Decompositions of the Kadomtsev-Petviashvili equation and their symmetry reductions

Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation allows the Burgers-STO(BSTO)decomposition,two types of reducible coupled BSTO decompositions and the BSTO-KdV decomposition.Furthermore,we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions.Using the framework of standard Lie point symmetry theory,these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.

Chinese Public's Willingness to Pay for CO＿2 Emissions Reductions: A Case Study from Four Provinces/Cities

Contingent Valuation Method(CVM) was used to investigate the Chinese public's willingness to pay(WTP) for a policy to reduce CO2 emissions. Face to face interviews were conducted to collect 1,653 valid questionnaires from Beijing, Shanghai, Shandong province, and Fujian province. A model was constructed to understand the factors that influence WTP. The results indicate that the Chinese public is willing to pay CN 201.86 annually to support the policy of reducing greenhouse gas emissions. Participants from Beijing show the highest WTP, followed by participants from Fujian and Shandong, while those from Shanghai report the lowest WTP. The findings reveal that participants with higher income, higher satisfaction with their current life, and awareness of climate issues are willing to pay more for CO2 emissions reductions. In addition, those who are young, male and members of the Communist Party also indicate a higher WTP. The results imply that translating the public's willingness to protect climate into actions should be taken into account in China's low carbon policy. There is a need to consider the difference in degree of willingness, among different social groups, to pay for emissions reductions if the market-based mechanisms such as carbon tax were designed to facilitate emissions reductions.

Lie Symmetries,1-Dimensional Optimal System and Optimal Reductions of(1+2)-Dimensional Nonlinear Schrodinger Equation

For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, classical symmetry algebra is found and 1-dimensional optimal system, up to conjugacy, is constructed. Its symmetry reductions are performed for each class, and someexamples of exact invainvariant solutions are given.

Painlevé property, local and nonlocal symmetries, and symmetry reductions for a (2+1)-dimensional integrable KdV equation

The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé expansion is used to find the Schwartz form, the Bäcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.

What Do Tariff Reductions Mean?

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Regio-and Stereo-selective Reductions of Steroidal 4-en-3,6-dione

The different regioselective and stereoselective products were obtained by the reduction of stigmast-4,22-dien-3,6-dione with NaBH4-CH3OH when different kinds of metal ions was added to the reaction.

Symmetry Reductions, Integrability and Solitary Wave Solutions to High-Order Modified Boussinesq Equations with Damping Term

Both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou are extended to reduce the high-order modified Boussinesq equation with the damping term (HMBEDT) arising in the general Fermi-Pasta-Ulam model. As a result, several types of similarity reductions are obtained. It is easy to show that the nonlinear wave equation is not integrable under the sense of AblowRz's conjecture from the reduction results obtained. In addition, kink-shaped solitary wave solutions, which are of important physical significance, are found for HMBEDT based on the obtained reduction equation.

New Similarity Reductions and Compacton Solutions for Boussinesq-Like Equations with Fully Nonlinear Dispersion

In this paper, similarity rcductions of Boussinesq-like equations with nonlinear dispersion (simply called B(m, n) equations) utt = (un)xx + (um) which is a generalized model of Boussinesq equation uts = (u2)xx + u and modified Bousinesq equation utt = (u3)xx + uxxxx, are considered by using the direct reduction method. As a result,several new types of similarity reductions are found. Based on the reduction equations and some simple transformations,we obtain the solitary wave solutions and compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they re-emerge with the same coherent shape) of B(1, n) equations and B(m, m)equations, respectively.

SIMILARITY REDUCTIONS FOR 2+1-DIMENSIONAL VARIABLE COEFFICIENT GENERALIZED KADOMTSEV-PETVIASHVILI EQUATION

With the aid of MATHEMATICA, the direct reduction method was extended and applied in 2+1_dimensional variable coefficient generalized Kadomtsev_Petviashvili equation(VCGKPE). As a result, several kinds of similarity reductions for VCGKPE are obtained which contain Painleve Ⅰ, Painleve Ⅱ and Painleve Ⅳ reductions.

