In this paper,we examine the functions a(n)and b(n),which respectively represent the number of cubic partitions and cubic partition pairs.Our work leads to the derivation of asymptotic formulas for both a(n)and b(n).A...In this paper,we examine the functions a(n)and b(n),which respectively represent the number of cubic partitions and cubic partition pairs.Our work leads to the derivation of asymptotic formulas for both a(n)and b(n).Additionally,we establish the upper and lower bounds of these functions,factoring in the explicit error terms involved.Crucially,our findings reveal that a(n)and b(n)both satisfy several inequalities such as log-concavity,third-order Turan inequalities,and strict log-subadditivity.展开更多
Recently,Andrews and Paule established the generating functions for the k-elongated plane partition function d_(k)(n)and proved a large number of results on d_(k)(n)with k=2,3.In particular,they posed some conjectures...Recently,Andrews and Paule established the generating functions for the k-elongated plane partition function d_(k)(n)and proved a large number of results on d_(k)(n)with k=2,3.In particular,they posed some conjectures on congruences modulo powers of 3 for d_(2)(n).Their work has attracted the attention of da Silva,Hirschhorn,Sellers and Smoot.Very recently,Smoot proved a congruence family for d_(2)(n)which implies one conjecture due to Andrews and Paule by using the localization method.In this paper,we prove the rest two conjectures given by Andrews and Paule.展开更多
Partition and entropy of partitions in quantum logic are introduced and their properties are investigated.The results are generalized to the general case of T-norm and T-conorm.
In combinatorics, a Stirling number of the second kind S (n,k)? is the number of ways to partition a set of n objects into k nonempty subsets. The empty subsets are also added in the models presented in the article in...In combinatorics, a Stirling number of the second kind S (n,k)? is the number of ways to partition a set of n objects into k nonempty subsets. The empty subsets are also added in the models presented in the article in order to describe properly the absence of the corresponding type i of state in the system, i.e. when its “share” Pi =0?. Accordingly, a new equation for partitions P (N, m)? in a set of entities into both empty and nonempty subsets was derived. The indistinguishableness of particles (N identical atoms or molecules) makes only sense within a cluster (subset) with the size?0≤ni ≥N. The first-order phase transition is indeed the case of transitions, for example in the simplest interpretation, from completely liquid state?typeL = {n1 =N, n2 = 0} to the completely crystalline state??typeC= {n1 =0, n2 = N }. These partitions are well distinguished from the physical point of view, so they are ‘typed’ differently in the model. Finally, the present developments in the physics of complex systems, in particular the structural relaxation of super-cooled liquids and glasses, are discussed by using such stochastic cluster-based models.展开更多
The study of the confluences of the roots of a given set of polynomials—root-pattern problem— does not appear to have been considered. We examine the situation, which leads us on to Young tableaux and tableaux repre...The study of the confluences of the roots of a given set of polynomials—root-pattern problem— does not appear to have been considered. We examine the situation, which leads us on to Young tableaux and tableaux representations. This in turn is found to be an aspect of multipartite partitions. We discover, and show, that partitions can be expressed algebraically and can be “differentiated” and “integrated”. We show a complete set of bipartite and tripartite partitions, indicating equivalences for the root-pattern problem, for select pairs and triples. Tables enumerating the number of bipartite and tripartite partitions, for small pairs and triples are given in an appendix.展开更多
Clustering data with varying densities and complicated structures is important,while many existing clustering algorithms face difficulties for this problem. The reason is that varying densities and complicated structu...Clustering data with varying densities and complicated structures is important,while many existing clustering algorithms face difficulties for this problem. The reason is that varying densities and complicated structure make single algorithms perform badly for different parts of data. More intensive parts are assumed to have more information probably,an algorithm clustering from high density part is proposed,which begins from a tiny distance to find the highest density-connected partition and form corresponding super cores,then distance is iteratively increased by a global heuristic method to cluster parts with different densities. Mean of silhouette coefficient indicates the cluster performance. Denoising function is implemented to eliminate influence of noise and outliers. Many challenging experiments indicate that the algorithm has good performance on data with widely varying densities and extremely complex structures. It decides the optimal number of clusters automatically.Background knowledge is not needed and parameters tuning is easy. It is robust against noise and outliers.展开更多
