In this paper, we give some characterizations of almost completely regular spaces and c-semistratifiable spaces（CSS） by semi-continuous functions. We mainly show that：（1）Let X be a space. Then the following state...In this paper, we give some characterizations of almost completely regular spaces and c-semistratifiable spaces（CSS） by semi-continuous functions. We mainly show that：（1）Let X be a space. Then the following statements are equivalent：（i） X is almost completely regular.（ii） Every two disjoint subsets of X, one of which is compact and the other is regular closed, are completely separated.（iii） If g, h ： X → I, g is compact-like, h is normal lower semicontinuous, and g ≤ h, then there exists a continuous function f ： X → I such that g ≤ f ≤ h;and（2） Let X be a space. Then the following statements are equivalent：（a） X is CSS;（b） There is an operator U assigning to a decreasing sequence of compact sets（Fj）j∈N,a decreasing sequence of open sets（U（n,（Fj）））n∈N such that（b1） Fn■U（n,（Fj）） for each n ∈ N;（b2）∩n∈NU（n,（Fj）） =∩n∈NFn;（b3） Given two decreasing sequences of compact sets（Fj）j∈N and（Ej）j∈N such that Fn■Enfor each n ∈ N, then U（n,（Fj））■U（n,（Ej）） for each n ∈ N;（c） There is an operator Φ ： LCL（X, I） → USC（X, I） such that, for any h ∈ LCL（X, I）,0 Φ（h） h, and 0 〈 Φ（h）（x） 〈 h（x） whenever h（x） 〉 0.展开更多
In the present, the authors investigate a new type of separation axioms, which they call it w s-regular. The authors obtained some of its basic properties and its characterizations. Also, the authors notice that the a...In the present, the authors investigate a new type of separation axioms, which they call it w s-regular. The authors obtained some of its basic properties and its characterizations. Also, the authors notice that the axiom of tO s-regularity is weaker than the regularity, stronger than s-regularity and it is independent of w -regularity. However, the authors showed that the w s-regularity and regularity are identical on the class of all locally countable spaces, while the concepts ofw s-regularity and s-regularity are same on the class of anti-locally countable spaces：; furthermore, they proved that the three concepts w s-regularity, s-regularity and w s-regularity are same on the class of extremally disconnected spaces. The authors characterized w s-regular Trspaces by g-open sets, and they proved that the w s-regularity is an open hereditary property and it is also a topologizal property. The w s-closure of subsets of topological spaces are investigated and characterized. The authors used the concepts w s-closure to obtain some characterizations of the w s-regular spaces. Behind those, the authors obtained some properties and characterizations of w -semi open sets.展开更多
Full waveform inversion(FWI)is a complex data fitting process based on full wavefield modeling,aiming to quantitatively reconstruct unknown model parameters from partial waveform data with high-resolution.However,this...Full waveform inversion(FWI)is a complex data fitting process based on full wavefield modeling,aiming to quantitatively reconstruct unknown model parameters from partial waveform data with high-resolution.However,this process is highly nonlinear and ill-posed,therefore achieving high-resolution imaging of complex biological tissues within a limited number of iterations remains challenging.We propose a multiscale frequency–domain full waveform inversion(FDFWI)framework for ultrasound computed tomography(USCT)imaging of biological tissues,which innovatively incorporates Sobolev space norm regularization for enhancement of prior information.Specifically,we investigate the effect of different types of hyperparameter on the imaging quality,during which the regularization weight is dynamically adapted based on the ratio of the regularization term to the data fidelity term.This strategy reduces reliance on predefined hyperparameters,ensuring robust inversion performance.The inversion results from both numerical and experimental tests(i.e.,numerical breast,thigh,and ex vivo pork-belly tissue)demonstrate the effectiveness of our regularized FWI strategy.These findings will contribute to the application of the FWI technique in quantitative imaging based on USCT and make USCT possible to be another high-resolution imaging method after x-ray computed tomography and magnetic resonance imaging.展开更多
