Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum leng...Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum length l such that there exists a sequenceB of length l overGcontaining k disjoint non-empty zero-sum subsequences.This paper studies the inverse problem associated with this invariant for the elementary abelian 2-groups C_(2)^(r).For r∈[2,4],we characterize the structures of zero-sum sequences of length D2(C_(2)^(r))and D2(C_(2)^(r))-1 in C_(2)^(r) that can be decomposed into at most two minimal zero-sum subsequences.For r∈[2,5],we characterize the structures of sequences of length D2(C_(2)^(r))-1.展开更多
The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to mod...The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi-cS-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this article improve and extend the corresponding results announced by many authors recently.展开更多
A p-group G is called a JC-group if the normal closure HG of every cyclic subgroup H satisfies｜G：HG｜≤p or｜HG：H｜≤p.In this paper, we classify the non-Dedekindian JC-groups for p 〉 2.
Theoretical background and an implementation of the p-group generation algorithm by Newman and O’Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant ...Theoretical background and an implementation of the p-group generation algorithm by Newman and O’Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant trees of finite p-groups.展开更多
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 ophiolit...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.展开更多
The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K...The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K2(R) =K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.展开更多
Based on a general theory of descendant trees of finite p-groups and the virtual periodicity isomorphisms between the branches of a coclass subtree, the behavior of algebraic invariants of the tree vertices and their ...Based on a general theory of descendant trees of finite p-groups and the virtual periodicity isomorphisms between the branches of a coclass subtree, the behavior of algebraic invariants of the tree vertices and their automorphism groups under these isomorphisms is described with simple transformation laws. For the tree of finite 3-groups with elementary bicyclic commutator qu-otient, the information content of each coclass subtree with metabelian main-line is shown to be finite. As a striking novelty in this paper, evidence is provided of co-periodicity isomorphisms between coclass forests which reduce the information content of the entire metabelian skeleton and a significant part of non-metabelian vertices to a finite amount of data.展开更多
In this paper, we characterize some simple Ka-groups only by using the group order and largest element orders, where a simple K4-group is a simple group of order containing exactly four distinct primes.
Let π be a set of primes. Isaacs established the π-theory of characters, which generalizes the theory of Brauer modular characters. Motivated by Isaacs＇s work, we introduce the definition of Mπ-groups and provide ...Let π be a set of primes. Isaacs established the π-theory of characters, which generalizes the theory of Brauer modular characters. Motivated by Isaacs＇s work, we introduce the definition of Mπ-groups and provide a characterization of Mπ-groups.展开更多
In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch in...In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].展开更多
Muon tomography is a capable imaging technique to measure the geometry of high-Z objects. However,most existed algorithms used in muon tomography have obscured the effects of angular distribution and momentum spectra ...Muon tomography is a capable imaging technique to measure the geometry of high-Z objects. However,most existed algorithms used in muon tomography have obscured the effects of angular distribution and momentum spectra of cosmic ray muons and reduced the spatial resolution. We present a modified multi-group model that takes into account these effects and calibrates the model by the material of lead. Performance tests establish that the model is capable of measuring the thickness of a Pb slab and identifying the material of an unknown slab on a reasonable exposure timescale, in both cases of complete and incomplete angular data. Results show that the modified multi-group model is helpful for improvements in image resolution in real applications.展开更多
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-induc...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.展开更多
The local scour around a new pile-group foundation of offshore wind turbine subjected to a bi-directional current was physically modeled with a bi-directional flow flume. In a series of experiments, the flow velocity ...The local scour around a new pile-group foundation of offshore wind turbine subjected to a bi-directional current was physically modeled with a bi-directional flow flume. In a series of experiments, the flow velocity and topography of the seabed were measured based on a system composed of plane positioning equipment and an ADV.Experimental results indicate that the development of the scour hole was fast at the beginning, but then the scour rate decreased until reaching equilibrium. Erosion would occur around each pile of the foundation. In most cases, the scour pits were connected in pairs and the outside widths of the scour holes were larger than the inner widths. The maximum scour depth occurred at the side pile of the foundation for each test. In addition, a preliminary investigation shows that the larger the flow velocity, the larger the scour hole dimensions but the shorter equilibrium time. The field maximum scour depth around the foundation was obtained based on the physical experiments with the geometric length scales of 1:27.0, 1:42.5 and 1:68.0, and it agrees with the scour depth estimated by the HEC-18 equation.展开更多
