关于线性微分多项式的Hayman-Yang不等式

下述问题得到彻底解决：在著名的Hayman-Yang不等式中，k阶导数f^(k)能否被替代换成一般的k阶线性微分多项式α0f α1f …αkf^(k)？一个例子表明本文中的结果是最基本的，定理的条件不能减弱。     

具有两项密指量的基本不等式

对Hayman—Yang不等式中导数f^（k）能否被替换成一般的线性微分多项式a0f＋a1f＇＋…＋akf^（k）进行了研究,并彻底解决了这一问题．实例表明,所得到的几个定理的条件是基本的．     

关于一类三角级数的和

讨论在力学、无线电技术和电信工程中经常碰到的以下三类三角级数 sum from k=1 to ∞_(sin)~(cos)(mk±s)x, sum from k=1 to ∞(-1)~(k +1)_(sin)~(cos)(mk±s)x; (1) sum from k=1 to ∞(1/mk±s)_(sin)~(cos)(mk±s)x sum from n=1 to ∞((-1)~(n+1)/mk±s)_(sin)~(cos)(mk±s)x; (2) sum from k=1 to ∞(1/mk±s)_(sin)~(cos)mkx, sum from k=1 to ∞((-1)~(n+1)/mk±s)_(sin)~(cos)mkx (3) (式中m是正整数,s是非负整数)的求和问题,使用了与文[1]中稍有不同的方法,并顺便指出了文[1]和[2]中的几处错误。     

食品溶液凝固点下降的解析计算方法探讨

本文探讨了食品冻结点下降的解析计算的新思想、新方法，得出ln{(1-Xs)/(1-Xs αXs βXs^2）}=A(1/TO-1/Tf)-B1n(To/Tf）。该式与实测结果吻合较好。     

DVB-T2协议中降低DMT峰值平均功率比的PTS技术

<正>1 DTM技术中PAPR DTM技术上,假定有若干个相互垂直的子载波,把这些子载波设定为n,基带域设定为X(k)(k=0,1,…,N-1),其对应的域信号式为x(n)=IFFT{X(k)}(n=0,1,…,N-1)。所以,x(n)的PAPR计算式可表示为:     

两个三角恒等式及其应用

用逼近论方法证明了下述两个三角恒等式:sin((m/2)-s′)ζcscm(ζ/2)=-(1/m)(sum from k=0 to m-1)sin(2ks′π)/(m)·(cos(ζ/2)-(kπ/m))/(sin(ζ/2)-(kπ/m)),(1)cos((m/2)-s′)ζcscm(ζ/2)=(1/m)(sum from k=0 to m-1)cos(2ks′π)/(m)·(cos(ζ/2)-(kπ/m))/(sin(ζ/2)-(kπ/m)).(2)式中 m、s′都是正整数,且0<′s相似文献   

确定离散系统线性调节器加权矩阵的参数化方法

考虑一个线性定常可控多变量离散系统X_(k+1)=AX_k+BU_K以及线性二次型性能指标∫=sum from k=0 to ∞ (X_k~T Q X_k)+U_k~TRU_k),Q≥0,R>0.由最优控制理论知,使上式极小的最优控制规律为U=-FX_k=-(R+B~TpB)~(-1) B~TPAX_k,式中P满足矩阵代数Riccati方程P=A~TPA-A~TPB(P+B~TPB)~(-1)B~TPA+Q因此,我们有最优闭环系统X_(k+1)=(A-BF)X_k=A_cX_k     

亚纯函数的正规族与分担集

应用Zalcman-Pang引理,研究了涉及分担集的亚纯函数正规族,所得定理推广了林国斌与陈俊凡的结果．设F为区域D内的一族亚纯函数,h为有穷正数,k为正整数,S={b1,b2},其中b1,b2是2个互异有穷复数,若Vf∈F,f-bi（i=1,2）的零点重级至少为k,且满足（1）f和L（f）分担集合S,（2）当L（f）（z）∈S时,f^（k＋1）（z）≠0且L′（f）（z）｜≤h,则F在区域D内正规．     

关于Lucas数的一类行列式的计算

研究了一类由Lucas数组成的行列式Ln(m,k，l)的计算问题，证明了当m≤n-2时有恒等式Ln(m，k，l)=0，当m=n-1时给出了一个计算其值的公式。     

特殊度条件下有向图的最大有向割

对于整数k,l≥0,用D(k,l)表示一类有向图的集合,这类图的每个顶点要么入度不超过k要么出度不超过l.研究了度条件下有向图中的最大有向割问题,目的是确定图类D(k,l)中有向图的最大有向割包含的弧的条数.对于包含m条弧的有向图,通过分析图的结构,采用数学归纳法,得到(1)若D∈D(2,3)∪D(3,2),则存在至少包含2m/7条弧的有向割;(2)设D∈D(k,k),若存在顶点集的一个二部划分(X,Y),使得X中点的入度与Y中点的出度都不超过k,并且起点在X中终点在Y中的弧的集合的导出图的基础图不含圈,则存在至少包含(1/4+1/(8k+4))m条弧的有向割.     

