Scholarly Publications - Mathematics

Permanent URI for this collectionhttps://hdl.handle.net/11693/115503

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Open Access
C∗-actions on Grassmann bundles and the cycle at infinity.
(Aarhus Universitet * Mathematica Scandinavica, 1988) Sertöz, S.
We describe the Grassmann Graph construction of MacPherson in the analytic category using a C∗-action and the corresponding BialynickiBirula decomposition. It is shown that the cycle at infinity is analytic in the compact Kaehler case.
Open Access
An isomorphism theorem for Dragilev spaces
(Birkhäuser-Verlag, 1988) Kocatepe, M.
Necessary and sufficient conditions for an Ly(a, l)-space to be isomorphic to some Lg(b, m)-space have been found.
Open Access
Residues of singular holomorphic foliations
(Cambridge University Press, 1989) Sertöz, S.
Open Access
Generalization of the Von Staudt-Clausen theorem
(Elsevier, 1989) Dibag, I.
The localization LS(x) of log(1 + x) at a set of primes S is defined by taking those powers of x in the logarithmic series for log(1 + x) which lie in the span of S. The functional inverse LS-1(x) of LS(x) also localizes the functional inverse ex - 1 of log(1 + x) and a generalization of the Von Staudt-Clausen theorem is proved for the even coefficients in the power series expansion for x LS-1(x). This reduces to the Von Staudt-Clausen theorem when S is the set of all primes and to a weaker version of Theorem 3.9 of I. Dibag (J. Algebra87 (1984), 332-341) when S consists of a single prime. © 1989.
Open Access
Multi-Hamiltonian structure of equations of hydrodynamic type
(A I P Publishing LLC, 1990) Gümral, H.; Nutku, Y.
We complete the discussion of the Hamiltonian structure of 2-component equations of hydrodynamic type by presenting the Hamiltonian operators for Euler's equation governing the motion of plane sound waves of nite amplitude and another quasi-linear second order wave equation. There exists a doubly in- nite family of conserved Hamiltonians for the equations of gas dynamics which degenerate into one, namely the Benney sequence, for shallow water waves. We present further in nite sequences of conserved quantities for these equations. In the case of multi-component equations of hydrodynamic type, we show that Kodama's generalization of the shallow water equations admits bi-Hamiltonian structure.
Open Access
Bi-Hamiltonian structure of the Kermack-McKendrick model for epidemics
(IOP Publishing, 1990) Nutku, Y.
The dynamical system proposed by Kermack and McKendrick to model the spread of epidemics is shown to admit bi-Hamiltonian structure without any restrictions on the rate constants. These two inequivalent Hamiltonian structures are compatible.
Open Access
Hamiltonian structure of the Lotka-Volterra equations
(Elsevier, 1990) Nutku, Y.
The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system. © 1990.
Open Access
Bi-Hamiltonian structure of a pair of coupled KdV equations
(Societa Italiana di Fisica (S I F), 1990) Nutku, Y.; Oğuz, O.
We point out a pair of coupled KdV equations which admits a bi-Hamiltonian structure. © 1990 Società Italiana di Fisica.
Open Access
The pair correlation of zeros of Dirichlet L-functions and primes in arithmetic progressions
(Springer-Verlag, 1991) Yildirim, C.Y.
We define a function which correlates the zeros of two Dirichlet L-functions to the modulus q and we prove an asymptotic estimate for averages of the pair correlation functions over all pairs of characters to (mod q). An analogue of Montgomery's pair correlation conjecture is formulated as to how this estimate can be extended to a greater domain for the parameters that are involved. Based on this conjecture we obtain results about the distribution of primes in an arithmetic progression (to a prime modulus q) and gaps between such primes. © 1991 Springer-Verlag.
Open Access
Spherical shock waves in general relativity
(1991) Nutku, Y.
We present the metric appropriate to a spherical shock wave in the framework of general relativity. This is a Petrov type-N vacuum solution of the Einstein field equations where the metric is continuous across the shock and the Riemann tensor suffers a step-function discontinuity. Spherical gravitational waves are described by type-N Robinson-Trautman metrics. However, for shock waves the Robinson-Trautman solutions are unacceptable because the metric becomes discontinuous in the Robinson-Trautman coordinate system. Other coordinate systems that have so far been introduced for describing Robinson-Trautman solutions also suffer from the same defect. We shall present the C0-form of the metric appropriate to spherical shock waves using Penrose's approach of identification with warp. Further extensions of Penrose's method yield accelerating, as well as coupled electromagnetic-gravitational shock-wave solutions. © 1991 The American Physical Society.
Open Access
A note on vanishing of the functor ext1 for Köthe spaces
(Springer-Verlag, 1991) Kocatepe, M.
In this note we study the relationship between the vanishing of Ext1(λ(A), λ(A)) and the existence of a regular basis in the Köthe space λ(A). We construct an example of a nuclear Köthe space λ(A) with no regular basis and such that Ext1(λ(A), λ(A))=0. Then we show that for some classes of Köthe spaces λ(A), the vanishing of Ext1(λ(A), λ(A)) yields a regular basis for λ(A). © 1991 Springer-Verlag.
