HIFSI ALTINOK1, M˙ITHAT KASAP2, DERYA DEN˙IZ3
1,3Fırat University, Elazı˘g, TURKEY
2S¸ırnak University, S¸ırnak, TURKEY
emails: 1[email protected];2fdd [email protected]; 3[email protected] In this study, we generalize and examine the sequence classes wβ(F, f ) , wβ,0(F, f ) and wβ,∞(F, f ) , where f is an unbounded modulus function and β ∈ (0, 1] is a real number, for sequences of fuzzy numbers and examine some inclusion relations between them.
MSC 2010: 40A05, 40A25, 40A30, 40C05, 03E72
Keywords: Sequence of fuzzy numbers, statistical convergence, modulus function, Ces`aro summa-bility
References
[1] A. Aizpuru, M. C. Listan-Garcia, and F. Rambla-Barreno, Density by moduli and statistical convergence. Quaest. Math. 37, (2014), 525-530.
[2] H. Altınok, Y. Altın and M. I¸sık, Statistical convergence and strong p−Ces`aro summability of order β in sequences of fuzzy numbers. Iranian J. of Fuzzy Systems 9 (2012), no. 2, 65-75.
[3] H. Altınok and M. Kasap, f −statistical convergence of order β for sequences of fuzzy numbers.
Journal of Intelligent & Fuzzy Systems 33 (2017), 705–712.
[4] V. K. Bhardwaj and S. Dhawan, f −statistical convergence of order α and strong Cesaro summability of order α with respect to a modulus. J. Inequal. Appl. 2015 (2015), no.332;
doi:10.1186/s13660-015-0850-x.
[5] ¨U. C¸ akan, and Y. Altın, Some classes of statistically convergent sequences of fuzzy numbers generated by a modulus function. Iranian Journal of Fuzzy Systems 12 (2015), no. 3, 47-55.
[6] R. C¸ olak, Statistical convergence of order α. In: Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Pub. (2010), 121–129.
[7] M. Matloka, Sequences of fuzzy numbers, BUSEFAL 28 (1986), 28-37.
On eccentricity based indices of generalized Petersen graphs
MEHMET S¸ER´IF ALDEM´IR1, ABDALLA KHDIR ABDALLA MANGURI2
1Van Yuzuncu Yil University, Van, Turkey
2 University of Sulaimani, Sulaymaniyah, Iraq
emails: 1[email protected]; 2[email protected]
In this study, we firstly calculate the eccentric connectivity and connective eccentricity indices for the generalized Petersen graphs.
MSC 2010: 05C12
Keywords: Eccentric connectivity index, Connective ecentricity index, Generalized Petersen graphs
On stratified domination and Zagreb indices
MEHMET S¸ER´IF ALDEM´IR1, ABDALLA KHDIR ABDALLA MANGURI2
1Van Yuzuncu Yil University, Van, Turkey
2 University of Sulaimani, Sulaymaniyah, Iraq
emails: 1[email protected], 2[email protected]
In this study, we firstly investigate the relationship between stratified domination number and Zagreb indices.
MSC 2010: 05C12
Keywords: The first Zagreb index, The second Zagreb index, Stratified domination
Inference algorithms for jump-diffusion approximations of multi-scale processes
DERYA ALTINTAN1, HEINZ KOEPPL2
1Department of Mathematics, Sel¸cuk University, Konya, Turkey
2Department of Electrical Engineering and Information Technology, Technische Universit¨at Darmstadt, Darmstadt, Germany
emails: 1[email protected];2[email protected]
In a biochemical system, the abundance of molecular species and the magnitude of reaction rates can vary in a wide range. This diversity leads to hybrid models which combine deterministic and stochastic modeling approaches. We proposed a jump-diffusion approximation to model biochemical processes with multi-scale nature [3]. The idea of the model is to partition reactions into fast, slow groups and to combine Markov chain updating scheme for the slow set with a diffusion (Langevin) approach updating scheme for the fast set. Based on the state vector representation of the jump-diffusion approximation which is defined as a summation of the random time change model and the Langevin equation, we proved that the joint probability density function of jump-diffusion approxi-mation satisfies the hybrid master equation which is the sumapproxi-mation of the corresponding chemical master equation and the Fokker-Planck equation [4].
In this study, we develop an inference algorithm to estimate the hidden states/parameters of reaction systems whose posterior distribution satisfies the hybrid master equation. To construct the algorithm, we combine particle filtering/smoothing methods [2] with Gibbs Monte Carlo Markov Chain scheme [1]. To illustrate the method, we implement the algorithm to biochemical processes.
