SANALDOKU YÖRESİ
bebbyt.be.itu.edu.tr


ÇALIŞMA GRUBUNUN AMACI
Bilgisayım Bilimi (ing: Science of Computing), uzbilimcil biçelendirimi (ing: Mathematical Modelling) gerçekleştirilmiş olan dizgeler için üretilen uzbilimcil denklemlerin kesin ya da yaklaşık çözümlerinin belirlenmesinde varolan yöntemlerin geliştirilimine ve daha işler yeni yöntemlerin tasarımına odaklanır. Bu bağlamda, sayısal yöntemler ve uygulayımcıl uzbilim (ing: Applied Mathematics) ile çok yakından ilintilidir. Ancak, tasarımlarını ve geliştirimlerini onlardan daha çok bilgisayım araçlarının yeti ve kısıtlarına göre biçimlendirir. Bu çerçevede kuramcıl (teorik) olgulara da önem verir ama tabandaki amaç uzbilimcil yöntem geliştirmektir. Bilişim Enstitüsü Bilgisayım Bilimi ve Yöntemleri Topluluğu (BEBBYT) kökenini 2000'li yılların başlarından almaktadır. Bu belirtilen amaca yönelik azımsanmayacak sayıda budunlararası (ing: international) yazı ve bildiri ile katkılar üretmiş ve üretmektedir.

YÜRÜTÜCÜLER

Prof. Dr. Metin Demiralp

ARAŞTIRMACILAR

1) Prof. Dr. N. Abdülbaki Baykara
2) Doç. Dr. M. Alper Tunga
3) Yard. Doç. Dr. İrem Yaman
4) Yard. Doç. Dr. Burcu Tunga
5) Dr. M. Engin Kanal
6) Muzaffer Ayvaz
7) Araş. Gör. Coşar Gözükırmızı
8) Araş. Gör. Evrim Korkmaz Özay
9) Öğr. Gör. Berfin Kalay
10) Semra Bayat
11) Araş. Gör. Süha Tuna
12) Araş. Gör. Ayla Okan
13) Zeynep Gündoğar
14) Öğr. Gör. Ercan Gürvit
15) Fatih Hunutlu
16) Araş. Gör. Derya Bodur
17) Gizem Özdemir
18) Bahar Zora Yolcu
19) Alparslan Pehlivan
20) Melike Ebru Kırkın

BEBBYT_Pic3

ARAŞTIRMACILAR

DONANIMLAR

Bilişim Enstitüsü'nde varolan olanaklardan ve İTÜ'de doktora öğrencilerine verilen 3 tasarıdan sağlanan kaynaklarla elde edilen donanımlar, ve de, bunların dışında bireycil olanaklardan yararlanılmaktadır.
BAŞLICA ÇALIŞMALAR VE TASARILAR

Yukarıda belirtilen İTÜ Doktora Tasarıları dışında herhangi bir kaynaktan tasarı başvurusuna gidilmemiştir. Topluluğun donanım gereksinimleri bu an için yeterli görünmekle birlikte zaman içinde güncelleştirim gereksinimi doğabilecek gibi görülmektedir. Bu an için, en önemli sıkıntı, budunlararası toplantılara katılım için kaynak sağlanımı olarak görünmektedir. İTÜ ve diğer üyelerin kuruluşlarından sağlananlar yanında bireycil çabalarla kaynak sağlanımına gidilmektedir.
Çalışmalar ayrıca yeniden ayrıntılandırarak belirtilmemektedir. İlerideki güncelleştirimlerde bu yola gidilebilecektir. Bu an için yukarıda belirtilen ana başlıklar altında çalışmalar tasarımlanıpsürdürülmektedir. Aşağıdaki yayınlardan da çalışmalarla ilgili görüş oluşturabilmek olanaklıdır.
ARAŞTIRIM ODAKLARI

Aşağıda belirtilenler ana odaklardır. Burada belirtilmeyen ikincil odaklar da söz konusudur. Ancak, bu belirtilen odakların yapılandırımına çok önemli özgün katkılar bebbyt topluluğunca getirilmiştir ve geliştirim sürdürülmektedir.
1) Yüksek Boyutlu Biçe Gösterilim (ing: High Dimensional Model Gösterilim, HDMR)
2) Çokdeğişkenliliği Yükseltilmiş Çarpımlar Gösterilimi (ing: Enhanced Multivariance Product Representation, EMPR)
3) Kronecker Üslü Toplamdiziler ve Uygulayımda Kullanımları (ing: Kronecker Power Series and Their Utilizations in Practise)
4) Olasılıkçıl Evrim Yaklaşımı ve Sıradan Türevli Denklem Çözümlerinde Kullanımı (ing: Probabilistic Evolution Approach and its Utilization in the Solutions of Ordinary Differential Equations)
5) Nicem Devimbilimde Beklenen Değer Denklemleri ve Onların Çözümünde Olasılıkçıl Evrim Yaklaşımı (ing: Expectation Value Equations in Quantum Dynamics and Probabilistic Evolution Approach in Their Solutions)
İçerik hazırlanmaktadır.
YAYINLAR

