Algebraic solution to interval equilibrium equations of truss structures

This paper considers a recently proposed interval algebraic model of linear equilibrium equations in mechanics. Based on the algebraic completion of classical interval arithmetic (called Kaucher arithmetic), this model provides much smaller ranges for the unknowns than the model based on classical interval arithmetic and fully conforms to the equilibrium principle. The general form of interval equilibrium equations for truss structures is presented. Two numerical approaches for finding the formal (algebraic) solution to the considered class of interval equilibrium equations are proposed. A methodology for adjusting interval parameters so that the equilibrium equations be completely satisfied is also presented. Numerical examples illustrate the theoretical considerations.     

A fast and robust method for damage detection of truss structures

Use of optimization search algorithms is recognized as an efficient method for solving structural damage identification problems. Although these algorithms demonstrated their robustness to identify the location and extent of multiple damages in structural systems, they impose so much computational efforts to the damage assessing process that it reduces their attraction. In this paper by utilizing the concept of residual force vector, an efficient approach based on a Truss Element Damage Index (TEDI) is defined to assist in a fast and reliable prediction of damaged elements. Based on the proposed technique, the first step focuses on location detection of most probable damaged members. The healthy members will then be eliminated from the total list of variables. This can reduce the computational effort significantly. In the second step to identify damaged locations and severities, the Genetic Algorithm is employed to search for the optimum solution in the new search space resulted from the first step. Three test examples are considered to investigate the efficiency of proposed method for damage identification.     

FEM Shakedown of uncertain structures by chance constrained programming

We present a new primal-dual numerical algorithm of the shakedown problem under uncertainty in which the material strength is considered as a normally distributed random variable. Using chance constrained programming, we obtain deterministic equivalent formulations based on upper bound and lower bound theorems which are dual to each other. The proposed algorithm is tested in numerical examples which are applied to civil engineering structures. The obtained solutions show good performance. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems

FEM discretizations of arbitrary order r are considered for a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits strong layers. A posteriori error bounds of interpolation type are derived in the maximum norm. An adaptive algorithm is devised to resolve the boundary layers. Numerical experiments complement our theoretical results.     

Exponential change of measure applied to term structures of interest rates and exchange rates

In this paper, we study the term structures of interest rates and foreign exchange rates through establishing a state-price deflator. The state-price deflator considered here can be viewed as an extension to the potential representation of the state-price density in [Rogers, L.C.G., 1997. The potential approach to the term structure of interest rates and foreign exchange rates. Mathematical Finance 7(2), 157-164]. We identify a risk-neutral probability measure from the state-price deflator by a technique of exponential change of measure for Markov processes proposed by [Palmowski, Z., Rolski, T., 2002. A technique for exponential change of measure for Markov processes. Bernoulli 8(6), 767-785] and present examples of several classes of diffusion processes (jump-diffusions and diffusions with regime-switching) to illustrate the proposed theory. A comparison between the exponential change of measure and the Esscher transform for identifying risk-neutral measures is also presented. Finally, we consider the exchange rate dynamics by virtue of the ratio of the current state-price deflators between two economies and then discuss the pricing of currency options.     

Alternative T-complete systems of shape functions applied in analytical Trefftz finite elements

The authors compare the behavior of hybrid Trefftz p-elements with two different types of shape functions identically fulfilling governing differential equations. Numerical examples include several boundary problems for Laplace, Poisson, and plane elasticity equations. Accuracy of the solutions, convergence properties, numerical stability and sensitivity for mesh distortion are investigated. It is shown that both systems of the functions can be efficiently applied, although they have different properties. © 1995 John Wiley & Sons, Inc.     

