Abstract
In this research, we use the Euler’s equation formula that constitutes a linear system and it’s application in bank audits. The solution of the systems can be obtained by Novel ...transformation.
Phantom dark energy (w<−1) can produce amplified cosmic acceleration at late times, thus increasing the value of H0 favored by CMB data and releasing the tension with local measurements of H0. We ...show that the best fit value of H0 in the context of the CMB power spectrum is degenerate with a constant equation-of-state parameter w, in accordance with the approximate effective linear equation H0+30.93w−36.47=0 (H0 in km sec−1 Mpc−1). This equation is derived by assuming that both Ω0mh2 and dA=∫0zrecdz/H(z) remain constant (for an invariant CMB spectrum) and equal to their best fit Planck/ΛCDM values as H0, Ω0m, and w vary. For w=−1, this linear degeneracy equation leads to the best fit H0=67.4 km sec−1 Mpc−1 as expected. For w=−1.22, the corresponding predicted CMB best fit Hubble constant is H0=74 km sec−1 Mpc−1, which is identical with the value obtained by local-distance ladder measurements, while the best fit matter density parameter is predicted to decrease, since Ω0mh2 is fixed. We verify the above H0−w degeneracy equation by fitting a wCDM model with fixed values of w to the Planck TT spectrum, showing also that the quality of fit (χ2) is similar to that of ΛCDM. However, when including SnIa, baryon acoustic oscillation, or growth data, the quality of fit becomes worse than ΛCDM when w<−1. Finally, we generalize the H0−w(z) degeneracy equation for the parametrization w(z)=w0+w1z/(1+z) and identify analytically the full w0−w1 parameter region (straight line) that leads to a best fit H0=74 km sec−1 Mpc−1 in the context of the Planck CMB spectrum. This exploitation of H0−w(z) degeneracy can lead to immediate identification of all parameter values of a given w(z) parametrization that can potentially resolve the H0 tension.
We consider general classes of Euler type linear and half‐linear difference equations, which are conditionally oscillatory. Applying the adapted Riccati technique, we improve known oscillation ...criteria for these equations. More precisely, our presented main criterion is the full oscillatory counterpart of a non‐oscillation criterion. Thus, in this paper, we enlarge the set of conditionally oscillatory Euler type difference equations. We highlight that our results are new even for linear equations with periodic coefficients. This fact is documented by simple examples of such equations at the end of this paper.
In this paper, we introduce a new oscillation criterion for Euler type half-linear difference equations with positive coefficients which are asymptotically periodic and bounded, respectively. As the ...mean of proving the criterion, the generalized adapted Riccati transformation is used. The presented main result is the oscillatory counterpart of a previously obtained non-oscillation criterion for the treated equations. Therefore, the result shows that the analyzed equations are conditionally oscillatory. Then we emphasize the novelty of the result in the linear case by several consequences.
Abstract
Hepatocellular carcinoma (HCC) is the cancers with a high incidence and mortality rate.. Its existence poses a great threat to people’s life and health. Recently, Glypican-3 (GPC3) has ...became one of the valuable markers for the diagnosis of HCC. In this study, a GPC3 aptasensor was constructed based on AuNPs@Fc-rGO and the specific recognition of GPC3 aptamer. AuNPs@Fc-rGO had electrochemical activity, signal amplification and biocompatibility. Under the optimized conditions, the value of peak current correlate linearly with the concentration of GPC3 from 0.01 to 10.0 μg/mL, the linear equation was Y = 6.8223-0.3225X with R
2
= 0.9925, and the LOD was 3.16 ng/mL. In addition, the experimental results show that the sensor has excellent stability and specificity. It provides a simple detection method for patients with early HCC.
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