Maximal Convergence Research Articles

Hermite–Birkhoff spline Quasi-Interpolation with application as dense output for Gauss–Legendre and Gauss–Lobatto Runge–Kutta schemes

Spline Quasi-Interpolation (QI) of even degree 2R on general partitions is introduced, where derivative information up to order R≥1 at the spline breakpoints is required and maximal convergence order can be proved. Relying on the B-spline basis with possible multiple inner knots, a family of quasi-interpolating splines with smoothness of order R is associated with each R≥1, since there is the possibility of using different local sequences of breakpoints to define each QI spline coefficient. By using suitable finite differences approximations of the necessary discrete derivative information, each QI spline in this family can be associated also with a twin approximant belonging to the same spline space, but requiring just function information at the breakpoints.Among possible different applications of the introduced QI scheme, a smooth continuous extension of the numerical solution of Gauss-Lobatto and Gauss-Legendre Runge-Kutta methods is here considered. When R>1, such extension is based on the use of the variant of the QI scheme with derivative approximation which preserves the approximation power of the original Runge-Kutta scheme.

Vergence eye movements impairments in schizophrenia and bipolar disorder

One of the most evaluated eye tracking tasks in schizophrenia (SZ) and bipolar disorder (BD) are smooth pursuit eye movements. They rely on the maintenance of slowly moving object on the fovea. While most of the studies evaluated tracking of a target that moves in the fronto-parallel plane, only two assessed vergence eye movements (VEM), which relies on the pursuit of object that moves in depth. The aim of our study was to compare VEM performance in SZ and BD. We evaluated 28 SZ patients, 32 BD patients and 25 healthy controls (HC). Participants underwent thorough optometric examination before eye tracking task. VEM were measured with the use of infrared eye tracker and dedicated vergence stimuli generator. SZ patients showed higher mean break and recovery points of fusion and shorter correct tracking time than HC. BD individuals revealed tracking accuracy deficits and higher number of saccades than HC. Compared to BD, SZ patients showed decrease of maximal convergence and divergence. Moreover, they presented tracking accuracy deficits of non-dominant eye: altered eyes positioning error during convergence and divergence gain. Exploratory analysis revealed significant gender differences between groups in terms of binocular VEM parameters. In this study we have recognized pattern of eye movement disturbances differentiating abovementioned groups. SZ patients showed decreased vergence tracking range with shorter tracking time and impaired accuracy of non-dominant eye, while BD patients showed higher number of saccades with decreased tracking accuracy. Neuroimaging studies are necessary to identify neuronal underpinnings of VEM impairments in SZ and BD.

Maximal Convergence and Interpolation on Unconnected Sets

A theorem of Grothmann states that interpolating polynomials to a holomorphic function on a compact set E is maximally convergent to f only if a subsequence of the interpolation points converges to the equilibrium distribution of E in the weak* sense. Grothmann’s proof applies only for connected sets E. The objective of this paper is to provide a new necessary condition for maximal convergence which is the crucial tool to prove Grothmann’s theorem for unconnected sets E.

The Neural Blending of Words and Movement: Event-Related Potential Signatures of Semantic and Action Processes during Motor-Language Coupling.

Behavioral embodied research shows that words evoking limb-specific meanings can affect responses performed with the corresponding body part. However, no study has explored this phenomenon's neural dynamics under implicit processing conditions, let alone by disentangling its conceptual and motoric stages. Here, we examined whether the blending of hand actions and manual action verbs, relative to nonmanual action verbs and nonaction verbs, modulates electrophysiological markers of semantic integration (N400) and motor-related cortical potentials during a lexical decision task. Relative to both other categories, manual action verbs involved reduced posterior N400 amplitude and greater modulations of frontal motor-related cortical potentials. Such effects overlapped in a window of ∼380-440 msec after word presentation and ∼180 msec before response execution, revealing the possible time span in which both semantic and action-related stages reach maximal convergence. These results allow refining current models of motor-language coupling while affording new insights on embodied dynamics at large.

