With the penetration of the Internet, virtual groups have become more and more popular. The reliability and accuracy of interpersonal perception in the virtual environment is an intriguing issue. Using the Social rela...With the penetration of the Internet, virtual groups have become more and more popular. The reliability and accuracy of interpersonal perception in the virtual environment is an intriguing issue. Using the Social relations model (SRM) [1], this paper investigates interpersonal perception in virtual groups from a multilevel perspective. In particular, it examines the following three areas: homophily, identification, and individual attraction, and explores how much of these directional and dyadic relational evaluations can be attributed to the effect of the actor, the partner, and the relationship.展开更多
This paper proposes a multi-criteria decision-making (MCGDM) method based on the improved single-valued neutrosophic Hamacher weighted averaging (ISNHWA) operator and grey relational analysis (GRA) to overcome the lim...This paper proposes a multi-criteria decision-making (MCGDM) method based on the improved single-valued neutrosophic Hamacher weighted averaging (ISNHWA) operator and grey relational analysis (GRA) to overcome the limitations of present methods based on aggregation operators. First, the limitations of several existing single-valued neutrosophic weighted averaging aggregation operators (i.e. , the single-valued neutrosophic weighted averaging, single-valued neutrosophic weighted algebraic averaging, single-valued neutrosophic weighted Einstein averaging, single-valued neutrosophic Frank weighted averaging, and single-valued neutrosophic Hamacher weighted averaging operators), which can produce some indeterminate terms in the aggregation process, are discussed. Second, an ISNHWA operator was developed to overcome the limitations of existing operators. Third, the properties of the proposed operator, including idempotency, boundedness, monotonicity, and commutativity, were analyzed. Application examples confirmed that the ISNHWA operator and the proposed MCGDM method are rational and effective. The proposed improved ISNHWA operator and MCGDM method can overcome the indeterminate results in some special cases in existing single-valued neutrosophic weighted averaging aggregation operators and MCGDM methods.展开更多
This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtap...This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtaposing letters in a set. Taking that as basis, several fundamental results related to free groups, such as Dyck’s Theorem, are proven. Then, the paper highlights three creative applications of the concept in classifying finite groups of a fixed order, representing all dihedral groups geometrically, and analyzing knots topologically. All three applications are of considerable significance in their respective topic areas and serve to illustrate the advantages and certain limitations of the approach flexibly and comprehensively.展开更多
In this paper,we study the proximal relation,regionally proximal relation and Banach proximal relation of a topological dynamical system for amenable group actions.A useful tool is the support of a topological dynamic...In this paper,we study the proximal relation,regionally proximal relation and Banach proximal relation of a topological dynamical system for amenable group actions.A useful tool is the support of a topological dynamical system which is used to study the structure of the Banach proximal relation,and we prove that above three relations all coincide on a Banach mean equicontinuous system generated by an amenable group action.展开更多
On 29th November 2004, BSI Group Chairman Sir David John and senior colleagues were in Beijing to meet with Management Systems’ clients of the BSI Group and to consolidate already established relationships with the C...On 29th November 2004, BSI Group Chairman Sir David John and senior colleagues were in Beijing to meet with Management Systems’ clients of the BSI Group and to consolidate already established relationships with the Chinese standards community. This trip came in the wake of last year’s visit of the Group Chairman to Beijing and Shanghai, which paved the way for the signing of a cooperation agreement between BSI and the Standardization Adminis-展开更多
The group decision making problem with linguistic pref- erence relations is studied. The concept of additive consistent linguistic preference relation is defined, and then some properties of the additive consistent li...The group decision making problem with linguistic pref- erence relations is studied. The concept of additive consistent linguistic preference relation is defined, and then some properties of the additive consistent linguistic preference relation are studied. In order to rank the alternatives in the group decision making with the linguistic preference relations, the weighted average is first utilized to combine the group linguistic preference relations to one linguistic preference relation, and then the transformation function is proposed to transform the linguistic preference relation to the multiplicative preference relation, and thus the Saaty's eigenvec- tor method (EM) of multiplicative preference relation is utilized to rank the alternatives in group decision making with the linguistic preference relations. Finally, an illustrative numerical example is given to verify the proposed method. A comparative study to the linguistic ordered weighted averaging (LOWA) operator method is also demonstrated.展开更多
