In this article, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderón-Zygmund type estimate in Be...In this article, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderón-Zygmund type estimate in Besov spaces with more general assumptions on coefficients for both homogeneous equations and non-homogeneous equations. This study of regularity estimates expands the Calderón-Zygmund theory in the Heisenberg group.展开更多
In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Su...In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.展开更多
Cleverly using the relation of independence spaces and B-matroids, this paper firstly deals with the properties of the closure operator of an independence space, followed by presenting the definitions and solving some...Cleverly using the relation of independence spaces and B-matroids, this paper firstly deals with the properties of the closure operator of an independence space, followed by presenting the definitions and solving some relative properties for the sub-independence spaces of an independence space with the help of circuits.展开更多
We study two flux qubits with a parameter coupling scenario. Under the rotating wave approximation, we truncate the 4-dimensional Hilbert space of a coupling flux qubits system to a 2-dimensional subspace spanned by t...We study two flux qubits with a parameter coupling scenario. Under the rotating wave approximation, we truncate the 4-dimensional Hilbert space of a coupling flux qubits system to a 2-dimensional subspace spanned by two dressed states ｜01} and ｜10}. In this subspace, we illustrate how to generate an Aharnov Anandan phase, based on which, we can construct a NOT gate （as effective as a C-NOT gate） in this coupling flux qubits system. FinMly, the fidelity of the NOT gate is also calculated in the presence of the simulated classical noise.展开更多
In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the...In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the k-Ricci curvature, in terms of the squared mean curvature, are also proved respectively.展开更多
A complementarity hypothesis concerning outsider and insider perspectives of a gargantuan black hole is proposed. The two thought experiments presented herein are followed by a brief discussion of a new interpretation...A complementarity hypothesis concerning outsider and insider perspectives of a gargantuan black hole is proposed. The two thought experiments presented herein are followed by a brief discussion of a new interpretation of black hole interior “space-and-time-reversal”. Specifically, it is proposed that the “singularity” space of the black hole interior is time-like and the expansion time of the black hole interior is space-like. The resemblance of this new insider interpretation to our own expanding and redshifting big bang universe is compelling.展开更多
<strong>Objective:</strong><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;"> To analyze the relationship between mi...<strong>Objective:</strong><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;"> To analyze the relationship between micropapillary pattern (MIP) and tumor spread through air space (STAS) and postoperative survival rate in patients with lung adenocarcinoma ≤ 2 cm. </span><b><span style="font-family:Verdana;">Methods:</span></b><span style="font-family:Verdana;"> Retrospective analyses were performed on clinical data of 575 patients with lung adenocarcinoma ≤ 2 cm, which were resected from 2009 to 2011. We analyzed the pathological findings on the resected specimens, with special reference to the presence/absence MIP and STAS, which have been reported to be a marker of poor prognosis of lung adenocarcinoma. Patients were divided into three according to the presence/absence of MIP and STAS: low</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">risk (MIP</span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;"> STAS</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">), medium</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">risk (either MIP or STAS + (one plus)) and high</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">risk group (+/+: double plus). Endpoint was postoperative survival rate, which was compared among three groups. </span><b><span style="font-family:Verdana;">Results:</span></b><span style="font-family:Verdana;"> There was no statistical difference in age, sex, and serum CEA level among three groups. In lobectomized patients, there was no statistical difference in prognosis among three groups;however, in sub-lobectomy group, patients with double + (+/+ for MIP and STAS) showed a lower survival rate than others (P < 0.001). </span><b><span style="font-family:Verdana;">Conclusion:</span></b><span style="font-family:Verdana;"> The presence of MIP and STAS reduced the survival rate in sub-lobectomized patients.</span></span></span></span>展开更多
In this paper, we aim to introduce and study some basic properties of upper and lower <em>M</em>-asymmetric irresolute multifunctions defined between asymmetric sets in the realm of bitopological spaces wi...In this paper, we aim to introduce and study some basic properties of upper and lower <em>M</em>-asymmetric irresolute multifunctions defined between asymmetric sets in the realm of bitopological spaces with certain minimal structures as a generalization of irresolute functions deal to Crossley and Hildebrand <a href="#ref1">[1]</a> and upper and lower irresolute Multifunctions deal to Popa <a href="#ref2">[2]</a>.展开更多
文摘In this article, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderón-Zygmund type estimate in Besov spaces with more general assumptions on coefficients for both homogeneous equations and non-homogeneous equations. This study of regularity estimates expands the Calderón-Zygmund theory in the Heisenberg group.
