Exponential Kleisli Monoids As Eilenberg-Moore Algebras,
2013
Universidade de Aveiro
Exponential Kleisli Monoids As Eilenberg-Moore Algebras, Dirk Hofmann, Frédéric Mynard, Gavin J. Seal
Mathematical Sciences: Faculty Publications
Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This result generalizes the classical identification of exponentiable topological spaces as those whose lattice of open subsets forms a continuous lattice.
A Generalized White Noise Space Approach To Stochastic Integration For A Class Of Gaussian Stationary Increment Processes,
2013
Chapman University
A Generalized White Noise Space Approach To Stochastic Integration For A Class Of Gaussian Stationary Increment Processes, Daniel Alpay, Alon Kipnis
Mathematics, Physics, and Computer Science Faculty Articles and Research
Given a Gaussian stationary increment processes, we show that a Skorokhod-Hitsuda stochastic integral with respect to this process, which obeys the Wick-Itô calculus rules, can be naturally defined using ideas taken from Hida’s white noise space theory. We use the Bochner-Minlos theorem to associate a probability space to the process, and define the counterpart of the S-transform in this space. We then use this transform to define the stochastic integral and prove an associated Itô formula.
Non-Commutative Stochastic Distributions And Applications To Linear Systems Theory,
2013
Chapman University
Non-Commutative Stochastic Distributions And Applications To Linear Systems Theory, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. Special inequalities which hold in this space allow to characterize its invertible elements and to develop an appropriate framework of non-commutative stochastic linear systems.
Representation Formulas For Hardy Space Functions Through The Cuntz Relations And New Interpolation Problems,
2013
Chapman University
Representation Formulas For Hardy Space Functions Through The Cuntz Relations And New Interpolation Problems, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz, Itzik Marziano
Mathematics, Physics, and Computer Science Faculty Articles and Research
We introduce connections between the Cuntz relations and the Hardy space H2 of the open unit disk D. We then use them to solve a new kind of multipoint interpolation problem in H2, where for instance, only a linear combination of the values of a function at given points is preassigned, rather than the values at the points themselves.
Approximation By Iterates Of Beta Operators,
2013
TÜBİTAK
Approximation By Iterates Of Beta Operators, Purshottam Narain Agrawal, Karunesh Kumar Singh, Vikas Kumar Mishra
Turkish Journal of Mathematics
In this paper, we study the degree of approximation by an iterative combination T_{n,k} of the beta operators introduced by Upreti [8].
On Characterization And Stability Of Alternate Dual Of G-Frames,
2013
TÜBİTAK
On Characterization And Stability Of Alternate Dual Of G-Frames, Ali Akbar Arefijamaal, Soheila Ghasemi
Turkish Journal of Mathematics
One of the essential applications of frames is that they lead to expansions of vectors in the underlying Hilbert space in terms of the frame elements. In this decomposition, dual frames have a key role. G-frames, introduced by Sun, cover many other recent generalizations of frames. In this paper, we give some characterizations of dual g-frames. Moreover, we prove that if two g-frames are close to each other, then we can find duals of them which are close to each other.
Scalar Curvature And Symmetry Properties Of Lightlike Submanifolds},
2013
TÜBİTAK
Scalar Curvature And Symmetry Properties Of Lightlike Submanifolds}, Cyriaque Atindogbe, Oscar Lungiambudila, Joel Tossa
Turkish Journal of Mathematics
In this paper, the induced Ricci tensor and the extrinsic scalar curvature on lightlike submanifolds are obtained. This scalar quantity extend the result given by C. Atindogbe in [1]. An example of extrinsic scalar curvature on one class of 2-degenerate manifolds is provided. We investigate lightlike submanifolds which are locally symmetric, semi-symmetric, Ricci semi-symmetric in indefinite spaces form. In the coisotropic case, we show that, under some conditions, these lightlike submanifolds are totally geodesic.
