Browsing by Author "Sermutlu, Emre"

Now showing 1 - 12 of 12

Citation Count: Sermutlu, Emre. "A close look at Newton–Cotes integration rules", Results in Nonlinear Analysis, Vol. 2, No. 2, pp. 48-60, (2019).
A close look at Newton–Cotes integration rules
(2019) Sermutlu, Emre; 17647
Newton–Cotes integration rules are the simplest methods in numerical integration. The main advantage of using these rules in quadrature software is ease of programming. In practice, only the lower orders are implemented or tested, because of the negative coefficients of higher orders. Most textbooks state it is not necessary to go beyond Boole’s 5-point rule. Explicit coefficients and error terms for higher orders are seldom given literature. Higher-order rules include negative coefficients therefore roundoff error increases while truncation error decreases as we increase the number of points. But is the optimal one really Simpson or Boole? In this paper, we list coefficients up to 19-points for both open and closed rules, derive the error terms using an elementary and intuitive method, and test the rules on a battery of functions to find the optimum all-round one.
Citation Count: Sermutlu, E., Eyyuboğlu, H:T: (2007). A new quadrature routine for improper and oscillatory integrals. Applied Mathematics&Computation, 189(1), 452-461. http://dx.doi.org/10.1016/j.amc.2006.08.176
A new quadrature routine for improper and oscillatory integrals
(Elsevier Science, 2007) Sermutlu, Emre; Eyyuboğlu, Halil T.; 17647; 7688
In MATLAB environment, a new quadrature routine based on Gaussian quadrature rule has been developed. Its performance is evaluated for improper integrals, rapidly oscillating functions and other types of functions requiring a. large number of evaluations. This performance is compared against the other quadrature routines written for MATLAB in terms of capability, accuracy and computation time. It is found that our routine rates quite favourably
Citation Count: Eyyuboğlu, H.T., Sermutlu, E. (2010). Calculation of average intensity via semi-analytic method. Applied Physisc B-Lasers And Optics, 98(4), 865-870. http://dx.doi.org/10.1007/s00340-009-3781-8
Calculation of average intensity via semi-analytic method
(Springer, 2010) Eyyuboğlu, Halil T.; Sermutlu, Emre; 7688; 17647
We present a semi-analytic approach to the solution of the quadruple Huygens-Fresnel integral which is used to calculate the average receiver intensity of a source beam after it has propagated in a turbulent atmosphere. Our approach is based on a self-designed MATLAB function that reduces a quadruple integral to a single one by sequential operations using a form that is readily available from tables. In this manner exact numerical evaluations are obtained, whilst lengthy hand derivations are avoided. Additionally, the computation time of the new approach is not much different from that of the complete analytic solution. Two application examples are cited, also establishing agreement with our previously published results
Citation Count: Sermutlu, E., (2005). Comparison of Newton–Cotes and Gaussian methods of quadrature. Applied Mathematics & Computation, 171(2), 1048-1057. http://dx.doi.org/10.1016/j.amc.2005.01.102
Comparison of Newton–Cotes and Gaussian methods of quadrature
(Elsevier Science, 2005) Sermutlu, Emre; 17647
We compare Newton-Cotes and Gauss methods of various orders. We give two MATLAB programs that evaluates integrals numerically for given order with given number of points. We make extensive tests with various functions and intervals using same number of points for each method and compare errors
Citation Count: Eyyuboğlu, H.T., Baykal, Y., Sermutlu, E. (2006). Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere. Optic Communications, 265(2), 399-405. http://dx.doi.org/10.1016/j.optcom.2006.03.071
Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere
(Elsevier Science, 2006) Eyyuboğlu, Halil T.; Baykal, Yahya; Sermutlu, Emre; 7688; 7812; 17647
It is shown that a general shaped laser beam will eventually approach a Gaussian average intensity profile after propagation in turbulent atmosphere. In our formulation, source field at the exit plane of the laser is taken as the product of arbitrary functions of source transverse coordinates with Gaussian exponential modulations. Following the expansion of the arbitrary functions in terms of Hermite polynomials, the average receiver intensity expression is derived using the extended Huygens–Fresnel principle and the conditions for the intensity profile to assume a Gaussian shape are stated. The results are illustrated by simulating various source field distributions.