Bu kesimde topluluğun üyelerinin budunlararası düzeyde yayınladıkları yazılar ve bildiriler sıralanmaktadır. Yazılar çoğunlukla SCI ve SCIE gönderim dizgelerine giren dergilerde basılmış olmakla birlikte onların dışında kalan ama yine saygın olan başka gönderim dizgelerince tanınan dergilerde de basılmışlardır. Burada belirtilmeyen ama bugünün araştırımlarına taban oluşturan azımsanmayacak sayıda yayın bulunmaktadır. Onlar için topluluk üyelerinin sanaldoku yörelerine (ing: web site) bakmakta yarar bulunmaktadır. Bildirilerde ise neredeyse bütünlük düzeyinde bilgi verilmektedir. Bunun nedeni de Metin Demiralp'in toplantılara katılımının topluluk kurulumu sonrasında ezici çoğunlukta bulunmasıdır. Yazı ve diğer yapıtlarda 2000 yılı ve sonrası gözönüne alınmıştır.

Budunlararası İncelenimli Dergilerdeki Yayınlar
1. Attila Aşkar and Metin Demiralp, "Variational time-dependent perturbation scheme based on the hydrodynamic analogy to Schrödinger's equation", J. Chem. Phys., 60(7), pp. 2762-2766, Apr. 1974, DOI: 10.1063/1.1681440 (PDF tutamağı)

2. Metin Demiralp, Erdoğan Şuhubi, "Discrete spectrum for a system of electrically charged particles", J. Math. Phys., 18(4), pp. 777-785, Apr. 1977, DOI: 10.1063/1.523307 (PDF tutamağı)

3. Metin Demiralp, "Zeroth order hyperharmonic series in the discrete spectrum of electrically charged particles", J. Chem. Phys., 72(6), pp. 3828-3836, Mar. 1980, DOI: 10.1063/1.439598 (PDF tutamağı)

4. Stuart D. Augustin, Metin Demiralp, and Herschel Rabitz, "Action-angle variables for the quantum three particle system", J. Chem. Phys., 73(1), pp. 268-280, Apr. 1980, DOI: 10.1063/1.439926 (PDF tutamağı)

5. Metin Demiralp and Herschel Rabitz, "Chemical kinetic functional sensitivity analysis: Elementary sensitivities", J. Chem. Phys., 74(6), pp. 3362-3375, Mar. 1980, DOI: 10.1063/1.441489 (PDF tutamağı)

6. Metin Demiralp and Herschel Rabitz, "Chemical kinetic functional sensitivity analysis: Derived sensitivities", J. Chem. Phys., 75(4), pp. 1810-1819, Aug. 1981, DOI: 10.1063/1.442260 (PDF tutamağı)

7. Metin Demiralp and N. Abdülbaki Baykara, "Analytic evaluation of certain zeroth order coulombic hyperangular interaction integrals", J. Math. Phys., 22(11), pp. 2427-2432, Nov. 1981, DOI: 10.1063/1.524825 (PDF tutamağı)

8. Metin Demiralp and N. Abdülbaki Baykara, "Upper and lower bounds to zeroth order Coulombic hyperangular interaction integrals", J. Math. Phys., 23(9), pp. 1622-1627, Sep. 1982, DOI: 10.1063/1.525572 (PDF tutamağı)

9. Metin Demiralp, "A characteristic function approach to the discrete spectrum of electrically charged particles", J. Math. Phys., 24(1), pp. 101-101, Jan. 1983, DOI: 10.1063/1.525577 (PDF tutamağı)

10. Metin Demiralp, "Exponential Factor Optimization in Characteristic Function Method for Electrically Charged Particles", I.J. Quan. Chem., 23(3), pp. 779-787, Mar. 1983, DOI: 10.1002/qua.560230303 (PDF tutamağı)

11. Metin Demiralp, "Rational approximations to the quantum mechanical representation for the solutions of the canonical equations", Bull. Tech. Univ. Istanbul, 36(1), pp. 109-124, 1983, DOI: -YOK- (PDF tutamağı)

12. N. Abdulbaki Baykara and Metin Demiralp, "Numerical evaluation of the zeroth order coulombic hyperangular interaction integral", Bull. Tech. Univ. Istanbul, 36(1), pp. 125-140, 1983, DOI: -YOK- (PDF tutamağı)

13. Naşit Arı and Metin Demiralp, "A characteristic function approach to the eigenvalues of an anharmonic oscillator", Bull. Tech. Univ. Istanbul, 36(3), pp. 345-359, 1983, DOI: -YOK- (PDF tutamağı)

