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Starting with the fractional Schrödinger equation and Fourier analysis, this paper presents a new L p -uncertainty principle for the positively-ordered Laplace pair { (− Δ) α 2 , (− Δ) β 2 }. [ABSTRACT FROM AUTHOR]

A 2- (v , k , λ) block design (P , B) is additive if, up to isomorphism, P can be represented as a subset of a commutative group (G , +) in such a way that the k elements of each block in B sum up to zero in G. If, for some suitable G , the embedding of P in G is also such that, conversely, any zero-sum k -subset of P is a block in B , then (P , B) is said to be strongly additive. In this paper we exhibit the very first examples of additive 2-designs that are not strongly additive, thereby settling an open problem posed in 2019. Our main counterexample is a resolvable 2- (16 , 4 , 2) design (F 4 × F 4 , B 2) , which decomposes into two disjoint isomorphic copies of the affine plane of order four. An essential part of our construction is a (cyclic) decomposition of the point-plane design of AG (4 , 2) into seven disjoint isomorphic copies of the affine plane of order four. This produces, in addition, a solution to Kirkman's schoolgirl problem. [ABSTRACT FROM AUTHOR]

• Intrusive generalised Polynomial Chaos (gPC). • More efficient than non-intrusive gPC. • Monte Carlo (MC) resolution of the gPC based reduced model. • Efficient uncertainty propagation with a combined MC/gPC Chaos resolution. • Analytic uncertain benchmarks from well-known benchmarks of the literature. In this paper, we are interested in taking into account uncertainties for k eff computations in neutronics. More generally, the material of this paper can be applied to propagate uncertainties in eigenvalue/eigenvector computations for the linear Boltzmann equation. In [1,2] , an intrusive MC solver for the gPC based reduced model of the instationary linear Boltzmann equation has been put forward. The MC-gPC solver presents interesting characteristics (mainly a better efficiency than non-intrusive strategies and spectral convergence): our aim is to recover these characteristics in an eigenvalue/eigenvector estimation context. This is done in practice at the price of few well identified modifications of an existing Monte Carlo implementation. [ABSTRACT FROM AUTHOR]

A challenge that faces high-order methods for industrial applications generally is turbulence modeling at high Reynolds numbers. Large eddy simulation is studied extensively for high-order methods, nevertheless, its computational cost is enormous for industrial applications. The hybrid LES/RANS compromises the computational cost and the modeling error, however, solving the Reynolds-averaged Navier-Stokes equations is a resilient task for high-order methods, due to the non-smooth profiles of the turbulence quantities. Taking into account the complexity with high-order methods and the fairly large modeling errors of the RANS modeling, low-order methods has proved to be more pragmatic. For instance, in the discontinuous Galerkin framework, the polynomial approximation for these quantities leads to large oscillations that obstructs the non-linear solver. To use the high-order methods for industrial cases it is essential to have reliable implementations of two-equation turbulence models in RANS formulations. In this paper, a RANS discretization based on hybridizable discontinuous Galerkin is presented for the standard, TNT, BSL and SST versions of the k − ω model for applications at Reynolds numbers up to 109. A particular focus is given to the treatment of the specific rate of turbulence dissipation ω in the high-order framework. The complexity increases with these types of models as the value of ω goes to infinity at solid walls. Additionally, with minor modifications to the numerical flux definition, the turbulence model formulation can be solved by discontinuous Galerkin method as well. The results show remarkable improvements regarding the error magnitudes and non-linear convergence rate (iterative error) compared to second-order finite volume based solvers. • Implementing and analyzing the two-equations k-omega models without using the logarithm of omega in the HDG framework. • Comparing the results for the turbulent flat plate test case between finite volume and HDG. • Presenting different mitigations to deal with the turbulence quantities transport equations in the high-order framework. [ABSTRACT FROM AUTHOR]

This paper uses structural complexity theory to study whether there is a chasm between knowing an object exists and getting one's hands on the object or its properties. In particular, we study the nontransparency of backbones. We show that, under the widely believed assumption that integer factoring is hard, there exist sets of boolean formulas that have obvious, nontrivial backbones yet finding the values of those backbones is intractable. We also show that, under the same assumption, there exist sets of boolean formulas that obviously have large backbones yet producing such a backbone is intractable. Furthermore, we show that if integer factoring is not merely worst-case hard but is frequently hard, as is widely believed, then the frequency of hardness in our two results is not too much less than that frequency. These results hold even if one's assumptions are, respectively, P ≠ NP ∩ coNP or that some NP ∩ coNP problem is frequently hard. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel algorithm to learn a Büchi automaton from a teacher who knows an ω -regular language. The learned Büchi automaton can be a nondeterministic Büchi automaton or a limit deterministic Büchi automaton. The learning algorithm is based on learning a formalism called family of DFAs (FDFAs) recently proposed by Angluin and Fisman. The main catch is that we use a classification tree structure instead of the standard observation table structure. The worst case storage space required by our algorithm is quadratically better than that required by the table-based algorithm proposed by Angluin and Fisman. We implement the proposed learning algorithms in the learning library ROLL (Regular Omega Language Learning), which also consists of other complete ω -regular learning algorithms available in the literature. Experimental results show that our tree-based learning algorithms have the best performance among others regarding the number of solved learning tasks. [ABSTRACT FROM AUTHOR]