On the Leibniz rule and Laplace transform for fractional derivatives

Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly. This paper investigates two typical applications: Lebiniz rule and Laplace transform. It is analytically shown that the commonly used Leibniz rule cannot be applied for Caputo derivative. Similarly, the well-known Laplace transform of Riemann-Liouville derivative is doubtful for n-th continuously differentiable function. By the aid of this series representation, the exact formula of Caputo Leibniz rule and the explanation of Riemann-Liouville Laplace transform are presented. Finally, three illustrative examples are revisited to confirm the obtained results

Controlling single-photon transport with three-level quantum dots in photonic crystals

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Learning-based Single-step Quantitative Susceptibility Mapping Reconstruction Without Brain Extraction

Quantitative susceptibility mapping (QSM) estimates the underlying tissue magnetic susceptibility from MRI gradient-echo phase signal and typically requires several processing steps. These steps involve phase unwrapping, brain volume extraction, background phase removal and solving an ill-posed inverse problem. The resulting susceptibility map is known to suffer from inaccuracy near the edges of the brain tissues, in part due to imperfect brain extraction, edge erosion of the brain tissue and the lack of phase measurement outside the brain. This inaccuracy has thus hindered the application of QSM for measuring the susceptibility of tissues near the brain edges, e.g., quantifying cortical layers and generating superficial venography. To address these challenges, we propose a learning-based QSM reconstruction method that directly estimates the magnetic susceptibility from total phase images without the need for brain extraction and background phase removal, referred to as autoQSM. The neural network has a modified U-net structure and is trained using QSM maps computed by a two-step QSM method. 209 healthy subjects with ages ranging from 11 to 82 years were employed for patch-wise network training. The network was validated on data dissimilar to the training data, e.g. in vivo mouse brain data and brains with lesions, which suggests that the network has generalized and learned the underlying mathematical relationship between magnetic field perturbation and magnetic susceptibility. AutoQSM was able to recover magnetic susceptibility of anatomical structures near the edges of the brain including the veins covering the cortical surface, spinal cord and nerve tracts near the mouse brain boundaries. The advantages of high-quality maps, no need for brain volume extraction and high reconstruction speed demonstrate its potential for future applications.Comment: 26 page

Racial and Ethnic Disparities in Health Care: An Examination of State Inpatient Databases in the Utilization of and Outcomes following Total Knee Arthroplasty

Title: Racial and Ethnic Disparities in Health Care: An Examination of State Inpatient Databases in the Utilization of and Outcomes following Total Knee Arthroplasty Background: The U.S. population is becoming more racially and ethnically diverse yet disparities in health care still exist. One area of medical care in which racial disparities have been identified is total knee arthroplasty (TKA)¬—an efficacious and cost-effective treatment option for individuals with advanced arthritis of the knee. Previous studies have documented that racial and ethnic minorities tend to have higher rates of adverse health outcomes and face more barriers utilizing the procedure. However, these studies predominantly focused on black and white disparities and were limited to Medicare patients or veterans. In this study, we sought to study racial disparities in TKA utilization and associated health outcomes using nationally representative data. Methods: We analyzed administrative data collected for the Hospital Cost and Utilization Project State Inpatient Databases (SID) from eight racially diverse states between 2001 and 2008. Patient race was categorized according to the SID: whites, blacks, Hispanics, Asians, Native Americans and mixed-race. Both crude and adjusted racial/ethnic disparities were evaluated. We also analyzed time trends in TKA utilization by race to assess whether access to TKA improved over time. Results:We identified a total of 547,380 admissions between 2001 and 2008 during which a TKA procedure was performed. In comparison with whites (4.65 per 1,000 population per year), blacks (3.90), Hispanics (3.71), Asians (3.89), Native Americans (4.40) and mixed-race (3.69) had lower rates of TKA utilization (P Conclusion: Minorities had lower rates of TKA utilization but higher rates of adverse health outcomes associated with the procedure, even after adjusting for patient and health care system related characteristics. Future studies that consider specific patient-level information with psychosocial and behavioral factors are needed