14. Metin Demiralp, "An evolution operator approach to approximate the solutions of ordinary differential equations", Bull. Tech. Univ. Istanbul, 37(4), pp. 425-445, 1984, DOI: -YOK- (PDF tutamağı)

15. Metin Demiralp, "Differentiation and recursion formulae for zeroth order hyperharmonic tau integrals of electrically charged particles", Bull. Tech. Univ. Istanbul, 38(1), pp. 113-126, 1985, DOI: -YOK- (PDF tutamağı)

16. Naşit Arı and Metin Demiralp, "Energy levels of a two-dimensional anharmonic oscillator: Characteristic function approach", J. Math. Phys., 26(6), pp. 1179-1185, Jun. 1985, DOI: 10.1063/1.526522 (PDF tutamağı)

17. Metin Demiralp, "A New Algebraic Approach to the Eigenvalue Problems of Linear Differential Operators Without Integration", I. J. Quan. Chem. , 29(2), pp. 221-227, Feb. 1986, DOI: 10.1002/qua.560290212 (PDF tutamağı)

18. Hasan Taşeli and Metin Demiralp, "Convergent perturbation studies in screened coulomb potential systems: analytic evaluations up to third order for the Yukawa case", Theor. Chim. Acta, 71(4), pp. 315-325, May 1987, DOI: 10.1002/qua.560290212 (PDF tutamağı)

19. N. A. Baykara and M. Demiralp, "Analytic Evaluation of Equipotential Hyperangular Interaction Integrals", Il Nuovo Cimento B, 100(2), pp. 161-171, Aug. 1987, DOI: 10.1007/BF02722889 (PDF tutamağı YOK)

20. M. Demiralp, N. A. Baykara, and H. Taşeli, "Convergent perturbation studies in screened coulomb potential systems: a high precision numerical via Laguerre basis set", Theor. Chim. Acta, 74(1), pp. 39-54, Jul. 1988, DOI: 10.1007/BF00570551 (PDF tutamağı)

21. N. A. Baykara and M. Demiralp, "Eigenlevel calculations for screened coulomb potential systems via an integration free algorithm: Space pruning technique", I. J. Quan. Chem., 34(3), pp. 231- 245, Sep. 1988, DOI: 10.1002/qua.560340306 (PDF tutamağı)

22. H. Taşeli and M. Demiralp, "Studies on algebraic methods to solve linear eigenvalue problems: generalised anharmonic oscillators", J. Phys. A: Math: Gen:, 21(20), pp. 3903-3919, Nov. 1988, DOI: 10.1088/0305-4470/21/20/010 (PDF tutamağı)

23. Metin Demiralp, "Rapidly converging threshold value calculations in screened coulomb potential systems: Critical values of the screening parameter for the Yukawa case", Theor. Chim. Acta, 75 (3), pp. 223-232, May 1989, DOI: 10.1007/BF00528567 (PDF tutamağı)

24. H. Taşeli, M. Demiralp, K. Kafalı, "Drag minimization in stokes flow", Int. J. Engng. Sci., 27(6), pp. 633-640, Jun. 1989, DOI: 10.1016/0020-7225(89)90016-5 (PDF tutamağı)

25. Metin Demiralp, S. Burhanettin Altan, "An integration-free algorithm for the solution of regular boundary value problems: space pruning approach", Int. J. Engng. Sci., 8(4), pp. 293-302, Apr. 1990, DOI: 10.1016/0020-7225(90)90102-O (PDF tutamağı)

26. Metin Demiralp, Herschel Rabitz, "Factorization of certain evolution operators using lie algebra: Formulation of the method", J. Math. Chem., 6(1), pp. 165-191, Dec. 1991, DOI: 10.1007/BF01192579 (PDF tutamağı)

27. Metin Demiralp, Herschel Rabitz, "Factorization of certain evolution operators using lie algebra: Convergence Theorems", J. Math. Chem. , 6(1), pp. 193-204, Dec. 1991, DOI: 10.1007/BF01192580 (PDF tutamağı)

28. Metin Demiralp, N. A. Baykara, H. Taşeli, "A basis set comparison in a variational scheme for the Yukawa potential", J. Math. Chem. , 11(1), pp. 311-323, Dec. 1992, DOI: 10.1007/BF01164211 (PDF tutamağı)

29. Metin Demiralp, Herschel Rabitz, "Lie algebraic factorization of multivariable evolution operators: Definition and the solution of the canonical problem", Int. J. Engng. Sci., 31(2), pp. 307-331, Feb. 1993, DOI: 10.1016/0020-7225(93)90043-T (PDF tutamağı)

30. Metin Demiralp, Herschel Rabitz, "Lie algebraic factorization of multivariable evolution operators: Convergence theorems for the canonical case", Int. J. Engng. Sci., 31(2), pp. 333-346, Feb. 1993, DOI: 10.1016/0020-7225(93)90044-U (PDF tutamağı)

