Let B(H) be the C^*-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B(H) preserving the star partial order in both directions if and only i...Let B(H) be the C^*-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B(H) preserving the star partial order in both directions if and only if one of the following assertions holds. (1) There exist a nonzero complex number a and two unitary operators U and V on H such that φ(X) = a UXV or φ(X) = α UX^* V for all X ∈B(H). (2) There exist a nonzero a and two anti-unitary operators U and V on H such that φ(X) = αUXV or φ(X) = aUX^* Vfor all X∈ B(H).展开更多
In this paper, the concept of C-left hyperideals is introduced in ordered semihypergroups, and several related properties are investigated. In particular, we discuss the relationships between the greatest left hyperid...In this paper, the concept of C-left hyperideals is introduced in ordered semihypergroups, and several related properties are investigated. In particular, we discuss the relationships between the greatest left hyperideals and C-left hyperideals of ordered semihypergroups. Furthermore, we introduce the concept of left bases of an ordered semihypergroup, and give out the sufficient and necessary conditions of the existence of the greatest C-left hyperideal of an ordered semihypergroup by the properties of left bases. The result about C-left ideals in ordered semigroups is generalized to the ordered semihypergroups.展开更多
In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and (gener...In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and (generalized) bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.展开更多
We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the...We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e<sup>2</sup> and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).展开更多
In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In...In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In particular, we prove that S is strongly semisimple if and only if each fuzzy left ideal of S is the intersection of all quasi-prime fuzzy left ideals of S containing it.展开更多
Let <em>G</em> be a group. <em>G</em> is right-orderable provided it admits a total order ≤ satisfying <em>hg</em><sub>1</sub> <span style="white-space:normal;&...Let <em>G</em> be a group. <em>G</em> is right-orderable provided it admits a total order ≤ satisfying <em>hg</em><sub>1</sub> <span style="white-space:normal;">≤ <span style="white-space:normal;"><em>hg</em><sub>2 </sub></span></span>whenever <em style="white-space:normal;">g</em><sub style="white-space:normal;">1</sub><span style="white-space:normal;"> </span><span style="white-space:normal;">≤ <i>g</i><sub>2</sub></span>. <em>G</em> is orderable provided it admits a total order ≤ satisfying both: <em style="white-space:normal;">hg</em><sub style="white-space:normal;">1</sub><span style="white-space:normal;"> </span><span style="white-space:normal;">≤ <em>hg</em><sub>2</sub></span> whenever <span style="white-space:nowrap;"><em>g</em><sub>1</sub> ≤ <em>g</em><sub>2</sub></span> and <em style="white-space:normal;">g</em><sub style="white-space:normal;">1</sub><em style="white-space:normal;">h</em><span style="white-space:normal;"> ≤ </span><em style="white-space:normal;">g</em><sub style="white-space:normal;">2</sub><em style="white-space:normal;">h</em> whenever <em>g</em><sub>1</sub> ≤ <em>g</em><sub>2</sub>. A classical result shows that free groups are orderable. In this paper, we prove that left-orderable groups and orderable groups are quasivarieties of groups both with undecidable theory. For orderable groups, we find an explicit set of universal axioms.展开更多
In this paper,we define intuitionistic fuzzy generalized bi-ideals in ordered semigroups and characterize regular and left weakly regular ordered semigroups in terms of intuitionistic fuzzy generalized bi-ideals.
This paper proposes a tunable zeroth-order resonator on a composite right/left-handed transmission line consisting of a transversely magnetized ferrite substrate periodically loaded by microstrip inductors. Based on t...This paper proposes a tunable zeroth-order resonator on a composite right/left-handed transmission line consisting of a transversely magnetized ferrite substrate periodically loaded by microstrip inductors. Based on the propagation theory of edge guided modes, the analysis procedure of this structure is introduced. The numerical results demonstrate the tunability of the resonant frequency by changing the DC bias magnetic field applied to the ferrite. In contrast to previous work, the proposed structure is easy to design and fabricate and does not require a chip component.展开更多
基金The NSF(11371233)of Chinathe Fundamental Research Funds(GK201301007)for the Central Universities
文摘Let B(H) be the C^*-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B(H) preserving the star partial order in both directions if and only if one of the following assertions holds. (1) There exist a nonzero complex number a and two unitary operators U and V on H such that φ(X) = a UXV or φ(X) = α UX^* V for all X ∈B(H). (2) There exist a nonzero a and two anti-unitary operators U and V on H such that φ(X) = αUXV or φ(X) = aUX^* Vfor all X∈ B(H).
