On the structure of the intersection of two middle third cantor sets

Motivated by the study of planar homoclinic bifurcations, in this paper we describe how the intersection of two middle third Cantor sets changes as the sets are translated across each other. The resulting description shows that the intersection is never empty; in fact, the intersection can be either finite or infinite in size. We show that when the intersection is finite then the number of points in the intersection will be either $2^n$ or $3\cdot 2^n$. We also explore the Hausdorff dimension of the intersection of two middle third Cantor sets as the sets are translated across one another. We show that the Hausdorff dimension of the intersection can take on any value from 0 to $\ln 2/\ln 3$; in addition, we show that for each Hausdorff dimension, between 0 and $\ln 2/\ln 3$, there is a dense set of translation parameters for which the intersections have that particular Hausdorff dimension

Multifractal Structure of Convolution of the Cantor Measure

AbstractThe multifractal structure of measures generated by iterated function systems (IFS) with overlaps is, to a large extend, unknown. In this paper we study the local dimension of the m-time convolution of the standard Cantor measure μ. By using some combinatoric techniques, we show that the set E of attainable local dimensions of μ contains an isolated point. This is rather surprising because when the IFS satisfies the open set condition, the set E is an interval. The result implies that the multifractal formalism fails without the open set condition

Direct Torque Control System and Sensorless Technique of Permanent Magnet Synchronous Motor

AbstractThe direct torque control theory has achieved great success in the control of induction motors. However, in the DTC drive system of Permanent Magnet Synchronous Machine (PMSM) proposed a few years ago, there are many basic theoretical problems that must be clarified. This paper describes an investigation about the effect of the zero voltage space vectors in the DTC system of PMSM and points out that if using the zero voltage space vectors rationally, not only can the DTC system be driven successfully but also the torque ripple is reduced and the performance of the system is improved. This paper also studies the sensorless technique in the DTC system of PMSM and configures the DTC system of PMSM with sensorless technique including zero voltage space vectors. Numerical simulations and experimental tests have proved the theory correct. In the condition of sensorless, the DTC system of PMSM is wide-rangely speed adjusting, and the ratio of speed adjustment is 1:100

Universal Quantum Optimization with Cold Atoms in an Optical Cavity

Cold atoms in an optical cavity have been widely used for quantum simulations of many-body physics, where the quantum control capability has been advancing rapidly in recent years. Here, we show the atom cavity system is universal for quantum optimization with arbitrary connectivity. We consider a single-mode cavity and develop a Raman coupling scheme by which the engineered quantum Hamiltonian for atoms directly encodes number partition problems (NPPs). The programmability is introduced by placing the atoms at different positions in the cavity with optical tweezers. The NPP solution is encoded in the ground state of atomic qubits coupled through a photonic cavity mode, that can be reached by adiabatic quantum computing (AQC). We construct an explicit mapping for the 3-SAT and vertex cover problems to be efficiently encoded by the cavity system, which costs linear overhead in the number of atomic qubits. The atom cavity encoding is further extended to quadratic unconstrained binary optimization (QUBO) problems. The encoding protocol is optimal in the cost of atom number scaling with the number of binary degrees of freedom of the computation problem. Our theory implies the atom cavity system is a promising quantum optimization platform searching for practical quantum advantage.Comment: 13 pages, 2 figure

Anti-proliferation effects of Sirolimus sustained delivery film in rabbit glaucoma filtration surgery

Purpose: To investigate the efficacy, safety, and mechanisms of Sirolimus sustained delivery film on prevention of scar formation in a rabbit model of glaucoma filtration surgery. Methods: Sixty-four New Zealand white rabbits who underwent trabeculectomy in the right eye were randomly allocated to one of the four treatment regimens: Sirolimus sustained delivery film treatment group (Group A), or drug-free film treatment group (Group B), or 30 ng/ml Sirolimus-soaked sponge treatment group (Group C), or no adjunctive treatment group (Group D), and each group consists of 16 rabbits. Intraocular pressure (IOP), morphologic changes of bleb, anterior chamber flare, and corneal endothelial cell count and complications were evaluated over a 28-day period follow-up time. Aqueous humor samples were gathered from Group A, and the concentration of Sirolimus was measured regularly post-operation. Rabbits were sacrificed on the 7th, 14th, and 28th day post-operation separately, and the fibroblast hypertrophy, infiltration of inflammatory, and proliferation of new collagen fiber formation in each group were evaluated with HE and Masson staining. Proliferative cell nuclear antigen (PCNA) and fibroblast apoptosis were evaluated by immunohistochemistry and terminal deoxynucleotidyl transferasemediated dUTP nick end labeling (TUNEL) assay at the 28th day post-operation. Results: Both Sirolimus sustained delivery film (Group A) and Sirolimus alone (Group C) were well tolerated in this model, and significantly prolonged bleb survival compared with no drug treatment group (Group B and D; p<0.001). Group A had the longest bleb survival time in comparison with other groups (p<0.001). There were significant differences in IOP readings between Group A and other groups at the last follow-up (p<0.05). The concentration of Group A maintained stable for over 2 weeks, drops from (10.56 +/- 0.05) ng/ml at day 3 to (7.74 +/- 0.05) ng/ml at day 14. The number of corneal endothelial cells of Group A was not statistically significant between pre and post-operation. Histologic examination demonstrated that eyes treated with Sirolimus, especially the Sirolimus sustained delivery film, showed an obvious reduction in subconjunctival fibroblast scar tissue formation compared with no drug treatment groups, and had minimal evidence of inflammatory cell infiltration and new collagen deposition in the subconjunctiva. Immunohistochemistry assay showed that PCNA-expression was lower in the Group A (16.25 +/- 3.24%) compared to other groups (p<0.01). TUNEL assay showed a significant increase in the number of apoptotic fibroblasts around the surgical area in Group A and Group C (9.75 +/- 1.71% and 8.50 +/- 1.92%) compared to the Group B and D (p<0.01). Conclusions: Sirolimus drug sustained delivery film can inhibit inflammatory cell activity, impede fibroblast proliferation activity, and induce fibroblast apoptosis in the filtration surgery sites in rabbit. The results indicate a safe and effective treatment strategy in anti-scaring treatment in glaucoma surgery.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000295289900001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Biochemistry & Molecular BiologyOphthalmologySCI(E)9ARTICLE270-712495-25061

Quantum information processing with superconducting qubits in a microwave field

We investigate the quantum dynamics of a Cooper-pair box with a superconducting loop in the presence of a nonclassical microwave field. We demonstrate the existence of Rabi oscillations for both single- and multi-photon processes and, moreover, we propose a new quantum computing scheme (including one-bit and conditional two-bit gates) based on Josephson qubits coupled through microwaves.Comment: 7 pages, 1 figur