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We report the effects of sodium phosphate dodecahydrate (Na3PO4·12H2O) as a foam stabilizer on the crystalline phases, microstructure, and properties of foamed glass–ceramics derived from solid industrial wastes. Our findings reveal that Na3PO4·12H2O acts as a pore structure stabilizer, enhancing pore uniformity by releasing P2O5 during decomposition. Additionally, it lowers the softening temperature and viscosity by supplying Na2O. X‐ray diffraction analysis demonstrates that Na3PO4·12H2O does not alter the primary crystal types but does influence the crystallinity and morphology. With an increase in Na3PO4·12H2O content, the porosity and water absorption improve, but the bulk density, thermal conductivity, and compressive strength decrease. The optimal properties are achieved with 4 wt% Na3PO4·12H2O, resulting in significantly higher compressive strength compared to foamed glass–ceramics prepared from other solid wastes. This study provides valuable guidelines for effectively reusing solid industrial wastes to fabricate foamed glass–ceramics. [ABSTRACT FROM AUTHOR]

The arithmetic crosscorrelation of binary m -sequences with coprime periods 2 n 1 − 1 and 2 n 2 − 1 (gcd ⁡ (n 1 , n 2) = 1) is determined. The result shows that the absolute value of arithmetic crosscorrelation of such binary m -sequences is not greater than 2 min ⁡ (n 1 , n 2) − 1. [ABSTRACT FROM AUTHOR]

Recently, there are extensive studies on perfect state transfer (PST for short) on graphs due to their significant applications in quantum information processing and quantum computations. However, there is not any general characterization of graphs that have PST in literature. In this paper, the authors present a depiction on weighted abelian Cayley graphs having PST. They give a unified approach to describe the periodicity and the existence of PST on some specific graphs. [ABSTRACT FROM AUTHOR]

Recently, there are extensive studies on perfect state transfer on graphs due to their significant applications in quantum information processing and quantum computations. However, most of the graphs previously investigated are abelian Cayley graphs. In this paper, we study perfect state transfer on Cayley graphs over dihedral groups. Using the representations of the dihedral group , we present some necessary and sufficient conditions for the Cayley graph to have a perfect state transfer between two distinct vertices for some connection set S. Based on these conditions, we show that cannot have PST if n is odd and S is conjugation-closed. For some even integers n, it is possible for to have PST, some concrete constructions are provided. [ABSTRACT FROM AUTHOR]

The notion of normal elements for finite fields extension was generalized as k-normal elements by Huczynska et al. (2013). Several methods to construct k-normal elements were presented by Alizadah et al. (2016) and Huczynska et al. (2013), and the criteria on k-normal elements were given by Alizadah et al. (2016) and Antonio et al. (2018). In the paper by Huczynska, S., Mullen, G., Panario, D. and Thomson, D. (2013), the number of k-normal elements for a fixed finite field extension was calculated and estimated. In this paper the authors present a new criterion on k-normal elements by using idempotents and show some examples. Such criterion was given for usual normal elements before by Zhang et al. (2015). [ABSTRACT FROM AUTHOR]

MDS codes and self-dual codes are important families of classical codes in coding theory. Therefore, it is of interest to investigate MDS self-dual codes. The existence of MDS self-dual codes over finite field ${\mathbb F}_{q}$ is competely solved for $q$ is even. In the literature, there are many known constructions of MDS self-dual codes for $q$ is odd. In this paper, we present a unified approach on the existence of MDS self-dual codes with concise statements and simplified proof. It is illustrated that some of known results can also be stated in this framework. Furthermore, we can obtain some new MDS self-dual codes, especially for the case when $q$ is not a square. [ABSTRACT FROM AUTHOR]

W-Mo-Cu alloy is a novel, potential pseudo-alloy but demand efficient and reliable manufacturing approaches. In this study, W-Mo-Cu alloys with (1–5 wt%) Co additives were fabricated using large current electric field sintering at a pressure of 25 MPa and a low temperature of 950 °C. The effects of Co on the microstructure and properties of the W-Mo-Cu alloys were investigated. The results revealed an activation effect of Co on W-Mo-Cu alloys. Increasing the Co content from 0 to 5 wt%, resulted in a substantial reduction of the calculated sintering activation energy by 69.6%, thereby enhancing the sinterability of W-Mo-Cu mixed powder and increasing the sintering densification degree of W-Mo-Cu alloy. During the sintering process, a large quantity of Co was enriched around the matrix particles and partially dissolved in the W, Cu, whereas a small number of matrix atoms dissolved into Co, which followed the classical activated sintering model. Moreover, an appropriate increase in the Co content was conducive to an optimal microstructure with increased sintering densification accompanied by increased hardness. However, the addition of Co adversely affected the electrical conductivity of W-Mo-Cu alloys. • Co exhibits activation effect on W-Mo-Cu alloys • Increasing Co content is conducive to increased sintering densification and hardness • Co adversely affects the electrical conductivity of W-Mo-Cu alloys [ABSTRACT FROM AUTHOR]

