Within high-risk industries, efficient management of safety is an important element of organisational efforts to reduce accidents. Most organisations such as nuclear, aviation and oil and gas sectors have a safety man...Within high-risk industries, efficient management of safety is an important element of organisational efforts to reduce accidents. Most organisations such as nuclear, aviation and oil and gas sectors have a safety management system (SMS) which provides sequence of organisational procedure to identify hazards, mitigation of risk, measure performance, investigate incidents and maintain an on-going continuous improvement. However, experts believe that when such complex organisations complement safety management system with isomorphic lessons and organisational learning strategies to manage safety, there will be a high propensity to aggressively reduce risk and save cost. Undoubtedly, learning from accidents/incidents is one of many ways to manage safely in any given organisation. As a result, this paper is intended to ascertain if organisations use isomorphic lessons and organisational learning as strong feature of organisation’s practice capable of promoting stronger safety culture;and if lessons learned from other high-risk sectors can help inform risk-based decisions in organisations. Risk experts and by extension the nuclear sector, could have learned from past accident such as the Three Mile Island of 1979 and employ lessons learned to forestall future occurrences. Primary data was gathered via online, and research population are health and safety professionals from aviation, nuclear, and the oil and gas sectors. The sample size recruited are aviation (n = 59, 25%);nuclear (n = 124, 54%);and oil and gas (n = 49, 21%). Statistical Package for the Social Sciences (SPSS) software was used to analyse 232 responses used for this paper.展开更多
A series of mesoporous alumina (MA) supported cobalt (Co/MA) catalysts with MA isomorphically substituted by zirconium (Zr) were synthesised and evaluated for their performance in the Fischer</span><span styl...A series of mesoporous alumina (MA) supported cobalt (Co/MA) catalysts with MA isomorphically substituted by zirconium (Zr) were synthesised and evaluated for their performance in the Fischer</span><span style="font-family:Verdana;">-</span><span style="font-family:""><span style="font-family:Verdana;">Tropsch synthesis. The Zr/(Zr + Al) atomic ratios varied from 1% - 15%. A zirconium-impregnated Co/MA catalyst prepared by wet impregnation with a Zr/(Zr + Al) atomic ratio of 5% was also evaluated to examine Zr incorporation’s effect method. The catalysts synthesised were characterised using N</span><sub><span style="font-family:Verdana;">2</span></sub><span style="font-family:Verdana;"> adsorption-desorption, X-ray Powder Diffraction (XRD), Transmission Electron Microscopy (TEM), and X-Ray Photoelectron Spectroscopy (XPS). It was found that Zr</span><sup><span style="font-family:Verdana;">4+</span></sup><span style="font-family:Verdana;"> ions were incorporated into the framework of MA and kept intact up to a Zr/(Zr + Al) atomic ratio of 5%. The cobalt dispersion and reducibility were improved as the Zr/(Zr + Al) atomic ratio increased to 50%. The performance of these catalysts for Fischer</span></span><span style="font-family:Verdana;">-</span><span style="font-family:""><span style="font-family:Verdana;">Tropsch synthesis was evaluated using a fixed bed reactor at temperature and pressure of 493 K and 20 bar, respectively. The feed syngas </span><span><span style="font-family:Verdana;">had an H</span><sub><span style="font-family:Verdana;">2</span></sub><span style="font-family:Verdana;">/CO ratio of 2, diluted with 10% Ar. For isomorphically</span></span><span