The main contents in this note are: 1. introduction; 2. locally compact groups and local fields; 3. calculus on fractals based upon local fields; 4. fractional calculus and fractals; 5. fractal function spaces and PDE...The main contents in this note are: 1. introduction; 2. locally compact groups and local fields; 3. calculus on fractals based upon local fields; 4. fractional calculus and fractals; 5. fractal function spaces and PDE on fractals.展开更多
Based on a representation lemma. Riesz type kernels on the local field K and on the integer ring O in K are coitstructed. Furthermore, we discuss approximation theorems for the Lipschitz class Lip(L ;α) ana the Lp bo...Based on a representation lemma. Riesz type kernels on the local field K and on the integer ring O in K are coitstructed. Furthermore, we discuss approximation theorems for the Lipschitz class Lip(L ;α) ana the Lp boundedness of such operators motivated by the open problem: Does σηfa,s→f for f ∈L1(O) (see M. H. Taible-son [6] and [5])?展开更多
Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. Finding general and verifiable ...Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. Finding general and verifiable conditions which imply that the wavelet systems are wavelet frames is among the core problems in time-frequency analysis. In this article, we establish some new inequalities for wavelet frames on local fields of positive characteristic by means of the Fourier transform. As an application, an improved version of the Li-Jiang inequality for wavelet frames on local fields is obtained.展开更多
We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or,...We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or, Gibbs-Butzer calculus）. Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D（C Kp） and locally compact group Kp^＋-（= Kp）, so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ（Kp）, σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr（Kp）, σ≥0, 1≤r 〈∞, is shown.展开更多
Let G be a Heisenberg group over local field K. In the paper we give some local maximal functions which define the Hardy spaces h(P)(G) equivalently, obtain the atomic decomposition of local Hardy spaces. We also give...Let G be a Heisenberg group over local field K. In the paper we give some local maximal functions which define the Hardy spaces h(P)(G) equivalently, obtain the atomic decomposition of local Hardy spaces. We also give some bounded convolution operators h(P)(G), from which we can characterize h(P)(G) by sqare functions.展开更多
The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function...The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function spaces' over Euclidian space by defining higher order continuous modulus in R, and point out that there is no need of higher order continuous modulus for describing the chain of function spaces over local fields.展开更多
In this paper,we consider the Riesz product dμ=^∞∏j=1(1+ajRexbjλj(x))dx in local fields,and we obtain the upper and lower bound of its Hausdorff dimension.
Development of robust electrocatalyst for oxygen reduction reaction(ORR)in a seawater electrolyte is the key to realize seawater electrolyte-based zinc-air batteries(SZABs).Herein,constructing a local electric field c...Development of robust electrocatalyst for oxygen reduction reaction(ORR)in a seawater electrolyte is the key to realize seawater electrolyte-based zinc-air batteries(SZABs).Herein,constructing a local electric field coupled with chloride ions(Cl-)fixation strategy in dual single-atom catalysts(DSACs)was proposed,and the resultant catalyst delivered considerable ORR performance in a seawater electrolyte,with a high half-wave potential(E_(1/2))of 0.868 V and a good maximum power density(Pmax)of 182 mW·cm^(−2)in the assembled SZABs,much higher than those of the Pt/C catalyst(E_(1/2):0.846 V;Pmax:150 mW·cm^(−2)).The in-situ characterization and theoretical calculations revealed that the Fe sites have a higher Cl^(−)adsorption affinity than the Co sites,and preferentially adsorbs Cl^(−)in a seawater electrolyte during the ORR process,and thus constructs a low-concentration Cl^(−)local microenvironment through the common-ion exclusion effect,which prevents Cl^(−)adsorption and corrosion in the Co active centers,achieving impressive catalytic stability.In addition,the directional charge movement between Fe and Co atomic pairs establishes a local electric field,optimizing the adsorption energy of Co sites for oxygen-containing intermediates,and further improving the ORR activity.展开更多
