A Note on Additive Characters of Locally Compact Fields

In this note, we give an elementary and constructive proof for that the additive character group of a locally compact field is isomorphic to itself as an additive topological group.

Additive characters and orthogonal systems of polynomials in several indeterminates over residue class rings

Let m, n and k be positive integers, m>1 and k≤n . Let Z m =Z/ m Z denote the residue class ring modulo m . Let Z denote the group of additive characters of ring Z m , x 0 denote the identity of Z . A necessary and sufficient condition for the system f\-1, ..., f\-k∈ Z m [ x\-1, ..., x\-n ] to be orthogonal is given: for all additive characters ψ 1, ..., ψ k ∈Z with ψ i≠x 0 for some i, 1≤i≤k, ∑(c\-1, ..., c\-n)∈ Z n m ψ(f\-1(c\-1, ..., c\-n))...ψ k(f\-k(c\-1, ..., c\-n))=0. As corollaries, the result of Shiue_Sun_Zhang and the result of Sun are obtained.

New strategy for reducing the EHL friction in steel contacts using additive-formed oleophobic boundary films

In this study we present a mechanism for the elastohydrodynamic(EHD)friction reduction in steel/steel contacts,which occurs due to the formation of oleophobic surface boundary layers from common boundary-lubrication additives.Several simple organic additives(amine,alcohol,amide,and fatty acid)with different molecular structures were employed as the model additives.It was found that the stronger chemisorption at 100℃,rather than the physisorption at 25℃,is more effective in friction reduction,which reaches 22%.What is more,EHD friction reduction was obtained in steel/steel contacts without use of the diamond-like carbon(DLC)coatings with their wetting or thermal effect,which was previously suggested as possible EHD friction reduction mechanism;yet about the same friction reduction of about 20%was obtained here—but with much simpler and less expensive technology,namely with the adsorbed oleophobic surface layers.A small variation in the additive’s molecular structure results in significant changes to the friction,indicating good potential in future EHD lubrication technology,where these additives could be designed and well optimised for notable reduction of the friction losses in the EHD regime.

Grain boundary and microstructure engineering of Inconel 690 cladding on stainless-steel 316L using electron-beam powder bed fusion additive manufacturing

This research explores the prospect of fabricating a face-centered cubic(fcc) Ni-base alloy cladding(Inconel 690) on an fcc Fe-base alloy(316 L stainless-steel) having improved mechanical properties and reduced sensitivity to corrosion through grain boundary and microstructure engineering concepts enabled by additive manufacturing(AM) utilizing electron-beam powder bed fusion(EPBF). The unique solidification and associated constitutional supercooling phenomena characteristic of EPBF promotes[100] textured and extended columnar grains having lower energy grain boundaries as opposed to random, high-angle grain boundaries, but no coherent {111} twin boundaries characteristic of conventional thermo-mechanically processed fcc metals and alloys, including Inconel 690 and 316 L stainless-steel.In addition to [100] textured grains, columnar grains were produced by EPBF fabrication of Inconel 690 claddings on 316 L stainless-steel substrates. Also, irregular 2–3 μm diameter, low energy subgrains were formed along with dislocation densities varying from 108 to 109 cm^2, and a homogeneous distribution of Cr_(23)C_6 precipitates. Precipitates were formed within the grains(with ~3 μm interparticle spacing),but not in the subgrain or columnar grain boundaries. These inclusive, hierarchical microstructures produced a tensile yield strength of 0.527 GPa, elongation of 21%, and Vickers microindentation hardness of 2.33 GPa for the Inconel 690 cladding in contrast to a tensile yield strength of 0.327 GPa, elongation of 53%, and Vickers microindentation hardness of 1.78 GPa, respectively for the wrought 316 L stainlesssteel substrate. Aging of both the Inconel 690 cladding and the 316 L stainless-steel substrate at 685?C for50 h precipitated Cr_(23)C_6 carbides in the Inconel 690 columnar grain boundaries, but not in the low-angle(and low energy) subgrain boundaries. In contrast, Cr_(23)C_6 carbides precipitated in the 316 L stainless-steel grain boundaries, but not in the low energy coherent {111} twin boundaries. Consequently, the Inconel690 subgrain boundaries essentially serve as surrogates for coherent twin boundaries with regard to avoiding carbide precipitation and corrosion sensitization.

