Modulation Theory Research Articles

MODULAR REHABILITATION SYSTEM AT THE STATIONARY PHASE OF REHABILITATION OF MILITARY MEN AFTER ACUTE NONREVMATIC MYOCARDITIS

The paper presents the experience of rehabilitation treatment for servicemen who had suffered from acute nonrheumatic myocarditis. The treatment was conducted in the 1469 Naval Clinical Hospital of the Northern Fleet with using an 8-modular system of medical rehabilitation activities: a laboratory-diagnostic cluster with a patient’s rehabilitation and expert evaluation and a rehabilitation prognosis; drug therapy, diet therapy, psychosomatic diagnosis and correction of the emotional state; therapeutic exercise with restoration of physical performance and adaptive health parameters; information cluster — providing the patient with a complete and accessible understanding of information about a healthy lifestyle; physiotherapeutic non-pharmacological correction of physiological disorders, activation of endogenous protective systems of the body; functional diagnostics complex: a study of restoration of functioning parameters for cardiovascular and respiratory systems, the development of the body’s adaptation to physical exertion. As a result of using the modular system, a decrease in the average bed-day during the rehabilitation phase for patient after mild acute myocarditis was 16,6% (from 17,5±1,3 to 14,6±2,7 days); after moderate myocarditis — 8.1% (from 22,3±2 to 20.5±1,8 days); and after severe — 5,9% (from 27,2±3,5 to 25,6±1,2 days). The rehabilitation program, which has been developed basing on principles of the theory of modules, is a dynamic, easily simulated system with a combination of variable and permanent elements, that allows to reduce the cost of treatment and rehabilitation in mild myocarditis by 10,6±0,9%, in moderate myocarditis — by 7,2±0,8%, and in severe myocarditis — by 3,7±0,4%.

Cogalois theory and drinfeld modules

In this paper, we generalize the results of [M. Sánchez-Mirafuentes and G. Villa–Salvador, Radical extensions for the Carlitz module, J. Algebra 398 (2014) 284–302] to rank one Drinfeld modules with class number one. We show that, in the present form, there does not exist a cogalois theory for Drinfeld modules of rank or class number larger than one. We also consider the torsion of the Carlitz module for the extension [Formula: see text].

Dispersive shock wave theory for nonintegrable equations.

We suggest a method for calculation of parameters of dispersive shock waves in the framework of Whitham modulation theory applied to nonintegrable wave equations with a wide class of initial conditions corresponding to propagation of a pulse into a medium at rest. The method is based on universal applicability of Whitham's "number of waves conservation law" as well as on the conjecture of applicability of its soliton counterpart to the above mentioned class of initial conditions which is substantiated by comparison with similar situations in the case of completely integrable wave equations. This allows one to calculate the limiting characteristic velocities of the Whitham modulation equations at the boundary with the smooth part of the pulse whose evolution obeys the dispersionless approximation equations. We show that explicit analytic expressions can be obtained for laws of motion of the edges. The validity of the method is confirmed by its application to similar situations described by the integrable Korteweg-de Vries (KdV) and nonlinear Schrödinger (NLS) equations and by comparison with the results of numerical simulations for the generalized KdV and NLS equations.

