Weak Z-Property of the Absolute Order on Groups Generated by Sets Closed Under Taking Inverses

International audience The absolute order on the hyperoctahedral group $B_n$ is investigated. It is shown that every closed interval in this order is shellable, those closed intervals which are lattices are characterized and their zeta polynomials are computed. Moreover, using the notion of strong constructibility, it is proved that the order ideal generated by the Coxeter elements of $B_n$ is homotopy Cohen-Macaulay and the Euler characteristic of the order complex of the proper part of this ideal is computed. Finally, an example of a non Cohen-Macaulay closed interval in the absolute order on the group $D_4$ is given and the closed intervals of $D_n$ which are lattices are characterized. Nous étudions l'ordre absolu sur le groupe hyperoctahédral $B_n$. Nous montrons que chaque intervalle fermé de cet ordre est shellable, caractérisons les treillis parmi ces intervalles et calculons les polynômes zêta de ces derniers. De plus, en utilisant la notion de constructibilité forte, nous prouvons que l'idéal engendré par les éléments de Coxeter de $B_n$ est Cohen-Macaulay pour l'homotopie, et nous calculons la caractéristique d'Euler du complexe associé à cet idéal. Pour finir, nous exhibons un exemple d'intervalle fermé non Cohen-Macaulay dans l'ordre absolu du groupe $D_4$, et caractérisons les intervalles fermés de $D_n$ qui sont des treillis.

Download Full-text

Determination of the absolute order of shadow moiré fringes by using two differently colored light sources

Applied Optics ◽

10.1364/ao.33.000130 ◽

1994 ◽

Vol 33 (1) ◽

pp. 130 ◽

Cited By ~ 10

Author(s):

Keun Cheol Yuk ◽

Jae Heung Jo ◽

Soo Chang

Keyword(s):

Light Sources ◽

Shadow Moire ◽

Shadow Moiré ◽

Absolute Order ◽

Moiré Fringes ◽

The Absolute

Download Full-text

Crossed-line grating method for determining the absolute order of shadow moire fringes

10.1117/12.324582 ◽

1998 ◽

Cited By ~ 1

Author(s):

Keun C. Yuk ◽

Jae Heung Jo ◽

Soo Chang

Keyword(s):

Shadow Moire ◽

Shadow Moiré ◽

Absolute Order ◽

Moiré Fringes ◽

The Absolute

Download Full-text

Bulk standards for low-temperature biological x-ray microanalysis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100111525 ◽

1984 ◽

Vol 42 ◽

pp. 282-283

Author(s):

P. Echlin ◽

M. McKoon ◽

E.S. Taylor ◽

C.E. Thomas ◽

K.L. Maloney ◽

...

Keyword(s):

Phase Separation ◽

Low Temperature ◽

Analytical Method ◽

Salt Solutions ◽

Absolute Concentration ◽

Cooling Process ◽

X Ray ◽

The Absolute ◽

Analytical Procedures ◽

Electrical Conductors

Although sections of frozen salt solutions have been used as standards for x-ray microanalysis, such solutions are less useful when analysed in the bulk form. They are poor thermal and electrical conductors and severe phase separation occurs during the cooling process. Following a suggestion by Whitecross et al we have made up a series of salt solutions containing a small amount of graphite to improve the sample conductivity. In addition, we have incorporated a polymer to ensure the formation of microcrystalline ice and a consequent homogenity of salt dispersion within the frozen matrix. The mixtures have been used to standardize the analytical procedures applied to frozen hydrated bulk specimens based on the peak/background analytical method and to measure the absolute concentration of elements in developing roots.

Download Full-text

A Quantitative Ultrastructural Study of Peripheral Blood Lymphocytes Containing Parallel Tubular Arrays in Epstein-Barr Virus and Cytomegalo-Virus Mononucleosis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100098769 ◽

1981 ◽

Vol 39 ◽

pp. 454-455

Author(s):

C. M. Payne ◽

P. M. Tennican

Keyword(s):

Peripheral Blood ◽

Lymphocyte Count ◽

Epstein Barr Virus ◽

Absolute Lymphocyte Count ◽

Peripheral Blood Lymphocytes ◽

Clinical State ◽

Barr Virus ◽

The Absolute ◽

Epstein Barr ◽

Tubular Arrays

In the normal peripheral circulation there exists a sub-population of lymphocytes which is ultrastructurally distinct. This lymphocyte is identified under the electron microscope by the presence of cytoplasmic microtubular-like inclusions called parallel tubular arrays (PTA) (Figure 1), and contains Fc-receptors for cytophilic antibody. In this study, lymphocytes containing PTA (PTA-lymphocytes) were quantitated from serial peripheral blood specimens obtained from two patients with Epstein -Barr Virus mononucleosis and two patients with cytomegalovirus mononucleosis. This data was then correlated with the clinical state of the patient.It was determined that both the percentage and absolute number of PTA- lymphocytes was highest during the acute phase of the illness. In follow-up specimens, three of the four patients' absolute lymphocyte count fell to within normal limits before the absolute PTA-lymphocyte count.In one patient who was followed for almost a year, the absolute PTA- lymphocyte count was consistently elevated (Figure 2). The estimation of absolute PTA-lymphocyte counts was determined to be valid after a morphometric analysis of the cellular areas occupied by PTA during the acute and convalescent phases of the disease revealed no statistical differences.

Download Full-text