In this manuscript,we consider two kinds of the Fokker-Planck-type systems in the whole space.The first part involves proving the global existence and the algebraic time decay rates of the mild solutions to the Fokker...In this manuscript,we consider two kinds of the Fokker-Planck-type systems in the whole space.The first part involves proving the global existence and the algebraic time decay rates of the mild solutions to the Fokker-Planck-Boltzmann equation near Maxwellians if initial data satisfies some smallness in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2)∩L_(k)^(p)L_(T)^(∞)L_(v)^(2).The second part proves the global existence of the mild solutions to the Vlasov-Poisson-Fokker-Planck system in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2),and we also obtain the exponential time decay rates,which are different from the algebraic time decay rates of the Fokker-Planck-Boltzmann equation.Our analysis is based on Lk1LT∞Lv2function space introduced by Duan et al.(Comm Pure Appl Math,2021,74:932-1020),the L_(k)^(1)∩L_(k)^(p) approach developed by Duan et al.(SIAM J Math Anal,2024,56:762-800),and the coercivity property of the Fokker-Planck operator.However,it is worth pointing out that the L_(k)^(1)∩L_(k)^(p)approach is not required for the Vlasov-Poisson-Fokker-Planck system,due to the influence of the electric field term,which is different from the Fokker-Planck-Boltzmann equation in this paper and in the work of Duan et al.(SIAM J Math Anal,2024,56:762-800).展开更多
In this paper, we first introduce the concept of the inclusive regular separation in L-fuzzy topological spaces. Then we compare the inclusive regular separation with pointed regular separation and regular separation,...In this paper, we first introduce the concept of the inclusive regular separation in L-fuzzy topological spaces. Then we compare the inclusive regular separation with pointed regular separation and regular separation, and discuss the implicative and non-implicative relations among the above three separations. Finally, we illustrate that the inclusive regular separation is harmonic with the inclusive normal separation and inclusive completely regular separation.展开更多
This paper discusses the reservoir space in carbonate rocks in terms of types,combination features,distribution regularity,and controlling factors,based on core observations and tests of the North Truva Oilfield,Caspi...This paper discusses the reservoir space in carbonate rocks in terms of types,combination features,distribution regularity,and controlling factors,based on core observations and tests of the North Truva Oilfield,Caspian Basin.According to the reservoir space combinations,carbonate reservoirs can be divided into four types,i.e.,pore,fracture-pore,pore-cavity-fracture,and pore-cavity.Formation and distribution of these reservoirs is strongly controlled by deposition,diagenesis,and tectonism.In evaporated platform and restricted platform facies,the reservoirs are predominately affected by meteoric fresh water leaching in the supergene-para-syngenetic period and by uplifting and erosion in the late stage,making both platform facies contain all the above-mentioned four types of reservoirs,with various pores,such as dissolved cavities and dissolved fractures,or structural fractures occasionally in favorable structural locations.In open platform facies,the reservoirs deposited continuously in deeper water,in an environment of alternative high-energy shoals（where pore-fracture-type reservoirs are dominant） and low-energy shoals（where pore reservoirs are dominant）.展开更多
Three classical compactification procedures are presented with nonstandard flavour. This is to illustrate the applicability of Nonstandard analytic tool to beginners interested in Nonstandard analytic methods. The gen...Three classical compactification procedures are presented with nonstandard flavour. This is to illustrate the applicability of Nonstandard analytic tool to beginners interested in Nonstandard analytic methods. The general procedure is as follows: A suitable equivalence relation is defined on an enlargement <sup>*</sup>X of the space X which is a completely regular space or a locally compact Hausdorff space or a locally compact Abelian group. Accordingly, every f in C(X,R) (the space of bounded continuous real valued functions on X) or Cc(X,R) (the space of continuous real valued functions on X with compact support) or the dual group <span style="white-space:nowrap;">Γ of the locally compact Abelian group G is extended to the set <img alt="" src="Edit_b9535172-924d-44f0-bab3-c49db17a3b7a.png" /> of the above mentioned equivalence classes. A compact topology on <img alt="" src="Edit_9d7962a3-b8a3-4693-b62a-078c8c4b4853.png" /> is obtained as the weak topology generated by these extensions of f. Then X is naturally imbedded densely in <img alt="" src="Edit_f7d403b2-eff3-4555-b8e7-1b106e06d2e7.png" />.展开更多