Abstract A novel W-Mo-Cu alloy, combining the advantages of W-Cu and Mo-Cu pseudo-alloy, was rapidly prepared by Gleeble thermo-mechanical simulator at a low temperature (975 °C) in a short time (5 min) due to the large current electric field (∼105 A). The effects of pressure (0–40 MPa) on the microstructure and properties of W-Mo-Cu alloys were comprehensively studied. It is proved that pressure contributes greatly to the sintering densification, since the driving force for atoms diffusion improves due to the elevated difference of vacancy concentration between the bulk of the powders and the neck-like zone by loading pressure. Results show that W-Mo-Cu alloys consist of W, Mo, Cu phase and a new phase of Cu 0.4 W 0.6 intermetallic compound. Appropriately increasing the sintering pressure is conducive to optimal microstructure with increased sintering densification, accompanied by increased micro-hardness and decreased electrical resistivity. In particular, after applying a pressure of 35 MPa, the relative density of the sample increases from 80.27% to 95.53%. The present study potentially offers valuable insights and guidance toward the preparation of W-Mo-Cu alloys. Highlights • The sintering densification is achieved with a short time and low temperature. • The sintering temperature is lower than the melting temperature of Cu. • With loading pressure, the driving force for atoms diffusion improves. • After applying a pressure of 35 MPa, the density increases from 80.27% to 95.53%. [ABSTRACT FROM AUTHOR]

Abstract Perfect state transfer (PST) has great significance due to its applications in quantum information processing and quantum computation. In this paper we present a characterization of the connected simple Cayley graph Γ = Cay (G , S) having PST, where G is an abelian group and S is a non-empty set of G. We show that many previous results on periodicity and existence of PST of circulant graphs (where the underlying group G is cyclic) and cubelike graphs (G = (F 2 n , +)) can be derived or generalized to arbitrary abelian case in unified and more simple ways from our characterization. We also get several new results including answers to some questions raised before. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a novel Mo-W-Cu alloy with the relative density of 94%, fine microstructure, good electrical conductivity and hardness is prepared at a low temperature (800 °C) in a short time (5 min) under the combined action of discharge plasma, high frequency impulse, electric field and hot pressed sintering. The phase evolution and the phase structure of new phases are discussed based on the comprehensive analysis of XRD and TEM. The results show that Mo-W-Cu alloy consists of W, Mo, Cu phase and the new phases including Mo-W ordered phase at the Mo/W interface, Cu 0.4 W 0.6 intermetallic compound at the W/Cu interface and Mo-Cu solid solution at the Mo/Cu interface. All of the new phases are BCC structure. The type of new phases obtained in this experiment is consistent with the calculation results based on the theory of Hume-Rothery, the correction theory of solid solution formation, and the theory of electronegativity. This presented research is expected to provide reference for the further research of Mo-W-Cu alloy. Highlights • A novel Mo-W-Cu alloy was prepared at a low temperature (800 °C) in a short time (5 min). • Mo-W ordered phase, Cu 0.4 W 0.6 intermetallic compound and Mo-Cu solid solution were found in the Mo-W-Cu alloy. • The ordering transformation of Mo, W atoms was demonstrated and the crystal cell model of Mo-W ordered phase was established. • Consistency evaluation was carried out with experimental results and theoretical calculation. [ABSTRACT FROM AUTHOR]

Relative generalized Hamming weights (RGHWs) of a linear code with respect to a linear subcode determine the security of the linear ramp secret sharing scheme based on the linear codes. They can be used to express the information leakage of the secret when some keepers of shares are corrupted. Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems. In this paper, we investigate the RGHWs of cyclic codes of two nonzeros with respect to its irreducible cyclic subcodes. We give two formulae for RGHWs of the cyclic codes. As applications of the formulae, explicit examples are computed. Moreover, RGHWs of cyclic codes in the examples are very large, comparing with the generalized Plotkin bound of RGHWs. So it guarantees very high security for the secret sharing scheme based on the dual codes. [ABSTRACT FROM AUTHOR]

In this study, we fabricated iron-based friction materials directly by in situ selective carbothermic reaction and vacuum sintering from vanadium-bearing titanomagnetite concentrate and evaluated the effects of Cr on the microstructure, properties, and tribological behavior. The results reveal that Cr dissolves in the Fe matrix and contributes to the formation and refinement of pearlite, thereby improving the sintering densification and properties of the material. After adding moderate Cr, the microstructure becomes denser and more homogeneous, with improved sintering densification, hardness, and tribological properties. The dominant wear mechanism changes from severe abrasive and oxidative wear to mild abrasive and oxidative wear, indicating a decreasing wear degree. However, for Cr content exceeding 2 wt%, the sintering densification and properties slightly deteriorate. In particular, the material with 2 wt% Cr exhibits the optimal overall properties, with a much lower friction coefficient and wear rate than the sample without Cr. This work provides practical guidelines for further research on the properties improvement of the friction material. • The iron-based friction materials were prepared directly from vanadium-bearing titanomagnetite concentrate. • Adding moderate Cr significantly enhanced the properties of the materials. • The material with 2 wt% Cr exhibited a much lower friction coefficient and wear rate. [ABSTRACT FROM AUTHOR]

