A sign pattern matrix is a matrix whose entries are from the set {+,-, 0}. For a real matrix B, sgn(B) is the sign pattern matrix obtained by replacing each positive respectively, negative, zero) entry of B by + (respectively, -, 0). For a sign pattern matrixA, the sign pattern class of A, denoted Q(A), is defined as { B : sgn(B)= A }. The minimum rank mr(A)(maximum rank MR(A)) of a sign pattern matrix A is the minimum (maximum) of the ranks of the real matrices in Q(A). Several results concerning sign patterns A that require almost unique rank, that is to say, the sign patterns A such that MR(A)= mr(A)+1 are established. In particular, a complete characterization of these sign patterns is obtained. Further, the results on sign patterns that require almost unique rank are extended to sign patterns A for which the spread is d =MR(A)-mr(A).

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The action of various operations on the cohomology of nilpotent Lie algebras is studied. In the cohomology of any Lie algebra, we show that the existence of certain nontrivial compositions of higher cohomology operations implies the existence of hypercube-like structures in cohomology, which in turn establishes the Toral Rank Conjecture for that Lie algebra. We provide examples in low dimensions and exhibit an infinite family of nilpotent Lie algebras of arbitrary dimension for which such structures exist. A new proof of the Toral Rank Conjecture is also given for free two-step nilpotent Lie algebras.

Inaug.-diss.--Breslau. / Lebenslauf. "Literaturverzeichnis": p. 73-74.

Inaug.-diss.--Breslau. / Lebenslauf. "Literaturverzeichnis": p. 73-74.

The action of various operations on the cohomology of nilpotent Lie algebras is studied. In the cohomology of any Lie algebra, we show that the existence of certain nontrivial compositions of higher cohomology operations implies the existence of hypercube-like structures in cohomology, which in turn establishes the Toral Rank Conjecture for that Lie algebra. We provide examples in low dimensions and exhibit an infinite family of nilpotent Lie algebras of arbitrary dimension for which such structures exist. A new proof of the Toral Rank Conjecture is also given for free two-step nilpotent Lie algebras.

No description available.

This thesis deals with univariate and multivariate rank methods in making statistical inference. It is assumed that the underlying distributions belong to the class of elliptical distributions. The class of elliptical distributions is an extension of the normal distribution and includes distributions with both lighter and heavier tails than the normal distribution. In the first part of the thesis the rank covariance matrices defined via the Oja median are considered. The Oja rank covariance matrix has two important properties: it is affine equivariant and it is proportional to the inverse of the regular covariance matrix. We employ these two properties to study the problem of estimating the rank covariance matrices when they have a certain structure. The second part, which is the main part of the thesis, is devoted to rank estimation in linear regression models with symmetric heteroscedastic errors. We are interested in asymptotic properties of rank estimates. Asymptotic uniform linearity of a linear rank statistic in the case of heteroscedastic variables is proved. The asymptotic uniform linearity property enables to study asymptotic behaviour of rank regression estimates and rank tests. Existing results are generalized and it is shown that the Jaeckel estimate is consistent and asymptotically normally distributed also for heteroscedastic symmetric errors.

我國辦理公務人員升等考試已有相當歷史，旨在鼓舞現職人員士氣，提供資深績優的現職人員升遷管道，以鼓勵久任、提振士氣；其通過考試者取得升等資格。但在公共行政文獻中對此則少有通盤討論者，本文嘗試以整合性觀點，對相關之升等（資）考試提供說明，列如中央暨地方機關公務人員升等考試、關務人員升等考試、警察人員升等考試、交通事業人員升資考試、台灣地區省（市）營事業機構人員升等考試、行政院所屬金融保險事業機構雇員升等考試…等。 / The Rank Promotion Examinations for Civil Service has been hold for a long time in the R.O.C. It means to boost the morale of public functionaries. It offers channels of advancement for the existing employees with excellent performances to keep them focused and to boost their morale. Public servants who pass the examination can acquire the status for promotion. But few of them have been investigated intergrated in public administration. Therefor, this article uses an integrated view on these relevant area.of Rank Promotion Examinations, Such examinations include the Rank Promotion Examinations for public functionaries of Central and Local Civil Service Organizations, Rank Promotion Examination for Customs Officers, Rank Promotion Examination for Police Personnel, Rank Promotion Examination for Transportation Enterprise Personnel, Rank Promotion Examination for Personnel of Province- and Special Municipality-Operated Businesses, Rank Promotion Examination for hired employees at Financial and Insurance Institutions under the Executive Yuan, etc.