Optimization of Grain Boundary Character Distribution in Fe-18Cr-18Mn-0.63N High-Nitrogen Austenitic Stainless Steel

Grain boundary engineering（GBE） is a practice of improving resistance to grain boundary failure of the material through increasing the proportion of low Σ coincidence site lattice（CSL） grain boundaries（special grain boundaries） in the grain boundary character distribution（GBCD）. The GBCD in a cold rolled and annealed Fe-18Cr-18Mn-0.63N high-nitrogen austenitic stainless steel was analyzed by electron back scatter difraction（EBSD）. The results show that the optimization process of GBE in the conventional austenitic stainless steel cannot be well applied to this high-nitrogen austenitic stainless steel. The percentage of low ΣCSL grain boundaries could increase from 47.3% for the solid solution treated high-nitrogen austenitic stainless steel specimen to 82.0% for the specimen after 5% cold rolling reduction and then annealing at 1423 K for 10 min.These special boundaries of high proportion efectively interrupt the connectivity of conventional high angle grain boundary network and thus achieve the GBCD optimization for the high-nitrogen austenitic stainless steel.

Microtexture Evolution and Grain Boundary Character Distribution of Interstitial-Free Steels With Moderate Levels of Cold Rolling Reductions

High-strength interstitial-free steel sheets have very good deep drawability when processed to have { 111 } recrystallization texture. The microtexture evolution and grain boundary character distribution of interstitial-free steels as a function of moderate levels of cold rolling reductions were investigated by the metallographic microscopy and electron backscatter diffraction technique. The results showed that there was a close relationship between micro- texture and grain boundary character distribution for interstitial-free steel, especially the distribution and features of some specific types of coincident-site lattice boundaries. In addition, a-fiber texture was weakened to vanish while 7- fiber texture strengthened gradually as cold rolling reduction was increased from 20% to 75 % for cold rolled and an- nealed samples. Accordingly, increasing the rolling reduction from 20 % to 750% would lead to a significant increase in the proportion of ∑3 boundaries. Also, it was found that the microtexture of 20% cold rolled sample would induce a high frequency of ∑11 grain boundaries, but the microtexture of 75% cold rolled sample would produce more ∑7 and ∑17 grain boundaries. It was suggested that texture played a significant role in the formation of grain boundary character distribution.

Role of grain boundary character on Bi segregation-induced embrittlement in ultrahigh-purity copper

Bismuth(Bi),as an impurity element in copper and copper-based alloys,usually has a strong tendency of grain boundary(GB)segregation,which depends on the GB characters.However,the influence of such a segregation on the properties of ultrahigh-purity copper has been rarely reported and the exact structural arrangements of Bi atoms at different GBs remain largely unclear.In this study,we investigated the influ-ence of trace amounts of Bi(50-300 wt ppm)on the ductility of an ultrahigh-purity copper(99.99999%)in the range of room temperature to 900°C.The tensile results show that the addition of Bi seriously damages the ductility of the ultrahigh-purity copper at temperatures of 450-900°C,which is due to the GB segregation of Bi.On this basis,such a segregation behavior at different types of GBs,including high and low angle GBs(HAGBs/LAGBs),and twin boundaries(TBs),via the scanning electron microscope-electron backscattered diffraction(SEM-EBSD)and aberration-corrected scanning transmission electron microscope(AC-STEM)investigations,combined with the first-principles calculations were systematically studied.The atomistic characterizations demonstrate an anisotropic Bi segregation,where severe enrich-ment of Bi atoms typically occurs at the HAGBs,while the absence of Bi adsorption prevails at LAGBs or TBs.In particular,the segregated Bi at random HAGBs exhibited the directional bilayer adsorption,while the special symmetrical7 HAGB presented a unique Bi-rich cluster superstructure.Our findings pro-vide a comprehensive experimental and computational understanding on the atomic-scale segregation of impurities in metallic materials.