A pure quantum state is called $k$ -uniform if all its reductions to k$ -qudit are maximally mixed. We investigate the general constructions of k$ -uniform pure quantum states of n$ subsystems with d$ levels. We provide one construction via symmetric matrices and the second one through the classical error-correcting codes. There are three main results arising from our constructions. First, we show that for any given even n\ge 2$ , there always exists an n/2$ -uniform n$ -qudit quantum state of level p$ for sufficiently large prime p$ . Second, both constructions show that there exist k$ -uniform n$ -qudit pure quantum states such that k$ is proportional to such that there exists a k$ -uniform n$ -qudit quantum state for all . In addition, by using the concatenation of algebraic geometry codes, we give an explicit construction of $k$ -uniform quantum state when $k$ tends to infinity. [ABSTRACT FROM AUTHOR]

In this paper, we present a construction of linear codes over \mathbb F2^{t} from Boolean functions, which is a generalization of Ding’s method. Based on this construction, we give two classes of linear codes \tilde \mathcal Cf and \mathcal Cf over \mathbb F2^{t} from a Boolean function f: \mathbb Fq\rightarrow \mathbb F 2 , where q=2^n and \mathbb F2^{t} is some subfield of \mathbb Fq . The complete weight enumerator of \tilde \mathcal Cf can be easily determined from the Walsh spectrum of f , while the weight distribution of the code f . As applications of this construction, we show several series of linear codes over \mathbb F2^t with two or three weights by using bent, semibent, monomial and quadratic Boolean function f . [ABSTRACT FROM PUBLISHER]

Since diffusion alloying and metallurgical bonding interfaces have been confirmed to be existed in W-Mo-Cu composite, the thermodynamic mechanism of phase formation is unclear yet. This paper aims at constructing the Gibbs free-energy change diagram for W-Mo-Cu ternary system and revealing the thermodynamic mechanism of the direct alloying among W, Mo and Cu which is not yet clear. The content combines the analysis of experimental results and calculated results based on Miedema's model. The large current electric field induces field emission and provides sufficient energy to overcome thermodynamic barriers and helps the atom diffusion at a relatively low temperature. The high-resolution electron microstructures show that new crystallite phases of (Mo, W), (Mo, Cu), (W, Cu), and amorphous phase (Mo, W) are formed in large current electric field sintering. Meanwhile, the Gibbs free-energy change diagram for W-Mo-Cu system shows that Mo effectively reduces the value of free-energy change, and when Mo content or sintering temperature is as high as possible, Gibbs free-energy change is as small as possible. Additionally, Gibbs free-energy change diagrams for W-Mo, W-Cu and Mo-Cu binary systems are also constructed during the derivation, and the results show that the crystalline and amorphous phases of (Mo, W) are the most easily to be formed, followed by that of (Mo, W) and finally that of (W, Cu). • The Gibbs free-energy change maps of phase formation for W-Cu, Mo-Cu, W-Mo, and W-Mo-Cu metal systems were constructed. • The alloying process of W-Mo-Cu composite was realized via large current electric field sintering. • The increase of Mo content decreases the Gibbs free-energy change of the W-Mo-Cu ternary metal system. • The ultrahigh electric current promotes the atom diffusion of the W-Mo-Cu composite. [ABSTRACT FROM AUTHOR]

The Ti 3 SiC 2 and Ti 3 SiC 2 /Pb composites were tested under dry sliding conditions against Ni-based alloys (Inconel 718) at elevated temperatures up to 800 °C using a pin-on-disk tribometer. Detailed tribo-chemical changes of Pb on sliding surface were discussed. It was found that the tribological behavior were insensitive to the temperature from 25 °C (RT) to 600 °C (friction coefficient ≈0.61–0.72, wear rate ≈10 −3 mm 3 N m −1 ). An amount of Pb in the composites played a key role in lubricating with the temperature below 800 °C. The friction coefficient (≈0.22) and wear rate (≈10 −7 mm 3 N m −1 ) at elevated temperatures were both decreased by the added PbO. The wear mechanisms of Ti 3 SiC 2 /Pb-Inconel 718 tribo-pair at elevated temperatures were believed to be the combined effect of abrasive wear and tribo-oxidation wear. During the sliding, two oxidization reactions proceed, 2Pb+O 2 =2PbO (below 600 °C) and 6PbO+O 2 =2Pb 3 O 4 (800 °C). The friction coefficient and wear rate of the composites were reduced due to the self-lubricating effect of the tribo-oxidation products. [ABSTRACT FROM AUTHOR]

