Let a= (ai)i=1 be a strictly increasing sequence of natural numbers and let be a space of Lebesgue measurable functions defined on [0,1). Let {y} denote the fractional part of the real number y. We say that a is an ∗ sequence if for each f ∈ we set AN ( f ,x) = (1/N) ∑N i=1 f ({aix}) (N = 1,2, . . .), then limN→∞AN ( f ,x) = ∫ 1 0 f (t)dt, almost everywhere with respect to Lebesgue measure. Let...

The starting point for this work is an old question of H. Furstenberg. Recall that a Borel probability measure on the torus T = R=Z is called p-invariant if p = , where p(x) def = p x (mod 1) and p def = 1 p . Suppose that is non-atomic, and is simultaneously 2and 3-invariant. Assume also that is ergodic under the joint action of 2; 3. Does it follow that is necessarily Lebesgue measure? In his...

The hydrogen solubility in zirconia (yttria stabilized zirconia, YSZ) using a tritium imaging plate (IP) technique has been measured in a temperature region ranging from 673K to 973K. The tritium distribution in the zirconia specimens was nearly uniform suggesting an equilibrated dissolution. The hydrogen solubility in specimens were rather low (around ppm or below) and showed Arrhenius type te...

A commercial Trikon Technologies, Inc. Pinnacle 8000 helicon source plasma system for semiconductor etching was characterized with a radio frequency compensated Langmuir probe. The plasma parameters, including electron temperature, ion and electron density were measured with changes in the process conditions. The coil current ratios for constant magnetic fields were varied to demonstrate flexib...

A direct probe of superparamagnetism was used to determine the complete anisotropy energy distribution of Co nanoparticle films. The films were composed of self-assembled lattices of uniform Co nanoparticles of 3 or 5 nm in diameter, and a variable temperature scanning-SQUID microscope was used to measure temperature-induced spontaneous magnetic noise in the samples. Accurate measurements of an...

Supercritical flow through a horizontal pipe leads to non-uniform peripheral wall temperature distribution even when the heat flux is kept constant and uniform. This attributed lower transfer coefficient at top section where denser fluid tends sink. Hence, obtain uniform temperature, designed roughness devised. Uniform sand-grain employed only partly cover half of wall. Numerical simulations we...

Abstract. A seminal theorem due to Weyl [14] states that if (an) is any sequence of distinct integers, then, for almost every x ∈ R, the sequence (anx) is uniformly distributed modulo one. In particular, for almost every x in the unit interval, the sequence (anx) is uniformly distributed modulo one for every computable sequence (an) of distinct integers. Call such an x UD random. Here it is sho...

In this paper we continue the investigation into the group of algebras with uniformly distributed invariants, U(k’), and its relation to the Schur subgroup S(K), undertaken in [6, 71. We maintain the notation of [6, 71. In the first section we investigate U(K) for a real quadratic field K. We calculate generators of U(K) explicitly. In the second section we investigate U(K) for other real field...

We have studied the presence of plateaus on the low-temperature magnetization of an antiferromagnetic spin-1 chain, as an external uniform magnetic field is varied. A crystal-field interaction is present in the model and the exchange constants follow a random quenched (Bernoulli or Gaussian) distribution. Using a transfer-matrix technique we calculate the largest Lyapunov exponent and, from it,...

We present the measurements and the theoretical model on the frequency dependent noise temperature of a lattice cooled hot electron bolometer (HEB) mixer in the terahertz frequency range. The experimentally observed increase of the noise temperature with frequency is a cumulative effect of the non-uniform distribution of the high frequency current in the bolometer and the charge imbalance, whic...