31. Metin Demiralp, Herschel Rabitz, "Optimally controlled quantum mole cular dynamics: A perturbation formulation and the existence of multiple solutions", Phys. Rev. A, 47(2), pp. 809-816, Feb. 1993, DOI: 10.1103/PhysRevA.47.809 (PDF tutamağı)

32. Metin Demiralp, Herschel Rabitz, "Optimally controlled quantum mole cular dynamics: The effect of nonlinearities on the magnitude and multiplicity of control field solutions", Phys. Rev. A, 47(2), pp. 831-837, Feb. 1993, DOI: 10.1103/PhysRevA.47.831 (PDF tutamağı)

33. N. A. Baykara, Metin Demiralp, "An auto-coherent variational scheme for Yukawa potential", J. Math. Chem., 16(1), pp. 167-183, Dec. 1994, DOI: 10.1007/BF01169205 (PDF tutamağı)

34. Metin Demiralp and Herschel Rabitz, "Optimal control in classical molecular dynamics: A perturbation formulation and the existence of multiple solutions", J. Math. Chem., 16(1), pp. 185-209, Dec. 1994, DOI: 10.1007/BF01169206 (PDF tutamağı)

35. Tanıl Ergenç and Metin Demiralp, "Formulation of some gaussian integ rals over Rn via generating functions", I. J. Comput. Math., 54(3-4), pp. 239-248, Oct. 1994, DOI: 10.1080/00207169408804354 (PDF tutamağı YOK)

36. Metin Demiralp, "Determination of the quantum motion of the one dimen sional harmonic oscillator via expectation value evolutions", Bull. Tech. Univ. Istanbul, 47(4), pp. 357-375, 1994, DOI: -YOK- (PDF tutamağı)

37. Metin Demiralp, Herschel Rabitz, "Upper and lower bounds on the control field and the quality of achieved optimally controlled quantum molecu lar motion", J. Math. Chem., 19(3), pp. 337-352, Sep. 1996, DOI: 10.1007/BF01166724 (PDF tutamağı)

38. Metin Demiralp and Herschel Rabitz, "Dispersion-free wave packets and feedback solitonic motion in controlled quantum dynamics", Phys. Rev. A, 55(1), pp. 673-677, Jan. 1997, DOI: 10.1103/PhysRevA. 55.673 (PDF tutamağı)

39. Hasan Taşeli, Metin Demiralp, "A new approach to the classical Stokes flow problem: Part I, Methodology and first-order analytical results", J. Comp. and Appl. Math., 78(2), pp. 213-232, Feb. 1997, DOI: 10.1016/S0377-0427(96)00141-0 (PDF tutamağı)

40. Metin Demiralp and Herschel Rabitz, "Assessing optimality and robustness of control over quantum dynamics", Phys. Rev. A, 57(4), pp. 2420-2425, Apr. 1998, DOI: 10.1103/PhysRevA.57.2420 (PDF tutamağı)

41. Metin Demiralp and Herschel Rabitz, "Assessing optimality and robustness for the control of dynamical systems", Phys. Rev. E, 61(3), pp. 2569-2578, Mar. 1998, DOI: 10.1103/PhysRevE.61.2569 (PDF tutamağı)

42. G. Li, M. Artamonov, H. Rabitz, S.-W. Wang, P. G. Georgopoulos, M. Demiralp, "High dimensional model representations generated from low order terms lp-RS-HDMR", J. Comput. Chem., 24(5), pp. 647-656, Apr. 2003, DOI: 10.1002/jcc.10232 (PDF tutamağı)

43. M. Alper Tunga, Metin Demiralp, "A Factorized High Dimensional Model Representation on the Partitioned Random Discrete Data", Applied Numerical Analysis and Computational Mathematics, 1(1), pp. 231-241, Mar. 2004, DOI: 10.1002/anac.200310020 (PDF tutamağı)

44. Burcu Tunga, Metin Demiralp, "Optimally Controlled Dynamics of One Dimensional Harmonic Oscillator: Linear Dipole Function and Quadratic Penalty", ANACM, Applied Numerical Analysis and Computational Mathematics, WILEY-VCH, 1(1), pp. 242-250, Mar. 2004, DOI:10.1002/anac.20031002 (PDF tutamağı)

45. Metin Demiralp, "Weighted Eigenvalue Problem Approach to the Critical Value Determination of Screened Coulomb Potential Systems", Applied Numerical Analysis and Computational Mathematics, 1(1), pp. 251-259, Mar. 2004, DOI: 10.1002/anac.200310022 (PDF tutamağı)

46. Tülin Kaman, Metin Demiralp, "A Parametric Sensitivity Analysis for the Solution of Extrema Evaluation Problems via a Dimensionality Reducing Approximation Method", ANACM, Applied Numerical Analysis and Computational Mathematics, 1(1), pp. 260-269, Mar. 2004, DOI: 10.1002/anac.200310023 (PDF tutamağı)

