Periodic and quasiperiodic motion for complex non-linear systems

A damped complex non-linear system corresponding to two coupled non-linear oscillators with a periodic damping force is investigated by an asymptotic perturbation method based on Fourier expansion and time rescaling. Four coupled equations for the amplitude and the phase of solutions are derived. Phase-locked solutions with period equal to the damping force period are possible only if the oscillators amplitudes are equal. On the contrary, if the oscillators amplitudes are different, periodic solutions exist only with a period different from the damping force period. These solutions are stable only for perturbations that conserve the phase difference and the square amplitude sum of the oscillators. Energy considerations are used in order to study existence and characteristics of quasiperiodic motion. We demonstrate that modulated motion can be also obtained for appropriate values of the detuning parameter and in this case an approximate analytic solution is easily constructed. If the detuning parameter decreases the modulation period increases and then diverges, an infinite-period bifurcation occurs and the resulting motion becomes unbounded. Analytic approximate solutions are checked by numerical integration.     

LC Separation and Online MS Characterization of Saturated and Unsaturated Alginic Acid Oligomers

We report the complete separation and characterization by online high-performance liquid chromatography-electrospray ionization mass spectrometry (LC-ESI-MS) of fully saturated alginic acid (AA) oligosaccharides from DP1 to beyond DP23, obtained by a chemical process, and unsaturated oligomers from DP1 to DP10, produced by lyase treatment. A series of negatively charged species of different m/z ratio are seen for each oligosaccharide. Smaller AA species, from DP1 to DP4, mainly furnish [M–H]^? anions whereas the DP5 to DP9-10 oligomers predominantly exist as the 2- charge state. The AA oligomers from DP10 to DP17 are mainly represented by the [M–3H]^3? anions whereas species from DP18 to DP23 are characterized by the 4? charge state. Online LC-ESI-MS enabled separation and simultaneous characterization of complex saturated and unsaturated AA oligomer mixtures without previous sample treatment, in particular extensive removal of salts to obtain species compatible with ESI-MS.     

Vibration control for the primary resonance of the van der Pol oscillator by a time delay state feedback

We investigate the primary resonance of an externally excited van der Pol oscillator under state feedback control with a time delay. By means of the asymptotic perturbation method, two slow-flow equations on the amplitude and phase of the oscillator are obtained and external excitation-response and frequency-response curves are shown. We discuss how vibration control and high amplitude response suppression can be performed with appropriate time delay and feedback gains. Moreover, energy considerations are used in order to investigate existence and characteristics of limit cycles of the slow-flow equations. A limit cycle corresponds to a two-period modulated motion for the van der Pol oscillator. We demonstrate that appropriate choices for the feedback gains and the time delay can exclude the possibility of modulated motion and reduce the amplitude peak of the primary resonance. Analytical results are verified with numerical simulations.     

The Asymptotic Perturbation Method for Nonlinear Continuous Systems

We apply the asymptotic perturbation (AP) method to the study of the vibrations of Euler--Bernoulli beam resting on a nonlinear elastic foundation. An external periodic excitation is in primary resonance or in subharmonic resonance in the order of one-half with an nth mode frequency. The AP method uses two different procedures for the solutions: introducing an asymptotic temporal rescaling and balancing the harmonic terms with a simple iteration. We obtain amplitude and phase modulation equations and determine external force-response and frequency-response curves. The validity of the method is highlighted by comparing the approximate solutions with the results of the numerical integration and multiple-scale methods.     

In Search for Multi-Target Ligands as Potential Agents for Diabetes Mellitus and Its Complications—A Structure-Activity Relationship Study on Inhibitors of Aldose Reductase and Protein Tyrosine Phosphatase 1B

Diabetes mellitus (DM) is a complex disease which currently affects more than 460 million people and is one of the leading cause of death worldwide. Its development implies numerous metabolic dysfunctions and the onset of hyperglycaemia-induced chronic complications. Multiple ligands can be rationally designed for the treatment of multifactorial diseases, such as DM, with the precise aim of simultaneously controlling multiple pathogenic mechanisms related to the disease and providing a more effective and safer therapeutic treatment compared to combinations of selective drugs. Starting from our previous findings that highlighted the possibility to target both aldose reductase (AR) and protein tyrosine phosphatase 1B (PTP1B), two enzymes strictly implicated in the development of DM and its complications, we synthesised 3-(5-arylidene-4-oxothiazolidin-3-yl)propanoic acids and analogous 2-butenoic acid derivatives, with the aim of balancing the effectiveness of dual AR/PTP1B inhibitors which we had identified as designed multiple ligands (DMLs). Out of the tested compounds, 4f exhibited well-balanced AR/PTP1B inhibitory effects at low micromolar concentrations, along with interesting insulin-sensitizing activity in murine C2C12 cell cultures. The SARs here highlighted along with their rationalization by in silico docking experiments into both target enzymes provide further insights into this class of inhibitors for their development as potential DML antidiabetic candidates.     