Improving Intergranular Stress Corrosion Cracking Resistance in a Fe–18Cr–17Mn–2Mo–0.85N Austenitic Stainless Steel Through Grain Boundary Character Distribution Optimization

The grain boundary character distribution(GBCD) optimization and its effect on the intergranular stress corrosion cracking(IGSCC) resistance in a cold-rolled and subsequently annealed Fe-18 Cr-17 Mn-2 Mo-0.85 N high-nitrogen nickel-free austenitic stainless steel were systematically explored.The results show that stacking faults and planar slip bands appearing at the right amount of deformation(lower than 10%) are beneficial cold-rolled microstructures to the GBCD optimization.The proportion of special boundaries gradually increases in the subsequent stages of recrystallization and grain growth,accompanying with the growth of twin-related domain in the experimental steel.In this way,the fraction of low ∑ coincidence site lattice(CSL) boundaries can reach as high as 82.85% for the specimen cold-rolled by 5% and then annealed at 1423 K for 72 h.After GBCD optimization,low ∑ CSL boundaries and the special triple junctions(J2,J3) of high proportion can greatly hinder the nitride precipitation along grain boundaries and enhance the capability for intergranular crack arrest,thus improving the IGSCC resistance of the experimental steel.

Grain boundary engineering for enhancing intergranular damage resistance of ferritic/martensitic steel P92

Ferritic/martensitic(F/M)steel is widely used as a structural material in thermal and nuclear power plants.However,it is susceptible to intergranular damage,which is a critical issue,under service conditions.In this study,to improve the resistance to intergranular damage of F/M steel,a thermomechanical process(TMP)was employed to achieve a grain boundary engineering(GBE)microstructure in F/M steel P92.The TMP,including cold-rolling thickness reduction of 6%,9%,and 12%,followed by austenitization at 1323 K for 40 min and tempering at 1053 K for 45 min,was applied to the as-received(AR)P92 steel.The prior austenite grain(PAG)size,prior austenite grain boundary character distribution(GBCD),and connectivity of prior austenite grain boundaries(PAGBs)were investigated.Compared to the AR specimen,the PAG size did not change significantly.The fraction of coincident site lattice boundaries(CSLBs,3≤Σ≤29)and Σ3^(n) boundaries along PAGBs decreased with increasing reduction ratio because the recrystallization fraction increased with increasing reduction ratio.The PAGB connectivity of the 6%deformed specimen slightly deteriorated compared with that of the AR specimen.Moreover,potentiodynamic polarization studies revealed that the intergranular damage resistance of the studied steel could be improved by increasing the fraction of CSLBs along the PAGBs,indicating that the TMP,which involves low deformation,could enhance the intergranular damage resistance.

ON THE EXISTENCE AND NODAL CHARACTER OF SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

In this paper we prove the existence of k-node solution of singular nonlinear boundary value problems for each k is-an-element-of N union {0}.

ON THE EXISTENCE AND NODAL CHARACTER OF THE SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2（O, +∞） into Lt2q（O, ∞）, v>2. When v=N-1 we can get the radial solutions of problem where 2*=2N/N-2 is the critical exponent of the Sobolev embedding H1（Rn）→LQ（RN）. Kurtz has discussed the existence of κ-node solution of （1.1）, （1.2） for each κ∈N U{0} when the growth rate of |u|l-1u+f（u） is lower then |u|v+3/v-1 i.e.

