Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk...Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk）,where p, q, d are integers greater than 1, in non-Archimedean normed spaces.展开更多
In this paper,using the fixed-point and direct methods,we prove the HyersUlam stability of the following m-Appolonius type functional equation：∑mi=1 f（z-xi）=mf（z-1/m2∑mi=1xi）-1/m∑1≤i〈j≤mf（xi＋xj）,where m ...In this paper,using the fixed-point and direct methods,we prove the HyersUlam stability of the following m-Appolonius type functional equation：∑mi=1 f（z-xi）=mf（z-1/m2∑mi=1xi）-1/m∑1≤i〈j≤mf（xi＋xj）,where m is a natural number greater than 1,in random normed spaces. 更多还原展开更多
The representation of additive functionals and local times for jump Markov processes are obtained.The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.
The perturbation of semigroup by a multiplicative functional with bounded variation is investigated in the frame of weak duality. The strong continuity and Schrodinger type equation of the perturbated semigroup are di...The perturbation of semigroup by a multiplicative functional with bounded variation is investigated in the frame of weak duality. The strong continuity and Schrodinger type equation of the perturbated semigroup are discussed. A few switching identities and formulae conerning dual additive functionals and Revuz measures are given.展开更多
In this study,we are interested in stochastic differential equations driven by GLévy processes.We illustrate that a certain class of additive functionals of the equations of interest exhibits the path-independent...In this study,we are interested in stochastic differential equations driven by GLévy processes.We illustrate that a certain class of additive functionals of the equations of interest exhibits the path-independent property,generalizing a few known findings in the literature.The study is ended with many examples.展开更多
A function f ： N → Ris called additive if f（mn） = f（m） ＋f （n） for all m, n with （m, n） = 1. Let μ（x） = maxn≤x（f（n） - f（n ＋ 1）） and v（x） = maxn≤x（f（n ＋ 1） - f（n））. In 1979, Ruzsa proved ...A function f ： N → Ris called additive if f（mn） = f（m） ＋f （n） for all m, n with （m, n） = 1. Let μ（x） = maxn≤x（f（n） - f（n ＋ 1）） and v（x） = maxn≤x（f（n ＋ 1） - f（n））. In 1979, Ruzsa proved that there exists a constant c such that for any additive function f, μ（x） ≤ cv（x^2） ＋ cf, where cf is a constant depending only on f. Denote by Raf the least such constant c. We cMl Raf Ruzsa＇s constant on additive functions. In this paper, we prove that Raf≤ 20.展开更多
Assume that B is a separable real Banach space and X(t) is a diffusion process on B. In thispaper, we will establish the representation theorem of martingale additive functionals of X(t).
Let B<sub>α</sub>（α）be an additive function on a ring of integers in the quadratic number field Q（（1/2）d）given by B<sub>α</sub>（α）=∑<sub>p丨α</sub><sup>*</sup...Let B<sub>α</sub>（α）be an additive function on a ring of integers in the quadratic number field Q（（1/2）d）given by B<sub>α</sub>（α）=∑<sub>p丨α</sub><sup>*</sup>N<sup>α</sup>（p）with a fixed α】0,where the asterisk means that the summation is over the non-associate prime divisors p of an integer α in Q（（1/2）d）,N（α）is the norm of α.In this paper we obtain the asymptotic formula of ∑<sub>N</sub>（α）≤<sub>x</sub> <sup>*</sup>B<sub>α</sub>（α）in the case where the class-number of Q（（1/2）d）is one.展开更多
Solid polymer electrolytes(SPEs)have become increasingly attractive in solid-state lithium-ion batteries(SSLIBs)in recent years because of their inherent properties of flexibility,processability,and interfacial compat...Solid polymer electrolytes(SPEs)have become increasingly attractive in solid-state lithium-ion batteries(SSLIBs)in recent years because of their inherent properties of flexibility,processability,and interfacial compatibility.However,the commercialization of SPEs remains challenging for flexible and high-energy-density LIBs.The incorporation of functional additives into SPEs could significantly improve the electrochemical and mechanical properties of SPEs and has created some historical milestones in boosting the development of SPEs.In this study,we review the roles of additives in SPEs,highlighting the working mechanisms and functionalities of the additives.The additives could afford significant advantages in boosting ionic conductivity,increasing ion transference number,improving high-voltage stability,enhancing mechanical strength,inhibiting lithium dendrite,and reducing flammability.Moreover,the application of functional additives in high-voltage cathodes,lithium-sulfur batteries,and flexible lithiumion batteries is summarized.Finally,future research perspectives are proposed to overcome the unresolved technical hurdles and critical issues in additives of SPEs,such as facile fabrication process,interfacial compatibility,investigation of the working mechanism,and special functionalities.展开更多
