This paper introduces a framework of in-out duality, merging insights from quantum mechanics with social sciences to illuminate the complex interplay between internal potentialities and external manifestations. It art...This paper introduces a framework of in-out duality, merging insights from quantum mechanics with social sciences to illuminate the complex interplay between internal potentialities and external manifestations. It articulates foundational, mathematical axioms (Entanglement, Homogeneity, Emergence, and Measurement) that underpin the dynamics of systems, emphasizing the interconnectedness and emergent behaviors resulting from internal and external interactions. By exploring quantum concepts like coherence, entanglement, and superposition, the paper proposes an interdisciplinary approach termed Quantum Social Mechanics. This approach challenges classical paradigms, advocating for a reevaluation of conventional notions through the lens of quantum principles. The paper argues that understanding the universe’s complexities requires a synthesis of motion states and potential states, suggesting a paradigm shift towards integrating quantum mechanics into the philosophical foundation of social theory. Through this comprehensive framework, the paper aims to foster a deeper understanding of the universe’s interconnected nature and the dynamic processes that govern the emergence of complex systems and behaviors.展开更多
Quantum Fisher information(QFI) plays an important role in quantum metrology,placing the ultimate limit to how precise we can estimate some unknown parameter and thus quantifying how much information we can extract.We...Quantum Fisher information(QFI) plays an important role in quantum metrology,placing the ultimate limit to how precise we can estimate some unknown parameter and thus quantifying how much information we can extract.We observe that both the wave and particle properties within a Mach–Zehnder interferometer can naturally be quantified by QFI.Firstly,the particle property can be quantified by how well one can estimate the a priori probability of the path taken by the particle within the interferometer.Secondly,as the interference pattern is always related to some phase difference,the wave property can be quantified by how well one can estimate the phase parameter of the original state.With QFI as the unified figure of merit for both properties,we propose a more general and stronger wave-particle duality relation than the original one derived by Englert.展开更多
The question of what magnetism is vital to quantum physics. We know what all other quantum phenomenon is, but we did not know what magnetism is. It is not enough to say it is a force because of a charge. That force mu...The question of what magnetism is vital to quantum physics. We know what all other quantum phenomenon is, but we did not know what magnetism is. It is not enough to say it is a force because of a charge. That force must be something, for consistencies sake it had to be tested. This paper was written in order to confirm the results that were received in the experiments that took place that led to the paper “Magnetism: Insights from the Thomas Young Experiment” where it was concluded the magnetic phenomenon is both a particle and a wave. Will different interference patterns confirm a khumalon and wave like behaviour? The khumalon is the name of the particle associated with magnetic phenomenon. This paper concludes by confirming what was discovered in mentioned paper. Magnetism organizes into a wave no matter the interference. Understanding this reality, it allows us to understand what is happening with simple magnetic interactions. When like poles meet because they can not occupy the same space they push each other. Opposite poles are antiparticles to each other and annihilate each other. South pole scientifically speaking is not attracted to the north pole, the reason why the magnets slam each other is because they are closing a magnetic vacuum caused by the particles annihilating each other. We can now start theorizing on why a lodestone attracts iron because we now know we are dealing with a particle.展开更多
The question of what magnetism is vital to quantum physics. We know what all other quantum phenomenon is, but we did not know what magnetism is. It is not enough to say it is a force because of a charge. That force mu...The question of what magnetism is vital to quantum physics. We know what all other quantum phenomenon is, but we did not know what magnetism is. It is not enough to say it is a force because of a charge. That force must be something, for consistencies sake it had to be tested. This paper was written in order to confirm the results that were received in the experiments that took place that led to the paper “Magnetism: Insights from the Thomas Young Experiment” where it was concluded the magnetic phenomenon is both a particle and a wave. Will different interference patterns confirm a khumalon and wave like behaviour? The khumalon is the name of the particle associated with magnetic phenomenon. This paper concludes by confirming what was discovered in mentioned paper. Magnetism organizes into a wave no matter the interference. Understanding this reality, it allows us to understand what is happening with simple magnetic interactions. When like poles meet because they can not occupy the same space they push each other. Opposite poles are antiparticles to each other and annihilate each other. South pole scientifically speaking is not attracted to the north pole, the reason why the magnets slam each other is because they are closing a magnetic vacuum caused by the particles annihilating each other. We can now start theorizing on why a lodestone attracts iron because we now know we are dealing with a particle.展开更多
