Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.Comment: 4 pages no figur

The Nullity of Bicyclic Signed Graphs

Let \Gamma be a signed graph and let A(\Gamma) be the adjacency matrix of \Gamma. The nullity of \Gamma is the multiplicity of eigenvalue zero in the spectrum of A(\Gamma). In this paper we characterize the signed graphs of order n with nullity n-2 or n-3, and introduce a graph transformation which preserves the nullity. As an application we determine the unbalanced bicyclic signed graphs of order n with nullity n-3 or n-4, and signed bicyclic signed graphs (including simple bicyclic graphs) of order n with nullity n-5

Refinement of primary Si in hypereutectic Al-Si alloys by intensive melt shearing

Hypereutectic Al-Si based alloys are gaining popularity for applications where a combination of light weight and high wear resistance is required. The high wear resistance arising from the hard primary Si particles comes at the price of extremely poor machine tool life. To minimize machining problems while exploiting outstanding wear resistance, the primary Si particles must be controlled to a uniform small size and uniform spatial distribution. The current industrial means of refining primary Si chemically by the addition of phosphorous suffers from a number of problems. In the present paper an alternative, physical means of refining primary Si by intensive shearing of the melt prior to casting is investigated. Al-15wt%Si alloy has been solidified under varying casting conditions (cooling rate) and the resulting microstructures have been studied using microscopy and quantitative image analysis. Primary Si particles were finer, more compact in shape and more numerous with increasing cooling rate. Intensive melt shearing led to greater refinement and more enhanced nucleation of primary Si than was achieved by adding phosphorous. The mechanism of enhanced nucleation is discussed.EPSRC (grant EP/H026177/1)

A right-handed isotropic medium with a negative refractive index

The sign of the refractive index of any medium is soley determined by the requirement that the propagation of an electromagnetic wave obeys Einstein causality. Our analysis shows that this requirement predicts that the real part of the refractive index may be negative in an isotropic medium even if the electric permittivity and the magnetic permeability are both positive. Such a system may be a route to negative index media at optical frequencies. We also demonstrate that the refractive index may be positive in left-handed media that contain two molecular species where one is in its excited state.Comment: 4.1 pages, 4 figures, submitted to Physical Review Letter

New n-mode squeezing operator and squeezed states with standard squeezing

We find that the exponential operator V=exp[ilamda (Q_1P_2+Q_2P_3+...+Q_{n-1}P_{n}+Q_{n}P_1)], Q_{i}, P_{i} are respectively the coordinate and momentum operators, is an n-mode squeezing operator which engenders standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive V's normally ordered expansion and obtain the n-mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.Comment: 8 pages, no figur

Criteria for the experimental observation of multi-dimensional optical solitons in saturable media

Criteria for experimental observation of multi-dimensional optical solitons in media with saturable refractive nonlinearities are developed. The criteria are applied to actual material parameters (characterizing the cubic self-focusing and quintic self-defocusing nonlinearities, two-photon loss, and optical-damage threshold) for various glasses. This way, we identify operation windows for soliton formation in these glasses. It is found that two-photon absorption sets stringent limits on the windows. We conclude that, while a well-defined window of parameters exists for two-dimensional solitons (spatial or spatiotemporal), for their three-dimensional spatiotemporal counterparts such a window \emph{does not} exist, due to the nonlinear loss in glasses.Comment: 8 pages, to appear in Phys. Rev.

Baseline characteristics and enrichment results from the SONAR trial

Aim: The SONAR trial uses an enrichment design based on the individual response to the selective endothelin receptor antagonist atrasentan on efficacy (the degree of the individual response in the urinary albumin‐to‐creatinine ratio [UACR]) and safety/tolerability (signs of sodium retention and acute increases in serum creatinine) to assess the effects of this agent on major renal outcomes. The patient population and enrichment results are described here. Methods: Patients with type 2 diabetes with an estimated glomerular filtration rate (eGFR) within 25 to 75 mL/min/1.73 m2 and UACR between 300 and 5000 mg/g were enrolled. After a run‐in period, eligible patients received 0.75 mg/d of atrasentan for 6 weeks. A total of 2648 responder patients in whom UACR decreased by ≥30% compared to baseline were enrolled, as were 1020 non‐responders with a UACR decrease of <30%. Patients who experienced a weight gain of >3 kg and in whom brain natriuretic peptide exceeded ≥300 pg/mL, or who experienced an increase in serum creatinine >20% (0.5 mg/dL), were not randomized. Results: Baseline characteristics were similar for atrasentan responders and non‐responders. Upon entry to the study, median UACR was 802 mg/g in responders and 920 mg/g in non‐responders. After 6 weeks of treatment with atrasentan, the UACR change in responders was −48.8% (95% CI, −49.8% to −47.9%) and in non‐responders was −1.2% (95% CI, −6.4% to 3.9%). Changes in other renal risk markers were similar between responders and non‐responders except for a marginally greater reduction in systolic blood pressure and eGFR in responders. Conclusions: The enrichment period has successfully identified a population with a profound UACR reduction without clinical signs of sodium retention in whom a large atrasentan effect on clinically important renal outcomes is possible. The SONAR trial aims to establish whether atrasentan confers renal protection

Generalized thermo vacuum state derived by the partial trace method

By virtue of the technique of integration within an ordered product (IWOP) of operators we present a new approach for deriving generalized thermo vacuum state which is simpler in form that the result by using the Umezawa-Takahashi approach, in this way the thermo field dynamics can be developed. Applications of the new state are discussed.Comment: 5 pages, no figure, revtex