BOUNDARY BLOW-UP RATE OF THE LARGE SOLUTION FOR AN ELLIPTIC COOPERATIVE SYSTEM

In this article we consider positive large solution of cooperative systems of the form -△u1=λ1u1 + a1u1u2^q1 -b1(x)u1^p1+1,-△u2=λ2u2 + a2u1^q2u2 -b2(x)u2^p2+1 in a bounded smooth domainΩ■ R^N(λi ∈ R, ai, bi>0, 0 < qi < pj, i, j ∈{1, 2}, i ≠ j), Based on the construction of certain sup and sub-solution, we show existence, uniqueness and blow-up rate of the large solution.

Blow-up rate and profile for a class of quasilinear parabolic system

This paper deals with positive solutions to a class of nonlocal and degenerate quasilinear parabolic system with null Dirichlet boundary conditions. The blow-up rate and blow-up profile are gained if the parameters and the initial data satisfy some conditions.

Uniform blow-up rate for compressible reactive gas model

The Dirichlet initial-boundary value problem of a compressible reactive gas model equation with a nonlocal nonlinear source term is investigated. Under certain conditions, it can be proven that the blow-up rate is uniform in all compact subsets of the domain, and the blow-up rate is irrelative to the exponent of the diffusion term, however, relative to the exponent of the nonlocal nonlinear source.

GLOBAL BLOWUP AND BLOWUP RATE ESTIMATES OF SOLUTIONS FOR A CLASS OF NONLINEAR NON-LOCAL REACTION-DIFFUSION PROBLEMS

In this paper, the global blowup properties of solutions for a class of nonlinear non-local reaction-diffusion problems are investigated by the methods of the prior estimates. Moreover, the blowup rate estimate of the solution is given.

铅银渣侧吹熔化-烟化过程中锑物相演化研究

我国铅锌矿产资源比较丰富,在湿法炼锌过程产生了大量的铅银渣,铅银渣中含有铅、银、锌、铜、锑等多种有价金属,铅银渣中有价金属的回收处理一直制约行业发展。目前,铅银渣在侧吹熔化-烟化过程中锑物相的演化规律尚缺乏系统的研究,因此本文通过热力学理论计算确定铅银渣中锑的存在形式,考察了反应温度、配碳比、保温时间对锑回收率的影响,并通过响应曲面法得出最优工艺条件。试验结果表明,铅银渣侧吹熔化-烟化过程中锑回收率的最优工艺:反应温度为1290℃,配碳比为17.60%,保温时间为125 min,在此条件下锑的回收率可达到82.54%。该研究为回收铅银渣中的锑以及实现铅银渣资源化利用提供了参考依据。

Diagnostic performance of dynamic contrast-enhanced magnetic resonance imaging parameters and serum tumor markers in rectal carcinoma prognosis