On the question of wave-particle duality, from the historic Bohr-Einstein debates a century ago, to this day, the view expressed in Niels Bohr’s Complementarity Principle has become well established, confirmed by num...On the question of wave-particle duality, from the historic Bohr-Einstein debates a century ago, to this day, the view expressed in Niels Bohr’s Complementarity Principle has become well established, confirmed by numerous experiments: If the observation is for wave nature, then the particle changes to wave, and if the observation is for particle nature, then the particle remains particle. However, recently this view has been challenged. With proof based on the definition of wave function, it has been shown that particle always remains particle and its wave function always remains wave, no mysterious change from particle to wave and vice versa.展开更多
A widely held view in time series analysis is the concept of duality that a finite order stationary autoregressive process of order p (AR(p)) is equivalent to an infinite order moving average (MA) process and a finite...A widely held view in time series analysis is the concept of duality that a finite order stationary autoregressive process of order p (AR(p)) is equivalent to an infinite order moving average (MA) process and a finite order invertible moving average of order q (MA(q)) is equivalent to an infinite order autoregressive (AR) process. The purpose of this paper is to demonstrate that the concept is not universally true. Thus, a finite order stationary autoregressive process of order p (AR(p)) can be written as an finite order moving average process and a finite order moving average process of order q (MA(q)) can be written as a finite order stationary autoregressive process. The regions of breakdown of concept of duality were determined for p = q = 1,2 using method of moments. The method involves equating non-zero autocovariances of the stationary AR(p) to the equivalent non-zero autocovariances of the invertible MA(p) to determine the region of non-duality. In such region of breakdown in duality, 1) both the Autocorrelation function and the Partial Autocorrelation function of the AR process and MA process cuts off after equal lags 2) a finite AR model can be adequately represented by a finite MA model of equal order and conversely with the same error variance and 3) negative values of the parameters of the AR process are equal in magnitude but opposite in direction to the parameters of the equivalent MA process and conversely. Empirical examples (simulation and real life examples) were used to illustrate these. Therefore, it has been recommended that caution should be exercised in using the concept of duality in time series analysis until future research proves otherwise.展开更多
The antisense transcript long non-coding RNA(lnc RNA)(antisense non-coding RNA in the INK4 locus, ANRIL) is an antisense of the cyclin-dependent kinase inhibitor 2 B(CDKN2B) gene on chromosome 9 p21 that contains an o...The antisense transcript long non-coding RNA(lnc RNA)(antisense non-coding RNA in the INK4 locus, ANRIL) is an antisense of the cyclin-dependent kinase inhibitor 2 B(CDKN2B) gene on chromosome 9 p21 that contains an overlapping 299-bp region and shares a bidirectional promoter with alternate open reading frame(ARF). In the context of gene regulation, ANRIL is responsible for directly recruiting polycomb group(Pc G) proteins, including polycomb repressive complex-1(PRC-1) and polycomb repressive complex-2(PRC-2), to modify the epigenetic chromatin state and subsequently inhibit gene expression in cis-regulation. On the other hand, previous reports have indicated that ANRIL is capable of binding to a specific site or sequence, including the Alu element, E2 F transcription factor 1(E2F1), and CCCTC-binding factor(CTCF), to achieve trans-regulation functions. In addition to its function in cell proliferation, adhesion and apoptosis, ANRIL is very closely associated with atherosclerosis-related diseases. The different transcripts and the SNPs that are related to atherosclerotic vascular diseases(ASVD-SNPs) are inextricably linked to the development and progression of atherosclerosis. Linear transcripts have been shown to be a risk factor for atherosclerosis, whereas circular transcripts are protective against atherosclerosis. Furthermore, ANRIL also acts as a component of the inflammatory pathway involved in the regulation of inflammation, which is considered to be one of the causes of atherosclerosis. Collectively, ANRIL plays an important role in the formation of atherosclerosis, and the artificial modification of ANRIL transcripts should be considered following the development of this disease.展开更多