MSC 2010: 60H30, 60J28, 92B05
Keywords: Deterministic modeling, stochastic modeling, diffusion (Langevin) approach, jump-diffusion approximation, chemical master equation, Fokker-Planck equation, Gibbs Monte Carlo Markov Chain
Acknowledgement: This work is supported by the Scientific and Technological Research Council of Turkey (T ¨UB˙ITAK) Program no:3501 Grant, no. 115E252.
References
[1] G. Casella, C. Robert, Monte Carlo Statistical Methods. Springer Texts in Statistics. Springer, 2nd edition, 2004.
[2] A. Doucet, A. M. Johansen, A tutorial on particle filtering and smoothing: Fifteen years later.
On the global exponential stability of nonlinear neutral differential equations with time-varying
delays
YENER ALTUN1, CEM˙IL TUNC¸2
1,2Van Y¨uz¨unc¨u Yıl University, Van, Turkey emails: 1[email protected];2[email protected];
In this study, we investigated the global exponential stability of the zero solution of a neutral differential equation with time-lags. We find sufficient conditions which guarantee the global expo-nential stability of the zero solution of the equation. We benefit from the Lyapunov functional as a basic tool and the obtained result includes and improves some ones in the literature. An example is given to illustrate the applicability and correctness of the obtained result by MATLAB-Simulink.
MSC 2010: 34K20, 34K40 93D05.
Keywords: Neutral differential equation, global exponential stability, Lyapunov functional, matrix inequality, multiple delays.
References
[1] H. Chen, Some improved criteria on exponential stability of neutral differential equation. Adv.
Difference Equ. 2012 (2012), no. 170, 1-9.
[2] P. Keadnarmol and T. Rojsiraphisal, Globally exponential stability of a certain neutral differential equation with time-varying delays. Adv. Difference Equ. 2014 (2014), no. 32, 1-10.
[3] C. Tun¸c, Exponential stability to a neutral differential equation of first order with delay. Ann.
Differential Equations 29 (2013), no. 3, 253256.
On the exponential stability in nonlinear neutral differential equations
YENER ALTUN1, CEM˙IL TUNC¸2, ABDULLAH Y˙I ˜G˙IT3
1,2,3 Van Y¨uz¨unc¨u Yıl University, Van, Turkey
emails: 1[email protected];2[email protected]; 3[email protected]
In this work, we consider a nonlinear time-varying delay system of neutral equations with periodic coefficients in the form
d
dt(y(t) + Dy(t − τ (t))) = A(t)y(t) + B(t)y(t − τ (t))) + F (t, y(t), y(t − τ (t))) where
kF (t, u, v)k ≤ q1kuk1+w1 + q2kvk1+w2, q1, q2, w1, w2 > 0
We obtain some new estimates characterizing the exponential decay of solutions at infinity and the attraction sets of the zero solution.
MSC 2010: 34K20, 34K40
Keywords: Neutral equation, Lyapunov- Krasovskii functional.
References
[1] G. V. Demidenko, and I. I. Matveeva, Estimates for solutions to a class of nonlinear time-delay systems of neutral type. Electron. J. Differential Equations 2015 (2015), No. 34, 14 pp.
[2] G. V. Demidenko, and I. I. Matveeva, Exponential stability of solutions to nonlinear time-delay systems of neutral type. Electronic Journal of Differential Equations 2016 (2016), No. 19, 1-20.
[3] M. A. Skvortsova, Asymptotic properties of solutions to systems of neutral type differential equations with variable delay. Journal of Mathematical Sciences 205 (2015), no. 3, 455-463.
On a new type of q-Baskakov-Kantorovich operators
NAZLIM DENIZ ARAL1, ZEYNEP SEVINC¸2
1,2 Bitlis Eren University, Bitlis, Turkey emails: 1[email protected]; 2[email protected]
In this work, we have introduced a new type of q-analogous of Baskakov-Kantorovich opera-tors and investigated their statistical approximation properties. By using a weighted modulus of smoothness, we have given some direct estimations for error in the case 0 < q < 1.
MSC 2010: 41A36, 41A30, 41A25
Keywords: q-analysis, q-Baskakov-Kantorovich operators
References
[1] N. I. Mahmudov, Statistical approximation of Baskakov and Baskakov-Kantorovich operators based on the q-integer. Cent. Eur. J. Math. 8 (2010), no. 4, 816-826.
[2] V. Gupta, C. Radu, Statistcal approximation properties of q-Baskakov-Kantorovich operators.
Cent. Eur. J. Math. 7 (2009), no. 4, 809-818.
[3] E. S¸im¸sek On a new type of q-Baskakov operators. S¨uleyman Demirel University, Journal of Natural and Applied Sciences (2009), no. 4, 809-818.