A COMPACT EMBEDDING RESULT FOR NONLOCAL SOBOLEV SPACES AND MULTIPLICITY OF SIGN-CHANGING SOLUTIONS FOR NONLOCAL SCHRÖDINGER EQUATIONS

For any s∈(0,1),let the nonlocal Sobolev space X^(s)(R^(N))be the linear space of Lebesgue measure functions from R^(N) to R such that any function u in X^(s)(R^(N))belongs to L2(R^(N))and the function(x,y)→(u(x)-u(y)√K(x-y)is in L^(2)(R^(N),R^(N)).First,we show,for a coercive function V(x),the subspace E:={u∈X^s(R^N):f_(R)^N}V(x)u^(2)dx<+∞}of X^(s)(R^(N))is embedded compactly into L^(p)(R^(N))for p\in[2,2_(s)^(*)),where 2_(s)^(*)is the fractional Sobolev critical exponent.In terms of applications,the existence of a least energy sign-changing solution and infinitely many sign-changing solutions of the nonlocal Schrödinger equation-L_(k)u+V(x)u=f(x,u),x∈R^N are obtained,where-L_(K)is an integro-differential operator and V is coercive at infinity.

Study of ionic wind based on dielectric barrier discharge of carbon fiber spiral electrode

Based on the idea that a large number of charged particles can be generated by a high-frequency alternating current(AC)dielectric barrier discharge(DBD),and charged particles can be accelerated directionally by a direct current(DC)electric field,a new type of ionic wind formation method is proposed in this paper.To this end,a carbon fiber spiral electrode serves as the generation electrode and a metal rod electrode as the collection electrode,with AC and DC potentials applied respectively to the generation electrode and the collection electrode to form an AC-DC coupled electric field.Under the action of the coupled electric field,a dielectric barrier discharge is formed on the carbon fiber spiral electrode,and the electrons generated by the discharge move from the generation electrode to the collection electrode in the opposite direction of the electric field vectors.During the movement,energy is transferred to the gas molecules by their colliding with neutral gas molecules,thereby forming a directional gas stream movement,i.e.ionic wind.In the research process,it is verified through electric field simulation analysis and discharge experiment that this method can effectively increase the number of charged particles in the discharge process,and the velocity of the ionic wind is nearly doubled.On this basis,the addition of a third electrode forms a distinct discharge region and an electron acceleration region,which further increases its velocity.The experimental result shows that the ionic wind speed reaches up to 2.98 m s^?1.Thanks to the ability of the electrode structure to generate an atmospheric pressure DBD plasma and form an ionic wind,we can create a noise-free air purification device without resorting to a fan,with this device having good application prospects in the field of air purification.

Inhibitory Effect of 16 Fungicides on Persimmon Anthracnose Pathogen Colletotrichum horii

In this research,the inhibitory effect of 16 fungicides on Colletotrichum horri causing persimmon anthracnose was investigated using mycelial growth method and spore germination method. The results showed that among the 16 tested fungicides,10% of Difenoconazole WG,33. 5% of Copper quinolate SC,25%of Bromothalonil EC,70% of Mancozeb WP,430 g/L of Tebuconazole SC,50% of Prochloraz-manganese chloride and 400 g/L of Flusilazole EC achieved the best inhibitory effect on mycelial growth of C. horri,with the inhibition rate of 100%; 70% of Polyram WG,33. 5% of Copper quinolate SC,25% of Bromothalonil EC,70% of Mancozeb WP,50% of Chlorobromoisocyanuric acid AF,50% of Triram WP and 400 g/L of Flusilazole achieved the best inhibitory effect on spore germination of C. horri,with the germination rate of 0. In conclusion,33. 5% of Copper quinolate SC,25% of Bromothalonil EC,70% of Mancozeb WP and 400 g/L of Flusilazole EC achieved the best inhibitory effect both in mycelial growth and spore germination,which could be used as the preference fungicides for the control of persimmon anthracnose,and 70% of Polyram WG and 50% of Triram WP achieved the secondly best inhibitory effect,which could be used as alternative fungicides. The results of this research could provide scientific evidence for the effective control of persimmon anthracnose,and more optional pesticides for utilization in the production practice of persimmon industry.

Biological Characteristics of Persimmon Anthracnose Pathogen Colletotrichum horii and Screening of Inhibitory Fungicides

This experiment studied the biological characteristics of Colletotrichum horii causing persimmon anthracnose using the crossing method and blood cell counting plate method,and screened inhibitory fungicides via assessing the effects of 16 common fungicides on the mycelial growth and spore germination. The results showed that the most suitable temperature for mycelial growth of C. horri is 25℃,the most suitable temperature for spore germination is 28℃; the suitable p H for mycelial growth of C. horri is 4. 0-6. 0,the most suitable p H for spore germination is 4. 0; the optimal carbon source is glucose and maltose,and the optimal source of nitrogen is beef extract. Among the 16 common fungicides,33. 5% copper quinolate SC,25% bromothalonil EC and 70% Mancozeb WP have the optimal inhibitory effects on the mycelial growth and spore germination of C. horri,and can be used as preferred agent for prevention and control of persimmon anthracnose,followed by70% Polyram WG,400 g/L Flusilazole EC and 50% Thiram WP,which can be used as alternative agents. The results are expected to provide experimental basis for effective control of persimmon anthracnose.

