Maximum principle for functional equations in the space of discontinuous functions of three variables

The paper is devoted to the maximum principles for functional equations in the space of measurable essentially bounded functions. The necessary and sufficient conditions for validity of corresponding maximum principles are obtained in a form of theorems about functional inequalities similar to the classical theorems about differential inequalities of the Vallee Poussin type. Assertions about the strong maximum principle are proposed. All results are also true for difference equations, which can be considered as a particular case of functional equations. The problems of validity of the maximum principles are reduced to nonoscillation properties and disconjugacy of functional equations. Note that zeros and nonoscillation of a solution in a space of discontinuous functions are defined in this paper. It is demonstrated that nonoscillation properties of functional equations are connected with the spectral radius of a corresponding operator acting in the space of essentially bounded functions. Simple sufficient conditions of nonoscillation, disconjugacy and validity of the maximum principles are proposed. The known nonoscillation results for equation in space of functions of one variable follow as a particular cases of these assertions. It should be noted that corresponding coefficient tests obtained on this basis cannot be improved. Various applications to nonoscillation, disconjugacy and the maximum principles for partial differential equations are proposed.     

Some Properties of Quasi-keep-range Operators and Their Applications

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MODELING HARVEST SCHEDULING IN MULTIFUNCTIONAL PLANNING OF FORESTS FOR LONGTERM WATER YIELD OPTIMIZATION

In this study, wood production and hydrologic functions of forests were accommodated within a planning procedure for separate working circles (areas dedicated to certain forest functions) that were delineated according to an Ecosystem‐Based Functional Planning approach. Mixed integer goal programming was used as the optimization technique. The timing and scheduling of a maintenance cutting (partial harvest) was the decision variable in the modeling effort, and an original formulation was developed as a multiobjective planning procedure. Four sample planning strategies were developed and model outputs were evaluated according to these strategies. Spatial characteristics of stands were considered, and used to prohibit the regeneration of adjacent stands during the same time period. Because of the positive relationship between qualified water production and standing timber volume in the forest, the model attempts to maximize qualified water production levels by increasing standing volume stocks in the forest through the delay of regeneration activities.     

Controllability for noninstantaneous impulsive semilinear functional differential inclusions without compactness

The first part of this paper considers the controllability for a functional semilinear differential inclusion governed by a family of operators $\{A\left(t\right):t\in [0,b]\}$ generating an evolution operator in a Banach space in the presence of noninstantaneous impulse effects. In the second part of this paper we study the controllability for a fractional noninstantaneous impulsive semilinear differential inclusion with delay, where the linear part is an infinitesimal generator of a $C_0?$semigroup. Using a weakly convergent criterion in the space of piecewise continuous functions and weak topology theory (for weak sequentially closed graph operators) we establish sufficient conditions to guarantee controllability results. Examples are given to illustrate the abstract results.     

Existence and uniqueness of periodic solutions for a kind of first order neutral functional differential equations

In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the first order neutral functional differential equation of the form

(x(t)+Bx(t−δ)^)′=g₁(t,x(t))+g₂(t,x(t−τ))+p(t).     

Synthesis of Chitosan Quaternary Ammonium Salts

Chitosan has a wide scale of applications1-3. Interestingly, some antibacterial and antifungal activities have been described with chitosan and modified chitosan derivatives4-6. In polycationic biocides, generally, it is reasonably assumed7 that the charge density of the polyelectrolyte increases with increase in the molecular weight of its single coil, which leads to the enhanced adsorption of polycations onto the negatively charged cell surface. This is also favorable for the binding of t…     

聚偏氟乙烯接枝甲基丙烯酸甲酯油水分离膜的研究

使用四乙基氢氧化铵(TEAH)液相本体改性聚偏氟乙烯(PVDF),以过氧化苯甲酰(BPO)为引发剂,将甲基丙烯酸甲酯(MMA)接枝到改性PVDF骨架上,合成聚偏氟乙烯接枝聚甲基丙烯酸甲酯(PVDF-gPMMA)共聚物,通过浸没沉淀法制备PVDF-g-PMMA亲水性油水分离膜.通过傅里叶红外光谱(FTIR)、扫描电镜(SEM)和过滤试验分析了膜的结构和性能.同时研究了TEAH浓度和改性时间对PVDF-g-PMMA膜表面接触角的影响.结果表明,TEAH使PVDF脱去HF产生碳碳双键且MMA成功接枝到改性的PVDF骨架上,膜内外孔隙分布均匀;PVDF-g-PMMA膜的接触角随着TEAH浓度的增加、改性时间的加长而减小.TEAH浓度为2.0 wt%,改性20 min制备的PVDF-g-PMMA膜,接枝率为27.1%,孔隙度为71.6%,平均孔径为78.9 nm,接触角降至55.9°,且在50 s内降为0;纯水通量提高到665.34 L/(m2·h),截留率和水通量恢复率分别达到95.6%和90.1%.与纯PVDF膜相比,PVDF-g-PMMA膜的分离性能显著提高.     

Spectral theory for commutative algebras of differential operators on Lie groups

The joint spectral theory of a system of pairwise commuting self-adjoint left-invariant differential operators L₁,…,Ln on a connected Lie group G is studied, under the hypothesis that the algebra generated by them contains a “weighted subcoercive operator” of ter Elst and Robinson (1998) [52]. The joint spectrum of L₁,…,Ln in every unitary representation of G is characterized as the set of the eigenvalues corresponding to a particular class of (generalized) joint eigenfunctions of positive type of L₁,…,Ln. Connections with the theory of Gelfand pairs are established in the case L₁,…,Ln generate the algebra of K-invariant left-invariant differential operators on G for some compact subgroup K of Aut(G).     

表面非金属掺杂对锐钛矿相TiO_2(101)面吸附NH_3特性的影响

采用基于密度泛函理论(DFT-D)体系下的第一性原理平面波超软赝势方法,研究了被不同非金属(B、C、N、F)掺杂的TiO_2(101)表面吸附NH_3的特性与作用机理.研究发现:被非金属掺杂后的表面对NH_3的吸附效果要优于未掺杂表面.不同元素掺杂对比发现:C掺杂后的表面吸附能最大,稳定后吸附距离最小,为最稳定吸附结构.通过Mulliken电荷分布和分态密度的分析,得到了不同吸附条件下NH_3在TiO_2掺杂表面的催化氧化还原作用机理,并发现各模型吸附能的不同是由于掺杂(X)位原子与NH_3分子的相互作用强弱不同所造成.掺杂原子在费米面附近的电子态密度贡献越强,掺杂原子与NH_3分子电荷转移的净值越小,吸附距离越小,吸附能越大,吸附更稳定.