Analytical Condition Research Articles

The Dynamical Behaviorof a Two Degrees of Freedom Oblique Impact System

The oblique impact phenomena is quite common in practical engineering. In this paper, by using the theory of discontinuous dynamical systems, we studied the complex dynamics behaviors of a two degrees of freedom oblique impact system. We can see that the dynamics of oblique impact is more complex than that of the direct impact. The occurrence or disappearance conditions of sticking motion and grazing motion on the separation boundaries are given in Section 3. The conditions here are necessary and sufficient, which generate better results than those obtained with only sufficient conditions. The results appropriately interpret the physical phenomenon of this oblique impact system, hence validate our conclusions. As a supplement, we also give the analytic conditions of the existence of periodic motions. Numerical simulations for sticking motion and grazing motion are presented at last.

Static and dynamic attractive-repulsive interactions in two coupled nonlinear oscillators.

Many systems exhibit both attractive and repulsive types of interactions, which may be dynamic or static. A detailed understanding of the dynamical properties of a system under the influence of dynamically switching attractive or repulsive interactions is of practical significance. However, it can also be effectively modeled with two coexisting competing interactions. In this work, we investigate the effect of time-varying attractive-repulsive interactions as well as the hybrid model of coexisting attractive-repulsive interactions in two coupled nonlinear oscillators. The dynamics of two coupled nonlinear oscillators, specifically limit cycles as well as chaotic oscillators, are studied in detail for various dynamical transitions for both cases. Here, we show that dynamic or static attractive-repulsive interactions can induce an important transition from the oscillatory to steady state in identical nonlinear oscillators due to competitive effects. The analytical condition for the stable steady state in dynamic interactions at the low switching time period and static coexisting interactions are calculated using linear stability analysis, which is found to be in good agreement with the numerical results. In the case of a high switching time period, oscillations are revived for higher interaction strength.

One-step electroreduction preparation of multilayered reduced graphene oxide/gold-palladium nanohybrid as a proficient electrocatalyst for development of sensitive hydrazine sensor

A facile and green method for preparation of gold/palladium (Au/Pd) bimetallic nanoparticles interleaved reduced graphene oxide (rGO) composite was presented. One-step electroreduction of Au/Pd precursors and graphene oxide synergistically produced a multilayered and well-structured nanohybrid on glassy carbon electrode, which was explored as a highly efficient electrocatalyst. This operation is easy and controllable, as compared with time-consuming and procedure-tedious hydrothermal synthesis. The morphology and chemical constituents were meticulously characterized. The remarkable electrocatalytic performance of the prepared nanohybrid was demonstrated by detection of a high-risk carcinogen pollutant, hydrazine. By optimizing the preparation condition and investigating the electrochemical behavior, we achieved the sensitive analysis of hydrazine with ultralow oxidation overpotential. Amperometry was employed for constructing the quantitative calibration curve; the steady-state current originating from hydrazine oxidation was proportional to the analytical concentration ranging from 0.1 μM to 200 μM, with the detection limit of 16 nM. Moreover, the nanohybrid displayed considerable anti-interfering ability with respect to hydrazine detection, as a variety of potentially coexisting substances produced negligible electrochemical response in the given analytical condition. Advantages including easy-to-preparation, high sensitivity and favorable selectivity, as well as broad linear response make the present method feasible for monitoring of hydrazine in water environment.

Constructing Mutually Unbiased Bases from Unextendible Maximally Entangled Bases

We study mutually unbiased bases (MUBs) in which all the bases are unextendible maximally entangled ones. We first present a necessary and sufficient condition of constructing a pair of MUBs in C2⊗C4. Based on this condition, an analytical and necessary condition for constructing MUBs is given. Moreover we illustrate our approach by some detailed examples in C2⊗C4. The results are generalized to C2⊗Cd(d≥3) and a concrete example in C2⊗C8 is given.

Scalar particle with the Darwin – Cox intrinsic structure in the external Coulomb field

The generalized Klein – Fock – Gordon equation for a particle with the Darwin–Cox structure allowing for a charge distribution of a particle over a sphere of finite radius is studied with regard to the external Coulomb field. The separation of variables is carried out, the obtained radial equation is significantly more complicated than the equation in the case of ordinary particles, it has essentially singular points r = 0 of rank 3, r = ∞ of rank 2 and 4 regular singular points. In the case of a minimum orbital momentum l = 0, the structure of singularities is simplified: there are essentially singular points r = 0, r = ∞ of rank 2 and 4 regular singular points. Frobenius solutions of this equation are constructed and the structure of the 7-term recurrence relations for the coefficients of the arising power series is investigated. As an analytical quantization condition, the generalized transcendence requirement of solutions is used; it allows one to obtain a fourth-degree algebraic equation for energy levels. The equation has 4 sets of roots depending on the orbital moment l and the main quantum number k = 1,2,3,… . The numerical analysis shows that one of the sets of the roots 0 < εl,k < mc2 can be interpreted as those corresponding to certain bound states of the particle in the Coulomb field.