Response control for the externally excited van der Pol oscillator with non-local feedback

A non-local control force is introduced in such a way to obtain a third-order nonlinear differential equation (jerk dynamics) and to control nonlinear vibrations in an externally excited van der Pol oscillator. Two first-order nonlinear ordinary differential equations governing the modulation of the amplitude and the phase of solutions are derived and subsequently the performance of the control strategy is investigated. Excitation amplitude–response and frequency–response curves are shown. In certain cases when the excitation amplitude is very low an approximate analytic solution corresponding to a modulated two-period quasi-periodic motion can be obtained for the uncontrolled system. Uncontrolled and controlled systems are compared and the appropriate choices for the feedback gains are found in order to reduce the amplitude peak of the response and to exclude the possibility of quasi-periodic motion. Numerical simulation confirms the validity of the new method.     

Vibration amplitude control for a van der Pol–Duffing oscillator with time delay

Periodic solutions for the fundamental resonance response of a van der Pol–Duffing system under time-delayed position and velocity feedbacks are investigated. Using the asymptotic perturbation method, two slow-flow equations for the amplitude and phase of the fundamental resonance response are derived. Their fixed points correspond to limit cycles (phase-locked periodic solutions) for the original system. In the uncontrolled system, periodic solutions exist only for fixed values of amplitude and phase and depend on the system parameters and excitation amplitude. In many cases, the amplitudes of periodic solutions do not correspond to the technical requirements. It is demonstrated that, if the vibration control terms are added, stable periodic solutions with arbitrarily chosen amplitude can be accomplished. Therefore, the results obtained show that an effective vibration amplitude control is possible if appropriate time delay and feedback gains are chosen.     

Glycosaminoglycan blotting on nitrocellulose membranes treated with cetylpyridinium chloride after agarose-gel electrophoretic separation

We describe a method for blotting and immobilizing several nonsulfated and sulfated complex polysaccharides on membranes made hydrophilic and positively charged by a cationic detergent after their separation by conventional agarose gel electrophoresis. Nitrocellulose membranes were derivatized with the cationic detergent cetylpyridinium chloride (CPC) and mixtures of glycosaminoglycans (GAGs) were capillary-blotted after their separation in agarose gel electrophoresis in barium acetate/1,2-diaminopropane. Single purified species of variously sulfated polysaccharides were transferred onto the derivatized membranes after electrophoresis with an efficiency of 100% and stained with alcian blue (irreversible staining) and toluidine blue (reversible staining) permitting about 0.1 nug threshold of detection. Nonsulfated polyanions, hyaluronic acid, a fructose-containing polysaccharide with a chondroitin backbone purified from Escherichia coli U1-41, and its defructosylated product, were also electrophoretically separated and transferred onto membranes. The limit of detection for desulfated GAGs was about 0.1-0.5 nug after irreversible or reversible staining. GAG extracts from bovine, lung and aorta, and human aorta and urine were separated by agarose gel electrophoresis and blotted on CPC-treated nitrocellulose membranes. The polysaccharide composition of these extracts was determined. The membrane stained with toluidine blue (reversible staining) was destained and the same lanes used for immunological detection or other applications. Reversible staining was also applied to recover single species of polysaccharides after electrophoretic separation of mixtures of GAGs and their transfer onto membranes. Single bands were released from the membrane with an efficiency of 70-100% for further biochemical characterization.     

Bound water is a quality discriminant of dried egg-pasta

Egg-pasta is a very popular food in Italy and its appreciation is growing in Europe and in the United States. In this work, the bound water has been demonstrated to be a quality discriminant parameter to distinguish the low-temperature dried egg-pasta with respect to the high-temperature dried egg-pasta. By the thermoanalytical profiles (TG and DTG), this systematic study scientifically proves the differences induced by the drying process on the egg-pasta samples: the low temperature dried egg-pasta (produced by the ‘Entroterra’ company, brand ‘La Pasta di Camerino’) shows the systematic lower amount of bound water when compared to other brand, high-temperature dried egg-pasta. The difference is constant either before or after the cooking process. Other physical parameters (thickness and width) confirmed the difference.