47. Ayşegül Kurşunlu, İrem Yaman, Metin Demiralp, "Optimal Control of One Dimensional Quantum Harmonic Oscillator Under an External Field With Quadratic Dipole Function and Penalty on Momentum: Construction of the Linearised Field Amplitude Integral Equation", Applied Numerical Analysis and Computational Mathematics, 1(1), pp. 270-279, Mar. 2004, DOI: 10.1002/anac.200310024 (PDF tutamağı)

48. İrem Yaman, Metin Demiralp, "High Dimensional Model Representation Approximation of an Evolution Operator with a First Order Partial Differential Operator Argument", Applied Numerical Analysis and Computational Mathematics, 1(1), pp. 280-289, Mar. 2004, DOI: 10.1002/anac.200310025 (PDF tutamağı)

49. M. A. Tunga, M. Demiralp, "A factorized high dimensional model representation on the nodes of a finite hyperprismatic regular grid", Appl. Math. and Comput., 164(3), pp. 865-883, May 2005, DOI: http://dx.doi.org/10.1016/j.amc.2004.06.056 (PDF tutamağı)

50. N. A. Baykara, İ. Yaman, M. Demiralp, "An Exponential Matrix Product Based Representation for Generalized Hypergeometric Functions of Type pFp", Appl. Numer. Anal. and Comput. Math., 2(1), pp. 19-33, May 2005, DOI: 10.1002/anac.200410020 (PDF tutamağı)

51. M. Demiralp, B. Tunga, "Instantaneous Stability and Robustness Investigations in Quantum Optimal Control: Harmonic Oscillator Under Linear Dipole and Quadratic Control Agents", Appl. Numer. Anal. and Comput. Math., 2(1), pp. 60-69, May 2005, DOI: 10.1002/anac.200410023 (PDF tutamağı)

52. M. Demiralp, S. Üsküplü, "Matrix Algebraic Infinite Product Representation for Generalized Hypergeometric Functions of Type p+1Fp ", Appl. Numer. Anal. and Comput. Math., 2(2), pp. 212-226, May 2005, DOI: 10.1002/anac.200410036 (PDF tutamağı)

53. M. Demiralp, G. Taşkın, "Relations Between the Matrix Algebraic Factorized Type Solutions at Different Singular Points for Generalized Hypergeometric Functions of Type p+1Fp", Appl. Numer. Anal. and Comput. Math. 2(2), pp. 227-237, Aug. 2005, DOI: 10.1002/ anac.200410037 (PDF tutamağı)

54. M. Demiralp, "Critical value calculations for the screening parameter of Hulthen potential", Appl. Math. and Comput. 168(2), pp. 1380-1399, Sep. 2005, DOI: 10.1016/j.bbr.2011.03.031 (PDF tutamağı)

55. M. Demiralp, "Convergence issues in the Gaussian weighted multidimensional fluctuation expansion for the univariate numerical integration", WSEAS Trans. Math. 4(4), pp. 486-492, 2005, ISSN: 1109-2769 (PDF tutamağı)

56. M. Alper Tunga, Metin Demiralp, "Hybrid High Dimensional Model Representation (HHDMR) on the Partitioned Data", J. Comput. and Appl. Math. 185 (1), pp. 107-132, Jan. 2006, DOI: 10.1016/j.cam.2005.01.030 (PDF tutamağı)

57. H. Rabitz, T. -S. Ho, M. Hsieh, R. Kosut, M. Demiralp, "Topology of optimally controlled quantum mechanical transition probability landscapes", Phy. Rev. A, 74(1), pp. 012721[9 pages], 2006, DOI: 10.1103/ PhysRevA.74.012721 (PDF tutamağı)

58. M. Demiralp, "Plain and Logarithmic High Dimensional Model Representation and the Effect of Their Types on Univariance Level", WSEAS Trans. Math., 5(5), pp. 582-588, 2006, ISSN: 1109-2769 (PDF tutamağı)

59. M. Demiralp, "Weight Parameters Optimization to Get Maximum Constancy in High Dimensional Model Representation", WSEAS Trans. Math., 5(11), pp. 1177-1181, 2006, ISSN: 1109-2769 (PDF tutamağı)

60. M. Demiralp, "Illustrative Implementations to Show How Logarithm Based High Dimensional Model Representation Works for Various Function Structures", WSEAS Trans. Computers 5(6), pp. 1339-1344, Jun. 2006 (PDF tutamağı)

61. M. Demiralp, "Importance and Measurement of Univariance in High Dimensional Model Representation for Multivariate Analysis", WSEAS Trans. Comp., 5, pp. 1738-1744, Sep. 2006, ISSN: 1109-2750 (PDF tutamağı)

62. M. A. Tunga, M. Demiralp, "A New Approach for Data Partitioning Through High Dimensional Model Representation", Int. J. Computer Math. 85(12), pp. 1779-1792, Dec. 2008, DOI: 10.1080/00207160701576095 (PDF tutamağı)