Citation Count: Eyyuboğlu, H.T...et al. (2008). Intensity fluctuations in J-Bessel-Gaussian beams of all orders propagating in turbulent atmosphere. Applied Physisc B-Lasers And Optics, 93(2-3), 605-611. http://dx.doi.org/10.1007/s00340-008-3230-0
Intensity fluctuations in J-Bessel-Gaussian beams of all orders propagating in turbulent atmosphere
(Springer, 2008) Eyyuboğlu, Halil T.; Sermutlu, Emre; Baykal, Yahya; Cai, Yangjian; Korotkova, Olga; 7688; 17647; 7812
The scintillation index of a J (n) -Bessel-Gaussian beam of any order propagating in turbulent atmosphere is derived and numerically evaluated at transverse cross-sections with the aid of a specially designed triple integral routine. The graphical outputs indicate that, just like the previously investigated J (0)-Bessel-Gaussian beam, higher-order members of the family also offer favorable scintillation characteristics at large source sizes. This advantage is maintained against rising beam orders. Viewed along the propagation axis, beams with lower orders and smaller widths exhibit smaller values of the scintillation index at shorter propagation distances and large values at longer propagation distances. Further, it is shown that the scintillation index of the J (n) -Bessel-Gaussian beams (n > 0) is larger than that of the fundamental Gaussian and the J (0)-Bessel-Gaussian beams only near the on-axis points, while remaining smaller towards the edges of the beam
Citation Count: Alzabut, J.O., Stamov, G.Tr., Sermutlu, E. (2010). On almost periodic solutions for an impulsive delay logarithmic population model. Mathematical And Computer Modelling, 51(5-6), 625-631. http://dx.doi.org/ 10.1016/j.mcm.2009.11.001
On almost periodic solutions for an impulsive delay logarithmic population model
(Pergamon-Elsevier Science LTD, 2010) Alzabut, Jehad; Stamov, G. T.; Sermutlu, Emre; 17647
By employing the contraction mapping principle and applying the Gronwall-Bellman inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solutions for an impulsive delay logarithmic population model. An example with its numerical simulations has been provided to demonstrate the feasibility of our results
Citation Count: Eyyuboğlu, H.T., Sermutlu, E. (2013). Partially coherent Airy beam and its propagation in turbulent media. Applied Physisc B-Lasers And Optics, 110(4), 451-457. http://dx.doi.org/10.1007/s00340-012-5278-0
Partially coherent Airy beam and its propagation in turbulent media
(Springer, 2013) Eyyuboğlu, Halil T.; Sermutlu, Emre; 7688; 17647
The properties of partially coherent Airy beam propagating in turbulent media are investigated. Firstly the variations in the intensity profile and the location of the Airy beam peak with respect to dislocation and width parameters are examined. On the source plane, it is shown that there is a threshold value of the dislocation parameter which determines whether the beam peak will lie on the negative or positive side of the axis. The changes in source beam power and source beam size with respect to dislocation and width parameters are also examined. Then analysis is made for partially coherent Airy beam propagating in turbulence against variations in propagation distance, dislocation and width parameters, structure constant and partial coherence. It is found that the peak of the Airy beam will always shift to the right for increasing propagation distance. But this shift will become less as the dislocation and width parameters are increased. Finally it is shown that higher levels of turbulence and partial coherence will lead to more spreading and shift the beam peak more toward the on-axis position.
Citation Count: Alzabut, J.O., Stamov, G.T., Sermutlu, E. (2011). Positive almost periodic solutions for a delay logarithmic population model. Mathematical And Computer Modelling, 53(1-2), 161-167. http://dx.doi.org/10.1016/j.mcm.2010.07.029
Positive almost periodic solutions for a delay logarithmic population model
(Pergamon-Elsevier Science LTD, 2011) Alzabut, Jehad; Stamov, G. T.; Sermutlu, Emre; 17647
By utilizing the continuation theorem of coincidence degree theory, we shall prove that a delay logarithmic population model has at least one positive almost periodic solution. An example is provided to illustrate the effectiveness of the proposed result
Citation Count: Eyyuboğlu, H.T., Baykal, Y., Sermutlu, E. (2008). Scintillation advantages of lowest order Bessel-Gaussian beams. Applied Physisc B-Lasers And Optics, 92(2), 229-235. http://dx.doi.org/10.1007/s00340-008-3096-1
Scintillation advantages of lowest order Bessel-Gaussian beams
(Springer, 2008) Eyyuboğlu, Halil T.; Baykal, Yahya; Sermutlu, Emre; 7688; 7812; 17647
For a weak turbulence propagation environment, the scintillation index of the lowest order Bessel-Gaussian beams is formulated. Its triple and single integral versions are presented. Numerical evaluations show that at large source sizes and large width parameters, when compared at the same source size, Bessel-Gaussian beams tend to exhibit lower scintillations than the Gaussian beam scintillations. This advantage is lost however for excessively large width parameters and beyond certain propagation lengths. Large width parameters also cause rises and falls in the scintillation index of off-axis positions toward the edges of the received beam. Comparisons against the fundamental Gaussian beam are made on equal source size and equal power basis.