In this paper, We show that the simple K\-3-groups can be characterized by the orders of their maximal abelian subgroups. That is, we have Theorem Let G be a finite group and M a simple K \-3-group. Then ...In this paper, We show that the simple K\-3-groups can be characterized by the orders of their maximal abelian subgroups. That is, we have Theorem Let G be a finite group and M a simple K \-3-group. Then G is isomorphic to M if and only if the set of the orders of the maximal abelian subgoups of G is the same as that of M .展开更多
The use of pan-ethnic-group products form knowledge primarily depends on a designer＇s subjective experience without user participation. The majority of studies primarily focus on the detection of the perceptual deman...The use of pan-ethnic-group products form knowledge primarily depends on a designer＇s subjective experience without user participation. The majority of studies primarily focus on the detection of the perceptual demands of consumers from the target product category. A pan-ethnic-group products form gene clustering method based on emotional semantic is constructed. Consumers＇ perceptual images of the pan-ethnic-group products are obtained by means of product form gene extraction and coding and computer aided product form clustering technology. A case of form gene clustering about the typical pan-ethnic-group products is investigated which indicates that the method is feasible. This paper opens up a new direction for the future development of product form design which improves the agility of product design process in the era of Industry 4.0.展开更多
In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multigroup SIQR （susceptible-infected-quarantined-removed） model is proposed for computer worms by explicitly c...In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multigroup SIQR （susceptible-infected-quarantined-removed） model is proposed for computer worms by explicitly considering anti-virus measures and the network infrastructure. Then, the basic reproduction number of worm R0 is derived and the global dynamics of the model are established. It is shown that if R0 is less than or equal to 1, the disease-free equilibrium is globally asymptotically stable and the worm dies out eventually, whereas, if R0 is greater than 1, one unique endemic equilibrium exists and it is globally asymptotically stable, thus the worm persists in the network. Finally, numerical simulations are given to illustrate the theoretical results.展开更多
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...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.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 11071150)the Natural Science Foundation of Shanxi Province (Grant No. 2012011001-3)Shanxi Scholarship Council of China (Grant No. [2011]8-59)
文摘We classify up to isomorphism those finite p-groups, for odd primes p, which contain a cyclic subgroup of index p3.
基金supported by the National Natural Science Foundation of China(No.12301425)。
文摘Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum length l such that there exists a sequenceB of length l overGcontaining k disjoint non-empty zero-sum subsequences.This paper studies the inverse problem associated with this invariant for the elementary abelian 2-groups C_(2)^(r).For r∈[2,4],we characterize the structures of zero-sum sequences of length D2(C_(2)^(r))and D2(C_(2)^(r))-1 in C_(2)^(r) that can be decomposed into at most two minimal zero-sum subsequences.For r∈[2,5],we characterize the structures of sequences of length D2(C_(2)^(r))-1.
基金supported by the Natural Science Foundation of Yunnan Province (2011FB074)
文摘The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi-cS-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this article improve and extend the corresponding results announced by many authors recently.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1152611411601245)+3 种基金the Natural Science Foundation of Guangdong Province(Grant No.2015A030313791)the Innovative Team Project of Guangdong Province(CHINA)(Grant No.2014KTSCX196)Guangdong Province Innovation Talent Project for Youths(Grant No.2015KQNCX107)the Appropriative Researching Fund for Doctors,Guangdong University of Education(Grant No.2013ARF07)
文摘A p-group G is called a JC-group if the normal closure HG of every cyclic subgroup H satisfies｜G：HG｜≤p or｜HG：H｜≤p.In this paper, we classify the non-Dedekindian JC-groups for p 〉 2.
文摘Theoretical background and an implementation of the p-group generation algorithm by Newman and O’Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant trees of finite p-groups.
文摘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.
文摘The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K2(R) =K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.
文摘Based on a general theory of descendant trees of finite p-groups and the virtual periodicity isomorphisms between the branches of a coclass subtree, the behavior of algebraic invariants of the tree vertices and their automorphism groups under these isomorphisms is described with simple transformation laws. For the tree of finite 3-groups with elementary bicyclic commutator qu-otient, the information content of each coclass subtree with metabelian main-line is shown to be finite. As a striking novelty in this paper, evidence is provided of co-periodicity isomorphisms between coclass forests which reduce the information content of the entire metabelian skeleton and a significant part of non-metabelian vertices to a finite amount of data.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117136411271301)+2 种基金the Natural Science Foundation Project of CQ CSTC(Grant No.2014jcyjA00004)the Science and Technology Project of Chongqing Education Committee(Grant No.KJ1400520)the Foundation Project of Chongqing Normal University(Grant No.14XYY026)
文摘In this paper, we characterize some simple Ka-groups only by using the group order and largest element orders, where a simple K4-group is a simple group of order containing exactly four distinct primes.
