Every symmetric polynomial p = p(x) = p(x1, . . . , xg) (with real coefficients) in g noncommuting variables x1, . . . , xg can be written as a sum and difference of squares of noncommutative polynomials:

Modified xanthan gum is often used in a variety of industries such as pharmaceuticals, the food industry, and oil industry. The use modified emulsions can solve two problems, stabilize thicken. This work dedicated to study oil-in-water emulsion stability. continuous phase consists aqueous solutions (XG-g-MMA), alkyl polyglycoside (APG), silicon dioxide nanoparticles (SiO2), kerosene was dispers...

PURPOSE To evaluate the efficacy and safety of two ophthalmic solutions in patients with mild to moderate dry eye. METHODS We performed a prospective, 2-month-long, randomized, double-blind, single-center, parallel clinical trial to compare the efficacy and safety of two ophthalmic solutions for dry eye treatment. Patients were randomly assigned to one of the two treatment groups, study group...

Today we shall discuss several examples of Gromov–Witten invariants, as well as some identities among them. We let X be a compact (almost-) Kähler manifold, and let Xg,n,d denote the moduli space of stable degree d maps into X of genus g curves with n marked points (q.v. the notes from previous lectures). Let us assume that we know what to make of [Xg,n,d]; as described last time, constructing ...

The present study was aimed at evaluating the possible use of inter polymer complexed (IPC) films of xanthan gum (XG) and cationic guar gum (CGG) for formulating domperidone bioadhesive films. Formation of bonds between -COO¯ groups of XG and -N(+)(CH(3))(3) groups of CGG was evident in the FTIR spectra of IPC films. Bioadhesive strength of the films was evaluated employing texture analyser. Wa...

To motivate the study of Siegel modular varieties and Borel-Serre compactifications let me recall Scholze’s theorem on torsion classes. We start from an Hecke eigenclass h ∈ H (Xg/Γ,Fp) where Xg is the locally symmetric domain for GLg, and we want to attach to it a continuous semisimple Galois representation ρh : GQ → GLg(Fp) such that the characteristic polynomials of the Frobenius classes at ...

Xanthan gum (XG) biopolymer-based soil treatment is an effective improvement method. In this study, we explored the effect of XG on undrained shear strength clays (kaolinite and montmorillonite) in chemically distinct pore fluids. Among fluids tested, kaolinite was highest kerosene, followed by deionized (DI) water brine. This study hypothesized that interparticle forces interactions dominated ...

Abstract Background In this work, viscoelasticity, flow behaviour, thixotropy and thermo-rheological properties of binary mixtures Lepidium perfoliatum seed gum (LPSG), as an emerging food gum, xanthan (XG) at various blending ratios 100:0, 75:25, 50:50, 25:75 0:100 were studied for a depth insight into their interaction. FTIR analyses also done to investigate the interaction between XG LPSG. R...