GRAIN BOUNDARY CHARACTER DISTRIBUTION, TEXTURE AND SUPERPLASTIC DEFORMATION BEHAVIOR OF AN Al-Li ALLOY

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Toward developing Ti alloys with high fatigue crack growth resistance by additive manufacturing

Fatigue crack growth behaviors were investigated by three-point bending tests for TA19 alloy fabricated by laser metal deposition and four kinds of heat-treated samples.The crack growth resistance of the TA19 samples in the near-threshold regime and Paris regime was evaluated through the experimental characterization and theoretical analysis of the interaction between fatigue crack andα/βphase inter-face,columnar prior-βgrain boundary and colony boundary.The results show that in the near-threshold regime,the fatigue crack propagation threshold and resistance increase with the increase of widths of lamellarαp phases and colonies,and the decrease of the number ofαlaths with an angle(ϕ)relative to the applied stress direction ranging from 75°to 90°.In the Paris regime,the fatigue cracking path can be deflected at colony boundaries or columnar prior-βgrain boundaries.The larger the deflection angle,the more tortuous the cracking path and the lower the fatigue crack growth rate.The angle(γ)of the columnar prior-βgrain growth direction relative to the build direction affects not onlyϕof differentαvariants,but also the fatigue cracking path deflection angle(θij)at columnar prior-βgrain boundaries.An optimal combination ofγ=0°-15°-0°-15°for several adjacent columnar prior-βgrains is derived from the theoretical analysis,and that can effectively avoidϕbeing in the range from 75°to 90°and makeθij as large as possible.Such findings provide a guide for the selection of scanning strategies and process parameters to additively manufacture Ti alloys with high fatigue damage tolerance.

Microstructure and impact toughness of 16MND5 reactor pressure vessel steel manufactured by electrical additive manufacturing

Electrical additive manufacturing can improve manufacturing efficiency and reduce the cost of 16MND5 reactor pres-sure vessel steel. Impact tests were conducted to compare the impact toughness of 16MND5 steels manufactured by the electrical additive manufacturing and conventional forging, respectively. It is found that the impact toughness of electrical additive manufacturing specimen was slightly higher than that of conventional forging specimen. The characterizations of microstructure show that there were large ferrites and carbides in electrical additive manufacturing specimen. The fracture mechanisms of electrical additive manufacturing specimen were that microvoids or microcracks were prone to nucleate at the large ferrite/bainite interface and large carbide/bainitic ferrite interface, where the stress concentration was high. In addi-tion, the block size and high-angle grain boundaries played a vital role in hindering crack propagation of electrical additive manufacturing specimen, helping to improve the impact energy and leading to a low ductile–brittle transition temperature. The results suggest that the electrical additive manufacturing technology was an effective method to enhance the impact toughness of 16MND5 steel.

Effects of cold-rolling reduction on the recrystallization texture and grain boundary of ferritic stainless steel

The study investigates the effects of cold-rolling reduction on the recrystallization-annealed Nb ＋ Ti stabilized ultra-pure ferritic stainless steel with 21% Cr in regards to its microstructure evolution, grain size,recrystallization texture, and grain boundary characteristic distribution and disorientation angle. The research employed the electron back scattered diffraction technique and its results have shown that the average grain size was reduced and the {111 / 〈 112 〉 component was strengthened,which rotated towards {5541 〈225 〉 and {4451 〈384 〉 ,with an increasing cold-rolling reduction. The number fraction of the low-angle grain boundary and the coincidence site lattice （CSL） boundary ,which was mainly made up of ∑3,∑7∑11 and ∑13b, also increased.