基金Supported by NSF of China(1117116911071155)the B.S.Foundation of Shandong Province(BS2012SF003)
文摘Let π be a set of primes. Isaacs established the π-theory of characters, which generalizes the theory of Brauer modular characters. Motivated by Isaacs＇s work, we introduce the definition of Mπ-groups and provide a characterization of Mπ-groups.
基金supported by Japan Society for the Promotion of Science (Grant Scientific Research (c), No. 24540219 to the first author, JSPS Fellows, No.237213 to the second author, and No. 222176 to the third author)
文摘In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].
基金supported by the Science and Technology Development Foundation of CAEP(No.2015B0103014)the National Natural Science Foundation of China(No.11605163)
文摘Muon tomography is a capable imaging technique to measure the geometry of high-Z objects. However,most existed algorithms used in muon tomography have obscured the effects of angular distribution and momentum spectra of cosmic ray muons and reduced the spatial resolution. We present a modified multi-group model that takes into account these effects and calibrates the model by the material of lead. Performance tests establish that the model is capable of measuring the thickness of a Pb slab and identifying the material of an unknown slab on a reasonable exposure timescale, in both cases of complete and incomplete angular data. Results show that the modified multi-group model is helpful for improvements in image resolution in real applications.
基金supported by Russian Foundation for Basic Research(Project No:06-05-64254)
文摘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.
基金financially supported by the National Key Research and Development Program of China(Grant No.2017YFC1404200)the Tianjin Key Program of Applied Foundation and Advanced-Tech Research,China(Grant No.18JCZDJC40200)+1 种基金the National High Technology Research and Development Program of China(863 Program,Grant No.2012AA051709)the National Natural Science Foundation of China(Grant No.51509183)
文摘The local scour around a new pile-group foundation of offshore wind turbine subjected to a bi-directional current was physically modeled with a bi-directional flow flume. In a series of experiments, the flow velocity and topography of the seabed were measured based on a system composed of plane positioning equipment and an ADV.Experimental results indicate that the development of the scour hole was fast at the beginning, but then the scour rate decreased until reaching equilibrium. Erosion would occur around each pile of the foundation. In most cases, the scour pits were connected in pairs and the outside widths of the scour holes were larger than the inner widths. The maximum scour depth occurred at the side pile of the foundation for each test. In addition, a preliminary investigation shows that the larger the flow velocity, the larger the scour hole dimensions but the shorter equilibrium time. The field maximum scour depth around the foundation was obtained based on the physical experiments with the geometric length scales of 1:27.0, 1:42.5 and 1:68.0, and it agrees with the scour depth estimated by the HEC-18 equation.
文摘In this paper, We show that the simple K\-3-groups can be characterized by the orders of their maximal abelian subgroups. That is, we have Theorem Let G be a finite group and M a simple K \-3-group. Then G is isomorphic to M if and only if the set of the orders of the maximal abelian subgoups of G is the same as that of M .
基金Supported by National Key Technology R&D Program,China(Grant No.2015BAH21F01)National 111 Project,China(Grant No.B13044)
文摘The use of pan-ethnic-group products form knowledge primarily depends on a designer＇s subjective experience without user participation. The majority of studies primarily focus on the detection of the perceptual demands of consumers from the target product category. A pan-ethnic-group products form gene clustering method based on emotional semantic is constructed. Consumers＇ perceptual images of the pan-ethnic-group products are obtained by means of product form gene extraction and coding and computer aided product form clustering technology. A case of form gene clustering about the typical pan-ethnic-group products is investigated which indicates that the method is feasible. This paper opens up a new direction for the future development of product form design which improves the agility of product design process in the era of Industry 4.0.
基金Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010526)the Six Projects Sponsoring Talent Summits of Jiangsu Province, China (Grant No. SJ209006)+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103223110003)the Ministry of Education Research in the Humanities and Social Sciences Planning Fund of China (Grant No. 12YJAZH120)the Graduate Student Innovation Research Project of Jiangsu Province, China (Grant Nos. CXLX11 0417 and CXLX11 0404)
文摘In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multigroup SIQR （susceptible-infected-quarantined-removed） model is proposed for computer worms by explicitly considering anti-virus measures and the network infrastructure. Then, the basic reproduction number of worm R0 is derived and the global dynamics of the model are established. It is shown that if R0 is less than or equal to 1, the disease-free equilibrium is globally asymptotically stable and the worm dies out eventually, whereas, if R0 is greater than 1, one unique endemic equilibrium exists and it is globally asymptotically stable, thus the worm persists in the network. Finally, numerical simulations are given to illustrate the theoretical results.
基金supported by the National Basic Research Program of China(No.2007CB411401)the Knowledge Innovation Program of the Chinese Academy of Sciences(No.KZCX2-YW-136)the National Natural Science Formation of China(No.40873028)
文摘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.