Dense Ti 3 SiC 2 /Pb composites were successfully synthesized from Ti 3 SiC 2 and PbO powders by spark plasma sintering. The reaction mechanism was discussed on the basis of thermodynamic principles. The sintering process was optimized and the sintering characteristics of the Ti 3 SiC 2 –PbO system were studied. The effects of PbO content on the density, micro-hardness, mechanical and tribological properties of the composites were investigated. Micro-hardness, flexural strength and compression strength of the composites were found to increase with the increase of PbO content, due to the grain refinement of Ti 3 SiC 2 . The maximum values of the flexural and compression strength were 480 and 1645 MPa, respectively. Additionally, the wear rates of Ti 3 SiC 2 /Pb—Inconel 718 alloy tribopairs decreased with the increase of PbO content at room temperature. [ABSTRACT FROM AUTHOR]

In order to improve the welding performance of WC–Co to steel, a multilayer functionally graded (WC–Co)–Ni composite (MFGWC) was successfully fabricated by sintering the multilayer green compact, and a Ni-rich layer was covered on the compact surface. The microstructure, composition and micro-hardness of the MFGWC were investigated in this paper, results showed that the MFGWC was composed of WC–Co substrate, multi-transitional layers and pure Ni layer. The key part, multi-transitional layers formed between Ni layer and WC–Co substrate, was obtained successfully. The micro-hardness of the composite gradually decreased from 1300 HV to 66 HV along the direction of WC–Co substrate to pure Ni layer, this was due to a decrease in the amount of WC particles and the corresponding increase of Ni phases. The multi-transitional layer played a role in reducing the residual stresses that were induced by the difference of thermal expansion between WC–Co substrate and steel. [ABSTRACT FROM AUTHOR]

In this paper a new criterion on normal bases of finite field extension F q n / F q is presented and explicit criterions for several particular finite field extensions are derived from this new criterion. [ABSTRACT FROM AUTHOR]

• Foamed glass-ceramics were prepared at 1000 °C through the one-step sintering process. • The one-step sintering process concurrently completed foaming and crystallizing process. • Borax was influential to both foaming and crystallizing process of foamed glass-ceramics. Foamed glass-ceramics were prepared at 1000 °C through the one-step sintering process by applying waste glass and slow-cooled high-titanium blast furnace slag as raw materials. This study investigated the effects of borax as the flux agent on the crystalline phases, microstructure, and properties of foamed glass-ceramics, respectively. It was found that the borax would decrease the system's softening temperature and viscosity, thus enhancing the foaming and crystallizing process. Besides, the XRD results showed that the main crystal types of foamed glass-ceramics presented no difference with different contents of borax addition, but their crystallinity and crystal morphology differed. With the increasing borax content, the porosity and water absorption increased, while the volume density, thermal conductivity, and compressive strength all decreased. In particular, the sample added with 6 wt% borax exhibited the optimal comprehensive properties. This study provided a practical guideline for effectively reusing solid industrial wastes to produce foamed glass-ceramics. [ABSTRACT FROM AUTHOR]

[Display omitted] • The sintering densification of W-Mo-Cu alloy was achieved with a short time and relatively low temperature. • The densification of W-Mo-Cu alloy was significantly improved using nano-sized Cu powders. • W-Mo-Cu alloy contained three new phases aside from W, Mo, and Cu phases. This study rapidly fabricated a novel W-Mo-Cu alloy by large current electric field sintering at a relatively low temperature, and the effects of the powder size of Cu on the densification, microstructure, and properties were comprehensively investigated. The particle size of Cu did not influence the phase type but significantly affected the densification, microstructure, and properties. XRD and TEM results showed that the alloy contained three new phases aside from W, Mo, and Cu phases, i.e., Mo-W ordered phase, Mo-Cu solid solution, and Cu 0.4 W 0.6 intermetallic compound. Copper powders with smaller sizes were beneficial to improving the distributional homogeneity of elements and the sintering densification. Therefore, the alloy prepared with 100 nm Cu powders had a denser and more homogeneous microstructure and better comprehensive properties than that prepared with 5 μm Cu powders. Overall, the W-Mo-Cu alloy prepared with 100 nm Cu powders at 980 °C proposed the best comprehensive properties, and its relative density can reach 98% approximately. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates linear guessing number introduced by Riis in connection with the network coding theory. This paper establishes properties of linear guessing number on undirected graphs. In particular, lower and upper bounds for linear guessing number are established. Finally, linear guessing numbers of product graphs are investigated. [Copyright &y& Elsevier]