style="font-family:Verdana;"> Zr-substituted Co/MA, the CO conversion and selectivity of diesel (C</span><sub><span style="font-family:Verdana;">10</span></sub><span style="font-family:Verdana;"> - C</span><sub><span style="font-family:Verdana;">20</span></sub><span style="font-family:Verdana;">) increased first and then decreased with increasing the Zr/(Zr + Al) atomic ratio. The maximum 38.9% CO conversion and 34.6% diesel (C</span><sub><span style="font-family:Verdana;">10</span></sub><span style="font-family:Verdana;"> - C</span><sub><span style="font-family:Verdana;">20</span></sub><span style="font-family:Verdana;">) selectivity were obtained at Zr/(Zr + Al) atomic ratio of 5%. The isomorphic substitution method was better than the wet impregnation method in CO conversion and diesel selectivity.展开更多
This paper provides several linear isomorphism theorems for certain nonsymmetric differential operators of sixth order under proper topologies about some complex parameters. From these results, one can, to a large ext...This paper provides several linear isomorphism theorems for certain nonsymmetric differential operators of sixth order under proper topologies about some complex parameters. From these results, one can, to a large extent, explain and control the stability of some objects in their moving processes.展开更多
Isomorphic substitution of ferric ion(Fe~(3+))by aluminum ion(Al~(3+))in iron(hydro)oxides is ubiquitous in natural environments.Aluminum substitution inevitably leads to changes in the microstructures,physicochemical...Isomorphic substitution of ferric ion(Fe~(3+))by aluminum ion(Al~(3+))in iron(hydro)oxides is ubiquitous in natural environments.Aluminum substitution inevitably leads to changes in the microstructures,physicochemical properties,and surface reactions of iron(hydro)oxides,which may have great impacts on the sequestration of nutrients and contaminants in soils and aquatic environments.Over the past decades,the structural properties and surface reactivity of Al-substituted iron(hydro)oxides have been intensively studied.Iron(hydro)oxides in various structural forms and with different Al substitution amounts present high application potentials in addressing environmental issues.A timely summary of the structural properties and interfacial reactions of the most common and representative Al-substituted iron(hydro)oxides is of significance.Herein,the effects of Al substitution on the structural properties and surface activities of iron(hydro)oxides were clarified according to the microstructure,crystal facets,surface site type and density,interfacial reaction mechanisms,and modeling parameters of iron(hydro)oxides.This review systematically elucidates how Al substitution affects the structural properties and surface reactions of iron(hydro)oxides,including the well crystallized goethite and hematite and the poorly crystallized ferrihydrite,providing theoretical guidance for further exploration of the mineralogical characteristics and environmental geochemical behaviors of iron(hydro)oxides.展开更多
Cobalt catalysts supported on a series of mesoporous SBA-15 materials isomorphically substituted with zirconium (Zr/Si atomic ratio=1/20) with different pore sizes (5.7 nm,7.8 nm,11.6 nm,17.6 nm) have been synthesized...Cobalt catalysts supported on a series of mesoporous SBA-15 materials isomorphically substituted with zirconium (Zr/Si atomic ratio=1/20) with different pore sizes (5.7 nm,7.8 nm,11.6 nm,17.6 nm) have been synthesized.The catalysts were characterized by transmission electron microscopy,29 Si solid state magic angle spinning (MAS)NMR,N2 adsorption-desorption measurements,X-ray powder diffraction,X-ray photoelectron spectroscopy,H2-temperature programmed reduction,H2-temperature programmed desorption and O2 