Ufuk Taneri | Eastern Mediterranean University (original) (raw)

Papers by Ufuk Taneri

Research paper thumbnail of The One-Particle Green's Function

Quantum Field Theory with Application to Quantum Nonlinear Optics, 2002

Research paper thumbnail of Introductive Backgrounds to Modern Quantum Mathematics with Application to Nonlinear Dynamical Systems

International Journal of Theoretical Physics, 2008

Research paper thumbnail of Analysis of bifurcations and stability properties of molecular systems

Dynamics and Stability of Systems, 1995

The dynamics and stability of a three-dimensional model of dissipative molecular systems are stud... more The dynamics and stability of a three-dimensional model of dissipative molecular systems are studied in detail The model considered is produced by an approximate quantum formulation, and it contains two parameters. It has been demonstrated analytically that the ...

Research paper thumbnail of On the structure of Picard–Fuchs type equations for Liouville–Arnold integrable Hamiltonian system on cotangent phase spaces

Journal of Mathematical Physics, 2001

There are studied in detail the structure properties of integral submanifold imbedding mapping fo... more There are studied in detail the structure properties of integral submanifold imbedding mapping for a class of algebraically Liouville integrable Hamiltonian systems on cotangent phase spaces and related with it so called Picard–Fuchs type equations. It is shown that these equations ...

Research paper thumbnail of Two-Mode Nonlinear Quantum Optics System: A Non-degenerate Parametric Quantum Optical Amplifier

Research paper thumbnail of Artificial Intelligence & Higher Education: Towards Customized Teaching and Learning, and Skills for an AI World of Work. Research & Occasional Paper Series: CSHE.6.2020

Center for Studies in Higher Education, 2020

Research paper thumbnail of Cancer incidence in North Cyprus (1990-2004) relative to European rates

Asian Pacific journal of cancer prevention : APJCP, 2008

Cancer incidence in North Cyprus (NC), deemed an interesting epidemiological case due to possible... more Cancer incidence in North Cyprus (NC), deemed an interesting epidemiological case due to possible contrasting prevailing factors in relation to South and North Europe (SE and NE), was evaluated for the period 1990-2004. Age standardized rates (ASRs) and average age of incidence (AAI) values were determined for 12 different cancers, separately for males and females. Annual trends were analyzed using linear regression slopes. Absolute values were compared by two-tailed t-tests. The order of prevalence for incidences of male (M) cancers were: lung, skin, colorectal, prostate, brain, bladder, liver and stomach. Similarly, for females (F) they were: breast, gynaecological, skin, colorectal, lung, liver, brain, stomach and bladder. The following cancer cases were more common than in SE and NE: lung (M) and skin (both genders). Breast (F), prostate, stomach (F), bladder (both sexes), cervix and corpus were less frequent; the rest were comparable. There was no difference in the annual trend...

Research paper thumbnail of A Nonlinear Quantum-Optical System at Equilibrium Radiative State

Research paper thumbnail of Creation and Annihilation Operators

Research paper thumbnail of The Wick Theorem and Feynman Diagrammatic Expansion

Research paper thumbnail of Introductory Background to Modern Quantum Mathematics with Application to Nonlinear Dynamical Systems

Further Progress in Analysis, 2009

Research paper thumbnail of Forced oscillations, bifurcations and stability of a molecular system Part 1: Non-resonance

International Journal of Systems Science, 1996

The stability and bifurcation behaviour of a three dimensional, non-autonomous model of a molecul... more The stability and bifurcation behaviour of a three dimensional, non-autonomous model of a molecular system is studied analytically. It is shown that quasi-periodic motions (on a torus) bifurcate from a periodic motion, and there exists a shift in the critical value of the parameter compared to that of the associated autonomous system which was studied earlier. The solutions and their

Research paper thumbnail of On Picard-Fuchs Type Equations Related to Integrable Hamiltonian Systems ∗

The structure properties of integral submanifold imbedding mapping for a class of algebraically L... more The structure properties of integral submanifold imbedding mapping for a class of algebraically Liouville integrable Hamiltonian systems on cotangent phase spaces are studied in relation with Picard -Fuchs type equations. It is shown that these equations can be constructed by making use of a given a priori set of invo- lutive invariants and proved that their solutions in the Hamilton-Jacobi separable variable case give rise to the integral submanifold imbedding mapping, which is known to be a main ingredient for Liouville-Arnold integrability by quadratures of the Hamiltonian system under consideration.

Research paper thumbnail of On the bifurcation analysis of a three-dimensional non-autonomous model of molecular systems

J Math Chem, 1997

Nonlinear dynamics of atomic and molecular systems have been receiving con-siderable attention. M... more Nonlinear dynamics of atomic and molecular systems have been receiving con-siderable attention. Miniaturization of electronic devices and the behaviour of fast computers, for example, requires a careful study of dynamics at atomic and molecular levels. It is ...

