scholarly journals Extremal Square-Free Words

10.37236/9264 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Jarosław Grytczuk ◽  
Hubert Kordulewski ◽  
Artur Niewiadomski
Keyword(s):  
Single Letter ◽  
Additional Property ◽  
Property A ◽  
Letter Alphabet ◽  
New Type ◽  
Free Word

A word is square-free if it does not contain nonempty factors of the form $XX$. In 1906 Thue proved that there exist arbitrarily long square-free words over a $3$-letter alphabet. We consider a new type of square-free words with additional property. A square-free word is called extremal if it cannot be extended to a new square-free word by inserting a single letter at any position. We prove that there exist infinitely many square-free extremal words over a $3$-letter alphabet. Some parts of our construction relies on computer verifications. It is not known if there exist any extremal square-free words over a $4$-letter alphabet.

scholarly journals Extremal Overlap-Free and Extremal $\beta$-Free Binary Words

10.37236/9703 ◽  
2020 ◽  
Vol 27 (4) ◽  
Author(s):  
Lucas Mol ◽  
Narad Rampersad ◽  
Jeffrey Shallit
Keyword(s):  
Real Number ◽  
Single Letter ◽  
Binary Word ◽  
Free Word

An overlap-free (or $\beta$-free) word $w$ over a fixed alphabet $\Sigma$ is extremal if every word obtained from $w$ by inserting a single letter from $\Sigma$ at any position contains an overlap (or a factor of exponent at least $\beta$, respectively). We find all lengths which admit an extremal overlap-free binary word. For every "extended" real number $\beta$ such that $2^+\leqslant\beta\leqslant 8/3$, we show that there are arbitrarily long extremal $\beta$-free binary words.

scholarly journals Experimental Study on Assembled Monolithic Concrete Shear Walls Built with Precast Two-Way Hollow Slabs

2014 ◽  
Vol 8 (1) ◽  
pp. 161-165 ◽  
Author(s):  
Zhijuan Sun ◽  
Yukun Mao ◽  
Jiliang Liu ◽  
Qinyan Zhao ◽  
Mingjin Chu
Keyword(s):  
Shear Failure ◽  
Precast Concrete ◽  
Shear Walls ◽  
Shear Wall ◽  
Shear Capacity ◽  
Property A ◽  
Joint Force ◽  
Vertical Reinforcement ◽  
New Type ◽  
Vertical Joint

Assembled shear wall built with precast two-way hollow slab is a new-typed shear wall built with precast concrete. In order to study its mechanical property, a quasi-static experiment is conducted with 1 reinforced concrete shear wall and 2 new type shear walls as the study objects. It was found that the internal and vertical joints of the wall body were vulnerable parts so that the new-typed shear wall experienced the loading process from the whole wall to the portioned wall. So, brittle shear failure can be avoided, deformability and anti-collapse performance are greatly improved, and shear capacity of wall body is reduced. The new-typed shear wall is reasonably structured, with convenient and reliable horizontal and vertical reinforcement, which leads to satisfactory vertical joint force-bearing capacity. Thus, it can be applied in practical construction.

scholarly journals Non-Repetitive Tilings

10.37236/1644 ◽  
2002 ◽  
Vol 9 (1) ◽  
Author(s):  
James D. Currie ◽  
Jamie Simpson
Keyword(s):  
Higher Dimensions ◽  
Two Dimensional ◽  
Dimensional Version ◽  
New Type ◽  
Free Word

In 1906 Axel Thue showed how to construct an infinite non-repetitive (or square-free) word on an alphabet of size 3. Since then this result has been rediscovered many times and extended in many ways. We present a two-dimensional version of this result. We show how to construct a rectangular tiling of the plane using 5 symbols which has the property that lines of tiles which are horizontal, vertical or have slope +1 or $-1$ contain no repetitions. As part of the construction we introduce a new type of word, one that is non-repetitive up to mod k, which is of interest in itself. We also indicate how our results might be extended to higher dimensions.

Hadrontherapy in the World and the Programmes of the Tera Foundation

1998 ◽  
Vol 84 (2) ◽  
pp. 188-199 ◽  
Author(s):  
Ugo Arnaldi
Keyword(s):  
Charged Hadron ◽  
Fast Neutrons ◽  
X Rays ◽  
Carbon Ions ◽  
Property A ◽  
New Type ◽  
Under Construction ◽  
Dose Deposition ◽  
Tumour Target ◽  
Initial Financing

Hadrontherapy was born in 1938, when neutron beams were used in cancer therapy, but it has become an accepted therapeutical modality only in the last five years. Fast neutrons are still in use, even if their limitations are now apparent. Charged hadron beams are more favorable, since the largest specific energy deposition occurs at the end of their range in matter. The most used hadrons are at present protons and carbon ions. Both allow a dose deposition which conforms to the tumour target. Radiobiological experiments and the results of the first clinical trials indicate that carbon ions have, on top of this macroscopic property, a different way of interacting with cells at the microscopic level. There are thus solid hopes to use carbon beams of about 4500 MeV to control tumours which are radioresistant both to X-rays and protons. After discussing these macroscopic and microscopic properties of hadrontherapy, the hospital-based facilities, running or under construction, are reviewed. The conclusion is that, while in USA and Japan twelve of these centres will be running around the year 2001, in Europe very little is foreseen to use hadrontherapy to treat deep-seated tumours. The most advanced programme is the Italian one, which is described in the last Sections of the report. The main activities concern the construction, near Milano, of a centre for protons and carbon ions called CNAO (National Centre for Oncological Hadrontherapy) and the development of new type of proton accelerators. The Istituto Superiore di Sanità in Rome obtained the initial financing for constructing, in collaboration with ENEA, a 3 GHz linac, which eventually will accelerate protons to 200 MeV, so as to allow deep protontherapy. These, and other hadrontherapy centres in Italy and Europe, will be connected with oncology centres, hospitals and clinics by a multimedial network called RITA, so that before referral each patient's case can be discussed directly by doctors, even located far away, with the experts sitting in the hadrontherapy centres.