titrations.The results indicated that larger pore size led to weaker interactions between cobalt and the supports which lowered the temperature of both reduction steps (Co3O4 → CoO and CoO→ Co0).The catalytic performances of the catalysts in Fischer-Tropsch synthesis (FTS) were tested in a fixed bed reactor.It was found that the FTS catalytic activity and product selectivity depended strongly on the pore size of the catalysts.The catalyst with a pore size of 7.8 nm showed the best FTS activity,and the catalyst with a pore size of 17.6 nm showed the highest selectivity to C12-C20 and C20+ hydrocarbons.展开更多
The maximum matching graph M（G） of a graph G is a simple graph whose vertices are the maximum matchings of G and where two maximum matchings are adjacent in M（G） if they differ by exactly one edge. In this paper, ...The maximum matching graph M（G） of a graph G is a simple graph whose vertices are the maximum matchings of G and where two maximum matchings are adjacent in M（G） if they differ by exactly one edge. In this paper, we prove that if a graph is isomorphic to its maximum matching graph, then every block of the graph is an odd cycle.展开更多
An n × n ω-circulant matrix which has a specific structure is a type of important matrix. Several norm equalities and inequalities are proved for ω-circulant operator matrices with ω = e^(iθ)(0≤θ < 2π) ...An n × n ω-circulant matrix which has a specific structure is a type of important matrix. Several norm equalities and inequalities are proved for ω-circulant operator matrices with ω = e^(iθ)(0≤θ < 2π) in this paper. We give the special cases for norm equalities and inequalities, such as the usual operator norm and the Schatten p-norms. Pinching type inequality is also proposed for weakly unitarily invariant norms. Meanwhile,we present that the set of ω-circulant matrices with complex entries has an idempotent basis. Based on this basis, we introduce an automorphism on the ω-circulant algebra and then show different operators on linear vector space that are isomorphic to the ω-circulant algebra. The function properties, other idempotent bases and a linear involution are discussed for ω-circulant algebra. These results are closely related to the special structure of ω-circulant matrices.展开更多
Definition 1. Let G be a finite group, S G╲{1}and S<sup>-1</sup>={s<sup>-1</sup>|s∈G}=S. The Cayley graph on G with respect to S, written as Γ（S; G）, is defined as V（Γ（S; G））, E（Γ（...Definition 1. Let G be a finite group, S G╲{1}and S<sup>-1</sup>={s<sup>-1</sup>|s∈G}=S. The Cayley graph on G with respect to S, written as Γ（S; G）, is defined as V（Γ（S; G））, E（Γ（S; G）={g, sg）|g∈G, s∈S}. If S generates G, then Γ（S; G） is connected; otherwise it consists of [G: 【S】] disjoint copies of Γ（S; 【S】）, where 【S】 denotes the subgroup of G which is generated by S.展开更多
An isomorphic fatorisation of a graph G=（V, E） is a partition {E1, E2, …Et} of the edge set E such that the subgraphs （V, E1）, （V, E2）, …（V, E1） are all isomorphic to each other. If there exists an isomorphi...An isomorphic fatorisation of a graph G=（V, E） is a partition {E1, E2, …Et} of the edge set E such that the subgraphs （V, E1）, （V, E2）, …（V, E1） are all isomorphic to each other. If there exists an isomorphic factorisation which divides graph G into t isomorphic subgraphs, we say G is divisible by t and write t|G. Obviously, a necessary condition for t|G is that t||E（G）|. This is called the divisibility condition for G and t. Harary et al, showed that whenever t=2 or 4, the divisibility condition is sufficient for t|K（m,n,8）. They conjecture展开更多
An isomorphic factorization of a graph G=（V, E） is a partition {E1,E2,…,Et} of the edge set E such that If G has an isomorphic factorization into exactly t isomorphic subgraphs we say that G is divisible by t.
