Research of the acoustic local effect of metamaterial is widely used in the fields of environmental science,military industry and biomedicine.In this paper,the metamaterial is designed by annular columnar structures.T...Research of the acoustic local effect of metamaterial is widely used in the fields of environmental science,military industry and biomedicine.In this paper,the metamaterial is designed by annular columnar structures.The acoustic local effect in slender columnar structure with two layers of rings in air is investigated.Results prove that when the plane acoustic wave is incident into the model,complex interference and diffraction occur.And at different frequencies,multipolar acoustic local effect existes and cycle distribution phenomenon is observed.It is noteworthy that this phenomenon has very weak relatedness with the materials and acoustic parameters of the model.The research of this metamaterial design in this paper has definite reference significance in the acoustic communication and amplification of the acoustic signal detection.展开更多
For a family of smooth functions defined in multi-dimensional space,we show that,under certain generic conditions,all minimal and maximal points are non-degenerate.
In a recent article, the authors provided an effective algorithm for both computing the global infimum of f and deciding whether or not the infimum of f is attained, where f is a multivariate polynomial over the field...In a recent article, the authors provided an effective algorithm for both computing the global infimum of f and deciding whether or not the infimum of f is attained, where f is a multivariate polynomial over the field R of real numbers. As a complement, the authors investigate the semi- algebraically connected components of minimum points of a polynomial function in this paper. For a given multivariate polynomial f over R, it is shown that the above-mentioned algorithm can find at least one point in each semi-algebraically connected component of minimum points of f whenever f has its global minimum.展开更多
In this paper we consider extreme points and support points for compact subclasses of normalized biholomorphic mappings of the Euclidean unit ball Bn in Cn. We consider the class So（Bn） of biholomorphic mappings on ...In this paper we consider extreme points and support points for compact subclasses of normalized biholomorphic mappings of the Euclidean unit ball Bn in Cn. We consider the class So（Bn） of biholomorphic mappings on Bn which have parametric representation, i.e., they are the initial elements f（-, O） of a Loewner chain f（x,t） = etz ＋ ... such that {e-tf（.,t）}t≥o is a normal family on Bn. We show that if f（.,O） is an extreme point （respectively a support point） of So（Bn）, then e-t f（., t） is an extreme point of So（Bn） for t≥0 （respectively a support point of So（Bn） for t C [O, t0] and some to〉 0）. This is a generalization to the n-dimensional case of work due to Pell. Also, we prove analogous results for mappings which belong to So（Bn） and which are bounded in the norm by a fixed constant. We relate the study of this class to reachable sets in control theory generalizing work of Roth. Finally we consider extreme points and support points for biholomorphic mappings of Bn generated by using extension operators that preserve Loewner chains.展开更多
基金National Natural Science Foundation of China(No.61671414)Natural Science Foundation for Young Scientists of Shanxi Province,China(No.201601D202035)
文摘Research of the acoustic local effect of metamaterial is widely used in the fields of environmental science,military industry and biomedicine.In this paper,the metamaterial is designed by annular columnar structures.The acoustic local effect in slender columnar structure with two layers of rings in air is investigated.Results prove that when the plane acoustic wave is incident into the model,complex interference and diffraction occur.And at different frequencies,multipolar acoustic local effect existes and cycle distribution phenomenon is observed.It is noteworthy that this phenomenon has very weak relatedness with the materials and acoustic parameters of the model.The research of this metamaterial design in this paper has definite reference significance in the acoustic communication and amplification of the acoustic signal detection.
基金supported by National Basic Research Program of China(973 Program)(Grant No.2013CB834100)National Natural Science Foundation of China(Grant Nos.11171146 and 11201222)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘For a family of smooth functions defined in multi-dimensional space,we show that,under certain generic conditions,all minimal and maximal points are non-degenerate.
基金supported by the National Natural Science Foundation of China under Grant No.11161034the Science Foundation of the Education Department of Jiangxi Province under Grant No.Gjj12012
文摘In a recent article, the authors provided an effective algorithm for both computing the global infimum of f and deciding whether or not the infimum of f is attained, where f is a multivariate polynomial over the field R of real numbers. As a complement, the authors investigate the semi- algebraically connected components of minimum points of a polynomial function in this paper. For a given multivariate polynomial f over R, it is shown that the above-mentioned algorithm can find at least one point in each semi-algebraically connected component of minimum points of f whenever f has its global minimum.
基金supported by the Natural Sciences and Engineering Research Council of Canada (Grant No. A9221)Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science, 2011 (Grant No. 22540213)the Romanian Ministry of Education and Research, UEFISCSU-CNCSIS(Grants Nos. PN-II-ID 524/2007, 525/2007)
文摘In this paper we consider extreme points and support points for compact subclasses of normalized biholomorphic mappings of the Euclidean unit ball Bn in Cn. We consider the class So（Bn） of biholomorphic mappings on Bn which have parametric representation, i.e., they are the initial elements f（-, O） of a Loewner chain f（x,t） = etz ＋ ... such that {e-tf（.,t）}t≥o is a normal family on Bn. We show that if f（.,O） is an extreme point （respectively a support point） of So（Bn）, then e-t f（., t） is an extreme point of So（Bn） for t≥0 （respectively a support point of So（Bn） for t C [O, t0] and some to〉 0）. This is a generalization to the n-dimensional case of work due to Pell. Also, we prove analogous results for mappings which belong to So（Bn） and which are bounded in the norm by a fixed constant. We relate the study of this class to reachable sets in control theory generalizing work of Roth. Finally we consider extreme points and support points for biholomorphic mappings of Bn generated by using extension operators that preserve Loewner chains.
