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1
Content available remote Infinite families of congruences modulo 5 and 9 for overpartitions
100%
EN
Let p͞(n) denote the number of overpartitions of n. Recently, a number of congruences modulo 5 and powers of 3 for p͞(n) were established by a number of authors. In particular, Treneer proved that the generating function for p͞(5n) modulo 5 is ∑∞n=0 p͞(5n)qn ≡ (q;q)6∞/(q2; q2)3∞ (mod 5). In this paper, employing elementary methods, we establish the generating function of p͞(5n) which yields the congruence due to Treneer. Furthermore, we prove some new congruences modulo 5 and 9 for p͞(n) by utilizing the fact that the generating functions for p͞(5n) modulo 5 and for p͞(3n) modulo 9 are eigenforms for half-integral weight Hecke operators.
2
Content available Prime counting function π
100%
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2013
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tom 5
71-76
PL
The aim of this paper is to derive new explicit formulas for thefunction π, where π(x) denotes the number of primes not exceeding x. Some justifications and generalisations of the formulas obtained by Willans (1964),Minac (1991) and Kaddoura and Abdul-Nabi (2012) are also obtained.
3
Content available Around the Wilson's theorem
100%
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2013
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tom 5
51-56
PL
In this paper some known conditions and new congruences characterising prime numbers are given. Some of them are obtained by the generalised Wilson theorem given by Gauss. The elementary proof of this theorem is also presented.
4
Content available Filters of lattices with respect to a congruence
88%
EN
Some properties of filters on a lattice L are studied with respect to a congruence on L. The notion of a θ-filter of L is introduced and these filters are then characterized in terms of classes of θ. For distributive L, an isomorphism between the lattice of θ-filters of L and the lattice of filters of $L_{/θ}$ is obtained.
5
88%
EN
We define Kripke semantics for propositional intuitionistic logic with Suszko’s identity (ISCI). We propose sequent calculus for ISCI along with cut-elimination theorem. We sketch a constructive interpretation of Suszko’s propositional identity connective.
6
Content available Many Faces of Lattice Tolerances
88%
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nr 4
EN
Our aim is to overview and discuss some of the most popular approaches to the notion of a tolerance relation in algebraic structures with the special emphasis on lattices.
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nr 1
EN
The present note is an Erratum for the two theorems of the paper "Congruences and ideals in a distributive lattice with respect to a derivation" by M. Sambasiva Rao.
EN
Purpose: This study aims to investigate whether controversial TV content impacts the effects of non – standard advertising such as sponsorship vignette among female viewers. Methodology: The present study used two field experiments (n = 222; n = 219) conducted as a Computer-Assisted Web Interview (CAWI) questionnaire, during which video material was presented. The study manipulated controversial and non-controversial and the variable of congruence and incongruence – through the argument of video material in the form of TV programs and advertising spots. Results: The empirical investigation revealed that controversial and incongruent content does not necessarily alter the effect of a sponsorship vignette. Loyal viewers who consistently follow programs were found to have higher purchase intent than less loyal ones. Implications: The results suggest that advertisers should consider placing their messages in the context of controversial TV programming, which does not have to be congruent with the ads displayed. Limitations: The stimuli applied in the studies were arbitrary, to a certain extent. The study did not investigate program’s about sex that fit the definition of controversiality. Originality/value: The study contributes to the existing literature on ad–content congruence by investigating consumer responses to innovative ad format: the sponsorship vignette. We investigated how specific content watched in longer periods of time (i.e. a series) may impact the advertising effectiveness of embedded sponsorship vignettes. This approach allowed us to demonstrate the importance of viewers’ loyalty towards a TV program, resulting in a change of the level of purchase intent of advertised product.
9
Content available remote Kongruencja logistyki : aspekt militarny i cywilny
75%
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tom Nr 31
301--312
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tom 140
241 - 253
EN
The article deals with the definition problems of the German adjective morphology with nominal reference, generally described as a three-class-system. We pretend to criticize especially the idea of an allomorph concept of congruence, which in our opinion is not able to represent correctly the functionality of the different criteria of application. Actually, even its combination with a quite more realistic vision of the theory of mono-inflexion will not change this impression. We also try to explain didactic consequences, which the traditional scheme of explication might have on learners with a native speaker’s background really based upon the principle of congruence in the mentioned context.
11
Content available remote Σ-genomorphism of algebraic structures
75%
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tom Vol. 36, nr 4
785--792
EN
For an algebraic structure A = (A, F, R) of type τ and a set Σ of open formulas of the first order language L(τ), the concept of Σ-closed subset of A was introduced in [3]. The set C Σ(A) of all Σ-closed subsets of A forms a complete lattice whose properties were studied in [3], [4] and [5]. Algebraic structures A, B of type τ are called CΣ-isomorphic (or Σ-isomorphic in [3]) if the lattices CΣ(A) and CΣ(B) are isomorphic. The CΣ-isomorphisms are investigated for so-called Σ-separable algebraic structures in [3]. The study of the Σ-isomorphisms of algebraic structures is continued in this paper. We introduce the concepts of Σ-genomorphism and Σ-isogenomorphism of algebraic structures and we formulate a sufficient condition under which two structures are isomorphic. We show that for Σ-separable structures the condition is also necessary. Further, we introduce the concepts of Σ-morphism, congruential E -morphism and congruence induced by a congruential Σ-morphism. We also prove Theorem on Σ-genomorphism and Theorem on Σ-morphism.