Paracontact Semi-Riemannian Submersions,
2013
TÜBİTAK
Paracontact Semi-Riemannian Submersions, Yilmaz Gündüzalp, Bayram Şahi̇n
Turkish Journal of Mathematics
In this paper, we first define the concept of paracontact semi-Riemannian submersions between almost paracontact metric manifolds, then we provide an example and show that the vertical and horizontal distributions of such submersions are invariant with respect to the almost paracontact structure of the total manifold. The study is focused on fundamental properties and the transference of structures defined on the total manifold. Moreover, we obtain various properties of the O'Neill's tensors for such submersions and find the integrability of the horizontal distribution. We also find necessary and sufficient conditions for a paracontact semi-Riemannian submersion to be totally geodesic. Finally, …
On Quasiconformal Harmonic Mappings Lifting To Minimal Surfaces,
2013
TÜBİTAK
On Quasiconformal Harmonic Mappings Lifting To Minimal Surfaces, Hakan Mete Taştan, Yaşar Polatoğlu
Turkish Journal of Mathematics
We prove a growth theorem for a function to belong to the class \sum(\mu;a) and generalize a Weierstrass-Enneper representation type theorem for the minimal surfaces given in [5] to spacelike minimal surfaces which lie in 3-dimensional Lorentz-Minkowski space L^3. We also obtain some estimates of the Gaussian curvature of the minimal surfaces in 3-dimensional Euclidean space R^3 and of the spacelike minimal surfaces in L^3.
A Note On Unmixed Ideals Of Veronese Bi-Type,
2013
TÜBİTAK
A Note On Unmixed Ideals Of Veronese Bi-Type, Monica La Barbiera
Turkish Journal of Mathematics
We classify the unmixed ideals of Veronese bi-type and in some cases we give a description of their associated prime ideals.
G-Frames As Special Frames,
2013
TÜBİTAK
G-Frames As Special Frames, Abas Askarizadeh, Mohammad Ali Dehghan
Turkish Journal of Mathematics
G-frames are generalizations of ordinary frames for Hilbert spaces. In the present paper we study frames, and operators on a special separable Hilbert C^*-module, B(H,K), where H and K are Hilbert spaces, and we prove that every g-frame for H is a frame for B(H,K) and vice versa. Also, we derive some relationships between g-Riesz bases for H and Riesz bases in B(H,K). Similar results for orthogonal bases will be discussed.
Integral Polytopes And Polynomial Factorization,
2013
TÜBİTAK
Integral Polytopes And Polynomial Factorization, Fati̇h Koyuncu
Turkish Journal of Mathematics
For any field F, there is a relation between the factorization of a polynomial f \in F[x_1,...,x_n] and the integral decomposition of the Newton polytope of f. We extended this result to polynomial rings R[x_1,...,x_n] where R is any ring containing some elements which are not zero-divisors. Moreover, we have constructed some new families of integrally indecomposable polytopes in \mb giving infinite families of absolutely irreducible multivariate polynomials over arbitrary fields.
On Pseudo Semi-Projective Modules,
2013
TÜBİTAK
On Pseudo Semi-Projective Modules, Truong Cong Quynh
Turkish Journal of Mathematics
A right R-module M is called semi-projective if, for any submodule N of M, every epimorphism \pi: M \rightarrow N and every homomorphism \alpha: M \rightarrow N, there exists a homomorphism \beta: M \rightarrow M such that \pi \beta = \alpha (see [11]). In this paper, we consider some generalizations of semi-projective module, that is quasi pseudo principally projective module. Some properties of this class of module are studied.
Generating Systems Of Differential Invariants And The Theorem On Existence For Curves In The Pseudo-Euclidean Geometry},
2013
TÜBİTAK
Generating Systems Of Differential Invariants And The Theorem On Existence For Curves In The Pseudo-Euclidean Geometry}, Djavvat Khadjiev, İdri̇s Ören, Ömer Pekşen
Turkish Journal of Mathematics
Let M(n, p) be the group of all motions of an n-dimensional pseudo-Euclidean space of index p. It is proved that the complete system of M(n,p)-invariant differential rational functions of a path (curve) is a generating system of the differential field of all M(n,p)-invariant differential rational functions of a path (curve), respectively. A fundamental system of relations between elements of the complete system of M(n,p)-invariant differential rational functions of a path (curve) is described.
Rings Over Which Every Module Has A Flat \\Delta-Cover,
2013
TÜBİTAK
Rings Over Which Every Module Has A Flat \\Delta-Cover, Pinar Aydoğdu
Turkish Journal of Mathematics
Let M be a module. A \delta-cover of M is an epimorphism from a module F onto M with a \delta-small kernel. A \delta-cover is said to be a flat \delta-cover in case F is a flat module. In the present paper, we investigate some properties of (flat) \delta-covers and flat modules having a projective \delta-cover. Moreover, we study rings over which every module has a flat \delta-cover and call them right generalized \delta-perfect rings. We also give some characterizations of \delta-semiperfect and \delta-perfect rings in terms of locally (finitely, quasi-, direct-) projective \delta-covers and flat \delta-covers.
