New construction of mutually unbiased bases for odd-dimensional state space

We study the construction of mutually unbiased bases in Hilbert space for composite dimensions d which are not prime powers.We explore the results for composite dimensions which are true for prime power dimensions.We then provide a method for selecting mutually unbiased vectors from the eigenvectors of generalized Pauli matrices to construct mutually unbiased bases.In particular,we present four mutually unbiased bases in C^(15).

Boundless Potential China-Africa cooperation in the space sector exemplifies mutually beneficial partnerships

Exports of Chinese satellites,joint construction of space infrastructure,and joint research and development of satellites...The recent years have seen substantial growth in China-Africa cooperation in the space sector,which is bringing tangible benefits to both sides.

Automatic Aggregation Enhanced Affinity Propagation Clustering Based on Mutually Exclusive Exemplar Processing

Affinity propagation(AP)is a widely used exemplar-based clustering approach with superior efficiency and clustering quality.Nevertheless,a common issue with AP clustering is the presence of excessive exemplars,which limits its ability to perform effective aggregation.This research aims to enable AP to automatically aggregate to produce fewer and more compact clusters,without changing the similarity matrix or customizing preference parameters,as done in existing enhanced approaches.An automatic aggregation enhanced affinity propagation(AAEAP)clustering algorithm is proposed,which combines a dependable partitioning clustering approach with AP to achieve this purpose.The partitioning clustering approach generates an additional set of findings with an equivalent number of clusters whenever the clustering stabilizes and the exemplars emerge.Based on these findings,mutually exclusive exemplar detection was conducted on the current AP exemplars,and a pair of unsuitable exemplars for coexistence is recommended.The recommendation is then mapped as a novel constraint,designated mutual exclusion and aggregation.To address this limitation,a modified AP clustering model is derived and the clustering is restarted,which can result in exemplar number reduction,exemplar selection adjustment,and other data point redistribution.The clustering is ultimately completed and a smaller number of clusters are obtained by repeatedly performing automatic detection and clustering until no mutually exclusive exemplars are detected.Some standard classification data sets are adopted for experiments on AAEAP and other clustering algorithms for comparison,and many internal and external clustering evaluation indexes are used to measure the clustering performance.The findings demonstrate that the AAEAP clustering algorithm demonstrates a substantial automatic aggregation impact while maintaining good clustering quality.

Canonical Transformations, Quantization, Mutually Unbiased and Other Complete Bases

Using ideas based on supersymmetric quantum mechanics, we design canonical transformations of the usual position and momentum to create generalized “Cartesian-like” positions, W, and momenta, Pw , with unit Poisson brackets. These are quantized by the usual replacement of the classical , x Px by quantum operators, leading to an infinite family of potential “operator observables”. However, all but one of the resulting operators are not Hermitian (formally self-adjoint) in the original position representation. Using either the chain rule or Dirac quantization, we show that the resulting operators are “quasi-Hermitian” relative to the x-representation and that all are Hermitian in the W-representation. Depending on how one treats the Jacobian of the canonical transformation in the expression for the classical momentum, Pw , quantization yields a) continuous mutually unbiased bases (MUB), b) orthogonal bases (with Dirac delta normalization), c) biorthogonal bases (with Dirac delta normalization), d) new W-harmonic oscillators yielding standard orthonormal bases (as functions of W) and associated coherent states and Wigner distributions. The MUB lead to W-generalized Fourier transform kernels whose eigenvectors are the W-harmonic oscillator eigenstates, with the spectrum (±1,±i) , as well as “W-linear chirps”. As expected, W,?Pw satisfy the uncertainty product relation: ΔWΔPw ≥1/2 , h=1.

Static and adaptive feedback control for synchronization of different chaotic oscillators with mutually Lipschitz nonlinearities

This paper addresses the control law design for synchronization of two different chaotic oscillators with mutually Lipschitz nonlinearities. For analysis of the properties of two different nonlinearities, an advanced mutually Lipschitz condition is proposed. This mutually Lipschitz condition is more general than the traditional Lipschitz condition. Unlike the latter, it can be used for the design of a feedback controller for synchronization of chaotic oscillators of different dynamics. It is shown that any two different Lipschitz nonlinearities always satisfy the mutually Lipschitz condition. Applying the mutually Lipschitz condition, a quadratic Lyapunov function and uniformly ultimately bounded stability, easily designable and implementable robust control strategies utilizing algebraic Riccati equation and linear matrix inequalities, are derived for synchronization of two distinct chaotic oscillators. Furthermore, a novel adaptive control scheme for mutually Lipschitz chaotic systems is established by addressing the issue of adaptive cancellation of unknown mismatch between the dynamics of different chaotic systems. The proposed control technique is numerically tested for synchronization of two different chaotic Chua＇s circuits and for obtaining identical behavior between the modified Chua＇s circuit and the R6ssler system.

