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The effects of twinning on the dynamic recrystallization (DRX) of the Mg-6.58Gd-5.7Y-0.55Zr alloy were investigated through uniaxial compression tests at 400 °C and 450 °C with an initial strain rate of 0.001–0.1 s −1 and were characterized through optical microscopy (OM), scanning electron microscopy (SEM), electron back-scattering diffraction (EBSD) and transmission electron microscopy (TEM). At a relatively high strain rate, extension twins can mainly be activated during the initial stage of hot compression, and the subsequent DRX is closely related to the twin-twin and twin-dislocation interactions. The intersected twin boundaries of the extension twins from multiple twin variants may provide effective DRX sites and promote microstructure refinement. However, extension twins from a single twin variant pair may quickly grow, soon swallowing the matrix and decreasing the DRX efficiency.

The loading rate significantly affects the mechanical properties of Mg alloys. However, the effects of strain rate on newly developed Mg–Gd–Y alloys at room temperature (RT) have rarely been investigated. Here, uniaxial tensile tests were conducted on a cast Mg-10Gd-3Y-0.5Zr (wt. %) alloy (GW103) in both as-aged and as-solutionized states with different grains sizes at RT and various strain rates. The results showed an anomalous positive strain-rate dependence of elongation in all the GW103 alloys investigated from 1 × 10−5 to 1 × 10−1 s−1. Careful microstructural characterization by slip trace analysis revealed that the exclusive deformation mechanism of pyramidal slip, non-Schmid behavior of basal slip, and slip transfer at 1 × 10−1 s−1; these induced the high RT ductility. The occurrence of pyramidal slip activity at high strain rates was suggested to be associated with rare earth solutes, fine precipitates, and local high stresses at grain boundaries due to dislocation pile-up. It was proposed that the increasing strain rate was approximately equivalent to decreases in grain size, enabling the generation of local stresses at grain boundaries, thus causing this anomalous phenomenon.

The microstructure evolution and plastic deformation mechanism of Mg-6.58Gd-5.7Y-0.55Zr alloy were investigated by uniaxial compression at temperatures ranging from 300 °C to 450 °C and with an initial strain rate of 0.1 s−1, and characterized by optical microscope (OM), scanning electron microscope (SEM) and electron back-scattering diffraction (EBSD). The effect of temperature on twinning behavior was focused in detail. At relatively low temperature, such as 300 °C, multiple twin variant pairs can be activated in one grain, and the twining process was dominated by nucleation. However, at high temperature, most of the twins activated in one grain belong to the single twin variant pair with the highest Schmid Factor (SF), and twin growth seems to represent the twinning behavior at 450 °C. The twinning behavior of Mg-6.58Gd-5.7Y-0.55Zr alloy at temperatures ranging from 300 °C to 450 °C basically follows Schmid law, and can be well understood in terms of variation of stress state and activated deformation modes with compression temperature.

Let $W=\{w_{1}, \ldots , w_{r}\}$ be a set of positive integers, $\lambda _{c}$ a positive integer, $\Lambda _{a}=(\lambda _{a}^{(1)}, \ldots \lambda _{a}^{(r)})$ an $r$ -tuple of positive integers, and $Q=(q_{1}, \ldots q_{r})$ an $r$ -tuple of positive rational numbers whose sum is 1. In 1996, Yang introduced variable-weight optical orthogonal code, $(n, W, \Lambda _{a}, \lambda _{c}, Q)$ -OOC, for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Some work had been done on the constructions of optimal $(n, W, \Lambda _{a}, 1, Q)$ -OOCs with unequal auto-correlation constraints for $W=\{3, 4\}$ and {3, 5}, while little is known on optimal $(n, W, \Lambda _{a}, 1, Q)$ -OOCs for $|W|\geq 3$ . In this paper, we focus our main attentions on $(n, \{3, 4, 5\}, \Lambda _{a}, 1, Q)$ -OOCs with $\Lambda _{a}\in \{(2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2)\}$ . Tight upper bounds on the maximum code size of $(n, \{3, 4, 5\}, \Lambda _{a}, 1, Q)$ -OOCs are obtained, and infinite classes of optimal $(n, \{3, 4, 5\}, \Lambda _{a}, 1, Q)$ -OOCs are constructed.

A multi-direction impact forging (MDIF) has been applied to a solutionized Mg-Gd-Y-Zr alloy in this work. An inhomogeneous microstructure, mostly fine grains, some twins and a few of coarse deformed grains were achieved with a weak and non-basal texture after 50 forging passes. Due to retarded DRX behavior by RE solute drag effect and the sharp drop of forging temperature, the alloy did not obtain a full DRX microstructure until 100 forging passes. During MDIF process, density of extension twins initially were induced in microstructure, which effectively refined the coarse grains by dividing and intersecting each other. In turn, those twining regions provided nucleation sites for DRX, and a continuous dynamic recrystallization converted most of the twin-matrix laminates to fine equi-axial grains. The ultimate tensile strength and elongation to failure of GW94 alloy were continuously improved during MDIF process, from less than 200 MPa and 2% of the initial solutionized specimen to more than 300 MPa and 7% of the one by 50 forging passes respectively.

