This commentary succinctly summarizes work in integrating case-based reasoning (CBR) with other reasoning modalities. Including CBR in mixed mode approaches promotes synergies and benefits beyond those achievable using CBR or other individual reasoning approaches alone. Numerous examples of hybrid systems, with pointers to significant references, are provided.

We introduce a notion of training methodology space (TM space) for specifying training methodologies in tile different disciplines and teaching traditions associated with computational linguistics and the human language technologies, and pin our approach to the concept of operational model; we also discuss different general levels of interactivity. A number of operational models are introduced,...

Solving the multi-hour survivable network design problem entails finding the most cost efficient network design given two or more demand matrices that represent network traffic for different (busy-)hours. In addition to capacity installations, feasible routings that satisfy the traffic requirements for all of the demand matrices need to be determined. The problem is formulated as a mixed-intege...

This paper proposes a trajectory planning and tracking approach for bilinear systems that approximate weakly nonlinear systems, based on orthogonal functions and especially the use of operational integration and product matrices. These operational tools allow the conversion of a bilinear differential state equation into an algebraic one depending on initial and final conditions. Arranging and s...

In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

*Correspondence: [email protected] Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, China Abstract This paper uses new fractional integration operational matrices to solve a class of fractional neutral pantograph delay differential equations. A fractional-order function space is constructed where the exact solution lies in, and a set of orthogonal bases are given. Us...

in this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. this leads to the characterization of a matrix for which the regularity index and the index are identical. further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.

In this paper, a numerical approach for solving systems of nonlinear fractional differential equations (FDEs) is presented Using the Euler wavelets technique and associated operational matrices integration, we try to solve those FDEs. The method’s major objective transform FDE into system algebraic that straightforward with matrix techniques. are constructed using polynomials, which have fewer ...

The fermionic, bosonic and supersymmetric variants of the colour-flavour transformation are derived for the orthogonal group. These transformations are then used to calculate the ensemble averages of characteristic polynomials of real random matrices. 1 Statement of main results Since the pioneering work of Wigner, many physical systems have been successfully studied with the help of random mat...