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ON THE ALTERNATING SUMS AND APPLICATION TO APOSTOL-BERNOULLI POLYNOMIALS
VELI KURT 장전수학회 2013 Proceedings of the Jangjeon mathematical society Vol.16 No.2
In recent years, a lot of mathematicians study some iden-tities and recurrence relations on the Bernoulli numbers and Bernoullipolynomials. Tuender H. J.; Yang S. proved some symmetry identitieson the Bernoulli numbers and Bernoulli polynomials. W. Wang et al. proved some symmetry identities relation on the Apostol-Bernoulli andApostol-Euler polynomials. D.-Q. Lu and H. M. Srivastava gave oneseries identities the generalized Apostol type polynomials. D. S. Kim,T. Kim, S. H. Lee and S.-H. Rim proved some symmetry propertiesand identities of Bernoulli and Euler polynomials associated with p-adicintegral on Zp.
A NEW APPROACH TO q-GENOCCHI NUMBERS AND POLYNOMIALS
Kurt, Veli,Cenkci, Mehmet Korean Mathematical Society 2010 대한수학회보 Vol.47 No.3
In this paper, new q-analogs of Genocchi numbers and polynomials are defined. Some important arithmetic and combinatoric relations are given, in particular, connections with q-Bernoulli numbers and polynomials are obtained.
SOME RELATION BETWEEN THE BERNSTEIN POLYNOMIALS AND SECOND KIND BERNOULLI POLYNOMIALS
VELI KURT 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.1
Recently, Jang and Kim in [4] introduced second kind Euler polynomials and second kind Genocchi polynomials. They proved some relations at these functions. Also, Ryoo in [17], [18], [19] introduced second kind Bernoulli polynomials, second kind Euler polynomials and second kind Genocchi polynomials. Ryoo calculated the numerical value of these functions. Also, he gave the distribution relation and di¤ernce relation.
A NEW APPROACH TO q-GENOCCHI NUMBERS AND POLYNOMIALS
Veli Kurt,Mehmet Cenkci 대한수학회 2010 대한수학회보 Vol.47 No.3
In this paper, new q-analogs of Genocchi numbers and polynomials are defined. Some important arithmetic and combinatoric relations are given, in particular, connections with q-Bernoulli numbers and polynomials are obtained.
ON THE (p, q)-POLY-KOROBOV POLYNOMIALS AND RELATED POLYNOMIALS
KURT, BURAK,KURT, VELI The Korean Society for Computational and Applied M 2021 Journal of applied mathematics & informatics Vol.39 No.1
D.S. Kim et al. [9] considered some identities and relations for Korobov type numbers and polynomials. In this work, we investigate the degenerate Korobov type Changhee polynomials and the (p,q)-poly-Korobov polynomials. We give a generalization of the Korobov type Changhee polynomials and the (p,q) poly-Korobov polynomials. We prove some properties and identities and explicit relations for these polynomials.
q-EXTENSIONS OF GENOCCHI NUMBERS
CENKCI MEHMET,CAN MUMUN,KURT VELI Korean Mathematical Society 2006 대한수학회지 Vol.43 No.1
In this paper q-extensions of Genocchi numbers are defined and several properties of these numbers are presented. Properties of q-Genocchi numbers and polynomials are used to construct q-extensions of p-adic measures which yield to obtain p-adic interpolation functions for q-Genocchi numbers. As an application, general systems of congruences, including Kummer-type congruences for q-Genocchi numbers are proved.
A RECURRENCE RELATION FOR BERNOULLI NUMBERS
CAN MUMUN,CENKCI MEHMET,KURT VELI Korean Mathematical Society 2005 대한수학회보 Vol.42 No.3
In this paper, using Gauss multiplication formula, a recurrence relation for Bernoulli numbers, generalizing Namias' results, is given.
$q$-Extensions of Genocchi Numbers
Mehmet Cenkci,M\,Veli Kurt 대한수학회 2006 대한수학회지 Vol.43 No.1
In this paper $q$-extensions of Genocchi numbers are defined and several properties of these numbers are presented. Properties of $q$-Genocchi numbers and polynomials are used to construct $q$-extensions of $p$-adic measures which yield to obtain $p$-adic interpolation functions for $q$-Genocchi numbers. As an application, general systems of congruences, including Kummer-type congruences for $q$-Genocchi numbers are proved.
Properties and Corrosion Resistance of AISI H13 Hot-Work Tool Steel with Borided B4C Powders
Ali Günen,İsmail Hakki Karahan,Mustafa Serdar Karakaş,Bülent Kurt,Yusuf Kanca,Vedat Veli Çay,Murat Yıldız 대한금속·재료학회 2020 METALS AND MATERIALS International Vol.26 No.9
In this study, the surface of AISI H13 steel was borided with powder blends of B4Cand NaBF4using the powder-pack methodat 800, 900 and 1000 °C for 2, 4 and 6 h. The structural and mechanical characteristics of the boride layers formed on thesurface were characterized using scanning electron microscopy, energy dispersive spectroscopy, X-ray diffractometry, 2Dsurface profilometry, microhardness and electrochemical corrosion (3.5 wt% NaCl) tests. The boride layer exhibited a singlephase structure (Fe2B) in samples coated at 800 °C and a dual-phase structure (FeB + Fe2B) at higher boriding temperatures(900 and 1000 °C). The boride layers were compact and crack-free in all boriding conditions. Depending on boridingparameters, the thickness, hardness and average surface roughness (Ra) of the coatings were found to range between 5.81and 102.46 μm, 1635–1915 HV and 0.315–0.650 μm, respectively. The borided AISI H13 steel displayed up to 33.5 timesand 2.4 times higher corrosion resistance than untreated AISI H13 steel and martensitic AISI 431 steel, respectively. Thissuggests potential use of borided AISI H13 steel in the steam turbines and marine applications as an alternative to the morecostly martensitic and duplex stainless steel grades. The corrosion resistance depended on the phase structure (single- ordual-layer), density, thickness and surface roughness of the boride coatings.