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There are several classical characterisations of the valuative dimension of a commutative ring. Constructive versions of this dimension have been given and proven to be equivalent to the classical notion within classical mathematics, and they can be used for the usual examples of commutative rings. To the contrary of the classical versions, the constructive versions have a clear computational content. This paper investigates the computational relationship between three possible constructive definitions of the valuative dimension of a commutative ring. In doing so, it proves these constructive versions to be equivalent within constructive mathematics. [ABSTRACT FROM AUTHOR]

Abstract The growth of tropical geometry has generated significant interest in the tropical semiring in the past decade. However, there are other semirings in tropical algebra that provide more information, such as the symmetrized (max ⁡ , +) , Izhakian's extended and Izhakian–Rowen's supertropical semirings. In this paper we identify in which of these upper-bound semirings we can express symmetric polynomials in terms of elementary ones. We show that in the case of idempotent semirings we can do this precisely when the Frobenius property is satisfied, that in the case of supertropical semirings this is always possible, and that in non-trivial symmetrized semirings this is never possible. Our results allow us to determine the tropical algebra semirings where an analogue of the Fundamental Theorem of Symmetric Polynomials holds and to what extent. [ABSTRACT FROM AUTHOR]

Abstract With the increasing use of composite material and external energy dissipation device in civil structures, the classical Rayleigh damping becomes an inappropriate assumption in structural damage identification. In this paper, a parametric sensitivity-based approach is developed to identify the structural damage and damping defect of non-classically damped shear-type building simultaneously. As the preliminary step, the complex eigenvalues and eigenvectors of damaged structure are obtained by a novel identification technique, which decouples the first-order modal analysis equation under physical coordinate so that the complex modal parameters of each mode can be identified independently. Thereafter, by analysing the sensitivities of complex eigenparameter, non-linear least square method is applied to identify the locations and magnitudes of damage with respect to stiffness reduction and damping defect. The proposed identification approach is illustrated by identifying the damage in a numerical five-storey shear building. The identification results show that the proposed approach can locate and quantify the stiffness reductions satisfactorily even when measurement noise is taken into account. However, in order to quantify the damping defects consistently, their locations need to be known as a priori. Highlights • A novel complex eigenparameter identification approach under state-space coordinate. • Damage identification on non-proportionally damped shear-type building. • Identify the stiffness reduction and damping defect simultaneously. • Identify the design parameters which locate and quantify the damages. • Numerical validation on a five-storey shear building by considering measurement noise. [ABSTRACT FROM AUTHOR]

In this paper we prove a new recurrence relation on the van der Waerden numbers, w ( r , k ) . In particular, if p is a prime and p ≤ k then w ( r , k ) > p ⋅ w r − r p , k − 1 . This recurrence gives the lower bound w ( r , p + 1 ) > p r − 1 2 p when r ≤ p , which generalizes Berlekamp’s theorem on 2-colorings, and gives the best known bound for a large interval of r . The recurrence can also be used to construct explicit valid colorings, and it improves known lower bounds on small van der Waerden numbers. [ABSTRACT FROM AUTHOR]

One of the most famous algorithmic meta-theorems states that every graph property which can be defined in counting monadic second order logic (CMSOL) can be checked in linear time on graphs of bounded treewidth, which is known as Courcelle’s Theorem (Courcelle, 1990). These algorithms are constructed as finite state tree automata and hence every CMSOL-definable graph property is recognizable. Courcelle also conjectured that the converse holds, i.e. every recognizable graph property is definable in CMSOL for graphs of bounded treewidth. In this paper we prove two special cases of this conjecture, first for the class of k -outerplanar graphs, which are known to have treewidth at most 3 k − 1 (Bodlaender, 1998) and for graphs of bounded treewidth without chordless cycles of length at least some constant ℓ . We furthermore show that for a proof of Courcelle’s Conjecture it is sufficient to show that all members of a graph class admit constant width tree decompositions whose bags and edges can be identified with MSOL-predicates. For graph classes that admit MSOL-definable constant width tree decompositions that have bounded degree or allow for a linear ordering of all nodes with the same parent we even give a stronger result: In that case, the counting predicates of CMSOL are not needed. [ABSTRACT FROM AUTHOR]

The generalised colouring numbers col r ( G ) and wcol r ( G ) were introduced by Kierstead and Yang as a generalisation of the usual colouring number, and have since then found important theoretical and algorithmic applications. In this paper, we dramatically improve upon the known upper bounds for generalised colouring numbers for graphs excluding a fixed minor, from the exponential bounds of Grohe et al. to a linear bound for the r -colouring number col r and a polynomial bound for the weak r -colouring number wcol r . In particular, we show that if G excludes K t as a minor, for some fixed t ≥ 4 , then col r ( G ) ≤ t − 1 2 ( 2 r + 1 ) and wcol r ( G ) ≤ r + t − 2 t − 2 ( t − 3 ) ( 2 r + 1 ) ∈ O ( r t − 1 ) . In the case of graphs G of bounded genus g , we improve the bounds to col r ( G ) ≤ ( 2 g + 3 ) ( 2 r + 1 ) (and even col r ( G ) ≤ 5 r + 1 if g = 0 , i.e. if G is planar) and wcol r ( G ) ≤ ( 2 g + r + 2 2 ) ( 2 r + 1 ) . [ABSTRACT FROM AUTHOR]