SIMILARITY REDUCTIONS FOR THE NONLINEAR EVOLUTION EQUATION ARISING IN THE FERMI-PASTA-ULAM PROBLEM

Four families of similarity reductions are obtained for the nonlinear evolution equation arising in the Fermi-Pasta-Ulam problem via using both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou.

Nonlocal symmetries and similarity reductions for Korteweg-de Vries-negative-order Korteweg-de Vries equation

The nonlocal symmetries are derived for the Korteweg–de Vries–negative-order Korteweg–de Vries equation from the Painlevétruncation method.The nonlocal symmetries are localized to the classical Lie point symmetries for the enlarged system by introducing new dependent variables.The corresponding similarity reduction equations are obtained with different constant selections.Many explicit solutions for the integrable equation can be presented from the similarity reduction.

Abundant Similarity Reductions and Dromion-Like Solutions to the Generalized Kroteweg-de Vries Equation in the (2+-1)-Dimensional Space

In this paper,eight types of (1-+1)-dimensional similarity reductions which contain variable coefficient equation,are obtained for the generalized KdV equation in (2+1)-dimensional space arising from the multidimensional isospectral flows associated with the second-order scalar operators by using the direct method.In addition,the cnoidal wave solution and dromion-like solution are also derived by using the reduced nonlinear ordinary differential equations.The (1+1) dromion obtained by Lou [J.Phys.A28 (1995) 7227] and Zhang [Chin.Phys.9 (2000) 1] is only a special case of our results.Moreover,some properties of the dromion-like solutions are analyzed.

Correlated Extra Reductions Defeat Fixed Window Exponentiation

The security of modular power algorithm is a very important research topic, which is the core operation of public key cryptography algorithm. Since the first timing attack was public in 1996, the attacker can exploit time differences between specific events to recover a secret key. In 2016, Dugardin took advantage of extra reductions to attack a regular exponentiation algorithm, which did not entirely adapt the fixed window method with Montgomery’s algorithm. The central thesis of this paper is that there exists a positive correlation between extra reductions of pre-computation and post-computation when the calculation has the same multiplier factor. In this article, basing on this dependency we present an attack method, and confirm the feasibility and effectiveness of it by conducting simulation experiments. Experimental results verify that the method can effectively attack modular power algorithm.

Large contributions of emission reductions and meteorological conditions to the abatement of PM_(2.5)in Beijing during the 24th Winter Olympic Games in 2022

To guarantee the blue skies for the 2022 Winter Olympics held in Beijing and Zhangjiakou from February 4 to 20,Beijing and its surrounding areas adopted a series of emission control measures.This provides an opportunity to determine the impacts of large-scale temporary control measures on the air quality in Beijing during this special period.Here,we applied the WRF-CMAQ model to quantify the contributions of emission reduction measures and meteorological conditions.Results show that meteorological conditions in 2022 decreased PM_(2.5)in Beijing by 6.9 and 11.8μg/m^(3)relative to 2021 under the scenarios with and without emission reductions,respectively.Strict emission reduction measures implemented in Beijing and seven neighboring provinces resulted in an average decrease of 13.0μg/m^(3)(-41.2%)in PM_(2.5)in Beijing.Over the entire period,local emission reductions contributed more to good air quality in Beijing than nonlocal emission reductions.Under the emission reduction scenario,local,controlled regions,other regions,and boundary conditions contributed 47.7%,42.0%,5.3%,and 5.0%to the PM_(2.5)concentrations in Beijing,respectively.The results indicate that during the cleaning period with the air masses from the northwest,the abatements of PM_(2.5)were mainly caused by local emission reductions.However,during the potential pollution period with the air masses from the east-northeast and west-southwest,the abatements of PM_(2.5)were caused by both local and nonlocal emission reductions almost equally.This implies that regional coordinated prevention and control strategies need to be arranged scientifically and rationally when heavy pollution events are forecasted.