By using lattice paths in the three-dimensional space we obtain bijectively an interpretation for the overpartitions of a positive integer n in terms of a set of plane partitions of n . We also exhibit two bijections ...By using lattice paths in the three-dimensional space we obtain bijectively an interpretation for the overpartitions of a positive integer n in terms of a set of plane partitions of n . We also exhibit two bijections between unrestricted partitions of n and different subsets of plane partitions of n .展开更多
Pachycereus marginatus (DC.) Britton & Rose and Ibervillea sonorae (S. Watson) Greene have been used in the Mexican traditional medicine for the treatment of various diseases, including cancer. The present study a...Pachycereus marginatus (DC.) Britton & Rose and Ibervillea sonorae (S. Watson) Greene have been used in the Mexican traditional medicine for the treatment of various diseases, including cancer. The present study aims to investigate the cytotoxic activity of these plants against a murine lymphoma. Soxhlet extraction of dried and powdered plant material was performed with methanol. Also, a further partitioning of these methanolic extracts with hexane and ethyl acetate was achieved. The in vitro cytotoxic activity against the murine lymphoma L5178Y-R cell line was assessed via the colorimetric MTT assay. The methanol extract from P. marginatus exhibited high cytotoxic activity (up to 94%) at concentrations ranging from 3.9 to 500 μg/mL;however, hexane and ethyl acetate partitions from this methanolic extract showed lower but significant (p < 0.05) concentration-dependent cytotoxicity (hexane partition up to 94% at 500 μg/mL;ethyl acetate partition up to 94% at 65.5 μg/mL). The methanolic extract and partitions derived from I. sonorae also showed significant (p < 0.05) and concentration-dependent cytotoxicity against L5178Y-R cells at concentrations ranging from 7.81 to 500 μg/mL (methanolic extract up to 63% at 500 μg/mL;hexane partition up to 76% at 250 μg/mL;ethyl acetate partition up to 73% at 500 μg/mL). These results demonstrate that the methanol extracts and partitions from P. marginatus and I. sonorae possess significant cytotoxic activity against the murine lymphoma L5178Y-R and validate the ethnobotanical use of these plants for the treatment of diseases consistent with cancer symptomatology. Previous scientific reports describe the isolation of isoquinoline alkaloids of P. marginatus as well as cucurbitacins from I. sonorae, phytochemicals that could be responsible for their observed cytotoxic activity in this research. The direct extraction with methanol of medicinal plants allows extracting of both high and low-polarity compounds, contrary to the simple extraction with water that only allows obtaining compounds of high polarity. The subsequent partition of the methanol extract with a solvent of low polarity (hexane) and another of medium polarity (ethyl acetate) allows making a preliminary fractionation of the bioactive molecules present in the plant that will facilitate the bioguided chromatographic isolation of the pure compounds responsible for the biological activity of the plant.展开更多
Heterostructured(HS)material with extraordinary mechanical properties has been regarded as one of the most promising structural materials.Here,we reported a new strategy for preparing heterostructured pure titanium la...Heterostructured(HS)material with extraordinary mechanical properties has been regarded as one of the most promising structural materials.Here,we reported a new strategy for preparing heterostructured pure titanium laminates that possess a good combination of strength and ductility by combining gradient structure(GS)and heterogeneous lamella structure(HLS).The deformation characteristic versus microstructure evolution of GS/HLS titanium laminates,namely the strain partitions between different-sized grains(480–25μm)was visualized using a scanning electron microscope(SEM)equipped with electron backscattered diffraction(EBSD)mode combined with the digital image correlation(SEM-DIC)with an ultrahigh spatial resolution for the first time.As a result,the hetero-deformation of unique GS/HLS structure by the characteristic of strain partitions could be accurately captured.While the hetero-deformation could result in the hetero-deformation induced(HDI)stress strengthening and HDI hardening,which were regarded as the key reason that the resulting GS/HLS Ti laminates showed a superior combination of strength and ductility.This could promote a more in-depth understanding of the strengtheningtoughening mechanism of heterostructured material.展开更多
