On the topology of the Kasparov groups and its applications

In this paper we establish a direct connection between stable approximate unitary equivalence for *-homomorphisms and the topology of the KK-groups which avoids entirely C^*-algebra extension theory and does not require nuclearity assumptions. To this purpose we show that a topology on the Kasparov groups can be defined in terms of approximate unitary equivalence for Cuntz pairs and that this topology coincides with both Pimsner's topology and the Brown-Salinas topology. We study the generalized Rørdam group , and prove that if a separable exact residually finite dimensional C^*-algebra satisfies the universal coefficient theorem in KK-theory, then it embeds in the UHF algebra of type 2^∞. In particular such an embedding exists for the C^*-algebra of a second countable amenable locally compact maximally almost periodic group.     

A proposal for a hybrid meta-strategy for combinatorial optimization problems

In this paper, we propose an algorithm named BDS (Bound-Driven Search) that combines features of exact and approximate methods. The proposed procedure may be seen as a local search algorithm that systematically explores (in a branch-and bound sense) the most promising nodes, thus preventing solutions from being reevaluated. Additionally, it can be regarded as an exact method as it may be able to guarantee that the solution found is optimal. We present the application of this new algorithm to a specific problem domain: the permutation flow shop scheduling problem with makespan objective. The subsequent computational experiments are encouraging, as the algorithm is able to yield exact or near exact solutions to most instances of the problem. Furthermore, the algorithm outperforms one of the best state-of-the-art algorithms for the problem.     

Random Databases with Approximate Record Matching

In many database applications in telecommunication, environmental and health sciences, bioinformatics, physics, and econometrics, real-world data are uncertain and subjected to errors. These data are processed, transmitted and stored in large databases. We consider stochastic modelling for databases with uncertain data and for some basic database operations (for example, join, selection) with exact and approximate matching. Approximate join is used for merging or data deduplication in large databases. Distribution and mean of the join sizes are studied for random databases. A random database is treated as a table with independent random records with a common distribution (or a set of random tables). These results can be used for integration of information from different databases, multiple join optimization, and various probabilistic algorithms for structured random data.     

Exact asymptotics of the characteristic polynomial of the symmetric Pascal matrix

We have obtained the exact asymptotics of the determinant . Inverse symbolic computing methods were used to obtain exact analytical expressions for all terms up to relative order L⁻¹⁴ to the leading term. This determinant is known to give weighted enumerations of cyclically symmetric plane partitions, weighted enumerations of certain families of vicious walkers and it has been conjectured to be proportional to the one point function of the O(1) loop model on a cylinder of circumference L. We apply our result to the loop model and give exact expressions for the asymptotics of the average of the number of loops surrounding a point and the fluctuation in this number. For the related bond percolation model at the critical point, we give exact expressions for the asymptotics of the probability that a point is on a cluster that wraps around a cylinder of even circumference and the probability that a point is on a cluster spanning a cylinder of odd circumference.     

New kink-shaped solutions and periodic wave solutions for the (2+1)-dimensional Sine-Gordon equation

New exact solutions including the kink-shaped solutions, bell-shaped solutions, periodic solutions, singular soliton solutions and rational solution for the (2 + 1)-dimensional Sine-Gordon equation are obtained using the tanh method, the -expansion method and the auxiliary function method, respectively.     

A multi-level search strategy for the 0-1 Multidimensional Knapsack Problem

We propose an exact method based on a multi-level search strategy for solving the 0-1 Multidimensional Knapsack Problem. Our search strategy is primarily based on the reduced costs of the non-basic variables of the LP-relaxation solution. Considering that the variables are sorted in decreasing order of their absolute reduced cost value, the top level branches of the search tree are enumerated following Resolution Search strategy, the middle level branches are enumerated following Branch & Bound strategy and the lower level branches are enumerated according to a simple Depth First Search enumeration strategy. Experimentally, this cooperative scheme is able to solve optimally large-scale strongly correlated 0-1 Multidimensional Knapsack Problem instances. The optimal values of all the 10 constraint, 500 variable instances and some of the 30 constraint, 250 variable instances of the OR-Library were found. These values were previously unknown.     

A note on exact complex travelling wave solutions for (2+1)-dimensional B-type Kadomtsev-Petviashvili equation

The -expansion method can be used for constructing exact travelling wave solutions of real nonlinear evolution equations. In this paper, we improve the -expansion method and explore new application of this method to (2+1)-dimensional B-type Kadomtsev-Petviashvili (BKP) equation. New types of exact complex travelling wave solutions of (2+1)-dimensional BKP equation are found. Some exact solutions of (2+1)-dimensional BKP equation obtained before are special cases of our results in this paper.     

Strong convergence of approximate solutions for nonlinear hyperbolic equation without convexity

Schonbek [M.E. Schonbek, Convergence of solutions to nonlinear dispersive equations, Comm. Partial Differential Equations 7 (1982) 959-1000] obtained the strong convergence of uniform bounded approximate solutions to hyperbolic scalar equation under the assumption that the flux function is strictly convex. While in this paper, by constructing four families of Lax entropies, we succeed in dealing with the non-convexity with the aid of the well-known Bernstein-Weierstrass theorem, and obtaining the strong convergence of uniform L^∞ or bounded viscosity solutions for scalar conservation law without convexity.     

