Differential Balanced Trees and (0,1) Matrices

* The research was supported by INTAS 00-397 and 00-626 Projects.

A Basis for Z-Graded Identities of Matrices over Infinite Fields

2000 Mathematics Subject Classification: 16R10, 16R20, 16R50

Z2-Graded Polynomial Identities for Superalgebras of Block-Triangular Matrices

000 Mathematics Subject Classification: Primary 16R50, Secondary 16W55.

Direct and Inverse Spectral Problems for (2N + 1)-Diagonal, Complex, Symmetric, Non-Hermitian Matrices

2000 Mathematics Subject Classification: 42C05.

A Representation of Binary Matrices

Христина Костадинова, Красимир Йорджев - В статията се обсъжда представянето на произволна бинарна матрица с помощта на последователност от цели неотрицателни числа. Разгледани са някои предимства и недостатъци на това представяне като алтернатива на стандартното, общоприето представяне чрез двумерен масив. Показано е, че представянето на бинарните матрици с помощта на наредени n-торки от естествени числа води до по-бързи алгоритми и до съществена икономия на оперативна памет. Използуван е апарата на обектно-ориентираното програмиране със синтаксиса и семантиката на езика C++.

Properties of the Bellman Gamma Distribution

2000 Mathematics Subject Classification: 62H10.

Using Covariance as a Similarity Measure for Document Language Identification in Hard Contexts

2000 Mathematics Subject Classification: C2P99.

Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring

2000 Mathematics Subject Classification: 15A15, 15A24, 15A33, 16S50.

On Majorization for Matrices

In this paper, we give several results for majorized matrices by using continuous convex function and Green function. We obtain mean value theorems for majorized matrices and also give corresponding Cauchy means, as well as prove that these means are monotonic. We prove positive semi-definiteness of matrices generated by differences deduced from majorized matrices which implies exponential convexity and log-convexity of these differences and also obtain Lypunov's and Dresher's type inequalities for these differences.

The Direct and Inverse Spectral Problems for some Banded Matrices

2000 Mathematics Subject Classification: 15A29.

Microporous polycaprolactone matrices for drug delivery and tissue engineering:the release behaviour of bioactives having extremes of aqueous solubility

Microporous polycaprolactone (PCL) matrices loaded with hydrophobic steroidal drugs or a hydrophilic drug - pilocarpine hydrochloride - were produced by precipitation casting using solutions of PCL in acetone. The efficiency of steroid incorporation in the final matrix (progesterone (56 %) testosterone (46 %) dexamethasone (80 %)) depended on the nature of the drug initially co-dissolved in the PCL solution. Approximately 90 % w/w of the initial load of progesterone, 85 % testosterone and 50 % dexamethasone was released from the matrices in PBS at 37°C over 8 days. Pilocarpine hydrochloride (PH)-loaded PCL matrices, prepared by dispersion of powder in PCL solution, released 70-90 % of the PH content over 12 days in PBS. Application of the Higuchi model revealed that the kinetics of steroid and PH release were consistent with a Fickian diffusion mechanism with corresponding diffusion coefficients of 5.8 × 10-9 (progesterone), 3.9 × 10 -9 (testosterone), 7.1 × 10-10 (dexamethasone) and 22 × 10-8 cm2/s (pilocarpine hydrochloride). The formulation techniques described are expected to be useful for production of implantable, insertable and topical devices for sustained delivery of a range of bioactive molecules of interest in drug delivery and tissue engineering.

An LP-based inconsistency monitoring of pairwise comparison matrices

A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent linear programming problem. The results can be applied in the process of filling in the matrix as the decision maker gets automatic feedback. As soon as a serious error occurs among the matrix elements, even due to a misprint, a significant increase in the inconsistency index is reported. The high inconsistency may be alarmed not only at the end of the process of filling in the matrix but also during the completion process. Numerical examples are also provided.

An inconsistency control system based on incomplete pairwise comparison matrices

Incomplete pairwise comparison matrix was introduced by Harker in 1987 for the case in which the decision maker does not fill in the whole matrix completely due to, e.g., time limitations. However, incomplete matrices occur in a natural way even if the decision maker provides a completely filled in matrix in the end. In each step of the total n(n–1)/2, an incomplete pairwise comparison is given, except for the last one where the matrix turns into complete. Recent results on incomplete matrices make it possible to estimate inconsistency indices CR and CM by the computation of tight lower bounds in each step of the filling in process. Additional information on ordinal inconsistency is also provided. Results can be applied in any decision support system based on pairwise comparison matrices. The decision maker gets an immediate feedback in case of mistypes, possibly causing a high level of inconsistency.

Pairwise comparison matrices and the error-free property of the decision maker

Pairwise comparison is a popular assessment method either for deriving criteria-weights or for evaluating alternatives according to a given criterion. In real-world applications consistency of the comparisons rarely happens: intransitivity can occur. The aim of the paper is to discuss the relationship between the consistency of the decision maker—described with the error-free property—and the consistency of the pairwise comparison matrix (PCM). The concept of error-free matrix is used to demonstrate that consistency of the PCM is not a sufficient condition of the error-free property of the decision maker. Informed and uninformed decision makers are defined. In the first stage of an assessment method a consistent or near-consistent matrix should be achieved: detecting, measuring and improving consistency are part of any procedure with both types of decision makers. In the second stage additional information are needed to reveal the decision maker’s real preferences. Interactive questioning procedures are recommended to reach that goal.

Pairwise comparison matrices: an empirical research

Our research focused on testing various characteristics of pairwise comparison (PC) matrices in controlled experiments. About 270 students have been involved in the test exercises and the final pool contained 450 matrices. Our team conducted experiments with matrices of different size obtained from different types of MADM problems. The matrix elements have been generated by different questioning orders, too. The cases have been divided into 18 subgroups according to the key factors to be analyzed. The testing environment made it possible to analyze the dynamics of inconsistency as the number of elements increased in a given case. Various types of inconsistency indices have been applied. The consequent behavior of the decision maker has also been analyzed in case of incomplete matrices using indicators to measure the deviation from the final ranking of alternatives and from the final score vector.