Analytical and Numerical Investigation of Radiation Enhancement by Anisotropic Metamaterial Shells

This paper presents analytical and numerical investigations of a 3D cylindrical metamaterial shell possessing a cylindrically anisotropic permeability that is excited by a finite-sized electric line source. A comprehensive field analysis of the system reveals that the compact metamaterial shell exhibits resonances akin to those observed in isotropic 2D cylindrical metamaterial structures, which may be used to enhance the radiated power of a nearby antenna. An analytical resonance condition that relates the dimensions of the cylindrical shell to its anisotropic effective-medium parameters is shown to be accurate in predicting the resonances of 2D and 3D metamaterial shells obtained using full-wave simulations. The effects of anisotropy and finite shell/antenna height on the system's near-fields, radiation patterns, and power-ratio enhancements are explored. It is shown through both theory and simulations that the condition for resonance is largely independent of shell/antenna height but that the quality factor reduces dramatically as these heights approach electrically small values. Also, a dispersion and loss analysis assuming Lorentz model is carried out, which indicates that practical metamaterial losses do not significantly degrade the power enhancement.

Control Limitations due to Zero Dynamics in a Single-Machine Infinite Bus Network

In this work, fundamental control limitations for rotor angle stability are considered. Limitations are identified by characterizing open-loop transfer function zeros for input-output combinations of certain power system configurations. Of particular interest are non-minimum phase (NMP) zeros that limit the achievable performance of the closed-loop system. By studying a single-machine infinite bus power system model, analytic conditions for the presence of NMP zeros are derived. They are shown to be closely linked to the destabilizing effect of automatic voltage regulators (AVRs). Depending on the control loop, it is found that NMP zeros may persist in the system even if the closed-loop system is stabilized through feedback control. A simulation study shows that NMP zeros introduced by AVR limit the achievable performance and stabilization using feedback control.

The Existence of Consensus Equilibria for Data Trading under the Framework of Internet of Things (IoT) with Blockchain Ecosystems

Abstract The goal of this paper is to use a new notion called “Consensus Game (CG)” with motivation from the mechanism design of blockchain economy under the consensus incentives from Bitcoin ecosystems in financial technology (Fintech) to study the existence of equilibria for the data trading under the framework of Internet of Things (IoT). By a fact that for a given sets of sensors, sensors may take action in cooperative, or noncooperative strategies (games), we formulate s model (called “Consensus Game of IoT”) to analyze this competitive situation among the sensors with the mixture of cooperative and noncooperative strategy (game). Then we provide the analytical condition for the existence of the consensus games of IoT in general. The application shows that the concept of consensus games of IoT may play a key role for the study of data trading under the framework of IoT associated with Blockchain ecosystems.

МЕЛКОМАСШТАБНАЯ ПЯТНИСТОСТЬ В ПРОСТРАНСТВЕННОЙ МОДЕЛИ ТРОФИЧЕСКОЙ СИСТЕМЫ ДИАТОМОВЫЕ МИКРОВОДОРОСЛИ – ГАРПАКТИКОИДЫ

A predator–prey model that describes littoral trophic communities consisting of diatom microalgae and benthic copepod crustaceans (order Harpacticoida) was built and investigated. The model is a system of three partial differential equations of the taxis–diffusion–reaction type. The Neumann boundary condition specifies zero-flux through the borders of a rectangular habitat. The movements of copepods is described by the classical Patlak – Keller – Segel flux expression, which includes both taxis and diffusion. The feeding migrations of consumers are modelled as indirect prey–taxis stimulated by harpacticoid satiety, i.e. with the diffusion coefficient being a decreasing function of individual satiety. Inasmuch as demographic processes in the predator population occur at slow time scale, the model includes no birth/death terms for predator. Hence, taking into account the boundary condition, the average density of predators remains constant. The analytical condition for the oscillatory instability of the homogeneous stationary state of species coexistence reveals the crucial role of the indirect prey–taxis for emergence of spatiotemporal patterns in the system. The proposed model can be viewed as the minimal model capable of explaining heterogeneity of the harpacticoid density. With parameters identified on the basis of field observation data, the model simulates small-scale spatial patterns with characteristic size and the expected lifetime of density patches typical for the considered community of benthic organisms. In spatially-heterogeneous dynamics both density of microalgae and individual consumption of harpacticoid copepods exceed equilibrium values observed without feeding migrations. This suggests that prey–taxis behavior is an evolutionary advantageous strategy