Mutually Pumped Phase-Conjugate Mirror: Sickle Configuration

A mutually pumped phase conjugator is demonstrated with a novel photorefractive crystal of copper-doped potassium sodium strontium barium niobate,in which the beams travel in a geometric path similar to the outline of a sickle.The maximum reflectivity is up to 168%.Faster response times are measured and are also simulated as a function of incident beam power ratio.Four available input geometries are found.The phase conjugation signals exist wide range of angular and positional alignment.No apparent cross talk is observed.The faster build-up process of phase conjugation beams is tentatively explained.

Polarization switching and synchronization of mutually coupled vertical-cavity surface-emitting semiconductor lasers

Polarization switching （PS） dynamics and synchronization performances of two mutually coupled vertical-cavity surface-emitting lasers （VCSELs） are studied theoretically in this paper. A group of dimensionless rate equations is derived to describe our model. While analysing the PS characteristics, we focus on the effects of coupling rate and frequency detuning regarding different mutual injection types. The results indicate that the x-mode injection defers the occurrence of PS, while the y-mode injection leads the PS to occur at a lower current. Strong enough polarization-selective injection can suppress the PS. Moreover, if frequency detuning is considered, the effects of polarization-selective mutual injection will be weakened. To evaluate the synchronization performance, the correlation coefficients and output dynamics of VCSELs with both pure mode and mixed mode polarizations are given. It is found that performance of complete synchronization is sensitive to the frequency mismatch but it is little affected by mixed mode polarizations, which is opposite to the case of injection-locking synchronization.

A new mutually destabilized reactive hydride system:LiBH4–Mg2NiH4

In this work,the hydrogen sorption properties of the LiBH4-Mg2NiH4 composite system with the molar ratio 2:2.5 were thoroughly investigated as a function of the applied temperature and hydrogen pressure.To the best of our knowledge,it has been possible to prove experimentally the mutual destabilization between LiBH4 and Mg2NiH4.A detailed account of the kinetic and thermodynamic features of the dehydrogenation process is reported here.

Mutually Assured Interdependence and the Building of a New Type of China-US Relations

Ever since the establishment of diplomatic ties between China and the United States,putting an end to the long period of isolation between the two countries,the bilateral relations have progressed from early limited engagement to a comprehensive interdependence with an increasingly high degree of mutual interests.As one of the most important bilateral relationships in the world,the overall China-US relationship has remained stable,providing an important guarantee for the world’s peaceful development,prosperity and stability.However,in recent years,the benign interactions between the two countries have been disrupted,exhibiting a tendency of antagonism in some areas.

Adaptive Isochronal Synchronization in Mutually Coupled Chaotic Systems

This paper studies the problem of isochronal synchronization of chaotic systems with time-delayed mutual coupling. Based on the invariance principle of differential equations, an adaptive feedback scheme is proposed for the stability of isochronal synchronization between two identical chaotic systems. Unlike the usual linear feedback, the variable feedback strength is automatically adapted to isochronally synchronize two identical chaotic systems with delay-coupled, so this scheme is analytical, and simple to implement in practice. Simulation results show that the isochronal synchronization behavior is determined by time delay.

Security of quantum key distribution with virtual mutually unbiased bases

In a perfect quantum key distribution(QKD)protocol,quantum states should be prepared and measured with mutually unbiased bases(MUBs).However,in a practical QKD system,quantum states are generally prepared and measured with imperfect MUBs using imperfect devices,possibly reducing the secret key rate and transmission distance.To analyze the security of a QKD system with imperfect MUBs,we propose virtual MUBs to characterize the quantum channel against collective attack,and analyze the corresponding secret key rate under imperfect state preparation and measurement conditions.More generally,we apply the advantage distillation method for analyzing the security of QKD with imperfect MUBs,where the error tolerance and transmission distance can be sharply improved.Our analysis method can be applied to benchmark and standardize a practical QKD system,elucidating the security analysis of different QKD protocols with imperfect devices.

BRIGHT PROSPECTS FOR MUTUALLY BENEFICIAL COOPERATION BETWEEN CHINA AND CAMBODIA--Exclusive interview with Chinese Ambassador to Cambodia Wang Wenbin

Exchanges between China and Cambodia date back at least 2,000 years.The time-honored traditional friendship is a valuable heritage of the two peoples and an important basis for mutually beneficial cooperation between the two countries in the new era.In 2024,China-Cambodia cooperation in the fields of economics,trade,energy,and people-to-people exchange has developed vigorously and delivered fruitful results.Cambodia’s vision to become an upper-middle income country by 2030 and a high-income country by 2050 aligns nicely with China’s second centenary goal of building itself into a modern socialist country in all respects by the middle of the 21st Century.

