Egzaktna rješenja poopčene kdv jednadžbe s promjenljivim koeficijentima

The generalized variable-coefficient Korteveg de Vries equation is investigated by means of the polynomial expansion method and many travelling-wave solutions are constructed, including the solitary wave, the triangular periodic wave and the rational solutions. The technique is straightforward to use and only minimal algebra is needed to find these solutions. A simple review of the method is finally given.Istražili smo poopćenu KdV jednadžbu s promjenljivim koeficijentima metodom razvoja po polinomima. Izvode se mnoga rješenja za putujuće valove, uključivši solitone, trokutne periodičke valove i racionalna rješenja. Postupak je izravan i rješenja se dobivanju vrlo jednostavnim računom. Izlaže se jednostavan pregled postupka

Efficient Video Quality Assessment Based on Spacetime Texture Representation

Mostexistingvideoqualitymetricsmeasuretemporaldistortions based on optical-flow estimation, which typically has limited descriptive power of visual dynamics and low efficiency. This paperpresents aunifiedandefficient framework to measure temporal distortions based on a spacetime texture representation of motion. We first propose an effective motion-tuning scheme to capture temporal distortions along motion trajectories by exploiting the distributive characteristic of the spacetime texture. Then we reuse the motion descriptors to build a self-information based spatiotemporal saliency model to guide the spatial pooling. At last, a comprehensive quality metric is developed by combining the temporaldistortionmeasurewithspatialdistortionmeasure. Our method demonstrates high efficiency and excellent correlation with the human perception of video quality

Testing the ns−H0n_s-H_0 scaling relation with Planck-independent CMB data

In early dark energy (EDE) resolution of Hubble tension, the spectral index $n_s$ of primordial scalar perturbation follows a scaling relation $\delta n_s\simeq 0.4\frac{\delta H_0}{H_0}$, where $H_0$ is the Hubble constant. However, this $n_s-H_0$ relation was obtained based on the datasets including Planck cosmic microwave background (CMB) data. In this paper, we investigate this scaling relation with Planck-independent CMB data, i.e. ACT and SPT-3G combined with WMAP(+BAO+Pantheon), respectively. Our results show that the WMAP+SPT-3G dataset also follows this scaling relation, while the WMAP+ACT dataset seems to favor smaller $n_s$, which is related to the fact that the critical redshift $z_c$, at which EDE is excited, favored by the WMAP+ACT dataset is lower and closer to the recombination time

Convergent Catalytic Asymmetric Synthesis of Esters of Chiral Dialkyl Carbinols

Because chiral dialkyl carbinols, as well as their derived esters, are significant as intermediates and end points in fields such as organic, pharmaceutical, and biological chemistry, the development of efficient approaches to their asymmetric synthesis is an important endeavor. In this report, we describe a method for the direct catalytic enantioselective synthesis of such esters, beginning with an alkyl halide (derived from an aldehyde and an acyl bromide), an olefin, and a hydrosilane, catalyzed by nickel, an earth-abundant metal. The method is versatile, tolerating substituents that vary in size and that bear a range of functional groups. We further describe a four-component variant of this process, wherein the alkyl halide is generated in situ, thus obviating the need to isolate either an alkyl electrophile or an alkylmetal, while still effecting an alkyl–alkyl coupling. Finally, we apply our convergent method to the efficient catalytic enantioselective synthesis of three esters that are bioactive themselves or that have been utilized in the synthesis of bioactive compounds

Convergent Catalytic Asymmetric Synthesis of Esters of Chiral Dialkyl Carbinols

Because chiral dialkyl carbinols, as well as their derived esters, are significant as intermediates and end points in fields such as organic, pharmaceutical, and biological chemistry, the development of efficient approaches to their asymmetric synthesis is an important endeavor. In this report, we describe a method for the direct catalytic enantioselective synthesis of such esters, beginning with an alkyl halide (derived from an aldehyde and an acyl bromide), an olefin, and a hydrosilane, catalyzed by nickel, an earth-abundant metal. The method is versatile, tolerating substituents that vary in size and that bear a range of functional groups. We further describe a four-component variant of this process, wherein the alkyl halide is generated in situ, thus obviating the need to isolate either an alkyl electrophile or an alkylmetal, while still effecting an alkyl–alkyl coupling. Finally, we apply our convergent method to the efficient catalytic enantioselective synthesis of three esters that are bioactive themselves or that have been utilized in the synthesis of bioactive compounds