A new concept of(Φ,ρ,α)-V-invexity for differentiable vector-valued functions is introduced,which is a generalization of differentiable scalar-valued(Φ,ρ)-invexity.Based upon the(Φ,ρ,α)-V-invex functions,suffi...A new concept of(Φ,ρ,α)-V-invexity for differentiable vector-valued functions is introduced,which is a generalization of differentiable scalar-valued(Φ,ρ)-invexity.Based upon the(Φ,ρ,α)-V-invex functions,sufficient optimality conditions and MondWeir type dual theorems are derived for a class of nondifferentiable multiobjective fractional programming problems in which every component of the objective function and each constraint function contain a term involving the support function of a compact convex set.展开更多
Advances on bidirectional intelligence are overviewed along three threads,with extensions and new perspectives.The first thread is about bidirectional learning architecture,exploring five dualities that enable Lmser s...Advances on bidirectional intelligence are overviewed along three threads,with extensions and new perspectives.The first thread is about bidirectional learning architecture,exploring five dualities that enable Lmser six cognitive functions and provide new perspectives on which a lot of extensions and particularlly flexible Lmser are proposed.Interestingly,either or two of these dualities actually takes an important role in recent models such as U-net,ResNet,and Dense Net.The second thread is about bidirectional learning principles unified by best yIng-yAng(IA)harmony in BYY system.After getting insights on deep bidirectional learning from a bird-viewing on existing typical learning principles from one or both of the inward and outward directions,maximum likelihood,variational principle,and several other learning principles are summarised as exemplars of the BYY learning,with new perspectives on advanced topics.The third thread further proceeds to deep bidirectional intelligence,driven by long term dynamics(LTD)for parameter learning and short term dynamics(STD)for image thinking and rational thinking in harmony.Image thinking deals with information flow of continuously valued arrays and especially image sequence,as if thinking was displayed in the real world,exemplified by the flow from inward encoding/cognition to outward reconstruction/transformation performed in Lmser learning and BYY learning.In contrast,rational thinking handles symbolic strings or discretely valued vectors,performing uncertainty reasoning and problem solving.In particular,a general thesis is proposed for bidirectional intelligence,featured by BYY intelligence potential theory(BYY-IPT)and nine essential dualities in architecture,fundamentals,and implementation,respectively.Then,problems of combinatorial solving and uncertainty reasoning are investigated from this BYY IPT perspective.First,variants and extensions are suggested for AlphaGoZero like searching tasks,such as traveling salesman problem(TSP)and attributed graph matching(AGM)that are turned into Go like problems with help of a feature enrichment technique.Second,reasoning activities are summarized under guidance of BYY IPT from the aspects of constraint satisfaction,uncertainty propagation,and path or tree searching.Particularly,causal potential theory is proposed for discovering causal direction,with two roads developed for its implementation.展开更多
We theoretically investigate the wave–particle duality based on a Raman atom interferometer, via the interaction between the atom and Raman laser, which is similar to the optical Mach–Zehnder interferometer. The wav...We theoretically investigate the wave–particle duality based on a Raman atom interferometer, via the interaction between the atom and Raman laser, which is similar to the optical Mach–Zehnder interferometer. The wave and which-way information are stored in the atomic internal states. For the φ- π- π /2 type of atom interferometer, we find that the visibility(V) and predictability(P) still satisfy the duality relation, P2+ V2≤ 1.展开更多
The quantum object is in general considered as displaying both wave and particle nature. By particle is understood an item localized in a very small volume of the space, and which cannot be simultaneously in two disjo...The quantum object is in general considered as displaying both wave and particle nature. By particle is understood an item localized in a very small volume of the space, and which cannot be simultaneously in two disjoint regions of the space. By wave, to the contrary, is understood a distributed item, occupying in some cases two or more disjoint regions of the space. The quantum formalism did not explain until today the so-called “collapse” of the wave-function, i.e. the shrinking of the wave-function to one small region of the space, when a macroscopic object is encountered. This seems to happen in “which-way” experiments. A very appealing explanation for this behavior is the idea of a particle, localized in some limited part of the wave-function. The present article challenges the concept of particle. It proves in the base of a variant of the Tan, Walls and Collett experiment, that this concept leads to a situation in which the particle has to be simultaneously in two places distant from one another—situation that contradicts the very definition of a particle. Another argument is based on a modified version of the Afshar experiment, showing that the concept of particle is problematic. The concept of particle makes additional difficulties when the wave-function passes through fields. An unexpected possibility to solve these difficulties seems to arise from the cavity quantum electrodynamics studies done recently by S. Savasta and his collaborators. It involves virtual particles. One of these studies is briefly described here. Though, experimental results are needed, so that it is too soon to conclude whether it speaks in favor, or against the concept of particle.