基金The NSF(11271040,11361027)of Chinathe Key Project(2014KZDXM055)of Department of Education of Guangdong Province+1 种基金the University Natural Science Project(KJ2015A161)of Anhui Provincethe NSF(2014A030313625)of Guangdong Province
文摘In this paper, the concept of C-left hyperideals is introduced in ordered semihypergroups, and several related properties are investigated. In particular, we discuss the relationships between the greatest left hyperideals and C-left hyperideals of ordered semihypergroups. Furthermore, we introduce the concept of left bases of an ordered semihypergroup, and give out the sufficient and necessary conditions of the existence of the greatest C-left hyperideal of an ordered semihypergroup by the properties of left bases. The result about C-left ideals in ordered semigroups is generalized to the ordered semihypergroups.
基金The NSF(10961014) of Chinathe NSF(0501332) of Guangdong Province+1 种基金the Excellent Youth Talent Foundation(2009SQRZ149) of Anhui Provincethe Fuyang Normal College Youth Foundation (2008LQ11)
文摘In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and (generalized) bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.
文摘We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e<sup>2</sup> and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).
基金The NSF (10961014) of Chinathe NSF (S2011010003681) of Guangdong Province+3 种基金the Science and Technology Projects (2010B010600039) of Guangdong Provincethe Excellent Youth Talent Foundation (2012SQRL115ZD) of Anhui Provincethe University Natural Science Project (KJ2012B133) of Anhui Provincethe NSF (2007LZ01) of Fuyang Normal College
文摘In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In particular, we prove that S is strongly semisimple if and only if each fuzzy left ideal of S is the intersection of all quasi-prime fuzzy left ideals of S containing it.
文摘Let <em>G</em> be a group. <em>G</em> is right-orderable provided it admits a total order ≤ satisfying <em>hg</em><sub>1</sub> <span style="white-space:normal;">≤ <span style="white-space:normal;"><em>hg</em><sub>2 </sub></span></span>whenever <em style="white-space:normal;">g</em><sub style="white-space:normal;">1</sub><span style="white-space:normal;"> </span><span style="white-space:normal;">≤ <i>g</i><sub>2</sub></span>. <em>G</em> is orderable provided it admits a total order ≤ satisfying both: <em style="white-space:normal;">hg</em><sub style="white-space:normal;">1</sub><span style="white-space:normal;"> </span><span style="white-space:normal;">≤ <em>hg</em><sub>2</sub></span> whenever <span style="white-space:nowrap;"><em>g</em><sub>1</sub> ≤ <em>g</em><sub>2</sub></span> and <em style="white-space:normal;">g</em><sub style="white-space:normal;">1</sub><em style="white-space:normal;">h</em><span style="white-space:normal;"> ≤ </span><em style="white-space:normal;">g</em><sub style="white-space:normal;">2</sub><em style="white-space:normal;">h</em> whenever <em>g</em><sub>1</sub> ≤ <em>g</em><sub>2</sub>. A classical result shows that free groups are orderable. In this paper, we prove that left-orderable groups and orderable groups are quasivarieties of groups both with undecidable theory. For orderable groups, we find an explicit set of universal axioms.
文摘In this paper,we define intuitionistic fuzzy generalized bi-ideals in ordered semigroups and characterize regular and left weakly regular ordered semigroups in terms of intuitionistic fuzzy generalized bi-ideals.
文摘This paper proposes a tunable zeroth-order resonator on a composite right/left-handed transmission line consisting of a transversely magnetized ferrite substrate periodically loaded by microstrip inductors. Based on the propagation theory of edge guided modes, the analysis procedure of this structure is introduced. The numerical results demonstrate the tunability of the resonant frequency by changing the DC bias magnetic field applied to the ferrite. In contrast to previous work, the proposed structure is easy to design and fabricate and does not require a chip component.