Objective To implement the national diagnosis related group(DRG)policy smoothly,and gradually move towards value medicine and fine management,some suggestions are put forward for improving medical service efficiency,s...Objective To implement the national diagnosis related group(DRG)policy smoothly,and gradually move towards value medicine and fine management,some suggestions are put forward for improving medical service efficiency,saving medical insurance fund,and reducing the burden of patients,so as to realize the win-win situation of medical insurance and patients.Methods Based on the experience of the United States,Australia,and Germany,the policy implementation background and development process in China were summarized.The advantages and disadvantages of single disease payment method,disease score payment method,and diagnosis related groups-prospective payment system(DRG-PPS)method were compared,and then the problems were found out.Results and Conclusion In view of the imperfect information system,lack of professional talents,and uneven progress of each pilot,it is proposed that relevant departments should pay more attention to the construction and improvement of coding and other information systems,cultivate professional talents,promote the reform of DRG payment technology specification and grouping technology combined with national pilot project,thus enhancing the application and in-depth development of DRG policy in China.展开更多
When two representations of the Lie algebra are coupled, the coupling integral kernels are presented to relate the coupled to uncoupled group-related coherent states. These kernels have a connection with usual couplin...When two representations of the Lie algebra are coupled, the coupling integral kernels are presented to relate the coupled to uncoupled group-related coherent states. These kernels have a connection with usual coupling coefficients. The explicit expressions of these kernels for SU(2), SO(4) and SUq(2) are given. When the direct product of three representations is formed in two ways, the recoupling integral kernels relating to the coupled group-related coherent states corresponding to two different schemes are introduced, and the relations between these kernels and the general recoupling coefficients are obtained. The properties of these kernels are discussed.展开更多
To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy gr...To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy grey multi-attribute group decision making based on the theories of fuzzy mathematics and grey system is presented. Furthermore, the grey interval relative degree and deviation degree is defined, and both the optimistic algorithm of the grey interval relational degree and the algorithm of deviation degree minimization for solving this new model are also given. Finally, a decision making example to demonstrate the feasibility and rationality of this new method is given, and the results by using these two algorithms are uniform.展开更多
Group decision making problems are investigated with uncertain multiplicative linguistic preference relations.An unbalanced multiplicative linguistic label set is introduced,which can be used by the experts to express...Group decision making problems are investigated with uncertain multiplicative linguistic preference relations.An unbalanced multiplicative linguistic label set is introduced,which can be used by the experts to express their linguistic preference information over alternatives.The uncertain linguistic weighted geometric mean operator is utilized to aggregate all the individual uncertain multiplicative linguistic preference relations into a collective one,and then a simple approach is developed to determine the experts' weights by utilizing the consensus degrees among the individual uncertain multiplicative linguistic preference relations and the collective uncertain multiplicative linguistic preference relations.Furthermore,a practical interactive procedure for group decision making is proposed based on uncertain multiplicative linguistic preference relations,in which a possibility degree formula and a complementary matrix are used to rank the given alternatives.Finally,the proposed procedure is applied to solve the group decision making problem of a manufacturing company searching the best global supplier for one of its most critical parts used in assembling process.展开更多
Intuitionistic fuzzy preference relation(IFPR) is a suitable technique to express fuzzy preference information by decision makers(DMs). This paper aims to provide a group decision making method where DMs use the IFPRs...Intuitionistic fuzzy preference relation(IFPR) is a suitable technique to express fuzzy preference information by decision makers(DMs). This paper aims to provide a group decision making method where DMs use the IFPRs to indicate their preferences with uncertain weights. To begin with, a model to derive weight vectors of alternatives from IFPRs based on multiplicative consistency is presented. Specifically, for any IFPR,by minimizing its absolute deviation from the corresponding consistent IFPR, the weight vectors are generated. Secondly,a method to determine relative weights of DMs depending on preference information is developed. After that we prioritize alternatives based on the obtained weights considering the risk preference of DMs. Finally, this approach is applied to the problem of technical risks assessment of armored equipment to illustrate the applicability and superiority of the proposed method.展开更多