About the Closed Quasi Injective S-Acts Over Monoids

The aim of introducing and studying the notion of closed quasi injective S-act is to create a basis facilitate for the exchange ideas between module theory and act theory. As well as it represents a generalization of the quasi-injective act. The quasi-injective act was first introduced and studied by A. M. Lopez, Jr. and J. K. Luedeman, 1979. Then the author was one of the researchers which introduced several generalizations for this notion from several aspects because of its importance. More accurately, the contribution of this paper to the field of competence can be summarized into three points as follows: First: The possibilities for applying the topic of this article helps researchers about how can connect class of injectivity with its generalizations. Second: Study the topic of this article contributes to the improvement of the vision for finding the corresponding between acts theory and module theory. Third: This article has dealt with the important subject in the field of science and knowledge especially in algebra and can take it as a basis for future work for the researchers who work on algebra. Now, in this paper, the concept of closed quasi injective acts over monoids is introduced which represents a generalization of quasi injective. Several characterizations of this concept are given to show the behavior of the property of closed quasi injective. Relationship of the concept of closed quasi injective acts over monoids with Hopfian, co-Hopfian and directly finite property are considered. This work gives the answer to the question of what are the conditions to be met in the subacts in order to inherit the property of closed quasi injectivity. We obtained the main result in this direction in proposition (2.5) and proposition (2.6). A part of this paper was devoted to studying the relationship among the class of closed quasi injective acts with some generalizations of injectivity.

基于TDLAS的气体检测技术算法

Tunable diode laser absorption spectroscopy(TDLAS) is a high sensitive and high resolution gas absorption spectrum detection technology, with fast response, high precision, excellent single mode characteristics and strong versatility. The temperature and concentration of the detected gas were calculated by measuring the absolute absorption intensity in the direct absorption method of TDLAS, but was easily affected by particle concentration and fluctuation of laser intensity. The laser was modulated through high frequency sinusoidal signal in the wavelength modulation method of TDLAS, making the laser output frequency and intensity modulated simultaneously, with the characteristics of high signal-to-noise ratio and sensitivity, but the gas parameters were determined by calibration experiments or complex algorithms. Therefore, the expression of harmonic terms containing molecular absorption information was deduced through the theory of absorption spectrum and wavelength modulation, and the relationship between harmonic signal and absolute absorption intensity of detected gas was analysed, establishing the measurement algorithm of absolute absorption intensity based on harmonic signal. The absorption spectral line of NH3 molecule near 1 531 nm was taken as an example for numerical analysis, and the relative errors between theoretical calculation (a=0) and simulation values were no more than 2% when the modulation amplitude reached up to a=0.032 cm-1(m=2), which further proved the reliability of on-line measurement algorithm.

ИССЛЕДОВАНИЕ ВЛИЯНИЯ ПРЕДВАРИТЕЛЬНОГО СОСТОЯНИЯ НА МЕХАНИЧЕСКИЕ СВОЙСТВА ВЯЗКОУПРУГИХ ТЕЛ

We present a new general statement of the problem on steady-state oscillations of a non-uniform viscoelastic body, taking into account the residual stress-strain state. To derive it, we use the theory of complex modules and the correspondence principle which makes it possible to write down the problem for viscoelastic bodies in the same form as the corresponding elasticity problems by replacing the elastic characteristics with the complex functions of vibration frequency. To describe the viscoelastic behavior, we employ a three-parameter model of the standard viscoelastic body consisting of instantaneous and long-term modules, as well as relaxation time. On the basis of the statement proposed, we consider the model problems on vibrations of inhomogeneous viscoelastic rods and pipes taking into account the presence of both pre-stress and residual strain. Within the problem for the viscoelastic rod, we analyze the longitudinal oscillations and consider the pre-stress and residual strain as functions of the longitudinal coordinate. Regarding the problem for the viscoelastic pipe, we consider the plane stress-strain state and assume that the oscillations are excited by the radial load; the mechanical properties of the cylinder and the residual stress-strain state depend on the radial coordinate. The numerical solutions in both cases are based on the shooting method. For both models problems under study, we present and observe the results of the comparative analysis of the effect of pre-stress and residual deformations on the amplitude-frequency characteristics (AFC), based on the computational experiments. We also provide the analysis of such an influence of each factor on the most sensitive frequencies values. The study conducted shows that for both rod and pipe the residual strain fields have a significantly greater effect on the AFC than the pre-stress fields do. This conclusion correlates with the results obtained previously for elastic bodies.