涉及重级的亚纯函数族的正规定则

针对徐焱的定理给出了其逆命题成立的条件,进一步改进了Hayman猜想.并得到了新的正规定则:k∈N,设F是D内亚纯函数族,(V)f∈F在D内的零点之级≥k+2,极点之级≥2,h(z)≠0是D上的亚纯函数,若f(k)(z)≠h(z),z∈D,则F在D内正规.     

The Arrhenius equation revisited

The Arrhenius equation has been widely used as a model of the temperature effect on the rate of chemical reactions and biological processes in foods. Since the model requires that the rate increase monotonically with temperature, its applicability to enzymatic reactions and microbial growth, which have optimal temperature, is obviously limited. This is also true for microbial inactivation and chemical reactions that only start at an elevated temperature, and for complex processes and reactions that do not follow fixed order kinetics, that is, where the isothermal rate constant, however defined, is a function of both temperature and time. The linearity of the Arrhenius plot, that is, Ln[k(T)] vs. 1/T where T is in °K has been traditionally considered evidence of the model's validity. Consequently, the slope of the plot has been used to calculate the reaction or processes' "energy of activation," usually without independent verification. Many experimental and simulated rate constant vs. temperature relationships that yield linear Arrhenius plots can also be described by the simpler exponential model Ln[k(T)/k(T(reference))] = c(T-T(reference)). The use of the exponential model or similar empirical alternative would eliminate the confusing temperature axis inversion, the unnecessary compression of the temperature scale, and the need for kinetic assumptions that are hard to affirm in food systems. It would also eliminate the reference to the Universal gas constant in systems where a "mole" cannot be clearly identified. Unless proven otherwise by independent experiments, one cannot dismiss the notion that the apparent linearity of the Arrhenius plot in many food systems is due to a mathematical property of the model's equation rather than to the existence of a temperature independent "energy of activation." If T+273.16°C in the Arrhenius model's equation is replaced by T+b, where the numerical value of the arbitrary constant b is substantially larger than T and T(reference), the plot of Ln k(T) vs. 1/(T+b) will always appear almost perfectly linear. Both the modified Arrhenius model version having the arbitrary constant b, Ln[k(T)/k(T(reference)) = a[1/ (T(reference)+b)-1/ (T+b)], and the exponential model can faithfully describe temperature dependencies traditionally described by the Arrhenius equation without the assumption of a temperature independent "energy of activation." This is demonstrated mathematically and with computer simulations, and with reprocessed classical kinetic data and published food results.     

酯水解行为与其烷基极化效应指数关系和酯与阿拉伯胶缔合行为的研究和应用

本文运用电导法测定了不同浓度的乙醇溶液中脂肪酸酯的水解速率常数(k),并对脂肪酸乙酯类化合物的分子结构、水解条件与k的关系进行了相关分析,并推导得出酯类化合物k与烷基极化效应指数PEI(R)及体系介电常数(ε)间的关系表达式:lgk=a+blgPEI(R)+clgε,为研究酯水解机理主要影响因素、预测其k和判断酯的结构提供了一定的理论依据。同时研究了38%(V/V)乙醇溶液中阿拉伯胶(简称GA)与脂肪酸酯之间的缔合行为,并建立了定量确定缔合常数(A)的方法,推导并验证了定量表达酯水解速率常数k与GA浓度(M)关系的数学表达式:k’=k/(1+AM),得出了GA对脂肪酸酯水解起禁阻作用的结论。其研究结果用于38°清香型汾酒稳定性的提高取得了令人满意的效果。     

Study of the OH and Cl-initiated oxidation, IR absorption cross-section, radiative forcing, and global warming potential of four C4-hydrofluoroethers

Infrared absorption cross-sections and OH and Cl reaction rate coefficients for four C4-hydrofluoroethers (CF3)2CHOCH3, CF3CH2OCH2CF3, CF3CF2CH2OCH3, and CHF2CF2CH2OCH3 are reported. Relative rate measurements at 298 K and 1013 hPa of OH and Cl reaction rate coefficients give k(OH+(CF3)2CHOCH3) = (1.27+/-0.13) x 10(-13), k(OH+CF3CH2OCH2CF3) = (1.51+/-0.24) x 10(-13), k(OH+CF3CF2CH2OCH3) = (6.42+/-0.33) x 10(-13), k(OH+CHF2CF2CH2OCH3) = (8.7 +/-0.5) x 10(-13), k(Cl+(CF3)2CHOCH3) = (8.4+/-1.3) x 10(-12), k(Cl+CF3CH2OCH2CF3) = (6.5+/-1.7) x 10(-13), k(Cl+CF3CF2CH2OCH3) = (4.0+/-0.8) x 10(-11), and k(Cl+CHF2CF2CH2OCH3) = (2.65+/-0.17) x 10(-11) cm3 molecule(-1) s(-1). The primary products of the OH and Cl reactions with the fluorinated ethers have been identified as esters, and OH and Cl reaction rate coefficients for one of these, CF3CH2OCHO, are reported: k(OH+CF3CH2OCHO) = (7.7+/-0.9) x 10(-14) and kCl+CF3CH2OCHO) = (6.3+/-1.9) x 10(-14) cm3 molecule(-1) s(-1) The rate coefficient for the Cl-atom reaction with CHF2CH2F is derived as k(Cl+CHF2CH2F) = (3.0+/-0.9) x 10(-14) cm3 molecule(-1) s(-1) at 298 K. The error limits include 3sigma from the statistical data analyses as well as the errors in the rate coefficients of the reference compounds employed. The tropospheric lifetimes of the hydrofluoroethers are estimated to be short tauOH((CF3)2CHOCH3) approximately 100 days, tauOH(CF3CH2OCH2CF3) approximately 80 days, tauOH(CF3CF2CH2OCH3) approximately 20 days, and tauOH(CHF2CF2CH2OCH3) approximately 14 days, and their global warming potentials are small compared to CFC-11.     

