A FAMILY OF FUNCTIONS ASSOCIATED WITH THREE TERM RELATIONS AND EISENSTEIN SERIES

Aygunes, Aykut Ahmet Korean Mathematical Society 2016 대한수학회보 Vol.53 No.6

Abstract. In this paper, for $a{\in}C$, we investigate functions $g_a$ and ${\psi}_a$ associated with three term relations. $g_a$ is defined by means of function ${\psi}_a$. By using these functions, we obtain some functional equations related to the Eisenstein series and the Riemann zeta function. Also we find a generalized difference formula of function $g_a$.

Removal of sulphate from landfill leachate by crystallization

Ahmet Aygun,Selim Dogan,Mehmet Emin Argun,Havva Ates 대한환경공학회 2019 Environmental Engineering Research Vol.24 No.1

The present study explores the applicability of response surface methodology (RSM) in conjunction with central composite design (CCD) matrix to statistically optimize ettringite crystallization process for the removal of sulphate from landfill leachate. A three factor-five coded level CCD with 20 runs, was performed to estimate the best fitted model. The RSM results indicated that the fitted quadratic regression model could be appropriate to predict sulfate removal efficiency. The pH was identified as the most dominant parameter affecting sulphate removal. 61.6% of maximum sulphate removal efficiency was obtained at pH of 11.06 for a 1.87 of Ca/SO₄ and 0.51 of Al/SO₄ molar ratios. The operating cost for ettringite crystallization at optimized conditions was calculated to be 0.52 $/m³. The significance of independent variables and their interactions were tested by analysis of variance. Scanning electron microscope (SEM) and SEM coupled with energy dispersive X-Ray spectroscopy results confirmed the formation of ettringite crystal and were used to describe its morphology features.

Electrocoagulation of Disperse Dyebath Wastewater: Optimization of Process Variables and Sludge Production

Aygun, Ahmet,Nas, Bilgehan,Sevimli, Mehmet Faik The Korean Electrochemical Society 2021 Journal of electrochemical science and technology Vol.12 No.1

This study was conducted to investigate the effect of initial pH, current density, and electrolysis time on process performance in terms of decolorization and chemical oxygen demand (COD) removal from disperse dyebath wastewater (DDW) by mono-polar parallel laboratory scale electrocoagulation (EC) process. COD reduction of 51.3% and decolorization of 92.8% were obtained with operating cost of 0.19 €/㎥ treated wastewater for Al-Al electrode pair, while 90.5% of decolorization and 49.2% of COD reduction were obtained with operating cost of 0.20 €/㎥ treated wastewater for an Fe-Fe electrode pair. The amount of sludge production were highly related to type of the electrode materials. At the optimum conditions, the amount of sludge produced were 0.18 kg/㎥ and 0.28 kg/㎥ for Al-Al and Fe-Fe electrode pairs, respectively. High decolorization can be explained by the hydrophobic nature of the disperse dye, while limited COD removal was observed due to the high dissolved organic matter of the DDW based on auxiliary chemicals. Energy, electrode, and chemical consumptions and sludge handling were considered as major cost items to find a cost-effective and sustainable solution for EC. The contribution of each cost items on operating cost were determined as 10.0%, 51.1%, 30.5% and 8.4% for Al-Al, and they were also determined as 9.0%, 38.0%, 40.5% and 12.5% for Fe-Fe, respectively. COD reduction and decolorization were fitted to first-order kinetic rule.

Application of sequencing batch biofilm reactor (SBBR) in dairy wastewater treatment

Ahmet Aygun,Arzu Ozturk,Bilgehan Nas 한국화학공학회 2019 Korean Journal of Chemical Engineering Vol.36 No.2

Application of lab-scale sequencing batch (SBR) and sequencing batch biofilm reactors (SBBR) for treatment of dairy wastewater was investigated under organic loading of 1,130-1,560 gBOD5/m3·d. The main characteristics of the dairy wastewater were: pH=4.9, chemical oxygen demand (COD)=16,264 mg/l; biological oxygen demand (BOD5)=10,536mg/l, PO4-P=342mg/l; total nitrogen (TN)=224mg/l. SBBR was filled with the Kaldnes K1 biocarrier at 30% of the volume of empty reactor. The SBR and SBBR were operated in fixed 24 h cycles, each consisting of 30 min fill up, 22 h aeration, 1.5 h settle, 30min decant, and idle with a hydraulic retention time (HRT) of 8 days. Operational parameters such as pH, dissolved oxygen (DO), mixed liquor suspended solid (MLSS), solids retention time (SRT) and sludge volume index (SVI) were monitored during the whole cycle. The effects of these parameters on the COD, nitrogen and phosphorus removal were discussed in this paper. As a result, adding biocarrier to the reactor had a positive effect on organic with COD removal of 63.5% for SBR and 81.8% for SBBR and nutrient removal with ammonium removal of 66.0% for SBR and 85.1% for SBBR in treatment of dairy wastewater.

