Some constructions of two-associate class PBIB designs

1987 ◽  
Vol 39 (3) ◽  
pp. 671-679
Author(s):  
Snigdha Banerjee ◽  
Sanpei Kageyama ◽  
Bhagwandas
Keyword(s):  
Associate Class

scholarly journals Optimality of Some Two-Associate-Class Partially Balanced Incomplete-Block Designs

1991 ◽  
Vol 19 (3) ◽  
pp. 1667-1671 ◽  
Author(s):  
C.-S. Cheng ◽  
R. A. Bailey
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Designs ◽  
Associate Class ◽  
Balanced Incomplete Block

scholarly journals The Bernstein Projector Determined by a Weak Associate Class of Good Cosets

2021 ◽  
Author(s):  
Yeansu Kim ◽  
Loren Spice ◽  
Sandeep Varma
Keyword(s):  
Fourier Transform ◽  
Characteristic Function ◽  
Lie Algebra ◽  
Equivalence Relation ◽  
Characteristic Zero ◽  
Closed Subset ◽  
Inverse Fourier Transform ◽  
Reductive Group ◽  
Associate Class ◽  
Weak Associate

Abstract Let ${\text G}$ be a reductive group over a $p$-adic field $F$ of characteristic zero, with $p \gg 0$, and let $G={\text G}(F)$. In [ 15], J.-L. Kim studied an equivalence relation called weak associativity on the set of unrefined minimal $K$-types for ${\text G}$ in the sense of A. Moy and G. Prasad. Following [ 15], we attach to the set $\overline{\mathfrak{s}}$ of good $K$-types in a weak associate class of positive-depth unrefined minimal $K$-types a ${G}$-invariant open and closed subset $\mathfrak{g}_{\overline{\mathfrak{s}}}$ of the Lie algebra $\mathfrak{g} = {\operatorname{Lie}}({\text G})(F)$, and a subset $\tilde{{G}}_{\overline{\mathfrak{s}}}$ of the admissible dual $\tilde{{G}}$ of ${G}$ consisting of those representations containing an unrefined minimal $K$-type that belongs to $\overline{\mathfrak{s}}$. Then $\tilde{{G}}_{\overline{\mathfrak{s}}}$ is the union of finitely many Bernstein components of ${G}$, so that we can consider the Bernstein projector $E_{\overline{\mathfrak{s}}}$ that it determines. We show that $E_{\overline{\mathfrak{s}}}$ vanishes outside the Moy–Prasad ${G}$-domain ${G}_r \subset{G}$, and reformulate a result of Kim as saying that the restriction of $E_{\overline{\mathfrak{s}}}$ to ${G}_r\,$, pushed forward via the logarithm to the Moy–Prasad ${G}$-domain $\mathfrak{g}_r \subset \mathfrak{g}$, agrees on $\mathfrak{g}_r$ with the inverse Fourier transform of the characteristic function of $\mathfrak{g}_{\overline{\mathfrak{s}}}$. This is a variant of one of the descriptions given by R. Bezrukavnikov, D. Kazhdan, and Y. Varshavsky in [8] for the depth-$r$ Bernstein projector.

scholarly journals Addenda to "Intra-Block Analysis for Factorials in Two-Associate Class Group Divisible Designs"

1958 ◽  
Vol 29 (3) ◽  
pp. 933-935 ◽  
Author(s):  
Ralph Allan Bradley ◽  
Clyde Young Kramer
Keyword(s):  
Class Group ◽  
Group Divisible Designs ◽  
Associate Class ◽  
Group Divisible

Associate class graph of zero-divisors of a commutative ring

2019 ◽  
Vol 19 (08) ◽  
pp. 2050155
Author(s):  
Gaohua Tang ◽  
Guangke Lin ◽  
Yansheng Wu
Keyword(s):  
Commutative Ring ◽  
Chromatic Number ◽  
Zero Divisor ◽  
New Class ◽  
Associate Class ◽  
Zero Divisor Graph ◽  
Zero Divisors ◽  
Class Graph

In this paper, we introduce the concept of the associate class graph of zero-divisors of a commutative ring [Formula: see text], denoted by [Formula: see text]. Some properties of [Formula: see text], including the diameter, the connectivity and the girth are investigated. Utilizing this graph, we present a new class of counterexamples of Beck’s conjecture on the chromatic number of the zero-divisor graph of a commutative ring.

A criterion for connectedness in two-associate class PBIB designs

1981 ◽  
Vol 5 (2) ◽  
pp. 211-212 ◽  
Author(s):  
N.R. Mohan
Keyword(s):  
Associate Class

scholarly journals Intra-Block Analysis for Factorials in Two-Associate Class Group Divisible Designs

1957 ◽  
Vol 28 (2) ◽  
pp. 349-361 ◽  
Author(s):  
Clyde Young Kramer ◽  
Ralph Allan Bradley
Keyword(s):  
Class Group ◽  
Group Divisible Designs ◽  
Associate Class ◽  
Group Divisible

Ranking of PBIBD's with Regard to A-Optimality Criterion Under A Mixed Model

1981 ◽  
Vol 30 (1-2) ◽  
pp. 57-64
Author(s):  
Sunanda Mukhopadhyay
Keyword(s):  
Fixed Effects ◽  
Mixed Model ◽  
Functional Form ◽  
Optimality Criterion ◽  
Association Schemes ◽  
Fixed Effects Model ◽  
Associate Class ◽  
Variance Formula ◽  
Average Variance

For the problem of estimation of all elementary treatment contraata, restrictina ourselves to PBIBD's with two clus association schemea under a mixed model we follow the approach of Sinha and Sinha (1969) to study the behaviour of tho average variance [Formula: see text] as a function of [Formula: see text] and also as a function of the auociation scheme to some extent. The functional form of [Formula: see text] turna out to be the Jame as that under fixed effects model and either [Formula: see text] for all admissible θ>0. We got that when a BIB dosian does not exist with tho alven parameters a GO design with [Formula: see text] if it exists, is A-optimal within the class of all PBIB designs with two associate class association schemes. This proves that in respect of A-optimality, the result of Chong (1978) can be extended to all GD designs with [Formula: see text] if we restrict ourselves to such PBIB dosigns.

Efficiency Bounds for Partially Balanced Change-Over Designs Based on M- Associate Class PBIB Designs

1985 ◽  
Vol 47 (1) ◽  
pp. 132-135
Author(s):  
D. Raghavarao ◽  
E. A. Blaisdell
Keyword(s):  
Associate Class

scholarly journals Tables of Two-Associate-Class Partially Balanced Designs.

1975 ◽  
Vol 24 (3) ◽  
pp. 230
Author(s):  
D. A. Preece ◽  
Willard H. Clatworthy
Keyword(s):  
Associate Class ◽  
Balanced Designs
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