Approximation par des Nombres Algébriques de Degré Borné et Dimension de Hausdorff

We compute the generalized Hausdorff measure of sets of real numbers close to infinitely many algebraic numbers of fixed degree. Thus, we provide an extension to results of Jarn?́k and of Baker and Schmidt.     

An application of the branch,bound, and remember algorithm to a new simple assembly line balancing dataset

The simple assembly line balancing problem (SALBP) is a well-studied NP-complete problem for which a new problem database of generated instances was published in 2013. This paper describes the application of a branch, bound, and remember (BB&R) algorithm using the cyclic best-first search strategy to this new database to produce provably exact solutions for 86% of the unsolved problems in this database. A new backtracking rule to save memory is employed to allow the BB&R algorithm to solve many of the largest problems in the database.     

Exact solutions for the generalized Klein–Gordon equation via a transformation and Exp-function method and comparison with Adomian’s method

In this paper, a suitable transformation and a so-called Exp-function method are used to obtain different types of exact solutions for the generalized Klein–Gordon equation. These exact solutions are in full agreement with the previous results obtained in Refs. [Sirendaoreji, Auxiliary equation method and new solutions of Klein–Gordon equations, Chaos, Solitons & Fractals 31 (4) (2007) 943–950; Huiqun Zhang, Extended Jacobi elliptic function expansion method and its applications, Communications in Nonlinear Science and Numerical Simulation, 12 (5) (2007) 627–635]. One of these exact solutions is compared with the approximate solutions obtained by the modified decomposition method. Accurate numerical results for a wider range of time are obtained after using different types of ADM-Padè approximation. Our results show that the Exp-function method is very effective in finding exact solutions for the problem considered while the modified decomposition method is very powerful in finding numerical solutions with good accuracy for nonlinear PDE without any need for a transformation or perturbation.     

On width of resonance for one-dimensional differential operators

In this paper, the resonance problems have been studied for one dimensional Schrö-dinger operator with a general class of potentials. We construct its approximate solution with exact bound, and use the approximate solution to get the asymptotic of width of resonance.     

An exact algorithm for team orienteering problems

Optimising routing of vehicles constitutes a major logistic stake in many industrial contexts. We are interested here in the optimal resolution of special cases of vehicle routing problems, known as team orienteering problems. In these problems, vehicles are guided by a reward that can be collected from customers, while the length of routes is limited. The main difference with classical vehicle routing problems is that not all customers have to be visited. The solution method we propose here is based on a Branch & Price algorithm. It is, as far as we know, the first exact method proposed for such problems, except for a preliminary work from Gueguen (Methodes de résolution exacte pour problémes de tournées de véhicules. Thése de doctorat, école Centrale Paris 1999) and a work from Butt and Ryan (Comput Oper Res 26(4):427–441 1999). It permits to solve instances with up to 100 customers.      

Graph designs for the eight-edge five-vertex graphs

The existence of graph designs for the two nonisomorphic graphs on five vertices and eight edges is determined in the case of index one, with three possible exceptions in total. It is established that for the unique graph with vertex sequence (3, 3, 3, 3, 4), a graph design of order n exists exactly when and n≠16, with the possible exception of n=48. For the unique graph with vertex sequence (2,3,3,4,4), a graph design of order n exists exactly when , with the possible exceptions of n∈{32,48}.     

The incidence game chromatic number

We introduce the incidence game chromatic number which unifies the ideas of game chromatic number and incidence coloring number of an undirected graph. For k-degenerate graphs with maximum degree Δ, the upper bound 2Δ+4k−2 for the incidence game chromatic number is given. If Δ≥5k, we improve this bound to the value 2Δ+3k−1. We also determine the exact incidence game chromatic number of cycles, stars and sufficiently large wheels and obtain the lower bound for the incidence game chromatic number of graphs of maximum degree Δ.     

Resolvable group divisible designs with block size four and general index

In this paper, we investigate the existence of resolvable group divisible designs (RGDDs) with block size four, group-type hⁿ and general index λ. The necessary conditions for the existence of such a design are n≥4, and . These necessary conditions are shown to be sufficient for all λ≥2, with the definite exceptions of (λ,h,n)∈{(3,2,6)}∪{(2j+1,2,4):j≥1}. The known existence result for λ=1 is also improved.     

Comparative evaluation of performance of national R&D programs with heterogeneous objectives: A DEA approach

The strategic importance of performance evaluation of national R&D programs is highlighted as the resource allocation draws more attention in R&D policy agenda. Due to the heterogeneity of national R&D programs’ objectives, however, it is intractably difficult to relatively evaluate multiple programs and, consequently, few studies have been conducted on the performance comparison of the R&D programs. This study measures and compares the performance of national R&D programs using data envelopment analysis (DEA). Since DEA allows each DMU to choose the optimal weights of inputs and outputs which maximize its efficiency, it can mirror R&D programs’ unique characteristics by assigning relatively high weights to the variables in which each program has strength. Every project in every R&D program is evaluated together based on the DEA model for comparison of efficiency among different systems. Kruskal–Wallis test with a post hoc Mann–Whitney U test is then run to compare performance of R&D programs. Two alternative approaches to incorporating the importance of variables, the AR model and output integration, are also introduced. The results are expected to provide policy implications for effectively formulating and implementing national R&D programs.