63. M. A. Tunga, M. Demiralp, "Bound analysis in univariately truncated Generalized High Dimensional Model Representation for random-data partitioning: Interval GHDMR", Appl. Numer. Math. 59(6), pp. 1431-1448, 2009, DOI:10.1016/j.apnum.2008.06.006 (PDF tutamağı)

64. Emre Demiralp, "Applications of High Dimensional Model Representations to Computer Vision", WSEAS Trans. on Math. 8(4), pp. 184-192, Jun. 2009 (PDF tutamağı)

65. E. Gürvit, N.A. Baykara and M. Demiralp, "Numerical Integration of Bivariate Functions over a Non Rectangular area by Using Fluctuationlessness Theorem", WSEAS Trans. on Math. 8(5), pp. 193-198, Jun. 2009 (PDF tutamağı)

66. N. Altay and M. Demiralp, "Fluctuationlessness Theorem and its Application to Boundary Value Problems of ODEs", WSEAS Trans. on Math. 8 (5), pp. 199-204, Jun. 2009 (PDF tutamağı)

67. C. Gözükırmızı and M. Demiralp, "The Application of the Fluctuation Expansion with Extended Basis Set to Numerical Integration", WSEAS Trans. on Math. 8(5), pp. 205-212, Jun. 2009 (PDF tutamağı)

68. M.A. Tunga and M. Demiralp, "A Reverse Technique for Lumping High Dimensional Model Representation", WSEAS Trans. on Math. 8(5), pp. 213-218, Jun. 2009 (PDF tutamağı)

69. S. Üsküplü and M. Demiralp, "Truncation Approximations for Two Term Recursive Universal Form of Matrix Ordinary Differential Equations", WSEAS Trans. on Math. 8(5), pp. 219-223, Jun. 2009 (PDF tutamağı)

70. S. Tuna, B. Tunga, N.A. Baykara and M. Demiralp, "Fluctuation free matrix representation based univariate integration in hybrid high dimensional model representation (HHDMR) over plain and factorized HDMR", WSEAS Trans. on Math. 8(6), pp. 225-230, Jun. 2009 (PDF tutamağı)

71. B. Tunga and M. Demiralp, "A nonlinear perturbative scheme to solve weight optimization problem of high dimensional model representation (HDMR)", WSEAS Trans. on Math. 8(6), pp. 231-237, Jun. 2009 (PDF tutamağı)

72. M. Demiralp, "Fluctuationlessness theorem to approximate univariate functions' matrix representations", WSEAS Trans. on Math. 8 (6), pp. 258-267, Jun. 2009 (PDF tutamağı)

73. E. Meral and M. Demiralp, "Determination of the external field amplitude and deviation parameter through expectation value based quantum optimal control of multiharmonic oscillators under linear control agents", J. Math. Chem. 46(3), pp. 834-852, Oct. 2009, DOI: 10.1007/ s10910-009-9550-4 (PDF tutamağı)

74. İ. Yaman and M. Demiralp, "A new rational approximation technique based on transformational high dimensional model representation", Numer. Algor. 52(3), pp. 385-407, Nov. 2009, DOI: 10.1007/ s11075-009-9279-y (PDF tutamağı)

75. B. Tunga and M. Demiralp, "Constancy maximization based weight optimization in high dimensional model representation", Numer. Algor. 52 (3), pp. 435-459, Nov. 2009, DOI: 10.1007/s11075-009-9291-2 (PDF tutamağı)

76. M. Demiralp, "No fluctuation approximation in any desired precision for univariate matrix representations", J. Math. Chem. 47(1), pp. 99-110, Jan. 2010, DOI: 10.1007/s10910-009-9533-5 (PDF tutamağı)

77. N. Altay and M. Demiralp, "Numerical solution of ordinary differential equations by fluctuationlessness theorem", J. Math. Chem. 47 (4), pp. 1323-1343, May 2010, DOI: 10.1007/s10910-009-9657-7 (PDF tutamağı)

78. S.Ü. Altınbaşak and M. Demiralp, "Solutions to linear matrix ordinary differential equations via minimal, regular and excessive space extension based universalization: Perturbative matrix splines, convergence and error estimate issues for polynomial coefficients in the homogeneous case", J. Math. Chem. 48(2), pp. 253-265, Aug. 2010, DOI: 10.1007/s10910-010-9665-7 (PDF tutamağı)

79. S.Ü. Altınbaşak and M. Demiralp, "Solutions to linear matrix ordinary differential equations via minimal, regular and excessive space extension based universalization: Convergence and error estimates for truncation approximants in the homogeneous case with premultiplying polynomial coefficient matrix", J. Math. Chem. 48(2), pp. 266-286, Aug. 2010, DOI: 10.1007/s10910-010-9667-5 (PDF tutamağı)

