Non-orthogonal Fusion Frames and the Sparsity of Fusion Frame Operators

Fusion frames have become a major tool in the implementation of distributed systems. The effectiveness of fusion frame applications in distributed systems is reflected in the efficiency of the end fusion process. This in turn is reflected in the efficiency of the inversion of the fusion frame operator S_WS_{\mathcal{W}}, which in turn is heavily dependent on the sparsity of S_WS_{\mathcal{W}}. We will show that sparsity of the fusion frame operator naturally exists by introducing a notion of non-orthogonal fusion frames. We show that for a fusion frame {W _i ,v _i } _i∈I , if dim(W _i )=k _i , then the matrix of the non-orthogonal fusion frame operator S_W{\mathcal{S}}_{{\mathcal{W}}} has in its corresponding location at most a k _i ×k _i block matrix. We provide necessary and sufficient conditions for which the new fusion frame operator S_W{\mathcal{S}}_{{\mathcal{W}}} is diagonal and/or a multiple of an identity. A set of other critical questions are also addressed. A scheme of multiple fusion frames whose corresponding fusion frame operator becomes an diagonal operator is also examined.     

Coherent Control of High Harmonic Generation Driven by Metal Nanotip Photoemission

Steering ultrafast electron dynamics with well-controlled laser fields is very important for generation of intense supercontinuum radiation. It can be achieved through coherent control of the symmetry of the interaction between strong-field laser fields and a metal nanotip. We employ a scheme of two-color laser pulses combined with a weak static field to realize the control of a single quantum path to generate high harmonic generation from a single solid-state nanoemitter. Moreover, a smooth and ultrabroad supercontinuum in the extreme ultraviolet region is obtained, which can produce a single attosecond pulse. Our findings are beneficial for efficient generation of isolated sub-100 as XUV pulses from solid-state sources.     

Angular velocity observer for space tether exploiting non-singular dynamics and vector measurements

Nonlinear Dynamics - Outstanding aerial capabilities that insects present in nature inspire researchers to undertake a challenge to develop a flapping aerial vehicle with performances unmatched by...     

Frame Fundamental Sensor Modeling and Stability of One-Sided Frame Perturbation

We demonstrate that for all linear devices and/or sensors, signal requisition and reconstruction is naturally a mathematical frame expansion and reconstruction issue, whereas the measurement is carried out via a sequence generated by the exact physical response function (PRF) of the device, termed sensory frame {h _n }. The signal reconstruction, on the other hand, will be carried out using the dual frame $\{\tilde{h}^{a}_{n}\}$ of an estimated sensory frame {h _n ^a }. This consequently results in a one-sided perturbation to a frame expansion, which resides in each and every signal and image reconstruction problem. We show that the stability of such a one-sided frame perturbation exits. Examples of image reconstructions in de-blurring are demonstrated.     

Second kind integral equation formulation for the mode calculation of optical waveguides

We present a second kind integral equation (SKIE) formulation for calculating the electromagnetic modes of optical waveguides, where the unknowns are only on material interfaces. The resulting numerical algorithm can handle optical waveguides with a large number of inclusions of arbitrary irregular cross section. It is capable of finding the bound, leaky, and complex modes for optical fibers and waveguides including photonic crystal fibers (PCF), dielectric fibers and waveguides. Most importantly, the formulation is well conditioned even in the case of nonsmooth geometries. Our method is highly accurate and thus can be used to calculate the propagation loss of the electromagnetic modes accurately, which provides the photonics industry a reliable tool for the design of more compact and efficient photonic devices. We illustrate and validate the performance of our method through extensive numerical studies and by comparison with semi-analytical results and previously published results.     

Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions

A Fredholm second kind integral equation (SKIE) formulation is constructed for the Dirichlet problem of the biharmonic equation in three dimensions. A fast numerical algorithm is developed based on the constructed SKIE. Its performance is illustrated via several numerical examples.     

Dual-wavelength Nd:YAG crystal laser at 1074 and 1112 nm

We reported an efficient laser-diode (LD) end-pumped CW dual-wavelength Nd:YAG crystal laser operating at 1074 and 1112 nm simultaneously, for the first time to our knowledge. The maximum output power was 3.15 W with an optical conversion efficiency of 23.6%. Considering the broad absorption of carbonylhemoglobin and hemoglobin located at about 538 and 555 nm, respectively, we proposed that this dual-wavelength laser is an important source for detecting carbon monoxide poisoning by simple frequency doubling.     

后交联法制备大孔吸附树脂及其对灯盏乙素的分离研究

通过种球溶胀法合成的粒径为15μm,交联度为80%的聚(苯乙烯-二乙烯苯)微球(PS-DVB),以三氯化铁为催化剂,通过悬挂双键后交联反应,制备出具有较高比表面积的大孔吸附树脂色谱填料;利用上述色谱填料装填成规格为4.6mm×250mm的色谱柱,对灯盏乙素进行高效液相色谱分离,以分离度、选择因子、柱效和保留时间为考察指标,研究了流动相比例、流动相流速、柱温和进样浓度等对分离过程的影响。在流动相为乙腈:0.4%冰乙酸(27:73,v:v),流速为1.0mL/min,柱温为30℃,进样浓度为300μg/mL的条件下,灯盏乙素和灯盏甲素的分离度为2.20,两组分可完全分离,保留时间为7.1min,为灯盏乙素的大规模制备提供了可能。     

流动注射一超声雾化器一电感耦合等离子体-原子发射光谱(FI-UN-ICP-AES)同时测定头发中多种元素条件的优化

建立了FI－UN－ICP－AES联用技术，用所发展技术进行了头发中多种微量元素的同时测定，对载流流速、积分时间、进样体积等进行了优化。多次注射测定的再现性（RSD）在0.6％一5．0％范围内，标准加入回收率为90％一101％。