It was found that phosphorylation of small peptide could improve the sensitivity in mass spectrometry. Density functional theory calculations showed that the energy for the protonation of N-(O,O'-dimethyl) phospho...It was found that phosphorylation of small peptide could improve the sensitivity in mass spectrometry. Density functional theory calculations showed that the energy for the protonation of N-(O,O'-dimethyl) phosphoryl glycylglycine is lower than that of glycylglycine. These could help to understanding the experimental results.展开更多
Multi-attribute group decision-making problems are considered where information on both attribute weights and value scores of consequences is incomplete.In group decision analysis,if preference information about alter...Multi-attribute group decision-making problems are considered where information on both attribute weights and value scores of consequences is incomplete.In group decision analysis,if preference information about alternatives is provided by participants,it should be verified whether there exist compromise weights that can support all the preference relations.The different compromise weight vectors may differ for the ranking of the alternatives.In the case that compromise weights exist,the method is proposed to find out all the compromise weight vectors in order to rank the alternatives.Based on the new feasible domain of attribute weights determined by all the compromise weight vectors and the incomplete information on value scores of consequences,dominance relations between alternatives are checked by a nonlinear goal programming model which can be transformed into a linear one by adopting a transformation.The checked dominance relations uniformly hold for all compromise weight vectors and the incomplete information on value scores of consequences.A final ranking of the alternatives can be obtained by aggregating these dominance relations.展开更多
Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pytha...Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pythagoras and the larger than life man of theoretical physics Einstein, we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We started from the basic principles of self similarity which came to prominence in science with the advent of the modern theory of nonlinear dynamical systems, deterministic chaos and fractals. This fundamental logico-mathematical thread related to partially ordered sets is then applied to show how the classical Newton’s kinetic energy E = 1/2mv<sup>2</sup> leads to Einstein’s celebrated maximal energy equation E = mc<sup>2</sup> and how in turn this can be dissected into the ordinary energy density E(O) = mc<sup>2</sup>/22 and the dark energy density E(D) = mc<sup>2</sup>(21/22) of the cosmos where m is the mass;v is the velocity and c is the speed of light. The important role of the exceptional Lie symmetry groups and ‘tHooft-Veltman-Wilson dimensional regularization in fractal spacetime played in the above is also highlighted. The author hopes that the unusual character of the analysis and presentation of the present work may be taken in a positive vein as seriously attempting to propose a different and new way of doing theoretical physics by treating number theory, set theory, group theory, experimental physics as well as conventional theoretical physics on the same footing and letting all these diverse tools lead us to the answer of fundamental questions without fear of being labelled in one way or another.展开更多
Using the metabelian property, regularity, p-commutativity and some properties of congruence, this paper gave the orders of automorphism groups of family Ф24, which are the groups of order p^6 determined by Rodney Ja...Using the metabelian property, regularity, p-commutativity and some properties of congruence, this paper gave the orders of automorphism groups of family Ф24, which are the groups of order p^6 determined by Rodney James, where p denotes an odd prime.展开更多
Based on the analyses of existing preference group decision-making(PGDM)methods with intuitionistic fuzzy preference relations(IFPRs),we present a new PGDM framework with incomplete IFPRs.A generalized multiplicative ...Based on the analyses of existing preference group decision-making(PGDM)methods with intuitionistic fuzzy preference relations(IFPRs),we present a new PGDM framework with incomplete IFPRs.A generalized multiplicative consistent for IFPRs is defined,and a mathematical programming model is constructed to supplement the missing values in incomplete IFPRs.Moreover,in this study,another mathematical programming model is constructed to improve the consistency level of unacceptably multiplicative consistent IFPRs.For group decisionmaking(GDM)with incomplete IFPRs,three reliable sources influencing the weights of experts are identified.Subsequently,a method for determining the weights of experts is developed by simultaneously considering three reliable sources.Furthermore,a targeted consensus process(CPR)is developed in this study with reference to the actual situation of the consensus level of each IFPR.Meanwhile,in response to the proposed multiplicative consistency definition,a novel method for determining the optimal priority weights of alternatives is redefined.Lastly,based on the above theory,a novel GDM method with incomplete IFPRs is developed,and the comparative and sensitivity analysis results demonstrate the utility and superiority of this work.展开更多
