Orientifold projections are an important ingredient in the geometrical engineering of Quantum Field Theory.However,an orientifold can break down the superconformal symmetry and no new superconformal fixed points are a...Orientifold projections are an important ingredient in the geometrical engineering of Quantum Field Theory.However,an orientifold can break down the superconformal symmetry and no new superconformal fixed points are admitted(scenario Ⅱ);nevertheless,in some cases,dubbed scenarios Ⅰ and Ⅲ orientifold,a new IR fixed point is achieved and,for scenario Ⅲ examples,some still not fully understood IR duality seems to emerge.Here we give an algebro-geometrical point of view of orientifold for toric varieties and we propose the existence of relevant operators that deform the starting oriented Conformal Field Theory triggering a flow.We briefly discuss a possible holographic description of this flow.展开更多
Rough set theory is a technique of granular computing. In this paper, we study a type of generalized rough sets based on covering. There are several literatures[1,40-43] exploring covering-based rough sets. Our focus ...Rough set theory is a technique of granular computing. In this paper, we study a type of generalized rough sets based on covering. There are several literatures[1,40-43] exploring covering-based rough sets. Our focus of this paper is on the dualities in rough operations.展开更多
We investigate dualities and inequalities related to noncommutative martingale Hardy-Orlicz spaces.More precisely,for a concave Orlicz functionΦ,we characterize the dual spaces of noncommutative martingale Hardy-Orli...We investigate dualities and inequalities related to noncommutative martingale Hardy-Orlicz spaces.More precisely,for a concave Orlicz functionΦ,we characterize the dual spaces of noncommutative martingale Hardy-Orlicz spaces HΦc(R)and hΦc(M),where R denotes a hyperfinite finite von Neumann algebra and M is a finite von Neumann algebra.The first duality is new even for classical martingales,which partially answers the problem raised by Conde-Alonso and Parcet(2016).We establish as well asymmetric martingale inequalities associated with Orlicz functions that are p-convex and q-concave for 0<p≤q<2.展开更多
Sugars are one of the major metabolites and are essential for nucleic acid synthesis and energy production.In addition,sugars can act as signaling molecules.To study sugar signaling at the systemic level,there is an u...Sugars are one of the major metabolites and are essential for nucleic acid synthesis and energy production.In addition,sugars can act as signaling molecules.To study sugar signaling at the systemic level,there is an urgent need to systematically identify sugar-sensing proteins and nucleic acids.I propose the terms“swodkoreceptor”and“swodkocrine signaling,”derived from the Polish word“slodki”meaning“sweet,”to comprise all sugar-sensing proteins and signaling events,respectively,regardless of their cellular location and signaling domains.This proposal is intended to facilitate the inclusion of proteins such as the Escherichia coli Lac I repressor as an allolactose receptor,human glucokinase regulatory protein(GCKR)as a fructose receptor,and other sugar-binding based allosterically regulated enzymes and transcription factors as sugar-sensing receptors.In addition,enzyme-interacting proteins whose interaction state is regulated by sugar binding have also been proposed as sugar receptors.The systemic study of protein-and nucleic-acid-based swodkoreceptors may help to identify organelle-specific swodkoreceptors and to also address receptor duality.The study of intra-and inter-organism swodkocrine signaling and its crosstalk with gasocrine signaling may help to understand the etiology of diseases due to dysregulation in sugar homeostasis and signaling.展开更多
Quantum gravity is an attempt to resolve incompatibilities between general relativity and quantum theory. Primordial field theory incorporates gravity and electrodynamics and has derived fermion mass gap, half integra...Quantum gravity is an attempt to resolve incompatibilities between general relativity and quantum theory. Primordial field theory incorporates gravity and electrodynamics and has derived fermion mass gap, half integral spin, and fractional charges. This paper extends PFT to hadron physics with a “solenoidal flux”-based explanation of quark confinement differing significantly from Lattice QCD “color flux”-based construction. The theory is presented qualitatively and used to predict hadronic and nuclear properties. Electrodynamic-based analogies help yield numerical results far more intuitively than corresponding QCD results. The origins of QCD and PFT are discussed. A more quantitative description of hadron dynamics is in progress.展开更多
