Determination of Elements of Groups Ⅲ A and ⅣA Using Microwave Plasma Torch Atomic Emission Spectrometry

The determination of the elements of groups ⅢA and ⅣA by means of microwave plasma torch atomic emission spectrometry(MPT AES) was studied systematically. Sample solutions were introduced into the plasma with a pneumatic nebulizer in continuous sampling mode and flow injection (FI) mode. The emission characteristics of these elements were investigated in details, and the basic data obtained are very important to the development of MPT AES. The analytical performances were examined. For most elements, the detection limits obtained by this method were principally the same as those obtained by inductively coupled plasma atomic emission spectrometry (ICP AES).

The Trace Elements are Bounded by Organic Functional Groups in Coal:A Studying Result Based on FTIR Analysis

The relationship between trace elements in coal and organic functional groups of coal, also some of aromatic structure, was investigated by using curve fitting of infrared spectra. Cluster analysis was also performed according to the degree of affinity of organic groups to the trace elements. The results show that there is a possibility that trace elements, especially LREE, were bound to peripheral organic functional groups of middle rank coal macromolecule. The most possible functional group that binds trace element is the hydroxyl, and to the less degree, the asymmetric -CH3 and 〉CH2 stretching, -CH3 stretching, etc. The degree of affinity of trace elements to different functional groups varies. The tendency obeys the natural structural changing law of trace elements-- the periodic law. The deviation of some trace elements from this regular trend is attributed to the deviation of intrinsic ＂confusion degree＂ （conventional molar entropy） of the matter system of coal basin, which is affected by the inner and outer factors during the evolution.

A RECOGNITION OF SIMPLE GROUPS PSL(3,q) BY THEIR ELEMENT ORDERS

For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.

Adsorption kinetics of platinum group elements onto macromolecular organic matter in seawater

Adsorption kinetics of the interaction between Pt, Pd and Rh(defined here as platinum group elements, PGEs)ions and macromolecular organic compounds(MOCs,>10 kDa), including humic acid, carrageenan and bovine serum albumin, and different cutoff fractions of natural organic matter(>1 kDa and >3 kDa) obtained from seawater using centrifugal ultrafiltration devices were investigated. For a given element, all the adsorption kinetics did not reach equilibrium except the interaction between Pt and >1 kDa cutoff, and between Pd and humic acid.For all the tested MOCs, the adsorption kinetics could be divided into two stages, a rapid adsorption process in the first 8 h and the desorption stage after the first 8 h until the equilibrium. The change trend of partition coefficient(log10Kd) values with experiment time was consistent with that of the kinetic curves. However, in the interaction between PGE ions and natural dissolved organic matter(NDOM), an obvious difference in the change trends of log10Kd and kinetic curves was observed. It indicated that the partition behavior of PGE ions interacting with NDOM in seawater was a combined effect of different organic constituents. The adsorption and log10Kd of PGEs in the >1 kDa NDOM fraction were higher and more stable than those in the >3 kDa NDOM fraction. The results also indicated that the 1–3 kDa NDOM may dominate the interaction between PGEs ions and NDOM. Moreover, no kinetic model could perfectly simulate the adsorption process. It indicated that the colloidal struction and morphology of MOCs or NDOM in seawater might be inhomogeneous. Hence, the interaction between PGE ions and organic matter in seawater was a complicated process and needs further research.

Main group metal elements for ambient-condition electrochemical nitrogen reduction

Electrocatalytic N_(2) reduction under ambient-condition is considered to be the most appealing strategy to the conventional Haber-Bosch process for synthetic ammonia to alleviate greenhouse emissions and reduce environmental pollution, mainly powered by renewable energy. Recent years, rapid advances have been gained in this attractive research field, and numerous electrocatalysts have been exploited. However, its conversion efficiency is still far behind the requirement of industrial applications owing to the breakage of the N≡N triple bond, which is an energetically challenging kinetically complex multistep reaction and the strong competing reaction of hydrogen evolution reaction. Recently, main group metal-based catalysts have been demonstrated promising application prospect for ammonia production, significantly boosting their further application in this field. However, a comprehensive review of main group metal-based catalysts towards electrochemical ammonia production applications is still lacking. In this review, the fundamentals of N_(2) reduction, such as the reaction pathways, the reaction potential and the challenges of N_(2) reduction have been comprehensively discussed. And then, the role, mechanism, and effect of each main group element-based catalysts used for N_(2) reduction (Li, K, Al, Ga, Sn, Sb, Bi, and their compounds) are systematically summarized. Finally, several state-of-the-art strategies to promote their NRR catalytic performance, as well as the existing problems and prospects are put forward. This review is expected to guide the design and establishment of more efficient electrocatalytic N_(2) reduction systems based on main group metal elements in the future.