Аспекты рациональности управленческих решений в сфере предпринимательства

This article features managerial decisions in business area, where the state plays the role of an external regulator of public relations and the main influencer. The legal tools that affect decision-making in business depend on the social mechanisms of business regulations. The author describes the position of the rational regulator that evaluates the decisions made by a business entity. Positive law is an integral part of objective reality and is a set of codified principles of legally appropriate behavior. Imperative and dispositive regulations of public relations in business area imply that a business entity can choose a model of managerial and entrepreneurial behavior based on the rules provided by the legislator. The active role of the state as an external regulator of the social relations reflects the problem of dissonance between legal and social norms underlying managerial decision-making, which leads to additional economic and transaction costs. The paper also features the problem of frustration conflict between the regulator and the business environment in the context of applying the rationality proposed by the state in business activities and the problem of choosing the right managerial decision for its subjects. By refusing from a radical and negative assessment of the entrepreneur's management decisions, the state can solve this problem. The state needs to be more tolerant to business risks as an alternative rationality, without identifying them with deviant behavior. By preventing alienation of business from the state, one can eliminate the conflict between law and favorable climate in business area, i.e. maximal convergence of social and legal norms.

Integrating permanent plot and palaeoecological data to determine subalpine post‐fire succession, recovery and convergence over 128 years

AbstractAimsPost‐fire succession in low‐productivity ecosystems is rarely directly measured. We test whether taxonomic, functional, or baseline convergence has occurred 128 years after a major fire in 1890 in a low‐productivity, fire‐susceptible subalpine ecosystem. The historical plots represent one of the longest‐running quantitative ecological studies in the world.LocationArthur's Pass, South Island, New Zealand.MethodsWe remeasured historical plots at sites established 42 years after the fire, and modernised previous chart quadrat data to percentage frequency. We tested whether taxonomic and functional dissimilarity within the site, and within environmentally similar transect groups, reduced over time. We used pollen data preserved in soil cores taken on the plots to test whether the site had returned to the reference pre‐fire baseline.ResultsThere is little evidence of taxonomic convergence across the site and dissimilarity remains high. Functional dissimilarity showed little reduction or evidence of convergence. Within maximally similar groups of transects, taxonomic and functional dissimilarity declined over time. Tree frequency increased significantly year‐on‐year. There is a lack of convergence with the pre‐fire baseline, accompanied by a reduction in the proportion of tree pollen represented on most transects.ConclusionsThe taxonomic rate of successional change has yet to slow, and a steady state has yet to be reached, suggesting it is too early to consider the site has attained maximal convergence. Palaeoecological data have allowed quantification of the effect of a novel fire regime to which the ecosystems are poorly adapted: we found compositional, structural, and dominant‐species differences between pre‐ and post‐fire vegetation. Combining permanent transects and palaeoecological data allows for a synthesis of data at multiple time scales, permitting investigations of long‐duration successions.

Faber-Laurent Series in Variable Smirnov Classes

In this work, the maximal convergence properties of partial sums of Faber-Laurent series in the variable exponent Smirnov classes of analytic functions defined on a doubly connected domain of the complex plane are investigated.

Non-satisfiability of a positivity condition for commutator-free exponential integrators of order higher than four

We consider commutator-free exponential integrators as put forward in Alverman and Fehske (J Comput Phys 230:5930–5956, 2011). For parabolic problems, it is important for the well-definedness that such an integrator satisfies a positivity condition such that essentially it only proceeds forward in time. We prove that this requirement implies maximal convergence order of four for real coefficients, which has been conjectured earlier by other authors.

Elimination of the Potentially Dangerous Asteroid “Apophis” Using Electric Rocket

A project of elimination of potentially dangerous asteroid Apophis which April 13, 2029 year approaches to Earth at a distance of 36,000 km is considered. The elimination is carried out by means of asteroid disintegration into small fragments as a result of nuclear explosion, which is produced 133 days before the moment of maximal convergence of the asteroid Apophis with Earth. In the project, a method of phased timely delivery of nuclear charge on the surface of the asteroid is proposed. In the first stage, the nuclear charge using carrier rocket “Delta” is delivered into Earth orbit. In the second stage, the charge using electric rocket is transferred from Earth orbit into the orbit of asteroid Apophis and is descended onto its surface. For implementation of the project, the design of electric rocket ER-7, which uses electric rocket engines type MARS and solar panels based on gallium arsenide is developed. Design of landing capsule, which has a chemical rocket engine and the container in which located the nuclear charge of 6 megaton is developed.

Maximal Convergence of Faber Series in Smirnov Classes with Variable Exponent

The maximal convergence properties of the partial sums of the Faber series in the variable exponent Smirnov classes are investigated.