In this study,we investigated worldvolume fermions on the flavor brane in the D0-D4/D8 model,which is holographically equivalent to four-dimensional quantum chromodynamics with instantons or equivalently with a theta ...In this study,we investigated worldvolume fermions on the flavor brane in the D0-D4/D8 model,which is holographically equivalent to four-dimensional quantum chromodynamics with instantons or equivalently with a theta angle.The action involving the worldvolume fermions was obtained by the T-duality rules in string theory,and we accordingly derived their effective five-dimensional and canonical four-dimensional forms by using the systematic dimensional reduction and decomposition of the spinor.Subsequently,we used the AdS/CFT dictionary to evaluate the two-point correlation function as the spectral function for the worldvolume fermions and interpreted the fermions as baryons by analyzing their quantum number with the baryon vertex in holography.In this sense,the interacted action involving the worldvolume fermions and gauge field on the flavor brane was finally derived in holography,which describes the various interactions of mesons and baryons with instantons in the large-N limit.Therefore,this study provides a holographic picture to describe baryons and their interactions based on string theory,particularly in the presence of instantons or a theta angle.展开更多
Wave-particle duality is one of the key features of quantum physics,characterized by the interference pattern.Meanwhile,Floquet spectroscopy is typically studied in the high-frequency region because the Floquet sideba...Wave-particle duality is one of the key features of quantum physics,characterized by the interference pattern.Meanwhile,Floquet spectroscopy is typically studied in the high-frequency region because the Floquet sidebands are very sharp,behaving like“particles”in frequency space,and no interference phenomena are observed.Here,we consider the larger quantum fluctuation region where the Floquet sidebands are broader,making interference between them possible.With the help of an optical lattice clock experimental platform and numerical simulations,such interference of Floquet modes in frequency space is clearly observed.Additionally,it exhibits many exotic phenomena,such as large Floquet sidebands between integer ones,sensitivity to the initial phase,and corresponding emergent symmetries.To analytically elucidate this,we propose the Floquet channel interference hypothesis,which surprisingly matches quantitatively well with both experimental and numerical results.Our research paves the way for developing a new type of interferometer that could be applicable to other Floquet systems.展开更多
In this work,the phase structure of a holographic s+d model with quartic potential terms from 4D Einstein–Gauss–Bonnet gravity is studied in the probe limit.We first show the qd-μphase diagram with a very small val...In this work,the phase structure of a holographic s+d model with quartic potential terms from 4D Einstein–Gauss–Bonnet gravity is studied in the probe limit.We first show the qd-μphase diagram with a very small value of the Gauss–Bonnet coefficientα=1×10-7and in the absence of the quartic terms to locate the suitable choice of the value of qd,where the system admits coexistent s+d solutions.Then we consider the various values of the Gauss–Bonnet coefficientαand present theα-μphase diagram to show the influence of the Gauss–Bonnet term on the phase structure.We also give an example of the re-entrant phase transition which is also realized in the holographic s+s and s+p models.After that we confirm the universality of the influence of the quartic term with coefficientλdon the d-wave solutions,which is similar to the case of s-wave and p-wave solutions previously studied in the s+p model.Finally we give the dependence of the special values of the quartic term coefficientλdon the Gauss–Bonnet coefficientα,below which the d-wave condensate grows to an opposite direction at the(quasi-)critical point,which is useful in realizing first order phase transitions in further studies of the holographic d-wave superfluids.展开更多
In this work,we investigate the shear elasticity and the shear viscosity in a simple holographic axion model with broken translational symmetry and rotational symmetry in space via the perturbation computation.We find...In this work,we investigate the shear elasticity and the shear viscosity in a simple holographic axion model with broken translational symmetry and rotational symmetry in space via the perturbation computation.We find that,in the case of spontaneous symmetry breaking,the broken translations and anisotropy both enhance the shear elasticity of the system.While in all cases,the broken symmetries introduce a double suppression of the shear viscosity,which is in contrast to the result from the study of the p-wave holographic superfluid where the shear viscosity is enhanced when the rotational symmetry is broken spontaneously.展开更多
Complex Field Theory (CFT) proposes that dark matter (DM) and dark energy (DE) are pervasive, complex fields of charged complex masses of equally positive and negative complex charges, respectively. It proposes that e...Complex Field Theory (CFT) proposes that dark matter (DM) and dark energy (DE) are pervasive, complex fields of charged complex masses of equally positive and negative complex charges, respectively. It proposes that each material object, including living creatures, is concomitant with a fraction of the charged complex masses of DM and DE in proportion to its mass. This perception provides new insights into the physics of nature and its constituents from subatomic to cosmic scales. This complex nature of DM and DE explains our inability to see DM or harvest DE for the last several decades. The positive complex DM is responsible for preserving the integrity of galaxies and all material systems. The negative complex charged DE induces a positive repelling force with the positively charged DM and contributes to the universe’s expansion. Both fields are Lorentz invariants in all directions and entangle the whole universe. The paper uses CFT to investigate zero-point energy, particle-wave duality, relativistic mass increase, and entanglement phenomenon and unifies Coulomb’s and Newton’s laws. The paper also verifies the existence of tachyons and explains the spooky action of quantum mechanics at a distance. The paper encourages further research into how CFT might resolve several physical mysteries in physics.展开更多
