Cu-0.4Cr (wt.%) alloys with the microalloying of Hf elements were subjected to a modified rolling–aging process achieve high strength, electrical conductivity and ductility simultaneously. Transmission electron microscopy X-ray line broadening analysis conducted characterize microstructures these alloys. Deformation twins high-density dislocations introduced into copper via Hf, improving mechan...

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...

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...

A study was conducted to examine the impact of matrix particle size on density, microstructure, and mechanical properties hybrid aluminum composites reinforced with Fe-based metallic glass (FMG) SiC particles. The were manufactured using spark plasma sintering (SPS) process. results showed that increasing led an increase in porosity content. distribution reinforcing particles found be more unif...

We introduce an elementary argument to the theory of distribution of sequences modulo one.

Polysynthetically-twinned titanium aluminide (PST-TiAl), a fully lamellar γ-TiAl+α2Ti3Al dual-phase alloy, is under evaluation for applications in rotary components in aircraft and automobile industries due to its high specific strength, and a high strength-retention capability at elevated-temperatures. However, the low ductility at roomto mid-high temperatures of the material hinders its appli...

Nano-twinned copper exhibits an unusual combination of ultrahigh strength and high ductility, along with increased strain-rate sensitivity. We develop a mechanistic framework for predicting the rate sensitivity and elucidating the origin of ductility in terms of the interactions of dislocations with interfaces. Using atomistic reaction pathway calculations, we show that slip transfer reactions ...