The topological pressure for subadditive sequence of discontinuous functions is defined on any invariant subset having a nested family of subsets in the compact metric space. Two subadditive variational principles ass...The topological pressure for subadditive sequence of discontinuous functions is defined on any invariant subset having a nested family of subsets in the compact metric space. Two subadditive variational principles associated with two different relatively weak conditions are developed for the defined topological pressure. As an application, we give an example on systems with nonzero Lyapunov exponents.展开更多
Bioactive glass-chitosan-alginate hybrid scaffolds （BG-C-A scaffolds） were fabricated using BG sol as a dual function additive, which behaves as both bioactive inorganic phase to confer the bioactivity and cross-lin...Bioactive glass-chitosan-alginate hybrid scaffolds （BG-C-A scaffolds） were fabricated using BG sol as a dual function additive, which behaves as both bioactive inorganic phase to confer the bioactivity and cross-linker to improve the structural stability and mechanical properties. The microstructure, physicochemical and mechanical properties, in vitro bioactivity and cellular biocompatibility of the scaffolds were investigated. The results indicated that BG component was successfully incorporated into the BG-C-A scaffolds through a facile BG sol-immersing method and the original interconnected microstructure could be well preserved. The obtained BG-C-A scaffolds showed improved mechanical properties and structural stability as compared to C-A scaffolds. At the same time, they presented excellent in vitro bioactivity and cellular compatibility. All these results demonstrated that these BG-C-A scaffolds have promising potential for tissue engineering.展开更多
Flexible lithium metal batteries with high capacity and power density have been regarded as the core power resources of wearable electronics.However,the main challenge lies in the limited electrochemical performance o...Flexible lithium metal batteries with high capacity and power density have been regarded as the core power resources of wearable electronics.However,the main challenge lies in the limited electrochemical performance of solid-state polymer electrolytes,which hinders further practical applications.Incorporating functional inorganic additives is an effective approach to improve the performance,including increasing ionic conductivity,achieving dendrite inhibiting capability,and improving safety and stability.Herein,this review summarizes the latest developments of functional inorganic additives in composite solid-state electrolytes for flexible metal batteries with special emphasis on their mechanisms,strategies,and cutting-edge applications,in particular,the relationship between them is discussed in detail.Finally,the perspective on future research directions and the key challenges on this topic are outlooked.展开更多
Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach mod...Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach modules over a unital Banach algebra.展开更多
The intention of this paper is to study new additive kind multi-dimensional functional equations inspired by several applications of difference equations in biology,control theory,economics,and computer science,as wel...The intention of this paper is to study new additive kind multi-dimensional functional equations inspired by several applications of difference equations in biology,control theory,economics,and computer science,as well as notable implementation of fuzzy ideas in certain situations involving ambiguity or vagueness.In the context of different fuzzy spaces,we demonstrate their various fundamental stabilities related to Ulam stability theory.An appropriate example is given to show how stability result fails when the singular case occurs.The findings of this study suggest that stability results are valid in situations with uncertain or imprecise data.The stability results obtained under these fuzzy spaces are compared with previous stability results.展开更多
In this work,we present a digital light processing(DLP)-flashing-based functionally graded additive manufacturing(FGAM)process for fabricating highly aesthetic zirconia(ZrO_(2))dental crowns with simultaneous color an...In this work,we present a digital light processing(DLP)-flashing-based functionally graded additive manufacturing(FGAM)process for fabricating highly aesthetic zirconia(ZrO_(2))dental crowns with simultaneous color and translucency gradation.Color gradation was achieved by controlled iron oxide(Fe2O3)doping(ranged from 0.0 to 0.10 wt%)in zirconia powders,whereas translucency gradation was simultaneously attained by controlling the isotropic cubic phase(c-ZrO_(2))in the sintered crowns using three different grades of yttria-stabilized ZrO_(2)(3,4,and 5 mol%yttria-stabilized ZrO_(2)powders,i.e.,3YSZ,4YSZ,and 5YSZ,respectively).The crowns were printed through flashing illumination:0.2 s flash time and 1 s off-time between consecutive ultraviolet(UV)flashes to overcome the scattering-induced overcuring associated to continuous printing that degraded the structural accuracy of the design