Synchronization of cyclic coupled hyperchaotic systems and its circuit implementation

Most of the available research works on cyclic coupling of chaotic systems focussed on either analytical and numerical results or numerical and experimental results. This research paper, investigates synchronization of two cyclic coupled hyperchaotic systems using analytical, numerical and experimental techniques. Based on Routh-Hurwitz criterion, analytical condition for stable synchronization of the hyperchaotic systems are derived. The results obtained from MultiSIM and analog circuit confirm the effectiveness and feasibility of the analytical results. It is worthy of note that the cyclic coupling synchronization scheme gives several synchronization options, save synchronization time and cost. Moreover, cyclic coupling synchronization scheme has potential applications in biological information transmission networks.

Harmonic Starlike Functions with Respect to Symmetric Points

In the paper we define classes of harmonic starlike functions with respect to symmetric points and obtain some analytic conditions for these classes of functions. Some results connected to subordination properties, coefficient estimates, integral representation, and distortion theorems are also obtained.

First-order perturbation theory for changes in the surrounding of open optical resonators.

The single-mode approximation of resonant state expansion has proven to give accurate first-order approximations of resonance shifts and linewidth changes when modifying the material properties inside open optical resonators. Here, we extend this first-order perturbation theory to modifications of the material properties in the surrounding medium. As a side product of our derivations, we retrieve the already known analytical normalization condition for resonant states. We apply our theory to two example systems: a metallic nanosphere and a periodic array of metallic nanoslits.

Crack resistance criterion of plane stress RC elements with prestressed reinforcement

An analytical condition for crack resistance of a specific plane stress reinforced concrete element with prestressed reinforcement is considered in this article. The specific concrete element is reinforced with orthogonally located prestressed rods that coincide with the directions of the coordinate axes. The crack resistance condition is constructed by generalizing of G.A. Geniev theory of plasticity of concrete and reinforced concrete on the region of existence of tensile stresses: “tension-tension” and “compression-tension”. A graphical interpretation of this condition is presented for a plane stressed element depending on the angle between the main force and the coordinate axes. As an example, the crack resistance condition of the support zone of a prestressed concrete beam of a monolithic reinforced concrete frame is considered.

DEVELOPMENT OF ANALYTICAL METHOD FOR IMATINIB MESYLATE BY ULTRAVIOLET SPECTROSCOPY

Objective: A simple, selective, sensitive, specific, and spectrophotometric method has been developed for the detection of imatinib mesylate in pure form and formulations.
 Methods: The analytical condition was optimized for the drug, carried out as per the International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use guidelines.
 Results: The drug shows absorption at 232.0 nm and obeyed beers law in the wide concentration range from 0.5 to 4.0 μg/ml. The lower limit of detection was found to be 0.331 μg/ml and the limit of quantification to be 1.004 μg/ml. The regression equation was found to be y = 0.08x. The precision of the method was found to be 99.04%±0.527% and the percentage of drug recovered by this method is 100.13%±1.375%.
 Conclusion: The method is simple and suitable for determination for imatinib mesylate in pure and pharmaceutical preparation.

When Good Loadings Go Bad: Robustness in Factor Analysis

ABSTRACT Structural misspecifications in factor analysis include using the wrong number of factors and omitting cross loadings or correlated errors. The impact of these errors on factor loading estimates is understudied. Factor loadings underlie our assessments of the validity and reliability of indicators. Thus knowing how structural misspecifications affect a factor loading is a key issue. This paper develops analytic conditions of when misspecifications affect Bollen’s (1996) model implied instrumental variable, two stage least squares (MIIV-2SLS) estimator of a factor loading. It shows that if an indicator equation is correctly specified, then correlated errors among other measures, mixing up causal indicators with reflective, omitting cross loadings, and omitting direct effects between indicators leave the MIIV-2SLS estimator of the factor loading unchanged. Alternatively, if the indicator or the scaling indicator equation is misspecified, then the loading is unlikely to be robust. The results are illustrated with hypothetical and empirical examples.

