Structure of quadratic inequalities

When A and B are n × n positive semi-definite matrices, and C is an n × n Hermitian matrix, the validity of a quadratic inequality $\text{(x}{}^1\text{Ax)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(x}{}^1\text{Bx)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? ¦x}{}^1\text{Cx¦}$ is shown to be equivalent to the existence of an n × n unitary matrix W such that $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{WB}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{+ B}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{W}{}^1\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 2C.}$ Some related inequalities are also discussed.     

Study of distribution of 169Yb, 69Ga and 111In in tumor tissues by macroautoradiography; comparison between viable and necrotic tumor tissues

The localization of 169Yb, 67Ga and 111In in tumor tissues was determined macroautoradiographically. 169Yb-citrate and 111In-citrate were injected intravenously to the rats subcutaneously transplanted Yoshida sarcoma and were injected intraperitoneally to the mice subcutaneously transplanted Ehrlich tumor. These animals were sacrificed 3, 24 and 48 hours after injection. These tumor tissues were frozen in n-hexane (-70 degrees C) cooled with dry ice-acetone. After this, these frozen tumor tissues were cut into serial thin sections (10 micron) in the cryostat (-20 degrees C). One of the slice of these sections was then placed on X-ray film and this film was developed after exposure of several days. On the other hand, next slice of these sections were then stained using the hematoxylin and eosin. From the observations of these autoradiogram and H-E stained slice, the following results were obtained. Concentration of 169Yb, 67Ga and 111In was predominant in viable tumor tissue rather than in necrotic tumor tissue, regardless of time after the administration. 67Ga and 111In were distributed uniformly in viable tumor tissue, but deposition of 169Yb was observed more avidly in viabl tumor tissue neighboring to necrotic tumor.     

Applicability of sodium sulfate as a solid electrolyte for a sulfur oxides sensor

The electromotive force (EMF) has been measured on SO₂O₂SO₃ concentration cells using undoped and 4 at.% yttrium-doped Na₂SO₄ as solid electrolytes at temperatures between 920 and 1120 K. Two types of electrolytes prepared by sintering and infiltration have proven to work basically well above 973 K. The observed EMF's are consistent with the values calculated from the Nernst equation in the wide concentration range of SO_x, showing that the ionic transference number is unity both in the undoped and yttrium-doped Na₂SO₄. A large difference in SO_x pressures between the anode and the cathode leads to the lowering of the EMF because of the permeation of gases through the macroscopic defects such as pores and cracks in the electrolyte. The experimental results suggest that improvement of the sinterability and the stabilization of the high temperature phase are the indispensable problems to solve for the practical application of Na₂SO₄ as a solid electrolyte to an SO_x sensor.     

A new strategy to sulfur heterocycles: Reactions of an allene episulfide with electrophiles

A variety of sulfur-containing five- and six-membered cyclic compounds was obtained by the acid-catalyzed and thermal reactions of an allene episulfide with various electrophiles.     

Mössbauer studies of ultrafine particles of NiO and α-Fe2O3

Ultrafine particles of antiferromagnetic NiO and ferromagnetic -Fe₂O₃, supported on a high area silica material, were studied with the Mössbauer effect. The superferromagnetic transition was observed as a function of particle size and temperature. From the temperature variation of the Mössbauer spectra, magnetic anisotropy constants and particle size distributions were determined. Small particles of -Fe₂O₃ show increasing quadrupole splitting as the particle size is decreased. This effect is attributed to a large quadrupole splitting for the surface shell which has a different electric field gradient than the particle core. Analysis of the spectra using a simple surface shell model gives an estimate of the thickness and the electric field gradient of this shell. In contrast to bulk NiO, small particles of NiO show predominantly trivalent Fe hyperfine spectra over a wide temperature range. The stability of the trivalent iron may be due to a slight oxygen atom excess in the NiO lattice resulting in trivalent charge stabilization.