80. B. Tunga and M. Demiralp, "The influence of the support functions on the quality of enhanced multivariate product representation", J. Math. Chem., 48(3), pp. 827-840, Oct. 2010, DOI: 10.1007/ s10910-010-9714-2 (PDF tutamağı)

81. E. Meral and M. Demiralp, "A perturbative approach to the solution for expectation value based quantum optimal control of multiharmonic oscillators under linear control agents", TWMS J. Pure Appl. Math. 1(1), pp. 53-67, 2010 (PDF tutamağı)

82. M. Demiralp, "Data Production For a Multivariate Function On an Orthogonal Hyperprismatic Grid Via Fluctuation Free Matrix Representation: Completely Filled Grid Case", Int. J. Elect. Eng. Comm. Eng., 1(1), pp. 61-76, 2010 (PDF tutamağı)

83. N.A. Baykara, E. Gürvit and M. Demiralp, "The fluctuationlessness approach to the numerical integration of functions with a single variable by integrating Taylor expansion with explicit remainder term", J. Math. Chem. 49(2), pp. 393-406, Feb. 2011, DOI: 10.1007/s10910-010- 9748-5 (PDF tutamağı)

84. M. Alper Tunga, "A Matrix Based Indexing HDMR method for multivariate data modelling", J. Math. Chem. 49(5), pp. 1092-1114, May 2011, DOI: 10.1007/s10910-011-9800-0 (PDF tutamağı)

85. A. Kurşunlu and M. Demiralp, "A fluctuation removal based univariate integration over prescribed nodes: Certain important aspects of one node fluctuation free integration", J. Math. Chem. 49(2), pp. 407-427, Feb. 2011, DOI: 10.1007/s10910-010-9749-4 (PDF tutamağı)

86. A. Kurşunlu and M. Demiralp, "A fluctuation removal based univariate integration over prescribed nodes: One node fluctuation free integration under higher order set of conditions with an extension to multinode case", J. Math. Chem. 49(2), pp. 428-443, Feb. 2011, DOI: 10.1007/s10910-010-9750-y (PDF tutamağı)

87. N. Altay and M. Demiralp, A high dimensional model representation based numerical method for solving ordinary differential equations, J. Math. Chem. 49(3), pp. 687-710, Mar. 2011, DOI: 10.1007/s10910-010- 9768-1 (PDF tutamağı)

88. B. Tunga and M. Demiralp, "Fluctuation free multivariate integration based logarithmic HDMR in multivariate function representation", J. Math. Chem. 49(4), pp. 894-909, Apr. 2011, DOI: 10.1007/s10910-010- 9786-z (PDF tutamağı)

89. B. Tunga and M. Demiralp, "Constancy maximization based weight optimization in high dimensional model representation for multivariate functions", J. Math. Chem 49(9), pp. 1996-2012, Oct. 2011, DOI: 10.1007/s10910 -010-9786-z (PDF tutamağı)

90. M. Demiralp, "Fluctuation expansion for a univariate function's matrix representation", TWMS Journal of Pure and Applied Mathematics., 2(2), pp. 176-193, Oct. 2011 (PDF tutamağı)

91. E. Kanal, N.A. Baykara and M. Demiralp, "Theory and algorithm of the inversion method for pentadiagonal matrices", J. Math. Chem. 50(1), pp. 289-299, Jan. 2012, DOI: 10.1007/s10910-011-9915-3 (PDF tutamağı)

92. M. Demiralp, E. Demiralp and L. Hernandez-Garcia, "A probabilistic foundation for dynamical systems: Theoretical background and mathematical formulation", J. Math. Chem., 50(4), pp. 850-869, Apr. 2012, DOI: 10.1007/s10910-011-9929-x (PDF tutamağı)

93. E. Demiralp, M. Demiralp and L. Hernandez-Garcia, "A probabilistic foundation for dynamical systems: Phenomenological reasoning and principal characteristics of probabilistic evolution", J. Math. Chem., 50(4), pp. 870-880, Apr. 2012, DOI: 10.1007/s10910- 011-9930-4 (PDF tutamağı)

94. E. Kanal and M. Demiralp, "A modified method of calculating high dimensional model representation (HDMR) terms for parallelization with MPI and CUDA", J. Supercomput., 62(1), pp. 199-213, Oct. 2012, DOI: 10.1007/s11227-011-0695-0 (PDF tutamağı)

95. B. Tunga and M. Demiralp, "A novel approximation method for multivariate data partitioning: Fluctuation free integration based HDMR", Eng. Comput., 29(7), pp. 743-765, 2012, DOI: 10.1108/02644401211257245 (PDF tutamağı)

96. M. Alper Tunga and Metin Demiralp, "Multivariate data modelling through Piecewise generalized HDMR method", J. Math. Chem., 51(7), pp. 1711-1726, 2012, DOI: 10.1007/s10910-012-0001-2 (PDF tutamağı)