Let n≥1 be an integer.In this article,we study the notions of Cartan-Eilenberg FP_(n)injective and Cartan-Eilenberg FP_(n)-flat complexes.We also investigate duality pairs relative to the Cartan-Eilenberg FP_(n)-inje...Let n≥1 be an integer.In this article,we study the notions of Cartan-Eilenberg FP_(n)injective and Cartan-Eilenberg FP_(n)-flat complexes.We also investigate duality pairs relative to the Cartan-Eilenberg FP_(n)-injective and Cartan-Eilenberg FP_(n)-flat complexes.As applications,we obtain that any complex admits Cartan-Eilenberg FP_(n)-injective(resp.,Cartan-Eilenberg FP_(n)-flat)cover and preenvelope and we characterize left n-coherent rings using these two classes of complexes.展开更多
The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left...The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC（C,H）and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,（C×lH H）×lH H≌Cv（H×lH H）,is obtained.展开更多
Father of modern linguistics, Ferdinand de Saussure has long been known to make outstanding contributions in the modern linguistics. This article focuses on his some basic theories in modern linguistics from three asp...Father of modern linguistics, Ferdinand de Saussure has long been known to make outstanding contributions in the modern linguistics. This article focuses on his some basic theories in modern linguistics from three aspects: the object of linguistics, levels of linguistics and his explanations about dualities.展开更多
We reexamine the charged AdS domain wall solution to the Einstein-Abelian-Higgs model proposed by Gubser et al. as holographic superconductors at quantum critical points and comment on their statement about the unique...We reexamine the charged AdS domain wall solution to the Einstein-Abelian-Higgs model proposed by Gubser et al. as holographic superconductors at quantum critical points and comment on their statement about the uniqueness of gravity solutions. We generalize their explorations from （3 ＋ 1）-dimensions to arbitrary n -b 1Ds and find that the n ＋1≥5D charged AdS domain walls are unstable against electric perturbations.展开更多
Wuthering heights, it lines with Heathcliff's love, hatred, revenge and awakeness. This paper will analysize the root of Heathcliff's tragedy and draw a rather balanced conclusion from the aspect of morality. ...Wuthering heights, it lines with Heathcliff's love, hatred, revenge and awakeness. This paper will analysize the root of Heathcliff's tragedy and draw a rather balanced conclusion from the aspect of morality. On one hand, he is a devil of his crazy,unreasonable revenge on others; on the other hand, he is a hero from the aspect of humanity because he insists in pursuing true love and never submits to the adversity. His life tragedy reveals the viciousness of the society and lashes the harm of spirit from the social sense of hierarchy.展开更多
In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both cla...In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself A quantum system considered here can be any quantum system： a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented： the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.展开更多
In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulat...In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulated perfectly with an ordinary quantum computer with n qubits and one auxiliary qudit. Using this model, we give the most general form of duality gates which is of the form ∑i=0^d-1piUi,and the pi ＇s are complex numbers with module less or equal to 1 and constrained by｜∑iPi｜≤1.展开更多
In this letter,we propose a duality computing mode,which resembles particle-wave duality property whena quantum system such as a quantum computer passes through a double-slit.In this mode,computing operations arenot n...In this letter,we propose a duality computing mode,which resembles particle-wave duality property whena quantum system such as a quantum computer passes through a double-slit.In this mode,computing operations arenot necessarily unitary.The duality mode provides a natural link between classical computing and quantum computing.In addition,the duality mode provides a new tool for quantum algorithm design.展开更多
In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames...In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.展开更多
文摘Orientifold projections are an important ingredient in the geometrical engineering of Quantum Field Theory.However,an orientifold can break down the superconformal symmetry and no new superconformal fixed points are admitted(scenario Ⅱ);nevertheless,in some cases,dubbed scenarios Ⅰ and Ⅲ orientifold,a new IR fixed point is achieved and,for scenario Ⅲ examples,some still not fully understood IR duality seems to emerge.Here we give an algebro-geometrical point of view of orientifold for toric varieties and we propose the existence of relevant operators that deform the starting oriented Conformal Field Theory triggering a flow.We briefly discuss a possible holographic description of this flow.
