprezentowane zostały wyniki badań ankietowych dotyczących oceny wpływu bliskości dóbr kultury na atrakcyjność miejsca zamieszkania i jakości środowiska zamieszkania w niewielkich miastach województwa Podkarpackiego. Badania środowiskowe wsparte zostały własnymi analizami, na podstawie których został oceniony charakter, funkcja, stan techniczny i wizualny obiektów zabytkowych jako ważnych elementów współczesnego wizerunku miasta oraz dowód na to, że architektura nie przemija, trwa.

EN

This article presents the results of a survey concerning an assessment of the impact of the nearness of cultural possessions on the attractiveness of a place of residence and the quality of a housing environment in some small towns in the Province of Podkarpacie. This environmental research was supported with the author's own analyses which helped to evaluate the character, function as well as technical and visual condition of historic objects as important elements of the contemporary image of a town which prove that architecture does not fade away - it remains.

7

Znaki, inskrypcje i ślady na powierzchni drewna w zabytkowych konstrukcjach dachowych

Mączyński D.

Wiadomości Konserwatorskie

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2009

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Nr 25

28--36

PL

Interdyscyplinarne badania drewnianych, zabytkowych konstrukcji dachowych ujawniły wiele nowych informacji naukowych, dotąd pomijanych i w związku z tym w niedostateczny sposób udokumentowanych. Analiza znaków ciesielskich pozwala na uzyska- nie informacji na temat jednorodności i kompletności konstrukcji oraz dokonanych w niej zmian. Pokazuje także ewolucję techniki budowlanej. Pęknięcia przebiegające przez znaki ciesielskie mogą świadczyć o tym, że do budowy użyto świeżo pozyskanego drewna. Napisy, podpisy i daty zachowane na powierzchniach elementów pozwalają ustalić czas powstania konstrukcji, jej przebudowy lub naprawy oraz mogą pomóc zidentyfikować wykonawców. Zupełnie nowym odkryciem są zachowane na niektórych elementach konstrukcji napisy handlowe. Świadczą one o przygotowywaniu części konstrukcji poza placem budowy i dostarczaniu jej w formie obrobionych elementów, prawie gotowych do montażu. Bada się także ślady pozostawione w czasie obróbki drewna przez tradycyjne narzędzia ciesielskie. Pozwala to ustalić dawne techniki obróbki drewna, kształt użytych narzędzi i metody wznoszenia konstrukcji. Można także stwierdzić, czy prace wykonywała jedna ekipa cieśli, czy też kilka zespołów. W szerszej perspektywie uzyskane z takich badań informacje mogą posłużyć do analizy historii rozwoju ciesielstwa i budownictwa na większych obszarach naszego kontynentu. Część z odkrywanych śladów nadal wymaga odpowiedniej interpretacji. W Polsce, w czasie remontów dawnych więźb dachowych, bardzo często zaleca się ociosać powierzchnie uszkodzonych elementów drewnianej konstrukcji. Jeśli nie wykonano odpowiednich badań i dokumentacji, po takim zabiegu ważne informacje naukowe ulegają całkowitemu zniszczeniu.

EN

Interdisciplinary research on historic wooden roof constructions revealed plenty of new scientific information, previously ignored and thus insufficiently documented. Analysis of carpenters’ marks allows for obtaining information concerning the homogeneity and completeness of construction as well as alterations made to it. Moreover, it illustrates the evolution of building techniques. The cracks running through carpenters’ marks could serve as evidence that freshly felled timber was used for construction work. Marks, signatures and dates preserved on the surface of elements allow for ascertaining the time when the construction was erected, rebuilt or repaired, and could help to identify the builders. Tradesmen’s marks, preserved on some construction elements, are a completely new discovery. They serve as proof that some sections of constructions were prepared outside the building site and delivered in the form of shaped elements almost ready for assembling. Traces left by the traditional carpenter’s tools during wood processing are also examined. It allows for identifying old techniques of wood working, the shape of tools used and methods of erecting buildings. It can be also stated whether the work was performed by one or several teams of carpenters. In a wider perspective, information obtained from such research can be useful for the analysis of the history of development of carpentry and construction work in larger areas of our continent. Some of the discovered traces still require appropriate interpretation. In Poland, during repair work on old roof constructions, it is frequently recommended to hew the surface of damaged elements of the wooden structure. If no appropriate examination and documentation had been done earlier, then after such treatment important scientific information is utterly destroyed.

8

Porings and poring algebras

Jun Y., Kim H., Neggers J.

Demonstratio Mathematica

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2006

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Vol. 39, nr 2

267-276

EN

In this paper we define an algebra of type (2,2,0) associated with posets called a poring and we study several properties of porings and the linear algebras having such porings as their bases. In particular, we show that if (P; *, .) is a standard poring then the distributive law (x . y) * z = (x * z) . (y * z) holds iff the poset P (or the poset X) is (C2 +1)-free.

9

Sposób wyznaczania miejsca kolizji pojazdów przy ograniczonych danych

Momot W., Pankiewicz B.

Zeszyty Naukowe Politechniki Świętokrzyskiej. Mechanika

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2004

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Z. 79

289-296

PL

W artykule przedstawiono sposób wyznaczania miejsca kolizji pojazdów w sytuacji, gdy nie pozwalają na to dowody rzeczowe. Wykorzystano przy tym równanie zachowania pędu i zachowania energii oraz warunek zamknięcia się czworoboku wektorów ilości ruchu kolidujących pojazdów, których kierunki i zwroty są zgodne z ustalonymi kierunkami ich ruchu przed zderzeniem i wynikającymi z przyjętego miejsca kolizji po niej.

EN

The paper presents the method of appoint place cars collision when keep on proof factual. Use for once condition catch quadrangle vectors momentum collisions

10

Place/Transition Petri Net Evolutions: Recording Ways, Analysis and Synthesis

Czaja L.

Fundamenta Informaticae

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2002

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Vol. 51, nr 1,2

43-58

EN

Four semantic domains for Place/Transition Petri nets and their relationships are considered. They are monoids of respectively: firing sequences, processes, traces and dependence graphs. For each of them the analysis and synthesis problem is stated and solved. The monoid of processes is defined in a non-standard way. Nets under consideration involve weights of arrows and capacities (finite or infinite) of places. However, the analysis and synthesis tasks require nets to be pure, i.e. each of their transition must have the pre-set and post-set disjoint.