Linked partitions were introduced by Dykema(Dykema K J. Multilinear function series and transforms in free probability theory. Adv. Math., 2005, 208(1):351–407) in the study of the unsymmetrized T-transform in free p...Linked partitions were introduced by Dykema(Dykema K J. Multilinear function series and transforms in free probability theory. Adv. Math., 2005, 208(1):351–407) in the study of the unsymmetrized T-transform in free probability theory.Permutation is one of the most classical combinatorial structures. According to the linear representation of linked partitions, Chen et al.(Chen W Y C, Wu S Y J, Yan C H. Linked partitions and linked cycles. European J. Combin., 2008, 29(6): 1408–1426) de?ned the concept of singly covered minimal elements. Let L(n, k) denote the set of linked partitions of [n] with k singly covered minimal elements and let P(n, k) denote the set of permutations of [n] with k cycles. In this paper, we mainly establish two bijections between L(n, k) and P(n, k). The two bijections from a different perspective show the one-to-one correspondence between the singly covered minimal elements in L(n, k) and the cycles in P(n, k).展开更多
In this paper, a new method for synchronization of chaotic systems is proposed. The method is based on the linear partitions of the chaotic system under consideration. A chaotic system is partitioned into a linear par...In this paper, a new method for synchronization of chaotic systems is proposed. The method is based on the linear partitions of the chaotic system under consideration. A chaotic system is partitioned into a linear part and a nonlinear part. Under some assumptions, another chaotic system which can synchronize with the original one can be contructed. The proposed method is easier to verify and more general than the conventional one in some sense.展开更多
This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be ded...This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the pentagonal number theorem.展开更多
The amount of data for decision making has increased tremendously in the age of the digital economy. Decision makers who fail to proficiently manipulate the data produced may make incorrect decisions and therefore har...The amount of data for decision making has increased tremendously in the age of the digital economy. Decision makers who fail to proficiently manipulate the data produced may make incorrect decisions and therefore harm their business. Thus, the task of extracting and classifying the useful information efficiently and effectively from huge amounts of computational data is of special importance. In this paper, we consider that the attributes of data could be both crisp and fuzzy. By examining the suitable partial data, segments with different classes are formed, then a multithreaded computation is performed to generate crisp rules (if possible), and finally, the fuzzy partition technique is employed to deal with the fuzzy attributes for classification. The rules generated in classifying the overall data can be used to gain more knowledge from the data collected.展开更多
For the sound insulation of a double-panel partition,the stud between two leaves creates a vibration transmission path,which can often be more critical and more important in the mid-frequency range than the airborne p...For the sound insulation of a double-panel partition,the stud between two leaves creates a vibration transmission path,which can often be more critical and more important in the mid-frequency range than the airborne path through the cavity.Owing to the fact that partitions with light-weight steel studs are commonly used in building construction,studies on the sound insulation effect of such studs have been conducted.Especially,a model,initiated by Gu and Wang(1983),has been widely studied during the past decades.In the model,the steel stud is considered as an elastic spring with its cross-section stiffness in the sound insulation index prediction of such a partition.Experimental results of different stud profiles have been reported from different testing laboratories and more information has been gained to understand the stiffness effect of the stud on the sound insulation of the double-leaf partitions.In this paper,the authors have given this subject a thorough review and have concluded that a critical problem needs further investigation on the determination of the stiffness of the connecting elements in the double-leaf partitions.展开更多
The authors provide optimized local trigonometric bases with nonuniform partitions which efficiently compress trigonometric functions. Numerical examples demonstrate that in many cases the proposed bases provide bette...The authors provide optimized local trigonometric bases with nonuniform partitions which efficiently compress trigonometric functions. Numerical examples demonstrate that in many cases the proposed bases provide better compression than the optimized bases with uniform partitions obtained by Matviyenko.展开更多