Metal oxides as support for constructing precious metal single-atom catalysts hold great promise for a wide range of industrial applications,but achieving a high-loading of thermally stable metal single atoms on such ...Metal oxides as support for constructing precious metal single-atom catalysts hold great promise for a wide range of industrial applications,but achieving a high-loading of thermally stable metal single atoms on such supports has been challenging.Herein,we report an innovative strategy for the fabrication of high-density single-atoms(Rh,Ru,Pd)catalysts on CaAl-layered double hydroxides(CaAl-LDH)via isomorphous substitution.The Rh species have occupied Ca^(2+)vacancies within CaAl-LDH laminate by ion-exchange,facilitating a substantial loading of isolated Rh single-atoms.Such catalysts displayed superior performance in the selective hydrogenation to quinoline,pivotal for liquid organic hydrogen storage,and the universality for the hydrogenation of N-heterocyclic aromatic hydrocarbons was also verified.Combining the experimental results and density functional theory calculations,the pathway of quinoline hydrogenation over Rh1CaAl-LDH was proposed.This synthetic strategy marks a significant advancement in the field of single-atom catalysts,expanding their horizons in green chemical processes.展开更多
We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan d...We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan derivations on Banach algebras are also provided.The results of this paper correct and improve the main results of[12,16,22,23]and improve the corresponding results in[2,9,27],but under weaker assumptions.展开更多
In open quantum systems,the Liouvillian gap characterizes the relaxation time toward the steady state.However,accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert sp...In open quantum systems,the Liouvillian gap characterizes the relaxation time toward the steady state.However,accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert space and the non-Hermitian nature of the Liouvillian superoperator.In this work,we propose a variational quantum algorithm for efficiently estimating the Liouvillian gap.By utilizing the Choi-Jamio lkowski isomorphism,we reformulate the problem as finding the first excitation energy of an effective non-Hermitian Hamiltonian.Our method employs variance minimization with an orthogonality constraint to locate the first excited state and adopts a two-stage optimization scheme to enhance convergence.Moreover,to address scenarios with degenerate steady states,we introduce an iterative energy-offset scanning technique.Numerical simulations on the dissipative XXZ model confirm the accuracy and robustness of our algorithm across a range of system sizes and dissipation strengths.These results demonstrate the promise of variational quantum algorithms for simulating open quantum many-body systems on near-term quantum hardware.展开更多
Let M and N be two factor von Neumann algebras that their dimensions are large than 1,η≠-1 a non zero complex number and Φa(not necessary linear)bijection between two factor von Neumann algebras satisfying Φ(I)=I....Let M and N be two factor von Neumann algebras that their dimensions are large than 1,η≠-1 a non zero complex number and Φa(not necessary linear)bijection between two factor von Neumann algebras satisfying Φ(I)=I.For all A,B∈M,define by A■B=AB+BA the Jordan product of A and B,A·_(η)B=AB+ηBA^(*)the Jordan η-*-product of A and B,respectively.Let Φ and Φ^(-1)preserve the mixed Jordan triple η-*-products.It is proved that Φ is a linear *-isomorphism if η is not real and Φ is the sum of a linear *-isomorphism and a conjugate linear *-isomorphism if η is real.展开更多
Let G be a p-mixed Warfield Abelian group and F a field of char F = p ≠ 0. It is proved that if for any group H the group algebras FH and FG are F-isomorphic, then H is isomorphic to G. This presentation enlarges a r...Let G be a p-mixed Warfield Abelian group and F a field of char F = p ≠ 0. It is proved that if for any group H the group algebras FH and FG are F-isomorphic, then H is isomorphic to G. This presentation enlarges a result of W. May argued when G is p-local Warfield Abelian and published in Proc. Amer. Math. Soc. （1988）.展开更多
It was shown by Formanek and Sibley that the group determined characterizes a finite groupG up to isomorphism. Hoehnke and Johnson (independelltly the suthors--using an argumentof Manslield) showed the corresponding r...It was shown by Formanek and Sibley that the group determined characterizes a finite groupG up to isomorphism. Hoehnke and Johnson (independelltly the suthors--using an argumentof Manslield) showed the corresponding result for k-characters, k = 1, 2, 3. The notion of kcharacters dates back to nobenius. They are determined by the group doterminaDt and maybe derived from the character table CT(G) provided one knows additionally the functionswhere C(C) = {Cg, g E G} denotes the set of conjugacy classes of G.The object of the paper is to present criteria for finite groups (more precisely for solublegroups G and H which are both semi-direct products of a similar type) when1. G and H have isomorphic spectral tables (i.e., they form a Brauer pair),2. G and H have isomorphic table of marks (in particular the Burnside rings are isomorphic),3. G and H have the same 2-characters.Using this the authors construct two non-iS.Omorphic soluble groups for which all these threerepresent at iont heor et ical invar taut s coincide.展开更多