and posed post-processing challenges and property deterioration.International Commision on Illumination’s Lab(CIELAB)color assessments indicated successful coloring indices(L^(*),a^(*),and b^(*)values)matching the graded appearance of natural teeth.Mechanical properties and sintering shrinkage were slightly affected by the Fe_(2)O_(3)and yttria contents of the various compositions.The highest translucency parameter(above 20)was possible with an undoped 5YSZ composition at the top part(incisor)of the crown.The processing challenges during FGAM of ceramic materials were successfully overcome through a flashing mechanism,and the color and translucency gradation of the ZrO_(2)dental crown was simultaneously maintained with enhanced printing precision,which is a potential breakthrough advancement in esthetic dentistry.展开更多
Some properties of a conditioned superdiffusion are investigated. By a basic property we obtain for it, a class of linear additive functionals, so-called weighted occupation time, is studied. At last, we get an intere...Some properties of a conditioned superdiffusion are investigated. By a basic property we obtain for it, a class of linear additive functionals, so-called weighted occupation time, is studied. At last, we get an interesting result about its extinctive property.展开更多
Osteoarthritis(OA)is the most common type of degenerative joint disease which affects 7%of the global population and more than 500 million people worldwide.One research frontier is the development of hydrogels for OA ...Osteoarthritis(OA)is the most common type of degenerative joint disease which affects 7%of the global population and more than 500 million people worldwide.One research frontier is the development of hydrogels for OA treatment,which operate either as functional scaffolds of tissue engineering or as delivery vehicles of functional additives.Both approaches address the big challenge:establishing stable integration of such delivery systems or implants.Adhesive hydrogels provide possible solutions to this challenge.However,few studies have described the current advances in using adhesive hydrogel for OA treatment.This review summarizes the commonly used hydrogels with their adhesion mechanisms and components.Additionally,recognizing that OA is a complex disease involving different biological mechanisms,the bioactive therapeutic strategies are also presented.By presenting the adhesive hydrogels in an interdisciplinary way,including both the fields of chemistry and biology,this review will attempt to provide a comprehensive insight for designing novel bioadhesive systems for OA therapy.展开更多
The influences of silica fume and aluminum sulfate on hydration process of sulfoaluminate cement were carried out by ring flow, setting time, hydration heat, XRD and DTG analyses. In addition, mortar mixtures with dif...The influences of silica fume and aluminum sulfate on hydration process of sulfoaluminate cement were carried out by ring flow, setting time, hydration heat, XRD and DTG analyses. In addition, mortar mixtures with different functional additives have been studied through compressive strength, flexural strength, volume stability at early age and porosity characterization tests. The results show that the addition of silica fume and aluminum sulfate reduces the fluidity and shortens the setting time of sulfoaluminate cement paste, promoting hydration process and increasing hydration products at early age. In the case of appropriate proportion of mortar, the inclusion of hydroxy propyl methyl cellulose, dispersible polypropylene fiber arid organic silicon kind of defoamer can control segregation and bleeding, improve mechanical strength and volume stability at early age, and modify the pore distribution of sulfoaluminate cement mortar, respectively. The sulfoaluminate cement mortar can carry out gravitational grouting in the absence of outside force, the compressive strength of 2 hours and 24 hours have reached 26 and 58 MPa respectively, and have good micro- expansion and tiny.pore distribution characterization.展开更多
Let Xn,n ≥ 1, be a sequence of independent random variables satisfying P(Xn = 0) = 1 - P(Xn = an) = 1 - 1/Pn, where an,n ≥ 1, is a sequence of real numbers, and Pn is the nth prime,set FN(x) = P (N Xn ≤ x). The aut...Let Xn,n ≥ 1, be a sequence of independent random variables satisfying P(Xn = 0) = 1 - P(Xn = an) = 1 - 1/Pn, where an,n ≥ 1, is a sequence of real numbers, and Pn is the nth prime,set FN(x) = P (N Xn ≤ x). The authors investigate a conjecture of Erdos in probabilistic number theory and show that in order for the sequence FN to be weakly convergent, it is both sufficient and necessary that there exist three numbers X0 and X1 < X2 such that limsup(FN(X2) - FN(X1)) > 0 holds, and Lo = N→ ∞ lim FN(X0) exists. Moreover, the authors point out that they can also obtain the same result in the weakened case of lim inf P(Xn = 0) > 0.展开更多
文摘Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk）,where p, q, d are integers greater than 1, in non-Archimedean normed spaces.