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2017
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nr 3(67)
120-131
EN
Among the main principles of implementing pedagogical conditions of formation of personal and professional skills of the future music teachers at the vocal training ckasses in higher school we singled out the following: the principle of physical self-improvement of students; the principle of social and civic orientation of professional activities of students of Art departments; the principle of improving performance skills during concerts and theatrical activities; the principle of cultural and aesthetic approach to training. The next step of our research is oriented at the study of criteria and levels of personal and professional development of future music teachers in the process of vocal studies at the university. Problems of professional and personal development of teachers of artistic disciplines have been revealed in the works of V. Orlov, A. Pietielin, Yu. Sverliuk et al . Despite the theoretical results obtained in these studies remains unexplored in theoretical terms, and at the same time, exacerbates the practical need for solving the problem of formation of personal and professional qualities of the future teacher of vocal music in the process of teaching. The purpose of the article isto outline and substantiate the criteria and levels of formation of personal and professional qualitiesofthefutureteachersofmusicinvocaltraining. The article considers the properties inherent in the student’s age, which influence the development of the conditions for the formation of personal and professional qualities of the future specialist. In view of these features, three groups of criteria have been singled out (criteria reflecting changes in the physical state of students which are directly related to the quality of singing, criteria reflecting the students’ conscious desire to participate in sponsorship and charitable activities, criteria reflecting activity in training and participation in festivals and professional competitions), and determined the levels of becoming of personal-professionalqualities. Continuing formation after Stanislavsky exploring the field of actoe’s perception, in which to the paramount importance belongs to consistency, balance of internal and external manifestations of mood, defined in this study as congruence, M. Chekhov draws attention to the so-called “sixth sense of the actor”– a sense of partner, which he defines as “the ability to be ready ... to open” towards his/her partners. The quality of congruence indicates how sincere is the person in the expression of his/her emotions, how the ability of displaying affection is developed. To identifying the components of congruence, important were data received as a result of peer review methodology of nonverbal communication of A. Kuznetsova.
13
Content available remote Standard QBCC-algebras
75%
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tom Vol. 36, nr 1
1--10
EN
The class of QBBC-algebras was introduced and studied by the authors in ioj. These algebras model properties of the logical connective implication "=>" in which tin- validity of formulas x => y and y => x does not imply the equivalence of x and y. In ihe paper the properties of standard QBCC-algebras derived from qosets are studied.
14
Content available remote A note on Browkin’s and Cao’s cancellation algorithm
63%
EN
In this paper, we follow our generalisation of the cancellation algorithm described in our previous paper [A. Tomski, M. Zakarczemny, On some cancellation algorithms, NNTDM. 23, 2017, p. 101–114]. For f being a natural-valued function defined on ℕs , s ≥1 we remove the divisors of all possible values of ƒ in the points in which the sum of coordinates is less than or equal to n. The least non-cancelled number is called the discriminator Dƒ(n). We find formulas, or at least an estimation for this discriminator, in the case of a broad class of sequences.
PL
Kontynuujemy badania nad generalizacją algorytmu sitowego Browkina i Cao, [A. Tomski, M. Zakarczemny, On some cancellation algorithms, NNTDM. 23, 2017, p. 101–114]. Niech f będzie funkcją o wartościach w zbiorze liczb naturalnych, określoną na ℕs , s ≥1. Usuwamy dzielniki wszystkich możliwych wartości funkcji ƒ, w punktach, w których suma współrzędnych nie przekracza n. Najmniejszą niewykreśloną liczbę naturalną nazywamy dyskryminatorem Dƒ(n). W artykule uogólniamy pojęcie dyskryminatora. Znajdujemy jawne wzory lub oszacowania na dyskryminator dla szerokiej klasy ciągów.
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nr (1/2017)
145-154
PL
W artykule opisano wyniki badań w dziedzinie komunikacji rodzinnej. Dwuletnie badania ukierunkowane były na komunikację między rodzicami i dziećmi. Skupiono się na tak zwanych „modelach” Satir – ukazujących postawy samozachowawcze, najczęściej podejmowane przez rodziców w przekazach rodzinnych. Dane pochodzą z autentycznych nagrań wspólnej, rodzinnej komunikacji, zaistniałej w konkretnych sytuacjach (na przykład dzieci przygotowujące się do szkoły, podczas uprawiania sztuki i rzemiosła, siedzące przy stole itp). Naszym celem było opisanie i analiza – w kontekście realizacji strategii samozachowawczych – konkretnych przykładów w zakresie komunikacji rodzinnej, stosowanej przez rodziców w relacji z dzieckiem.
EN
This paper describes the part of results of research into family communications. Our two years’ investigation was targeted at communication between parents and children. The focus was on so called “Satir Models” of self-preservation positions taken by parents in family communications most frequently. The data come from authentic recordings of common communications in families related to specific situations (for example, children getting ready for a day at school, during art and craft activities, sitting at the table, etc.). Our aim is to describe and analyse concrete examples of family communications used by parents in the child directed speech to fulfil the self-preservation strategies.
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