scholarly journals Variations on Twins in Permutations

10.37236/9734 ◽  
2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Andrzej Dudek ◽  
Jarosław Grytczuk ◽  
Andrzej Ruciński
Keyword(s):  
Extremal Function ◽  
The Other ◽  
Random Permutations ◽  
Probabilistic Argument ◽  
Other Hand ◽  
Almost All ◽  
Correct Size

Let $\pi$ be a permutation of the set $[n]=\{1,2,\dots, n\}$. Two disjoint order-isomorphic subsequences of $\pi$ are called twins. How long twins are contained in every permutation? The well known Erdős-Szekeres theorem implies that there is always a pair of twins of length $\Omega(\sqrt{n})$. On the other hand, by a simple probabilistic argument Gawron proved that for every $n\geqslant 1$ there exist permutations with all twins having length $O(n^{2/3})$. He conjectured  that the latter bound is the correct size of the longest twins guaranteed in every permutation. We support this conjecture by showing that almost all permutations contain twins of length  $\Omega(n^{2/3}/\log n^{1/3})$. Recently, Bukh and Rudenko have tweaked our proof and removed the log-factor. For completeness, we also present our version of their proof (see Remark 2 below on the interrelation between the two proofs).  In addition, we study several variants of the problem with diverse restrictions imposed on the twins. For instance, if we restrict attention to twins avoiding a fixed permutation $\tau$, then the corresponding extremal function equals $\Theta(\sqrt{n})$, provided that $\tau$ is not monotone. In case of block twins (each twin occupies a segment) we prove that it is $(1+o(1))\frac{\log n}{\log\log n}$, while for random permutations it is twice as large. For twins that jointly occupy a segment (tight twins), we prove that for every $n$ there are permutations avoiding them on all segments of length greater than $24$.

Starość w nauczaniu św. Bazylego Wielkiego

Vox Patrum ◽  
2011 ◽  
Vol 56 ◽  
pp. 339-348
Author(s):  
Bogdan Czyżewski
Keyword(s):  
Old Age ◽  
Spiritual Maturity ◽  
The Other ◽  
Interesting Aspect ◽  
Other Hand ◽  
Physical Suffering ◽  
Way Of Thinking ◽  
Almost All

Although St. Basil did not live 50 years, the topic of the old age appears in his works quite often. On the other hand, it is clear that Basil does not discuss this issue in one par­ticular work or in the longer argumentation. The fragmentary statements about old age can be found in almost all his works, but most of them can be found in the correspondence of Basil. In this paper we present the most important ad the most interesting aspect of teach­ing of Basil the Great. As these certificates show that the bishop of Caesarea looked at the old age maturely, rationally estimated passage of time, which very often makes a man different. He experienced it, for example as a spiritual and physical suffering, which often were connected with his person. He saw a lot of aspect of the old age, especially its advan­tages – spiritual maturity and wisdom. What is more, he pointed also to passage of time, which leads a man to eternity, which should be prepared to, regardless how old he is. In his opinion fear is not seen opinions of St. Basil present really Christian way of thinking, well-balanced and calm.

Resolving the Lourinia armata (Claus, 1866) complex with remarks on the monophyletic status of Louriniidae, Monard 1927 (Copepoda: Harpacticoida)

Zootaxa ◽  
2021 ◽  
Vol 5051 (1) ◽  
pp. 346-386
Author(s):  
SÜPHAN KARAYTUĞ ◽  
SERDAR SAK ◽  
ALP ALPER ◽  
SERDAR SÖNMEZ
Keyword(s):  
Comparative Evaluation ◽  
Species Complex ◽  
Detailed Examination ◽  
The Other ◽  
Phylogenetic Position ◽  
Nicobar Island ◽  
Other Hand ◽  
The Family ◽  
Close Relationship ◽  
Almost All

