The problem of representing a positive semidefinite function (=psd) as a sum of squares (=sos) is a very old matter in real algebra and real geometry. Still, it is a difficult question always appealing the specialists. Concerning real analytic germs we can summarize what is known in a few statements. Let X be a irreducible real analytic set germ of dimension d. Any psd f of X is an sos of merom...

a total of 260709 monthly test day milk records of 30903 first lactation holstein cows was used to determine the best function to describe the lactation curve. the records were obtained from first lactation holstein of 216 herds from 1988 to 2006 in khorasan province. the functions used in current study were wood’s incomplete gamma function, ali and schaeffer function, and legendre function of ...

Given a large data matrix A ∈ Rn×n, we consider the problem of determining whether its entries are i.i.d. from some known marginal distribution Aij ∼ P0, or instead A contains a principal submatrix AQ,Q whose entries have marginal distribution Aij ∼ P1 6= P0. As a special case, the hidden (or planted) clique problem is finding a planted clique in an otherwise uniformly random graph. Assuming un...

In recent years, Sum–Of–Squares (SOS) method has attracted increasing interest as a new approach for stability analysis and controller design of nonlinear dynamic systems. This paper utilizes SOS method to design a robust nonlinear controller for longitudinal dynamics of a hypersonic aircraft model. Specifically, the searching of the nonlinear robust controller is reformulated as a robust SOS/r...

This paper presents gain scheduling (GS) control of a Variable Speed Control Moment Gyroscope (VSCMG) based on sum of squares (SOS). Nonlinear motion equations of the VSCMG are complicated because they contain sine and cosine of angles of gimbals. The dynamics varies depending on an attitude of a spacecraft. In this study, the difficulty of control design of the VSCMG is solved by two methods. ...