The Use of Cationic Agents to Increase the Efficiency of Titanium Dioxide in Paper

Handsheets were made with a bleached sulfite pulp, titanium dioxide and cationic agents. The optical properties of these sheets were studied in order to determine and compare the efficiency of the titanium dioxide retained. The cationic agents used in this study were a quaternary ammonium salt, a polyamide, cationic starches made with these two chemicals, and a commercial cationic starch. When the optical properties of handsheets made from these substances were compared, it was found that the quaternary ammonium salt gave the highest opacity but the lowest retention. The polyamide gave lower opacities but higher retentions. The cationic starches made from these cationic chemicals showed slightly lower opacities than the cationic chemicals by themselves but they gave much higher retentions. The commercial cationic starch gave intermediate retention but lower opacity. It was concluded that the quaternary ammonium salt gave the best dispersion of the titanium dioxide but gave the lowest cationic charge to the pigment. The polymide gave a slightly poorer dispersion but gave a much higher charge to the pigment. The cationic starches gave the best retention through a combination of mechanical and physio-chemical retention, but did not disperse the pigment too well

Increasing efficiency of switching type regulator circuits Patent

Switching series regulator with gating control networ

The Application of Zeta Potential for the Effective Retention of Titanium Dioxide in Chemically Modified Systems

This study was done to determine how to obtain maximum effective filler retention in a fiber and titanium dioxide system. Retention of fillers in a fibrous system is greatly influenced through the use of high molecular weight polymers. It was found that by using cationic and anionic polymers in the same system, a synergistic effect results which yields a higher effective retention than if either polymers were used along. Furthermore, by precisely controlling the amounts of each polymer so as to obtain the isoelectric point in zeta potential; the peak effective retention is reached

A Symposium on the Fair Trade Laws: Part IV: Indirect Methods of Evading the Fair Trade Laws

In this paper, we build infinitely many non-radial sign-changing solutions to the critical problem (P)−Δu=|u|[Formula presented]u, in Ω,u=0, on ∂Ω on the annulus Ω:=x∈RN:a<|x|<b, N≥3. In particular, for any integer k large enough, we build a non-radial solution which look like the unique positive solution u0to (P) crowned by k negative bubbles arranged on a regular polygon with radius r0such that r0[Formula presented]u0(r0)=:maxa≤r≤b⁡r[Formula presented]u0(r)

Existence and phase separation of entire solutions to a pure critical competitive elliptic system

We establish the existence of a positive fully nontrivial solution $(u,v)$ to the weakly coupled elliptic system% \left\{ \begin{tabular} [c]{l}% $-\Delta u=\mu_{1}|u|^{{2}^{\ast}-2}u+\lambda\alpha|u|^{\alpha-2}|v|^{\beta }u,$\\ $-\Delta v=\mu_{2}|v|^{{2}^{\ast}-2}v+\lambda\beta|u|^{\alpha}|v|^{\beta{-2}% }v,$\\ $u,v\in D^{1,2}(\mathbb{R}^{N}),$% \end{tabular} \ \right. where $N\geq4,$ $2^{\ast}:=\frac{2N}{N-2}$ is the critical Sobolev exponent, $\alpha,\beta\in(1,2],$ $\alpha+\beta=2^{\ast},$ $\mu_{1},\mu_{2}>0,$ and $\lambda<0.$ We show that these solutions exhibit phase separation as $\lambda\rightarrow-\infty,$ and we give a precise description of their limit domains. If $\mu_{1}=\mu_{2}$ and $\alpha=\beta$, we prove that the system has infinitely many fully nontrivial solutions, which are not conformally equivalent

Symmetries, Hopf fibrations and supercritical elliptic problems

We consider the semilinear elliptic boundary value problem $$-\Delta u=\left\vert u\right\vert ^{p-2}u\text{ in }\Omega,\text{\quad }u=0\text{ on }\partial\Omega,$$ in a bounded smooth domain $\Omega$ of $\mathbb{R}^{N}$ for supercritical exponents $p>\frac{2N}{N-2}.$ Until recently, only few existence results were known. An approach which has been successfully applied to study this problem, consists in reducing it to a more general critical or subcritical problem, either by considering rotational symmetries, or by means of maps which preserve the Laplace operator, or by a combination of both. The aim of this paper is to illustrate this approach by presenting a selection of recent results where it is used to establish existence and multiplicity or to study the concentration behavior of solutions at supercritical exponents