An attempt was made to test if Lourinia armata (Claus, 1866)—as it is currently diagnosed—represents a species complex. Detailed examination and comparisons of several specimens collected from different localities suggest that L. armata indeed represents a complex of four closely related morphospecies that can be differentiated from one another by only detailed observations. One of the four species is identified as Lourinia aff. armata and the other three species are described as new to science and named as Lourinia wellsi sp. nov., L. gocmeni sp. nov., and L. aldabraensis sp. nov. Detailed review of previous species records indicates that the genus Lourinia Wilson, 1924 is distributed worldwide. Ceyloniella nicobarica Sewell, 1940, originally described from Nicobar Island and previously considered a junior subjective synonym of L. armata is reinstated as Lourinia nicobarica (Sewell, 1940) comb. nov. on the basis of the unique paddle-shaped caudal ramus seta V. It is postulated that almost all of these records are unreliable in terms of representing true Lourinia aff. armata described herein. On the other hand, the comparative evaluation of the illustrations and descriptions in the published literature indicates the presence of several new species waiting to be discovered in the genus Lourinia.                 It has been determined that, according to updated modern keys, the recent inclusion of the monotypic genus Archeolourinia Corgosinho & Schizas, 2013 in the Louriniidae is not justified since Archeolourinia shermani Corgosinho & Schizas, 2013 does not belong to this family but should be assigned to the Canthocamptidae. On the other hand, it has been argued that the exact phylogenetic position of the Louriniidae still remains problematic since none of the diagnostic characters supports the monophyly of the family within the Oligoarthra. It has also been argued that the close relationship between Louriniidae and Canthocamptidae is supported since both families share the homologous sexual dimorphism (apophysis) on P3 endopod. The most important characteristic that can possibly be used to define Louriniidae is the reduction of maxilliped.  

scholarly journals STUDENTS’ PERCEPTION OF USING “DICTIONARY POCKET” AS A MEDIUM TO IMPROVE THEIR VOCABULARY MASTERY

2019 ◽  
Vol 2 (3) ◽  
pp. 319
Author(s):  
Titi Mariah ◽  
Yanti Yusanti ◽  
Ula Nisa El Fauziah
Keyword(s):  
The Other ◽  
Second Grade ◽  
Learning To Read ◽  
Other Hand ◽  
Qualitative Descriptive ◽  
Almost All ◽  
Descriptive Method

Vocabulary known as an essential skill for learning to read, speak, write and listen. It is important to find the appropriate technique in order to improve students’ vocabulary mastery. The researchers did research with focuses on students’ perception towards using “dictionary pocket” in order to improve their vocabulary mastery. It was conducted using a qualitative descriptive method. To collect the data, the researchers use the instruments of an open-ended questionnaire and interview section. The samples were 36 students of second grade from Broadcasting major at SMK Negeri 1 Cimahi. The result of the questionnaire shows that it was found that almost all of the students feel that with learn vocabulary can be easier when they use the technique of remembering dictionary pocket. They also agree that dictionary pocket is an appropriate technique which is used to learn vocabulary. In the other hand, the result of interview shows, the students concede that they are feel helped and being motivated. It can be sum up that dictionary pocket is suitable to strengthen their vocabulary mastery. Dictionary pocket is useful enough because it can help them when they forget the word.

The No-Three-In-Line Problem

1968 ◽  
Vol 11 (4) ◽  
pp. 527-531 ◽  
Author(s):  
Richard K. Guy ◽  
Patrick A. Kelly
Keyword(s):  
Finite Number ◽  
The Other ◽  
Probabilistic Argument ◽  
Number Of Solutions ◽  
Other Hand ◽  
Image Position

Let Sn be the set of n2 points with integer coordinates n (x, y), 1 ≤ x, y <n. Let fn be the maximum cardinal of a subset T of Sn such that no three points of T are collinear. Clearly fn < 2n.For 2 ≤ n ≤ 10 it is known ([2], [3] for n = 8, [ 1] for n = 10, also [4], [6]) that fn = 2n, and that this bound is attained in 1, 1, 4, 5, 11, 22, 57, 51 and 156 distinct configurations for these nine values of n. On the other hand, P. Erdös [7] has pointed out that if n is prime, fn ≥ n, since the n points (x, x2) reduced modulo n have no three collinear. We give a probabilistic argument to support the conjecture that there is only a finite number of solutions to the no-three-in-line problem. More specifically, we conjecture that