展开更多
A class of functions called quasi B s invex and pseudo B s invex functions are introduced by using the concept of symmetric gradient. The examples of quasi B s invex and pseudo B s invex functions are given. The suffi...A class of functions called quasi B s invex and pseudo B s invex functions are introduced by using the concept of symmetric gradient. The examples of quasi B s invex and pseudo B s invex functions are given. The sufficient optimality conditions and Mond Weir type duality results are obtained for a nondifferentiable nonlinear semi infinite programming problem involving quasi B s invex and pseudo B s invex functions.展开更多
Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function.The dualities for the scalar convex compos...Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function.The dualities for the scalar convex composed optimization problems and for general vector optimization problems are studied.A general approach for studying duality in vector optimization problems is presented.展开更多
The double-slit experiment demonstrates the quantum physics particle-wave duality problem. Over the last decades many interpretations were introduced to the quantum theory perception problem. In most cases there was u...The double-slit experiment demonstrates the quantum physics particle-wave duality problem. Over the last decades many interpretations were introduced to the quantum theory perception problem. In most cases there was use of unclear terms, or obscure processes in these interpretations, such as particle splitting. In this paper we propose a novel concept to explain the experiment based on two postulates: The Equivalence of Form (EoF), and the particles connection to other particles, effectively functioning as a group. These two condi-tions are necessary to maintain wave qualities in the collective relations, and therefore cannot exist in a sin-gle particle. De Broglie introduced the mathematical relation of particle to wave;however, he did not specify the conditions for that. The proposed interpretation is a new way of looking at particles as a united group, the Kevutsa, which has a higher order level of matter. A series of identical particles maintain additional qualities to show a large united, correlated motion that we observe as waves transport through systems.展开更多
A Mond-Weir type second-order dual continuous programming problem associated with a class of nondifferentiable continuous programming problems is formulated. Under second-order pseudo-invexity and second-order quasi-i...A Mond-Weir type second-order dual continuous programming problem associated with a class of nondifferentiable continuous programming problems is formulated. Under second-order pseudo-invexity and second-order quasi-invexity various duality theorems are established for this pair of dual continuous programming problems. A pair of dual continuous programming problems with natural boundary values is constructed and the proofs of its various duality results are briefly outlined. Further, it is shown that our results can be regarded as dynamic generalizations of corresponding (static) second-order duality theorems for a class of nondifferentiable nonlinear programming problems already studied in the literature.展开更多
Existing explanations for several major phenomena in physics may need to be reconsidered in light of the description of a natural force termed KELEA (kinetic energy limiting electrostatic attraction). Three examples a...Existing explanations for several major phenomena in physics may need to be reconsidered in light of the description of a natural force termed KELEA (kinetic energy limiting electrostatic attraction). Three examples are selected for discussion in this paper: i) The proposed wave-particle duality of electrons;ii) cold fusion;and iii) superconductivity. The current interpretations of these enigmatic concepts are incomplete and not fully validated by scientific methods. The observations underlying these processes are seemingly consistent with KELEA acting as a repelling force between opposite electrical charges. Relatively simple experiments can be designed to either confirm or exclude KELEA in these and in various other currently perplexing physical phenomena.展开更多
In this paper, two duality results are established under generalized ρ-convexity conditions for a class of multiobjective fractional programmign involvign differentiable n-sten functions.
