Equilibrium,pseudoequilibrium and sliding-mode heteroclinic orbit in a Filippov-type plant disease model

Plant diseases have caused tremendous crop losses and have massive impacts on food security and environment. Modeling the spread of plant diseases and understanding the dynamics of the resulting plant disease models may provide practical insights on designing effective control measures. In this paper, by incorporating cultural strategies and economic threshold policy, we present a Filippov-type plant disease model. The resulting model has state dependent discontinuous right-hand side and thus non-smooth analysis and generalized Lyapunov approach are employed for model analysis. We show that the model exhibits the phenomena of stable equilibrium, unstable pseudoequilibrium as well as sliding-mode heteroclinic orbit. Biological implications of our results in implementing control strategies for plant diseases are also discussed.     

Further studies on stability analysis of nonlinear Roesser-type two-dimensional systems

This paper is concerned with further relaxations of the stability analysis of nonlinear Roesser-type two-dimensional （2D） systems in the Takagi-Sugeno fuzzy form. To achieve the goal, a novel slack matrix variable technique, which is homogenous polynomially parameter-dependent on the normalized fuzzy weighting functions with arbitrary degree, is developed and the algebraic properties of the normalized fuzzy weighting functions are collected into a set of augmented matrices. Consequently, more information about the normalized fuzzy weighting functions is involved and the relaxation quality of the stability analysis is significantly improved. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed result.     

Molecular dynamics and quantum chemical approaches in the study of the hydration of protonated cyclohexyldiamines

Explicit hydration of the neutral and charged cyclohexylamine and of the cyclohexyldiamine isomers in their mono- or diprotonated forms is investigated through classical molecular dynamics (MD) simulations in aqueous solutions combined with DFT calculations in amine–water complexes. The MD studies performed in the monoamines reveal that the structure of the hydration shell around the neutral amino group (NH₂) is quite distinct from that around the charged one (NH₃⁺). On average, the number of water molecules surrounding the two groups is calculated to be ～2 and 3–4, respectively. The variation of the hydration structure prompted by the groups’ proximity is discussed based on the data found for the mono- and diprotonated diamines. To have a more detailed picture of the water molecules’ arrangement around the amino groups and of the amine–water hydrogen bonds, geometry optimisations in hydrates with up to six water molecules are carried out at the B3LYP/aug-cc-pVDZ level. Complexation energies are also computed. The main findings emerging from these calculations are found to be very helpful to rationalise the mutual influence of the amino groups and therefore to better elucidate the MD findings. The complementary nature of the two research methods is emphasised as an excellent tool in order to closely examine the hydration of polyamines, as exemplified for the cyclohexyldiamines.     

Structure and cooperativity of the hydrogen bonds in sodium dihydrogen triacetate

Geometry and energetics of low energy conformers of sodium dihydrogen triacetate (SDHTA) and its anion are studied using density functional theory (DFT) at the Becke, Lee‐Yang‐Parr hybrid functional (BLYP) and Becke, three‐parameter, Lee‐Yang‐Parr hybrid functional (B3LYP) levels. For both cases, two structures of comparable energy are found, which have different symmetry with respect to the two hydrogen bonds (HBs). DFT‐based Born–Oppenheimer molecular dynamics simulations are performed for SDHTA, which show that both structures are visited at room temperature conditions. The trajectory analysis further reveals that the two HBs behave anticooperative, that is, on average elongation of one HB is accompanied by a compression of the other one. This is in accord with nuclear magnetic resonance (NMR) experimental studies for a similar counter ion–dihydrogen triacetate complex. © 2012 Wiley Periodicals, Inc.     

一个1+1维Boussinesq系统的Darboux变换及其应用

主要考虑1+1维Boussinesq系统的一个Darboux变换,反复利用该Darboux变换,可以从该系统的一个已知解出发,通过代数运算和求导运算得到系统的新解.     

Reactions Occurring in Gels of Lithium Tetraalkyl Borates Promoted by Supermolecular Structure of Complexes

As Li[BOR'(OR)₃] and Li[B(OR)₄] complexes, where R’ and R are alkyls of iso- and normal structure, are formed from boron alkoxides and lithium in solutions of low dielectric permittivity, they are involved in autocatalytic polyassociation to give viscoelastic systems (gels) possessing a mechanical memory [1].     

Homodiselenacalix[4]arenes: Molecules with Unique Channelled Crystal Structures

A synthetic route towards homodiselenacalix[4]arene macrocycles is presented, based on the dynamic covalent chemistry of diselenides. The calixarene inner rim is decorated with either alkoxy or tert‐butyl ester groups. Single‐crystal X‐ray analysis of two THF solvates with methoxy and ethoxy substituents reveals the high similarity of their molecular structures and alterations on the supramolecular level. In both crystal structures, solvent channels are present and differ in both shape and capacity. Furthermore, the methoxy‐substituted macrocycle undergoes a single‐crystal‐to‐single‐crystal transformation during which the molecular structure changes its conformation from 1,3‐alternate (loaded with THF/water) to 1,2‐alternate (apohost form). Molecular modelling techniques were applied to explore the conformational and energetic behaviour of the macrocycles.     

Noether symmetry and conserved quantity for a Hamilton system with time delay

In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are discussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed,the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results.     

Attainment of Emulsions with Liquid Crystal from Marigold Oil Using the Required HLB Method

Development of new formulations for topical use and cosmetic and pharmaceutical delivery agents has increased the complexity of emulsified systems. Liquid crystals, known since the nineteenth century are the third phase of an emulsion, being responsible for increasing its stability and the solubility of substances poorly soluble in water, or the oily phase, modulating the release of drugs imprisoned in its structure and promoting hydration of the skin surface. In the present work we developed oil/water emulsions, making use of Marigold oil (Calendula officinalis L) and ethoxylated fat alcohols as surfactant. The required HLB value for marigold oil was determined to be 6.0. The surfactants were associated in lipophilic/hydrophilic pairs. The lipophilic surfactants were Ceteth‐2 and Steareth‐2 and the hydrophilic surfactants were Steareth‐20, Ceteareth‐20, Ceteareth‐5, and Ceteth‐10. To identify the liquid crystalline phases, the emulsions were analyzed by polarized light microscopy. The physical stability was evaluated by rheology and zeta potential analysis. All emulsions presented lamellar liquid crystal structures. Results showed that this type of surfactant is able to produce liquid crystal in the system, with slight difference in appearance, influencing the physical stability, according to the methods applied.