文摘Rough set theory is a technique of granular computing. In this paper, we study a type of generalized rough sets based on covering. There are several literatures[1,40-43] exploring covering-based rough sets. Our focus of this paper is on the dualities in rough operations.
基金supported by National Natural Science Foundation of China(Grant Nos.12125109,11971484 and 12001541)Natural Science Foundation of Hunan(Grant No.2021JJ40714)Changsha Municipal Natural Science Foundation(Grant No.kq2014118)。
文摘We investigate dualities and inequalities related to noncommutative martingale Hardy-Orlicz spaces.More precisely,for a concave Orlicz functionΦ,we characterize the dual spaces of noncommutative martingale Hardy-Orlicz spaces HΦc(R)and hΦc(M),where R denotes a hyperfinite finite von Neumann algebra and M is a finite von Neumann algebra.The first duality is new even for classical martingales,which partially answers the problem raised by Conde-Alonso and Parcet(2016).We establish as well asymmetric martingale inequalities associated with Orlicz functions that are p-convex and q-concave for 0<p≤q<2.
基金supported by the National Science Centre grants,Grant/Award Number:SONATA-BIS 2020/38/E/NZ3/00090 and SONATA 2021/43/D/NZ3/01798。
文摘Sugars are one of the major metabolites and are essential for nucleic acid synthesis and energy production.In addition,sugars can act as signaling molecules.To study sugar signaling at the systemic level,there is an urgent need to systematically identify sugar-sensing proteins and nucleic acids.I propose the terms“swodkoreceptor”and“swodkocrine signaling,”derived from the Polish word“slodki”meaning“sweet,”to comprise all sugar-sensing proteins and signaling events,respectively,regardless of their cellular location and signaling domains.This proposal is intended to facilitate the inclusion of proteins such as the Escherichia coli Lac I repressor as an allolactose receptor,human glucokinase regulatory protein(GCKR)as a fructose receptor,and other sugar-binding based allosterically regulated enzymes and transcription factors as sugar-sensing receptors.In addition,enzyme-interacting proteins whose interaction state is regulated by sugar binding have also been proposed as sugar receptors.The systemic study of protein-and nucleic-acid-based swodkoreceptors may help to identify organelle-specific swodkoreceptors and to also address receptor duality.The study of intra-and inter-organism swodkocrine signaling and its crosstalk with gasocrine signaling may help to understand the etiology of diseases due to dysregulation in sugar homeostasis and signaling.
文摘Quantum gravity is an attempt to resolve incompatibilities between general relativity and quantum theory. Primordial field theory incorporates gravity and electrodynamics and has derived fermion mass gap, half integral spin, and fractional charges. This paper extends PFT to hadron physics with a “solenoidal flux”-based explanation of quark confinement differing significantly from Lattice QCD “color flux”-based construction. The theory is presented qualitatively and used to predict hadronic and nuclear properties. Electrodynamic-based analogies help yield numerical results far more intuitively than corresponding QCD results. The origins of QCD and PFT are discussed. A more quantitative description of hadron dynamics is in progress.