Open Access
Bi-Hamiltonian structure of N-component Kodama equations
(1992) Gümral, Hasan
The author presents a simple way of constructing the second Hamiltonian operators for N-component Kodama equations. Using dimensional analysis he is led to an ansatz for the Hamiltonian operator as well as the conserved quantities in terms of ratios of polynomials. The coefficients of these polynomials are determined from the Jacobi identities. The resulting bi-Hamiltonian structure consists of generalization of Cavalcante and McKean's work (1982) for N=2 and his earlier results for N=3,4.
Open Access
Signatures of black holes in string theory
(1992) Gürses, Metin
The effect of string theory on the four-dimensional classical Einstein equations is investigated. It is shown that the throats of nonrotating charged black holes are exact solutions of the gravitational field equations with string correction terms.
Open Access
Uniqueness of the solutions of sigma models in non-Riemannian background
(Kluwer Academic Publishers, 1992) Gürses, M.
It is proved that the boundary value problems of some sigma-models in a non-Riemannian background have unique solutions. Sigma models on Riemannian backgrounds, sigma models with a Wess-Zumino-Witten term, the Ward model, and the self-dual Yang-Mills equations are among these models. © 1992 Kluwer Academic Publishers.
Open Access
Asymptotic solution of transonic nozzle flows with homogeneous condensation. II. Supercritical flows
(A I P Publishing LLC, 1992) Delale, C. F.; Schnerr, G. H.; Zierep, J.
A detailed analysis of supercritical transonic nozzle flows with stationary normal shock waves is presented. A classification scheme based on the normal shock location is obtained using asymptotic methods, and four distinct supercritical flow regimes are distinguished. A simple shock fitting technique that determines the shock location within any desired precision is introduced. Consequently, an algorithm that exhibits the asymptotic solution in each supercritical flow regime is developed for the expansion of moist air in nozzles with atmospheric supply conditions by utilizing the classical nucleation theory and the Hertz-Knudsen droplet growth law. Good agreement with the recent static pressure measurements and visualized shock locations is achieved in relatively slender nozzles when the condensed phase is assumed to consist purely of water drops. © 1993 American Institute of Physics.
Open Access
On the transition from ferromagnetism to antiferromagnetism on twofold Cayley tree
(Kluwer Academic Publishers, 1992) Delale, C.F.
A fixed-point conversion theorem which shows the transition from ferromagnetism to antiferromagnetism on twofold Cayley tree is proved. The ferromagnetic and antiferromagnetic maps are shown to be related by an involution and in zero field the stable fixed points of the ferromagnetic map are converted to a stable two-cycle of the antiferromagnetic map. A reduced one-dimensional analysis in zero field yields precisely the same results. © 1992 Società Italiana di Fisica.
Open Access
Schlesinger transformations of Painlevé II-V
(1992) Mug̃an, U.; Fokas, A.S.
The explicit form of the Schlesinger transformations for the second, third, fourth, and fifth Painlevé equations is given. © 1992 American Institute of Physics.
Open Access
A network model for rigid-body motion
(Kluwer Academic Publishers, 1992) Tokad, Y.
In the formulation of equations of motion of three-dimensional mechanical systems, the techniques utilized and developed to analyze the electrical networks based on linear graph theory can conveniently be used. The success of this approach, however, relies on the availability of a complete and adequate mathematical model of the rigid body valid in the three-dimensional motion. This article is devoted to the derivation of such a mathematical model for the rigid body as a (k + 1)-port component. In this derivation, the dynamic properties of the rigid body are automatically included as a consequence of the analytical procedures used in the article. In this model, a general form of the terminal equations is given. In many applications, however, its special form, also given in this article, is used. © 1992 Kluwer Academic Publishers.
Open Access
Asymptotic solution of transonic nozzle flows with homogeneous condensation. I. Subcritical flows
(A I P Publishing LLC, 1992) Delale, C.F.; Schnerr G.H.; Zierep J.
The one-dimensional (1-D) asymptotic solution of subcritical transonic nozzle flows with nonequilibrium homogeneous condensation is presented. An algorithm based on a local iterative scheme that exhibits the asymptotic solution in distinct condensation zones is developed for transonic moist air expansions under atmospheric supply conditions. Two models that characterize the state of the condensed phase as water drops or ice crystals are employed, together with the classical nucleation theory and Hertz-Knudsen droplet growth law. It is shown that the 1-D asymptotic predictions are in good agreement with the recent static pressure measurements of moist air expansions in relatively slender nozzles when the condensed phase is assumed to consist purely of water drops. © 1993 American Institute of Physics.
Open Access
Exact solutions of topologically massive gravity with a cosmological constant
(Institute of Physics Publishing Ltd., 1993) Nutku, Y.
Exact solutions of the Deser-Jackiw-Templeton field equations including a cosmological constant are presented. They generalize the finite-action homogeneous, anisotropic vacuum solutions of topologically massive gravity. We find that only Vuorio-type solutions, where any two of the constant scale factors coincide, admit a cosmological constant. One of these solutions can be dressed up to yield a two parameter black hole solution of topologically massive gravity.