BACKGROUND Rectal carcinoma(RC),one of the most common malignancies globally,presents an increasing incidence and mortality year by year,especially among young people,which seriously affects the prognosis and quality of life of patients.At present,dynamic contrast-enhanced magnetic resonance imaging(DCE-MRI)parameters and serum carbohydrate antigen 19-9(CA19-9)and CA125 Levels have been used in clinical practice to evaluate the T stage and differentiation of RC.However,the accuracy of these evaluation modalities still needs further research.This study explores the application and value of these methods in evaluating the T stage and differentiation degree of RC.AIM To analyze the diagnostic performance of DCE-MRI parameters combined with serum tumor markers(TMs)in assessing pathological processes and prognosis of RC patients.METHODS A retrospective analysis was performed on 104 RC patients treated at Yantai Yuhuangding Hospital from May 2018 to January 2022.Patients were categorized into stages T1,T2,T3,and T4,depending on their T stage and differentiation degree.In addition,they were assigned to low(L group)and moderate-high differentiation(M+H group)groups based on their differentiation degree.The levels of DCE-MRI parameters and serum CA19-9 and CA125 in different groups of patients were compared.In addition,the value of DCE-MRI parameters[volume transfer constant(Ktrans),rate constant(Kep),and extravascular extracellular volume fraction(Ve)in assessing the differentiation and T staging of RC patients was discussed.Furthermore,the usefulness of DCE-MRI parameters combined with serum CA19-9 and CA125 Levels in the evaluation of RC differentiation and T staging was analyzed.RESULTS Ktrans,Ve,CA19-9 and CA125 were higher in the high-stage group and L group than in the low-stage group and M+H Group,respectively(P<0.05).The areas under the curve(AUCs)of the Ktran and Ve parameters were 0.638 and 0.694 in the diagnosis of high and low stages,respectively,and 0.672 and 0.725 in diagnosing moderate-high and low differentiation,respectively.The AUC of DCE-MRI parameters(Ktrans+Ve)in the diagnosis of high and low stages was 0.742,and the AUC in diagnosing moderate-high and low differentiation was 0.769.The AUCs of CA19-9 and CA-125 were 0.773 and 0.802 in the diagnosis of high and low stages,respectively,and 0.834 and 0.796 in diagnosing moderate-high and low differentiation,respectively.Then,we combined DCE-MRI(Ktrans+Ve)parameters with CA19-9 and CA-125 and found that the AUC of DCE-MRI parameters plus serum TMs was 0.836 in the diagnosis of high and low stages and 0.946 in the diagnosis of moderate-high and low differentiation.According to the Delong test,the AUC of DCE-MRI parameters plus serum TMs increased significantly compared with serum TMs alone in the diagnosis of T stage and differentiation degree(P<0.001).CONCLUSION The levels of the DCE-MRI parameters Ktrans and Ve and the serum TMs CA19-9 and CA125 all increase with increasing T stage and decreasing differentiation degree of RC and can be used as indices to evaluate the differentiation degree of RC in clinical practice.Moreover,the combined evaluation of the above indices has a better effect and more obvious clinical value,providing important guiding importance for clinical condition judgment and treatment selection.

具零阶耗散的Degasperis-Procesi方程的Blow-up现象

研究了具有零阶耗散的Degasperis-Procesi方程的初值问题,应用Kato定理得到了方程初值问题解的局部适定性,然后研究了解的blow-up现象.

BLOW-UP ESTIMATES FOR A NON-NEWTONIAN FILTRATION SYSTEM

The prior estimate and decay property of positive solutions are derived for a system of quasi- linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blowup estimates for a class quasi-linear reaction-diffusion systems ( non-Newtonian filtration systems) are established, which extends the result of semi-linear reaction diffusion( Fujita type) systems.

BLOW-UP RESULTS AND ASYMPTOTIC BEHAVIOR OF THE EMDEN-FOWLER EQUATION u″=|u|~p

In this article the author works with the ordinary differential equation u＂ = ｜u｜^p for some p 〉 0 and obtains some interesting phenomena concerning blow-up, blow-up rate, life-span, stability, instability, zeros and critical points of solutions to this equation.

Process for improving the ladle free- opening rate for high aluminum steel in continuous casting

Steel 20Mn23AlV is a type of high aluminum steel with a very low ladle free-opening rate. The aluminum composition of 20Mn23AlV ranges from 1.6% to 2.45% ,which is significantly higher than other types of steel. According to the real condition of 40 t ladle in steel-making plant of Baosteel Special Steel Company, previous works show that the key factors affecting the ladle free-opening rate of high aluminum steel in continuous casting are：sand material, accessories baking, ladle nozzle cleaning, the process and amount of adding sand, and the rate of argon stirring during refining. Therefore, improving the ladle filler sand quality, baking all of the raw materials, controlling the addition of ladle filler sand, cleaning the ladle nozzle, and optimizing argon stirring during the refining process can resolve the problem of a low ladle free-opening rate of high aluminum steel caused by the long ladle time of liquid steel.