The stabilizer (additive) method and non-additive method for constructing asymmetric quantum codes have been established. In this paper, these methods are generalized to inhomogeneous quantum codes. [ABSTRACT FROM AUTHOR]

W–Mo–Cu alloy was fabricated by large current electric field sintering at a low temperature of 950 °C. The interrupted sintering at different sintering stages was performed to identify the phases and microstructure evolution during the densification process. The transmission electron microscope (TEM) images clearly show that the nanoscale phases form and distribute at the boundaries of W, Mo, and Cu phases. Moreover, the high-resolution TEM images incorporating with a selected area fast Fourier transform and inverse fast Fourier transform (IFFT) treatment present the structure of formed phases. Meanwhile, the lattice parameters calculated through X-ray diffraction patterns and IFFT images jointly evidence the existence of defects and atom diffusion during the sintering. The dislocations and lattice strain induced by the ultrahigh current and pressure provide the stored energy and nucleation sites, thus promoting the diffusion of elements and the formation of fine grains. • The microstructure and phase evolutions of W–Mo–Cu alloy were studied. • The (W, Mo) solid solution, (Mo, Cu) solid solution, and Cu 0.4 W 0. 6 intermetallic compound were fabricated. • Pressure and ultrahigh current induced the strain of grains, changed lattice structure, and promoted the atoms diffusion. [ABSTRACT FROM AUTHOR]

In this study, we fabricated a novel ternary alloy of W–Mo–Cu by constant and cyclic large current electric field sintering at a relatively low temperature (950 °C) and within a short time (5 min). We subsequently investigated the effects of the electro-thermal cycles on the densification, microstructure, and properties of the sintered alloy. The electro-thermal cycles process generated greater amounts of Joule heating and provided more energy under the additional effect of field emission by repeating the heating and cooling treatments. W–Mo–Cu alloy was experimentally proven to densify significantly under the effect of electro-thermal cycles. Indeed, as compared with the microstructures of W–Mo–Cu alloy prepared via constant temperature sintering, the microstructures derived by cyclical sintering were far denser. It was also found that the relative density and hardness of cyclically sintered W–Mo–Cu alloy were higher, and its electrical resistivity was lower than those of constantly sintered alloy. In general, cyclically sintered W–Mo–Cu alloy, with 10 wt% Cu added, exhibited optimal comprehensive properties. It can be concluded that cyclic large current electric field sintering is a promising method for preparing W–Mo–Cu alloy with enhanced densification and properties. • The sintering densification of W–Mo–Cu alloy is achieved with a short time and relatively low temperature. • The cyclic sintering process generated greater amounts of Joule heating than constant sintering process. • W–Mo–Cu alloy was proven to densify significantly under the effect of the electro-thermal cycles. [ABSTRACT FROM AUTHOR]

Abstract: The present investigation was conducted to research the brazing between a functionally graded WC–Co/Ni component and 410 stainless steel with Cu–Zn filler alloy. In the joint, γ phase was suppressed due to isothermal solidification and (Cu,Ni)-based solid solution was formed between the braze and Ni layer, which contributed to the intimate bonding of the WC–Co/Ni component and stainless steel. The functionally graded WC–Co/Ni component was beneficial to relaxing stresses and improving the strength of the cemented carbide/stainless steel joints. [Copyright &y& Elsevier]

Abstract: A functionally graded WC–Co/Ni composite (FGWC) and 410 stainless steel (410ss) were successfully bonded by diffusion bonding. With the bonding temperature or holding time increasing, the tensile strength of the joints increased firstly and then decreased. The maximum tensile strength of the FGWC/410ss joints was 195MPa bonded at 950°C for 80min. A diffusion layer was formed between the Ni layer and the 410ss as a result of the interdiffusion of Ni and Fe. The Ni layer could release the residual stresses of the FGWC/410ss joints. The fracture of the FGWC/410ss joints occurred in the Ni layer by the way of ductile fracture. [Copyright &y& Elsevier]

Abstract: Composite of TiC/Fe was in situ synthesized by field-assisted combustion synthesis method (FACS) in one step from elemental powders of Fe, Cu, Ti and C. The effect of carbon source and graphite particle size on the combustion synthesis of TiC/Fe composites was investigated. With the action of an electric field, a relatively low ignition temperature between 740 and 774°C for the combustion synthesis of Fe–Cu–Ti–C system can be achieved. It was shown that the ignition temperature using carbon black as carbon source was lower than that of using graphite of the same size. In addition, the ignition temperature decreased with the decrease of graphite size. The shrinkages of the synthesized products during the synthesis reaction were measured. The Vickers microhardness value were in a range of 166–284HV. [Copyright &y& Elsevier]