Effets de la coupe à blanc et de la coupe par bandes sur la régénération obtenue après 5 ans dans des pessières noires du Québec

1995 ◽  
Vol 25 (2) ◽  
pp. 329-342 ◽  
Author(s):  
Pierre Pominville ◽  
Jean-Claude Ruel
Keyword(s):  
Black Spruce ◽  
Spruce Budworm ◽  
Lower Proportion ◽  
The Other ◽  
Balsam Fir ◽  
Clear Cutting ◽  
Other Hand ◽  
The One ◽  
Almost All ◽  
Coupe À Blanc

An experiment was conducted to compare the effects of traditional clear-cutting with those of strip cutting on regeneration of black spruce, Piceamariana (Mill.) B.S.P., stands on scarified and unscarified uplands and on lowlands. To that effect, regeneration surveys were done before cutting, in the following year, and 3 and 5 years after cutting. Five years after harvesting, strip cutting led to higher coniferous stocking than clear-cutting on scarified uplands and on lowlands. On unscarified uplands, the gain attributable to strip cutting was not significant. The coniferous stocking of strip cuts on scarified uplands was not greater than on unscarified uplands. So the efficiency of scarification could not be proved in that study. Stocking obtained after 5 years remained closely related to the one observed immediately after harvesting in the strip cufs as in the clear-cuttings. This is particularly true for balsam fir, Abiesbalsamea (L.) Mill. In the strip cuts, the balsam fir stocking was constant while the one of black spruce increased. This could have an impact on the evolution of the composition of the new stands and, consequently, on their vulnerability to spruce budworm, Choristoneurafumiferana (Clem.). The majority of the clear-cuttings were well regenerated 5 years after harvesting. Their average coniferous stocking was slightly above 60%. However, 48% of the clear-cuttings did not reach this level when only unscarified plots on uplands were considered. Advance growth was abundant in those plots but suffered high losses during harvesting. Consequently, reducing the losses during harvesting would result in a lower proportion of clear-cuttings with insufficient coniferous stocking 5 years after cutting. On the other hand, almost all the strip cuts with insufficient regeneration after harvesting were well regenerated 5 years later. Thus, strip cutting could be an interesting option on sites with insufficient advance growth and on sites well regenerated before cutting but where important losses during harvesting are anticipated.

scholarly journals Conflict between Individual and Society : A Brief Review of Victims and Survivors in Anita Desai's Fiction

2019 ◽  
pp. 738-743
Author(s):  
Dr. Pinky
Keyword(s):  
The Other ◽  
Anita Desai ◽  
Other Hand ◽  
Long Run ◽  
Set Up ◽  
Almost All ◽  
Social Affairs

Anita Desai's novels catch the shattered psyche of the individuals who are striving for defining themselves in the form of identity in the familial and social set-up but it is hard to say that all the characters are strong enough to survive after dealing with the cruelties of life. Apart from a few, they become the victims of their personal and social affairs of life. It may be observed that almost all the protagonists of Anita Desai are sensitive or hypersensitive that makes them victims. On the other hand, some characters try hard to cope with the abnormalities of life but in the long run they also surrender yet they are able to survive. Through a brief study of the selected novels of Anita Desai, this paper will try to examine who are the victims and who are the survivors?

scholarly journals Bilingual (English to Bengali) Technical E- Dictionary for Aviation OOV Words

2019 ◽  
Vol 9 (2) ◽  
pp. 3777-3781
Keyword(s):  
The Other ◽  
The Core ◽  
Other Hand ◽  
Almost All ◽  
Multiple Languages ◽  
Dictionary Translation