Research paper thumbnail of The Equilibrium Radiative States of a Nonlinear Quantum-Optical System

Research paper thumbnail of The Electromagnetic Dirac-Fock-Podolsky Problem and Symplectic Properties of the Maxwell and Yang-Mills Type …

Based on analysis of reduced geometric structures on fibered manifolds, invariant under action of... more Based on analysis of reduced geometric structures on fibered manifolds, invariant under action of a certain symmetry group, we construct the symplectic structures associated with connection forms on suitable principal fiber bundles. The application to the non-standard Hamiltonian analysis of the Maxwell and Yang-Mills type dynamical systems is presented. A symplectic reduction theory of the classical Maxwell electromagnetic field equations is formulated, the important Lorentz condition, ensuring the existence of electromagnetic waves [5, 6], is naturally included into the Hamiltonian picture, thereby solving the well known Dirac, Fock and Podolsky problem [10]. The symplectically reduced Poissonian structures and the related classical minimal interaction principle, concerning the Yang-Mills type equations, are considered.

Research paper thumbnail of Exact Computation of Spectral Densities for a Langevin Dynamic Modelling the Relaxation of a Protein Near Its Equilibrium

Stochastic Analysis and Related Topics VIII, 2003

170 Paul Malliavin and Ufuk Taneri Then the Brownian motion is characterized by the following two... more 170 Paul Malliavin and Ufuk Taneri Then the Brownian motion is characterized by the following two properties: • for each interval/ -7=*/(0)(1.3) V И I is a gaussian normal variable, and • given two disjoint intervals Ii,/2, ВД,(/?)*/Z (/?))= 0.(1.4) It results from these two properties that ß ...

Research paper thumbnail of Quantum mathematics: Backgrounds and some applications to nonlinear dynamical systems

Nonlinear Oscillations, 2008

UDC 517.9 The backgrounds of quantum mathematics, a new discipline in mathematical physics, are d... more UDC 517.9 The backgrounds of quantum mathematics, a new discipline in mathematical physics, are discussed and analyzed from both historical and analytical points of view. The magic properties of the second quantization method, invented by Fock in 1934, are demonstrated, and an impressive application to the theory of nonlinear dynamical systems is considered. Von Neumann first applied the spectral theory of self-adjoint operators on Hilbert spaces to explain the radiation spectra of atoms and the related matter stability [2] (1926); Fock was the first to introduce the notion of many-particle Hilbert space, named a Fock space, and introduced related creation and annihilation operators acting on it [3] (1932); Weyl understood the fundamental role of the notion of symmetry in physics and developed a physics-oriented group theory; moreover, he showed the importance of different representations of classical matrix groups for physics and studied unitary representations of the Heisenberg-Weyl group related to creation and annihilation operators on a Fock space [4] (1931). At the end of the 20th century, new developments were due to Faddeev with co-workers (quantum inverse spectral theory transform [5], 1978); Drinfeld, Donaldson, and Witten (quantum groups and algebras, quantum topology, and quantum superanalysis [6-8], 1982-1994);

Research paper thumbnail of The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems

We study the problem of the complete integrability of nonlinear oscillatory dynamical systems con... more We study the problem of the complete integrability of nonlinear oscillatory dynamical systems connected, in particular, both with the Cartan decomposition of a Lie algebra G = K P , where K is the Lie algebra of a fixed subgroup K ⊂ G with respect to an involution σ : G → G on the Lie group G, and with a Poisson action of special type on a symplectic matrix manifold. * () → G + * () λ gives us a Lax-type representation and a complete set of commuting invariants related to it. This scheme appeared to be very useful when proving the Liouville integrability of many finite-dimensional systems such as Kowalevskaya's top [5], Neumann-type systems [6, 7], etc. Below, we study the problem of the complete integrability of nonlinear oscillatory dynamical systems connected, in particular, both with the Cartan decomposition of a Lie algebra G = K P, where K is the Lie algebra of a fixed subgroup K ⊂ G with respect to an involution σ : G → G on the Lie group G, and with a Poisson action of special type on a symplectic matrix manifold. 2. Integrable Systems on T * ((((K)))) : General Scheme Consider a Lie group G and an involution σ on G. If K ⊂ G is its fixed subgroup, then the Lie algebra G of the Lie group G admits the Cartan decomposition G = K P with the induced involution mapping σ = id on K and σ =-id on P. Also denote G * = K * P * via the dual decomposition of the adjoint space G *. The cotangent space T K * () Ӎ K × K * results by means of left translations on K.