Hydrogen partitioning between liquid iron alloys and silicate melts governs its distribution and cycling in Earth’s deep interior.Existing models based on simplified Fe-H systems predict strong hydrogen sequestration...Hydrogen partitioning between liquid iron alloys and silicate melts governs its distribution and cycling in Earth’s deep interior.Existing models based on simplified Fe-H systems predict strong hydrogen sequestration into the core.However,these models do not account for the modulating effects of major light elements such as oxygen and silicon in the core during Earth’s primordial differentiation.In this study,we use first-principles molecular dynamics simulations,augmented by machine learning techniques,to quantify hydrogen chemical potentials in quaternary Fe-O-Si-H systems under early core-mantle boundary conditions(135 GPa,5000 K).Our results demonstrate that the presence of 5.2 wt%oxygen and 4.8 wt%silicon reduces the siderophile affinity of hydrogen by 35%,decreasing its alloy-silicate partition coefficient from 18.2(in the case of Fe-H)to 11.8(in the case of Fe-O-Si-H).These findings suggest that previous estimates of the core hydrogen content derived from binary system models require downward revision.Our study underscores the critical role of multicomponent interactions in core formation models and provides first-principles-derived constraints to reconcile Earth’s present-day hydrogen reservoirs with its accretionary history.展开更多
To obtain materials capable of efficiently separating acetylene(C_(2)H_(2))from carbon dioxide(CO_(2))and eth-ylene(C_(2)H_(4)),In this work,based on the pore space partition strategy,a pacs-metal-organic framework(MO...To obtain materials capable of efficiently separating acetylene(C_(2)H_(2))from carbon dioxide(CO_(2))and eth-ylene(C_(2)H_(4)),In this work,based on the pore space partition strategy,a pacs-metal-organic framework(MOF):(NH_(2)Me_(2))_(2)[Fe_(3)(μ_(3)-O)(bdc)_(3)][In(FA)_(3)Cl_(3)](Fe‑FAIn‑bdc)was synthesized successfully by using the metal-formate com-plex[In(FA)_(3)Cl_(3)]^(3-)as the pore partition units,where bdc^(2-)=terephthalate,FA-=formate.Owing to the pore partition effect of this metal-organic building block,fruitful confined spaces are formed in the network of Fe‑FAIn‑bdc,endowing this MOF with superior separation performance of acetylene and carbon dioxide.According to the adsorp-tion test,this MOF exhibited a high adsorption capacity for C_(2)H_(2)(50.79 cm^(3)·g^(-1))at 298 K and 100 kPa,which was much higher than that for CO_(2)(29.99 cm^(3)·g^(-1))and C_(2)H_(4)(30.94 cm^(3)·g^(-1))under the same conditions.Ideal adsorbed solution theory(IAST)calculations demonstrate that the adsorption selectivity of Fe‑FAIn‑bdc for the mixture of C_(2)H_(2)/CO_(2)and C_(2)H_(2)/C_(2)H_(4)in a volume ratio of 50∶50 was 3.08 and 3.65,respectively,which was higher than some reported MOFs such as NUM-11 and SNNU-18.CCDC:_(2)453954.展开更多
Abstract In this article,we investigate the arithmetic behavior of the function D_3(n)which counts the number of 3-regular tripartitions of n.For example,we show that forα≥1 and n≥0,■and
基金supported by the National Natural Science Foundation of China(12371327)the Natural Science Foundation of Chongqing(cstc2021jcyj-msxmX0107).
文摘In this paper,we examine the functions a(n)and b(n),which respectively represent the number of cubic partitions and cubic partition pairs.Our work leads to the derivation of asymptotic formulas for both a(n)and b(n).Additionally,we establish the upper and lower bounds of these functions,factoring in the explicit error terms involved.Crucially,our findings reveal that a(n)and b(n)both satisfy several inequalities such as log-concavity,third-order Turan inequalities,and strict log-subadditivity.
基金Supported by the National Natural Science Foundation of China(Grant No.12371334)the Natural Science Foundation of Jiangsu Province(Grant No.BK20221383)。
文摘Recently,Andrews and Paule established the generating functions for the k-elongated plane partition function d_(k)(n)and proved a large number of results on d_(k)(n)with k=2,3.In particular,they posed some conjectures on congruences modulo powers of 3 for d_(2)(n).Their work has attracted the attention of da Silva,Hirschhorn,Sellers and Smoot.Very recently,Smoot proved a congruence family for d_(2)(n)which implies one conjecture due to Andrews and Paule by using the localization method.In this paper,we prove the rest two conjectures given by Andrews and Paule.
文摘Partition and entropy of partitions in quantum logic are introduced and their properties are investigated.The results are generalized to the general case of T-norm and T-conorm.