Many methods for multinational License Plate Detection (LPD) have been proposed in recent times but most of them are not sophisticated enough to handle complex backgrounds. Moreover, their ability to handle various environmental and illumination conditions has been limited and still needs improvement. In this paper, we propose a novel technique to detect license plates of vehicles regardless of their color, size, and content. As the rear vehicle lights are an essential part of any vehicle, we reduce the image processing area to eliminate the complex background by detecting the rear-lights as the license plates are in a certain range of these lights. Heuristic Energy Map (HEM) of the vertical edge information in the Region of Interest (ROI) is calculated and area with the dense edges is selected using a unique histogram approach which is considered to be the license plate. The proposed algorithm is tested on 855 images from various countries including China, Pakistan, Serbia, Italy and various states of America. Experimental results show that the proposed method is able to detect license plates 90.4% of times despite of complex backgrounds in 0.25 s on average that can achieve real time performance. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithm for implicitizing tensor product surfaces of bi-degree ( m , n ) with no base points, assuming that there are no moving planes of bi-degree ( m − 1 , n − 1 ) following the surface. The algorithm is based on some structural results: (1) There are exactly 2 n linearly independent moving planes of bi-degree ( m , n − 1 ) following the surface; (2) mn linearly independent moving quadrics of bi-degree ( m − 1 , n − 1 ) following the surface can be constructed from the 2 n linearly independent moving planes; (3) The mn linearly independent moving quadrics form a compact determinant of order mn which exactly gives the implicit equation of the rational surface. Complexity analysis and experimental results show that the new algorithm is significantly more efficient than the previous methods. [ABSTRACT FROM AUTHOR]

In this paper we propose a new iterative penalty-projection algorithm for a monolithic fluid-structure interaction solver. Projection methods, that split the computation of the velocity from the pressure, are very popular in fluid dynamics since the boundary errors generated by the projection method are localized mainly near the boundary layers where the incorrect pressure boundary conditions are imposed. However, when solid regions are taken into account, the pressure projected field cannot satisfy fully coupled boundary constraints imposed on external solid surfaces such as stress-free conditions, and, due to the rigidity of the medium, the boundary errors propagate deeply in the interior. In order to reduce the projection errors we propose a one-step penalty-projection method in the fluid domain and an iterative penalty-projection method in the solid region. This technique decouples the pressure-velocity degrees of freedom and, as a consequence, the computational cost. In order to verify the accuracy and robustness of the proposed method we compare the results between this splitting velocity-pressure algorithm and the coupled one. These numerical results show stability and robustness of the proposed algorithm with a strong reduction of the computational effort. [ABSTRACT FROM AUTHOR]

In 1994 Lazard proposed an improved projection operation for cylindrical algebraic decomposition (CAD). For the proof he introduced a certain notion of valuation of a multivariate Puiseux series at a point. However a gap in one of the key supporting results for the improved projection was subsequently noticed. In this paper we show that Lazard's projection is valid for CAD construction for so-called well-oriented polynomial sets. Our proof does not make use of Lazard's notion of valuation, however. [ABSTRACT FROM AUTHOR]

This paper introduces stochastic weighted particle algorithms for the solution of multi-compartment population balance equations. In particular, it presents a class of fragmentation weight transfer functions which are constructed such that the number of computational particles stays constant during fragmentation events. The weight transfer functions are constructed based on systems of weighted computational particles and each of it leads to a stochastic particle algorithm for the numerical treatment of population balance equations. Besides fragmentation, the algorithms also consider physical processes such as coagulation and the exchange of mass with the surroundings. The numerical properties of the algorithms are compared to the direct simulation algorithm and an existing method for the fragmentation of weighted particles. It is found that the new algorithms show better numerical performance over the two existing methods especially for systems with significant amount of large particles and high fragmentation rates. [ABSTRACT FROM AUTHOR]

This paper studies the equivalence of tractability for classes of Λ std of function evaluations and Λ all of all continuous linear functionals for L 2 -approximation in the average-case setting. For the normalized error criterion, we show that the power of Λ std is the same as that of Λ all for all notions of exponential tractability and algebraic tractability, in the sense that there exist algorithms using function values at some deterministic points which enjoy the same tractability properties as those using optimally chosen linear functionals. Moreover, for the absolute error criterion, we also show that the power of Λ std is the same as that of Λ all for all notions of exponential tractability and algebraic tractability under certain assumptions on the trace of the covariance operators. In particular, we give a partial answer to three problems raised by E. Novak and H. Woźniakowski in the book " Tractability of multivariate problems" (Open problems 116-118, EMS Tracts in Mathematics, vol.18, Zürich, 2012) , proving that the same results hold under weaker conditions. Finally, we apply our results to the tensor product L 2 -approximation. [ABSTRACT FROM AUTHOR]