Determination of humic substances in deep groundwater from sedimentary formations by the carbon concentration-based DAX-8 resin isolation technique

ABSTRACTConcentrations of humic substance (HS) in deep groundwater from sedimentary formations were determined by the carbon concentration-based DAX-8 resin isolation technique. The groundwater samples were collected from test galleries at depths of 140, 250 and 350 m at the Horonobe Underground Research Laboratory (URL) in Hokkaido, and two observation wells with different depths of 560 and 1050 m in Niigata, Japan. The analytical condition was optimized for the groundwater samples with a high salinity and a high concentration of dissolved organic matters (DOMs). The analytical results showed that the HS concentrations varied from 7.8 to 23.5 mg-C dm−3, depending on the depth and the area. The HS proportions to DOM (%HS) were evaluated to be 58 – 67% and slightly decreased in the deeper groundwater. The regression analysis showed that the HS concentrations are positively correlated with the DOM concentrations. In addition, the low deviation of the %HS values from the slope in the regression equation indicated that the slight variation of %HS can be trivial in the prediction of the concentration of HS. In previous studies, HS concentrations in the groundwater had been determined with a large uncertainty and potential usage of the regression equation for the prediction had not been elucidated. Therefore, the results in this study can provide useful information on the HS concentration and its prediction from the DOM concentration in deep groundwater from sedimentary formations.

Investigation of assembly, power direction and load sharing in concentric face gear split-torque transmission system

As a special transmission mechanism used in aeronautical transmission field, a concentric face gear split-torque transmission system (CFGSTTS) is investigated in this study, with the focus on the work performances of the system including assembly, power direction and load sharing. Considering the complicated layout with multiple asymmetric power branches, the assembly condition of CFGSTTS is deduced and validated. To simulate this closed-loop system whose power directions are unknown in advance, a new finite element model which greatly differs from the conventional model in analytical step, boundary condition and grid division is developed. By the application of the new model, the power directions of branches in CFGSTTS are determined. On the premise of meeting the assembly conditions, the effect of factors including load condition, distribution angle, layout form and the number of idlers on power directions in CFGSTTS is researched, and the impact of those factors on load sharing is also explored. The results reveal that the power directions in CFGSTTS are alterable, and the load sharing coefficients are affected obviously by structural parameters.

Kobayashi–Hitchin correspondence for analytically stable bundles

We prove the existence of an Hermitian–Einstein metric on holomorphic vector bundles with an Hermitian metric satisfying the analytic stability condition, under some assumption for the underlying Kähler manifolds. We also study the curvature decay of the Hermitian–Einstein metrics. It is useful for the study of the classification of instantons and monopoles on the quotients of four-dimensional Euclidean space by some types of closed subgroups. We also explain examples of doubly periodic monopoles corresponding to some algebraic data.

Study of Abnormal Group Velocities in Flexural Metamaterials

Generally, it has been known that the optical branch of a simple one-dimensional periodic structure has a negative group velocity at the first Brillouin zone due to the band-folding effect. However, the optical branch of the flexural wave in one-dimensional periodic structure doesn’t always have negative group velocity. The problem is that the condition whether the group velocity of the flexural optical branch is negative, positive or positive-negative has not been studied yet. In consequence, who try to achieve negative group velocity has suffered from trial-error process without an analytic guideline. In this paper, the analytic investigation for this abnormal behavior is carried out. In particular, we discovered that the group velocity of the optical branch in flexural metamaterials is determined by a simple condition expressed in terms of a stiffness ratio and inertia ratio of the metamaterial. To derive the analytic condition, an extended mass-spring system is used to calculate the wave dispersion relationship in flexural metamaterials. For the validation, various numerical simulations are carried out, including a dispersion curve calculation and three-dimensional wave simulation. The results studied in this paper are expected to provide new guidelines in designing flexural metamaterials to have desired wave dispersion curves.

Towards a theory of multi-parameter geometrical variational problems: Fibre bundles, differential forms, and Riemannian quasiconvexity

We are concerned with the existence and associated gauge problems of a general class of geometrical minimisation problems, with action integrals defined via differential forms over fibre bundles. We find natural algebraic and analytic conditions which give rise to an associated gauge theory. Moreover, we propose the notion of “Riemannian quasiconvexity” for cost functions whose variables are differential forms on Riemannian manifolds, which extends the classical quasiconvexity condition in the Euclidean settings. The existence of minimisers under the Riemannian quasiconvexity condition has been established. This work may serve as a tentative generalisation of the framework developed in the recent paper [Arch. Ration. Mech. Anal. 234 (2019), pp. 317–349] by Dacorogna–Gangbo.