Application of Reduced-set Pareto-Lipschitzian Optimization to truss optimization

In this paper, a recently proposed global Lipschitz optimization algorithm Pareto-Lipschitzian Optimization with Reduced-set (PLOR) is further developed, investigated and applied to truss optimization problems. Partition patterns of the PLOR algorithm are similar to those of DIviding RECTangles (DIRECT), which was widely applied to different real-life problems. However here a set of all Lipschitz constants is reduced to just two: the maximal and the minimal ones. In such a way the PLOR approach is independent of any user-defined parameters and balances equally local and global search during the optimization process. An expanded list of other well-known DIRECT-type algorithms is used in investigation and experimental comparison using the standard test problems and truss optimization problems. The experimental investigation shows that the PLOR algorithm gives very competitive results to other DIRECT-type algorithms using standard test problems and performs pretty well on real truss optimization problems.     

Comparison of theories for stability of truss structures. Part 1: Computation of critical load

Two largely different theories, i.e. the geometric nonlinear eigenvalue theory and the geometric nonlinear critical point theory, of the stability analysis for truss structures are reviewed by the authors. In this paper, it is pointed out through numerical examples as well as thoroughly theoretical investigations that the eigenvalue theory leads to mistakenly very large solutions of critical load. Though it is correct in theory, the applicability of the critical point theory was inadequately extended to all shallow trusses. To overcome the shortcomings of the stability theories, the authors present two theories of their own with two new approaches for geometric nonlinear analysis and for finding the critical loads for shallow truss structures. Several conclusions are drawn, including: (1) the geometric nonlinear eigenvalue theory is mistaken and (2) the capabilities of various theories are discussed.     

Comparison of theories for stability of truss structures. Part 2: Computation of critical solution of stability

Critical solution of stability is the optimum solution of cross-sectional area with stability constraint. By applying the linear Eulerian theory of stability, the critical solution with discrete variables for general truss structures is computed in this paper. Then, in order to compare the results with the ones in previous publications and to reveal the applicability of various theories of stability, the critical solutions with continuous cross-sectional areas are computed for several examples by applying various theories of stability.     

Asymptotic vulnerability of positional voting rules to coalitional manipulation

Voting rule performances are sometimes evaluated according to their respective resistances to allow profitable misrepresentation of individual preferences. This seems to be a hard task when scoring systems with possibly non integer weights are involved. In this paper, it is shown how one can still obtain asymptotic results in these settings. Our analysis for three-candidate elections provides a characterization of unstable voting situations at which a positional voting rule is manipulable by some coalition not larger than an arbitrary proportion of the electorate. This allows us to address a conjecture by Pritchard and Wilson (2007). That is, under the Impartial Anonymous Culture (IAC), the plurality rule asymptotically minimizes the vulnerability to coalitional manipulation when the size of the manipulating coalition is unrestricted. This later result is no longer valid when only manipulation by small coalitions is considered: now, the Borda rule tends to outperform other rules. Furthermore, the vulnerability of a positional voting rule to coalitional manipulation is not affected by increasing the size of the manipulating coalition from 0.5 to 1.     

Alternative Models of Salesmen's Response to Financial Incentives

The assumption underlying any sales force incentive compensation plan is that salesmen react to financial incentives according to some definite and consistent pattern. In order to influence salesmen's activities through financial compensation a manager must know the “rule” salesmen follow in reacting to money incentives. There is relatively little theoretical and empirical research in this area and the partial findings do not support the presence of a single behavioural pattern in response to financial incentives.This paper describes a model mainly based on a series of linear programs simulating salesmen's reactions to financial incentives under alternative basic behavioural hypotheses. By determining which hypothesis best explains actual data, a sales manager can possibly identify and infer the rule followed by his salesmen, and adjust the compensation scheme accordingly. The implications of such results for compensating salesmen are noted and a sample application of the model to an actual situation is described.     

Modeling criminality: the impact of emotions,norms and interaction structures

Criminal behavior has been explained in the literature by rational or normative arguments. We propose a game theory framework of criminal behavior integrating both concepts. Specifically the modeling includes three factors, namely the gain from criminality, the adherence to a legal norm and social pressure from criminal peers. We show that criminality cannot be lower with increasing gain from criminality, lower adherence to the legal norm or higher social pressure from criminal peers. Finally, we observe by agent-based simulations that small local interaction structures lead to spatial segregation in criminality in the case where a polymorphic equilibrium is expected.     

