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UNSOLVED PROBLEMS IN BCK-ALGEBRAS
Dudek, Wieslaw A. The Youngnam Mathematical Society Korea 2001 East Asian mathematical journal Vol.17 No.1
We present old unsolved problems on BCK-sequences connected with convex congruences on BCK-algebras. We posed also some new problems on subalgebras.
FINITE BCK-ALGEBRAS ARE SOLVABLE
Dudek, Wieslaw A. Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.2
We present a short and very elementary proof that each finite BCK-algebra is solvable. It is a positive answer to the question posed in [4].
Dudek, Wieslaw A.,Jun, Young-Bae The Youngnam Mathematical Society Korea 2008 East Asian mathematical journal Vol.24 No.2
As a generalization of BCI-algebras, the notion of pseudo-BCI algebras is introduced, and some of their properties are investigated. Characterizations of pseudo-BCI algebras are established. Some conditions for a pseudo-BCI algebra to be a pseudo-BCK algebra are given.
GENERAL TYPES OF (α,β)-FUZZY IDEALS OF HEMIRINGS
Jun, Y.B.,Dudek, W.A.,Shabir, M.,Kang, Min-Su The Honam Mathematical Society 2010 호남수학학술지 Vol.32 No.3
W. A. Dudek, M. Shabir and M. Irfan Ali discussed the properties of (${\alpha},{\beta}$)-fuzzy ideals of hemirings in [9]. In this paper, we discuss the generalization of their results on (${\alpha},{\beta}$)-fuzzy ideals of hemirings. As a generalization of the notions of $({\alpha},\;\in{\vee}q)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q)$-fuzzy k-ideals, the concepts of $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideals are defined, and their characterizations are considered. Using a left (right) ideal (resp. h-ideal, k-ideal), we construct an $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideal (resp. $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideal, $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideal). The implication-based fuzzy h-ideals (k-ideals) of a hemiring are considered.
Overactive Bladder Symptoms Negatively Affect Sleep Quality of Patients With Depression
Mikolaj Przydacz,Tomasz Golabek,Przemyslaw Dudek,Michal Skalski,Jerzy Sobanski,Katarzyna Klasa,Katarzyna Gronostaj,Dominika Dudek,Piotr Chlosta 대한배뇨장애요실금학회 2021 International Neurourology Journal Vol.25 No.1
Purpose: An established link exists between overactive bladder (OAB) syndrome and impaired sleep. However, earlier research on this subject only focused on the general population, and certain patient subgroups have not been examined adequately. Depressed patients constitute a unique population because of a possible bidirectional relationship between OAB and depression. Thus, we investigated the association between OAB symptoms and sleep quality in patients with depression. Methods: In this prospective, cross-sectional study, we analyzed data on depression, sleep quality, and OAB symptoms from depressed patients treated at our department of adult psychiatry. Data were collected with the Hamilton Rating Scale for Depression, the Holland Sleep Disorders Questionnaire, the Athens Insomnia Scale, and the OAB Module of the International Consultation on Incontinence Questionnaire. Results: In total, 102 patients treated for depression were enrolled. Thirteen patients (12.7%) met the diagnostic threshold of OAB with the International Consultation on Incontinence Questionnaire OAB Module. Patients with depression and concomitant OAB had significantly higher scores on the Holland Sleep Disorders Questionnaire than patients classified as non- OAB (P<0.01). OAB patients also had a higher risk of insomnia relative to non-OAB individuals (P<0.05). In addition, the relationship between OAB symptoms and sleep quality in patients with depression was independent from age and sex. Conclusions: In our cohort composed exclusively of individuals treated for depression, OAB symptoms were present in a significant proportion of patients, and OAB negatively affected sleep quality. Therefore, we recommend that OAB symptoms should be assessed collectively in patients with depression.
전영배,Wieslaw A. Dudek 영남수학회 2008 East Asian mathematical journal Vol.24 No.2
As a generalization of BCI-algebras, the notion of pseudo-BCI algebras is introduced, and some of their properties are investigated. Characterizations of pseudo-BCI algebras are established. Some conditions for a pseudo-BCI algebra to be a pseudo-BCK algebra are given.
Adsorption of Methylene Blue on Titanate Nanotubes Synthesized with Ultra-Small Fe3O4 Nanoparticles
Maciej Marc,Mirosław R. Dudek,Jacek J. Kozioł,Bartłomiej Zapotoczny 성균관대학교(자연과학캠퍼스) 성균나노과학기술원 2018 NANO Vol.13 No.12
Modified titanate nanotubes (TNT) were tested for their adsorption of methylene blue (MB) from water solutions. They were obtained from the TiO2 nanopowder using a standard alkaline hydrothermal method but in the stage of acid washing, when the titanate flakes begin to roll into nanotubes, magnetite nanoparticles were added. The Fe3O4 magnetic nanoparticles with diameter of around 2 nm and 12nm were used in the tests. Significantly stronger adsorption of MB was observed when smaller nanoparticles were used compared to using larger nanoparticles and compared to the case of unmodified nanotubes. It was shown that the increased adsorption of MB is associated with a more negative value of -potential for titanates modified by the ultra-small nanoparticles. In the adsorption experiment, pH 7 was selected. These results may prove to be of great importance in the case of potential applications corresponding to the use of such material for wastewater purification.
A NOTE ON THE AUSTIN'S GROUPOIDS
Cho, Jung-R.,Dudek, Jozef The Youngnam Mathematical Society Korea 2006 East Asian mathematical journal Vol.22 No.2
On a groupoid satisfying the Austin's identity, every n-ary linear term is essentially n-ary. That is, if a term has no variables appearing more than once, then the term depends on every variable it involves.
A NOTE ON DEFINING IDENTITIES OF DISTRIBUTIVE LATTICES
Kim, Woo-Hyun,Cho, Jung-Rae,Dudek, Jozef The Youngnam Mathematical Society Korea 2003 East Asian mathematical journal Vol.19 No.1
There are many conditions or identities for a lattice to be distributive. In this paper, we study some identities on algebras of type (2,2) and find another set of identities defining distributive lattices. We also study certain identities which define algebras of type (2,2) whose subalgebras generated by two elements are all distributive lattices with at most 4 elements.