scholarly journals A Positive Answer for 3IM+1CM Problem with a General Difference Polynomial

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Huicai Xu ◽  
Shugui Kang ◽  
Qingcai Zhang
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Analytic Functions ◽  
Positive Answer ◽  
The Other ◽  
Main Difficulty ◽  
New Methods ◽  
Other Hand ◽  
Difference Polynomial ◽  
General Difference

In this paper, the 3IM+1CM theorem with a general difference polynomial L z , f will be established by using new methods and technologies. Note that the obtained result is valid when the sum of the coefficient of L z , f is equal to zero or not. Thus, the theorem with the condition that the sum of the coefficient of L z , f is equal to zero is also a good extension for recent results. However, it is new for the case that the sum of the coefficient of L z , f is not equal to zero. In fact, the main difficulty of proof is also from this case, which causes the traditional theorem invalid. On the other hand, it is more interesting that the nonconstant finite-order meromorphic function f can be exactly expressed for the case f ≡ − L z , f . Furthermore, the sharpness of our conditions and the existence of the main result are illustrated by examples. In particular, the main result is also valid for the discrete analytic functions.

On Commutation Properties of the Composition Relation of Convergent and Divergent Permutations (Part I)

2014 ◽  
Vol 58 (1) ◽  
pp. 13-22
Author(s):  
Roman Wituła ◽  
Edyta Hetmaniok ◽  
Damian Słota
Keyword(s):  
Finite Order ◽  
Convergent Series ◽  
The Other ◽  
Other Hand ◽  
The Family ◽  
Composition Relation ◽  
The Continuum

Abstract In the paper we present the selected properties of composition relation of the convergent and divergent permutations connected with commutation. We note that a permutation on ℕ is called the convergent permutation if for each convergent series ∑an of real terms, the p-rearranged series ∑ap(n) is also convergent. All the other permutations on ℕ are called the divergent permutations. We have proven, among others, that, for many permutations p on ℕ, the family of divergent permutations q on ℕ commuting with p possesses cardinality of the continuum. For example, the permutations p on ℕ having finite order possess this property. On the other hand, an example of a convergent permutation which commutes only with some convergent permutations is also presented.

scholarly journals On Properties of Differences Polynomials about Meromorphic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Jianming Qi ◽  
Jie Ding ◽  
Wenjun Yuan
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Special Class ◽  
Meromorphic Functions ◽  
Value Distribution ◽  
Class Difference ◽  
Difference Polynomial

We study the value distribution of a special class difference polynomial about finite order meromorphic function. Our methods of the proof are also different from ones in the previous results by Chen (2011), Liu and Laine (2010), and Liu and Yang (2009).

Double jumps of minimal degrees over cardinals

1982 ◽  
Vol 47 (2) ◽  
pp. 329-334
Author(s):  
C. T. Chong
Keyword(s):  
Positive Answer ◽  
The Other ◽  
Total Function ◽  
Peculiar Property ◽  
Other Hand ◽  
Power Set

Jockusch and Posner [4] showed that every minimal ω-degree is GL2. This is achieved by exhibiting a function f recursive in 0′ which dominates every function of minimal ω-degree. The function f has the peculiar property that for every s, f(s) is defined after a search (using 0′) over the power set of Ls (Gödel's constructible hierarchy at the level s). It can be seen that a function defined in a similar manner over an infinite successor cardinal k will not be a total function, since for example if k = ρ+, then f(ρ) will not be defined until after all the subsets of ρ have been examined, and this will take at least k steps. The following questions then naturally arise: (i) For successor cardinals k, is there a function dominating every set of minimal k-degree? (ii) For arbitrary cardinals k, is every minimal k-degree GL2 (i.e. b″ = (b ∨ 0′) for b of minimal k-degree)? In this paper we answer (i) in the negative and provide a positive answer to (ii), assuming V = L. We show in fact that if k is a successor cardinal and h ≤k 0′, then there is a function of minimal k-degree below 0′ not dominated by h (Theorem 1). This implies that any refinement of the function f described above will not be able to remove the difficulties encountered. On the other hand, we introduce the notion of ‘strong domination’ to provide a positive answer to (ii) (Theorem 2 and Corollary 1). We end this paper by indicating that for limit cardinals k, there is a function below 0′ dominating every function of minimal k-degree.

