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.     

A Sharp Condition for the Ground State of Difference Equation

This note is concerned with a novel inequality condition for the existence of ground states of partial difference systems. Our result is potentially applicable to the estimation of eigenvalues of the loaded strings and nets.     

A new 4-D non-equilibrium fractional-order chaotic system and its circuit implementation

A new 4-D fractional-order chaotic system without equilibrium point is proposed in this paper. There is no chaotic behavior for its corresponding integer-order system. By computer simulations, we find complex dynamical behaviors in this system, and obtain that the lowest order for exhibiting a chaotic attractor is 3.2. We also design an electronic circuit to realize this 4-D fractional-order chaotic system and present some experiment results.     

A novel design of membrane mirror with small deformation and imaging performance analysis in infrared system

A method of diminishing the shape error of membrane mirror is proposed in this paper. The inner inflating pressure is considerably decreased by adopting the pre-shaped membrane. Small deformation of the membrane mirror with greatly reduced shape error is sequentially achieved. Primarily a finite element model of the above pre-shaped membrane is built on the basis of its mechanical properties. Then accurate shape data under different pressures can be acquired by iteratively calculating the node displacements of the model. Shape data are applicable to build up deformed reflecting surfaces for the simulative analysis in ZEMAX. Finally, ground-based imaging experiments of 4-bar targets and nature scene are conducted. Experiment results indicate that the MTF of the infrared system can reach to 0.3 at a high spatial resolution of 10l p/mm, and texture details of the nature scene are well-presented. The method can provide theoretical basis and technical support for the applications in lightweight optical components with ultra-large apertures.     

Performance investigation of an advanced tracked prime mover on the low bearing soil

This study has presented a performance investigation of an advanced tracked prime mover for the operation of agricultural goods and other operations on peat terrain. The maximum and continuous traction torque of the prime mover has been developed by designing an advanced controller for controlling the intelligent system. The prime mover’s mobility is studied with ultrasonic displacement sensor, torque transducer, National Instrument cRIO-9004 Compact-RIO Real-time Controller Unit (RCU), a National Instrument TPC 2106T Touch Panel Control (TPC), a Trimble AG132 GPS antenna and receiver unit, and a Dlink DIR-655 router. The fuzzy logic controller (FLC) has been equipped with the prime mover hydraulic system to increase the traction torque of the hydraulic motor when the prime mover’s sinkage is more than or equal to 70 mm. The prime mover’s design demonstrates good potential in traversing peat terrain as the measured tractive effort was found to be 48% of the vehicle’s gross weight while the recommended tractive effort is in the range of 30–36% of the vehicle’s gross weight.     

CdSe quantum dot-dispersed DOBAMBC: an electro-optical study

Cadmium selenide quantum dot (CdSe QD) has been used as a dopant in ferroelectric liquid crystal (FLC) 2-methylbutyl 4-(4-decyloxybenzylideneamino) cinnamate (DOBAMBC). Effect of CdSe QD in DOBAMBC on its different electro-optical (E-O) properties has been studied in the SmC* phase. The optical micrographs recorded for the pure and composite material are showing good dispersion of QDs in the FLC matrix. Micrographs of unaligned sample cell revealed that CdSe QDs induce homeotropic alignment of FLC molecules. An appreciable change in the value of E-O parameters like tilt angle, spontaneous polarisation and response time with shifting of SmA–SmC* phase transition temperature has been observed for CdSe QD–DOBAMBC composite. The observed properties of composite system have been discussed on the basis of surface properties of QDs in FLC system.