Photomagnetic effect in n-type InSb at 77 °K

The steady-state odd photomagnetic effect was studied at liquid-nitrogen temperatures (77 °K) in n-type InSb having a carrier density of 4.2 · 10¹⁶ cm^-3. When the rate of surface recombination on the illuminated surface is higher than on the dark surface, the photomagnetic effect becomes negative in suitable magnetic fields.Translated from Izvestiya VUZ. Fizika, No. 7, pp. 28–31, June, 1970.The authors thank V. A. Gridin for useful discussions.     

Relatively thin and sparse subsets of groups

Let G be a group with identity e and let I \mathcal{I} be a left-invariant ideal in the Boolean algebra P_G {\mathcal{P}_G} of all subsets of G. A subset A of G is called I \mathcal{I} -thin if gA ?A ? I gA \cap A \in \mathcal{I} for every g ∈ G\{e}. A subset A of G is called I \mathcal{I} -sparse if, for T every infinite subset S of G, there exists a finite subset F ⊂ S such that ?_{g ? F} gA ? F \bigcap\nolimits_{g \in F} {gA \in \mathcal{F}} . An ideal I \mathcal{I} is said to be thin-complete (sparse-complete) if every I \mathcal{I} -thin (I \mathcal{I} -sparse) subset of G belongs to I \mathcal{I} . We define and describe the thin-completion and the sparse-completion of an ideal in P_G {\mathcal{P}_G} .     

On the Decay of Infinite Products of Trigonometric Polynomials

We consider infinite products of the form f(=_k=1 m _k(2^-k), where {m _k} is an arbitrary sequence of trigonometric polynomials of degree at most n with uniformly bounded norms such that m _k(0)= 1 for all k. We show that f() can decrease at infinity not faster than O(^-n) and present conditions under which this maximal decay is attained. This result can be applied to the theory of nonstationary wavelets and nonstationary subdivision schemes. In particular, it restricts the smoothness of nonstationary wavelets by the length of their support. This also generalizes well-known similar results obtained for stable sequences of polynomials (when all m _k coincide). By means of several examples, we show that by weakening the boundedness conditions one can achieve exponential decay.