Diophantine方程x~3-8=py~2解的研究

研究丢番图方程正整数解的情况.运用初等方法及同余理论,证明了Diophantine方程x3-8=py2,当p是奇素数且p=3(24k+19)(24k+20)+1,其中k是非负整数,则方程x3-8=py2无正整数解.给出了丢番图方程x3-8=py2无正整数解的一个充要条件.     

关于亚纯函数及其k阶导数的惟一性

研究亚纯函数与其k阶导数分担一个IM公共值和一个CM公共值在一定条件下的惟一性问题,考虑吴桂荣有关亚纯函数及其k阶导数具有1CM公共值在一定条件下的惟一性问题,利用构造辅助函数结合Nevanlinna第二基本定理的方法证明了:设f与g为非常数亚纯函数,1为f(k)与g(k)的CM公共值,k∈N,∞为f与g的IM公共值,如果(k+1)-Nr,1f+(k+1)-Nr,1g+2(k+1)N-(r,f)+(1/2)N-D(r,f)(λ+o(1))T(r)(r∈I),其中λ1/2,T(r)=max{T(r,f),T(r,g)},-ND表示相应于f与g所有极点的重级均不相同的f极点的精简密指量,则f(z)≡g(z)或者f(k)(z).g(k)(z)≡1.     

Atmospheric fate of dichlorvos: photolysis and OH-initiated oxidation studies

The OH-initiated oxidation of dichlorvos (a widely used insecticide) has been investigated under atmospheric conditions at the large outdoor European photoreactor (EUPHORE) in Valencia, Spain. The rate constant of OH reaction with dichlorvos, k, was measured by using a conventional relative rate technique where 1,3,5-trimethylbenzene (TMB) and cyclohexane were taken as references. With the use of the rate constants of 5.67 x 10(-11) and of 6.97 x 10(-12) cm3 molecule(-1) s(-1) for the reactions OH + TMB and OH + cyclohexane, respectively, the resulting value of the OH reaction rate constant with dichlorvos was derived to be k = (2.6 +/- 0.3) x 10(-11) cm3 molecule(-1) s(-1). The tropospheric lifetime of dichlorvos with respect to reaction with OH radical has been estimated to be around 11 h. The major carbon-containing products observed for the OH reaction with dichlorvos in air under sunlight condition were phosgene and carbon monoxide. The formation of a very stable toxic primary product such as phosgene associated with the relatively short lifetime of dichlorvos may make the use of this pesticide even more toxic for humans when released into the atmosphere.     

Mechanism and kinetics of cyanogen chloride formation from the chlorination of glycine

Glycine is an important precursor of cyanogen chloride (CNCl)--a disinfection byproduct (DBP) found in chlorinated drinking water. To model CNCl formation from glycine during chlorination, the mechanism and kinetics of the reaction between glycine and free chlorine were investigated. Kinetic experiments indicated that CNCI formation was limited by either the decay rates of N,N-dichloroglycine or a proposed intermediate, N-chloroiminocarboxylate, CIN=CHCO2-. Only the anionic form of N,N-dichloroglycine, NCl2CH2CO2-, however, decays to form CNCl, while the protonated neutral species forms N-chloromethylimine. At pH > 6, glycine-nitrogen is stoichiometrically converted to CNCI, while conversion decreases at lower pH due to the formation of N-chloromethylimine. Under conditions relevant to drinking water treatment, i.e., at pH 6 to 8 and with free chlorine in excess, a simplified rate expression for the concentration of glycine-nitrogen converted to CNCl, [CNCl]f, applies: dt/d[CNCl]f = k2*[Cl2-Gly](T,o)exp(-k2*t) where [Cl2-Gly]T,o is the initial concentration of total N,N-dichloroglycine, k2* is the first-order decay constant for CIN=CHCO2-, k2*(s(-1)) = 10(12)(+/-4) exp(-1.0(+/-0.3) x 10(4)/T), and T is the absolute temperature in K. Kinetic expressions for d[CNCl]/dt when free chlorine is in excess, however, must also account for the significant decay of CNCl by hypochlorite-catalyzed hydrolysis, which has been characterized in previous studies. Although CNCl formation is independent of the free chlorine concentration, higher chlorine concentrations promote its hydrolysis.