Msplit and MP estimation. A wider range of robustness

2017 ◽  
Author(s):  
Robert Duchnowski ◽  
Zbigniew Wisniewski
Keyword(s):  
Measurement Errors ◽  
Probabilistic Models ◽  
Interesting Property ◽  
The Other ◽  
Estimation Methods ◽  
Excess Kurtosis ◽  
New Methods ◽  
Other Hand ◽  
Functional Models ◽  
M Estimation

Msplit and MP estimations are new methods of assessing the parameters of functional models of geodetic observations. The first method assumes that each observation can be assigned to either of some functional models which differ from each other in competitive parameters. While the latter method is based on the assumption that distributions of measurement errors differ from the normal one in asymmetry and excess kurtosis. The theoretical properties indicate that both methods are also robust against outliers. However, the sense of robustness is a little wider than in the case of M-estimation. In Msplit estimation the outliers are treated as variables with competitive functional models (in relation to models of “good” observations) while robustness of MP estimation depends on the mentioned parameters of probabilistic models of observations. This paper shows that on one hand robustness is an interesting property of the methods in question, but on the other hand it broadens possible application of such estimation methods.

scholarly journals On the Exponent of the NK0-Groups of Virtually Infinite Cyclic Groups

2002 ◽  
Vol 45 (2) ◽  
pp. 180-195 ◽  
Author(s):  
Francis X. Connolly ◽  
Stratos Prassidis
Keyword(s):  
Large Class ◽  
The Other ◽  
Main Difficulty ◽  
Cyclic Subgroups ◽  
Cyclic Groups ◽  
Other Hand

AbstractIt is known that the K-theory of a large class of groups can be computed from the K-theory of their virtually infinite cyclic subgroups. On the other hand, Nil-groups appear to be the obstacle in calculations involving the K-theory of the latter. The main difficulty in the calculation of Nil-groups is that they are infinitely generated when they do not vanish. We develop methods for computing the exponent of NK0-groups that appear in the calculation of the K0-groups of virtually infinite cyclic groups.

scholarly journals THE IMPORTANCE OF SAVA’S SPELLING BOOK IN THE BEGINNERS’ COURSE OF READING AND WRITING AND IN THE TEACHING OF SERBIAN CULTURE

2020 ◽  
Author(s):  
Biljana Samardžić ◽  
◽  
Daliborka Škipina ◽  
Keyword(s):  
Teaching Methods ◽  
Teaching Method ◽  
The Other ◽  
Literary Language ◽  
Pedagogical Approach ◽  
Reading And Writing ◽  
New Methods ◽  
Other Hand ◽  
Slavonic Language ◽  
New Knowledge

The authors of this paper deal with the pedagogical and philological significance of Sava’s Spelling Book printed in Russia (Moscow) in 1692, in the Russian-Slavonic language. This spelling book is about 100 years younger than the First Serbian Spelling Book (The Spelling Book of Sava Inok of the monastery Dečani). This spelling book of the Russian recension reached all the way to the Serbian lands, being, on one hand, the precedent, and on the other hand, the follower to the books that are to appear in Serbia and its new literary language. The authors of this paper explain in a detailed way the method of letter teaching by which each letter (Slavonic, Greek, and Latin) is being assigned a corresponding picture. This points out to the pedagogical approach to the acquisition of new knowledge (the basics of reading and writing) which uses pictures of animals and plants in order to facilitate the process of letter learning. In his lecture, KarionIstomin, the author of the spelling book, suggested totally new teaching methods i.e. the new methods. Namely, Sava’s Spelling book is the precursor of contemporary spelling books, since all of them use the connection between letters and pictures as the basis of their teaching method.