Let X be an Ahlfors d-regular space and rn a d-regular measure on X. We prove that a measure μ on X is d-homogeneous if and only if μ is mutually absolutely continuous with respect to m and the derivative Dmμ（x） ...Let X be an Ahlfors d-regular space and rn a d-regular measure on X. We prove that a measure μ on X is d-homogeneous if and only if μ is mutually absolutely continuous with respect to m and the derivative Dmμ（x） is an A1 weight. Also, we show by an example that every Ahlfors d-regular space carries a measure which is d-homogeneous but not d-regular.展开更多
A novel linear microprobe array(LMPA)has been developed by a conventional microfabrication method from silicon.The LMPA leverages the properties of conventional microwire with additional features of naturally formed r...A novel linear microprobe array(LMPA)has been developed by a conventional microfabrication method from silicon.The LMPA leverages the properties of conventional microwire with additional features of naturally formed regular spacing.With the help of periodic microprobe arrays and double-side V-grooves fabricated in advance between each pair of the two microprobes’rear ends,the number of microprobe units for assembly in one array can be flexibly chosen by cleavage fracture from the LMPA.The fabrication method was demonstrated and the prototype device was assessed by electrochemical impedance spectroscopy(EIS)and in vivo test.The SNR of the spikes recorded was 6.展开更多
We investigate the low regularity local and global well-posedness of the Cauchy problem for the coupled Klein-Gordon-Schr¨odinger system with fractional Laplacian in the Schr¨odinger equation in R^（1＋1）. ...We investigate the low regularity local and global well-posedness of the Cauchy problem for the coupled Klein-Gordon-Schr¨odinger system with fractional Laplacian in the Schr¨odinger equation in R^（1＋1）. We use Bourgain space method to study this problem and prove that this system is locally well-posed for Schr¨odinger data in H^（s_1） and wave data in H^（s_2） × H^（s_2-1）for 3/4- α ＆lt; s_1≤0 and-1/2 ＆lt; s_2 ＆lt; 3/2, where α is the fractional power of Laplacian which satisfies 3/4 ＆lt; α≤1. Based on this local well-posedness result, we also obtain the global well-posedness of this system for s_1 = 0 and-1/2 ＆lt; s_2 ＆lt; 1/2 by using the conservation law for the L^2 norm of u.展开更多
基金Supported by the Project of Young Creative Talents of Guangdong Province(Grant No.2014KQNCX161)the Ph D Start-up Fund of Natural Science Foundation of Guangdong Province(Grant No.2014A030310187)+3 种基金the National Natural Science Foundation of China(Grant Nos.11526158613792111471153)the Research Fund for Higher Education of Fujian Province of China(Grant No.2013J01029)
文摘In this paper, we give some characterizations of almost completely regular spaces and c-semistratifiable spaces（CSS） by semi-continuous functions. We mainly show that：（1）Let X be a space. Then the following statements are equivalent：（i） X is almost completely regular.（ii） Every two disjoint subsets of X, one of which is compact and the other is regular closed, are completely separated.（iii） If g, h ： X → I, g is compact-like, h is normal lower semicontinuous, and g ≤ h, then there exists a continuous function f ： X → I such that g ≤ f ≤ h;and（2） Let X be a space. Then the following statements are equivalent：（a） X is CSS;（b） There is an operator U assigning to a decreasing sequence of compact sets（Fj）j∈N,a decreasing sequence of open sets（U（n,（Fj）））n∈N such that（b1） Fn■U（n,（Fj）） for each n ∈ N;（b2）∩n∈NU（n,（Fj）） =∩n∈NFn;（b3） Given two decreasing sequences of compact sets（Fj）j∈N and（Ej）j∈N such that Fn■Enfor each n ∈ N, then U（n,（Fj））■U（n,（Ej）） for each n ∈ N;（c） There is an operator Φ ： LCL（X, I） → USC（X, I） such that, for any h ∈ LCL（X, I）,0 Φ（h） h, and 0 〈 Φ（h）（x） 〈 h（x） whenever h（x） 〉 0.