For any prime power q,a polynomial f(X)∈F_(q)[X]is“exceptional”if it induces bijections of F_(q)k for infinitely many k;this condition is known to be equivalent to f(X)inducing a bijection of F_(q)k for at least on...For any prime power q,a polynomial f(X)∈F_(q)[X]is“exceptional”if it induces bijections of F_(q)k for infinitely many k;this condition is known to be equivalent to f(X)inducing a bijection of F_(q)k for at least one k with qk⩾deg(f)4.In this paper,we introduce the notion of an“exceptional”extension of local fields of any characteristic,and show that if f(X)∈F_(q)[X]is exceptional in the classical sense,then the field extension F_(q)(X)/F_(q)(f(X))yields an exceptional local field extension upon passing to the completion at a degree-1 place.We describe all exceptional local field extensions of degree coprime to the residue characteristic,determine the relationship between the exceptionality of a local field extension and the exceptionality of a subextension,and give various Galois-theoretic characterizations of exceptional local field extensions.As a consequence,we obtain three new proofs,using quite different tools,of a theorem of Guralnick and Müller(1997)about ramification indices in exceptional maps between curves over F_(q).This theorem generalizes a result of Lenstra,which subsumes earlier conjectures of Carlitz and Wan.展开更多
The slow-proton-fast-electron process severely limits the catalytic efficiency of oxygen evolution reaction.A method is proposed to accelerate proton transfer by building up local electric fields.Modifying acetic,etha...The slow-proton-fast-electron process severely limits the catalytic efficiency of oxygen evolution reaction.A method is proposed to accelerate proton transfer by building up local electric fields.Modifying acetic,ethanedioic and propanetricarboxylic(C_(6)H_(8)O_(6))ligands on BiVO_(4)surface results in a potential difference between BiVO_(4)and ligands that generates a local electric field which serves as a driving force for proton transfer.Among the ligands,carrying the strongest electron-withdrawing ability,the modification of C_(6)H_(8)O_(6) forms the strongest local electric field and leads to the fastest proton transfer and the smallest thermodynamic overpotential.C_(6)H_(8)O_(6)-BiVO_(4)exhibits 3.5 times photocurrent density as high as that of pure BiVO_(4),which is 3.50 mA cm^(-2)at 1.23 VRHE.The onset potential of C_(6)H_(8)O_(6)-BiVO_(4)shifts negatively from 0.70 to 0.38 VRHE.The mechanism for OER transitions from thermodynamically high energy proton-coupled electron transfer to thermodynamically low energy electron transfer as proton transfer is accelerated.展开更多
In the present paper we propose a new hierarchical management scheme within suitable extensions of 2-adic numbers, in which the subfields are treated as classes, and the communications are realized by computation on e...In the present paper we propose a new hierarchical management scheme within suitable extensions of 2-adic numbers, in which the subfields are treated as classes, and the communications are realized by computation on elliptic curves. The security of our system is much stronger than that of the traditional public key cryptographic systems.展开更多
Thermoelectric materials provide a renewable and eco-friendly solution to mitigate energy shortages and to reduce environmental pollution via direct heat-to-electricity conversion. Discovery of the novel thermoelectri...Thermoelectric materials provide a renewable and eco-friendly solution to mitigate energy shortages and to reduce environmental pollution via direct heat-to-electricity conversion. Discovery of the novel thermoelectric materials and optimization of the state-of-the-art material systems lie at the core of the thermoelectric society, the basic concept behind these being comprehension and manipulation of the physical principles and transport properties regarding thermoelectric materials. In this mini-review, certain examples for designing high-performance bulk thermoelectric materials are presented from the perspectives of both real objects and local fields. The highlights of this topic involve the Rashba effect, Peierls distortion, local magnetic field, and local stress field, which cover several aspects in the field of thermoelectric research. We conclude with an overview of future developments in thermoelectricity.展开更多
Lattices in Euclidean spaces are important research objects in geometric number theory,and they have important applications in many areas,such as cryptology.The shortest vector problem(SVP)and the closest vector probl...Lattices in Euclidean spaces are important research objects in geometric number theory,and they have important applications in many areas,such as cryptology.The shortest vector problem(SVP)and the closest vector problem(CVP)are two famous computational problems about lattices.In this paper,we consider p-adic lattices in local fields,and define the p-adic analogues of SVP and CVP in local fields.The authors find that,in contrast with lattices in Euclidean spaces,the situation is different and interesting.The SVP in Euclidean spaces corresponds to the Longest Vector Problem(LVP)in local fields.The authors develop relevant algorithms,indicating that these problems are computable.展开更多