Abstract: A functionally graded WC–Co/Ni composite (FGWC) is successfully fabricated. The FGWC is composed of WC–Co layer, transitional layer and Ni layer. The transitional layer with graded variation of WC particles and Ni phases serves as the buffer zone to relax thermal stress. Liquid phase sintering has considerable influence on the forming process of the transitional layer. The microhardness values of the transitional layer gradually decrease along the direction of WC–Co layer to Ni layer. [Copyright &y& Elsevier]

Abstract: The brazed joints of WC–Co cemented carbide and 3Cr13 stainless steel using Ni electroplated on Cu–Zn alloy as interlayer were investigated. The shear strength of the WC–Co/interlayer/3Cr13 joints increased firstly and then decreased with the increase of brazing temperature or brazing time. The maximum shear strength value of the brazed joints was 154MPa at 1100°C for 10min. The characterizations of the WC–Co/interlayer/3Cr13 joints were studied by SEM, EDS and XRD. The results showed that the brazed joints fractured in the bulk WC–Co substrates near the interlayer. The added Ni promoted the formation of interdiffusion zone, which possessed positive effects on the bond strength of the WC–Co/interlayer/3Cr13 joints. Austenite solid solution was formed in the WC–Co/interlayer/3Cr13 joint, and the majority of austenite solid solution presented as columnar crystal. The number of austenite crystals on the WC–Co/interlayer interface was tremendously more than that on the interlayer/3Cr13 interface. [Copyright &y& Elsevier]

The quantum codes have been generalized to inhomogeneous case and the stabilizer construction has been established to get additive inhomogeneous quantum codes in [Sci. China Math., 2010, 53: 2501-2510]. In this paper, we generalize the known constructions to construct non-additive inhomogeneous quantum codes and get examples of good d-ary quantum codes. [ABSTRACT FROM AUTHOR]

In this paper, the value of I\max({\cal C}) for codebooks \cal C=\cal C(D) constructed by certain almost difference sets D in \BBF^\timesq is determined and expressed in terms of Jacobi sums from which it shows that such codebooks nearly meet the Welch bound. This result is an answer of a question raised by C.Ding and T.Feng in refid="ref2"/. We also present another series of codebooks which nearly meet the Welch bound, where the codebook is constructed by a subset D\varepsilon in additive group R=\BBFq1\oplus\BBFq2. When q1=q2, D\varepsilon is an almost difference set of R. [ABSTRACT FROM AUTHOR]

Abstract: Using electric-current-assisted combustion synthesis (ECACS) in a Gleeble thermal simulation instrument, composites of TiC/Fe-Cu have been in-situ synthesized directly from elemental powders of iron, copper, titanium and graphite. This study was focused on the effect of pressure on the combustion synthesis of TiC/Fe-Cu composites and the properties of TiC/Fe-Cu composites. With the aid of a high electric current, a relatively low onset temperature for the combustion reaction, between 747°C and 768°C, could be achieved. The ignition temperature decreased with the increase of the pressure in the heating process. The final products of samples were composed of Fe, Cu, TiC and the pressure had little influence on the phase composition. All the titanium carbide particles were fine and in a range of about 0.2μm–0.35μm. When the pressure increased, the density and microhardness of sample increased, so the wear resistance improved. [Copyright &y& Elsevier]

Let χ be a character of order N=2t(t ⩾ 4) over a finite field 픽q = 픽pf with p ≡ 7, 9 (mod 16). In this paper, we evaluate explicitly the Gauss sums G(χr) related to the group generated by the character χ. [ABSTRACT FROM AUTHOR]

In this paper we generalize two remarkable results on cryptographic properties of Boolean functions given by Tu and Deng [8] to the vectorial case. Firstly we construct vectorial bent Boolean functions $F:\,\mathbb{F}_2^n\, \to \,\mathbb{F}_2^m$ with good algebraic immunity for all cases 1 ⩽ m ⩽ n, and with maximum algebraic immunity for some cases (n,m). Then by modifying F, we get vectorial balanced functions $F'\,:\,\mathbb{F}_2^n\, \to \,\mathbb{F}_2^m$ with optimum algebraic degree, good nonlinearity and good algebraic immunity for all cases $1\, \leqslant\, m \leqslant \,\frac{n}{2}$, and with maximum algebraic immunity for some cases (n,m). Moreover, while Tu-Deng's results are valid under a combinatorial hypothesis, our results (Theorems 4 and 5) are true without this hypothesis. [ABSTRACT FROM AUTHOR]