Citation Count: Eyyuboğlu, H.T...et al. (2009). Scintillation index of modified Bessel-Gaussian beams propagating in turbulent media. Journal of the Optical Society of America A-Optics Image Science and Vision, 26(2), 387-394.
Scintillation index of modified Bessel-Gaussian beams propagating in turbulent media
(Optical Soc Amer, 2009) Eyyuboğlu, Halil T.; Baykal, Yahya; Sermutlu, Emre; Korotkova, Olga; Cai, Yangjian; 7688; 7812; 17647
The scintillation index is formulated for modified Bessel-Gaussian beams propagating in weakly turbulent media. Numerical calculations applied directly to the derived triple integral show that, for off-axis positions, the modified Bessel-Gaussian beams of higher than zero order scintillate less than Gaussian beams at large input beam sizes and low beam orders with the increasing width parameter initially contributing positively to this phenomenon of less scintillation. As the beam order exceeds two, this advantage is diminished. The modified Bessel-Gaussian beam of order zero is a special case, however, exhibiting lowest scintillation at small input beam sizes. When considered against the propagation length, higher-order modified Bessel-Gaussian beams continue to offer less scintillation than those of order zero. At various radial positions, the scintillation index of modified Bessel-Gaussian beams with orders higher than zero attains small values toward the beam edges but rises sharply when approaching the beam axis. The effect of inner and outer scales of turbulence is also studied, and it is found that while increasing the inner scale of turbulence seems to cause increases in scintillation, the influence of the outer scale is hardly noticeable
Citation Count: Samad, Abdul...at all (2021). "Selection of an Effective Hand Sanitizer to Reduce COVID-19 Effects and Extension of TOPSIS Technique Based on Correlation Coefficient under Neutrosophic Hypersoft Set", Complexity, Vol. 2021.
Selection of an Effective Hand Sanitizer to Reduce COVID-19 Effects and Extension of TOPSIS Technique Based on Correlation Coefficient under Neutrosophic Hypersoft Set
(2021) Samad, Abdul; Zulqarnain, Rana Muhammad; Sermutlu, Emre; Ali, Rifaqat; Siddique, Imran; Jarad, Fahd; Abdeljawad, Thabet; 234808
Correlation coefficients are used to tackle many issues that include indistinct as well as blurred information excluding is not able to deal with the general fuzziness along with obscurity of the problems that have various information. The correlation coefficient (CC) between two variables plays an important role in statistics. Likewise, the accuracy of relevance assessment depends on the information in a set of discourses. The data collected for numerous statistical studies is full of exceptions. The concept of the neutrosophic hypersoft set (NHSS) is a parameterized family that deals with the subattributes of the parameters and is a proper extension of the neutrosophic soft set to accurately assess the deficiencies, anxiety, and uncertainty in decision-making. Compared with existing research, NHSS can accommodate more uncertainty, which is the most significant technique for describing fuzzy information in the decision-making process. The core objective of follow-up research is to develop the concept and characteristics of CC and the weighted correlation coefficient (WCC) of NHSS. We also introduced some aggregation operators in the considered environment, which can help us establish a prioritization technique for order preference by similarity to the ideal solution (TOPSIS) based on CC and WCC under NHSS. A decision-making strategy is established to solve multicriteria group decision-making (MCGDM) problems utilizing developed methodology. Moreover, the proposed method is utilized for the selection of an effective hand sanitizer during the COVID-19 pandemic to ensure the validity of the proposed approach. The practicality, effectivity, and flexibility of the current approach are proved through comparative analysis with the assistance of some existing studies.