On Transition to Turbulence and Synthesis of Alternative Approaches

In the study of complex systems, controversial debates often arise among advocates of different schools of thought. In this article, we examine how such controversies should be addressed, with the problem of transition to turbulence as a primary example. It is shown that, in many cases, these controversies may be resolved by first noting that the alternative theories proposed may not be mutually exclusive. Indeed, they may even be mutually complementary, if they were originally developed to address similar issues in different physical contexts. In any case, for the validity of the alternative theories proposed, each should be separately and fully supported from both the theoretical and empirical points of view. Each applies to a specific physical context, and each stands on its own merits and limitations. Synthesis into a broader theory may then be achieved, if commonality is identified among the different alternative theories proposed. To demonstrate this conciliatory approach, we begin with an examination of the move toward resolution of the well‐known controversy over the problem of transition to turbulence from the steady laminar flow in the boundary layer over a flat plate. Several other long‐standing controversies have been successfully addressed on the basis of this approach. In addition to the problem of transition to turbulence, we considered, in some detail, two additional examples: (1) the global structures of spiral galaxies; and (2) the theory of jet noise. In all three cases, it is shown that the model approach is meritorious despite the limitations. Synthesis, with a conciliatory approach to apparent conflicts, will be recommended in general as a new part of an extended paradigm in applied mathematics. It is an approach appropriate to situations where an ideal theory, with universal applicability, is elusive. Parallel development of several alternative theories is natural, and a final synthesis is needed. In contrast, it should be noted that the same perspective is generally not expected useful if the controversies concern the unique solution of well‐defined mathematical issues. The potential success of the application of this conciliatory perception and approach to other areas of science are discussed (see Section 5 ).     

An optimization approach to the reconstruction of positional DNA sequencing by hybridization with errors

Positional DNA sequencing by hybridization (PSBH) is a recently proposed enhancement of DNA sequencing by hybridization (SBH, potentially a powerful alternative to the DNA sequencing by gel electrophoresis). It has been discussed in many papers and applied to large scale sequencing by hybridization. However, the computational part of PSBH reconstruction is a difficult problem, especially for the occurrence of hybridization errors. So far the problem has not been solved well. Taking PSBH as a combinatorial optimization problem, a novel reconstruction approach to PSBH is presented in this paper. The proposed approach accepts both the negative and positive errors and can greatly reduce ambiguities in the reconstruction of PSBH. The computational experiment shows that our algorithm works satisfactorily and correctly on the test data, especially for the positive errors and k-tuple repetitions.     

Spectral behaviour of GMRES applied to singular systems

The purpose of this paper is to develop a spectral analysis of the Hessenberg matrix obtained by the GMRES algorithm used for solving a linear system with a singular matrix. We prove that the singularity of the Hessenberg matrix depends on the nature of A and some other criteria such as the zero eigenvalue multiplicity and the projection of the initial residual on particular subspaces. We also show some new results about the distinct kinds of breakdown which may occur in the algorithm when the system is singular.      

An estimate of the stability defect for a positional absorption set subjected to discriminant transformations

We study the problem of reconstruction of functions from the values of the nth differences with step 1/n taken at the point 0. The problem is solved for functions that are analytic in special domains containing the interval [0, 1].     

Some examples of statistical estimation applied to earthquake data

Likelihood methods are described for fitting cyclic Poisson and Hawkes' self-exciting models to Kawasumi's historical earthquake series and to more recent data supplied by the Japan Meteorological Agency. Identification of the model is discussed from the standpoint of an entropy maximization principle. The cyclic effect is shown to be not statistically significant after clustering has been allowed for; its physical significance therefore remains questionable.