文摘In this paper,using the fixed-point and direct methods,we prove the HyersUlam stability of the following m-Appolonius type functional equation：∑mi=1 f（z-xi）=mf（z-1/m2∑mi=1xi）-1/m∑1≤i〈j≤mf（xi＋xj）,where m is a natural number greater than 1,in random normed spaces. 更多还原
基金supported by the National Nature Science Foundation of China(10271091)
文摘The representation of additive functionals and local times for jump Markov processes are obtained.The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.
基金Project supported in part by the National Natural Science Foundation of China (No.19501035).
文摘The perturbation of semigroup by a multiplicative functional with bounded variation is investigated in the frame of weak duality. The strong continuity and Schrodinger type equation of the perturbated semigroup are discussed. A few switching identities and formulae conerning dual additive functionals and Revuz measures are given.
文摘In this study,we are interested in stochastic differential equations driven by GLévy processes.We illustrate that a certain class of additive functionals of the equations of interest exhibits the path-independent property,generalizing a few known findings in the literature.The study is ended with many examples.
基金Supported by National Natural Science Foundation of China(Grant Nos.11071121and11126302)supported by Natural Science Foundation of the Jiangsu Higher Education Institutions(GrantNo.11KJB110006) the Foundation of Nanjing University of Information Science&Technology(Grant No.20110421)
文摘A function f ： N → Ris called additive if f（mn） = f（m） ＋f （n） for all m, n with （m, n） = 1. Let μ（x） = maxn≤x（f（n） - f（n ＋ 1）） and v（x） = maxn≤x（f（n ＋ 1） - f（n））. In 1979, Ruzsa proved that there exists a constant c such that for any additive function f, μ（x） ≤ cv（x^2） ＋ cf, where cf is a constant depending only on f. Denote by Raf the least such constant c. We cMl Raf Ruzsa＇s constant on additive functions. In this paper, we prove that Raf≤ 20.
文摘Assume that B is a separable real Banach space and X(t) is a diffusion process on B. In thispaper, we will establish the representation theorem of martingale additive functionals of X(t).
基金Project supported by the National Natural Science Foundation of China.
文摘Let B<sub>α</sub>（α）be an additive function on a ring of integers in the quadratic number field Q（（1/2）d）given by B<sub>α</sub>（α）=∑<sub>p丨α</sub><sup>*</sup>N<sup>α</sup>（p）with a fixed α】0,where the asterisk means that the summation is over the non-associate prime divisors p of an integer α in Q（（1/2）d）,N（α）is the norm of α.In this paper we obtain the asymptotic formula of ∑<sub>N</sub>（α）≤<sub>x</sub> <sup>*</sup>B<sub>α</sub>（α）in the case where the class-number of Q（（1/2）d）is one.
基金supported by the Australian Research Council(ARC)Discovery Projects(DP210103266 and DP1701048343)the Griffith University Ph.D.Scholarships.
文摘Solid polymer electrolytes(SPEs)have become increasingly attractive in solid-state lithium-ion batteries(SSLIBs)in recent years because of their inherent properties of flexibility,processability,and interfacial compatibility.However,the commercialization of SPEs remains challenging for flexible and high-energy-density LIBs.The incorporation of functional additives into SPEs could significantly improve the electrochemical and mechanical properties of SPEs and has created some historical milestones in boosting the development of SPEs.In this study,we review the roles of additives in SPEs,highlighting the working mechanisms and functionalities of the additives.The additives could afford significant advantages in boosting ionic conductivity,increasing ion transference number,improving high-voltage stability,enhancing mechanical strength,inhibiting lithium dendrite,and reducing flammability.Moreover,the application of functional additives in high-voltage cathodes,lithium-sulfur batteries,and flexible lithiumion batteries is summarized.Finally,future research perspectives are proposed to overcome the unresolved technical hurdles and critical issues in additives of SPEs,such as facile fabrication process,interfacial compatibility,investigation of the working mechanism,and special functionalities.