<strong>Background: </strong><span style="font-family:""><span style="font-family:Verdana;">One of the main objectives of hospital managements is to control the length ...<strong>Background: </strong><span style="font-family:""><span style="font-family:Verdana;">One of the main objectives of hospital managements is to control the length of stay (LOS). Successful control of LOS of inpatients will result in reduction in the cost of care, decrease in nosocomial infections, medication side effects, and better management of the limited number of available patients’ beds. The length of stay (LOS) is an important indicator of the efficiency of hospital management by improving the quality of treatment, and increased hospital profit with more efficient bed management. The purpose of this study was to model the distribution of LOS as a function of patient’s age, and the Diagnosis Related Groups (DRG), based on electronic medical records of a large tertiary care hospital. </span><b><span style="font-family:Verdana;">Materials and Methods: </span></b><span style="font-family:Verdana;">Information related to the research subjects were retrieved from a database of patients admitted to King Faisal Specialist Hospital and Research Center hospital in Riyadh, Saudi Arabia between January 2014 and December 2016. Subjects’ confidential information was masked from the investigators. The data analyses were reported visually, descriptively, and analytically using Cox proportional hazard regression model to predict the risk of long-stay when patients’ age and the DRG are considered as antecedent risk factors. </span><b><span style="font-family:Verdana;">Results: </span></b><span style="font-family:Verdana;">Predicting the risk of long stay depends significantly on the age at admission, and the DRG to which a patient belongs to. We demonstrated the validity of the Cox regression model for the available data as the proportionality assumption is shown to be satisfied. Two examples were presented to demonstrate the utility of the Cox model in this regard.</span></span>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
文摘With the penetration of the Internet, virtual groups have become more and more popular. The reliability and accuracy of interpersonal perception in the virtual environment is an intriguing issue. Using the Social relations model (SRM) [1], this paper investigates interpersonal perception in virtual groups from a multilevel perspective. In particular, it examines the following three areas: homophily, identification, and individual attraction, and explores how much of these directional and dyadic relational evaluations can be attributed to the effect of the actor, the partner, and the relationship.
文摘This paper proposes a multi-criteria decision-making (MCGDM) method based on the improved single-valued neutrosophic Hamacher weighted averaging (ISNHWA) operator and grey relational analysis (GRA) to overcome the limitations of present methods based on aggregation operators. First, the limitations of several existing single-valued neutrosophic weighted averaging aggregation operators (i.e. , the single-valued neutrosophic weighted averaging, single-valued neutrosophic weighted algebraic averaging, single-valued neutrosophic weighted Einstein averaging, single-valued neutrosophic Frank weighted averaging, and single-valued neutrosophic Hamacher weighted averaging operators), which can produce some indeterminate terms in the aggregation process, are discussed. Second, an ISNHWA operator was developed to overcome the limitations of existing operators. Third, the properties of the proposed operator, including idempotency, boundedness, monotonicity, and commutativity, were analyzed. Application examples confirmed that the ISNHWA operator and the proposed MCGDM method are rational and effective. The proposed improved ISNHWA operator and MCGDM method can overcome the indeterminate results in some special cases in existing single-valued neutrosophic weighted averaging aggregation operators and MCGDM methods.
文摘This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtaposing letters in a set. Taking that as basis, several fundamental results related to free groups, such as Dyck’s Theorem, are proven. Then, the paper highlights three creative applications of the concept in classifying finite groups of a fixed order, representing all dihedral groups geometrically, and analyzing knots topologically. All three applications are of considerable significance in their respective topic areas and serve to illustrate the advantages and certain limitations of the approach flexibly and comprehensively.
