844 research outputs found
On the Stanley Depth of Squarefree Veronese Ideals
Let be a field and . In 1982, Stanley defined what is
now called the Stanley depth of an -module , denoted \sdepth(M), and
conjectured that \depth(M) \le \sdepth(M) for all finitely generated
-modules . This conjecture remains open for most cases. However, Herzog,
Vladoiu and Zheng recently proposed a method of attack in the case when with being monomial -ideals. Specifically, their method
associates with a partially ordered set. In this paper we take advantage of
this association by using combinatorial tools to analyze squarefree Veronese
ideals in . In particular, if is the squarefree Veronese ideal
generated by all squarefree monomials of degree , we show that if , then \sdepth(I_{n,d})= \floor{\binom{n}{d+1}\Big/\binom{n}{d}}+d,
and if and , then d+3\le \sdepth(I_{n,d}) \le
\floor{\binom{n}{d+1}\Big/\binom{n}{d}}+d.Comment: 10 page
Back to the drawing board : architecture, sculpture, and the digital image
Wissenschaftliches Kolloquium vom 19. bis 22. April 2007 in Weimar an der Bauhaus-Universität zum Thema: ‚Die Realität des Imaginären. Architektur und das digitale Bild
The Reversal Ratio of a Poset
Felsner and Reuter introduced the linear extension diameter of a partially
ordered set , denoted \mbox{led}(\mathbf{P}), as the maximum
distance between two linear extensions of , where distance is
defined to be the number of incomparable pairs appearing in opposite orders
(reversed) in the linear extensions. In this paper, we introduce the reversal
ratio of as the ratio of the linear extension
diameter to the number of (unordered) incomparable pairs. We use probabilistic
techniques to provide a family of posets on at most
elements for which the reversal ratio , where
is a constant. We also examine the questions of bounding the reversal ratio
in terms of order dimension and width.Comment: 10 pages, 2 figures; Accepted for publication in ORDE
Asymptotic Enumeration of Labelled Interval Orders
Building on work by Zagier, Bousquet-M\'elou et al., and Khamis, we give an
asymptotic formula for the number of labelled interval orders on an -element
set.Comment: 6 page
Responsibility accounting (RA) as a tool to enhance cost control. A position paper of retail outlets in Zimbabwe.
This research sought to explore the impact of responsibility accounting as a tool to enhance cost control in businesses. A case study of Zimbabwean retail outlets was used and both theoretical and historical data was collected over half a year period to deduce recommendations from this study. The research observed unwillingness from management in most retail outlets to delegate responsibilities. Management highlighted their greatest fear to delegation being, unskilled subordinates yet the research exposed power hungriness on management’s part. To improve the businesses’ operations, responsibility accounting was recommended, were willingness to delegation of responsibilities was encouraged, a clearly definition of lines of command and decentralisation of decision making to branches was vied for. Key terms: Responsibility accounting, Cost control, Control activity, Segregation of duties, Retail outlets, Zimbabwe.
Electronic structure of the substitutional versus interstitial manganese in GaN
Density-functional studies of the electron states in the dilute magnetic
semiconductor GaN:Mn reveal major differences for the case of the Mn impurity
at the substitutional site Mn_Ga versus the interstitial site Mn_I. The
splitting of the two-fold and the three-fold degenerate Mn(d)states in the gap
are reversed between the two cases, which is understood in terms of the
symmetry-controlled hybridization with the neighboring atoms. In contrast to
Mn_Ga, which acts as a deep acceptor, Mn_I acts as a donor, suggesting the
formation of Coulomb-stabilized complexes such as (Mn_Ga Mn_I Mn_Ga), where the
acceptor level of Mn_Ga is passivated by the Mn_I donor. Formation of such
passivated clusters might be the reason for the observed low carrier-doping
efficiency of Mn in GaN. Even though the Mn states are located well inside the
gap,the wave functions are spread far away from the impurity center. This is
caused by the hybridization with the nitrogen atoms, which acquire small
magnetic moments aligned with the Mn moment. Implications of the differences in
the electronic structure for the optical properties are discussed
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