Weighted sums of squares in local rings and their completions, II

2009 ◽  
Vol 266 (1) ◽  
pp. 21-42 ◽  
Author(s):  
Claus Scheiderer
Keyword(s):  
Sums Of Squares ◽  
Weighted Sums ◽  
Local Rings

Weighted sums of squares in local rings and their completions, I

2009 ◽  
Vol 266 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Claus Scheiderer
Keyword(s):  
Sums Of Squares ◽  
Weighted Sums ◽  
Local Rings

A solution to weighted sums of squares as a square

2012 ◽  
Vol 43 (8) ◽  
pp. 1099-1108
Author(s):  
Christopher S. Withers ◽  
Saralees Nadarajah
Keyword(s):  
Sums Of Squares ◽  
Weighted Sums

scholarly journals A Welch-type test for comparing K linear contrasts under heteroscedasticity with applications to meta-analysis

2021 ◽  
Author(s):  
Elena Kulinskaya ◽  
Emily Knight ◽  
Haiyan Gao
Keyword(s):  
Meta Analysis ◽  
Null Distribution ◽  
Effect Sizes ◽  
Sums Of Squares ◽  
Weighted Sums ◽  
Control Groups ◽  
Type Test ◽  
Linear Contrasts ◽  
One Way Anova

A test for comparing linear contrasts with heteroscedasticity, both across components of each contrast and between the contrasts, is developed under assumption of normality. The test is based on the weighted sums of squares. This is an extension of methods for weighted one-way ANOVA developed in Welch (1951) under the null, and in Kulinskaya et al. (2000) [12] underthe alternatives. We provide very accurate approximations to the null distribution and to the distribution under alter natives. The quality of these approximations is studied by simulation. The main application is the I by 2 layout which is widespread in meta-analysis. Our methods allow the homo-geneity of effect sizes across I studies to be tested, without the assumption of equal variances in the treatment and the control groups.

scholarly journals Representation of positive semidefinite elements as sum of squares in 2-dimensional local rings

2022 ◽  
Vol 116 (2) ◽  
Author(s):  
José F. Fernando
Keyword(s):  
Residue Field ◽  
Classical Problem ◽  
Positive Semidefinite ◽  
Sum Of Squares ◽  
Sums Of Squares ◽  
Local Rings ◽  
Local Case ◽  
Real Geometry ◽  
Excellent Ring ◽  
The One

AbstractA classical problem in real geometry concerns the representation of positive semidefinite elements of a ring A as sums of squares of elements of A. If A is an excellent ring of dimension $$\ge 3$$ ≥ 3 , it is already known that it contains positive semidefinite elements that cannot be represented as sums of squares in A. The one dimensional local case has been afforded by Scheiderer (mainly when its residue field is real closed). In this work we focus on the 2-dimensional case and determine (under some mild conditions) which local excellent henselian rings A of embedding dimension 3 have the property that every positive semidefinite element of A is a sum of squares of elements of A.

scholarly journals Towards a computational proof of Vizing's conjecture using semidefinite programming and sums-of-squares

2021 ◽  
Vol 107 ◽  
pp. 67-105
Author(s):  
Elisabeth Gaar ◽  
Daniel Krenn ◽  
Susan Margulies ◽  
Angelika Wiegele
Keyword(s):  
Semidefinite Programming ◽  
Sums Of Squares

scholarly journals Correction to: Classification of non-local rings with genus two zero-divisor graphs

2021 ◽  
Vol 25 (4) ◽  
pp. 3355-3356
Author(s):  
T. Asir ◽  
K. Mano ◽  
T. Tamizh Chelvam
Keyword(s):  
Zero Divisor ◽  
Local Rings ◽  
Non Local ◽  
Genus Two
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