Effect of boron addition on microstructure and mechanical properties of an additively manufactured superalloy

The effect of boron addition(0.010,0.015,and 0.020 wt.%)on the microstructure and mechanical properties of an additively manufactured superalloy was examined.The as-built microstructure was investigated by scanning electron microscopy and transmission electron microscopy.The results demonstrate that boron precipitates as M_(3)B_(2)boride at the grain boundary.The increase in boron content increases the amount ofγ/γ′eutectic and the size and fraction of M_(3)B_(2)boride.Boron creates nanoscale fine borides at grain boundaries,which significantly reinforces grain boundaries.The mechanical property analysis indicated that the addition of boron improved the tensile ductility at 760℃and stress rupture properties at 760℃/780 MPa.However,with the excessive addition of boron,the mechanical property was reduced.

Effects of initial grain size and strain on grain boundary engineering of high-nitrogen CrMn austenitic stainless steel

18 Mn18 Cr0.5 N steel with an initial grain size of 28–177 μm was processed by 2.5%–20% cold rolling and annealing at 1000°C for 24 h,and the grain boundary character distribution was examined via electron backscatter diffraction.Low strain(2.5%) favored the formation of low-Σ boundaries.At this strain,the fraction of low-Σ boundaries was insensitive to the initial grain size.However,specimens with fine initial grains showed decreasing grain size after grain boundary engineering processing.The fraction of low-Σ boundaries and the(Σ9 + Σ27)/Σ3 value decreased with increasing strain; furthermore,the specimens with fine initial grain size were sensitive to the strain.Finally,the effects of the initial grain size and strain on the grain boundary engineering were discussed in detail.

An approach to offline handwritten Chinese character recognition based on segment evaluation of adaptive duration

This paper presents a methodology for off-line handwritten Chinese character recognition based on mergence of consecutive segments of adaptive duration. The handwritten Chinese character string is partitioned into a sequence of consecutive segments, which are combined to implement dissimilarity evaluation within a sliding window whose durations are determined adaptively by the integration of shapes and context of evaluations. The average stroke width is estimated for the handwritten Chinese character string, and a set of candidate character segmentation boundaries is found by using the integration of pixel and stroke features. The final decisions on segmentation and recognition are made under minimal arithmetical mean dissimilarities. Experiments proved that the proposed approach of adaptive duration outperforms the method of fixed duration, and is very effective for the recognition of overlapped, broken, touched, loosely configured Chinese characters.

Character Development in a Multilingual International School and Its Use of Self-Assessment Tools

This article describes a multiyear initiative of a multilingual multicultural international school that has come to adopt and internalize character development as part of its identity.That is,character education has been treated as a central tenet and core value that permeates the school and binds the community.It has not been regarded as a supplemental or enhancement project,but rather integral to the general educational program.Built from a principled framework with sound theoretical backing,the infusion of character education at this international school has resulted in the crafting of new standards and the introduction of teacher and student self-assessment tools.In that vein,in this article,we share how the school has come to embrace character development and has forged personalized ways for stakeholders,including teachers and multilingual learners,to engage in improving teaching and learning.

The Role of Grain Boundaries in Organic-Inorganic Hybrid Perovskite Solar Cells and its Current Enhancement Strategies:A Review

Grain boundaries(GBs)in perovskite polycrystalline films are the most sensitive place for the formation of the defect states and the accumulation of impurities.Thus,abundant works have been carried out to explore their properties and then try to solve the induced problems.Currently,two important issues remain.First,the role of GBs in charge carrier dynamics is unclear due to their component complexity/defect tolerance nature and the insufficiency in testing accuracy.Some works conclude that GBs are benign,while others consider GBs as carrier recombination centers.Things for sure are the deterioration in ion transport and perovskite decomposition.Second,to solve the known hazards of GBs,a lot of additives have been added to anchoring ions and passivate defects.But in most of those works,GBs and perovskite surfaces are treated in the same manner ignoring the fact that GB is essentially a homogeneous junction in a narrow and slender space,while surface is a heterogeneous junction with a stratified structure.In this review,we focus on works insight into GBs and additives for them.Additionally,we also discuss the prospects of the maturity of GB exploration toward upscaling the manufacture of perovskite photovoltaic and related optoelectronic devices.