基金Supported by the National Natural Science Foundation of China (10971100)supported by a grant from Postdoctoral Science Research Program of Jiangsu Province (0701049C)+1 种基金the Fundamental Research Funds for the Central Universitiessupported by National Basic Research Program of China (973 Program)(2007CB814800)
文摘The topological pressure for subadditive sequence of discontinuous functions is defined on any invariant subset having a nested family of subsets in the compact metric space. Two subadditive variational principles associated with two different relatively weak conditions are developed for the defined topological pressure. As an application, we give an example on systems with nonzero Lyapunov exponents.
基金supported by the National Natural Science Foundation of China(No. 51773209)the National Basic Research Program(No. 2017YFC1103300)the Strategic Priority Research Program of Chinese Academy of Sciences(No. XDB12020300)
文摘Bioactive glass-chitosan-alginate hybrid scaffolds （BG-C-A scaffolds） were fabricated using BG sol as a dual function additive, which behaves as both bioactive inorganic phase to confer the bioactivity and cross-linker to improve the structural stability and mechanical properties. The microstructure, physicochemical and mechanical properties, in vitro bioactivity and cellular biocompatibility of the scaffolds were investigated. The results indicated that BG component was successfully incorporated into the BG-C-A scaffolds through a facile BG sol-immersing method and the original interconnected microstructure could be well preserved. The obtained BG-C-A scaffolds showed improved mechanical properties and structural stability as compared to C-A scaffolds. At the same time, they presented excellent in vitro bioactivity and cellular compatibility. All these results demonstrated that these BG-C-A scaffolds have promising potential for tissue engineering.
基金supported by the Natural Science Foundation of China(No.22179062,52125202,22171136,and U2004209)financial support by the Fundamental Research Funds for the Central Universities(No.30922010303)the financial support by the Natural Science Foundation of Jiangsu Province(BK20220079).
文摘Flexible lithium metal batteries with high capacity and power density have been regarded as the core power resources of wearable electronics.However,the main challenge lies in the limited electrochemical performance of solid-state polymer electrolytes,which hinders further practical applications.Incorporating functional inorganic additives is an effective approach to improve the performance,including increasing ionic conductivity,achieving dendrite inhibiting capability,and improving safety and stability.Herein,this review summarizes the latest developments of functional inorganic additives in composite solid-state electrolytes for flexible metal batteries with special emphasis on their mechanisms,strategies,and cutting-edge applications,in particular,the relationship between them is discussed in detail.Finally,the perspective on future research directions and the key challenges on this topic are outlooked.
基金supported by the National Natural Science Foundation of China (10671013,60972089,11171022)
文摘Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach modules over a unital Banach algebra.
基金The second author is supported by the Science and Engineering Research Board(SERB)of India(MTR/2020/000534).
文摘The intention of this paper is to study new additive kind multi-dimensional functional equations inspired by several applications of difference equations in biology,control theory,economics,and computer science,as well as notable implementation of fuzzy ideas in certain situations involving ambiguity or vagueness.In the context of different fuzzy spaces,we demonstrate their various fundamental stabilities related to Ulam stability theory.An appropriate example is given to show how stability result fails when the singular case occurs.The findings of this study suggest that stability results are valid in situations with uncertain or imprecise data.The stability results obtained under these fuzzy spaces are compared with previous stability results.
基金supported by the Nano&Material Technology Development Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Science and ICT(RS2024-00407234).
文摘In this work,we present a digital light processing(DLP)-flashing-based functionally graded additive manufacturing(FGAM)process for fabricating highly aesthetic zirconia(ZrO_(2))dental crowns with simultaneous color and translucency gradation.Color gradation was achieved by controlled iron oxide(Fe2O3)doping(ranged from 0.0 to 0.10 wt%)in zirconia powders,whereas translucency gradation was simultaneously attained by controlling the isotropic cubic phase(c-ZrO_(2))in the sintered crowns using three different grades of yttria-stabilized ZrO_(2)(3,4,and 5 mol%yttria-stabilized ZrO_(2)powders,i.e.,3YSZ,4YSZ,and 5YSZ,respectively).The crowns were printed through flashing illumination:0.2 s flash time and 1 s off-time between consecutive ultraviolet(UV)flashes to overcome the scattering-induced overcuring associated to continuous printing that degraded the structural accuracy of the design and posed post-processing challenges and property deterioration.International Commision on Illumination’s Lab(CIELAB)color assessments indicated successful coloring indices(L^(*),a^(*),and b^(*)values)matching the graded appearance of natural teeth.Mechanical properties and sintering shrinkage were slightly affected by the Fe_(2)O_(3)and yttria contents of the various compositions.The highest translucency parameter(above 20)was possible with an undoped 5YSZ composition at the top part(incisor)of the crown.The processing challenges during FGAM of ceramic materials were successfully overcome through a flashing mechanism,and the color and translucency gradation of the ZrO_(2)dental crown was simultaneously maintained with enhanced printing precision,which is a potential breakthrough advancement in esthetic dentistry.