E-dictionaries, quite common today are available for multiple languages in monolingual, bilingual and multilingual forms. In NLP they form the core of a series of tools that are used to understand words, sentences and in turn the language itself. These E-Dictionaries work well for any language domain as a whole. For almost all languages E-dictionaries are available, but once specialized technical domains are encountered these E-Dictionaries are quite useless. Aviation is one such specialized domain for which no E-Dictionary, translation or transliteration tool exist. On the other hand the need for such tools for specialized domains are increasing. The tool discussed in this paper is an attempt to bridge the gap that currently exists between English and Bengali languages.

scholarly journals Stationarity as a path property

2019 ◽  
Vol 39 (2) ◽  
pp. 403-422
Author(s):  
Yi Shen ◽  
Tony S. Wirjanto
Keyword(s):  
Stochastic Process ◽  
Stationary Process ◽  
The Other ◽  
Mild Conditions ◽  
Other Hand ◽  
Distributional Property ◽  
Shift Invariance ◽  
Stationarity Test ◽  
Path Property ◽  
Almost All

Traditionally, stationarity refers to shift invariance of the distribution of a stochastic process. In this paper, we rediscover stationarity as a path property instead of a distributional property. More precisely, we characterize a set of paths, denoted by A, which corresponds to the notion of stationarity. On one hand, the set A is shown to be large enough, so that for any stationary process, almost all of its paths are in A. On the other hand, we prove that any path in A will behave in the optimal way under any stationarity test satisfying some mild conditions.

Phylogenetic analyses of Fusarium graminearum strains from cereals in Italy, and characterisation of their molecular and chemical chemotypes

2014 ◽  
Vol 65 (1) ◽  
pp. 52 ◽  
Author(s):  
S. Somma ◽  
A. L. Petruzzella ◽  
A. F. Logrieco ◽  
G. Meca ◽  
O. S. Cacciola ◽  
...  
Keyword(s):  
Species Composition ◽  
Durum Wheat ◽  
Fusarium Graminearum ◽  
Species Complex ◽  
Phylogenetic Analyses ◽  
Sensu Stricto ◽  
The Other ◽  
Other Hand ◽  
Fusarium Graminearum Species Complex ◽  
Almost All

The Fusarium graminearum species complex (FGSC) is a pathogen of durum wheat and other cereals worldwide. The complex consists of at least 15 species that can produce various mycotoxins, including trichothecenes, associated with human and animals toxicoses. In particular, deoxynivalenol (DON), nivalenol (NIV) and their different acetylated derivatives can be produced by the different chemotypes of the complex. In this study, 90 strains, isolated mainly from wheat in Italy and belonging to the FGSC, were assessed for their phylogeny and their chemotype and trichothecene genotype. Almost all strains of the FGSC belonged to F. graminearum sensu stricto, whereas two strains were F. cortaderiae. On the other hand, all three chemotypes, 3ADON, 15ADON and NIV, occurred; 15ADON was the most common molecular chemotype. The data show that the species composition of the Italian FGSC is homogeneous, whereas wide chemotype variability can occur within F. graminearum sensu stricto.

scholarly journals Séance du jeudi 4 octobre, matin.: Président de Séance : G. Righini.: Solar Site Testing

1963 ◽  
Vol 19 ◽  
pp. 193-220 ◽  
Author(s):  
K. O. Kiepenheuer
Keyword(s):  
Solar Disk ◽  
The Other ◽  
Atmospheric Effects ◽  
The Sun ◽  
Site Testing ◽  
Low Contrast ◽  
Other Hand ◽  
Optical Effects ◽  
All Optical ◽  
Almost All

While at night almost all optical effects of the atmosphere have to be investigated by using stellar images, the solar observer has at his disposal the solar disk of about half a degree in diameter, covered all over with low contrast details of about 1″, the granules, and confined to the sky by a sharp limb. This enables him to observe all effects occuring within the area of the Sun simultaneously, to follow even the propagation of certain atmospheric effects across the disk. On the other hand he has only the Sun and cannot — as night astronomers might do — extend his observations to all directions in the sky.

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