文摘In combinatorics, a Stirling number of the second kind S (n,k)? is the number of ways to partition a set of n objects into k nonempty subsets. The empty subsets are also added in the models presented in the article in order to describe properly the absence of the corresponding type i of state in the system, i.e. when its “share” Pi =0?. Accordingly, a new equation for partitions P (N, m)? in a set of entities into both empty and nonempty subsets was derived. The indistinguishableness of particles (N identical atoms or molecules) makes only sense within a cluster (subset) with the size?0≤ni ≥N. The first-order phase transition is indeed the case of transitions, for example in the simplest interpretation, from completely liquid state?typeL = {n1 =N, n2 = 0} to the completely crystalline state??typeC= {n1 =0, n2 = N }. These partitions are well distinguished from the physical point of view, so they are ‘typed’ differently in the model. Finally, the present developments in the physics of complex systems, in particular the structural relaxation of super-cooled liquids and glasses, are discussed by using such stochastic cluster-based models.
文摘The study of the confluences of the roots of a given set of polynomials—root-pattern problem— does not appear to have been considered. We examine the situation, which leads us on to Young tableaux and tableaux representations. This in turn is found to be an aspect of multipartite partitions. We discover, and show, that partitions can be expressed algebraically and can be “differentiated” and “integrated”. We show a complete set of bipartite and tripartite partitions, indicating equivalences for the root-pattern problem, for select pairs and triples. Tables enumerating the number of bipartite and tripartite partitions, for small pairs and triples are given in an appendix.
基金Supported by the National Key Research and Development Program of China(No.2016YFB0201305)National Science and Technology Major Project(No.2013ZX0102-8001-001-001)National Natural Science Foundation of China(No.91430218,31327901,61472395,61272134,61432018)
文摘Clustering data with varying densities and complicated structures is important,while many existing clustering algorithms face difficulties for this problem. The reason is that varying densities and complicated structure make single algorithms perform badly for different parts of data. More intensive parts are assumed to have more information probably,an algorithm clustering from high density part is proposed,which begins from a tiny distance to find the highest density-connected partition and form corresponding super cores,then distance is iteratively increased by a global heuristic method to cluster parts with different densities. Mean of silhouette coefficient indicates the cluster performance. Denoising function is implemented to eliminate influence of noise and outliers. Many challenging experiments indicate that the algorithm has good performance on data with widely varying densities and extremely complex structures. It decides the optimal number of clusters automatically.Background knowledge is not needed and parameters tuning is easy. It is robust against noise and outliers.
文摘By using lattice paths in the three-dimensional space we obtain bijectively an interpretation for the overpartitions of a positive integer n in terms of a set of plane partitions of n . We also exhibit two bijections between unrestricted partitions of n and different subsets of plane partitions of n .
文摘Pachycereus marginatus (DC.) Britton & Rose and Ibervillea sonorae (S. Watson) Greene have been used in the Mexican traditional medicine for the treatment of various diseases, including cancer. The present study aims to investigate the cytotoxic activity of these plants against a murine lymphoma. Soxhlet extraction of dried and powdered plant material was performed with methanol. Also, a further partitioning of these methanolic extracts with hexane and ethyl acetate was achieved. The in vitro cytotoxic activity against the murine lymphoma L5178Y-R cell line was assessed via the colorimetric MTT assay. The methanol extract from P. marginatus exhibited high cytotoxic activity (up to 94%) at concentrations ranging from 3.9 to 500 μg/mL;however, hexane and ethyl acetate partitions from this methanolic extract showed lower but significant (p < 0.05) concentration-dependent cytotoxicity (hexane partition up to 94% at 500 μg/mL;ethyl acetate partition up to 94% at 65.5 μg/mL). The methanolic extract and partitions derived from I. sonorae also showed significant (p < 0.05) and concentration-dependent cytotoxicity against L5178Y-R cells at concentrations ranging from 7.81 to 500 μg/mL (methanolic extract up to 63% at 500 μg/mL;hexane partition up to 76% at 250 μg/mL;ethyl acetate partition up to 73% at 500 μg/mL). These results demonstrate that the methanol extracts and partitions from P. marginatus and I. sonorae possess significant cytotoxic activity against the murine lymphoma L5178Y-R and validate the ethnobotanical use of these plants for the treatment of diseases consistent with cancer symptomatology. Previous scientific reports describe the isolation of isoquinoline alkaloids of P. marginatus as well as cucurbitacins from I. sonorae, phytochemicals that could be responsible for their observed cytotoxic activity in this research. The direct extraction with methanol of medicinal plants allows extracting of both high and low-polarity compounds, contrary to the simple extraction with water that only allows obtaining compounds of high polarity. The subsequent partition of the methanol extract with a solvent of low polarity (hexane) and another of medium polarity (ethyl acetate) allows making a preliminary fractionation of the bioactive molecules present in the plant that will facilitate the bioguided chromatographic isolation of the pure compounds responsible for the biological activity of the plant.
