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Geometric Aspects of Mirror Symmetry
"... Abstract. The geometric aspects of mirror symmetry are reviewed, with an eye towards future developments. Given a mirror pair (X, Y) of Calabi–Yau threefolds, the bestunderstood mirror statements relate certain small corners of the moduli spaces of X and of Y. We will indicate how one might go beyo ..."
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Cited by 27 (1 self)
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Abstract. The geometric aspects of mirror symmetry are reviewed, with an eye towards future developments. Given a mirror pair (X, Y) of Calabi–Yau threefolds, the bestunderstood mirror statements relate certain small corners of the moduli spaces of X and of Y. We will indicate how one might go
Geometrical aspects in Equilibrium Thermodynamics
"... We discuss different aspects of the present status of the Statistical Physics focusing the attention on the nonextensive systems, and in particular, on the so called small systems. Multimicrocanonical Distribution and some of its geometric aspects are presented. The same could be a very atractive w ..."
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Cited by 1 (0 self)
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We discuss different aspects of the present status of the Statistical Physics focusing the attention on the nonextensive systems, and in particular, on the so called small systems. Multimicrocanonical Distribution and some of its geometric aspects are presented. The same could be a very atractive
Geometric aspects of the Daugavet property
 J. Funct. Anal
, 2000
"... Let X be a closed subspace of a Banach space Y and J be the inclusion map. We say that the pair (X,Y) has the Daugavet property if for every rank one bounded linear operator T from X to Y the following equality ‖J + T ‖ = 1 + ‖T ‖ (1) holds. A new characterization of the Daugavet property in terms ..."
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Cited by 19 (3 self)
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Let X be a closed subspace of a Banach space Y and J be the inclusion map. We say that the pair (X,Y) has the Daugavet property if for every rank one bounded linear operator T from X to Y the following equality ‖J + T ‖ = 1 + ‖T ‖ (1) holds. A new characterization of the Daugavet property in terms of weak open sets is given. It is shown that the operators not fixing copies of ℓ1 on a Daugavet pair satisfy (1). Some hereditary properties are found: if X is a Daugavet space and Y is its subspace, then Y is also a Daugavet space provided X/Y has the RadonNikod´ym property; if Y is reflexive, then X/Y is a Daugavet space. Becides, we prove that if (X,Y) has the Daugavet property and Y ⊂ Z, then Z can be renormed so that (X,Z) possesses the Daugavet property and the equivalent norm coincides with the
Geometrical aspects of vibrational stabilization.
"... Many mechanical systems exhibit a surprising stabilization effect when subjected to high frequency vibrations. The class of such systems includes, besides the wellknown inverted pendulum [1], [2], more complex systems such as particles with vibrating constraints, including multiple pendula [3], an ..."
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vibrational forcing. We describe a new geometrical explanation of the stabilization effect. This explanation shows a perhaps unexpected relationship between the above mentioned stabilization phenomena on the one hand and the temperatureinduced deformations of materials on the other.
Geometric Aspects of Quantum Spin States
 COMMUN. MATH. PHYS.
, 1994
"... A number of interesting features of the ground states of quantum spin chains are analyzed with the help of a functional integral representation of the system's equilibrium states. Methods of general applicability are introduced in the context of the SU(2S+l)invariant quantum spinS chains with ..."
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Cited by 53 (16 self)
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. The method reveals the geometric aspects of the listed phenomena, and gives a precise sense to a picture of the ground state in which the spins are grouped into random clusters of zero total spin. E.g., within such
Geometric aspects of multiagent systems
 Electron. Notes Theoret. Comput. Sci
, 2003
"... Recent advances in Multiagent Systems (MAS) and Epistemic Logic within Distributed Systems Theory, have used various combinatorial structures that model both the geometry of the systems and the Kripke model structure of models for the logic. Examining one of the simpler versions of these models, int ..."
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Cited by 3 (2 self)
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, interpreted systems, and the related Kripke semantics of the logic S5n (an epistemic logic with nagents), the similarities with the geometric / homotopy theoretic structure of groupoid atlases is striking. These latter objects arise in problems within algebraic Ktheory, an area of algebra linked
Results 1  10
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333,303