This paper deals with some problems of multiobjective posynomial geometric programming. AKuhn-Tucker type optimality sufficient condition of this programming is derived. Moreover,a dual problemassociated with multiobj...This paper deals with some problems of multiobjective posynomial geometric programming. AKuhn-Tucker type optimality sufficient condition of this programming is derived. Moreover,a dual problemassociated with multiobjective posynomial geometric programming is given, and weak duality,direct dualityand inverse duality theorems are proved.展开更多
Quantum criticality is closely related to the existence of two phases with unrelated symmetry breaking. In this paper,we study Néel and Kekulé valence bond state(VBS) quantum criticality in Dirac semimetals ...Quantum criticality is closely related to the existence of two phases with unrelated symmetry breaking. In this paper,we study Néel and Kekulé valence bond state(VBS) quantum criticality in Dirac semimetals with four-fermion interactions.Our results show that all possible dynamical masses yield the same critical coupling, which exhibits the phenomenon that all possible phases meet at a multicritical point(e.g., a tricritical point for the Néel, Kekulé-VBS and semimetallic phases).In terms of the well-established Wess–Zumino–Witten field theory, we investigate the typical criticality for the transition between Néel and Kekulé-VBS phases, and the compatible Néel–Kekulé-VBS mass matrices imply the existence of a nonLandau transition between the Néel and Kekulé-VBS phases. We show the existence of mutual duality in the defect-driven Néel–Kekulé-VBS transition near the non-Landau critical point and find that this mutual duality results from the presence of a mutual Chern–Simons term. We also study the mutual duality based on dual topological excitations.展开更多
The aim of this paper is to prove duality and reflexivity of generalized Lipschitz spaces ∧_(α,p,q)~k(R),α∈R and 1 ≤ p,q ≤∞,in the context of Dunkl harmonic analysis.
文摘This paper introduces a framework of in-out duality, merging insights from quantum mechanics with social sciences to illuminate the complex interplay between internal potentialities and external manifestations. It articulates foundational, mathematical axioms (Entanglement, Homogeneity, Emergence, and Measurement) that underpin the dynamics of systems, emphasizing the interconnectedness and emergent behaviors resulting from internal and external interactions. By exploring quantum concepts like coherence, entanglement, and superposition, the paper proposes an interdisciplinary approach termed Quantum Social Mechanics. This approach challenges classical paradigms, advocating for a reevaluation of conventional notions through the lens of quantum principles. The paper argues that understanding the universe’s complexities requires a synthesis of motion states and potential states, suggesting a paradigm shift towards integrating quantum mechanics into the philosophical foundation of social theory. Through this comprehensive framework, the paper aims to foster a deeper understanding of the universe’s interconnected nature and the dynamic processes that govern the emergence of complex systems and behaviors.
文摘Quantum Fisher information(QFI) plays an important role in quantum metrology,placing the ultimate limit to how precise we can estimate some unknown parameter and thus quantifying how much information we can extract.We observe that both the wave and particle properties within a Mach–Zehnder interferometer can naturally be quantified by QFI.Firstly,the particle property can be quantified by how well one can estimate the a priori probability of the path taken by the particle within the interferometer.Secondly,as the interference pattern is always related to some phase difference,the wave property can be quantified by how well one can estimate the phase parameter of the original state.With QFI as the unified figure of merit for both properties,we propose a more general and stronger wave-particle duality relation than the original one derived by Englert.
文摘The question of what magnetism is vital to quantum physics. We know what all other quantum phenomenon is, but we did not know what magnetism is. It is not enough to say it is a force because of a charge. That force must be something, for consistencies sake it had to be tested. This paper was written in order to confirm the results that were received in the experiments that took place that led to the paper “Magnetism: Insights from the Thomas Young Experiment” where it was concluded the magnetic phenomenon is both a particle and a wave. Will different interference patterns confirm a khumalon and wave like behaviour? The khumalon is the name of the particle associated with magnetic phenomenon. This paper concludes by confirming what was discovered in mentioned paper. Magnetism organizes into a wave no matter the interference. Understanding this reality, it allows us to understand what is happening with simple magnetic interactions. When like poles meet because they can not occupy the same space they push each other. Opposite poles are antiparticles to each other and annihilate each other. South pole scientifically speaking is not attracted to the north pole, the reason why the magnets slam each other is because they are closing a magnetic vacuum caused by the particles annihilating each other. We can now start theorizing on why a lodestone attracts iron because we now know we are dealing with a particle.