Platinum-group Element Geochemistry of Magnetite from Porphyry-Cu-Mo Deposits and their Host Rocks(Siberia,Russia)

The concentrations of platinum-group elements （PGE） have been analyzed in primary magmatic magnetite samples from the Zhireken, Shakhtama and Aksug porphyry Cu-Mo deposits （Siberia, Russia） by laser ablation-inductively coupled plasma mass spectrometry to determine the range of PGE contents in magnetites and to check whether magnetite from two main rock suites （barren plutonic suite and mineralized porphyry suite） has distinct PGE composition. The results presented here indicate that magnetites are enriched in PGE relative to whole-rocks. Comparison of ore-related porphyry and barren plutonic suites shows that magnetite exhibit relatively similar PGE distribution patterns in both suites. Variations in Rh and Ru contents were controlled by the oxygen fugacity during magma crystallization.

Geochemistry and mineralogy of platinum-group elements(PGE)in chromites from CentralnoyeⅠ,Polar Urals,Russia

The Polar Urals region of northern Russia is well known for large chromium （Cr）-bearing massifs with major chromite orebodies, including the Centralnoye I deposit in the Ray-Iz ultramafic massif of the Ural ophiolite belt. New data on platinum （Pt）-group elements （PGE）, geochemistry and mineralogy of the host dunite shows that the deposit has anomalous iridium （Ir） values. These values indicate the predominance of ruthenium--osmium--iridium （Ru--Os--Ir）-bearing phases among the platinum-group mineral （PGM） assemblage that is typical of mantle-hosted chromite ores. Low Pt values in chromites and increased Pt values in host dunites might reflect the presence of cumulus PGM grains. The most abundant PGM found in the chromite is erlichmanite （up to 15 μm）. Less common are cuproiridsite （up to 5 μm）, irarsite （up to 4--5 μm）, and laurite （up to 4 μm）. The predominant sulfide is heazlewoodite, in intergrowth with Ni--Fe alloys, sporadically with pentlandite, and rarely with pure nickel. Based on the average PGE values and esti- mated Cr-ore resources, the Centralnoye I deposit can be considered as an important resource of PGE.

ABUNDANCE AND DISTRIBUTION OF PLATINUM-GROUP ELEMENTS (PGE) IN PERIDOTITE FROM THE DAGZHUKA OPHIOLITE IN TIBET:IMPLICATIONS FOR MANTLE METASOMATISM

Information on abundance and distribution of platinum\|group elements (PGE) in peridotite from ophiolite is relevant to understand the nature and evolution of the upper mantle. The ophiolite suite outcropping along the famous suture zone of Yarlung Zangbo River, Tibet, has attracted wide attention of geologists both in China and abroad. The Dagzhuka ophiolite of in the suture zone is thought to display a complete ophiolitic sequence. The peridotite from the Dazhuka ophiolite is composed of fairly fresh or unaltered lherzolite, harzburgite and minor dunite which are the upper mantle residuum formed by 15%～35% partial melting. In this paper we have mainly studied the abundance and distribution of PGE in the harzburgites and lherzolites. The harzburgites and lherzolites preserve total PGE contents of 28 37×10 -9 ～50 67×10 -9 respectively higher than Primitive mantle or the peridotite from some typical ophiolites and Alpine. They all have fractionated chondrite\|normalized PGE patterns with positive slopes from Ir to Pd (Fig.1), and Pd/Ir=1 13～2 40>1, Pd/Rh=2 23～7 49>1, and Pd/Pt=0 26～1 16 (average 0 67) higher than Primitive mantle (1 11, 2 35, 0 57) or CI\|chondrite (1 01, 2 73, 0 53). Consequently, the Dagzhuka peridotite are PGE\|enriched, but otherwise possess residual characteristics arising from a minimum of 15% partial melting. It is suggested that mantle residuum by partial melting have low total PGE contents, fractionated chondrite\|normalized PGE patterns with negative or slightly flat slopes from Ir to Pd, and Pd/Ir<1. But, the total PGE contents, chondrite\|normalized PGE patterns and Pt/Ir, Pd/Rh and Pd/Pt values of the Dagzhuka peridotite are completely inconsistent with a residual origin. Partial melting would have partitioned all sulfide in the source into the melt. In fact, no sulfide or silicate melt remained in the Dagzhuka peridotite. Therefore, PGE in Dagzhuka peridotite are not present in sulfides. The PGE\|enrichment and fractionation of the Dagzhuka peridotites seem to arise from mantle metasomatism of melts/fluid enrich incompatible elements include Pt and Pt, but not from residual or percolation of sulfides. The enrichment of Cs, Rb, Ba, Th, U and LREE in Dagzhuka peridotite also give a hint of the mantle metasomatism. The abundance and distribution of PGE in the peridotite from the Dagzhuka ophiolite show the nature and evolution of the Dagzhuka upper mantle are distinctive.

