Hasil untuk "math.GR"

Jesmin Sultana, Tanha Tabassum Nunna, Shaikh Sharif Hasan et al.

LIXIN MAO

AbstractLet R be a graded ring. We introduce the concepts of Ding gr-injective and Ding gr-projective R-modules, which are the graded analogues of Ding injective and Ding projective modules. Several characterizations and properties of Ding gr-injective and Ding gr-projective modules are obtained. In addition, we investigate the relationships among Gorenstein gr-flat, Ding gr-injective and Ding gr-projective modules.

Michael Gr�ter, Kjell-Ove Widman

G. Gr�tzer, H. Lakser

Mark Gross

Mark Gross

Klaus Gr�ning

Hans G. Kellerer

Yuji Kamoi, Wolfgang Vogel

Gebhard Gr�bl, Christian Reitberger

E. Gr�nbergs

Koppe

P. Vaškas

Nikolai Andreevich Tyurin

New examples of Lagrangian submanifolds of the complex Grassmannian $\operatorname{Gr}(1, n)$ with the standard Kähler form are presented. The scheme of their construction is based on two facts: first, we put forward a natural correspondence between the Lagrangian submanifolds of a symplectic manifold obtained by symplectic reduction and the Lagrangian submanifolds of a large symplectic manifold carrying a Hamiltonian action of some group, to which this reduction is applied; second, we show that for some choice of generators of the action of $\mathrm T^k$ on $\operatorname{Gr}(1, n)$, $k=2, …, n-1$, and for suitable values of the moment map there exists an isomorphism $\operatorname{Gr}(1, n)//\mathrm T^k \cong \operatorname{tot}(\mathbb{P}(\tau) \times …\times\mathbb{P}(\tau) \to \operatorname{Gr}(1, n-k))$, where the total space of the Cartesian product of $k$ copies of the projectivization of the tautological bundle $\tau \to \operatorname{Gr}(1, n-k)$ is on the right. Combining these two facts we obtain a lower bound for the number of topologically distinct smooth Lagrangian submanifolds in the original Grassmannian $operatorname{Gr}(1, n)$. Bibliography: 5 titles.

Robert Laterveer

Daniel B. Szyld

B. G. Pachpatte

In this paper we establish some new inequalities of Ostrowski and Gr"uss type, involving three functions whose second derivatives are bounded. The analysis used in the proofs is fairly elementary and based on the integral identities for twice differentiable functions.

B. G. Pachpatte

In the present paper we establish some new integral inequalities similar to that of Trapezoid and Gr"uss inequalities by using a fairly elementary analysis.

J. Pecaric