文摘The question of what magnetism is vital to quantum physics. We know what all other quantum phenomenon is, but we did not know what magnetism is. It is not enough to say it is a force because of a charge. That force must be something, for consistencies sake it had to be tested. This paper was written in order to confirm the results that were received in the experiments that took place that led to the paper “Magnetism: Insights from the Thomas Young Experiment” where it was concluded the magnetic phenomenon is both a particle and a wave. Will different interference patterns confirm a khumalon and wave like behaviour? The khumalon is the name of the particle associated with magnetic phenomenon. This paper concludes by confirming what was discovered in mentioned paper. Magnetism organizes into a wave no matter the interference. Understanding this reality, it allows us to understand what is happening with simple magnetic interactions. When like poles meet because they can not occupy the same space they push each other. Opposite poles are antiparticles to each other and annihilate each other. South pole scientifically speaking is not attracted to the north pole, the reason why the magnets slam each other is because they are closing a magnetic vacuum caused by the particles annihilating each other. We can now start theorizing on why a lodestone attracts iron because we now know we are dealing with a particle.
文摘On the question of wave-particle duality, from the historic Bohr-Einstein debates a century ago, to this day, the view expressed in Niels Bohr’s Complementarity Principle has become well established, confirmed by numerous experiments: If the observation is for wave nature, then the particle changes to wave, and if the observation is for particle nature, then the particle remains particle. However, recently this view has been challenged. With proof based on the definition of wave function, it has been shown that particle always remains particle and its wave function always remains wave, no mysterious change from particle to wave and vice versa.
文摘A widely held view in time series analysis is the concept of duality that a finite order stationary autoregressive process of order p (AR(p)) is equivalent to an infinite order moving average (MA) process and a finite order invertible moving average of order q (MA(q)) is equivalent to an infinite order autoregressive (AR) process. The purpose of this paper is to demonstrate that the concept is not universally true. Thus, a finite order stationary autoregressive process of order p (AR(p)) can be written as an finite order moving average process and a finite order moving average process of order q (MA(q)) can be written as a finite order stationary autoregressive process. The regions of breakdown of concept of duality were determined for p = q = 1,2 using method of moments. The method involves equating non-zero autocovariances of the stationary AR(p) to the equivalent non-zero autocovariances of the invertible MA(p) to determine the region of non-duality. In such region of breakdown in duality, 1) both the Autocorrelation function and the Partial Autocorrelation function of the AR process and MA process cuts off after equal lags 2) a finite AR model can be adequately represented by a finite MA model of equal order and conversely with the same error variance and 3) negative values of the parameters of the AR process are equal in magnitude but opposite in direction to the parameters of the equivalent MA process and conversely. Empirical examples (simulation and real life examples) were used to illustrate these. Therefore, it has been recommended that caution should be exercised in using the concept of duality in time series analysis until future research proves otherwise.
基金supported by grants from the Shenzhen Science and Technology Project(No.201401027)
文摘The antisense transcript long non-coding RNA(lnc RNA)(antisense non-coding RNA in the INK4 locus, ANRIL) is an antisense of the cyclin-dependent kinase inhibitor 2 B(CDKN2B) gene on chromosome 9 p21 that contains an overlapping 299-bp region and shares a bidirectional promoter with alternate open reading frame(ARF). In the context of gene regulation, ANRIL is responsible for directly recruiting polycomb group(Pc G) proteins, including polycomb repressive complex-1(PRC-1) and polycomb repressive complex-2(PRC-2), to modify the epigenetic chromatin state and subsequently inhibit gene expression in cis-regulation. On the other hand, previous reports have indicated that ANRIL is capable of binding to a specific site or sequence, including the Alu element, E2 F transcription factor 1(E2F1), and CCCTC-binding factor(CTCF), to achieve trans-regulation functions. In addition to its function in cell proliferation, adhesion and apoptosis, ANRIL is very closely associated with atherosclerosis-related diseases. The different transcripts and the SNPs that are related to atherosclerotic vascular diseases(ASVD-SNPs) are inextricably linked to the development and progression of atherosclerosis. Linear transcripts have been shown to be a risk factor for atherosclerosis, whereas circular transcripts are protective against atherosclerosis. Furthermore, ANRIL also acts as a component of the inflammatory pathway involved in the regulation of inflammation, which is considered to be one of the causes of atherosclerosis. Collectively, ANRIL plays an important role in the formation of atherosclerosis, and the artificial modification of ANRIL transcripts should be considered following the development of this disease.
