Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws

In this paper,we study systems of conservation laws in one space dimension.We prove that for classical solutions in Sobolev spaces H^(s),with s>3/2,the data-to-solution map is not uniformly continuous.Our results apply to all nonlinear scalar conservation laws and to nonlinear hyperbolic systems of two equations.

Bird species composition and conservation challenges in the Gaoligong Mountains, one of the most diverse bird areas in the world

The Gaoligong Mountains(GLGM),located in southwestern China,extend north to south along the western border of the Hengduan Mountains,spanning approximately 600 km.In this study,we consolidated findings from 17 bird surveys conducted in the GLGM between 2010 and 2022.We found that the GLGM harbors tremendous bird diversity,with a total of 796 documented bird species in the region.Nearly a quarter(23.0%)of these species are listed as state key protected species or as Chinese and global threatened species.Analysis of species richness at the county level showed a decreasing trend with increasing latitude,with the greatest diversity in Yingjiang(661 species).Observations indicated that the GLGM belongs to the Oriental realm,primarily composed of bird species from southern and southwestern China.The GLGM plays an important role in avian conservation by sheltering exceptional bird diversity,providing corridors and flyways for bird migration and dispersal,and mitigating the effects of climate change.In response to the conservation needs of birds and other wildlife,the Chinese government has established numerous protected areas within the GLGM.Despite these efforts,avian conservation still faces considerable challenges in the GLGM due to limitations in the protected area network,transboundary nature of the regions,and existing gaps in monitoring and research.

ENERGY CONSERVATION FOR THE WEAK SOLUTIONS TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOW

In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.

Diversity of Orchids in Terms of Their Distribution, Uses and Conservation in Annapurna Conservation Area of Nepal

The Annapurna Conservation Area (ACA), the first conservation area and the largest protected area (PA) in Nepal, is incredibly rich in biodiversity. Notwithstanding this, orchids in the ACA have not been explored enough yet thus making the need for ambitious research to be carried out. Previous study only included 81 species of orchids within ACA. This study aims to update the record of species and genera richness in the ACA. In total 198 species of orchids, belonging to 67 genera (40% and 62% of the total recorded orchid species and genera in Nepal) has been recorded in ACA. This represents an increase of 144% in species and 56% in genera over the previous data. Out of the 198 species, 99 were epiphytes, 6 were holomycotrophic and 93 were terrestrial. Among the 67 genera, Bulbophyllum (17) species were dominant, followed by Dendrobium (16), Herminium (10), Coelogyne, Plantanthera (9 each), Eria, Habenaria, Oberonia (8 each), Calanthe (7), and Liparis (6). Fifty-six species were found to be ornamentally significant and 85 species medicinally significant.

Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation

This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.

THE LIMITING PROFILE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS WITH A SHRINKING SELF-FOCUSING CORE

In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are bounded given functions whose self-focusing cores{x∈R^(N)|Q_(n)(x)>0} shrink to a set with finitely many points as n→∞.Motivated by the work of Fang and Wang[13],we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points,and we build the localized concentrated bound state solutions for the above equation systems.

Assessing the conservation impact of Chinese indigenous chicken populations between ex-situ and in-situ using genome-wide SNPs

Conservation programs require rigorous evaluation to ensure the preservation of genetic diversity and viability of conservation populations. In this study, we conducted a comparative analysis of two indigenous Chinese chicken breeds, Gushi and Xichuan black-bone, using whole-genome SNPs to understand their genetic diversity, track changes over time and population structure. The breeds were divided into five conservation populations(GS1, 2010, ex-situ;GS2, 2019, ex-situ;GS3, 2019, in-situ;XB1, 2010, in-situ;and XB2, 2019, in-situ) based on conservation methods and generations. The genetic diversity indices of three conservation populations of Gushi chicken showed consistent trends, with the GS3 population under in-situ strategy having the highest diversity and GS2 under ex-situ strategy having the lowest. The degree of inbreeding of GS2 was higher than that of GS1 and GS3. Conserved populations of Xichuan black-bone chicken showed no obvious changes in genetic diversity between XB1 and XB2. In terms of population structure, the GS3 population were stratified relative to GS1 and GS2. According to the conservation priority, GS3 had the highest contribution to the total gene and allelic diversity in GS breed, whereas the contribution of XB1 and XB2 were similar. We also observed that the genetic diversity of GS2 was lower than GS3, which were from the same generation but under different conservation programs(in-situ and ex-situ). While XB1 and XB2 had similar levels of genetic diversity. Overall, our findings suggested that the conservation programs performed in ex-situ could slow down the occurrence of inbreeding events, but could not entirely prevent the loss of genetic diversity when the conserved population size was small, while in-situ conservation populations with large population size could maintain a relative high level of genetic diversity.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

