Finite pp-groups with a minimal non-abelian subgroup of index pp (IV)

In this paper, we completely classify the finite $p$-groups $G$ such that $\Phi(G')G_3\le C_p^2$, $\Phi(G')G_3\le Z(G)$ and $G/\Phi(G')G_3$ is minimal non-abelian. This paper is a part of the classification of finite $p$-groups with a minimal non-abelian subgroup of index $p$. Together with other four papers, we solve a problem proposed by Y. Berkovich

Precision metrology using weak measurements

Weak values and measurements have been proposed as means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur with highly suppressed probabilities. This raises three vital questions in weak-measurement-based metrology, namely, (Q1) Does post-selection enhance the measurement precision? (Q2) Does weak measurement offer better precision than strong measurement? (Q3) Is it possible to beat the standard quantum limit or to achieve the Heisenberg limit with weak measurement using only classical resources? We analyse these questions for two prototypical, and generic, measurement protocols and show that while the answers to the first two questions are negative for both protocols, the answer to the last is affirmative for measurements with phase-space interactions, and negative for configuration space interactions. Our results, particularly the ability of weak measurements to perform at par with strong measurements in some cases, are instructive for the design of weak-measurement-based protocols for quantum metrology.Comment: 5+5 pages, 2 figure

Treatment of osteoporotic vertebral compressive fractures with percutaneous kyphoplasty and oral Zishengukang

AbstractObjectiveTo observe the therapeutic effect of percutaneous kyphoplasty (PKP) and oral Zishengukang (ZSGK) for the treatment of osteoporotic vertebral compression fractures (OVCFs).MethodsSeventy patients were randomly divided into a control group (PKP group) and an experimental group (PKP plus ZSGK group). The 35 patients in the experimental group were prescribed 6 g oral ZSGK three times a day for 90 days after PKP. Visual analog pain scale (VAS), Oswestry functional score, vertebral height and Cobb's angle were recorded and compared before treatment and at one week, one month and three months after treatment.ResultsVertebral height and Cobb's angle significantly improved and VAS and Oswestry functional score were significantly lower in both groups after PKP than pre-operatively (P<0.01). Three months after treatment, VAS and Oswestry functional score in the experimental group were lower than controls (P<0.05), even though vertebral height and Cobb's angle were comparable (P>0.05).ConclusionPKP combined with oral ZSGK provide superior short-term and long-term symptom control after OVCF than PKP alone

Experimental test of contextuality in quantum and classical systems

Contextuality is considered as an intrinsic signature of non-classicality, and a crucial resource for achieving unique advantages of quantum information processing. However, recently there have been debates on whether classical fields may also demonstrate contextuality. Here we experimentally configure a contextuality test for optical fields, adopting various definitions of measurement events, and analyse how the definitions affect the emergence of non-classical correlations. The heralded single photon state, a typical non-classical light field, manifests contextuality in our setup, while contextuality for classical coherent fields strongly depends on the specific definition of measurement events which is equivalent to filtering the non-classical component of the input state. Our results highlight the importance of definition of measurement events to demonstrate contextuality, and link the contextual correlations to non-classicality defined by quasi-probabilities in phase space.Comment: 17 pages, 7 figure

Simulating broken PT\cal PT-symmetric Hamiltonian systems by weak measurement

By embedding a $\cal PT$-symmetric (pseudo-Hermitian) system into a large Hermitian one, we disclose the relations between $\cal{PT}$-symmetric Hamiltonians and weak measurement theory. We show that the amplification effect in weak measurement on a conventional quantum system can be used to effectively simulate a local broken $\cal PT$-symmetric Hamiltonian system, with the pre-selected state in the $\cal PT$-symmetric Hamiltonian system and its post-selected state resident in the dilated Hamiltonian system.Comment: 4 pages; with Supplemental Materia

Finite p-groups all of whose non-abelian proper subgroups are generated by two elements

AbstractIn this paper, we classify the finite p-groups all of whose non-abelian proper subgroups are generated by two elements

Planning and coordinated response mechanism of economic and ecological services in urban expansion

Against the backdrop of urban sustainable development around the world, how to coordinate both economic growth and ecological benefits in urban space becomes an important problem. Therefore, this study simulated and predicted the spatiotemporal changes in urban economy and ecosystem service value (E.S.V.) equivalent ratio under the current policies by 2030, and analysed how adjusting planning policies influences economy and ecology. This process was based on the future land use simulation (F.L.U.S.) model of coupled neural network, and on methods assessing the spatial changes in ecosystem services and land economy. This study aims to analyse urban land economy and E.S.V., and assess how China’s land spatial planning guides and promotes high-quality urban economic development. Results show that artificial intelligence (A.I.) simulation can forecast the results of spatial planning policies of national lands, to make policy-making more forwardlooking. The guidance of planning policies on urban expansion accelerates the increase in economic value of urban residential and commercial lands, thereby promoting the economic growth. However, adjusted planning policies may lead to ecological destruction. So, this study provides model verifications and path guidance to realise coordinated sustainable development between economy and ecology, serving as an important reference to formulating proper policies for urban development