Enhanced near field focus steering of rectangular nanoslit metasurface structure

<sec> Surface plasmon polaritons (SPPs) are electromagnetic excitations propagating along the metal-dielectric interface. The SPPs excited by the metal micro/nano structures have the ability to manipulate the light on a subwavelength scale. The SPPs are of interest to researchers for its excellent subwavelength field confinement and local field enhancement. So far, the SPPs have found numerous applications in optical tweezers, biological sensors, and near-field holographic imaging, due to its subwavelength focusing. </sec><sec> In order to achieve enhanced near field subwavelength focusing, we propose a metasurface structure in this paper, which is composed of rectangular nanoslit circular arrays and multilayer annular slits. The function of the inner ring arrays is to excite SPPs and the outer ring slits is to enhance focusing. The electric field expression of SPP is studied analytically and theoretically, and then the principle of rectangular nanoslit to excite SPP and the inner ring array structure to generate central focusing are explained. The parameters of the structure are optimized, and the focusing characteristics of the metasurface structure under different polarization light are studied by using the finite difference time domain method. Furthermore, we explain the principle of the external structure enhancing focusing by introducing the theory of Fresnel zone plate and depth modulation. The analytical expressions and simulations show that when the incident polarized light has a wavelength of 980 nm, the focal spot having a full width at half maximum of about 650 nm, and the distribution of the coupled field can be approximately expressed by the first kind Bessel function. Compared with the former single circular array structure, the composite structure proposed in this paper has a good effect of both enhancing the central focusing and inhibiting the outer field divergence, and the center focal spot intensity is doubled. In addition, the electric field excited by the arbitrary linearly polarized light is also discussed, the electric field satisfies the form of the polarization angle sinusoidal function multiplied by a Bessel function. <sec> The research results of our study have some applications in subwavelength light modulation, near-field imaging, optical tweezers, and subwavelength scale optical information processing and so on. </sec></sec>

Theory of Relative Dependency:
 Higher Coupling Concentration in Smaller Modules and its Implications for Software Refactoring and Quality

Our recent studies have repeatedly found that smaller modules are proportionally more defect-prone. In this paper, we formulated and tested a hypothesis stating that smaller modules are proportionally more coupled given that dependencies caused by coupling has been consistently associated with defect-proneness. We found strong evidence supporting this hypothesis. Further, we found that refactoring practices exacerbate this effect. Based on the highly consistent results obtained in this study, we state an empirically-based theory for software modules called the theory of relative dependency: In large scale software systems, smaller modules will be proportionally more dependent compared to larger ones. The implications of our findings for practice are twofold: (1) we now have an empirically supported mechanism explaining the observations that defect concentration is higher in smaller modules, which can be used by practitioners as an evidence while seeking resources and support to revise or amend the existing quality assurance and quality control practices in their organizations; (2) for projects that refactor extensively, such as those using agile methods, focusing defect detection and correction activities on smaller modules will lead to even more effective defect detection.

Shared Aperture Multibeam Forming of Time‐Modulated Linear Array

A novel technique is proposed in this paper for shared aperture multibeam forming in a complex time‐modulated linear array. First, a uniform line array is interleaved randomly to form two sparse array subarrays. Subsequently, the theory of time modulation for linear arrays is applied in the constructed subarrays. In the meantime, the switch‐on time sequences for each element of the two subarrays are optimized by an optimized differential evolution (DE) algorithm, i.e., the scaling factor of the sinusoidal iterative chaotic system and the adaptive crossover probability factor are used to enhance the diversity of the population. Lastly, the feasibility of the new technique is verified by the comparison between this technique and the basic multibeam algorithm in a shared aperture and the algorithm of iterative FFT. The results of simulations confirm that the proposed algorithm can form more desired beams, and it is superior to other similar approaches.

Two-fold homotopy of 2-crossed module maps of commutative algebras

We address the homotopy theory of 2-crossed modules of commutative algebras. In particular, we define the concept of a two-fold homotopy between a pair of one-fold homotopies connecting 2-crossed module maps . We also prove that if the domain 2-crossed module is free up to order one (i.e., if the bottom algebra is a polynomial algebra) then we have a 2-groupoid of 2-crossed module maps and their homotopies and two-fold homotopies.