ON THE STABILITY OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC DIFFERENTIAL EQUATIONS

In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic solution.We also present examples of some applications.

Conservation genomics provides insights into genetic resilience and adaptation of the endangered Chinese hazelnut, Corylus chinensis

Global climate change has increased concerns regarding biodiversity loss.However,many key conservation issues still required further research,including demographic history,deleterious mutation load,adaptive evolution,and putative introgression.Here we generated the first chromosome-level genome of the endangered Chinese hazelnut,Corylus chinensis,and compared the genomic signatures with its sympatric widespread C.kwechowensis-C yunnanensis complex.We found large genome rearrangements across all Corylus species and identified species-specific expanded gene families that may be involved in adaptation.Population genomics revealed that both C.chinensis and the C.kwechowensis-C.yunnanensis complex had diverged into two genetic lineages,forming a consistent pattern of southwestern-northern differentiation.Population size of the narrow southwestern lineages of both species have decreased continuously since the late Miocene,whereas the widespread northern lineages have remained stable(C.chinensis) or have even recovered from population bottlenecks(C.kwechowensis-C.yunnanensis complex) during the Quaternary.Compared with C.kwechowensis-C. yunnanensis complex,C.chinensis showed significantly lower genomic diversity and higher inbreeding level.However,C.chinensis carried significantly fewer deleterious mutations than C.kwechowensis-C. yunnanensis complex,as more effective purging selection reduced the accumulation of homozygous variants.We also detected signals of positive selection and adaptive introgression in different lineages,which facilitated the accumulation of favorable variants and formation of local adaptation.Hence,both types of selection and exogenous introgression could have mitigated inbreeding and facilitated survival and persistence of C.chinensis.Overall,our study provides critical insights into lineage differentiation,local adaptation,and the potential for future recovery of endangered trees.

Investigation of Cavitation in NaCl Solutions in a Sonochemical Reactor Using the Foil Test Method

Ultrasonic baths and sonochemical reactors are widely used in industrial applications dealing with surface cleaningand chemical synthesis. The processes of erosion, cleaning and structuring of the surface can be typically controlledby changing relevant influential parameters. In particular, in this work, we experimentally investigate theeffect of NaCl concentration (0–5.5 mol/L) on the erosion of an aluminum foil under ultrasonic exposure at afrequency of 28 kHz. Special attention is paid to the determination of cavitation zones and their visualizationusing heat maps. It is found that at low NaCl concentration (0.3 mol/L), the foil destruction rate is higher thanin distilled water. At higher concentrations of salt, cavitation takes place mainly in the upper part of the container.

THE GLOBAL EXISTENCE OF STRONG SOLUTIONS TO THERMOMECHANICAL CUCKER-SMALE-STOKES EQUATIONS IN THE WHOLE DOMAIN

We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.