基金National Natural Science Foundation of China(No.11071110)
文摘A new concept of(Φ,ρ,α)-V-invexity for differentiable vector-valued functions is introduced,which is a generalization of differentiable scalar-valued(Φ,ρ)-invexity.Based upon the(Φ,ρ,α)-V-invex functions,sufficient optimality conditions and MondWeir type dual theorems are derived for a class of nondifferentiable multiobjective fractional programming problems in which every component of the objective function and each constraint function contain a term involving the support function of a compact convex set.
基金supported by the Zhi-Yuan Chair Professorship Start-up Grant (WF220103010) from Shanghai Jiao Tong University
文摘Advances on bidirectional intelligence are overviewed along three threads,with extensions and new perspectives.The first thread is about bidirectional learning architecture,exploring five dualities that enable Lmser six cognitive functions and provide new perspectives on which a lot of extensions and particularlly flexible Lmser are proposed.Interestingly,either or two of these dualities actually takes an important role in recent models such as U-net,ResNet,and Dense Net.The second thread is about bidirectional learning principles unified by best yIng-yAng(IA)harmony in BYY system.After getting insights on deep bidirectional learning from a bird-viewing on existing typical learning principles from one or both of the inward and outward directions,maximum likelihood,variational principle,and several other learning principles are summarised as exemplars of the BYY learning,with new perspectives on advanced topics.The third thread further proceeds to deep bidirectional intelligence,driven by long term dynamics(LTD)for parameter learning and short term dynamics(STD)for image thinking and rational thinking in harmony.Image thinking deals with information flow of continuously valued arrays and especially image sequence,as if thinking was displayed in the real world,exemplified by the flow from inward encoding/cognition to outward reconstruction/transformation performed in Lmser learning and BYY learning.In contrast,rational thinking handles symbolic strings or discretely valued vectors,performing uncertainty reasoning and problem solving.In particular,a general thesis is proposed for bidirectional intelligence,featured by BYY intelligence potential theory(BYY-IPT)and nine essential dualities in architecture,fundamentals,and implementation,respectively.Then,problems of combinatorial solving and uncertainty reasoning are investigated from this BYY IPT perspective.First,variants and extensions are suggested for AlphaGoZero like searching tasks,such as traveling salesman problem(TSP)and attributed graph matching(AGM)that are turned into Go like problems with help of a feature enrichment technique.Second,reasoning activities are summarized under guidance of BYY IPT from the aspects of constraint satisfaction,uncertainty propagation,and path or tree searching.Particularly,causal potential theory is proposed for discovering causal direction,with two roads developed for its implementation.
基金supported by the National Natural Science Foundation of China(Grant No.51275523)the Special Research Fund for the Doctoral Program of Higher Education,China(Grant No.20134307110009)
文摘We theoretically investigate the wave–particle duality based on a Raman atom interferometer, via the interaction between the atom and Raman laser, which is similar to the optical Mach–Zehnder interferometer. The wave and which-way information are stored in the atomic internal states. For the φ- π- π /2 type of atom interferometer, we find that the visibility(V) and predictability(P) still satisfy the duality relation, P2+ V2≤ 1.
文摘The quantum object is in general considered as displaying both wave and particle nature. By particle is understood an item localized in a very small volume of the space, and which cannot be simultaneously in two disjoint regions of the space. By wave, to the contrary, is understood a distributed item, occupying in some cases two or more disjoint regions of the space. The quantum formalism did not explain until today the so-called “collapse” of the wave-function, i.e. the shrinking of the wave-function to one small region of the space, when a macroscopic object is encountered. This seems to happen in “which-way” experiments. A very appealing explanation for this behavior is the idea of a particle, localized in some limited part of the wave-function. The present article challenges the concept of particle. It proves in the base of a variant of the Tan, Walls and Collett experiment, that this concept leads to a situation in which the particle has to be simultaneously in two places distant from one another—situation that contradicts the very definition of a particle. Another argument is based on a modified version of the Afshar experiment, showing that the concept of particle is problematic. The concept of particle makes additional difficulties when the wave-function passes through fields. An unexpected possibility to solve these difficulties seems to arise from the cavity quantum electrodynamics studies done recently by S. Savasta and his collaborators. It involves virtual particles. One of these studies is briefly described here. Though, experimental results are needed, so that it is too soon to conclude whether it speaks in favor, or against the concept of particle.
