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Correction : Proc. Jangjeon Math. Soc. 8(2005), No. 2, pp. 123-130
P. M. Vassilev,M. V. Vassilev-Missana,K. T. Atanassov 장전수학회 2006 Proceedings of the Jangjeon mathematical society Vol.9 No.2
In the above paper the following corrections should be taken into account. Everywhere in the text the expression \an integer k satisfying (1)" should be read as \an integer k satisfying (2)". In the Proof of Lemma 3 variable s should be changed to k. On page 123 instead of [4] should be read [2] and in the last row instead of [3] should be read [2]; on page 129 in section \Final remarks" instead of [2] should be read [4]. In the text there are some other misprints, e.g., it is written that there are four instead of ¯ve assertions, but we hope that the benevolent reader will not hold this against us.
CLOSURE OPERATIONS AND THE DESCENDING CHAIN CONDITION
Vassilev, Janet C. Korean Mathematical Society 2017 대한수학회지 Vol.54 No.6
In this note, we define and compare some closures which behave somewhat like the radical closure. Using these closures as a starting point allows us to classify all semiprime closures on the nodal curve. Several examples provided show how these closures can differ significantly in the non-Noetherian setting.
Note on Some Identities Involving Mobius Function
Vassilev-Missana 장전수학회 2010 Proceedings of the Jangjeon mathematical society Vol.13 No.1
In the present paper two new identities ((2) and (10)) about multiplicative arithmetic functions that do not vanish anywhere on the set of positive integers are proposed and proved. These identities use the famous Möbius function. Also many other interesting identities are obtained as corollaries from them.
On an estimate from above for the remainder sum of certain series related to Euler's gamma function
P. Vassilev 장전수학회 2014 Advanced Studies in Contemporary Mathematics Vol.24 No.1
In the present paper we investigate the remainder term of the series (formula), which may be represented by Euler`s gamma function and the Pocchammer symbol and an estimate from above for this remainder term is obtained.
Note on a new proof of Bolzano-Weierstrass theorem
Mladen Vassilev - Missana 장전수학회 2017 Advanced Studies in Contemporary Mathematics Vol.27 No.4
In the paper, a new proof of the well-known Bolzano-Weierstrass Theorem is proposed.
ON ONE TRINOMIAL EQUATION AND ITS SOLUTION
Peter Vassilev 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.4
In the paper the question about the solution of the trinomial equation zn - pz - 1 = 0 is studied. It is shown that for p < 0 this equation has exactly one zero in the open interval (0, 1). That zero is expressed in seven different ways as infinite series. The radius of convergence of these series is found.
On Reassessment of Expert Evaluations in the Case of Intuitionistic Fuzziness
Peter Vassilev 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.4
In the present paper an Open Problem proposed by K. Atanassov is com-pletely solved. As a result a possible approach for correction of inconsistent expert estimates is provided. The solution is constructed by selecting a specific p-intuitionistic fuzzy set and then mapping it to the traditional interpretation triangle of the intuitionistic fuzzy sets.
On a class of conjectures equivalent to the strong Goldbach's conjecture
Peter Vassilev 장전수학회 2006 Advanced Studies in Contemporary Mathematics Vol.13 No.1
In the paper are considered two different semigroups whose elements are positive integer-value multiplicative functions. Each element of the union of these semigroups generates an assertion that presents a conjecture equivalent (as proved in the paper) to the Strong Goldbach's Conjecture (see [1], [2]): SG: Every even number greater than or equal to 8 is a sum of two odd distinct primes. Our investigation presents a new point of view for the Goldbach's Conjecture and suggests a strong generalization of some of the results in [2] and [3]. (Remark. The classical Goldbach's Conjecture: Every even number greater than 4 is a sum of two primes is a corollary from SG.)
RINGS WHOSE ELEMENTS ARE SUMS OF FOUR COMMUTING IDEMPOTENTS
Danchev, Peter Vassilev The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.2
We completely characterize the isomorphic class of those associative unitary rings whose elements are sums of four commuting idempotents. Our main theorem enlarges results due to Hirano-Tominaga (Bull. Austral. Math. Soc., 1988), Tang et al. (Lin. & Multilin. Algebra, 2019), Ying et al. (Can. Math. Bull., 2016) as well as results due to the author in (Alban. J. Math., 2018), (Gulf J. Math., 2018), (Bull. Iran. Math. Soc., 2018) and (Boll. Un. Mat. Ital., 2019).
CLOSURE OPERATIONS AND THE DESCENDING CHAIN CONDITION
Janet C. Vassilev 대한수학회 2017 대한수학회지 Vol.54 No.6
In this note, we define and compare some closures which behave somewhat like the radical closure. Using these closures as a starting point allows us to classify all semiprime closures on the nodal curve. Several examples provided show how these closures can differ significantly in the non-Noetherian setting.