基金supported by the National Natural Science Foundation of China(Grant No.12005033)the Fundamental Research Funds for the Central Universities(Grant No.3132024192)。
文摘In this study,we investigated worldvolume fermions on the flavor brane in the D0-D4/D8 model,which is holographically equivalent to four-dimensional quantum chromodynamics with instantons or equivalently with a theta angle.The action involving the worldvolume fermions was obtained by the T-duality rules in string theory,and we accordingly derived their effective five-dimensional and canonical four-dimensional forms by using the systematic dimensional reduction and decomposition of the spinor.Subsequently,we used the AdS/CFT dictionary to evaluate the two-point correlation function as the spectral function for the worldvolume fermions and interpreted the fermions as baryons by analyzing their quantum number with the baryon vertex in holography.In this sense,the interacted action involving the worldvolume fermions and gauge field on the flavor brane was finally derived in holography,which describes the various interactions of mesons and baryons with instantons in the large-N limit.Therefore,this study provides a holographic picture to describe baryons and their interactions based on string theory,particularly in the presence of instantons or a theta angle.
基金supported by the National Natural Science Foundation of China(Grant No.12274045)support from the National Natural Science Foundation of China(Grant Nos.12274046,11874094,12147102,and 12347101)+2 种基金the Natural Science Foundation of Chongqing(Grant No.CSTB2022NSCQ-JQX0018)the Fundamental Research Funds for the Central Universities(Grant No.2021CDJZYJH-003)the Xiaomi Foundation/Xiaomi Young Talents Program。
文摘Wave-particle duality is one of the key features of quantum physics,characterized by the interference pattern.Meanwhile,Floquet spectroscopy is typically studied in the high-frequency region because the Floquet sidebands are very sharp,behaving like“particles”in frequency space,and no interference phenomena are observed.Here,we consider the larger quantum fluctuation region where the Floquet sidebands are broader,making interference between them possible.With the help of an optical lattice clock experimental platform and numerical simulations,such interference of Floquet modes in frequency space is clearly observed.Additionally,it exhibits many exotic phenomena,such as large Floquet sidebands between integer ones,sensitivity to the initial phase,and corresponding emergent symmetries.To analytically elucidate this,we propose the Floquet channel interference hypothesis,which surprisingly matches quantitatively well with both experimental and numerical results.Our research paves the way for developing a new type of interferometer that could be applicable to other Floquet systems.
基金supported by the National Natural Science Foundation of China(Grant No.11965013)supported by Yunnan High-level Talent Training Support Plan Young&Elite Talents Project(Grant No.YNWR-QNBJ-2018-181)。
文摘In this work,the phase structure of a holographic s+d model with quartic potential terms from 4D Einstein–Gauss–Bonnet gravity is studied in the probe limit.We first show the qd-μphase diagram with a very small value of the Gauss–Bonnet coefficientα=1×10-7and in the absence of the quartic terms to locate the suitable choice of the value of qd,where the system admits coexistent s+d solutions.Then we consider the various values of the Gauss–Bonnet coefficientαand present theα-μphase diagram to show the influence of the Gauss–Bonnet term on the phase structure.We also give an example of the re-entrant phase transition which is also realized in the holographic s+s and s+p models.After that we confirm the universality of the influence of the quartic term with coefficientλdon the d-wave solutions,which is similar to the case of s-wave and p-wave solutions previously studied in the s+p model.Finally we give the dependence of the special values of the quartic term coefficientλdon the Gauss–Bonnet coefficientα,below which the d-wave condensate grows to an opposite direction at the(quasi-)critical point,which is useful in realizing first order phase transitions in further studies of the holographic d-wave superfluids.
基金supported by the National Natural Science Foundation of China(NSFC)under Grants Nos.12275038 and 12375054。
文摘In this work,we investigate the shear elasticity and the shear viscosity in a simple holographic axion model with broken translational symmetry and rotational symmetry in space via the perturbation computation.We find that,in the case of spontaneous symmetry breaking,the broken translations and anisotropy both enhance the shear elasticity of the system.While in all cases,the broken symmetries introduce a double suppression of the shear viscosity,which is in contrast to the result from the study of the p-wave holographic superfluid where the shear viscosity is enhanced when the rotational symmetry is broken spontaneously.
