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Strong rate of convergence for the Euler-Maruyama approximation of SDEs with Hö ...
In this paper, we consider a numerical approximation of the stochastic differential equation (SDE) $$X_{t}=x_{0}+ \int_{0}^{t} b(s, X_{s}) \mathrm{d}s + L_{t},~x_{0} \in \mathbb{R}^{d},~t \in [0,T],$$ where the drift coefficient ... Read More >
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Large-scale heterogeneous service systems with general packing constraints
A service system with multiple types of customers, arriving according to Poisson processes, is considered. The system is heterogeneous in that the servers also can be of multiple types. Each customer has an independent exponenti ... Read More >
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On bounds for the effective differential Nullstellensatz
Understanding bounds for the effective differential Nullstellensatz is a central problem in differential algebraic geometry. Recently, several bounds have been obtained using Dicksonian and antichains sequences (with a given gro ... Read More >
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Stability of the Brascamp-Lieb constant and applications
We prove that the best constant in the general Brascamp-Lieb inequality is a locally bounded function of the underlying linear transformations. As applications we deduce certain very general Fourier restriction, Kakeya-type, and ... Read More >
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Invariant dimensions and maximality of geometric monodromy action
Let X be a smooth separated geometrically connected variety over F_q and f:Y-> X a smooth projective morphism. We compare the invariant dimensions of the l-adic representation V_l and the F_l-representation \bar V_l of the geome ... Read More >
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The Lyapunov dimension formula for the global attractor of the Lorenz system
The exact Lyapunov dimension formula for the Lorenz system has been analytically obtained first due to G.A.Leonov in 2002 under certain restrictions on parameters, permitting classical values. He used the construction technique ... Read More >
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On the utility of Robinson-Amitsur ultrafilters. II
We extend the result of arXiv:0911.5414 about embedding of ideal-determined algebraic systems into ultraproducts, to arbitrary algebraic systems, and to ultraproducts over $\kappa$-complete ultrafilters. We also discuss the scop ... Read More >
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Roots with common tails
Some cubic polynomials over the integers have three distinct real roots with continued fractions that all have the same common tail. We characterize the polynomials for which this happens, and then investigate the situation for ... Read More >
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Stochastic Stability for Fiber Expanding Maps via a Perturbative Spectral Approa ...
We consider small perturbations of expanding maps induced by skew-product mappings whose base dynamics are not invertible necessarily. Adopting a previously developed perturbative spectral approach, we show stability of the dens ... Read More >
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Entire functions of several variables of bounded index
This monograph is devoted to the theory of entire functions of several variables. A definition of bounded index was supposed by B. Lepson. We generalised his definition for several variables and obtained criteria of L-index boun ... Read More >