On the relative Galois module structure of rings of integers in tame extensions

Let $F$ be a number field with ring of integers $O_F$ and let $G$ be a finite group. We describe an approach to the study of the set of realisable classes in the locally free class group $Cl(O_FG)$ of $O_FG$ that involves applying the work of the second-named author in the context of relative algebraic $K$ theory. When $G$ is of odd order, we show (subject to certain conditions) that the set of realisable classes is a subgroup of $Cl(O_FG)$. This may be viewed as being a partial analogue of a classical theorem of Shafarevich on the inverse Galois problem for soluble groups in the setting of Galois module theory.

Rings and Modules Whose Socles are Relative Ejective

Lifting homomorphism from modules to modules or even from certain submodule to the modules have been important both in ring and module theory. In this note we study rings and modules whose socles are relative ejective. Moreover we reduce our consideration to rings and modules with injective socles which provides the dual notion to PSmodules.

DECIDABILITY OF THE THEORY OF MODULES OVER PRÜFER DOMAINS WITH INFINITE RESIDUE FIELDS

AbstractWe provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains with infinite residue fields in terms of a suitable generalization of the prime radical relation. For Bézout domains these conditions are also necessary.

Brain-Inspired Motion Learning in Recurrent Neural Network With Emotion Modulation

Based on basic emotion modulation theory and the neural mechanisms of generating complex motor patterns, we introduce a novel emotion-modulated learning rule to train a recurrent neural network, which enables a complex musculoskeletal arm and a robotic arm to perform goal-directed tasks with high accuracy and learning efficiency. Specifically, inspired by the fact that emotions can modulate the process of learning and decision making through neuromodulatory system, we present a model of emotion generation and modulation to adjust the parameters of learning adaptively, including the reward prediction error, the speed of learning, and the randomness in action selection. Additionally, we use Oja learning rule to adjust the recurrent weights in delayed-reinforcement tasks, which outperforms the Hebbian update rule in terms of stability and accuracy. In the experimental section, we use a musculoskeletal model of the human upper limb and a robotic arm to perform goal-directed tasks through trial-and-reward learning, respectively. The results show that emotion-based methods are able to control the arm with higher accuracy and a faster learning rate. Meanwhile, emotional Oja agent is superior to emotional Hebbian one in term of performance.

A nonlinear measurement method of polarization aberration in immersion projection optics by spectrum analysis of aerial image.

Polarization aberrations (PA) can be presented by Jones pupil and can also impact the imaging performance of immersion projection optics significantly. Precise PA measurement is most important for resolution enhancement technology and holistic lithography at 7nm node and below, in order to improve the pattern fidelity and processing stability. However, the current imaging-based measurement method of PA by linear approximation has not taken the coupling effect of the PA coefficients into account. This paper proposes a nonlinear measurement method of PA based on a rigorous nonlinear model to improve the measurement accuracy significantly. In this invention, the new spectrum modulation theory is developed to establish a rigorous quadratic form of PA and aerial image spectrum. A hybrid genetic algorithm is developed to solve the quadratic form inversely to obtain the PA accurately. An overall simulation validates that this method provides a superior quality of PA measurement with very high precision of 10-4λ.