Tools and Technology for Language Documentation and Revitalization

2018 ◽  
pp. 224-247
Author(s):  
Keren Rice ◽  
Nicholas Thieberger
Keyword(s):  
Digital Media ◽  
Language Revitalization ◽  
The Other ◽  
Language Documentation ◽  
Limited Availability ◽  
New Methods ◽  
Other Hand

A defining feature of new methods of documenting languages is the advance in technologies for recording, transcribing, annotating, managing, and analyzing language records, which then facilitates delivering that documentation for use in various forms, in particular for language revitalization efforts. It is the affordances offered by these new methods that have expanded the possibilities of language documentation to create richer records and enabling collaboration over distance, both between linguists and between linguists and speakers. Digital materials can serve multiple purposes, often unforeseen by the original recorder. Analog recordings had limited availability in single locations and access to timepoints within a recording was labor intensive and slow. Digital media on the other hand can be instantly accessed in many locations, and permits citation to the level of a word or even a phoneme and thus offers verification of analyses with reference to the primary recordings.

לֹא and the Biblical Hebrew Negative Response

2018 ◽  
Vol 68 (3) ◽  
pp. 402-414
Author(s):  
Dong-Hyuk Kim
Keyword(s):  
Biblical Hebrew ◽  
Negative Answer ◽  
Positive Answer ◽  
The Other ◽  
Negative Response ◽  
Content Type ◽  
Other Hand

Abstract It is agreed that Biblical Hebrew (BH) does not have a word for “Yes!” and that the BH positive answer uses what linguists call the echo system. On the other hand, לֹא used independently as a negative answer is frequently understood as a negative answer particle (“No!”). Upon considering the evidence from BH and languages in general, the first half of this paper argues that לֹא used as such is a negative verbal clause, with the verbal part being omitted. The second half attempts to schematize various forms of the BH negative responses using לֹא.

scholarly journals TOWARDS A MATHEMATICAL LIBRARY FOR UNUMs, AN ALTERNATIVE TO IEEE 754 FLOATING POINT NUMBERS

2017 ◽  
Author(s):  
Thomas Risse
Keyword(s):  
Analytic Functions ◽  
Numerical Results ◽  
The Other ◽  
Floating Point ◽  
Other Hand ◽  
Is Development ◽  
The One ◽  
Floating Point Numbers

The 1985 IEEE 754 standard for the representation of and the arithmetic with floating point numbers has been reconsidered. On the one hand today, its technological assumptions are by no means longer valid. On the other hand, the irritating numerical phenomena which have been collected cast a doubt as to whether this much uncertainty in numerical results is fate. Fortunately, around 2015, Gustafson proposed UNUMs, a modification of the IEEE 754 standard with the potential to heal the said shortcomings. Till now, there are some attempts to implement his ideas, both in software and in hardware. With these activities well under way, the other necessity is development of a mathematical library for UNUMs when one wants UNUMs to become the new floating point standard. This paper presented the ideas leading to UNUMs, gave some hints on floating point units for UNUMs and illustrated the difficulties in developing the said mathematical library by the example of approximating zeroes of analytic functions.  

scholarly journals Uniqueness of difference polynomials

2021 ◽  
Vol 6 (10) ◽  
pp. 10485-10494
Author(s):  
Xiaomei Zhang ◽  
◽  
Xiang Chen ◽  
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Complex Numbers ◽  
Nonzero Constant ◽  
Transcendental Meromorphic Function ◽  
Difference Polynomial ◽  
Difference Polynomials

<abstract><p>Let $ f(z) $ be a transcendental meromorphic function of finite order and $ c\in\Bbb{C} $ be a nonzero constant. For any $ n\in\Bbb{N}^{+} $, suppose that $ P(z, f) $ is a difference polynomial in $ f(z) $ such as $ P(z, f) = a_{n}f(z+nc)+a_{n-1}f(z+(n-1)c)+\cdots+a_{1}f(z+c)+a_{0}f(z) $, where $ a_{k} (k = 0, 1, 2, \cdots, n) $ are not all zero complex numbers. In this paper, the authors investigate the uniqueness problems of $ P(z, f) $.</p></abstract>

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