scholarly journals Covering Theorems for FINASIGS VIII—almost all conjugacy classes in An have exponent ≤4

1978 ◽  
Vol 25 (2) ◽  
pp. 210-214 ◽  
Author(s):  
J. L. Brenner
Keyword(s):  
Conjugacy Class ◽  
Conjugacy Classes ◽  
The Other ◽  
Alternating Group ◽  
Other Hand ◽  
Covering Theorems ◽  
Image Position ◽  
Almost All

AbstractThe product of two subsets C, D of a group is defined as . The power Ce is defined inductively by C0 = {1}, Ce = CCe−1 = Ce−1C. It is known that in the alternating group An, n > 4, there is a conjugacy class C such that CC covers An. On the other hand, there is a conjugacy class D such that not only DD≠An, but even De≠An for e<[n/2]. It may be conjectured that as n ← ∞, almost all classes C satisfy C3 = An. In this article, it is shown that as n ← ∞, almost all classes C satisfy C4 = An.

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.

On functional Nörlund methods

1970 ◽  
Vol 67 (1) ◽  
pp. 47-60 ◽  
Author(s):  
B. Choudhary
Keyword(s):  
The Other ◽  
Integral Transformations ◽  
Other Hand ◽  
Nörlund Means ◽  
The One ◽  
Image Position

Integral transformations analogous to the Nörlund means have been introduced and investigated by Kuttner, Knopp and Vanderburg(6), (5), (4). It is known that with any regular Nörlund mean (N, p) there is associated a functionregular for |z| < 1, and if we have two Nörlund means (N, p) and (N, r), where (N, pr is regular, while the function is regular for |z| ≤ 1 and different) from zero at z = 1, then q(z) = r(z)p(z) belongs to a regular Nörlund mean (N, q). Concerning Nörlund means Peyerimhoff(7) and Miesner (3) have recently obtained the relation between the convergence fields of the Nörlund means (N, p) and (N, r) on the one hand and the convergence field of the Nörlund mean (N, q) on the other hand.

scholarly journals Distribution of rational points on the real line

1973 ◽  
Vol 15 (2) ◽  
pp. 243-256 ◽  
Author(s):  
T. K. Sheng
Keyword(s):  
Algebraic Number ◽  
Rational Number ◽  
Real Line ◽  
Rational Points ◽  
The Other ◽  
Liouville Numbers ◽  
The Real ◽  
Other Hand ◽  
Image Position

It is well known that no rational number is approximable to order higher than 1. Roth [3] showed that an algebraic number is not approximable to order greater than 2. On the other hand it is easy to construct numbers, the Liouville numbers, which are approximable to any order (see [2], p. 162). We are led to the question, “Let Nn(α, β) denote the number of distinct rational points with denominators ≦ n contained in an interval (α, β). What is the behaviour of Nn(α, + 1/n) as α varies on the real line?” We shall prove that and that there are “compressions” and “rarefactions” of rational points on the real line.

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.

Configuration of Quadrivalent Atoms

1929 ◽  
Vol 25 (2) ◽  
pp. 219-221
Author(s):  
T. M. Lowry
Keyword(s):  
The Other ◽  
Tetrahedral Configuration ◽  
X Ray ◽  
Metallic Atom ◽  
Other Hand ◽  
Function Change ◽  
The One ◽  
Image Position ◽  
Octahedral Configuration ◽  
As If

Two alternative views have been expressed in regard to the configuration of quadrivalent atoms. On the one hand le Bel and van't Hoff assigned to quadrivalent carbon a tetrahedral configuration, which has since been confirmed by the X-ray analysis of the diamond. On the other hand, Werner in 1893 adopted an octahedral configuration for radicals of the type MA6, e.g. inand then suggested that “the molecules [MA4]X2 are incomplete molecules [MA6]X2. The radicals [MA4] result from the octahedrally-conceived radicals [MA6] by loss of two groups A, but with no function-change of the acid residue…. They behave as if the bivalent metallic atom in the centre of the octahedron could no longer bind all six of the groups A and lost two of them leaving behind the fragment [MA4]” (p. 303).

Numbers badly approximate by fractions with prime denominator

1995 ◽  
Vol 118 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Glyn Harman
Keyword(s):  
Continued Fraction ◽  
Arithmetic Progressions ◽  
The Other ◽  
Strong Result ◽  
Infinitely Many Solutions ◽  
Continued Fraction Expansion ◽  
Primes In Arithmetic Progressions ◽  
Prime Variable ◽  
Image Position ◽  
Almost All

We write ‖x‖ to denote the least distance from x to an integer, and write p for a prime variable. Duffin and Schaeffer [l] showed that for almost all real α the inequalityhas infinitely many solutions if and only ifdiverges. Thus f(x) = (x log log (10x))−1 is a suitable choice to obtain infinitely many solutions for almost all α. It has been shown [2] that for all real irrational α there are infinitely many solutions to (1) with f(p) = p−/13. We will show elsewhere that the exponent can be increased to 7/22. A very strong result on primes in arithmetic progressions (far stronger than anything within reach at the present time) would lead to an improvement on this result. On the other hand, it is very easy to find irrational a such that no convergent to its continued fraction expansion has prime denominator (for example (45– √10)/186 does not even have a square-free denominator in its continued fraction expansion, since the denominators are alternately divisible by 4 and 9).

A System of Linear Equations with an Infinity of Unknowns

1924 ◽  
Vol 22 (3) ◽  
pp. 282-286
Author(s):  
E. C. Titchmarsh
Keyword(s):  
Present Note ◽  
Linear Equations ◽  
The Other ◽  
System Of Linear Equations ◽  
Other Hand ◽  
Image Position ◽  
Monotonic Character

I have collected in the present note some theorems regarding the solution of a certain system of linear equations with an infinity of unknowns. The general form of the equations isthe numbers a1, a2, … c1, c2, … being given. Equations of this type are of course well known; but in studying them it is generally assumed that the series depend for convergence on the convergence-exponent of the sequences involved, e.g. that and are convergent. No assumptions of this kind are made here, and in fact the series need not be absolutely convergent. On the other hand rather special assumptions are made with regard to the monotonic character of the sequences an and cn.

The extreme points of some classes of polynomials

1985 ◽  
Vol 101 (1-2) ◽  
pp. 99-110 ◽  
Author(s):  
D. A. Brannan ◽  
J. G. Clunie
Keyword(s):  
Extreme Points ◽  
The Other ◽  
Other Hand ◽  
Image Position

SynopsisWe study the extreme points of two classes of polynomials of degree at most n:It turns out that f ∈ Ext if and only if Re f(eiθ) has exactly 2n zeros in [0, 2π). On the other hand, if f∈Hn and 1−|f(eiθ)|2 has 2n zeros in [0, 2π), then either f ∈ Ext Hn or else f(z) = α + βzn where |α|+|β| = l and αβ≠0; if 1−|f(eiθ)|2 has 2m zeros, 2n, then f may or may not belong to Ext Hn.

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

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