The article is devoted to proving the inconsistency of set theory arising from the existence of strange trees. All steps of the proof rely on common informal set-theoretic reasoning, but they take into account the pro...The article is devoted to proving the inconsistency of set theory arising from the existence of strange trees. All steps of the proof rely on common informal set-theoretic reasoning, but they take into account the prohibitions that were introduced into axiomatic set theories in order to overcome the difficulties encountered by the naive Cantor set theory. Therefore, in fact, the article is about proving the inconsistency of existing axiomatic set theories, in particular, the ZFC theory.展开更多
The article is devoted to completing the proof of the inconsistency of set theory. In this article and in the two preceding ones, all steps of the proof are based on generally accepted informal set-theoretic reasoning...The article is devoted to completing the proof of the inconsistency of set theory. In this article and in the two preceding ones, all steps of the proof are based on generally accepted informal set-theoretic reasoning, but consider the prohibitions that were included in axiomatic set theories in order to overcome the difficulties encountered by the naive Cantor set theory. Therefore, in fact, the articles are about proving the inconsistency of existing axiomatic set theories, in particular, the ZFC theory.展开更多
文摘Within high-risk industries, efficient management of safety is an important element of organisational efforts to reduce accidents. Most organisations such as nuclear, aviation and oil and gas sectors have a safety management system (SMS) which provides sequence of organisational procedure to identify hazards, mitigation of risk, measure performance, investigate incidents and maintain an on-going continuous improvement. However, experts believe that when such complex organisations complement safety management system with isomorphic lessons and organisational learning strategies to manage safety, there will be a high propensity to aggressively reduce risk and save cost. Undoubtedly, learning from accidents/incidents is one of many ways to manage safely in any given organisation. As a result, this paper is intended to ascertain if organisations use isomorphic lessons and organisational learning as strong feature of organisation’s practice capable of promoting stronger safety culture;and if lessons learned from other high-risk sectors can help inform risk-based decisions in organisations. Risk experts and by extension the nuclear sector, could have learned from past accident such as the Three Mile Island of 1979 and employ lessons learned to forestall future occurrences. Primary data was gathered via online, and research population are health and safety professionals from aviation, nuclear, and the oil and gas sectors. The sample size recruited are aviation (n = 59, 25%);nuclear (n = 124, 54%);and oil and gas (n = 49, 21%). Statistical Package for the Social Sciences (SPSS) software was used to analyse 232 responses used for this paper.
文摘A series of mesoporous alumina (MA) supported cobalt (Co/MA) catalysts with MA isomorphically substituted by zirconium (Zr) were synthesised and evaluated for their performance in the Fischer</span><span style="font-family:Verdana;">-</span><span style="font-family:""><span style="font-family:Verdana;">Tropsch synthesis. The Zr/(Zr + Al) atomic ratios varied from 1% - 15%. A zirconium-impregnated Co/MA catalyst prepared by wet impregnation with a Zr/(Zr + Al) atomic ratio of 5% was also evaluated to examine Zr incorporation’s effect method. The catalysts synthesised were characterised using N</span><sub><span style="font-family:Verdana;">2</span></sub><span style="font-family:Verdana;"> adsorption-desorption, X-ray Powder Diffraction (XRD), Transmission Electron Microscopy (TEM), and X-Ray Photoelectron Spectroscopy (XPS). It was found that Zr</span><sup><span style="font-family:Verdana;">4+</span></sup><span style="font-family:Verdana;"> ions were incorporated into the framework of MA and kept intact up to a Zr/(Zr + Al) atomic ratio of 5%. The cobalt dispersion and reducibility were improved as the Zr/(Zr + Al) atomic ratio increased to 50%. The performance of these catalysts for Fischer</span></span><span style="font-family:Verdana;">-</span><span style="font-family:""><span style="font-family:Verdana;">Tropsch synthesis was evaluated using a fixed bed reactor at temperature and pressure of 493 K and 20 bar, respectively. The feed syngas </span><span><span style="font-family:Verdana;">had an H</span><sub><span style="font-family:Verdana;">2</span></sub><span style="font-family:Verdana;">/CO ratio of 2, diluted with 10% Ar. For isomorphically</span></span><span style="font-family:Verdana;"> Zr-substituted Co/MA, the CO conversion and selectivity of diesel (C</span><sub><span style="font-family:Verdana;">10</span></sub><span style="font-family:Verdana;"> - C</span><sub><span style="font-family:Verdana;">20</span></sub><span style="font-family:Verdana;">) increased first and then decreased with increasing the Zr/(Zr + Al) atomic ratio. The maximum 38.9% CO conversion and 34.6% diesel (C</span><sub><span style="font-family:Verdana;">10</span></sub><span style="font-family:Verdana;"> - C</span><sub><span style="font-family:Verdana;">20</span></sub><span style="font-family:Verdana;">) selectivity were obtained at Zr/(Zr + Al) atomic ratio of 5%. The isomorphic substitution method was better than the wet impregnation method in CO conversion and diesel selectivity.