Riemann problems and dispersive shocks in self-focusing media

The dynamical behavior resulting from an initial discontinuity in focusing media is investigated using a combination of numerical simulations and Whitham modulation theory for the focusing nonlinear Schrodinger equation. Initial conditions with a jump in either or both the amplitude and the local wavenumber are considered. It is shown analytically and numerically that the space-time plane divides into expanding domains in which the solution is described by a slow modulation of genus-zero, genus-one or genus-two solutions, their precise arrangement depending on the specifics of the initial datum

Analytical magnetic field prediction of flux switching machine with segmental rotor

To deeply study the segmental rotor flux switching machine (SRFSM), an analytical subdomain model is first developed to achieve the magnetic field distribution and electromagnetic performance such as back-electromotive force (EMF), cogging torque, electromagnetic torque, unbalanced magnetic pull, and eddy current losses in the permanent magnet (PM) and rotor support. Then, the number of rotor segments is determined according to the magnetic field modulation theory, and the effect of rotor segment number on the amplitude and total harmonic distortion of speed-normalised back-EMF is investigated as well. Using the proposed analytical model, the magnetic field regulation capacity and PM demagnetisation withstand capacity of the series and parallel hybrid excited SRFSMs are investigated and compared. The PM and parallel hybrid excited SRFSM prototype machines with 12 stator slots and 7 rotor segments are manufactured and tested to validate the proposed analytical model.

Modulation theory solution for nonlinearly resonant, fifth‐order Korteweg–de Vries, nonclassical, traveling dispersive shock waves

AbstractA new class of resonant dispersive shock waves was recently identified as solutions of the Kawahara equation— a Korteweg–de Vries (KdV) type nonlinear wave equation with third‐ and fifth‐order spatial derivatives— in the regime of nonconvex, linear dispersion. Linear resonance resulting from the third‐ and fifth‐order terms in the Kawahara equation was identified as the key ingredient for nonclassical dispersive shock wave solutions. Here, nonlinear wave (Whitham) modulation theory is used to construct approximate nonclassical traveling dispersive shock wave (TDSW) solutions of the fifth‐ order KdV equation without the third derivative term, hence without any linear resonance. A self‐similar, simple wave modulation solution of the fifth order, weakly nonlinear KdV–Whitham equations is obtained that matches a constant to a heteroclinic traveling wave via a partial dispersive shock wave so that the TDSW is interpreted as a nonlinear resonance. The modulation solution is compared with full numerical solutions, exhibiting excellent agreement. The TDSW is shown to be modulationally stable in the presence of sufficiently small third‐order dispersion. The Kawahara–Whitham modulation equations transition from hyperbolic to elliptic type for sufficiently large third‐order dispersion, which provides a possible route for the TDSW to exhibit modulational instability.

Flux singularities in multiphase wavetrains and the Kadomtsev‐Petviashvili equation with applications to stratified hydrodynamics

AbstractThis paper illustrates how the singularity of the wave action flux causes the Kadomtsev‐Petviashvili (KP) equation to arise naturally from the modulation of a two‐phased wavetrain, causing the dispersion to emerge from the classical Whitham modulation theory. Interestingly, the coefficients of the resulting KP are shown to be related to the associated conservation of wave action for the original wavetrain, and therefore may be obtained prior to the modulation. This provides a universal form for the KP as a dispersive reduction from any Lagrangian with the appropriate wave action flux singularity. The theory is applied to the full water wave problem with two layers of stratification, illustrating how the KP equation arises from the modulation of a uniform flow state and how its coefficients may be extracted from the system.

Quantitative Evaluation of the Topologies and Electromagnetic Performances of Dual-Three-Phase Flux-Switching Machines

Hybrid-excited flux-switching machines based on permanent magnet (PM) flux-switching machines were proposed to achieve improved torque–speed characteristics. However, due to the reduction of PM volume, decreases in torque density and efficiency are usually inevitable. Thus, it is necessary to make a comprehensive comparison between the dual-three-phase hybrid-excited flux-switching machines and their PM flux-switching counterparts. To obtain a full understanding of flux-switching machines, PM flux-switching machines with U-shaped stator cores and alternate-pole magnets or C-shaped stator cores are considered. From the perspective of the frequency domain, this paper not only gives a comprehensive evaluation and comparison of the above-mentioned six flux-switching machines, but also reveals the theoretical mechanism that results in their different electromagnetic behavior in a unified way by the general field modulation theory, which is the main contribution of this paper.