Recent Development in Simultaneous Multi-Element Determination of the Platinum Group Elements and Gold in Geological and Environmental Samples

In recent years, the modern methods of multi-element analysis of precious metals have attracted wide attention in scientific research and industry. The application and development in the decomposition of samples, separation and enrichment, and modern instrumental analysis of the platinum-group elements (PGEs) and gold in geological and environmental samples have been reviewed. Finally, the tendency of analysis of precious metals is also prospected.

Platinum-Group Element Geochemical Characteristics of the Picrites and High-Ti Basalts in the Binchuan Area,Yunnan Province

The Binchuan area of Yunnan is located in the western part of the Emeishan large igneous province in the western margin of the Yangtze Block. In the present study, the Wuguiqing profile in thickness of about 1440 m is mainly composed of high-Ti basalts, with minor picrites in the lower part and andesites, trachytes, and rhyolites in the upper part. The picrites have relatively higher platinum- group element （PGE） contents （PGE=16.3-28.2 ppb）, with high Cu/Zr and Pd/Zr ratios, and low S contents （5.03-16.9 ppm）, indicating the parental magma is S-unsaturated and generated by high degree of partial melting of the Emeishan large igneous province （ELIP） mantle source. The slightly high Cu/Pd ratios （11 000-24 000） relative to that of the primitive mantle suggest that 0.007% sulfides have been retained in the mantle source. The PGE contents of the high-Ti basalts exhibit a wider range （~PGE=0.517-30.8 ppb）. The samples in the middle and upper parts are depleted in PGE and have ~Nd （260 Ma） ratios ranging from -2.8 to -2.2, suggesting that crustal contamination of the parental magma during ascent triggered sulfur saturation and segregation of about 0.446%-0.554% sulfides, and the sulfide segregation process may also provide the ore-forming material for the magmatic Cu-Ni-PGE sulfide deposits close to the studied basalts. The samples in this area show Pt- Pd type primitive mantle-normalized PGE patterns, and the Pd/Ir ratios are higher than that of the primitive mantle （Pd/Ir=l）, indicating that the obvious differentiation between Ir-group platinum- group elements （IPGE） and Pd-group platinum-group elements （PPGE） are mainly controlled by olivine or chromites fractionation during magma evolution. The Pd/Pt ratios of most samples are higher than the average ratio of mantle （Pd/Pt=0.55）, showing that the differentiation happened between Pt and Pd. The differentiation in picrites may be relevant to Pt hosted in discrete refractory Pt-alloy phase in the mantle; whereas the differentiation in the high-Ti basalts is probably associated with the fractionation of Fe-Pt alloys, coprecipitating with Ir-Ru-Os alloys. Some high-Ti basalt samples exhibit negative Ru anomalies, possibly due to removal of laurite collected by the early crystallized chromites.