文摘This paper provides several linear isomorphism theorems for certain nonsymmetric differential operators of sixth order under proper topologies about some complex parameters. From these results, one can, to a large extent, explain and control the stability of some objects in their moving processes.
基金financially supported by the National Natural Science Foundation of China(Nos.42207352,42007020,and 42007015)the Natural Science Fund for Excellent Young Scholars of Hainan Province,China(No.324YXQN421)。
文摘Isomorphic substitution of ferric ion(Fe~(3+))by aluminum ion(Al~(3+))in iron(hydro)oxides is ubiquitous in natural environments.Aluminum substitution inevitably leads to changes in the microstructures,physicochemical properties,and surface reactions of iron(hydro)oxides,which may have great impacts on the sequestration of nutrients and contaminants in soils and aquatic environments.Over the past decades,the structural properties and surface reactivity of Al-substituted iron(hydro)oxides have been intensively studied.Iron(hydro)oxides in various structural forms and with different Al substitution amounts present high application potentials in addressing environmental issues.A timely summary of the structural properties and interfacial reactions of the most common and representative Al-substituted iron(hydro)oxides is of significance.Herein,the effects of Al substitution on the structural properties and surface activities of iron(hydro)oxides were clarified according to the microstructure,crystal facets,surface site type and density,interfacial reaction mechanisms,and modeling parameters of iron(hydro)oxides.This review systematically elucidates how Al substitution affects the structural properties and surface reactions of iron(hydro)oxides,including the well crystallized goethite and hematite and the poorly crystallized ferrihydrite,providing theoretical guidance for further exploration of the mineralogical characteristics and environmental geochemical behaviors of iron(hydro)oxides.
基金supported by the National Natural Science Foundation of China(20590360 and 20773166)
文摘Cobalt catalysts supported on a series of mesoporous SBA-15 materials isomorphically substituted with zirconium (Zr/Si atomic ratio=1/20) with different pore sizes (5.7 nm,7.8 nm,11.6 nm,17.6 nm) have been synthesized.The catalysts were characterized by transmission electron microscopy,29 Si solid state magic angle spinning (MAS)NMR,N2 adsorption-desorption measurements,X-ray powder diffraction,X-ray photoelectron spectroscopy,H2-temperature programmed reduction,H2-temperature programmed desorption and O2 titrations.The results indicated that larger pore size led to weaker interactions between cobalt and the supports which lowered the temperature of both reduction steps (Co3O4 → CoO and CoO→ Co0).The catalytic performances of the catalysts in Fischer-Tropsch synthesis (FTS) were tested in a fixed bed reactor.It was found that the FTS catalytic activity and product selectivity depended strongly on the pore size of the catalysts.The catalyst with a pore size of 7.8 nm showed the best FTS activity,and the catalyst with a pore size of 17.6 nm showed the highest selectivity to C12-C20 and C20+ hydrocarbons.