基金supported by NSF of China(11671057)NSF of Chongqing(cstc2020jcyj-msxm X0694)the Fundamental Research Funds for the Central Universities(2018CDQYST0023)。
文摘In this paper,we study the proximal relation,regionally proximal relation and Banach proximal relation of a topological dynamical system for amenable group actions.A useful tool is the support of a topological dynamical system which is used to study the structure of the Banach proximal relation,and we prove that above three relations all coincide on a Banach mean equicontinuous system generated by an amenable group action.
文摘On 29th November 2004, BSI Group Chairman Sir David John and senior colleagues were in Beijing to meet with Management Systems’ clients of the BSI Group and to consolidate already established relationships with the Chinese standards community. This trip came in the wake of last year’s visit of the Group Chairman to Beijing and Shanghai, which paved the way for the signing of a cooperation agreement between BSI and the Standardization Adminis-
基金The paper was supported by 'Excellent Innovative Research Group Funds Project from National Science Foundation (Ratifying No. 7012001)' and the National Nature Science Foundation (Ratifying No. 70371038) .
基金supported by the National Natural Science Foundation of China(70771025)Hohai University Central University Special Fund Basic Scientific Research and Operational Costs
文摘The group decision making problem with linguistic pref- erence relations is studied. The concept of additive consistent linguistic preference relation is defined, and then some properties of the additive consistent linguistic preference relation are studied. In order to rank the alternatives in the group decision making with the linguistic preference relations, the weighted average is first utilized to combine the group linguistic preference relations to one linguistic preference relation, and then the transformation function is proposed to transform the linguistic preference relation to the multiplicative preference relation, and thus the Saaty's eigenvec- tor method (EM) of multiplicative preference relation is utilized to rank the alternatives in group decision making with the linguistic preference relations. Finally, an illustrative numerical example is given to verify the proposed method. A comparative study to the linguistic ordered weighted averaging (LOWA) operator method is also demonstrated.
基金General Projects of Social Science Planning Fund of Liaoning Province(L19BGL034)Shenyang Philosophy and Social Science Planning Fund Project(SZ202001L)Key Projects of Shenyang Social Science Fund(SYSK2020-04-01).
文摘Objective To implement the national diagnosis related group(DRG)policy smoothly,and gradually move towards value medicine and fine management,some suggestions are put forward for improving medical service efficiency,saving medical insurance fund,and reducing the burden of patients,so as to realize the win-win situation of medical insurance and patients.Methods Based on the experience of the United States,Australia,and Germany,the policy implementation background and development process in China were summarized.The advantages and disadvantages of single disease payment method,disease score payment method,and diagnosis related groups-prospective payment system(DRG-PPS)method were compared,and then the problems were found out.Results and Conclusion In view of the imperfect information system,lack of professional talents,and uneven progress of each pilot,it is proposed that relevant departments should pay more attention to the construction and improvement of coding and other information systems,cultivate professional talents,promote the reform of DRG payment technology specification and grouping technology combined with national pilot project,thus enhancing the application and in-depth development of DRG policy in China.
文摘When two representations of the Lie algebra are coupled, the coupling integral kernels are presented to relate the coupled to uncoupled group-related coherent states. These kernels have a connection with usual coupling coefficients. The explicit expressions of these kernels for SU(2), SO(4) and SUq(2) are given. When the direct product of three representations is formed in two ways, the recoupling integral kernels relating to the coupled group-related coherent states corresponding to two different schemes are introduced, and the relations between these kernels and the general recoupling coefficients are obtained. The properties of these kernels are discussed.
基金This project was supported by the National Natural Science Foundation of China (70671050 70471019)the Key Project of Hubei Provincial Department of Education (D200627005).