Threshold Effects in the Decay of Heavy b' and t' Quarks

A sequential fourth generation is still viable, but the t' and b' quarks are constrained to be not too far apart in mass. The t'{\to}bW and b'{\to}tW decay channels are still being pursued at the Tevatron, which would soon be surpassed by the LHC. We use a convolution method with up to five-body final state to study t' and b' decays. We show how the two decay branches for m_{b'} below the tW threshold, b'{\to}tW^* and t^*W, merge with b'{\to}tW above the threshold. We then consider the heavy-to-heavy transitions b'{\to}t^{\prime(*)}W^{(*)} (or t'{\to}b^{\prime(*)}W^{(*)}), as they are not suppressed by quark mixing. We find that, because of the threshold sensitivity of the branching fraction of t'{\to}b'W^* (or b'{\to}t'W^*), it is possible to measure the strength of the CKM mixing element V_{t'b} (or V_{tb'}), especially when it is rather small. We urge the experiments to pursue and separate the t'{\to}b'W^* (or b'{\to}t'W^*) decay in their search program

Astragaloside IV liposomes ameliorates adriamycin-induced nephritic syndrome in rats

Background: Radix Astragali was one of the main compositions of ‘Modified Danggui Buxue Decoction’  used for treatment of various kidney diseases. Astragaloside IV was the active composition of Radix Astragali. Astragaloside IV liposomes were used for the treatment of adriamycin-induced nephropathy (AN) rats. The aim of the study was to study the effect of astragaloside IV liposomes on AN rats, and to test through  regulating the expression of nephrin, integrins and integrin-linked kinase (ILK) in renal  tissues.Methods: The rats were given a single tail intravenous injection of adriamycin (6 mg/kg) within 1 week,  and then divided into four groups including normal, model, benazepril and astragaloside IV liposomes group. They were all orally administered dosage of benazepril and astragaloside IV liposomes once daily for 8 weeks.Results: Astragaloside IV liposomes significantly reduced the proteinuria of AN rats at 28, 42 and 56 days. astragaloside IV liposomes could increase the mRNA and protein expression of nephrin, integrin α3, down-regulate the expression of ILK to alleviate the podocyte damage and restore glomerular selective filtration function.Conclusions: Astragaloside IV liposomes could enhance renal function and protect podocyte to  ameliorate the adriamycin-induced nephritic syndrome.Key words：Astragaloside IV, Liposomes, Ardiamycin-induce nephropathy, Podocyt

Structure and electronic properties of the (3×3\sqrt{3}\times \sqrt{3})R30∘R30^{\circ} SnAu2_2/Au(111) surface alloy

We have investigated the atomic and electronic structure of the ($\sqrt{3}\times \sqrt{3}$)$R30^{\circ}$ SnAu$_2$/Au(111) surface alloy. Low energy electron diffraction and scanning tunneling microscopy measurements show that the native herringbone reconstruction of bare Au(111) surface remains intact after formation of a long range ordered ($\sqrt{3}\times \sqrt{3}$)$R30^{\circ}$ SnAu$_2$2/Au(111) surface alloy. Angle-resolved photoemission and two-photon photoemission spectroscopy techniques reveal Rashba-type spin-split bands in the occupied valence band with comparable momentum space splitting as observed for the Au(111) surface state, but with a hole-like parabolic dispersion. Our experimental findings are compared with density functional theory (DFT) calculation that fully support our experimental findings. Taking advantage of the good agreement between our DFT calculations and the experimental results, we are able to extract that the occupied Sn-Au hybrid band is of (s, d)-orbital character while the unoccupied Sn-Au hybrid bands are of (p, d)-orbital character. Hence, we can conclude that the Rashba-type spin splitting of the hole-like Sn-Au hybrid surface state is caused by the significant mixing of Au d- to Sn s-states in conjunction with the strong atomic spin-orbit coupling of Au, i.e., of the substrate.Comment: Copyright: https://journals.aps.org/authors/transfer-of-copyright-agreement; All copyrights by AP

Effect of Powder Particle Size on the Fabrication of Ti-6Al-4V using Laser Metal Deposition from Elemental Powder Mixture

Direct LMD (laser metal deposition) was used to fabricate thin-wall Ti-6Al-4V using the powder mixture of Ti-6 wt.%Al-4 wt.%V. SEM (scanning electron microscopy), OM (optical microscopy) and EDS (energy dispersive spectroscopy) were employed to examine the chemical composition and microstructure of the as-deposited sections. Vickers hardness tests were then applied to characterize the mechanical properties of the deposit samples which were fabricated using pre-mixed elemental powders. The EDS line scans indicated that the chemical composition of the samples was homogenous across the deposit. After significant analysis, some differences were observed among two sets of deposit samples which varied in the particle size of the mixing Ti-6wt.%Al-4wt.%V powder. It could be found that the set with similar particle number for Ti, Al and V powder made composition much more stable and could easily get industry qualified Ti-6Al-4V components