Formulas For The Fourier Coefficients Of Cusp Form For Some Quadratic Forms (Correction To A Paper By Ahmet Tekcan With The Same Title), Bariş Kendi̇rli̇
Turkish Journal of Mathematics
In this study M_1(\Gamma _0(3) ,\chi _{-3}) , M_2(\Gamma_0(5), \chi _5) and M_3(\Gamma _0(7),\chi _{-7}) have been examined and the formulas for the Fourier Coefficients of theta series and the representation number of positive integers by some quadratic forms 3x_1^2+3x_1x_2+x_2^2, 5(x_1^2+x_1x_2+x_1x_3+x_1x_4+x_2^2+x_2x_3+ x_2x_4+x_3^2+x_3x_4)+2x_4^2, and 7(x_1^2+x_1x_2+x_1x_3+x_1x_4+x_1x_5+x_2^2+x_2x_3+x_2x_4+x_2x_5+ x_3^2+x_3x_4+x_3x_5+x_4^2+x_4x_5+x_5^2+7(x_1x_6+x_2x_6+x_3x_6+ x_4x_6+x_5x_6)+3x_6^2, are determined. This work is a correction to a paper of the same title by Ahmet Tekcan [5].
Asymptotics Of The Ruin Probability With Claims Modeled By \\Alpha-Stable Aggregated Ar(1) Process,
2013
TÜBİTAK
Asymptotics Of The Ruin Probability With Claims Modeled By \\Alpha-Stable Aggregated Ar(1) Process, Karina Perilioglu, Donata Puplinskaite
Turkish Journal of Mathematics
We study the asymptotics of the ruin probability in a discrete time risk insurance model with stationary claims following the aggregated heavy-tailed AR(1) process discussed in Puplinskaite and Surgailis (2010). The present work is based on the general characterization of the ruin probability with claims modeled by stationary \alpha-stable process in Mikosch and Samorodnitsky (2000). We prove that for the aggregated AR(1) claims' process, the ruin probability decays with exponent \alpha(1-H), where H \in [1/\alpha, 1) is the asymptotic self-similarity index of the claim process, 1< \alpha < 2. This result agrees with the decay rate of the ruin probability with claims modeled by increments of linear fractional motion in Mikosch and Samorodnitsky (2000) and also with other characterizations of long memory of the aggregated AR(1) process with infinite variance in Puplinskaite and Surgailis (2010).
On The Existence Of (400, 57, 8) Non-Abelian Difference Sets,
2013
TÜBİTAK
On The Existence Of (400, 57, 8) Non-Abelian Difference Sets, Adegoke Solomon Osifodunrin
Turkish Journal of Mathematics
Difference sets with parameters (\frac{q^{d + 1} - 1}{q - 1}, \frac{q^d - 1}{q - 1}, \frac{q^{d - 1} - 1}{q - 1}), where q is a prime power and d \geq 1, are known to exist in cyclic groups and are called classical Singer difference sets. We study a special case of this family with q = 7 and d = 3 in search of more difference sets. According to GAP, there are 220 groups of order 400 out of which 10 are abelian. E. Kopilovich and other authors showed that the remaining nine abelian groups of order 400 …
Gorenstein Transpose With Respect To A Semidualizing Bimodule,
2013
TÜBİTAK
Gorenstein Transpose With Respect To A Semidualizing Bimodule, Zengfeng Liu, Xiaoguang Yan
Turkish Journal of Mathematics
Let S and R be rings and _SC_R be a semidualizing bimodule. We first give the definitions of C-transpose and n-C-torsionfree and give a criterion for a module A to be G_C-projective by some property of the C-transpose of A. Then we introduce the notion of C-Gorenstein transpose of a module over two-sided Noetherian rings. We prove that a module M in \mod R^{op} is a C-Gorenstein transpose of a module A \in \mod S if and only if M can be embedded into a C-transpose of A with the cokernel G_C-projective. Finally we investigate some homological properties of the …
The Total Graph Of A Finite Commutative Ring,
2013
TÜBİTAK
The Total Graph Of A Finite Commutative Ring, Ali Ramin
Turkish Journal of Mathematics
Let R be a commutative ring with Z(R), its set of zero-divisors and \mbox{Reg}(R), its set of regular elements. Total graph of R, denoted by T(\Gamma(R)), is the graph with all elements of R as vertices, and two distinct vertices x,y \in R, are adjacent in T(\Gamma(R)) if and only if x+y \in Z(R). In this paper, some properties of T(\Gamma(R)) have been investigated, where R is a finite commutative ring and a new upper bound for vertex-connectivity has been obtained in this case. Also, we have proved that the edge-connectivity of T(\Gamma(R)) coincides with the minimum degree if and …