Platinum-Group Elements Geochemistry and Chromian Spinel Composition in Podiform Chromitites and Associated Peridotites from the Cheshmeh-Bid Deposit, Neyriz, Southern Iran: Implications for Geotectonic Setting

Dunite and serpentinized harzburgite in the Cheshmeh-Bid area, northwest of the Neyriz ophiolite in Iran, host podiform chromitite that occur as sehlieren-type, tabular and aligned massive lenses of various sizes. The most important chromitite ore textures in the Cheshmeh-Bid deposit are massive, nodular and disseminated. Massive chromitite, dunite, and harzburgite host rocks were analyzed for trace and platinum-group elements geochemistry. Chromian spinel in chromitite is characterized by high Cr#（0.72-0.78）, high Mg#（0.62-0.68） and low TiO2 （0.12 wt%-0.2 wt%） content. These data are similar to those of chromitites deposited from high degrees of mantle partial melting. The Cr# of chromian spinel ranges from 0.73 to 0.8 in dunite, similar to the high-Cr chromitite, whereas it ranges from 0.56 to 0.65 in harzburgite. The calculated melt composition of the high-Cr chromitites of the Cheshmeh-Bid is 11.53 wt%-12.94 wt% A1203, 0.21 wt%-0.33 wt% TiO2 with FeO/MgO ratios of 0.69-0.97, which are interpreted as more refractory melts akin to boninitic compositions. The total PGE content of the Cheshmeh-Bid chromitite, dunite and harzburgite are very low （average of 220.4, 34.5 and 47.3 ppb, respectively）. The Pd/Ir ratio, which is an indicator of PGE fractionation, is very low （0.05- 0.18） in the Cheshmeh-Bid chromitites and show that these rocks derived from a depleted mantle. The chromitites are characterized by high-Cr#, low Pd ＋ Pt （4-14 ppb） and high IPGE/PPGE ratios （8.2- 22.25）, resulting in a general negatively patterns, suggesting a high-degree of partial melting is responsible for the formation of the Cheshmeh-Bid chromitites. Therefore parent magma probably experiences a very low fractionation and was derived by an increasing partial melting. These geochemical characteristics show that the Cheshmeh-Bid chromitites have been probably derived from a boninitic melts in a supra-subduction setting that reacted with depleted peridotites. The high-Cr chromitite has relatively uniform mantle-normalized PGE patterns, with a steep slope, positive Ru and negative Pt, Pd anomalies, and enrichment of PGE relative to the chondrite. The dunite （total PGE = 47.25 ppb） and harzburgite （total PGE =3 4.5 ppb） are highly depleted in PGE and show slightly positive slopes PGE spidergrams, accompanied by a small positive Ru, Pt and Pd anomalies and their PdJIrn ratio ranges between 1.55-1.7and 1.36-1.94, respectively. Trace element contents of the Cheshmeh-Bid chromitites, such as Ga, V, Zn, Co, Ni, and Mn, are low and vary between 13-26, 466-842, 22-84, 115- 179, 826-1210, and 697-1136 ppm, respectively. These contents are compatible with other boninitic chromitites worldwide. The chromian spinel and bulk PGE geochemistry for the Cheshmeh-Bid chromitites suggest that high-Cr chromitites were generated from Cr-rich and, Ti- and Al-poor honinitic melts, most probably in a fore-arc tectonic setting related with a supra-subduction zone, similarly to other ophiolites in the outer Zagros ophiolitic belt.

3D finite element analysis on pile-soil interaction of passive pile group

The interaction between pile and soft soil of the passive pile group subjected to soil movement was analyzed with three-dimensional finite element model by using ANSYS software. The soil was assumed to be elastic-plastic complying with the Drucker-Prager yield criterion in the analysis. The large displacement of soil was considered and contact elements were used to evaluate the interaction between pile and soil. The influences of soil depth of layer and number of piles on the lateral pressure of the pile were investigated, and the lateral pressure distributions on the (2×1) pile group and on the (2×2) pile group were compared. The results show that the adjacent surcharge may result in significant lateral movement of the soft soil and considerable pressure on the pile. The pressure acting on the row near the surcharge is higher than that on the other row, due to the "barrier" and arching effects in pile groups. The passive load and its distribution should be taken into account in the design of the passive piles.