文摘In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.
基金Supported by NSF of Mathematical Special Foundation of Hebei Province(08M005)Supported by NSF of Educational Department of Hebei Province(2006105)
文摘Cleverly using the relation of independence spaces and B-matroids, this paper firstly deals with the properties of the closure operator of an independence space, followed by presenting the definitions and solving some relative properties for the sub-independence spaces of an independence space with the help of circuits.
基金Project supported by the National Basic Research Program of China (Grant Nos. 2011CBA00106 and 2009CB929102)the National Natural Science Foundation of China (Grant Nos. 11161130519 and 10974243)the Fundamental Research Funds for the Central Universities, China (Grant No. CDJXS11100012)
文摘We study two flux qubits with a parameter coupling scenario. Under the rotating wave approximation, we truncate the 4-dimensional Hilbert space of a coupling flux qubits system to a 2-dimensional subspace spanned by two dressed states ｜01} and ｜10}. In this subspace, we illustrate how to generate an Aharnov Anandan phase, based on which, we can construct a NOT gate （as effective as a C-NOT gate） in this coupling flux qubits system. FinMly, the fidelity of the NOT gate is also calculated in the presence of the simulated classical noise.
文摘In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the k-Ricci curvature, in terms of the squared mean curvature, are also proved respectively.
文摘A complementarity hypothesis concerning outsider and insider perspectives of a gargantuan black hole is proposed. The two thought experiments presented herein are followed by a brief discussion of a new interpretation of black hole interior “space-and-time-reversal”. Specifically, it is proposed that the “singularity” space of the black hole interior is time-like and the expansion time of the black hole interior is space-like. The resemblance of this new insider interpretation to our own expanding and redshifting big bang universe is compelling.
文摘<strong>Objective:</strong><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;"> To analyze the relationship between micropapillary pattern (MIP) and tumor spread through air space (STAS) and postoperative survival rate in patients with lung adenocarcinoma ≤ 2 cm. </span><b><span style="font-family:Verdana;">Methods:</span></b><span style="font-family:Verdana;"> Retrospective analyses were performed on clinical data of 575 patients with lung adenocarcinoma ≤ 2 cm, which were resected from 2009 to 2011. We analyzed the pathological findings on the resected specimens, with special reference to the presence/absence MIP and STAS, which have been reported to be a marker of poor prognosis of lung adenocarcinoma. Patients were divided into three according to the presence/absence of MIP and STAS: low</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">risk (MIP</span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;"> STAS</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">), medium</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">risk (either MIP or STAS + (one plus)) and high</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">risk group (+/+: double plus). Endpoint was postoperative survival rate, which was compared among three groups. </span><b><span style="font-family:Verdana;">Results:</span></b><span style="font-family:Verdana;"> There was no statistical difference in age, sex, and serum CEA level among three groups. In lobectomized patients, there was no statistical difference in prognosis among three groups;however, in sub-lobectomy group, patients with double + (+/+ for MIP and STAS) showed a lower survival rate than others (P < 0.001). </span><b><span style="font-family:Verdana;">Conclusion:</span></b><span style="font-family:Verdana;"> The presence of MIP and STAS reduced the survival rate in sub-lobectomized patients.</span></span></span></span>
文摘In this paper, we aim to introduce and study some basic properties of upper and lower <em>M</em>-asymmetric irresolute multifunctions defined between asymmetric sets in the realm of bitopological spaces with certain minimal structures as a generalization of irresolute functions deal to Crossley and Hildebrand <a href="#ref1">[1]</a> and upper and lower irresolute Multifunctions deal to Popa <a href="#ref2">[2]</a>.