文摘To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy grey multi-attribute group decision making based on the theories of fuzzy mathematics and grey system is presented. Furthermore, the grey interval relative degree and deviation degree is defined, and both the optimistic algorithm of the grey interval relational degree and the algorithm of deviation degree minimization for solving this new model are also given. Finally, a decision making example to demonstrate the feasibility and rationality of this new method is given, and the results by using these two algorithms are uniform.
基金supported by the National Natural Science Foundation of China (70571087)the National Science Fund for Distinguished Young Scholars of China (70625005)
文摘Group decision making problems are investigated with uncertain multiplicative linguistic preference relations.An unbalanced multiplicative linguistic label set is introduced,which can be used by the experts to express their linguistic preference information over alternatives.The uncertain linguistic weighted geometric mean operator is utilized to aggregate all the individual uncertain multiplicative linguistic preference relations into a collective one,and then a simple approach is developed to determine the experts' weights by utilizing the consensus degrees among the individual uncertain multiplicative linguistic preference relations and the collective uncertain multiplicative linguistic preference relations.Furthermore,a practical interactive procedure for group decision making is proposed based on uncertain multiplicative linguistic preference relations,in which a possibility degree formula and a complementary matrix are used to rank the given alternatives.Finally,the proposed procedure is applied to solve the group decision making problem of a manufacturing company searching the best global supplier for one of its most critical parts used in assembling process.
基金partly supported by the National Natural Science Foundation of China(71371053)the Social Science Foundation of Fujian Province(FJ2015C111)
文摘Intuitionistic fuzzy preference relation(IFPR) is a suitable technique to express fuzzy preference information by decision makers(DMs). This paper aims to provide a group decision making method where DMs use the IFPRs to indicate their preferences with uncertain weights. To begin with, a model to derive weight vectors of alternatives from IFPRs based on multiplicative consistency is presented. Specifically, for any IFPR,by minimizing its absolute deviation from the corresponding consistent IFPR, the weight vectors are generated. Secondly,a method to determine relative weights of DMs depending on preference information is developed. After that we prioritize alternatives based on the obtained weights considering the risk preference of DMs. Finally, this approach is applied to the problem of technical risks assessment of armored equipment to illustrate the applicability and superiority of the proposed method.
基金The authors thank the National Natural Science Foundation of China(No.39870415)the Ministry of Science and Technology of China,the Education Ministry of China and Tsinghua University for financial suport.
文摘It was found that phosphorylation of small peptide could improve the sensitivity in mass spectrometry. Density functional theory calculations showed that the energy for the protonation of N-(O,O'-dimethyl) phosphoryl glycylglycine is lower than that of glycylglycine. These could help to understanding the experimental results.
基金supported by the Humanities and Social Sciences Foundation of Ministry of Education of China(09YJC630229)Scientific Research Foundation of Guangxi University for Nationalities for Talent Introduction(200702YZ01)Science and Technology Project of State Ethnic Affairs Commission(09GX03)
文摘Multi-attribute group decision-making problems are considered where information on both attribute weights and value scores of consequences is incomplete.In group decision analysis,if preference information about alternatives is provided by participants,it should be verified whether there exist compromise weights that can support all the preference relations.The different compromise weight vectors may differ for the ranking of the alternatives.In the case that compromise weights exist,the method is proposed to find out all the compromise weight vectors in order to rank the alternatives.Based on the new feasible domain of attribute weights determined by all the compromise weight vectors and the incomplete information on value scores of consequences,dominance relations between alternatives are checked by a nonlinear goal programming model which can be transformed into a linear one by adopting a transformation.The checked dominance relations uniformly hold for all compromise weight vectors and the incomplete information on value scores of consequences.A final ranking of the alternatives can be obtained by aggregating these dominance relations.