Time-fractional Davey–Stewartson equation:Lie point symmetries,similarity reductions,conservation laws and traveling wave solutions

As a celebrated nonlinear water wave equation,the Davey–Stewartson equation is widely studied by researchers,especially in the field of mathematical physics.On the basis of the Riemann–Liouville fractional derivative,the time-fractional Davey–Stewartson equation is investigated in this paper.By application of the Lie symmetry analysis approach,the Lie point symmetries and symmetry groups are obtained.At the same time,the similarity reductions are derived.Furthermore,the equation is converted to a system of fractional partial differential equations and a system of fractional ordinary differential equations in the sense of Riemann–Liouville fractional derivative.By virtue of the symmetry corresponding to the scalar transformation,the equation is converted to a system of fractional ordinary differential equations in the sense of Erdélyi–Kober fractional integro-differential operators.By using Noether’s theorem and Ibragimov’s new conservation theorem,the conserved vectors and the conservation laws are derived.Finally,the traveling wave solutions are achieved and plotted.

Meteorological influences on co-occurrence of O_(3) and PM_(2.5)pollution and implication for emission reductions in Beijing-Tianjin-Hebei

Co-occurrence of surface ozone(O_(3))and fine particulate matter(PM_(2.5))pollution(CP)was frequently observed in Beijing-Tianjin-Hebei(BTH).More than 50%of CP days occurred during April-May in BTH,and the CP days reached up to 11 in two months of 2018.The PM_(2.5)or O_(3) concentration associated with CP was lower than but close to that in O_(3) and PM_(2.5)pollution,indicating compound harms during CP days with double-high concentrations of PM_(2.5)and O_(3).CP days were significantly facilitated by joint effects of the Rossby wave train that consisted of two centers associated with the Scandinavia pattern and one center over North China as well as a hot,wet,and stagnant environmental condition in BTH.After 2018,the number of CP days decreased sharply while the meteorological conditions did not change significantly.Therefore,changes in meteorological conditions did not really contribute to the decline of CP days in 2019 and 2020.This implies that the reduction of PM_(2.5)emission has resulted in a reduction of CP days(about 11 days in 2019 and 2020).The differences in atmospheric conditions revealed here were helpful to forecast the types of air pollution on a daily to weekly time scale.The reduction in PM_(2.5)emission was the main driving factor behind the absence of CP days in 2020,but the control of surface O_(3) must be stricter and deeper.

Symmetries and symmetry reductions of the combined KP3 and KP4 equation

To find symmetries,symmetry groups and group invariant solutions are fundamental and significant in nonlinear physics.In this paper,the finite point symmetry group of the combined KP3 and KP4(CKP34)equation is found by means of a direct method.The related point symmetries can be obtained simply by taking the infinitesimal form of the finite point symmetry group.The point symmetries of the CKP34 equation constitute an infinite dimensional KacMoody-Virasoro algebra.The point symmetry invariant solutions of the CKP34 equation are obtained via the standard classical Lie point symmetry method.

Surface-modified Ag@Ru-P25 for photocatalytic CO_(2) conversion with high selectivity over CH_(4) formation at the solid–gas interface

Systematic optimization of the photocatalyst and investigation of the role of each component is important to maximizing catalytic activity and comprehending the photocatalytic conversion of CO_(2) reduction to solar fuels.A surface-modified Ag@Ru-P25 photocatalyst with H_(2)O_(2) treatment was designed in this study to convert CO_(2) and H_(2)O vapor into highly selective CH4.Ru doping followed by Ag nanoparticles(NPs)cocatalyst deposition on P25(TiO_(2))enhances visible light absorption and charge separation,whereas H_(2)O_(2) treatment modifies the surface of the photocatalyst with hydroxyl(–OH)groups and promotes CO_(2) adsorption.High-resonance transmission electron microscopy,X-ray photoelectron spectroscopy,X-ray absorption near-edge structure,and extended X-ray absorption fine structure techniques were used to analyze the surface and chemical composition of the photocatalyst,while thermogravimetric analysis,CO_(2) adsorption isotherm,and temperature programmed desorption study were performed to examine the significance of H_(2)O_(2) treatment in increasing CO_(2) reduction activity.The optimized Ag1.0@Ru1.0-P25 photocatalyst performed excellent CO_(2) reduction activity into CO,CH4,and C2H6 with a~95%selectivity of CH4,where the activity was~135 times higher than that of pristine TiO_(2)(P25).For the first time,this work explored the effect of H_(2)O_(2) treatment on the photocatalyst that dramatically increases CO_(2) reduction activity.