scholarly journals COMPLEX STRUCTURES AND SEMANTICS IN FREE WORD ASSOCIATION

2012 ◽  
Vol 15 (03n04) ◽  
pp. 1250054 ◽  
Author(s):  
PIETRO GRAVINO ◽  
VITO D. P. SERVEDIO ◽  
ALAIN BARRAT ◽  
VITTORIO LORETO
Keyword(s):  
Human Brain ◽  
Word Association ◽  
Semantic Network ◽  
Free Association ◽  
Small World ◽  
South Florida ◽  
Characteristic Scale ◽  
Property A ◽  
Word Associations ◽  
Free Word

We investigate the directed and weighted complex network of free word associations in which players write a word in response to another word given as input. We analyze in details two large datasets resulting from two very different experiments: On the one hand the massive multiplayer web-based Word Association Game known as Human Brain Cloud, and on the other hand the South Florida Free Association Norms experiment. In both cases, the networks of associations exhibit quite robust properties like the small world property, a slight assortativity and a strong asymmetry between in-degree and out-degree distributions. A particularly interesting result concerns the existence of a characteristic scale for the word association process, arguably related to specific conceptual contexts for each word. After mapping, the Human Brain Cloud network onto the WordNet semantics network, we point out the basic cognitive mechanisms underlying word associations when they are represented as paths in an underlying semantic network. We derive in particular an expression describing the growth of the HBC graph and we highlight the existence of a characteristic scale for the word association process.

scholarly journals On the supports of recognizable series over a field and a single letter alphabet

2011 ◽  
Vol 111 (23-24) ◽  
pp. 1096-1098 ◽  
Author(s):  
Guillaume Chapuy ◽  
Ines Klimann
Keyword(s):  
Single Letter ◽  
Letter Alphabet

Insertion-deletion systems with substitutions I

Computability ◽  
2021 ◽  
pp. 1-27
Author(s):  
Martin Vu ◽  
Henning Fernau
Keyword(s):  
Single Letter ◽  
Context Dependency ◽  
Insertions And Deletions ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
Substitution Site ◽  
New Type ◽  
Left And Right ◽  
Context Free

In this paper, we discuss the addition of substitutions as a further type of operations to (in particular, context-free) insertion-deletion systems, i.e., in addition to insertions and deletions we allow single letter replacements to occur. We investigate the effect of the addition of substitution rules on the context dependency of such systems, thereby also obtaining new characterizations of and even normal forms for context-sensitive (CS) and recursively enumerable (RE) languages and their phrase-structure grammars. More specifically, we prove that for each RE language, there is a system generating this language that only inserts and deletes strings of length two without considering the context of the insertion or deletion site, but which may change symbols (by a substitution operation) by checking a single symbol to the left of the substitution site. When we allow checking left and right single-letter context in substitutions, even context-free insertions and deletions of single letters suffice to reach computational completeness. When allowing context-free insertions only, checking left and right single-letter context in substitutions gives a new characterization of CS. This clearly shows the power of this new type of rules.

scholarly journals Automatic Calibration of an Unsteady River Flow Model by Using Dynamically Dimensioned Search Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Fu-Ru Lin ◽  
Nan-Jing Wu ◽  
Chen-Hao Tu ◽  
Ting-Kuei Tsay
Keyword(s):  
Flow Model ◽  
River Flow ◽  
Search Algorithm ◽  
Research Problem ◽  
High Water ◽  
Test Case ◽  
Property A ◽  
New Type ◽  
The Stability ◽  
Two Parameters

Dynamically dimensioned search (DDS) algorithm is a new-type heuristic algorithm which was originally developed by Tolson and Shoemaker in 2007. In this study, the DDS algorithm is applied to automate the calibration process of an unsteady river flow model in the Tamsui River basin, which was developed by Wu et al. (2007). Data observed during 2012 and 2013 are collected in this study. They are divided into three groups, one for the test case, one for calibration, and one for the validation. To prove that the DDS algorithm is capable of solving this research problem and the convergence property, a test simulation is first performed. In the studied area, the whole river systems are divided into 20 reaches, and each reach has two parameters (nd and nu) to be determined. These two parameters represent resistance coefficients for low- and high-water conditions. Comparing with another algorithm, it is shown that the DDS algorithm has not only improved on the efficiency but also increased the stability of calibrated results.

The Microstructure of Shock-Synthesized Diamond

1967 ◽  
Vol 25 ◽  
pp. 324-325
Author(s):  
Lucien F. Trueb
Keyword(s):  
Single Crystals ◽  
Preferred Orientation ◽  
High Magnification ◽  
Texture Pattern ◽  
Shock Process ◽  
New Type ◽  
Diffraction Diagram

A new type of synthetic industrial diamond formed by an explosive shock process has been recently developed by the Du Pont Company. This material consists of a mixture of two basically different forms, as shown in Figure 1: relatively flat and compact aggregates of acicular crystallites, and single crystals in the form of irregular polyhedra with straight edges.Figure 2 is a high magnification micrograph typical for the fibrous aggregates; it shows that they are composed of bundles of crystallites 0.05-0.3 μ long and 0.02 μ. wide. The selected area diffraction diagram (insert in Figure 2) consists of a weak polycrystalline ring pattern and a strong texture pattern with arc reflections. The latter results from crystals having preferred orientation, which shows that in a given particle most fibrils have a similar orientation.

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