97. Evrim Korkmaz Özay and Metin Demiralp, "Combined small scale high dimensional model representation", J. Math. Chem., 50(7), pp. 2023-2042, 2012, DOI: 10.1007/s10910-012-0018-6 (PDF tutamağı)

98. Burcu Tunga and Metin Demiralp, "Hybrid HDMR method with an optimized hybridity parameter in multivariate function representation", J. Math. Chem., 50(8), pp. 2223-2232, Sep. 2012, DOI: 10.1007/s10910 -012-0026-6 (PDF tutamağı)

99. Emre Demiralp, Renee J. Thompson, Jutta Mata, Susanne M. Jaeggi, Martin Buschkuel, Lisa Feldman Barret, Phoebe C. Elsworth, Metin Demiralp, Luis Hernandez-Garcia, Patricia J. Deldin, Ian H. Gotlib and John Jonides, "Feeling Blue or Turquoise? Emotional Differentiation in Major Depressive Disorder", Psychological Science, 23(11), pp. 1410-1416, Nov. 2012, DOI:10.1177/0956797612444903(PDF tutamağı)

100. Metin Demiralp and Emre Demiralp, "A contemporary linear representation theory for ordinary differential equations: probabilistic evolutions and related approximants for unidimensional autonomous systems", J. Math. Chem., 51(1), pp. 58-72, Jan. 2013, DOI: 10.1007/s10910-012 -0070-2 (PDF tutamağı)

101. Metin Demiralp and Emre Demiralp, "A contemporary linear representation theory for ordinary differential equations: multilinear algebra in folded arrays (folarrs) perspective and its use in multidimensional case", J. Math. Chem., 51(1), pp. 38-57, Jan. 2013, DOI: 10.1007/s10910-012-0064-0 (PDF tutamağı)

102. j. Vigo-Aguiar, "Mathematical modeling for chemistry related applications", J. Math. Chem., 51(4), pp. 1135-1138, Apr. 2013, DOI: 10.1007/s10910-012-0112-9 (PDF tutamağı)

103. M. Demiralp, "A probabilistic evolution approach trilogy, part 1: quantum expectation value evolutions, block triangularity and conicality, truncation approximants and their convergence", J. Math. Chem., 51(4), pp. 1170-1186, Apr. 2013, DOI: 10.1007/s10910-012-0079-6 (PDF tutamağı)

104. M. Demiralp and N. A. Baykara, "A probabilistic evolution approach trilogy, part 2: spectral issues for block triangular evolution matrix, singularities, space extension", J. Math. Chem., 51(4), pp. 1187-1197, Apr. 2013, DOI: 10.1007/s10910-012-0080-0 (PDF tutamağı)

105. M. Demiralp and B. Tunga, "A probabilistic evolution approach trilogy, part 3: Temporal variation of state variable expectation values from Liouville equation perspective", J. Math. Chem., 51(4), pp. 1198-1210, Apr. 2013, DOI:10.1007/s10910-012-0081-z (PDF tutamağı)

106. Süha Tuna and Burcu Tunga, "A novel piecewise multivariate function approximation method via universal matrix representation", J. Math. Chem., 51, pp. 1784-1801, 2013, DOI:10.1007/s10910-013-0179-y (PDF tutamağı)

107. M. A. Tunga and M. Demiralp, "Bound Analysis Through HDMR for Multivariate Data Modelling", J. Math. Model. Algor., 12(3), pp. 265-276, Sep. 2013, DOI: 10.1007/s10852-012-9211-7 (PDF tutamağı)

108. M. A. Tunga and M. Demiralp, "A novel method for multivariate data modelling: Piecewise generalized EMPR", J. Math. Chem., 51(10), pp. 2654-2667, Nov. 2013, DOI:10.1007/s10910-013-0228-6 (PDF tutamağı)

109. F. Hunutlu, N. A. Baykara and M. Demiralp, "Truncation approximants to probabilistic evolution of ordinary differential equations under initial conditions via bidiagonal evolution matrices: simple case", I. J. Comput. Math., 90(11), Nov. 2013, DOI:10.1080/00207160.2013.774385 (PDF tutamağı)

110. Coşar Gözükırmızı, M. Demiralp, "Probabilistic evolution approach for the solution of explicit autonomous ordinary differential equations. Part 1: Arbitrariness and equipartition theorem in Kronecker power series", J. Math. Chem., 52(3), Mar. 2014, DOI:10.1007/s10910-013-0298-5 (PDF tutamağı)

111. Coşar Gözükırmızı, M. Demiralp, "Probabilistic evolution approach for the solution of explicit autonomous ordinary differential equations. Part 2: Kernel separability, space extension, and, series solution via telescopic matrices", J. Math. Chem., 52(3), Mar. 2014, DOI:10.1007/s10910-013-0299-4 (PDF tutamağı)
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