Technical Studies of Controlling Jujube Witches Broom Disease with Resistant Rootstock

[Objectives]The paper was to screen and identify the control effect of resistant rootstock on jujube witches broom disease.[Methods]The seeds or branches of disease-free plants were collected from wild jujube bushes infected by witches broom disease,and 5434 seedlings were obtained by sowing or cutting.The virus was inoculated by grafting diseased bark.After 6 years of preliminary screening,40 plants with resistance to jujube witches broom disease were obtained.Taking these resistant plants as the rootstocks,the susceptible variety‘long red jujube’was grafted at a height of 40 cm.When the plants grew to appropriate thickness,diseased bark was grafted to‘long red jujube’and rootstock to transmit the virus.After 18 years of observation and judgment,4 rootstock strains with high resistance or immunity to jujube witches broom disease were finally determined,namely 90801,90803,90806 and 908011.The susceptible variety‘long red jujube’was grafted to 4 rootstocks and inoculated the virus through diseased bark grafting method.[Results]The resistant rootstock had obvious disease resistance effect.When the branches of 90801 and 90803 rootstocks were grafted to the trunk of diseased trees,the symptoms of jujube witches broom disease gradually alleviated till disappeared.[Conclusions]Using germplasm with high resistance or immunity to jujube witches broom disease as rootstock can effectively prevent the spread of jujube witches broom disease,and bridging the trunk of diseased trees with branches from resistant rootstock has certain therapeutic effect.

Effects of Different Density-reducing Methods on Canopy Microenvironment, Tree Growth and Fruit Quality in Closed Apple Orchard

In order to optimize and transform closed mature apple orchards with standard rootstocks and improve the quality of fruit,taking a closed Red Fuji apple orchard as the test object,the effects of different density-reducing methods(deinterlacing,removing every other plant in each row,removing every other plant every other row)on the canopy microenvironment,tree structure,leaf photosynthesis and fruit quality were studied.The results showed that different density-reducing methods significantly reduced the orchard coverage and increased the crown transmittance.Among them,the deinterlacing treatment was the best in improving the population structure of the closed orchard,as it reduced the orchard coverage rate by 55.68 percentage points and the canopy transmittance by 82.38 percentage points,compared with the control(CK).Different density-reducing methods all could significantly reduce the branch amount in the closed orchard and optimized the branch composition.The three density-reducing methods decreased the number of branches per plant by 18.96%,12.41%and 19.58%,respectively,compared with the CK.And compared with the CK,the proportion of short branches and leafy branches to the total branches was increased by 17.13%,14.27%and 7.37%,respectively,and the proportion of long branches and developmental branches to the total branches was decreased by 24.47%,18.04%and 10.79%,respectively.The effects of the different density-reducing methods on the temperature,relative light intensity,SPAD and leaf photosynthetic rate in canopies all followed an order of deinterlacing>removing every other plant in each row>removing every other plant every other row>CK,while those on the relative humidity showed an order of deinterlacing>removing every other plant in each row>removing every other plant every other row>CK,while those on the relative humidity showed an order of deinterlacing<removing every other plant in each row<removing every other plant every other row<CK.The average single fruit weight(238.3 g),coloring index(89.2),smoothness index(83.2),soluble solid content(15.1%)and high quality fruit rate(82.4%)of the deinterlacing treatment were higher than those of other treatments,and the values were 18.2%,11.4%,5.85%,26.9%and 25.2%higher than the CK,respectively.The use of dein￣terlacing to reduce density is the best for improving the microenvironment of closed apple orchards and improving the photosynthetic efficiency and fruit quality.

Evaluation on Application and Spraying Effect of Air-Assisted Sprayer in Apple Orchard with Dwarfing Rootstocks

The application and spraying effect of 3 WG-1200 A air-assisted sprayer in dwarfing rootstock apple orchard were evaluated by investigating the droplet density, coverage and volume median diameter(VMD) in different canopy layers(2.0, 1.5, 1.0 m) and five directions(east, south, west, north and middle) of apple trees. The results showed that the droplet density was 166.99 per square centimeter, the coverage was 48.23%, and the VMD was 138.63 μm. The droplet density in different canopy layers of the trees had consistent trend with the coverage. The droplet density and coverage in the upper and middle canopy(2.0 m and 1.5 m) had no significant difference, but they were both higher than those in the lower canopy, while the VMD in different canopy layers showed an opposite trend. The change trends of the coverage and VMD in the five directions were consistent, and the values in the middle and east were the highest, followed by the north, south and west, respectively. The results indicated that droplet characteristics of the 3 WG-1200 A air-assisted sprayer met the basic requirements for pest and pathogen control. This study provides a theoretical basis and data support for the application and improvement of orchard application equipments in dwarfing rootstock apple orchard.

A new structural reliability index based on uncertainty theory

The classical probabilistic reliability theory and fuzzy reliability theory cannot directly measure the uncertainty of structural reliability with uncertain variables, i.e., subjective random and fuzzy variables. In order to simultaneously satisfy the duality of randomness and subadditivity of fuzziness in the reliability problem, a new quantification method for the reliability of structures is presented based on uncertainty theory, and an uncertainty-theory-based perspective of classical Cornell reliability index is explored. In this paper, by introducing the uncertainty theory, we adopt the uncertain measure to quantify the reliability of structures for the subjective probability or fuzzy variables, instead of probabilistic and possibilistic measures. We utilize uncertain variables to uniformly represent the subjective random and fuzzy parameters, based on which we derive solutions to analyze the uncertainty reliability of structures with uncertainty distributions. Moreover, we propose the Cornell uncertainty reliability index based on the uncertain expected value and variance.Experimental results on three numerical applications demonstrate the validity of the proposed method.