Temporal and spatial variation and prediction of water yield and water conservation in the Bosten Lake Basin based on the PLUS-InVEST model

To comprehensively evaluate the alterations in water ecosystem service functions within arid watersheds,this study focused on the Bosten Lake Basin,which is situated in the arid region of Northwest China.The research was based on land use/land cover(LULC),natural,socioeconomic,and accessibility data,utilizing the Patch-level Land Use Simulation(PLUS)and Integrated Valuation of Ecosystem Services and Tradeoffs(InVEST)models to dynamically assess LULC change and associated variations in water yield and water conservation.The analyses included the evaluation of contribution indices of various land use types and the investigation of driving factors that influence water yield and water conservation.The results showed that the change of LULC in the Bosten Lake Basin from 2000 to 2020 showed a trend of increasing in cultivated land and construction land,and decreasing in grassland,forest,and unused land.The unused land of all the three predicted scenarios of 2030(S1,a natural development scenario;S2,an ecological protection scenario;and S3,a cultivated land protection scenario)showed a decreasing trend.The scenarios S1 and S3 showed a trend of decreasing in grassland and increasing in cultivated land;while the scenario S2 showed a trend of decreasing in cultivated land and increasing in grassland.The water yield of the Bosten Lake Basin exhibited an initial decline followed by a slight increase from 2000 to 2020.The areas with higher water yield values were primarily located in the northern section of the basin,which is characterized by higher altitude.Water conservation demonstrated a pattern of initial decrease followed by stabilization,with the northeastern region demonstrating higher water conservation values.In the projected LULC scenarios of 2030,the estimated water yield under scenarios S1 and S3 was marginally greater than that under scenario S2;while the level of water conservation across all three scenarios remained rather consistent.The results showed that Hejing County is an important water conservation function zone,and the eastern part of the Xiaoyouledusi Basin is particularly important and should be protected.The findings of this study offer a scientific foundation for advancing sustainable development in arid watersheds and facilitating efficient water resource management.

Design of low-alloying and high-performance solid solution-strengthened copper alloys with element substitution for sustainable development

Solid solution-strengthened copper alloys have the advantages of a simple composition and manufacturing process,high mechanical and electrical comprehensive performances,and low cost;thus,they are widely used in high-speed rail contact wires,electronic component connectors,and other devices.Overcoming the contradiction between low alloying and high performance is an important challenge in the development of solid solution-strengthened copper alloys.Taking the typical solid solution-strengthened alloy Cu-4Zn-1Sn as the research object,we proposed using the element In to replace Zn and Sn to achieve low alloying in this work.Two new alloys,Cu-1.5Zn-1Sn-0.4In and Cu-1.5Zn-0.9Sn-0.6In,were designed and prepared.The total weight percentage content of alloying elements decreased by 43%and 41%,respectively,while the product of ultimate tensile strength(UTS)and electrical conductivity(EC)of the annealed state increased by 14%and 15%.After cold rolling with a 90%reduction,the UTS of the two new alloys reached 576 and 627MPa,respectively,the EC was 44.9%IACS and 42.0%IACS,and the product of UTS and EC(UTS×EC)was 97%and 99%higher than that of the annealed state alloy.The dislocations proliferated greatly in cold-rolled alloys,and the strengthening effects of dislocations reached 332 and 356 MPa,respectively,which is the main reason for the considerable improvement in mechanical properties.

Influence of ecological function protection zone on the water conservation in Gansu-Qinghai Contiguous Region of the upper Yellow River

The implementation of Ecological Function Protection Zone(EFPZ)policy is significant for the ecological restoration and conservation of soil and water in the territory space.This manuscript analyzed and quantified the impact of EFPZ on the regional water conservation function,based on land use data from 2005,2008,2010,2015 and 2020,by conducting a counterfactual simulation along with the GeoSOS-FLUS model and the InVEST model.The results demonstrate that the delineation of EFPZ can significantly influence the water conservation.(1)From 2010 to 2020,as the EFPZ was implemented,the water conservation in the study area was increasing year by year,with a growth rate of 0.03×10^(8) m^(3)∙a^(-1).On the other hand,the simulated water conservation capacity without the implementation of EFPZ decreased year by year,with a decrease rate of 0.01×10^(8) m^(3)∙a^(-1).(2)The EFPZ accounts for only 23%of the total area,but the contribution rate of water conservation reaches 80%.The actual values of water conservation and average water yield per unit pixel in the EFPZ show an increasing trend both internally and externally,while the counterfactual simulation values exhibit a decreasing trend.(3)The water conservation is much higher within the EFPZ than without EFPZ.The implementation of EFPZ has a significant effect on the improvement of the water conservation capacity in Maqu EFPZ and Yellow River Source EFPZ.The protection effectiveness should be enhanced in Qilian Mountain EFPZ and afforestation activities need to be carefully considered in Loess Plateau EFPZ.