The distributional dimension of fractal sets in R^n has been systematically studied by Triebel by virtue of the theory of function spaces. In this paper, we first discuss some important properties about the B-type spa...The distributional dimension of fractal sets in R^n has been systematically studied by Triebel by virtue of the theory of function spaces. In this paper, we first discuss some important properties about the B-type spaces and the F-type spaces on local fields, then we give the definition of the distributional dimension dimD in local fields and study the relations between distributional dimension and Hausdorff dimension. Moreover, the analysis expression of the Hausdorff dimension is given. Lastly, we define the Fourier dimension in local fields, and obtain the relations among all the three dimensions. Keywords local field, B-type space, F-type space, distributional dimension, Hausdorff dimension Fourier dimension展开更多
The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on t...The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R^n and the local field K are compared,so that one may interpret the essential differences between the analyses on R^n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m<(ln 2/ln 3).展开更多
Basic facts for Gabor frame {Eu（m）bTu（n）ag}m, n∈P on local field are investigated. Accurately, that the canonical dual of frame {Eu（m）bTu（n）ag}m,n∈P also has the Gabor structure is showed; that the product a...Basic facts for Gabor frame {Eu（m）bTu（n）ag}m, n∈P on local field are investigated. Accurately, that the canonical dual of frame {Eu（m）bTu（n）ag}m,n∈P also has the Gabor structure is showed; that the product ab decides whether it is possible for {Eu（m）bTu（n）ag}m,n∈P to be a frame for L^2（K） is discussed; some necessary conditions and two sufficient conditions of Gabor frame for L^2 （K） are established. An example is finally given.展开更多
In this article,we introduce the notion of general multiresolution structure(GMS)in the reducing subspace over local fields.We show that the GMS is admitted by an arbitrary reducing subspace and characterize all those...In this article,we introduce the notion of general multiresolution structure(GMS)in the reducing subspace over local fields.We show that the GMS is admitted by an arbitrary reducing subspace and characterize all those GMSs which admit a pyramids decomposition.Towards the culmination,we obtain a frame-like expansion for signals in reducing subspaces in terms of GMS over local fields.展开更多
In this note, we give an elementary and constructive proof for that the additive character group of a locally compact field is isomorphic to itself as an additive topological group.
A plasma screening model that accounts for electronic exchange-correlation effects and ionic nonideality in dense quantum plasmas is proposed.This model can be used as an input in various plasma interaction models to ...A plasma screening model that accounts for electronic exchange-correlation effects and ionic nonideality in dense quantum plasmas is proposed.This model can be used as an input in various plasma interaction models to calculate scattering cross-sections and transport properties.The applicability of the proposed plasma screening model is demonstrated using the example of the temperature relaxation rate in dense hydrogen and warm dense aluminum.Additionally,the conductivity of warm dense aluminum is computed in the regime where collisions are dominated by electron-ion scattering.The results obtained are compared with available theoretical results and simulation data.展开更多
The long-term enhancement in glutamate receptor mediated excitatory responses has been observed in stroke model. This pathological form of plasticity, termed post-ischemic long-term potentiation （i-LTP）, points to f...The long-term enhancement in glutamate receptor mediated excitatory responses has been observed in stroke model. This pathological form of plasticity, termed post-ischemic long-term potentiation （i-LTP）, points to functional reorganization after stroke. Little is known, however, about whether and how this i-LTP would affect subsequent induction of synaptic plasticity. Here, we first directly confirmed that i-LTP was induced in the endothelin-l-induced ischemia model as in other in vitro models. We also demonstrated increased expression of NR2B, CaMKII and p-CaMKII, which are reminiscent of i-LTP. We further induced LTP of field excitatory post- synaptic potentials （fEPSPs） on CA1 hippocampal neurons in peri-infarct regions of the endothelin-l-induced mini-stroke model. We found that LTP of fEPSPs, induced by high-frequency stimulation, displayed a progressive impairment at 12 and 24 hours after ischemia. Moreover, using in vivo multi-channel recording, we found that the local field potential, which represents electrical property of cell ensembles in more restricted regions, was also dam- pened at these two time points. These results suggest that i-LTP elevates the induction threshold of subsequent synap- tic plasticity. Our data helps to deepen the knowledge of meta-synaptic regulation of plasticity after focal ischemia.展开更多
文摘The main contents in this note are: 1. introduction; 2. locally compact groups and local fields; 3. calculus on fractals based upon local fields; 4. fractional calculus and fractals; 5. fractal function spaces and PDE on fractals.