Geodynamic significance and genesis of chromitites from the Islahiye ophiolite(Gaziantep,SE Anatolia)as constrained by platinum group element(PGE)compositions and mineral chemistry characteristics

Chromitites associated with intensely altered dunites and harzburgites from fourteen dif ferent localities in the Islahiye ophiolites(SE Anatolia)is reported here for the first time.These chromitites were observed as lenticular and banded bodies with disseminated and massive textures and containing magnesiochromite grains with the following composition:CrO=58.91–59.74 wt%,Al_(2)O_(3)=10.85–11.20 wt%,and TiO=0.09–0.13 wt%.The Mg#[Mg/(Mg+Fe)]values of magnesiochromite from the Islahiye ophiolite range between 0.52 and 0.60 and their Cr#[Cr/(Cr+Al)]values vary from 0.7802 to 0.7844.These contents vary with a constant pattern,coincident with the estimated parental liquids that have originated from the derivative of a single bulk of boninitic magma together with Al,Ti-poor,and Cr-rich initial contents.The chromitites are serpentinised in almost all parts of the study area,and harzburgite and dunite can be observed in different locations.Although the overall composition of platinum group elements(PGE)in most examined chromitites varies between 97 and 191 ppb,three chromitites from the Islahiye region present enrichments in overall PGE(up to 214 ppb).The mineralogical and geochemical features of chromitites from the Islahiye region exhibit a robust similarity to podiform chromitites in the mantle fragment of supra–subduction zone type ophiolitic bodies.The estimated parental magmas of the investigated chromites are consistent with the diff erentiation of arcrelated melts and do not suggest an oceanic spreading centre tectonic environment.The Islahiye chromites are enriched in IPGE(Ir,Os,Ru),with the occasional presence of Ru and Ir and higher Os contents in chromite.Furthermore,we did not find any platinum group minerals(PGM)associated with the serpentine silicate sample matrix,which would have stated a secondary enrichment in PGEs.All chromitites in the investigated region have high Cr and low Ti values,are defined as magnesiochromite and were crystallised from a characteristic boninitic magma.

Analysis of platinum-group elements in drill core samples from the Meishan Permian-Triassic boundary section, China

There is a long-standing controversy of what triggered the extinction at the Permian-Triassic boundary, the most severe mass extinction in the geologic record, including flood basaltic volcanism and/or bolide impact hypothesis. In order to clarify various pieces of evidence for the mass extinction event at the Permian-Triassic boundary, some researchers from some laboratories throughout the world have made a comprehensive study on a group of samples from the Meishan area of China. Some fresh core samples from the Permian-Triassic boundary in the Meishan area were analyzed in this study. The results showed that there is no Ir anomaly. Moreover, the PGEs patterns of those samples show obvious differentiation characteristics, that is different from the case encountered in meteorites. So no evidence supports the hypothesis of extraterrestrial impact. In contrast, the PGEs patterns are similar to those of Siberian and Emeishan basalts, which indicates that those PGEs are derived mainly from the basalts, lending a support to the correlation between mass extinction at the Permian-Triassic boundary and flood basaltic volcanism. This study has also confirmed the results for samples from section C prior to the analysis of the samples.

Geochemistry of platinum-group elements in the podiform chromitites and associated peridotites of the Nain ophiolites,Central Iran:Implications for geotectonic setting

The Nain ophiolite complex with an extent of[600 km2 is a part of the Central Iranian ophiolite,which is related to the opening and subsequent closure of the Neo-Tethys Ocean.Dunite and serpentinized harzburgite in the Nain area host podiform chromitites that occur as three(eastern Hajhossein,western Hajhossein,and Soheil Pakuh)schlieren-type tabular and aligned massive lenses with various sizes.The most common chromitite ore textures are massive,nodular,disseminated,and banded,reflecting crystal settling processes.The Cr#[Cr/(Cr+Al)]ranges from 0.43 to 0.81(average 0.63).The Mg#[Mg/(Mg+Fe2+)]varies from 0.25 to 0.78(average0.62).The Nain ophiolite and hosted chromitite are generally characterized by high Cr#,reflecting crystallization from a very hot boninite magma in a MORB setting.The high Cr#in the Nain chromitite also indicates a high degree of melting(15%–35%)of the depleted peridotite.The average total PGE content in the ophiolitic host rock(harzburgite and dunite)and chromite are 107 and 221 ppb,respectively.The Nain ophiolite and chromitite have high IPGE/PPGE and negative Pt*(Pt/Pt*=0.6)anomaly,which is a characteristic of high Cr#chromitite.The U-shaped REE pattern of dunite host rock suggests the interaction of depleted mantle peridotite with boninitic melt.Geochemical data suggest that the Nain chromitites are related to the boninitic magma emplacement in a suprasubduction zone.