基金Supported by National Natural Science of Foundation of China (Grant Nos. 10531070, 10721101)KJCX YW-S7 of CAS
文摘The maximum matching graph M（G） of a graph G is a simple graph whose vertices are the maximum matchings of G and where two maximum matchings are adjacent in M（G） if they differ by exactly one edge. In this paper, we prove that if a graph is isomorphic to its maximum matching graph, then every block of the graph is an odd cycle.
基金supported by National Natural Science Foundation of China(Grant Nos.11301251 and 11301252)the Applied Mathematics Enhancement Program of Linyi UniversityChina
文摘An n × n ω-circulant matrix which has a specific structure is a type of important matrix. Several norm equalities and inequalities are proved for ω-circulant operator matrices with ω = e^(iθ)(0≤θ < 2π) in this paper. We give the special cases for norm equalities and inequalities, such as the usual operator norm and the Schatten p-norms. Pinching type inequality is also proposed for weakly unitarily invariant norms. Meanwhile,we present that the set of ω-circulant matrices with complex entries has an idempotent basis. Based on this basis, we introduce an automorphism on the ω-circulant algebra and then show different operators on linear vector space that are isomorphic to the ω-circulant algebra. The function properties, other idempotent bases and a linear involution are discussed for ω-circulant algebra. These results are closely related to the special structure of ω-circulant matrices.
文摘Definition 1. Let G be a finite group, S G╲{1}and S<sup>-1</sup>={s<sup>-1</sup>|s∈G}=S. The Cayley graph on G with respect to S, written as Γ（S; G）, is defined as V（Γ（S; G））, E（Γ（S; G）={g, sg）|g∈G, s∈S}. If S generates G, then Γ（S; G） is connected; otherwise it consists of [G: 【S】] disjoint copies of Γ（S; 【S】）, where 【S】 denotes the subgroup of G which is generated by S.
文摘An isomorphic fatorisation of a graph G=（V, E） is a partition {E1, E2, …Et} of the edge set E such that the subgraphs （V, E1）, （V, E2）, …（V, E1） are all isomorphic to each other. If there exists an isomorphic factorisation which divides graph G into t isomorphic subgraphs, we say G is divisible by t and write t|G. Obviously, a necessary condition for t|G is that t||E（G）|. This is called the divisibility condition for G and t. Harary et al, showed that whenever t=2 or 4, the divisibility condition is sufficient for t|K（m,n,8）. They conjecture
文摘An isomorphic factorization of a graph G=（V, E） is a partition {E1,E2,…,Et} of the edge set E such that If G has an isomorphic factorization into exactly t isomorphic subgraphs we say that G is divisible by t.
文摘Metal oxides as support for constructing precious metal single-atom catalysts hold great promise for a wide range of industrial applications,but achieving a high-loading of thermally stable metal single atoms on such supports has been challenging.Herein,we report an innovative strategy for the fabrication of high-density single-atoms(Rh,Ru,Pd)catalysts on CaAl-layered double hydroxides(CaAl-LDH)via isomorphous substitution.The Rh species have occupied Ca^(2+)vacancies within CaAl-LDH laminate by ion-exchange,facilitating a substantial loading of isolated Rh single-atoms.Such catalysts displayed superior performance in the selective hydrogenation to quinoline,pivotal for liquid organic hydrogen storage,and the universality for the hydrogenation of N-heterocyclic aromatic hydrocarbons was also verified.Combining the experimental results and density functional theory calculations,the pathway of quinoline hydrogenation over Rh1CaAl-LDH was proposed.This synthetic strategy marks a significant advancement in the field of single-atom catalysts,expanding their horizons in green chemical processes.
文摘We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan derivations on Banach algebras are also provided.The results of this paper correct and improve the main results of[12,16,22,23]and improve the corresponding results in[2,9,27],but under weaker assumptions.
