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GENERALIZATION OF q-APOSTOL-TYPE EULERIAN NUMBERS AND POLYNOMIALS, AND THEIR INTERPOLATION FUNCTIONS
I. N. Cangul,A. S. Cevik,Y. Simsek 장전수학회 2015 Advanced Studies in Contemporary Mathematics Vol.25 No.2
In a recent paper [16], generating functions in terms of non- negative real parameters, q-Eulerian type polynomials and numbers (or q-Apostol type Frobenius-Euler numbers and polynomials) have been constructed by Y. Simsek. Additionally, some identities for these poly- nomials and numbers based on the generating functions and functional equations have been derived. Finally, a multiplication formula for the generalized Apostol type Frobenius-Euler polynomials has been given. In this paper, as a continuing study of [16], we will essentially present generalizations of the above material and, dierently from aforemen- tioned paper, we will express the interpolation functions related to these numbers and polynomials.
Formulas and relations for Bernoulli-type numbers and polynomials derive from Bessel function
Selin Selen Ozbek Simsek,Yilmaz Simsek 대한수학회 2023 대한수학회논문집 Vol.38 No.4
The main purpose of this paper is to give some new identities and properties related to Bernoulli type numbers and polynomials associated with the Bessel function of the first kind. We give symmetric properties of the Bernoulli type numbers and polynomials. Moreover, using generating functions and the Fa \`{a} di Bruno's formula, we derive some new formulas and relations related to not only these polynomials, but also the Bernoulli numbers and polynomials and the Euler numbers and polynomials.
THE BEHAVIOR OF THE TWISTED p-ADIC (h, q)-L-FUNCTIONS AT s = 0
Simsek, Yilmaz Korean Mathematical Society 2007 대한수학회지 Vol.44 No.4
The main result of this paper is to construct the derivative twisted p-adic (h, q)-L-functions at s = 0. We obtain twisted version of Theorem 4 in [17]. We also obtain twisted (h, q)-extension of Proposition 1 in [3].
Importance of Serum SELDI-TOF-MS Analysis in the Diagnosis of Early Lung Cancer
Simsek, Cebrail,Sonmez, Ozlem,Yurdakul, Ahmet Selim,Ozmen, Fusun,Zengin, Nurullah,Keyf, Atilla Isan,Kubilay, Dilek,GUlbahar, Ozlem,Karatayli, Senem Ceren,Bozdayi, Mithat,Ozturk, Can Asian Pacific Journal of Cancer Prevention 2013 Asian Pacific journal of cancer prevention Vol.14 No.3
Background: Different methods of diagnosis have been found to be inefficient in terms of screening and early diagnosis of lung cancer. Cancer cells produce proteins whose serum levels may be elevated during the early stages of cancer development. Therefore, those proteins may be recognized as potential cancer markers. The aim of this study was to differentiate healthy individuals and lung cancer cases by analyzing their serum protein profiles and evaluate the efficacy of this method in the early diagnosis of lung cancer. Materials and Methods: 170 patients with lung cancer, 53 under high risk of lung cancer, and 47 healthy people were included in our study. Proteomic analysis of the samples was performed with the SELDI-TOF-MS approach. Results: The most discriminatory peak of the high risk group was 8141. When tree classification analysis was performed between lung cancer and the healthy control group, 11547 was determined as the most discriminatory peak, with a sensitivity of 85.5%, a specificity of 89.4%, a positive predictive value (PPV) of 96.7% and a negative predictive value (NPV) of 62.7%. Conclusions: We determined three different protein peaks 11480, 11547 and 11679 were only present in the lung cancer group. The 8141 peak was found in the high-risk group, but not in the lung cancer and control groups. These peaks may prove to be markers of lung cancer which suggests that they may be used in the early diagnosis of lung cancer.
ON q-ANALGUE OF THE TWISTED L-FUNCTIONS AND q-TWISTED BERNOULLI NUMBERS
Simsek, Yilmaz Korean Mathematical Society 2003 대한수학회지 Vol.40 No.6
The aim of this work is to construct twisted q-L-series which interpolate twisted q-generalized Bernoulli numbers. By using generating function of q-Bernoulli numbers, twisted q-Bernoulli numbers and polynomials are defined. Some properties of this polynomials and numbers are described. The numbers $L_{q}(1-n,\;X,\;{\xi})$ is also given explicitly.
ON TWISTED GENERALIZED EULER NUMBERS
Simsek, Yilmaz Korean Mathematical Society 2004 대한수학회보 Vol.41 No.2
In this paper, we shall construct generating function of twisted generalized Euler numbers. By using this function, we shall define twisted generalized Euler polynomials and numbers. We shall give some basic properties of these polynomials and numbers.
Simsek, Ela Nur,Uysal, Tuna Asian Pacific Journal of Cancer Prevention 2013 Asian Pacific journal of cancer prevention Vol.14 No.11
Apoptotic and cytotoxic activity of plant extracts obtaining from naturally growing Cynara syriaca in Turkey and cultivated C cardunculus against DLD1 colorectal cancer cells was determined. Extracts from wild and cultivated Cynara species were obtained from their vegetative parts and receptacles using hexane and applied with five different dose (0.1-1 mg/ml) as well as apigenin for MTT tests for three time periods (24, 48 and 72 hours). After cells were treated with $IC_{50}$ doses for each extract total DNA and RNA were isolated for determination of the cause of cell death. From isolated RNAs, cDNA were synthesized and amplification of p21, BCL-2 and BAX gene regions was carried out. Consequently, we found that pro-apoptotic (BAX) gene expression and a cell cycle inhibitor (p21) were induced in the presence of our artichoke extracts. In contrast, anti-apoptotic BCL-2 gene expression was reduced compared to the control group. In addition DNA fragmentation results demonstrated DLD1 cell death via apoptosis.
p-ADIC q-HIGHER-ORDER HARDY-TYPE SUMS
SIMSEK YILMAZ Korean Mathematical Society 2006 대한수학회지 Vol.43 No.1
The goal of this paper is to define p-adic Hardy sums and p-adic q-higher-order Hardy-type sums. By using these sums and p-adic q-higher-order Dedekind sums, we construct p-adic continuous functions for an odd prime. These functions contain padic q-analogue of higher-order Hardy-type sums. By using an invariant p-adic q-integral on $\mathbb{Z}_p$, we give fundamental properties of these sums. We also establish relations between p-adic Hardy sums, Bernoulli functions, trigonometric functions and Lambert series.
ON ELLIPTIC ANALOGUE OF THE HARDY SUMS
Simsek, Yilmaz,Kim, Dae-Yeoul,Koo, Ja-Kyung Korean Mathematical Society 2009 대한수학회보 Vol.46 No.1
Main purpose of this paper is to define an elliptic analogue of the Hardy sums. Some results, which are related to elliptic analogue of the Hardy sums, are given.