文摘Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pythagoras and the larger than life man of theoretical physics Einstein, we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We started from the basic principles of self similarity which came to prominence in science with the advent of the modern theory of nonlinear dynamical systems, deterministic chaos and fractals. This fundamental logico-mathematical thread related to partially ordered sets is then applied to show how the classical Newton’s kinetic energy E = 1/2mv<sup>2</sup> leads to Einstein’s celebrated maximal energy equation E = mc<sup>2</sup> and how in turn this can be dissected into the ordinary energy density E(O) = mc<sup>2</sup>/22 and the dark energy density E(D) = mc<sup>2</sup>(21/22) of the cosmos where m is the mass;v is the velocity and c is the speed of light. The important role of the exceptional Lie symmetry groups and ‘tHooft-Veltman-Wilson dimensional regularization in fractal spacetime played in the above is also highlighted. The author hopes that the unusual character of the analysis and presentation of the present work may be taken in a positive vein as seriously attempting to propose a different and new way of doing theoretical physics by treating number theory, set theory, group theory, experimental physics as well as conventional theoretical physics on the same footing and letting all these diverse tools lead us to the answer of fundamental questions without fear of being labelled in one way or another.
基金The Science Research Foundation of Chongqing Municipal Education Commission of China(KJ050611)
文摘Using the metabelian property, regularity, p-commutativity and some properties of congruence, this paper gave the orders of automorphism groups of family Ф24, which are the groups of order p^6 determined by Rodney James, where p denotes an odd prime.
基金supported by the National Natural Science Foundation of China(Nos.71740021,11861034,and 61966030)the Humanities Social Science Programming Project of Ministry of Education of China(No.20YJA630059)+1 种基金the Natural Science Foundation of Jiangxi Province of China(No.20192BAB207012)the Natural Science Foundation of Qinghai Province of China(No.2019-ZJ-7086).
文摘Based on the analyses of existing preference group decision-making(PGDM)methods with intuitionistic fuzzy preference relations(IFPRs),we present a new PGDM framework with incomplete IFPRs.A generalized multiplicative consistent for IFPRs is defined,and a mathematical programming model is constructed to supplement the missing values in incomplete IFPRs.Moreover,in this study,another mathematical programming model is constructed to improve the consistency level of unacceptably multiplicative consistent IFPRs.For group decisionmaking(GDM)with incomplete IFPRs,three reliable sources influencing the weights of experts are identified.Subsequently,a method for determining the weights of experts is developed by simultaneously considering three reliable sources.Furthermore,a targeted consensus process(CPR)is developed in this study with reference to the actual situation of the consensus level of each IFPR.Meanwhile,in response to the proposed multiplicative consistency definition,a novel method for determining the optimal priority weights of alternatives is redefined.Lastly,based on the above theory,a novel GDM method with incomplete IFPRs is developed,and the comparative and sensitivity analysis results demonstrate the utility and superiority of this work.
文摘<strong>Background: </strong><span style="font-family:""><span style="font-family:Verdana;">One of the main objectives of hospital managements is to control the length of stay (LOS). Successful control of LOS of inpatients will result in reduction in the cost of care, decrease in nosocomial infections, medication side effects, and better management of the limited number of available patients’ beds. The length of stay (LOS) is an important indicator of the efficiency of hospital management by improving the quality of treatment, and increased hospital profit with more efficient bed management. The purpose of this study was to model the distribution of LOS as a function of patient’s age, and the Diagnosis Related Groups (DRG), based on electronic medical records of a large tertiary care hospital. </span><b><span style="font-family:Verdana;">Materials and Methods: </span></b><span style="font-family:Verdana;">Information related to the research subjects were retrieved from a database of patients admitted to King Faisal Specialist Hospital and Research Center hospital in Riyadh, Saudi Arabia between January 2014 and December 2016. Subjects’ confidential information was masked from the investigators. The data analyses were reported visually, descriptively, and analytically using Cox proportional hazard regression model to predict the risk of long-stay when patients’ age and the DRG are considered as antecedent risk factors. </span><b><span style="font-family:Verdana;">Results: </span></b><span style="font-family:Verdana;">Predicting the risk of long stay depends significantly on the age at admission, and the DRG to which a patient belongs to. We demonstrated the validity of the Cox regression model for the available data as the proportionality assumption is shown to be satisfied. Two examples were presented to demonstrate the utility of the Cox model in this regard.</span></span>
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.