基金supported by the National Natural Science Foundation of China(Grant Nos.12375013 and 12275090)the Guangdong Basic and Applied Basic Research Fund(Grant No.2023A1515011460)Guangdong Provincial Quantum Science Strategic Initiative(Grant No.GDZX2200001)。
文摘In open quantum systems,the Liouvillian gap characterizes the relaxation time toward the steady state.However,accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert space and the non-Hermitian nature of the Liouvillian superoperator.In this work,we propose a variational quantum algorithm for efficiently estimating the Liouvillian gap.By utilizing the Choi-Jamio lkowski isomorphism,we reformulate the problem as finding the first excitation energy of an effective non-Hermitian Hamiltonian.Our method employs variance minimization with an orthogonality constraint to locate the first excited state and adopts a two-stage optimization scheme to enhance convergence.Moreover,to address scenarios with degenerate steady states,we introduce an iterative energy-offset scanning technique.Numerical simulations on the dissipative XXZ model confirm the accuracy and robustness of our algorithm across a range of system sizes and dissipation strengths.These results demonstrate the promise of variational quantum algorithms for simulating open quantum many-body systems on near-term quantum hardware.
文摘Let M and N be two factor von Neumann algebras that their dimensions are large than 1,η≠-1 a non zero complex number and Φa(not necessary linear)bijection between two factor von Neumann algebras satisfying Φ(I)=I.For all A,B∈M,define by A■B=AB+BA the Jordan product of A and B,A·_(η)B=AB+ηBA^(*)the Jordan η-*-product of A and B,respectively.Let Φ and Φ^(-1)preserve the mixed Jordan triple η-*-products.It is proved that Φ is a linear *-isomorphism if η is not real and Φ is the sum of a linear *-isomorphism and a conjugate linear *-isomorphism if η is real.
文摘Let G be a p-mixed Warfield Abelian group and F a field of char F = p ≠ 0. It is proved that if for any group H the group algebras FH and FG are F-isomorphic, then H is isomorphic to G. This presentation enlarges a result of W. May argued when G is p-local Warfield Abelian and published in Proc. Amer. Math. Soc. （1988）.
文摘It was shown by Formanek and Sibley that the group determined characterizes a finite groupG up to isomorphism. Hoehnke and Johnson (independelltly the suthors--using an argumentof Manslield) showed the corresponding result for k-characters, k = 1, 2, 3. The notion of kcharacters dates back to nobenius. They are determined by the group doterminaDt and maybe derived from the character table CT(G) provided one knows additionally the functionswhere C(C) = {Cg, g E G} denotes the set of conjugacy classes of G.The object of the paper is to present criteria for finite groups (more precisely for solublegroups G and H which are both semi-direct products of a similar type) when1. G and H have isomorphic spectral tables (i.e., they form a Brauer pair),2. G and H have isomorphic table of marks (in particular the Burnside rings are isomorphic),3. G and H have the same 2-characters.Using this the authors construct two non-iS.Omorphic soluble groups for which all these threerepresent at iont heor et ical invar taut s coincide.
文摘The article is devoted to proving the inconsistency of set theory arising from the existence of strange trees. All steps of the proof rely on common informal set-theoretic reasoning, but they take into account the prohibitions that were introduced into axiomatic set theories in order to overcome the difficulties encountered by the naive Cantor set theory. Therefore, in fact, the article is about proving the inconsistency of existing axiomatic set theories, in particular, the ZFC theory.
文摘The article is devoted to completing the proof of the inconsistency of set theory. In this article and in the two preceding ones, all steps of the proof are based on generally accepted informal set-theoretic reasoning, but consider the prohibitions that were included in axiomatic set theories in order to overcome the difficulties encountered by the naive Cantor set theory. Therefore, in fact, the articles are about proving the inconsistency of existing axiomatic set theories, in particular, the ZFC theory.