The concept of a ( q , k , λ , t ) almost difference family (ADF for short) was introduced by Ding and Yin as a useful generalization of the concept of an almost difference set. Some results had been obtained for the existences of ( q , K , λ ) -ADFs, where K = { k 1 , k 2 , ź , k r } is a set of positive integers. In this note, new cyclic ( q , K , λ ) -ADFs are obtained via cyclotomy.

Variable-weight optical orthogonal code (OOC) was introduced by Yang for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. It is proved that optimal $(v, \{3, 5\}, 1, (1/2, 1/2))$-OOCs exist for some complete congruence classes of $v$. In this paper, for $Q\in \{(2/3,1/3), (3/4,1/4)\}$, by using skew starters, it is also proved that optimal $(v, \{3,5\}, 1, Q)$-OOCs exist for some complete congruence classes of $v$.

A novel multi-directional impact forging (MDIF) process was successfully applied to a Mg–Gd–Y-Zr alloy and the superplasticity of the MDIFed alloy was investigated. It was shown that the initial microstructure after MDIF had a unique characteristic of coarse grains decorated by profuse tension twins. Tensile tests at various temperatures and initial strain rates displayed that the MDIFed alloy exhibited superplasticity at temperatures higher than 400 °C, especially the maximum elongation of about 300% was achieved at 450 °C and 5 × 10 −4 s −1 . It was observed that the initial twin lamellas diminished and even vanished with the occurrence of static recrystallization (SRX) during preheating. The detailed microstructural analysis revealed that SRX during preheating and dynamic recrystallization (DRX) during tensile testing conduced to the superplasticity. With strain rate sensitivity exponent m -value of about 0.32, the superplastic deformation mechanism was supposed to be predominated by glide-controlled dislocation creep assisted by grain boundaries sliding.

Let $$M=(m_{i,j})$$M=(mi,j) be a magic square, where $$0\le m_{i,j}\le n^2-1$$0≤mi,j≤n2-1, $$0\le i, j\le n-1$$0≤i,j≤n-1. M is called diagonally ordered if both the main diagonal and the back diagonal, when traversed from left to right, have strictly increasing values. Let $$M=nA+B$$M=nA+B, where $$A=(a_{i,j})$$A=(ai,j), $$B=(b_{i,j})$$B=(bi,j), $$0\le a_{i,j}, \ b_{i,j}\le n-1$$0≤ai,j,bi,j≤n-1 for $$0\le i, j\le n-1$$0≤i,j≤n-1. M is called rational if both A and B possess the property that the sums of the n numbers in every row and every column are the same; otherwise, M is said to be irrational. In this paper, a pair of weakly diagonally ordered irrational orthogonal matrices (WDOIOM for short) is introduced to construct an irrational diagonally ordered magic square (IDOMS). It is proved that there exists a WDOIOM(n) for each positive integer $$n\ge 5$$nź5, and there does not exist a WDOIOM(n) for $$n\in \{2,3,4\}$$nź{2,3,4}. Consequently, it is proved that there exists an IDOMS(n) for each positive integer $$n\ge 5$$nź5, and there does not exist an IDOMS(n) for $$n\in \{2,3,4\}$$nź{2,3,4}.

In present research the serrated flow has been observed successfully after a critical amount of strain. Two relationships between the critical strain and temperature i.e. normal and inverse, corresponding to each serration type were studied. In order to investigate systematically the onset of serrated flow and serration type in NZ31 alloy, samples in solutionized condition were tensile tested at the temperature ranging from 100 °C to 300 °C with the strain rate ranging from 1×10−4 s−1 to 1×10−2 s−1. Results showed that normal critical strain appeared with type A and B serrated flow at temperature from 150°C to 250 °C, and inverse critical strain appeared with type C at temperature from 275 °C to 300 °C. Through analyzing the mechanism of three serration types, we found that the production of serration required improvement in diffusion for solute atoms for pinning process at low temperature, and enhance the moving ability of dislocations for unpinning process at high temperature, which need the assistance of the strain and stress respectively. So, in this work, the critical strain for pinning and the critical stress for unpinning processes were defined, which give a better explanation to the variation tendency of two definitions in accordance with temperature. Furthermore, this relationship results in the critical strain for onset of serrated flow changing from normal to inverse and corresponding different serrations.

Let W = { w 1 , w 2 , ? , w r } be an ordering of a set of r integers greater than 1, ? a = ( λ a ( 1 ) , λ a ( 2 ) , ? , λ a ( r ) ) be an r -tuple of positive integers, λ c be a positive integer, and Q = ( q 1 , q 2 , ? , q r ) be an r -tuple of positive rational numbers whose sum is 1. In 1996, Yang introduced variable-weight optical orthogonal code ( ( n , W , ? a , λ c , Q ) -OOC) for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Some work had been done on the constructions of optimal ( n , { 3 , 4 } , ? a , 1 , Q ) -OOCs with unequal auto- and cross-correlation constraints. In this paper, we focus our main attention on ( n , { 3 , 5 } , ? a , 1 , Q ) -OOCs, where ? a ? { ( 1 , 2 ) , ( 2 , 1 ) , ( 2 , 2 ) } . Tight upper bounds on the maximum code size of an ( n , { 3 , 5 } , ? a , 1 , Q ) -OOC are obtained, and infinite classes of optimal balanced ( n , { 3 , 5 } , ? a , 1 ) -OOCs are constructed.