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On the Fibonacci Almost Convergent Sequence Space and Fibonacci Core
DEMIRIZ, SERKAN,KARA, EMRAH EVREN,BASARIR, METIN Department of Mathematics 2015 Kyungpook mathematical journal Vol.55 No.2
In the present paper, by using the Fibonacci difference matrix, we introduce the almost convergent sequence space $\hat{c}^f$. Also, we show that the spaces $\hat{c}^f$and $\hat{c}$ are linearly isomorphic. Further, we determine the ${\beta}$-dual of the space $\hat{c}^f$ and characterize some matrix classses on this space. Finally, Fibonacci core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.
Domain of Euler-totient matrix operator in the space $\mathcal{L}_{p}$
Serkan Demiriz,Sezer Erdem 강원경기수학회 2020 한국수학논문집 Vol.28 No.2
The most apparent aspect of the present study is to introduce a new sequence space $\Phi^\star(\mathcal{L}_{p})$ derived by double Euler-Totient matrix operator. We examine its topological and algebraic properties and give an inclusion relation. In addition to those, the $\alpha-$, $\beta(bp)-$ and $\gamma-$duals of the space $\Phi^\star(\mathcal{L}_{p})$ are determined and finally, some 4-dimensional matrix mapping classes related to this space are characterized.
A Retrospective Multicenter Evaluation of Cutaneous Melanomas in Turkey
Gamsizkan, Mehmet,Yilmaz, Ismail,Buyukbabani, Nesimi,Demirkesen, Cuyan,Demiriz, Murat,Cetin, Emel Dikicioglu,Ince, Umit,Akalin, Taner,Demirkan, Nese Calli,Lebe, Banu,Erdem, Ozlem,Gokoz, Ozay,Sakiz, Da Asian Pacific Journal of Cancer Prevention 2014 Asian Pacific journal of cancer prevention Vol.15 No.23
Background: We defined melanoma distribution in a large series of Turkish patients and evaluated the prognostic parameters of melanomas. Materials and Methods: A total of 1574 patients' data was retrospectively collected at 18 centers in Turkey. Demographic characteristics were questioned and noted. Prognostic parametres were evaluated based on sentinel lymph node involvement. Results: Mean age was 56.7 (4-99) years. While 844 (53.6%) cases were male, 730 (46.4%) cases were female. One thousand four hundred forty-seven (92%) cases were invasive melanoma and 127 (8%) cases were in-situ melanoma. The most common histopathological form was the superficial spreading melanoma (SSM) which was found in 549 patients (37.9%). It was followed by nodular melanoma in 379 (26.2%), acral lentiginous melanoma (ALM) in 191 (13.2%) and lentigo maligna melanoma in 132 (9.1%), respectively. On univariate analysis, lymphovascular invasion (p<0.001), tumor thickness (p<0.001), histopathological subtype (p<0.001), Clark level (p=0.001), ulceration (p<0.001), ${\geq}6/mm^2$ mitosis (p=0.005), satellite formation (p=0.001) and gender (p=0.03) were found to be associated with sentinel lymph node positivity. Regression was associated with sentinel lymph node negativity (p=0.017). According to multivariate analysis, lymphovascular invasion and tumor thickness were significant independent predictive factors of SLN positivity. Patient age, tumor localization, precursor lesions, lymphocytic infiltration and neurotropism were not related with sentinel lymph node involvement. Conclusions: In this retrospective analysis, it was found that the prevalence of SSM is at a lower rate while the prevalence of ALM is at a higher rate when compared to western countries. According to Breslow index; most of the melanoma lesions' thickness were greater than 2 mm, corresponding Clark IV. Vascular invasion and tumor thickness are the most important factors for sentinel lymph node involvement.