Abstract: Composites of WC–Co have been synthesized and consolidated simultaneously at the ignition temperature of 794°C by a field-assisted combustion synthesis method (EFACS), where the electric field was generated by a Gleeble thermal simulation instrument. Then, with the aid of high-temperature XRD results, the combustion synthesis process of an 88wt% (W+C)–12wt% Co system was studied according to quenching at different temperatures by turning off the electric field. A four-step model describing the process of combustion synthesis of WC–Co composites under an electric field, which is controlled by solid diffusion among the reactant atoms, is proposed. From the preheating period to the solid diffusion period, the solid diffusion among reactant atoms enhance with the increase of temperature. From the solid diffusion period to the combustion period, the 2W(s) +C(s) =W2C(s) reaction may occurs at some interfaces between W and C atoms. During combustion period, 2W(s) +C(s) =W2C(s) occurs firstly and follows the reaction of W2C(s) +C(s) =2WC(s). Co melts and then reacts to W, W2C in order to form WC and Co3W3C, with that Co3W3C carbonizes to form WC and Co. After the combustion period, the remaining phases of W2C and Co3W3C can be carbonized to form WC with the increase of temperature, and the morphology of tungsten carbide changes from spheroid to polyhedrons as the temperature rises. [Copyright &y& Elsevier]

Abstract: Composites of VC/Fe have been synthesized from reactant mixtures of graphite, iron, and ferrovanadium by a field-assisted combustion synthesis method in a Gleeble thermal simulation instrument. With the aid of a high electric current, a relatively low onset temperature for the combustion reaction, between 691°C and 813°C, could be achieved. The ignition temperature and ignition delay time of the reaction decreased with the increase of the reactant V content and the preset heating rate of the process, and the decrease of ferrovanadium particle size. These technologic parameters also affected the final phase and grain size of vanadium carbide particles in the products. [Copyright &y& Elsevier]

MDS self-dual codes over finite fields have attracted a lot of attention in recent years by their theoretical interests in coding theory and applications in cryptography and combinatorics. In this paper we present a series of MDS self-dual codes with new length by using generalized Reed-Solomon codes and extended generalized Reed-Solomon codes as the candidates of MDS codes and taking their evaluation sets as a union of cyclotomic classes. The conditions on such MDS codes being self-dual are expressed in terms of cyclotomic numbers. [ABSTRACT FROM AUTHOR]

In this paper, we prepared a series of (80- x)W x Mo20Cu (x = 10, 20, 30, 40, 50, 60, 70 wt%) alloys with spark plasma sintering. The non-dense ternary alloy was designed into dense binary alloy through the component reconstruction, which is based on the sintered samples' microstructures and the interrelationship of the components. The physical property models used for dense binary alloys were applied in W–Mo–Cu alloy. Then three physical property models of W–Mo–Cu alloy were established and the accuracy of the models was validated by the experimental properties. The results show that the physical properties of W–Mo–Cu alloy can be well predicted with the combination of different models. The effects of relative density and composition on physical properties (electrical conductivity, thermal conductivity and thermal expansion coefficient) of W–Mo–Cu alloy were analyzed with the predicted results by models. Three types of pore distributions are found in W–Mo–Cu alloy sintered by spark plasma sintering, and based on the pore distributions, three physical models are established by designing the non-dense ternary alloy into dense binary alloy. [Display omitted] • Successfully established the physical property models of W–Mo–Cu alloy. • The relationship between the relative density, composition and properties of W–Mo–Cu alloy were studied. • The physical properties of W–Mo–Cu alloy with different composition were predicted. [ABSTRACT FROM AUTHOR]

Abstract: In the process of intensified sintering of iron powders under the action of an electric field with low voltage and high current, the effect of sintering temperature and sintering time on the densification process were investigated by means of thermal simulation. Both the metalloscope results and the statistic analysis of the distribution of pores in sintered compacts show that an electric field is not only providing the Joule heat for a compact, but also accelerating the diffusion among iron atoms in the sintering process, which leads to intensified sintering. The relative density of the sintered compact can be over 95% at relatively low sintering temperature (800°C) or within relatively short sintering time (2min) at high temperature. Both sintering temperature and sintering time have effect on the process of iron powder densification. In this study, a sintering temperature of 1100°C and a sintering time of 4min lead to over 97% consolidation for iron powder compact. [Copyright &y& Elsevier]

Abstract: Let where p is an odd prime, , and . Let Tr be the trace mapping from to and . In this paper we determine the value distribution of following two kinds of exponential sums and where is the canonical additive character of . As an application, we determine the weight distribution of the cyclic codes and over with parity-check polynomial and , respectively, where , and are the minimal polynomials of , and over , respectively, for a primitive element π of . [Copyright &y& Elsevier]

Abstract: A linear error-block code is a natural generalization of the classical error-correcting code and has applications in experimental design, high-dimensional numerical integration and cryptography. This article formulates the concept of a linear error-block code and derives basic results for this kind of code by direct analogy to the classical case. Some problems for further research are raised. [Copyright &y& Elsevier]

Abstract: Let be the minimal value of size of all possible unextendible product bases in the tensor product space . We have trivial lower bounds and upper bound . Alon and Lovász determined all cases such that . In this paper we determine all cases such that by presenting a sharper upper bound. We also determine several cases such that by using a result on 1-factorization of complete graphs. [Copyright &y& Elsevier]