Copper slag assisted coke reduction of phosphogypsum for sulphur dioxide preparation

The reduction of phosphogypsum(PG)to lime slag and SO_(2)using coke can effectively alleviate the environmental problems caused by PG.However,the PG decomposition temperature remains high and the product yield remains poor.By adding additives,the decomposition temperature can be further reduced and PG decomposition rate and product yield can be improved.However,the use of current additives such as Fe_(2)O_(3)and SiO_(2)brings the problem of increasing economic cost.Therefore,it is proposed to use solid waste copper slag(CS)as a new additive to reduce PG to prepare SO2,which can reduce the cost and meet the environmental benefits at the same time.The effects of proportion,temperature and thermostatic time on PG decomposition are investigated by experimental and kinetic analysis combined with FactSage thermodynamic calculations to optimize the roasting conditions.Finally,the reaction mechanism is proposed.It is found that adding CS to the coke and PG system can increase the rate of PG decomposition and SO_(2)yield while lowering the PG decomposition temperature.For example,when the CS/PG mass ratio increases from 0 to 1,PG decomposition rate increases from 83.38%to 99.35%,SO_(2)yield increases from 78.62%to 96.81%,and PG decomposition temperature decreases from 992.4℃to 949.6℃.The optimal reaction parameters are CS/PG mass ratio of 1,Coke/PG mass ratio of 0.06 at 1100℃for 20 min with 99.35%PG decomposition rate and 96.81%SO_(2) yield.The process proceeds according to the following reactions:2CaSO_(4)+ 0.7C + 0.8Fe_(2)SiO_(4)→0.8Ca_(2)SiO_(4)+ 0.2Ca_(2)Fe_(2)O_(5)+ 0.4Fe_(3)O_(4)+2SO_(2)+ 0.7CO_(2)Finally,a process for decomposing PG with coke and CS is proposed.

A cascade of in situ conversion of bicarbonate to CO_(2) and CO_(2) electroreduction in a flow cell with a Ni-N-S catalyst

Combination of CO_(2) capture using inorganic alkali with subsequently electrochemical conversion of the resultant HCO_(3)^(-)to high-value chemicals is a promising route of low cost and high efficiency.The electrochemical reduction of HCO_(3)^(-)is challenging due to the inaccessible of negatively charged molecular groups to the electrode surface.Herein,we adopt a comprehensive strategy to tackle this challenge,i.e.,cascade of in situ chemical conversion of HCO_(3)^(-)to CO_(2) and CO_(2) electrochemical reduction in a flow cell.With a tailored Ni-N-S single atom catalyst(SACs),where sulfur(S)atoms located in the second shell of Ni center,the CO_(2)electroreduction(CO_(2)ER)to CO is boosted.The experimental results and density functional theory(DFT)calculations reveal that the introduction of S increases the p electron density of N atoms near Ni atom,thereby stabilizing^(*)H over N and boosting the first proton coupled electron transfer process of CO_(2)ER,i.e.,^(*)+e^(-)+^(*)H+^(*)CO_(2)→^(*)COOH.As a result,the obtained catalyst exhibits a high faradaic efficiency(FE_(CO)~98%)and a low overpotential of 425 mV for CO production as well as a superior turnover frequency(TOF)of 47397 h^(-1),outcompeting most of the reported Ni SACs.More importantly,an extremely high FECOof 90%is achieved at 50 mA cm^(-2)in the designed membrane electrode assembly(MEA)cascade electrolyzer fed with liquid bicarbonate.This work not only highlights the significant role of the second coordination on the first coordination shell of the central metal for CO_(2)ER,but also provides an alternative and feasible strategy to realize the electrochemical conversion of HCO_(3)^(-)to high-value chemicals.