文摘Based on a representation lemma. Riesz type kernels on the local field K and on the integer ring O in K are coitstructed. Furthermore, we discuss approximation theorems for the Lipschitz class Lip(L ;α) ana the Lp boundedness of such operators motivated by the open problem: Does σηfa,s→f for f ∈L1(O) (see M. H. Taible-son [6] and [5])?
基金supported by NBHM, Department of Atomic Energy, Government of India (Grant No. 2/48(8)/2016/NBHM(R.P)/R&D II/13924)
文摘Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. Finding general and verifiable conditions which imply that the wavelet systems are wavelet frames is among the core problems in time-frequency analysis. In this article, we establish some new inequalities for wavelet frames on local fields of positive characteristic by means of the Fourier transform. As an application, an improved version of the Li-Jiang inequality for wavelet frames on local fields is obtained.
文摘We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or, Gibbs-Butzer calculus）. Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D（C Kp） and locally compact group Kp^＋-（= Kp）, so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ（Kp）, σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr（Kp）, σ≥0, 1≤r 〈∞, is shown.
文摘Let G be a Heisenberg group over local field K. In the paper we give some local maximal functions which define the Hardy spaces h(P)(G) equivalently, obtain the atomic decomposition of local Hardy spaces. We also give some bounded convolution operators h(P)(G), from which we can characterize h(P)(G) by sqare functions.
文摘The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function spaces' over Euclidian space by defining higher order continuous modulus in R, and point out that there is no need of higher order continuous modulus for describing the chain of function spaces over local fields.
文摘In this paper,we consider the Riesz product dμ=^∞∏j=1(1+ajRexbjλj(x))dx in local fields,and we obtain the upper and lower bound of its Hausdorff dimension.
基金supported by the National Natural Science Foundation of China(52164028,52274297)the Start-up Research Foundation of Hainan University(KYQD(ZR)20008,KYQD(ZR)21125,KYQD(ZR)23169))+1 种基金Collaborative Innovation Center of Marine Science and Technology of Hainan University(XTCX2022HYC14)Innovative Research Project for Postgraduate Students in Hainan Province(Qhyb2024-95).
文摘Development of robust electrocatalyst for oxygen reduction reaction(ORR)in a seawater electrolyte is the key to realize seawater electrolyte-based zinc-air batteries(SZABs).Herein,constructing a local electric field coupled with chloride ions(Cl-)fixation strategy in dual single-atom catalysts(DSACs)was proposed,and the resultant catalyst delivered considerable ORR performance in a seawater electrolyte,with a high half-wave potential(E_(1/2))of 0.868 V and a good maximum power density(Pmax)of 182 mW·cm^(−2)in the assembled SZABs,much higher than those of the Pt/C catalyst(E_(1/2):0.846 V;Pmax:150 mW·cm^(−2)).The in-situ characterization and theoretical calculations revealed that the Fe sites have a higher Cl^(−)adsorption affinity than the Co sites,and preferentially adsorbs Cl^(−)in a seawater electrolyte during the ORR process,and thus constructs a low-concentration Cl^(−)local microenvironment through the common-ion exclusion effect,which prevents Cl^(−)adsorption and corrosion in the Co active centers,achieving impressive catalytic stability.In addition,the directional charge movement between Fe and Co atomic pairs establishes a local electric field,optimizing the adsorption energy of Co sites for oxygen-containing intermediates,and further improving the ORR activity.
基金supported by the Natural Science Foundation of Hunan Province of China(Grant No.2020JJ4164).