Research paper thumbnail of Структура вакуума, специальная теория относительности и квантовая механика: возврат к теоретико-полевому безгеометрическому подходу

Теоретическая и математическая физика, 2009

Research paper thumbnail of The One-Particle Green's Function

Quantum Field Theory with Application to Quantum Nonlinear Optics, 2002

Research paper thumbnail of Introductive Backgrounds to Modern Quantum Mathematics with Application to Nonlinear Dynamical Systems

International Journal of Theoretical Physics, 2008

Research paper thumbnail of Analysis of bifurcations and stability properties of molecular systems

Dynamics and Stability of Systems, 1995

The dynamics and stability of a three-dimensional model of dissipative molecular systems are stud... more The dynamics and stability of a three-dimensional model of dissipative molecular systems are studied in detail The model considered is produced by an approximate quantum formulation, and it contains two parameters. It has been demonstrated analytically that the ...

Research paper thumbnail of On the structure of Picard–Fuchs type equations for Liouville–Arnold integrable Hamiltonian system on cotangent phase spaces

Journal of Mathematical Physics, 2001

There are studied in detail the structure properties of integral submanifold imbedding mapping fo... more There are studied in detail the structure properties of integral submanifold imbedding mapping for a class of algebraically Liouville integrable Hamiltonian systems on cotangent phase spaces and related with it so called Picard–Fuchs type equations. It is shown that these equations ...

Research paper thumbnail of Two-Mode Nonlinear Quantum Optics System: A Non-degenerate Parametric Quantum Optical Amplifier

Research paper thumbnail of Artificial Intelligence & Higher Education: Towards Customized Teaching and Learning, and Skills for an AI World of Work. Research & Occasional Paper Series: CSHE.6.2020

Center for Studies in Higher Education, 2020

Research paper thumbnail of Cancer incidence in North Cyprus (1990-2004) relative to European rates

Asian Pacific journal of cancer prevention : APJCP, 2008

Cancer incidence in North Cyprus (NC), deemed an interesting epidemiological case due to possible... more Cancer incidence in North Cyprus (NC), deemed an interesting epidemiological case due to possible contrasting prevailing factors in relation to South and North Europe (SE and NE), was evaluated for the period 1990-2004. Age standardized rates (ASRs) and average age of incidence (AAI) values were determined for 12 different cancers, separately for males and females. Annual trends were analyzed using linear regression slopes. Absolute values were compared by two-tailed t-tests. The order of prevalence for incidences of male (M) cancers were: lung, skin, colorectal, prostate, brain, bladder, liver and stomach. Similarly, for females (F) they were: breast, gynaecological, skin, colorectal, lung, liver, brain, stomach and bladder. The following cancer cases were more common than in SE and NE: lung (M) and skin (both genders). Breast (F), prostate, stomach (F), bladder (both sexes), cervix and corpus were less frequent; the rest were comparable. There was no difference in the annual trend...

Research paper thumbnail of A Nonlinear Quantum-Optical System at Equilibrium Radiative State

Research paper thumbnail of Creation and Annihilation Operators

Research paper thumbnail of The Wick Theorem and Feynman Diagrammatic Expansion

Research paper thumbnail of Introductory Background to Modern Quantum Mathematics with Application to Nonlinear Dynamical Systems

Further Progress in Analysis, 2009

Research paper thumbnail of Forced oscillations, bifurcations and stability of a molecular system Part 1: Non-resonance

International Journal of Systems Science, 1996

The stability and bifurcation behaviour of a three dimensional, non-autonomous model of a molecul... more The stability and bifurcation behaviour of a three dimensional, non-autonomous model of a molecular system is studied analytically. It is shown that quasi-periodic motions (on a torus) bifurcate from a periodic motion, and there exists a shift in the critical value of the parameter compared to that of the associated autonomous system which was studied earlier. The solutions and their

Research paper thumbnail of On Picard-Fuchs Type Equations Related to Integrable Hamiltonian Systems ∗

The structure properties of integral submanifold imbedding mapping for a class of algebraically L... more The structure properties of integral submanifold imbedding mapping for a class of algebraically Liouville integrable Hamiltonian systems on cotangent phase spaces are studied in relation with Picard -Fuchs type equations. It is shown that these equations can be constructed by making use of a given a priori set of invo- lutive invariants and proved that their solutions in the Hamilton-Jacobi separable variable case give rise to the integral submanifold imbedding mapping, which is known to be a main ingredient for Liouville-Arnold integrability by quadratures of the Hamiltonian system under consideration.

Research paper thumbnail of On the bifurcation analysis of a three-dimensional non-autonomous model of molecular systems

J Math Chem, 1997

Nonlinear dynamics of atomic and molecular systems have been receiving con-siderable attention. M... more Nonlinear dynamics of atomic and molecular systems have been receiving con-siderable attention. Miniaturization of electronic devices and the behaviour of fast computers, for example, requires a careful study of dynamics at atomic and molecular levels. It is ...

