scholarly journals Simple sufficient condition for subspace to be completely or genuinely entangled

2021 ◽  
Author(s):  
Maciej M Demianowicz ◽  
Grzegorz Rajchel-Mieldzioć ◽  
Remigiusz Augusiak
Keyword(s):  
Sufficient Condition ◽  
Simple Sufficient Condition

scholarly journals A finite model-theoretical proof of a property of bounded query classes within PH

2004 ◽  
Vol 69 (4) ◽  
pp. 1105-1116 ◽  
Author(s):  
Leszek Aleksander Kołodziejczyk
Keyword(s):  
Normal Form ◽  
Model Theory ◽  
Finite Model ◽  
Sufficient Condition ◽  
Finite Model Theory ◽  
Finite Models ◽  
Constructible Function ◽  
Simple Sufficient Condition

Abstract.We use finite model theory (in particular, the method of FM-truth definitions, introduced in [MM01] and developed in [K04], and a normal form result akin to those of [Ste93] and [G97]) to prove:Let m ≥ 2. Then:(A) If there exists k such that NP⊆ Σm TIME(nk)∩ Πm TIME(nk), then for every r there exists kr such that :(B) If there exists a superpolynomial time-constructible function f such that NTIME(f), then additionally .This strengthens a result by Mocas [M96] that for any r, .In addition, we use FM-truth definitions to give a simple sufficient condition for the arity hierarchy to be strict over finite models.

A simple sufficient condition for triviality of obstructions in the orbifold construction for subfactors

2017 ◽  
Vol 121 (1) ◽  
pp. 101
Author(s):  
Toshihiko Masuda
Keyword(s):  
Sufficient Condition ◽  
Principal Graph ◽  
Simple Sufficient Condition ◽  
Orbifold Construction

We present a simple sufficient condition for triviality of obstructions in the orbifold construction. As an application, we can show the existence of subfactors with principal graph $D_{2n}$ without full use of Ocneanu's paragroup theory.

scholarly journals A Restless Bandit Model for Resource Allocation, Competition, and Reservation

2021 ◽  
Author(s):  
Jing Fu ◽  
Bill Moran ◽  
Peter G. Taylor
Keyword(s):  
Resource Allocation ◽  
Numerical Experiments ◽  
Asymptotic Optimality ◽  
Sufficient Condition ◽  
Limited Capacity ◽  
Index Policy ◽  
Asymptotically Optimal ◽  
Restless Bandit ◽  
Simple Sufficient Condition ◽  
Resource Capacity

In “A Restless Bandit Model for Resource Allocation, Competition and Reservation,” J. Fu, B. Moran, and P. G. Taylor study a resource allocation problem with varying requests and with resources of limited capacity shared by multiple requests. This problem is modeled as a set of heterogeneous restless multi-armed bandit problems (RMABPs) connected by constraints imposed by resource capacity. Following Whittle’s idea of relaxing the constraints and Weber and Weiss’s proof of asymptotic optimality, the authors propose an index policy and establish conditions for it to be asymptotically optimal in a regime where both arrival rates and capacities increase. In particular, they provide a simple sufficient condition for asymptotic optimality of the policy and, in complete generality, propose a method that generates a set of candidate policies for which asymptotic optimality can be checked. Via numerical experiments, they demonstrate the effectiveness of these results even in the pre-limit case.

Lacunas in two-dimensional wave propagation

1967 ◽  
Vol 63 (3) ◽  
pp. 819-825 ◽  
Author(s):  
R. Burridge
Keyword(s):  
Wave Propagation ◽  
Second Order ◽  
Sufficient Condition ◽  
Two Dimensional ◽  
Two Space Dimensions ◽  
Simple Sufficient Condition ◽  
General Work ◽  
Dimensional Wave

AbstractA simple sufficient condition is given for the existence of a lacuna in two-dimensional wave propagation governed by an equation of the second order. This work was inspired by Petrowsky's very general work (Petrowsky (3)) but for waves in two space dimensions we do not need the sophisticated machinery developed by him.

Quasirandom Groups

2008 ◽  
Vol 17 (3) ◽  
pp. 363-387 ◽  
Author(s):  
W. T. GOWERS
Keyword(s):  
Finite Group ◽  
Sufficient Condition ◽  
Large Product ◽  
Simple Sufficient Condition ◽  
Free Subset

Babai and Sós have asked whether there exists a constant c > 0 such that every finite group G has a product-free subset of size at least c|G|: that is, a subset X that does not contain three elements x, y and z with xy = z. In this paper we show that the answer is no. Moreover, we give a simple sufficient condition for a group not to have any large product-free subset.

scholarly journals Stable Polarized del Pezzo Surfaces

2018 ◽  
Vol 2020 (18) ◽  
pp. 5477-5505 ◽  
Author(s):  
Ivan Cheltsov ◽  
Jesus Martinez-Garcia
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Del Pezzo Surfaces ◽  
Sufficient Condition ◽  
Kähler Metric ◽  
Simple Sufficient Condition ◽  
Del Pezzo ◽  
Kahler Metric

Abstract We give a simple sufficient condition for $K$-stability of polarized del Pezzo surfaces and for the existence of a constant scalar curvature Kähler metric in the Kähler class corresponding to the polarization.

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