Concentration of Platinum Group Elements during the Early Earth Evolution: A Review

Numerous unique geological processes [1] took place during the early Earth evolution;several of them, especially those occurring in the Hadean—Early Archean and later, are reflected in the modern geological (geophysical, geochemical, etc.) pattern. One such significant enigmatic feature is the preservation of extremely dense and heavy platinum group elements (PGEs): Pt, Pd, Rh, Ru, Ir, Os. Concentration of PGEs during this period could have taken place in two ways: 1) presence of particular matter capable of preserving PGEs near the earth's surface, 2) transportation of PGEs by magma flows from deep lithospheric (asthenospheric) layers (slabs) to the subsurface. Clearly, much of the dense and heavy PGEs did not sink through to the Earth’s mantle (core) at the time of the magma-ocean, and occur near Earth’s surface in abundances for formation of ore deposits with PGE concentrations found to be 2 - 3 orders of magnitude greater than those in their host media. Their enrichments are associated in numerous cases with such enigmatic phenomena as formation of anorthosites and anorthosite-bearing layered magmatic intrusions. PGE deposits and mineralization zones are also found in associations with chromitites, dunites and serpentinites. In this review, problems related to the initial concentration and preservation of PGEs, their association with anorthosites, and formation of layered intrusions are discussed in detail. The main aim of this article is analysis of the requirements—initial concentration and preservation of PGE and PGM (Platinum Group Minerals) during the early Earth evolution, as well as examination of the distribution behavior of some PGEs in different ore deposits and meteorites. It is supposed that meteoritic bombardment of Earth has played a significant role in formation of PGEs deposits. Some conclusions made in this article may be useful for developing and enhancing strategies of prospecting for PGEs deposits.

A Determinant Criterion of Invertible Elements in Group Algebras

An embedding from a group algebra to a matrix algebra is given in this paper. By using it, a criterion for an invertible element in a group algebra is proven.

Group Decision-Making Model of Renal Cancer Surgery Options Using Entropy Fuzzy Element Aczel-Alsina Weighted Aggregation Operators under the Environment of Fuzzy Multi-Sets

Since existing selection methods of surgical treatment schemes of renal cancer patients mainly depend on physicians’clinical experience and judgments,the surgical treatment options of renal cancer patients lack their scientifical and reasonable information expression and group decision-making model for renal cancer patients.Fuzzy multi-sets(FMSs)have a number of properties,which make them suitable for expressing the uncertain information of medical diagnoses and treatments in group decision-making(GDM)problems.To choose the most appropriate surgical treatment scheme for a patient with localized renal cell carcinoma(RCC)(T1 stage kidney tumor),this article needs to develop an effective GDM model based on the fuzzy multivalued evaluation information of the renal cancer patients.First,we propose a conversionmethod of transforming FMSs into entropy fuzzy sets(EFSs)based on the mean and Shannon entropy of a fuzzy sequence in FMS to reasonably simplify the information expression and operations of FMSs and define the score function of an entropy fuzzy element(EFE)for ranking EFEs.Second,we present the Aczel-Alsina t-norm and t-conorm operations of EFEs and the EFE Aczel-Alsina weighted arithmetic averaging(EFEAAWAA)and EFE Aczel-Alsina weighted geometric averaging(EFEAAWGA)operators.Third,we develop a multicriteria GDM model of renal cancer surgery options in the setting of FMSs.Finally,the proposed GDM model is applied to two clinical cases of renal cancer patients to choose the best surgical treatment scheme for a renal cancer patient in the setting of FMSs.The selected results of two clinical cases verify the efficiency and rationality of the proposed GDM model in the setting of FMSs.

ON DENSITY OF SMOOTH ELEMENTS FOR AN ACTION OF AN AMENABLE GROUP

The aim of this paper is to prove the problem 2.2.2 in Bratteli's paper, It is proved that the problem is true for amenable group action.