Charu Goel

King George's Medical University | CSM · Department of Physiology

In 1888, Hilbert proved that the cone $\mathcal{P}_{n+1,2d}$ of positive semidefinite forms in $n+1$ variables of degree $2d$ coincides with its subcone $\Sigma_{n+1,2d}$ of those forms that are representable as finite sums of squares if and only if $(n+1,2d) = (2,2d)_{d\geq1}$ or $(n+1,2)_{n\geq1}$ or $(3,4)$. These are the Hilbert cases. In [GHK2...

For n , d ∈ ℕ, the cone 𝓟 n +1,2 d of positive semidefinite real forms in n + 1 variables of degree 2 d contains the subcone Σ n +1,2 d of those representable as finite sums of squares of real forms. Hilbert [11] proved that these cones coincide exactly in the Hilbert cases ( n + 1, 2 d ) with n + 1 = 2 or 2 d = 2 or ( n + 1, 2 d ) = (3, 4). In thi...

The cone $\mathcal{P}_{n+1,2d}$ ($n,d\in\mathbb{N}$) of all positive semidefinite (PSD) real forms in $n+1$ variables of degree $2d$ contains the subcone $\Sigma_{n+1,2d}$ of those that are representable as finite sums of squares (SOS) of real forms of half degree $d$. In 1888, Hilbert proved that these cones coincide exactly in the Hilbert cases $...

Background: Traditional lectures (using PowerPoint presentation or chalk and board) have become less effective, monotonous, and involve less student-teacher interaction. Introducing peer-assisted learning (PAL) may improve learning by increased student-teacher interaction, making interesting, and more effective for better student outcome, producing...

Hilbert proved in 1888 that a positive semidefinite (psd) real form is a sum of squares (sos) of real forms if and only if or or , where n is the number of variables and 2d the degree of the form. We study the analogue for even symmetric forms. We establish that an even symmetric n-ary 2d-ic psd form is sos if and only if or or or .

Background: Type 2 diabetes mellitus (DM) has a strong genetic component. Individuals of a parent with type 2 DM have an increased (40%) risk of diabetes. If both parents have type 2 DM, the risk approaches to 70%. Thus, this study was designed to evaluate cardiovascular parasympathetic functions in offsprings of type 2 diabetic parents. Aims and O...

In this paper we consider a famous theorem of Hilbert from 1888 stating that a positive semidefinite (psd) real form is a sum of squares (sos) of real forms if and only if $n=2$ or $d=1$ or $(n,2d)=(3,4)$, where $n$ is the number of variables and $2d$ the degree of the form. In 1976, Choi and Lam proved the analogue of Hilbert's Theorem for symmetr...