文摘In the present, the authors investigate a new type of separation axioms, which they call it w s-regular. The authors obtained some of its basic properties and its characterizations. Also, the authors notice that the axiom of tO s-regularity is weaker than the regularity, stronger than s-regularity and it is independent of w -regularity. However, the authors showed that the w s-regularity and regularity are identical on the class of all locally countable spaces, while the concepts ofw s-regularity and s-regularity are same on the class of anti-locally countable spaces：; furthermore, they proved that the three concepts w s-regularity, s-regularity and w s-regularity are same on the class of extremally disconnected spaces. The authors characterized w s-regular Trspaces by g-open sets, and they proved that the w s-regularity is an open hereditary property and it is also a topologizal property. The w s-closure of subsets of topological spaces are investigated and characterized. The authors used the concepts w s-closure to obtain some characterizations of the w s-regular spaces. Behind those, the authors obtained some properties and characterizations of w -semi open sets.
基金supported by the National Natural Science Foundation of China(Grant No.12474461)the Basic and Frontier Exploration Project Independently Deployed by Institute of Acoustics,Chinese Academy of Sciences(Grant No.JCQY202402)the Goal-Oriented Project Independently Deployed by Institute of Acoustics,Chinese Academy of Sciences(Grant No.MBDX202113).
文摘Full waveform inversion(FWI)is a complex data fitting process based on full wavefield modeling,aiming to quantitatively reconstruct unknown model parameters from partial waveform data with high-resolution.However,this process is highly nonlinear and ill-posed,therefore achieving high-resolution imaging of complex biological tissues within a limited number of iterations remains challenging.We propose a multiscale frequency–domain full waveform inversion(FDFWI)framework for ultrasound computed tomography(USCT)imaging of biological tissues,which innovatively incorporates Sobolev space norm regularization for enhancement of prior information.Specifically,we investigate the effect of different types of hyperparameter on the imaging quality,during which the regularization weight is dynamically adapted based on the ratio of the regularization term to the data fidelity term.This strategy reduces reliance on predefined hyperparameters,ensuring robust inversion performance.The inversion results from both numerical and experimental tests(i.e.,numerical breast,thigh,and ex vivo pork-belly tissue)demonstrate the effectiveness of our regularized FWI strategy.These findings will contribute to the application of the FWI technique in quantitative imaging based on USCT and make USCT possible to be another high-resolution imaging method after x-ray computed tomography and magnetic resonance imaging.
基金supported by the National Natural Science Foundation of China(11801285,12326337)。
文摘In this manuscript,we consider two kinds of the Fokker-Planck-type systems in the whole space.The first part involves proving the global existence and the algebraic time decay rates of the mild solutions to the Fokker-Planck-Boltzmann equation near Maxwellians if initial data satisfies some smallness in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2)∩L_(k)^(p)L_(T)^(∞)L_(v)^(2).The second part proves the global existence of the mild solutions to the Vlasov-Poisson-Fokker-Planck system in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2),and we also obtain the exponential time decay rates,which are different from the algebraic time decay rates of the Fokker-Planck-Boltzmann equation.Our analysis is based on Lk1LT∞Lv2function space introduced by Duan et al.(Comm Pure Appl Math,2021,74:932-1020),the L_(k)^(1)∩L_(k)^(p) approach developed by Duan et al.(SIAM J Math Anal,2024,56:762-800),and the coercivity property of the Fokker-Planck operator.However,it is worth pointing out that the L_(k)^(1)∩L_(k)^(p)approach is not required for the Vlasov-Poisson-Fokker-Planck system,due to the influence of the electric field term,which is different from the Fokker-Planck-Boltzmann equation in this paper and in the work of Duan et al.(SIAM J Math Anal,2024,56:762-800).
基金the National Natural Science Foundation of China (10471083)Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE
文摘In this paper, we first introduce the concept of the inclusive regular separation in L-fuzzy topological spaces. Then we compare the inclusive regular separation with pointed regular separation and regular separation, and discuss the implicative and non-implicative relations among the above three separations. Finally, we illustrate that the inclusive regular separation is harmonic with the inclusive normal separation and inclusive completely regular separation.