Experimental investigation of measurement incompatibility of mutually unbiased bases

Incompatible measurements are of fundamental importance to re-vealing the peculiar features of quantum theory,and are also use-ful resources in various quantum information tasks.In this work,we investigate the quantum incompatibility of mutually unbiased bases(MUBs)within the operational framework of quantum resource the-ory,and report an experimental validation via the task of state dis-crimination.In particular,we construct an experimentally friendly witness to detect incompatible MUBs,based on the probability of cor-rectly discriminating quantum states.Furthermore,we prove that the noise robustness of MUBs can be retrieved from violating the above witness.Finally,we experimentally test the incompatibility of MUBs of dimensionality ranging from 2 to 4,and demonstrate that it is more robust to noise,as either the dimensionality of measurements or the number of MUBs increases.Our results may aid the exploration of the essential roles of incompatible measurements in both theoretical and practical applications in quantum information.

On Well-posed Mutually Nearest and Mutually Furthest Point Problems in Banach Spaces

Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance. Moreover, let denote the closure of the set . We prove that the set of all , such that the minimization (resp. maximization) problem min(A,G) (resp. max(A,G)) is well posed, contains a dense G δ-subset of , thus extending the recent results due to Blasi, Myjak and Papini and Li.

China-Latin America Green Cooperation under the Global Development Initiative

The international development environment is entering a chaotic and volatile period.The world economy remains sluggish,while geopolitical conflicts,climate change,food crisis and a multitude of other challenges become more closely intertwined and mutually reinforcing.In this context,countries across the world have been prompted to look for healthy,feasible and sustainable solutions to keep their socioeconomic development momentum on track.

Unity of Knowing and Doing

Chinese President Xi Jinping has emphasized the unity of knowing and doing on a number of occasions,saying that knowing is the premise,while doing is putting knowledge to work,and these two ideas have a mutually reinforcing relationship.UNITY of knowing and doing is a key concept in ancient Chinese philosophy.Discussions on knowing and doing can be traced back to the pre-Qin period(before 221 B.C.).

Crossed Canvas

As the first representative of the African Film Association in Asia,Luc Bendza is dedicated to promoting the dynamism of African cinema among Chinese filmmakers.On the occasion of the 14th Beijing International Film Festival,he succeeded in organising the African Film Promotion Conference in Beijing on 22 April.Bendza hopes this will promote Sino-African cooperation and exchange in the field of cinema,especially through coproductions,which he believes are mutually beneficial.The event brought together African and Chinese producers and directors who presented their joint film projects planned for the next two years.These collaborations characterise the fusion of Chinese and African elements,ranging from characters and actors to the locations and languages.

A Taste of Success

Cooperation between China and Cameroon has reached extraordinary heights over the past two decades,which has deepened both the diplomatic and economic ties.This mutually beneficial partnership has made China the leading buyer of Cameroonian products,with a market share of 25.8 percent in 2021,and the leading supplier,with a market share of 17.5 percent in 2020,according to data from the National Institute of Statistics of Cameroon.

Dynamic State Estimation Based Protection of Mutually Coupled Transmission Lines

Mutually coupled lines create challenges for legacy protection schemes.In this paper,a dynamic state estimation based protection(EBP)method is proposed to address these challenges.The method requires GPS synchronized measurements at both ends of the line and a high fidelity model of the protected line.The paper presents the dynamic model of the protected line and its impact on the performance of the protection scheme.Numerical simulations prove that the method can correctly identify faults,independent of position and type.The work also demonstrates the advantages of the proposed method versus legacy protection functions such as distance protection and line differential.These advantages include reliable and faster detection of internal low impedance faults,inter-circuit faults,and high impedance faults,even in cases of 1)partially coupled lines and 2)lack of measurements in adjacent lines.

Tuning the diffusion constant to optimize the readout of positional information of spatial concentration patterns

Positional information encoded in spatial concentration patterns is crucial for the development of multicellular organisms.However,it is still unclear how such information is affected by the physically dissipative diffusion process.Here we study one-dimensional patterning systems with analytical derivation and numerical simulations.We find that the diffusion constant of the patterning molecules exhibits a nonmonotonic effect on the readout of the positional information from the concentration patterns.Specifically,there exists an optimal diffusion constant that maximizes the positional information.Moreover,we find that the energy dissipation due to the physical diffusion imposes a fundamental upper limit on the positional information.