Effect of varying normal stress on stability and dynamic motion of a spring-slider system with rate- and state-dependent friction

Incorporating rate and state friction laws, stability of linearly stable （i.e., with stiffness greater than the critical value） spring-slider systems subjected to triggering perturbations was analyzed under variable normal stress condition, and comparison was made between our results and that of fixed normal stress cases revealed in previous studies. For systems associated with the slip law, the critical mag- nitude of rate steps for triggering unstable slips are found to have a similar pattern to the fixed normal stress case, and the critical velocity steps scale with a/（b - a） when k = kcr for both cases. The rate-step boundaries for the variable normal stress cases are revealed to be lower than the fixed normal stress case by 7 %-16 % for a relatively large ct = 0.56 with （b - a）/a ranging from 0.25 to 1, indicating easier triggering under the variable normal stress condition with rate steps. The difference between fixed and variable normal stress cases decreases when the α value is smaller. In the same slip- law-type systems, critical displacements to trigger instability are revealed to be little affected by the variable normal stress condition. When k 〉 kcr（V,）, a spring-slider system with the slowness law is much more stable than with the slip law,suggesting that the slowness law fits experimental data better when a single state variable is adopted. In stick-slip motions, the variable normal stress case has larger stress drops than the constant normal stress case. The variable normal stress has little effect on the range of slip velocity in systems associated with the slowness law, whereas systems associated with the slip law have a slowest slip velocity immensely smaller than the fixed normal stress case, by ~ 10 orders of magnitude.

THE BLOW-UP PROPERLIES OF SOLUTIONS TO SEMILINEAR HEAT EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

This paper deals with the blow-up properties of solutions to semilinear heat equation ut-uxx= up in (0, 1) × (0, T) with the Neumann boundary condition ux(0, t) = 0, u:x1, t) = 1 on [0, T). The necessary and sufficient conditions under which all solutions to have a finite time blow-up and the exact blow-up rates are established. It is proved that the blow-up will occur only at the boundary x = 1. The asymptotic behavior near the blow-up time is also studied.

Effect of cooling rate on evolution of superconducting phases during decomposition and recrystallization of (Bi,Pb)-2223 core in Ag-sheathed tape

The reformation of (Bi,Pb)-2223 from the liquid or melt is very important for a melting process of (Bi,Pb)-2223 tape. By combination of quenching experiment with X-ray diffraction (XRD) analysis, the effect of cooling rate on the evolution of three superconducting phases in the (Bi,Pb)-2223 core of Ag-sheathed tape was investigated. The results show that (Bi,Pb)-2223 reformation from the melt seems to experience different routes during slowly cooling at different rates. One is that (Bi,Pb)-2223 phase reformed directly from the melt, and no Bi-2212 participate in this process. The other is that (Bi,Pb)-2223 is converted from the intermediate product, Bi-2212, which formed from the melt during the first cooling stage. Due to the inherent sluggish formation kinetics of (Bi,Pb)-2223 from Bi-2212, only partial (Bi,Pb)-2223 can finally be reformed with the second route.

On the Blow-up Phenomena of Cauchy Problem for the Camassa-Holm Equation

We focus on the blow-up phenomena of Cauchy problem for the Camassa-Holm equation. Blow-up can occur only in the form of wave-breaking, i.e. the solution is bounded but its slope becomes unbounded in finite time. We proved that there is such a point that its slope becomes infinite exactly at breaking time. We also gave the precise blow-up rate and the blow-up set.

APPROCHING A BLOW-UP POINT IN ONE-DIMENSIONAL SEMILINEAR HEAT SYSTEMS

In this paper, using self-similar variablies technique we consider asymptotic behavior of blowing up solution of Cauchy problem and Dirichlet problem for onedimensional heat systems near blow-up time.

Effect of gas blowing nozzle angle on multiphase flow and mass transfer during RH refining process

A three-dimensional mathematical model was developed to investigate the effect of gas blowing nozzle angles on multiphase flow,circulation flow rate,and mixing time during Ruhrstahl-Heraeus(RH) refining process.Also,a water model with a geometric scale of 1:4 from an industrial RH furnace of 260 t was built up,and measurements were carried out to validate the mathematical model.The results show that,with a conventional gas blowing nozzle and the total gas flow rate of 40 L·min^(-1),the mixing time predicted by the mathematical model agrees well with the measured values.The deviations between the model predictions and the measured values are in the range of about 1.3%–7.3% at the selected three monitoring locations,where the mixing time was defined as the required time when the dimensionless concentration is within 3% deviation from the bath averaged value.In addition,the circulation flow rate was 9 kg·s^(-1).When the gas blowing nozzle was horizontally rotated by either 30° or 45°,the circulation flow rate was found to be increased by about 15% compared to a conventional nozzle,due to the rotational flow formed in the up-snorkel.Furthermore,the mixing time at the monitoring point 1,2,and 3 was shortened by around 21.3%,28.2%,and 12.3%,respectively.With the nozzle angle of 30° and 45°,the averaged residence time of 128 bubbles in liquid was increased by around 33.3%.

