Inertia, Knowledge Sources and Diversity in Collaborative Problem-solving

Innovation is at the core of firms’ competitiveness. External knowledge is increasingly leveraged in the efforts to increase innovation performance by solving innovation related problems and thereby developing new technology, products or services. Using internal knowledge sources can be beneficial when pursuing minor performance improvements in existing technologies. However, reliance on internal knowledge sources carries a risk of organizational inertia related to problem understanding and solution development in the shape of path-dependencies and preferences for exploitation and reapplication of existing knowledge. Such inertia may imbue innovation processes related to the development of new technologies with reduced novelty and an inability to recognize alternative and potentially more attractive solutions. As a result, over-reliance on internal knowledge sources is likely to inhibit the ability to solve problems and reduce innovation performance related to the development of new technology. In contrast, a growing stream of research shows the positive effect on problem-solving and innovation performance from drawing on diverse knowledge sources outside the firm. Through collaborative efforts involving universities, customers, competitors and suppliers in problem-solving firms can gain complementary perspectives, insights and technological knowledge as they pursue the development of innovative technologies

THE INSTRUCTION TO OVERCOME THE INERT KNOWLEDGE ISSUE IN SOLVING MATHEMATICAL PROBLEM

One characteristic of typical mathematical problem is that it requires bunch of relevant prior knowledge. This knowledge is built consecutively and is recalled whenever needed to promote student to solve the problem. The process undertaken by the solver to utilize existing relevant prior knowledge while solving the problem is called access. However, this access is possible subject to disturbance for some reasons. This literature study addresses some factors that can distract access: factor related to metaprocess and factor related to deficit structure. The variants included in both factors have been proved through research as the contributors of the accessibility of relevant prior knowledge. Knowledge that cannot be accessed is called inert knowledge, the main reason for why solver face the difficulty to find the answer to given mathematical problem. The explanation leads to the suggestion of how to tackle the inertia of particular knowledge. One of them are through the instruction setting. Realistic Mathematics Education as one of approaches in learning can be a possible alternative for the issue of inert knowledge. Keywords.  Mathematical problem solving, prior knowledge, access, inert knowledge, Realistic Mathematics Education &nbsp

Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes' theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a "virtual" spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this "virtual" body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The following typos present in the Journal version are HERE corrected: 1) Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3) Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6

The Event Calculus Assessed

The range of applicability of the Full Event Calculus is proven to be the Ksp-IA class in the Features and Fluents taxonomy. The proof is given with respect to the original definition of this preference logic, where no adjustments of the language or reasoning method were necessary. The result implies that the claims on the expressiveness and problem-solving power of this logic were indeed correct

Case Based Reasoning and TRIZ : a coupling for Innovative conception in Chemical Engineering

With the evolutions of the surrounding world market, researchers and engineers have to propose technical innovations. Nevertheless, Chemical Engineering community demonstrates a small interest for innovation compared to other engineering fields. In this paper, an approach to accelerate inventive preliminary design for Chemical Engineering is presented. This approach uses Case Based Reasoning (CBR) method to model, to capture, to store and to make available the knowledge deployed during design. CBR is a very interesting method coming from Artificial Intelligence, for routine design. Indeed, in CBR the main assumption is that a new problem of design can be solved with the help of past successful ones. Consequently, the problem solving process is based on past successful solutions therefore the design is accelerated but creativity is limited and not stimulated. Our approach is an extension of the CBR method from routine design to inventive design. One of the main drawbacks of this method is that it is restricted in one particular domain of application. To propose inventive solution, the level of abstraction for problem resolution must be increased. For this reason CBR is coupled with the TRIZ theory (Russian acronym for Theory of solving inventive problem). TRIZ is a problem solving method that increases the ability to solve creative problems thanks to its capacity to give access to the best practices in all the technical domains. The proposed synergy between CBR and TRIZ combines the main advantages of CBR (ability to store and to reuse rapidly knowledge) and those of TRIZ (no trade off during resolution, inventive solutions). Based on this synergy, a tool is developed and a mere example is treated

Exact Analytic Solution for the Rotation of a Rigid Body having Spherical Ellipsoid of Inertia and Subjected to a Constant Torque

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" In particular: typos present in Eq. 28 of the Journal version are HERE correcte