文摘For any prime power q,a polynomial f(X)∈F_(q)[X]is“exceptional”if it induces bijections of F_(q)k for infinitely many k;this condition is known to be equivalent to f(X)inducing a bijection of F_(q)k for at least one k with qk⩾deg(f)4.In this paper,we introduce the notion of an“exceptional”extension of local fields of any characteristic,and show that if f(X)∈F_(q)[X]is exceptional in the classical sense,then the field extension F_(q)(X)/F_(q)(f(X))yields an exceptional local field extension upon passing to the completion at a degree-1 place.We describe all exceptional local field extensions of degree coprime to the residue characteristic,determine the relationship between the exceptionality of a local field extension and the exceptionality of a subextension,and give various Galois-theoretic characterizations of exceptional local field extensions.As a consequence,we obtain three new proofs,using quite different tools,of a theorem of Guralnick and Müller(1997)about ramification indices in exceptional maps between curves over F_(q).This theorem generalizes a result of Lenstra,which subsumes earlier conjectures of Carlitz and Wan.
文摘The slow-proton-fast-electron process severely limits the catalytic efficiency of oxygen evolution reaction.A method is proposed to accelerate proton transfer by building up local electric fields.Modifying acetic,ethanedioic and propanetricarboxylic(C_(6)H_(8)O_(6))ligands on BiVO_(4)surface results in a potential difference between BiVO_(4)and ligands that generates a local electric field which serves as a driving force for proton transfer.Among the ligands,carrying the strongest electron-withdrawing ability,the modification of C_(6)H_(8)O_(6) forms the strongest local electric field and leads to the fastest proton transfer and the smallest thermodynamic overpotential.C_(6)H_(8)O_(6)-BiVO_(4)exhibits 3.5 times photocurrent density as high as that of pure BiVO_(4),which is 3.50 mA cm^(-2)at 1.23 VRHE.The onset potential of C_(6)H_(8)O_(6)-BiVO_(4)shifts negatively from 0.70 to 0.38 VRHE.The mechanism for OER transitions from thermodynamically high energy proton-coupled electron transfer to thermodynamically low energy electron transfer as proton transfer is accelerated.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10990011, 60763009）
文摘In the present paper we propose a new hierarchical management scheme within suitable extensions of 2-adic numbers, in which the subfields are treated as classes, and the communications are realized by computation on elliptic curves. The security of our system is much stronger than that of the traditional public key cryptographic systems.
基金This study was funded by the National Key RK：D Program of China （Grant No. 2017YFA0303503）, the National Natural Science Foundation of China （Grant Nos. 21622107, 11621063, and U1532265）, the Key Research Pro- gram of Frontier Sciences （Grant No. QYZDY-SSW-SLH011）, the Youth Innovation Promotion Association CAS （Grant No. 2016392）, the Fundamental Research Funds of Central University （Grant No. WK2340000075）, and the Major Program of Development Foundation of Hefei Center for Physical Science and Technology （Grant No. 2017FXZY003）.
文摘Thermoelectric materials provide a renewable and eco-friendly solution to mitigate energy shortages and to reduce environmental pollution via direct heat-to-electricity conversion. Discovery of the novel thermoelectric materials and optimization of the state-of-the-art material systems lie at the core of the thermoelectric society, the basic concept behind these being comprehension and manipulation of the physical principles and transport properties regarding thermoelectric materials. In this mini-review, certain examples for designing high-performance bulk thermoelectric materials are presented from the perspectives of both real objects and local fields. The highlights of this topic involve the Rashba effect, Peierls distortion, local magnetic field, and local stress field, which cover several aspects in the field of thermoelectric research. We conclude with an overview of future developments in thermoelectricity.
基金supported by the National Key Research and Development Project under Grant No.2018YFA0704705。
文摘Lattices in Euclidean spaces are important research objects in geometric number theory,and they have important applications in many areas,such as cryptology.The shortest vector problem(SVP)and the closest vector problem(CVP)are two famous computational problems about lattices.In this paper,we consider p-adic lattices in local fields,and define the p-adic analogues of SVP and CVP in local fields.The authors find that,in contrast with lattices in Euclidean spaces,the situation is different and interesting.The SVP in Euclidean spaces corresponds to the Longest Vector Problem(LVP)in local fields.The authors develop relevant algorithms,indicating that these problems are computable.