文摘Complex Field Theory (CFT) proposes that dark matter (DM) and dark energy (DE) are pervasive, complex fields of charged complex masses of equally positive and negative complex charges, respectively. It proposes that each material object, including living creatures, is concomitant with a fraction of the charged complex masses of DM and DE in proportion to its mass. This perception provides new insights into the physics of nature and its constituents from subatomic to cosmic scales. This complex nature of DM and DE explains our inability to see DM or harvest DE for the last several decades. The positive complex DM is responsible for preserving the integrity of galaxies and all material systems. The negative complex charged DE induces a positive repelling force with the positively charged DM and contributes to the universe’s expansion. Both fields are Lorentz invariants in all directions and entangle the whole universe. The paper uses CFT to investigate zero-point energy, particle-wave duality, relativistic mass increase, and entanglement phenomenon and unifies Coulomb’s and Newton’s laws. The paper also verifies the existence of tachyons and explains the spooky action of quantum mechanics at a distance. The paper encourages further research into how CFT might resolve several physical mysteries in physics.
基金Supported by the National Natural Science Foundation of China(Grant No.12061061)the Science and Technology Project of Gansu Province(Grant No.22JR5RA153).
文摘Let n≥1 be an integer.In this article,we study the notions of Cartan-Eilenberg FP_(n)injective and Cartan-Eilenberg FP_(n)-flat complexes.We also investigate duality pairs relative to the Cartan-Eilenberg FP_(n)-injective and Cartan-Eilenberg FP_(n)-flat complexes.As applications,we obtain that any complex admits Cartan-Eilenberg FP_(n)-injective(resp.,Cartan-Eilenberg FP_(n)-flat)cover and preenvelope and we characterize left n-coherent rings using these two classes of complexes.
基金The National Natural Science Foundation of China(No.10871042)the Natural Science Foundation of Jiangsu Province(No.BK2009258)
文摘The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC（C,H）and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,（C×lH H）×lH H≌Cv（H×lH H）,is obtained.
文摘Father of modern linguistics, Ferdinand de Saussure has long been known to make outstanding contributions in the modern linguistics. This article focuses on his some basic theories in modern linguistics from three aspects: the object of linguistics, levels of linguistics and his explanations about dualities.
基金Supported by Beijing Municipal Natural Science Foundation under Grant No.Z2006015201001
文摘We reexamine the charged AdS domain wall solution to the Einstein-Abelian-Higgs model proposed by Gubser et al. as holographic superconductors at quantum critical points and comment on their statement about the uniqueness of gravity solutions. We generalize their explorations from （3 ＋ 1）-dimensions to arbitrary n -b 1Ds and find that the n ＋1≥5D charged AdS domain walls are unstable against electric perturbations.
文摘Wuthering heights, it lines with Heathcliff's love, hatred, revenge and awakeness. This paper will analysize the root of Heathcliff's tragedy and draw a rather balanced conclusion from the aspect of morality. On one hand, he is a devil of his crazy,unreasonable revenge on others; on the other hand, he is a hero from the aspect of humanity because he insists in pursuing true love and never submits to the adversity. His life tragedy reveals the viciousness of the society and lashes the harm of spirit from the social sense of hierarchy.
基金The project supported by the National Fundamental Research Program under Grant No. 001CB309308, National Natural Science Foundation of China under Grant Nos. 10325521 and 60433050, and the SRFDP Program of the Ministry of Education of China
文摘In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself A quantum system considered here can be any quantum system： a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented： the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.
基金supported by the National Fundamental Research Program Grant Nos.2006CB921106, 2009CB929042National Natural Science Foundation of China under Grant Nos. 10874098, 10775076, and 60433050
文摘In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulated perfectly with an ordinary quantum computer with n qubits and one auxiliary qudit. Using this model, we give the most general form of duality gates which is of the form ∑i=0^d-1piUi,and the pi ＇s are complex numbers with module less or equal to 1 and constrained by｜∑iPi｜≤1.
基金the National Fundamental Research Program under Grant No.2006CB921106National Natural Science Foundation of China under Grant Nos.10325521 and 60433050
文摘In this letter,we propose a duality computing mode,which resembles particle-wave duality property whena quantum system such as a quantum computer passes through a double-slit.In this mode,computing operations arenot necessarily unitary.The duality mode provides a natural link between classical computing and quantum computing.In addition,the duality mode provides a new tool for quantum algorithm design.
文摘In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.