基金financially supported by the National Nature Science Foundation of China(Grant Nos.51771064,51971079,and 51501040)。
文摘Heterostructured(HS)material with extraordinary mechanical properties has been regarded as one of the most promising structural materials.Here,we reported a new strategy for preparing heterostructured pure titanium laminates that possess a good combination of strength and ductility by combining gradient structure(GS)and heterogeneous lamella structure(HLS).The deformation characteristic versus microstructure evolution of GS/HLS titanium laminates,namely the strain partitions between different-sized grains(480–25μm)was visualized using a scanning electron microscope(SEM)equipped with electron backscattered diffraction(EBSD)mode combined with the digital image correlation(SEM-DIC)with an ultrahigh spatial resolution for the first time.As a result,the hetero-deformation of unique GS/HLS structure by the characteristic of strain partitions could be accurately captured.While the hetero-deformation could result in the hetero-deformation induced(HDI)stress strengthening and HDI hardening,which were regarded as the key reason that the resulting GS/HLS Ti laminates showed a superior combination of strength and ductility.This could promote a more in-depth understanding of the strengtheningtoughening mechanism of heterostructured material.
基金The NSF(11601020,11501014) of China2017 Commercial Specialty Project(19005757053) of BTBU2018 Postgraduate Research Capacity Improvement Project(19008001491) of BTBU
文摘Linked partitions were introduced by Dykema(Dykema K J. Multilinear function series and transforms in free probability theory. Adv. Math., 2005, 208(1):351–407) in the study of the unsymmetrized T-transform in free probability theory.Permutation is one of the most classical combinatorial structures. According to the linear representation of linked partitions, Chen et al.(Chen W Y C, Wu S Y J, Yan C H. Linked partitions and linked cycles. European J. Combin., 2008, 29(6): 1408–1426) de?ned the concept of singly covered minimal elements. Let L(n, k) denote the set of linked partitions of [n] with k singly covered minimal elements and let P(n, k) denote the set of permutations of [n] with k cycles. In this paper, we mainly establish two bijections between L(n, k) and P(n, k). The two bijections from a different perspective show the one-to-one correspondence between the singly covered minimal elements in L(n, k) and the cycles in P(n, k).
基金Supported by the Climbing Programme-National Key Project for Fundamental Research under Grant NSC 92097
文摘In this paper, a new method for synchronization of chaotic systems is proposed. The method is based on the linear partitions of the chaotic system under consideration. A chaotic system is partitioned into a linear part and a nonlinear part. Under some assumptions, another chaotic system which can synchronize with the original one can be contructed. The proposed method is easier to verify and more general than the conventional one in some sense.
文摘This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the pentagonal number theorem.
文摘The amount of data for decision making has increased tremendously in the age of the digital economy. Decision makers who fail to proficiently manipulate the data produced may make incorrect decisions and therefore harm their business. Thus, the task of extracting and classifying the useful information efficiently and effectively from huge amounts of computational data is of special importance. In this paper, we consider that the attributes of data could be both crisp and fuzzy. By examining the suitable partial data, segments with different classes are formed, then a multithreaded computation is performed to generate crisp rules (if possible), and finally, the fuzzy partition technique is employed to deal with the fuzzy attributes for classification. The rules generated in classifying the overall data can be used to gain more knowledge from the data collected.