Research paper thumbnail of The Equilibrium Radiative States of a Nonlinear Quantum-Optical System

Research paper thumbnail of The Electromagnetic Dirac-Fock-Podolsky Problem and Symplectic Properties of the Maxwell and Yang-Mills Type …

Based on analysis of reduced geometric structures on fibered manifolds, invariant under action of... more Based on analysis of reduced geometric structures on fibered manifolds, invariant under action of a certain symmetry group, we construct the symplectic structures associated with connection forms on suitable principal fiber bundles. The application to the non-standard Hamiltonian analysis of the Maxwell and Yang-Mills type dynamical systems is presented. A symplectic reduction theory of the classical Maxwell electromagnetic field equations is formulated, the important Lorentz condition, ensuring the existence of electromagnetic waves [5, 6], is naturally included into the Hamiltonian picture, thereby solving the well known Dirac, Fock and Podolsky problem [10]. The symplectically reduced Poissonian structures and the related classical minimal interaction principle, concerning the Yang-Mills type equations, are considered.

Research paper thumbnail of Exact Computation of Spectral Densities for a Langevin Dynamic Modelling the Relaxation of a Protein Near Its Equilibrium

Stochastic Analysis and Related Topics VIII, 2003

170 Paul Malliavin and Ufuk Taneri Then the Brownian motion is characterized by the following two... more 170 Paul Malliavin and Ufuk Taneri Then the Brownian motion is characterized by the following two properties: • for each interval/ -7=*/(0)(1.3) V И I is a gaussian normal variable, and • given two disjoint intervals Ii,/2, ВД,(/?)*/Z (/?))= 0.(1.4) It results from these two properties that ß ...

Research paper thumbnail of Quantum mathematics: Backgrounds and some applications to nonlinear dynamical systems

Nonlinear Oscillations, 2008

UDC 517.9 The backgrounds of quantum mathematics, a new discipline in mathematical physics, are d... more UDC 517.9 The backgrounds of quantum mathematics, a new discipline in mathematical physics, are discussed and analyzed from both historical and analytical points of view. The magic properties of the second quantization method, invented by Fock in 1934, are demonstrated, and an impressive application to the theory of nonlinear dynamical systems is considered. Von Neumann first applied the spectral theory of self-adjoint operators on Hilbert spaces to explain the radiation spectra of atoms and the related matter stability [2] (1926); Fock was the first to introduce the notion of many-particle Hilbert space, named a Fock space, and introduced related creation and annihilation operators acting on it [3] (1932); Weyl understood the fundamental role of the notion of symmetry in physics and developed a physics-oriented group theory; moreover, he showed the importance of different representations of classical matrix groups for physics and studied unitary representations of the Heisenberg-Weyl group related to creation and annihilation operators on a Fock space [4] (1931). At the end of the 20th century, new developments were due to Faddeev with co-workers (quantum inverse spectral theory transform [5], 1978); Drinfeld, Donaldson, and Witten (quantum groups and algebras, quantum topology, and quantum superanalysis [6-8], 1982-1994);

Research paper thumbnail of The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems

We study the problem of the complete integrability of nonlinear oscillatory dynamical systems con... more We study the problem of the complete integrability of nonlinear oscillatory dynamical systems connected, in particular, both with the Cartan decomposition of a Lie algebra G = K P , where K is the Lie algebra of a fixed subgroup K ⊂ G with respect to an involution σ : G → G on the Lie group G, and with a Poisson action of special type on a symplectic matrix manifold. * () → G + * () λ gives us a Lax-type representation and a complete set of commuting invariants related to it. This scheme appeared to be very useful when proving the Liouville integrability of many finite-dimensional systems such as Kowalevskaya's top [5], Neumann-type systems [6, 7], etc. Below, we study the problem of the complete integrability of nonlinear oscillatory dynamical systems connected, in particular, both with the Cartan decomposition of a Lie algebra G = K P, where K is the Lie algebra of a fixed subgroup K ⊂ G with respect to an involution σ : G → G on the Lie group G, and with a Poisson action of special type on a symplectic matrix manifold. 2. Integrable Systems on T * ((((K)))) : General Scheme Consider a Lie group G and an involution σ on G. If K ⊂ G is its fixed subgroup, then the Lie algebra G of the Lie group G admits the Cartan decomposition G = K P with the induced involution mapping σ = id on K and σ =-id on P. Also denote G * = K * P * via the dual decomposition of the adjoint space G *. The cotangent space T K * () Ӎ K × K * results by means of left translations on K.

Research paper thumbnail of Структура вакуума, специальная теория относительности и квантовая механика: возврат к теоретико-полевому безгеометрическому подходу

Теоретическая и математическая физика, 2009