Observation of Non-Hermitian Quantum Correlation Criterion in Mesoscopic Optomechanical System

Although many quantum correlation criteria have been proposed successively in recent years, it is still an open question how to observe these criteria with the non–Hermitian terms in themselves. We propose an indirect scheme in this paper to observe non-Hermitian criteria and to judge whether or not quantum correlation exists in the system even though the expectation value measurement of non-Hermitian operator is invalid in quantum mechanics system. Our idea is to establish a critical state of mesoscopic oscillator under mean–field approximation, and the oscillator state will take place transition when the quantum correlation destroys the mean–field approximation. The non–Hermitian measurement will replace the position measurement in this process and it can be seen as a non–destructive detection. We give an example to explain this idea in a designed mesoscopic optomechanical system.     

A note on general solution of Stokes equations

Li et al. (2015) claim that it is sufficient to use two harmonic functions to express the general solution of Stokes equations. In this paper, we demonstrate that this is not true in a general case and that we in fact need three scalar harmonic functions to represent the general solution of Stokes equations (Venkatalaxmi et al., 2004).     

Self-propulsion of flapping bodies in viscous fluids: Recent advances and perspectives

Flapping-powered propulsion is used by many animals to locomote through air or water. Here we review recent experimental and numerical studies on self-propelled mechanical systems powered by a flapping motion. These studies improve our understanding of the mutual interaction between actively flapping bodies and surrounding fluids. The results obtained in these works provide not only new insights into biolocomotion but also useful information for the bio-mimetic design of artificial flyers and swimmers.     

Numerical analysis of stress distribution in the upper arm tissues under an inflatable cuff: Implications for noninvasive blood pressure measurement

An inflatable cuff wrapped around the upper arm is widely used in noninvasive blood pressure measurement. However, the mechanical interaction between cuff and arm tissues, a factor that potentially affects the accuracy of noninvasive blood pressure measurement, remains rarely addressed. In the present study, finite element (FE) mod-els were constructed to quantify intra-arm stresses generated by cuff compression, aiming to provide some theoretical evi-dence for identifying factors of importance for blood pressure measurement or explaining clinical observations. Obtained results showed that the simulated tissue stresses were highly sensitive to the distribution of cuff pressure on the arm sur-face and the contact condition between muscle and bone. In contrast, the magnitude of cuff pressure and small variations in elastic properties of arm soft tissues had little influence on the efficiency of pressure transmission in arm tissues. In par-ticular, it was found that a thickened subcutaneous fat layer in obese subjects significantly reduced the effective pres-sure transmitted to the brachial artery, which may explain why blood pressure overestimation occurs more frequently in obese subjects in noninvasive blood pressure measurement.     

Cohomology theories in triangulated categories

Let C be a triangulated category with a proper class E of triangles.We prove that there exists an Avramov–Martsinkovsky type exact sequence in C,which connects E-cohomology,E-Tate cohomology and E-Gorenstein cohomology.     

Unconditional uniqueness of solution for $$\dot H^{s_c }$$ critical 4th order NLS in high dimensions

In this paper, we study the unconditional uniqueness of solution for the Cauchy problem of Ḣ^s_c(0 ≤ s_c < 2) critical nonlinear fourth-order Schrödinger equations i∂_tu + Δ²u-εu=λ|u|^αu. By employing paraproduct estimates and Strichartz estimates, we prove that unconditional uniqueness of solution holds in C_t(I; Ḣ^s_c(R^d)) for d ≥ 11 and min{1^-, (8)/(d-4)} ≥ α >(-(d-4)+√4(d-4)²+64)/4.     

On the Characterization of Maximal Planar Graphs with a Given Signed Cycle Domination Number

Let G =(V, E) be a simple graph. A function f : E → {+1,-1} is called a signed cycle domination function(SCDF) of G if ∑_(e∈E(C))f(e) ≥ 1 for every induced cycle C of G. The signed cycle domination number of G is defined as γ'_(sc)(G) = min{∑_(e∈E)f(e)| f is an SCDF of G}. This paper will characterize all maximal planar graphs G with order n ≥ 6 and γ'_(sc)(G) = n.     

Highly efficient heterogeneous procedure for the synthesis of fructone fragrancy

A novel heterogeneous strong acid catalyst was synthesized through the copolymerization of p-toluenesulfonic acid and paraformaldehyde and utilized for the synthesis of fructone. The results showed that the catalyst was very efficient for the reaction with the yield over 95%. The advantages of extremely high density of acidity, high thermal and chemical stability, low cost for the simple synthetic procedure, and reusability made the catalyst one of the best choices for the reaction.     

Lamellar metal-organic complex and its rod-like nanoparticles prepared with ultrasonic technique

Metal-organic complex (H3NCH2CH2NH2)3[MoO2(OC6H4O)2] with a lamellar morphology has been syn- thesized. Its crystal structure was confirmed by single-crystal X-ray diffraction. The morphology of the crystal was observed by scanning electron microscopy (SEM). The metal-organic nanoparticles have been prepared by using an ultrasonic method. The morphology of the as-prepared nanoparticles was observed by transmission electron microscopy (TEM). The possible formation mechanism has also been proposed.     

Matrix-assisted pulsed laser evaporation of polyimide thin films and the XPS study

Compared with the traditional thin film techniques, the matrix-assisted pulsed laser evaporation (MAPLE) technique has many advantages in the deposition of polymer and organic thin films. It has a wide range of applications in many fields, such as non-linear optics, luminescent devices, electronics, various sensors. We have successfully deposited polyimide thin films by using the MAPLE technique. These films were characterized with XPS. The XPS spectra showed that the single-photon effect is ob-vious at low laser fluence and the chemical bonds will be broken, resulting in decomposition of the films. Contrarily, the single-photon effect will decrease and the multi-photon effect and the photothermal effect will increase at high laser fluence, resulting in the protection of the structure of the polyimide thin films and the obvious decrease in decomposition. High laser fluence is more suitable for the deposition of polymer and organic thin films than low laser fluence.