基金supported by the National Major Science and Technology Project (No.2016ZX05030002)
文摘This paper discusses the reservoir space in carbonate rocks in terms of types,combination features,distribution regularity,and controlling factors,based on core observations and tests of the North Truva Oilfield,Caspian Basin.According to the reservoir space combinations,carbonate reservoirs can be divided into four types,i.e.,pore,fracture-pore,pore-cavity-fracture,and pore-cavity.Formation and distribution of these reservoirs is strongly controlled by deposition,diagenesis,and tectonism.In evaporated platform and restricted platform facies,the reservoirs are predominately affected by meteoric fresh water leaching in the supergene-para-syngenetic period and by uplifting and erosion in the late stage,making both platform facies contain all the above-mentioned four types of reservoirs,with various pores,such as dissolved cavities and dissolved fractures,or structural fractures occasionally in favorable structural locations.In open platform facies,the reservoirs deposited continuously in deeper water,in an environment of alternative high-energy shoals（where pore-fracture-type reservoirs are dominant） and low-energy shoals（where pore reservoirs are dominant）.
文摘Three classical compactification procedures are presented with nonstandard flavour. This is to illustrate the applicability of Nonstandard analytic tool to beginners interested in Nonstandard analytic methods. The general procedure is as follows: A suitable equivalence relation is defined on an enlargement <sup>*</sup>X of the space X which is a completely regular space or a locally compact Hausdorff space or a locally compact Abelian group. Accordingly, every f in C(X,R) (the space of bounded continuous real valued functions on X) or Cc(X,R) (the space of continuous real valued functions on X with compact support) or the dual group <span style="white-space:nowrap;">Γ of the locally compact Abelian group G is extended to the set <img alt="" src="Edit_b9535172-924d-44f0-bab3-c49db17a3b7a.png" /> of the above mentioned equivalence classes. A compact topology on <img alt="" src="Edit_9d7962a3-b8a3-4693-b62a-078c8c4b4853.png" /> is obtained as the weak topology generated by these extensions of f. Then X is naturally imbedded densely in <img alt="" src="Edit_f7d403b2-eff3-4555-b8e7-1b106e06d2e7.png" />.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10971056 and 10771164)
文摘Let X be an Ahlfors d-regular space and rn a d-regular measure on X. We prove that a measure μ on X is d-homogeneous if and only if μ is mutually absolutely continuous with respect to m and the derivative Dmμ（x） is an A1 weight. Also, we show by an example that every Ahlfors d-regular space carries a measure which is d-homogeneous but not d-regular.
基金supported the National Basic Research Program of China("973"Project)(Grant Nos.2011CB933203 and 2011CB933102)the National Hi-Tech Research and Development Program of China("863"Project)(Grant Nos.2012AA030308 and 2013AA032204)+1 种基金the National Natural Science Foundation of China(Grant Nos.61275200,61335010,61178051 and 61178082)the National Important Scientific Apparatus Developing Project(Grant No.2011YQ04008204)
文摘A novel linear microprobe array(LMPA)has been developed by a conventional microfabrication method from silicon.The LMPA leverages the properties of conventional microwire with additional features of naturally formed regular spacing.With the help of periodic microprobe arrays and double-side V-grooves fabricated in advance between each pair of the two microprobes’rear ends,the number of microprobe units for assembly in one array can be flexibly chosen by cleavage fracture from the LMPA.The fabrication method was demonstrated and the prototype device was assessed by electrochemical impedance spectroscopy(EIS)and in vivo test.The SNR of the spikes recorded was 6.
基金supported by National Natural Science Foundation of China (Grant No. 11201498)
文摘We investigate the low regularity local and global well-posedness of the Cauchy problem for the coupled Klein-Gordon-Schr¨odinger system with fractional Laplacian in the Schr¨odinger equation in R^（1＋1）. We use Bourgain space method to study this problem and prove that this system is locally well-posed for Schr¨odinger data in H^（s_1） and wave data in H^（s_2） × H^（s_2-1）for 3/4- α ＆lt; s_1≤0 and-1/2 ＆lt; s_2 ＆lt; 3/2, where α is the fractional power of Laplacian which satisfies 3/4 ＆lt; α≤1. Based on this local well-posedness result, we also obtain the global well-posedness of this system for s_1 = 0 and-1/2 ＆lt; s_2 ＆lt; 1/2 by using the conservation law for the L^2 norm of u.