文摘For the sound insulation of a double-panel partition,the stud between two leaves creates a vibration transmission path,which can often be more critical and more important in the mid-frequency range than the airborne path through the cavity.Owing to the fact that partitions with light-weight steel studs are commonly used in building construction,studies on the sound insulation effect of such studs have been conducted.Especially,a model,initiated by Gu and Wang(1983),has been widely studied during the past decades.In the model,the steel stud is considered as an elastic spring with its cross-section stiffness in the sound insulation index prediction of such a partition.Experimental results of different stud profiles have been reported from different testing laboratories and more information has been gained to understand the stiffness effect of the stud on the sound insulation of the double-leaf partitions.In this paper,the authors have given this subject a thorough review and have concluded that a critical problem needs further investigation on the determination of the stiffness of the connecting elements in the double-leaf partitions.
基金the National Natural Science Foundation of China(No.10371122)Tianyuan Fund for Mathematics(No.A0324648)
文摘The authors provide optimized local trigonometric bases with nonuniform partitions which efficiently compress trigonometric functions. Numerical examples demonstrate that in many cases the proposed bases provide better compression than the optimized bases with uniform partitions obtained by Matviyenko.
基金supported by the National Key R&D Program of China(Grant No.2022YFF0503203)National Natural Science Foundation of China(NSFC)projects(Grant Nos.42441826 and 42173041)+1 种基金the Key Research Program of the Institute of Geology and Geophysics,Chinese Academy of Sciences(Grant No.IGGCAS-202204)the computational facilities of the Computer Simulation Laboratory at IGGCAS and the Beijing Super Cloud Computing Center(BSCC).
文摘Hydrogen partitioning between liquid iron alloys and silicate melts governs its distribution and cycling in Earth’s deep interior.Existing models based on simplified Fe-H systems predict strong hydrogen sequestration into the core.However,these models do not account for the modulating effects of major light elements such as oxygen and silicon in the core during Earth’s primordial differentiation.In this study,we use first-principles molecular dynamics simulations,augmented by machine learning techniques,to quantify hydrogen chemical potentials in quaternary Fe-O-Si-H systems under early core-mantle boundary conditions(135 GPa,5000 K).Our results demonstrate that the presence of 5.2 wt%oxygen and 4.8 wt%silicon reduces the siderophile affinity of hydrogen by 35%,decreasing its alloy-silicate partition coefficient from 18.2(in the case of Fe-H)to 11.8(in the case of Fe-O-Si-H).These findings suggest that previous estimates of the core hydrogen content derived from binary system models require downward revision.Our study underscores the critical role of multicomponent interactions in core formation models and provides first-principles-derived constraints to reconcile Earth’s present-day hydrogen reservoirs with its accretionary history.
文摘To obtain materials capable of efficiently separating acetylene(C_(2)H_(2))from carbon dioxide(CO_(2))and eth-ylene(C_(2)H_(4)),In this work,based on the pore space partition strategy,a pacs-metal-organic framework(MOF):(NH_(2)Me_(2))_(2)[Fe_(3)(μ_(3)-O)(bdc)_(3)][In(FA)_(3)Cl_(3)](Fe‑FAIn‑bdc)was synthesized successfully by using the metal-formate com-plex[In(FA)_(3)Cl_(3)]^(3-)as the pore partition units,where bdc^(2-)=terephthalate,FA-=formate.Owing to the pore partition effect of this metal-organic building block,fruitful confined spaces are formed in the network of Fe‑FAIn‑bdc,endowing this MOF with superior separation performance of acetylene and carbon dioxide.According to the adsorp-tion test,this MOF exhibited a high adsorption capacity for C_(2)H_(2)(50.79 cm^(3)·g^(-1))at 298 K and 100 kPa,which was much higher than that for CO_(2)(29.99 cm^(3)·g^(-1))and C_(2)H_(4)(30.94 cm^(3)·g^(-1))under the same conditions.Ideal adsorbed solution theory(IAST)calculations demonstrate that the adsorption selectivity of Fe‑FAIn‑bdc for the mixture of C_(2)H_(2)/CO_(2)and C_(2)H_(2)/C_(2)H_(4)in a volume ratio of 50∶50 was 3.08 and 3.65,respectively,which was higher than some reported MOFs such as NUM-11 and SNNU-18.CCDC:_(2)453954.
文摘Abstract In this article,we investigate the arithmetic behavior of the function D_3(n)which counts the number of 3-regular tripartitions of n.For example,we show that forα≥1 and n≥0,■and