Plastic Flow Modeling of Ti-5 Al-2 Sn-2 Zr-4 Mo-4 Cr Alloy at Elevated Temperatures and High Strain Rates

The true stress-sWain relationships of Ti-5A1-2Sn-2Zr-4Mo-4Cr（TC17） alloy with a wide range of strain rates were investigated by tmiaxial quasi-static and dynamic compression tests, respectively. Quasi- static compression tests were carried out with Instron 8874 test machine, while dynamic compression tests were performed with the split Hopkinson pressure bar （SHPB） which was installed with heating device and synchro- assembly system. The dynamic mechanical behaviors tests of TC17 were carded out from room temperature to 800 ℃ at intervals of 200 ℃ and at high sWain rates （5 500-1 9200 s-l）. The stress-strain curves considering temperature-sWain rate coupling actions were obtained. The Johnson-Cook constitutive model was developed through data fitting of the stress-sWain curves. The material constants in the developed constitutive model can be determined using isothermal and adiabatic stress-strain curves at different strain rates. The Johnson-Cook constitutive model provided satisfied prediction of the plastic flow stress for TC17 alloy.

THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS

This paper deals with the blow-up properties of solutions to the systems ut u(t) - Delta u = e(v(xo,t)), v(t) - Delta v = e(u(xo,t)) in Omega x (0,T) subject to either initial conditions or the initial and boundary-value conditions. The authors show that under certain conditions the solution blows up in finite time and prove that the set of all blow-up points is the whole region. Moreover, the exact blow-up rates are also derived.

Performance Analysis of Outage Probability and Error Rate of Square M-QAM in Mobile Wireless Communication Systems over Generalized α-μ Fading Channels with Non-Gaussian Noise

This paper derives new and exact closed-form expressions for the average symbol error rate(SER) of square M-ary quadrature amplitude modulation(M-QAM) in wireless communication systems over theα-μfading channels subject to an additive non-Gaussian noise. The obtained expressions take into account static and mobile wireless receivers. In addition, a closed-form expression for the outage probability in mobile networks is obtained. Please note that all derived expressions in this paper a valid for integer and non-integer values of the fading parameters. Analytical results are presented to study the impact of noise shaping parameter, severity of fading, and mobility on the average SER. Monte-Carlo simulations results are also provided to validate the accuracy of the analytical results.

NO_3^-/NH_4^+ ratios affect plant growth, chlorophyll content,respiration rate, and morphological structure in Malus hupehensis seedlings

Malus hupehensis （Pamp.） Rehd. is a widely cultivated rootstock in China. We studied the effect of three NO3-/NH4＋ ratios （100/0, 50/50, and 0/100, molar basis） at total nitrogen （N） concentration of 8 mmoL L-1 in a nutrient solution on M. hupehensis seedlings. Plant biomass, NO3- and NH4＋concentrafion, chlorophyll con- tent, respiratory rate, and cellular structure were investi- gated. M. hupehensis seedlings at the NO3-/NH4＋ ratio of 50/50 had the highest level of fresh weight, dry weight, shoot length, and chlorophyll （a, b, and a ＋ b） content, but the lowest respiration rate in the leavesand roots. In addition, thickness and numbers of palisade and spongy tissue cells of the leaves were greater with this treatment than with other treatments. At the NO3-/NH4＋ ratio of 100/0, the leaves and roots had higher NO3- concentration and lower NH4＋ concentration. However, the opposite trend occurred at the NO3-/NH4＋ ratio of 0/100. Chloro- phyll （a, b, and a ＋ b） content was lowest at the NO3-/NH4＋ ratio of 100/0 than at the other ratios. At the NO3-/ NH4＋ ratio of 0/100, oxygen （02） consumption increased in the leaves and roots, and irregular epidermis and cortex cells were observed in the root apical meristematic and mature region. Our results indicated that the NO3-INH4＋ ratio at 50/50 was suitable for growth of M. hupehensis seedling to achieve the highest biomass production and efficiency.