基金the Natural Science Foundation of Shaanxi Province and the Science Foundation of Shaanxi Provincial Educational CommitteeP.R.China
文摘A class of functions called quasi B s invex and pseudo B s invex functions are introduced by using the concept of symmetric gradient. The examples of quasi B s invex and pseudo B s invex functions are given. The sufficient optimality conditions and Mond Weir type duality results are obtained for a nondifferentiable nonlinear semi infinite programming problem involving quasi B s invex and pseudo B s invex functions.
基金Supported by the Natural Science Foundation of Fujian Province（S0650021）
文摘Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function.The dualities for the scalar convex composed optimization problems and for general vector optimization problems are studied.A general approach for studying duality in vector optimization problems is presented.
文摘The double-slit experiment demonstrates the quantum physics particle-wave duality problem. Over the last decades many interpretations were introduced to the quantum theory perception problem. In most cases there was use of unclear terms, or obscure processes in these interpretations, such as particle splitting. In this paper we propose a novel concept to explain the experiment based on two postulates: The Equivalence of Form (EoF), and the particles connection to other particles, effectively functioning as a group. These two condi-tions are necessary to maintain wave qualities in the collective relations, and therefore cannot exist in a sin-gle particle. De Broglie introduced the mathematical relation of particle to wave;however, he did not specify the conditions for that. The proposed interpretation is a new way of looking at particles as a united group, the Kevutsa, which has a higher order level of matter. A series of identical particles maintain additional qualities to show a large united, correlated motion that we observe as waves transport through systems.
文摘A Mond-Weir type second-order dual continuous programming problem associated with a class of nondifferentiable continuous programming problems is formulated. Under second-order pseudo-invexity and second-order quasi-invexity various duality theorems are established for this pair of dual continuous programming problems. A pair of dual continuous programming problems with natural boundary values is constructed and the proofs of its various duality results are briefly outlined. Further, it is shown that our results can be regarded as dynamic generalizations of corresponding (static) second-order duality theorems for a class of nondifferentiable nonlinear programming problems already studied in the literature.
文摘Existing explanations for several major phenomena in physics may need to be reconsidered in light of the description of a natural force termed KELEA (kinetic energy limiting electrostatic attraction). Three examples are selected for discussion in this paper: i) The proposed wave-particle duality of electrons;ii) cold fusion;and iii) superconductivity. The current interpretations of these enigmatic concepts are incomplete and not fully validated by scientific methods. The observations underlying these processes are seemingly consistent with KELEA acting as a repelling force between opposite electrical charges. Relatively simple experiments can be designed to either confirm or exclude KELEA in these and in various other currently perplexing physical phenomena.
文摘In this paper, two duality results are established under generalized ρ-convexity conditions for a class of multiobjective fractional programmign involvign differentiable n-sten functions.
文摘This paper deals with some problems of multiobjective posynomial geometric programming. AKuhn-Tucker type optimality sufficient condition of this programming is derived. Moreover,a dual problemassociated with multiobjective posynomial geometric programming is given, and weak duality,direct dualityand inverse duality theorems are proved.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11647111,11504285,and 11674026)the Research Start-up Funds of Guizhou University,China(Grant No.201538)
文摘Quantum criticality is closely related to the existence of two phases with unrelated symmetry breaking. In this paper,we study Néel and Kekulé valence bond state(VBS) quantum criticality in Dirac semimetals with four-fermion interactions.Our results show that all possible dynamical masses yield the same critical coupling, which exhibits the phenomenon that all possible phases meet at a multicritical point(e.g., a tricritical point for the Néel, Kekulé-VBS and semimetallic phases).In terms of the well-established Wess–Zumino–Witten field theory, we investigate the typical criticality for the transition between Néel and Kekulé-VBS phases, and the compatible Néel–Kekulé-VBS mass matrices imply the existence of a nonLandau transition between the Néel and Kekulé-VBS phases. We show the existence of mutual duality in the defect-driven Néel–Kekulé-VBS transition near the non-Landau critical point and find that this mutual duality results from the presence of a mutual Chern–Simons term. We also study the mutual duality based on dual topological excitations.
文摘The aim of this paper is to prove duality and reflexivity of generalized Lipschitz spaces ∧_(α,p,q)~k(R),α∈R and 1 ≤ p,q ≤∞,in the context of Dunkl harmonic analysis.