文摘Some properties of a conditioned superdiffusion are investigated. By a basic property we obtain for it, a class of linear additive functionals, so-called weighted occupation time, is studied. At last, we get an interesting result about its extinctive property.
基金supported by the National Natural Science Foundation of China (52103184, 82102593)the China Postdoctoral Science Foundation (XJ2021051, 2020TQ0129, 2021M693960)+3 种基金the"Young Talent Support Plan"and Funding for Basic Scientific Research of Xi’an Jiaotong Universitysupported by a Grant from Science Foundation Ireland (SFI)co-funded under the European Regional Development Fund (13/RC/2073_P2)the funds received from European Union Horizon 2020 Programme (H2020-MSCA-IF-2017) under the Marie Sklodowska-Curie Individual Fellowship (797716).
文摘Osteoarthritis(OA)is the most common type of degenerative joint disease which affects 7%of the global population and more than 500 million people worldwide.One research frontier is the development of hydrogels for OA treatment,which operate either as functional scaffolds of tissue engineering or as delivery vehicles of functional additives.Both approaches address the big challenge:establishing stable integration of such delivery systems or implants.Adhesive hydrogels provide possible solutions to this challenge.However,few studies have described the current advances in using adhesive hydrogel for OA treatment.This review summarizes the commonly used hydrogels with their adhesion mechanisms and components.Additionally,recognizing that OA is a complex disease involving different biological mechanisms,the bioactive therapeutic strategies are also presented.By presenting the adhesive hydrogels in an interdisciplinary way,including both the fields of chemistry and biology,this review will attempt to provide a comprehensive insight for designing novel bioadhesive systems for OA therapy.
基金Funded by the National Natural Science Foundation of China(No.51178363)the Major State Basic Research Development Program of China("973" Program)(No.2009CB23201-1)
文摘The influences of silica fume and aluminum sulfate on hydration process of sulfoaluminate cement were carried out by ring flow, setting time, hydration heat, XRD and DTG analyses. In addition, mortar mixtures with different functional additives have been studied through compressive strength, flexural strength, volume stability at early age and porosity characterization tests. The results show that the addition of silica fume and aluminum sulfate reduces the fluidity and shortens the setting time of sulfoaluminate cement paste, promoting hydration process and increasing hydration products at early age. In the case of appropriate proportion of mortar, the inclusion of hydroxy propyl methyl cellulose, dispersible polypropylene fiber arid organic silicon kind of defoamer can control segregation and bleeding, improve mechanical strength and volume stability at early age, and modify the pore distribution of sulfoaluminate cement mortar, respectively. The sulfoaluminate cement mortar can carry out gravitational grouting in the absence of outside force, the compressive strength of 2 hours and 24 hours have reached 26 and 58 MPa respectively, and have good micro- expansion and tiny.pore distribution characterization.
基金Supported by National Natural Science Foundation of China
文摘Let Xn,n ≥ 1, be a sequence of independent random variables satisfying P(Xn = 0) = 1 - P(Xn = an) = 1 - 1/Pn, where an,n ≥ 1, is a sequence of real numbers, and Pn is the nth prime,set FN(x) = P (N Xn ≤ x). The authors investigate a conjecture of Erdos in probabilistic number theory and show that in order for the sequence FN to be weakly convergent, it is both sufficient and necessary that there exist three numbers X0 and X1 < X2 such that limsup(FN(X2) - FN(X1)) > 0 holds, and Lo = N→ ∞ lim FN(X0) exists. Moreover, the authors point out that they can also obtain the same result in the weakened case of lim inf P(Xn = 0) > 0.