Development of endemicity and conservation importance indices for tropical forests and the floral diversity assessment of Mt.Natoo in Benguet,Philippines

The scientific community faces the challenge of measuring progress toward biodiversity targets and indices have been traditionally used.However,recent inventories in secondary tropical mountain forests using traditional biodiversity indices have yielded results that are indistinct with primary ones.This shows the need to develop complementary indices that goes beyond species count but integrates the distribution and conservation status of the species.This study developed endemicity and conservation importance index for tropical forest that incorporated the distribution and conservation status of the species.These indices were applied to Mt.Natoo,a remnant primary mossy forest in Buguias,Benguet,Philippines,that resulted to endemicity index of 81.07 and conservation importance index of 42.90.Comparing these with secondary forest sites with comparable Shannon-Wiener,Simpson,Evenness and Margalef’s indices,our endemicity and conservation indices clearly differentiates primary forest(our study site)with higher values from secondary forests with much lower values.Thus,we are proposing these indices for a direct but scientifically-informed identification of specific sites for conservation and protection in tropical forests.Additionally,our study documented a total of 168 vascular plant species(79 endemic and 12 locally threatened species)in Mt.Nato-o.Majority are of tropical elements for both generic and species levels with some temperate elements that could be attributed to the site's high elevation and semi-temperate climate.These are important baseline information for conservation plans and monitoring of tropical mossy forests.

An integrable generalization of the Fokas–Lenells equation:Darboux transformation, reduction and explicit soliton solutions

Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically.

Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy

Based on the Landau-Lifshitz-Gilbert(LLG)equation,the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H_(k).The evolution of three-component magnetization is solved analytically under the condition of H=nH_(k)(n=3,1 and 0).It is found that with an increase of H or a decrease of the initial polar angle of magnetization,the relaxation time decreases and the angular frequency of magnetization increases.For comparison,the analytical solution for H_(k)=0 is also given.When the magnetization becomes stable,the angular frequency is proportional to the total effective field acting on the magnetization.The analytical solutions are not only conducive to the understanding of the precession relaxation of magnetization,but also can be used as a standard model to test the numerical calculation of LLG equation.

Study of the Relationship Between New Ionic Interaction Parameters and Salt Solubility in Electrolyte Solutions Based on Molecular Dynamics Simulation

Studying the relationship between ionic interactions and salt solubility in seawater has implications for seawater desalination and mineral extraction.In this paper,a new method of expressing ion-to-ion interaction is proposed by using molecular dynamics simulation,and the relationship between ion-to-ion interaction and salt solubility in a simulated seawater water-salt system is investigated.By analyzing the variation of distance and contact time between ions in an electrolyte solution,from both spatial and temporal perspectives,new parameters were proposed to describe the interaction between ions:interaction distance(ID),and interaction time ratio(ITR).The best correlation between characteristic time ratio and solubility was found for a molar ratio of salt-to-water of 10:100 with a correlation coefficient of 0.96.For the same salt,a positive correlation was found between CTR and the molar ratio of salt and water.For type 1-1,type 2-1,type 1-2,and type 2-2 salts,the correlation coefficients between CTR and solubility were 0.93,0.96,0.92,and 0.98 for a salt-to-water molar ratio of 10:100,respectively.The solubility of multiple salts was predicted by simulations and compared with experimental values,yielding an average relative deviation of 12.4%.The new ion-interaction parameters offer significant advantages in describing strongly correlated and strongly hydrated electrolyte solutions.

THE EXISTENCE AND UNIQUENESS OF TIME-PERIODIC SOLUTIONS TO THE NON-ISOTHERMAL MODEL FOR COMPRESSIBLE NEMATIC LIQUID CRYSTALS IN A PERIODIC DOMAIN

In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.