文摘The distributional dimension of fractal sets in R^n has been systematically studied by Triebel by virtue of the theory of function spaces. In this paper, we first discuss some important properties about the B-type spaces and the F-type spaces on local fields, then we give the definition of the distributional dimension dimD in local fields and study the relations between distributional dimension and Hausdorff dimension. Moreover, the analysis expression of the Hausdorff dimension is given. Lastly, we define the Fourier dimension in local fields, and obtain the relations among all the three dimensions. Keywords local field, B-type space, F-type space, distributional dimension, Hausdorff dimension Fourier dimension
基金This work supported by the National Natural Science Foundation of China(Grant No.10571084)
文摘The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R^n and the local field K are compared,so that one may interpret the essential differences between the analyses on R^n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m<(ln 2/ln 3).
基金Project supported by the National Natural Science Foundation of China (No. 10571084, No. 10671062) the Postdoctoral Science Foundation of China (No. 2005037694)the Natural Science Foundation of the Education Department of Henan Province of China (No. 2006110001).
文摘Basic facts for Gabor frame {Eu（m）bTu（n）ag}m, n∈P on local field are investigated. Accurately, that the canonical dual of frame {Eu（m）bTu（n）ag}m,n∈P also has the Gabor structure is showed; that the product ab decides whether it is possible for {Eu（m）bTu（n）ag}m,n∈P to be a frame for L^2（K） is discussed; some necessary conditions and two sufficient conditions of Gabor frame for L^2 （K） are established. An example is finally given.
文摘In this article,we introduce the notion of general multiresolution structure(GMS)in the reducing subspace over local fields.We show that the GMS is admitted by an arbitrary reducing subspace and characterize all those GMSs which admit a pyramids decomposition.Towards the culmination,we obtain a frame-like expansion for signals in reducing subspaces in terms of GMS over local fields.
基金The NNSF(10201013 and 10171046)of Chinathe China Postdoctoral Science Foun-dation.
文摘In this note, we give an elementary and constructive proof for that the additive character group of a locally compact field is isomorphic to itself as an additive topological group.
基金funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan Grant No.AP19678033“The study of the transport and optical properties of hydrogen at high pressure.”。
文摘A plasma screening model that accounts for electronic exchange-correlation effects and ionic nonideality in dense quantum plasmas is proposed.This model can be used as an input in various plasma interaction models to calculate scattering cross-sections and transport properties.The applicability of the proposed plasma screening model is demonstrated using the example of the temperature relaxation rate in dense hydrogen and warm dense aluminum.Additionally,the conductivity of warm dense aluminum is computed in the regime where collisions are dominated by electron-ion scattering.The results obtained are compared with available theoretical results and simulation data.
基金supported by Major State Basic Research Program of China(Grant No.2013CB733801)
文摘The long-term enhancement in glutamate receptor mediated excitatory responses has been observed in stroke model. This pathological form of plasticity, termed post-ischemic long-term potentiation （i-LTP）, points to functional reorganization after stroke. Little is known, however, about whether and how this i-LTP would affect subsequent induction of synaptic plasticity. Here, we first directly confirmed that i-LTP was induced in the endothelin-l-induced ischemia model as in other in vitro models. We also demonstrated increased expression of NR2B, CaMKII and p-CaMKII, which are reminiscent of i-LTP. We further induced LTP of field excitatory post- synaptic potentials （fEPSPs） on CA1 hippocampal neurons in peri-infarct regions of the endothelin-l-induced mini-stroke model. We found that LTP of fEPSPs, induced by high-frequency stimulation, displayed a progressive impairment at 12 and 24 hours after ischemia. Moreover, using in vivo multi-channel recording, we found that the local field potential, which represents electrical property of cell ensembles in more restricted regions, was also dam- pened at these two time points. These results suggest that i-LTP elevates the induction threshold of subsequent synap- tic plasticity. Our data helps to deepen the knowledge of meta-synaptic regulation of plasticity after focal ischemia.