A new technique for reaction casting is put forward in this paper. According to the results of the temperature field and X-ray diffraction patterns, and combined with the theoretical analysis, it is proven that iron matrix composites with low volume fractions of TiC reinforcement can be produced by this technique. The process includes four steps for the reactants: added to iron matrix, dissolve and diffuse in the melt, absorb the thermal energy from the melt for reaction, and synthesize TiC in situ. The first step is the key to this approach, which is unique, novel and significantly different from the previous techniques. [Copyright &y& Elsevier]

In this paper we determine all elliptic curves En:y2=x3-n2x with the smallest 2-Selmer groups Sn=Sel2(En(Q))={1} and Sn′=Sel2(En′(Q))={±1,±n}(En′:y2=x3+4n2x) based on the 2-descent method. The values of n for such curves En are described in terms of graph-theory language. It is well known that the rank of the group En(Q) for such curves En is zero, the order of its Tate-Shafarevich group is odd, and such integers n are non-congruent numbers. [Copyright &y& Elsevier]

• Mo–W–Cu alloys are prepared at a low temperature and in a short time. • The microwave field enables complete penetration of radiation to Mo, W, and Cu particles. • New phases including Mo–W ordered phase, Mo–Cu solid solution, and Cu 0.4 W 0.6 intermetallic compound are formed in this alloy. • Mo–W–Cu alloys exhibit better densification and comprehensive properties than Mo-Cu alloys. In this study, we fabricated a new type of Mo–W–Cu alloys by microwave sintering at a low temperature (1000 °C) in a short time (5 min) and characterized the phases, microstructures, and properties of the alloys. Through calculating the skin depth, it was proved that the microwave field enabled complete penetration of radiation to Mo, W, and Cu particles, thus effectively promoting the diffusion and solid solution among Mo, W, and Cu. XRD and TEM results showed that Mo-W-Cu alloys contained three new phases besides Mo, W, Cu phases, i.e., Mo-W ordered phase, Mo-Cu solid solution, and Cu 0.4 W 0.6 intermetallic compound. It was also found that Mo–W–Cu alloys exhibited better densification and comprehensive properties than Mo-Cu alloys. The number and size of the sintering necks varied with the W content from 10 to 50 wt% among which the optimal microstructure and properties were obtained at 30 wt% W. This study could provide useful guidelines for further research of the densification and properties of microwave sintered Mo-W-Cu alloys. [ABSTRACT FROM AUTHOR]

Presents information on a study which focused on the direct and recursive constructions for aperiodic and periodic complementary binary sequences (PCS). Definitions and preliminaries; Construction of ACS and PCS; Conclusions.

Normal bases are widely used in applications of Galois fields and Galois rings in areas such as coding, encryption symmetric algorithms (block cipher), signal processing, and so on. In this paper, we study the normal bases for Galois ring extension R / Z p r , where R = GR (p r , n). We present a criterion on the normal basis for R / Z p r and reduce this problem to one of finite field extension R ¯ / Z ¯ p r = F q / F p (q = p n) by Theorem 1. We determine all optimal normal bases for Galois ring extension. [ABSTRACT FROM AUTHOR]

• Study of foam glass-ceramics for sound barriers on traffic networks. • Three sub-structure factors were introduced to modify Johnson-Allard model. • Sound absorption model of foam glass-ceramics was established. Foam glass-ceramics have the characteristics of broadband sound absorption, lightweight and high-strength, which can be utilized in sound barriers on traffic networks. Due to the complexity of microstructure, there is no sound absorption model suitable for foam glass-ceramics at present. In order to realize the prediction of sound absorption performance, a sound absorption model based on Johnson-Allard model was studied in this paper. The results show that the sound absorption coefficient of foam glass-ceramics only can be accurately predicted by Johnson-Allard model in a relatively low frequency band (500∼1250 Hz). Therefore, to broaden the applicability of the model to acoustic frequencies, three sub-structure factors were introduced to modify Johnson-Allard model with the influence of microstructure on the sound absorption performance fully considered. The results show that the modified Johnson-Allard model has high accuracy in predicting the sound absorption coefficient of foam glass-ceramics in the full frequency band of traffic network noise. [ABSTRACT FROM AUTHOR]

The generalized Hamming weights dr(C) of a linear code C are a natural generalization of the minimum Hamming distance d(C)[=d_{1}(C)] and have become an important research object in coding theory since Wei’s originary work in 1991. In this paper, two general formulas on dr(C) for irreducible cyclic codes are presented using Gauss sums and the weight hierarchy \{d_{1}(C), d_{2}(C), \ldots , d_{k}(C)\}~(k=\dim C)$ is completely determined for several cases. [ABSTRACT FROM AUTHOR]