DERIVATIVE FORMULAE FOR MODULAR FORMS AND THEIR PROPERTIES

Aygunes, Aykut Ahmet Korean Mathematical Society 2015 대한수학회지 Vol.52 No.2

In this paper, by using the modular forms of weight nk ($2{\leq}n{\in}\mathbb{N}$ and $k{\in}\mathbb{Z}$), we construct a formula which generates modular forms of weight 2nk+4. This formula consist of some known results in [14] and [4]. Moreover, we obtain Fourier expansion of these modular forms. We also give some properties of an operator related to the derivative formula. Finally, by using the function $j_4$, we obtain the Fourier coefficients of modular forms with weight 4.

Treatment of reactive dyebath wastewater by electrocoagulation process: Optimization and cost-estimation

Ahmet Aygun,Bilgehan Nas,Mehmet Faik Sevimli 한국화학공학회 2019 Korean Journal of Chemical Engineering Vol.36 No.9

Reactive dyestuff is commonly used in the textile industry. Reactive dyebath wastewater (RDW) was treated with a batch, monopolar, parallel lab scale electrocoagulation process (EC) having 0.042m2 effective electrode area. The effects of process parameters, such as initial pH, current density and electrolysis period on COD and color removal efficiency, were investigated by using response surface methodology (RSM). At the optimal conditions, 85.8% color and 76.9% COD removal were obtained with 1.84 €/m3 operating cost for Al electrode, while 92.0% decolorization and 80.9% COD removal were obtained with 1.56 €/m3 operating cost for an iron electrode. The iron electrode was found superior to aluminum as a sacrificial anode material in terms of COD and color removal with low cost. The cost of electrical energy, electrode, and chemical consumptions for electrocoagulation were considered to find an optimum and feasible solution. As a result, the operating cost consists of approximately 2% for energy, 28% for electrode and 70% for chemical consumption for both electrodes. Based upon the data, it is clearly seen that operating cost covers mostly for HCI to adjust pH due to the high pH and alkalinity of RDW, which was neglected in many studies. The first-order reaction kinetics with a higher slope for the color were well fitted, resulting in faster color removal than that of COD for both electrodes.

A family of functions associated with three term relations and Eisenstein series

Aykut Ahmet Aygunes 대한수학회 2016 대한수학회보 Vol.53 No.6

In this paper, for $a\in \mathbb{C}$, we investigate functions $g_{a}$ and $ \psi _{a}$ associated with three term relations. $g_{a}$ is defined by means of function $\psi _{a}$. By using these functions, we obtain some functional equations related to the Eisenstein series and the Riemann zeta function. Also we find a generalized difference formula of function $g_{a}$.

Unification of multiple Lerch zeta type functions

A. Ahmet Aygunes,Yilmaz Simsek 장전수학회 2011 Advanced Studies in Contemporary Mathematics Vol.21 No.4

In this work, we study on the family of multiple Lerch zeta type functions. By apply-ing Leibnitz derivative formula to generating function of the unification of Bernoulli,Euler and Genocchi numbers of higher order. We define multiple unification of Lerch zeta type functions. We also give some remarks and applications related to these functions.

DERIVATIVE FORMULAE FOR MODULAR FORMS AND THEIR PROPERTIES

Aykut Ahmet Aygunes 대한수학회 2015 대한수학회지 Vol.52 No.2

In this paper, by using the modular forms of weight nk (2 ≤ n ∈ N and k ∈ Z), we construct a formula which generates modular forms of weight 2nk+4. This formula consist of some known results in [14] and [4]. Moreover, we obtain Fourier expansion of these modular forms. We also give some properties of an operator related to the derivative formula. Finally, by using the function j4, we obtain the Fourier coefficients of modular forms with weight 4.