Stability analysis of structurally unstable man–machine system involving time delays

In this paper, a structurally unstable man–machine system is considered and a rigorous mathematical analysis is performed to study the influence of time delays in the control force on stability of the equilibrium solution of this system. Results on stability, instability and conditions for the preservation of stability (instability), besides the existence of bifurcation are presented.     

Triple Positive Solutions of Boundary Value Problems for High-order Fractional Differential Equation at Resonance with Singularities

In this paper, we investigate the existence of triple positive solutions of boundary value problems for high-order fractional differential equation at resonance with singularities by using the fixed point index theory and the Leggett-Williams theorem. The spectral theory and some new height functions are also employed to establish the existence of triple positive solutions. The nonlinearity involved is arbitrary fractional derivative, and permits singularity.     

Unraveling the mystery of efficacy in Chinese medicine formula: New approaches and technologies for research on pharmacodynamic substances

Traditional Chinese medicine (TCM) is the key to unlock treasures of Chinese civilization. TCM and its compound play a beneficial role in medical activities to cure diseases, especially in major public health events such as novel coronavirus epidemics across the globe. The chemical composition in Chinese medicine formula is complex and diverse, but their effective substances resemble “mystery boxes”. Revealing their active ingredients and their mechanisms of action has become focal point and difficulty of research for herbalists. Although the existing research methods are numerous and constantly updated iteratively, there is remain a lack of prospective reviews. Hence, this paper provides a comprehensive account of existing new approaches and technologies based on previous studies with an in vitro to in vivo perspective. In addition, the bottlenecks of studies on Chinese medicine formula effective substances are also revealed. Especially, we look ahead to new perspectives, technologies and applications for its future development. This work reviews based on new perspectives to open horizons for the future research. Consequently, herbal compounding pharmaceutical substances study should carry on the essence of TCM while pursuing innovations in the field.     

Sample evaporation in conventional split/splitless GC injectors. Part 3: Retaining the liquid in the vaporizing chamber

As most sample liquids tend to pass through an empty injector insert at a speed which is too high to enable complete evaporation, movement of the liquid must be arrested before it reaches the column entrance. Stopping the liquid means deposition on to a surface; this, however, is possible only after the temperature of the surface has been cooled to (or below) the boiling point of the liquid (solvent). The performance of different means of stopping the liquid has been tested visually (by the method described in Part 2). Baffles on the wall of the injector insert had hardly any effect on evaporation: the band of liquid leaving the syringe needle performed a perfect slalorn around them. The inverted cup proved more efficient, but the best performance was obtained from a light plug of glass wool: owing to its low thermal mass, the first fibers to be met by the liquid are immediately cooled to the solvent boiling point, allowing the liquid to wet it. The sample liquid is sucked up by the glass wool, from where the sample evaporates relatively slowly, often over a period of several seconds.     

Heteroatom derivatives of indene: V. Vibrational spectra of benzimidazole

Infrared and Raman measurements for benzimidazole are presented and discussed, including its argon-matrix infrared spectrum. To assist in the assignment, benzimidazole's harmonic force fields for the 321G* and 631G* levels were scaled by scaled factors derived by fitting the respective computed force fields of other indene derivatives to previously reported experimental vibrational frequencies. Comparison to the best set of experimental wavenumbers, usually taken from the matrix, shows mean 321G* and 631G* deviations of 7.0 and 5.8 cm⁻¹ for the planar modes, and 14.0 and 6.8 cm⁻¹ for the nonplanar modes, respectively, with much of the error residing in imino-hydrogen group modes. Standard entropies are derived with the matrix wavenumbers and the methods of statistical mechanics. An attempt to determine standard entropies by calorimetric methods was unsuccessful. The triple-point temperature T_tp and enthalpy of fusion Δ¹_crH_m only are reported.     

Reduced matrix effects for anionic compounds with paired ion electrospray ionization mass spectrometry

It is well-known that matrix effects in high performance liquid chromatography coupled to electrospray ionization mass spectrometry (HPLC-ESI-MS) can seriously compromise quantitative analysis and affect method reproducibility. Paired ion electrospray ionization (PIESI) mass spectrometry is an approach for analyzing ultra-low levels of anions in the positive ion mode. This approach uses a structurally optimized ion pairing reagent to post-column associate with the anionic analyte, subsequently forming positively charged complexes. These newly formed complex ions are often more surface-active as compared to either the native anion or the ion pairing reagent. No studies have examined whether or not the PIESI approach mitigates matrix effects. Consequently, a controlled study was done using five analytes in highly controlled and reproducible synthetic groundwater and urine matrices. In addition, two different mass spectrometers (linear ion trap and triple quadrupole) were used. Compared to the negative ion mode, the PIESI-MS approach was less susceptible to matrix effects when performed on two different MS platforms. Using PIESI-MS, less dilution of the sample is needed to eliminate ionization suppression which, in turn, permits lower limits of detection and quantitation.     

Factorization method and new potentials from the inverted oscillator

In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in particular, only very specific second-order transformations produce non-singular real potentials. It will be shown that these transformations turn out to be the so-called complex ones. Moreover, we will study the factorization method applied to the inverted oscillator and the algebraic structure of the new Hamiltonians.     

Optimal feedback gains of a delayed proportional-derivative (PD) control for balancing an inverted pendulum

In the dynamics analysis and synthesis of a con-trolled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a sys-tematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost charac-teristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial val-ues around the origin are fixed. The main results are checked by numerical simulation.