Fixed-Time Homogeneous Integral Controller

Abstract We propose a homogeneous integral controller with positive homogeneity degree, for systems with relative degree two and three. Its design and the convergence proof is achieved by the construction of an explicit homogenous Lyapunov function. A combination of this controller, with a discontinuous one developed by the authors in a previous work, allows to achieve: (i) fixed time convergence, that is that the maximal convergence time is a constant independent of the size of the initial conditions; (ii) insensitivity to Lipschitz (matched) perturbations, i.e. perturbations with bounded derivative; and (iii) providing a continuous control signal, and thus reducing the chattering effect of a discontinuous controller.

The relaxed gradient based iterative algorithm for solving matrix equations [formula omitted

In this paper, we first present a relaxed gradient based iterative (RGI) algorithm for solving matrix equations A1XB1=F1 and A2XB2=F2. The idea is from (Niu et al., 2011; Xie and Ma, 2016) in which efficient algorithms were developed for solving the Sylvester matrix equations. Then the RGI algorithm is extended to solve the generalized linear matrix equations of the form AiXBi=Fi,(i=1,2,…,N). For any initial value, it is proved that the iterative solution converges to their true solution under some appropriate assumptions. Finally, a numerical example is given to illustrate that the introduced iterative algorithm is more efficient than gradient based maximal convergence rate iterative (GI) algorithm of Ding et al. (2010) in speed, elapsed time and iterative steps.

Relationship between Summertime Intraseasonal Oscillations and Submonthly Wave Patterns under Meridional Periodic Fluctuations

Abstract In this study, submonthly wave patterns under the periodically fluctuating Japan–South China Sea (JSCS) pattern were separated into intraseasonal oscillation (ISO) westerly and easterly phases. The composite results showed that the wave patterns in the westerly JSCS high and low phases were more effectively organized and situated in a more intense monsoon trough than their counterparts in the easterly phase. Tropical cyclones (TCs) tended to occur over cyclonic systems of the wave patterns where minimal vertical shear axes were also located. More TCs formed in the westerly JSCS phases near areas where maximal moisture convergence was located. Taiwan experienced heavier rainfall during the westerly JSCS phases because the ISO enhanced the monsoon troughs for the cyclonic system of the wave pattern to develop near Taiwan in the westerly JSCS high phase. Additionally, in the westerly JSCS low phase, a stronger southeasterly mean flow generated by the ISO steered the wave pattern and TCs farther west and thus closer to Taiwan. Therefore, the ISO influenced the mean state circulation systems and then steered TCs and the wave patterns to affect Taiwan’s weather.

Nicht-konservative weich strukturvariable Regelungen mit invers-polynomialen Selektionsstrategien

Zusammenfassung Der Beitrag stellt notwendige und hinreichende Existenzbedingungen weich strukturvariabler Regelungen mit invers-polynomialen Selektionsstrategien für lineare Strecken mit einer Eingangsgröße und Stellgrößenbeschränkung vor. Das resultierende Regelgesetz wird bezüglich einer Ljapunov-Funktion-basierten unteren Grenze der Konvergenzrate optimiert. Der konvergenzoptimale Regler ist ein Zweipunktregler mit einer einfachen parameterabhängigen Selektionsstrategie. Ein sättigender High-Gain-Regler wird als stetige Approximation dieses Regelgesetzes vorgestellt. Dieser vermeidet die Nachteile des unstetigen Regelgesetzes auf Kosten einer suboptimalen Konvergenzrate.

On stabilizing linear systems with input saturation via soft variable structure control laws

A large number of control methods deal with stabilizing single-input linear systems with input saturation. The linear full-state feedback is one of the most used, yielding either nonsaturating or high gain controls, whereby the saturating effects of the latter are reduced by means of anti-windup structures. Among the nonlinear controls, the time optimal control, in this case a bang–bang type control, yields the fastest time response, but its switching surface is generally not characterizable. Related to the speed of the time response is the convergence rate, which can be determined using invariant sets. The most used ones are the ellipsoidal sets, since they can be analyzed using powerful tools such as the Lyapunov equation and designed via convex optimization. For this reason, they are also used for designing soft variable structure controls. The paper presents a nonconservative design method for a stabilizing control of this type employing implicit Lyapunov functions (iLF). A nonsaturating control law is given, including some infinitely densely nested and contractive invariant sets of the equilibrium state. The control law is then optimized by maximizing the iLF-based lower bound of the convergence rate. The maximal convergence control is shown to be of bang–bang type, with a parameter dependent switching scheme. To overcome possible difficulties of a switching controller, a saturating high gain control is also presented.

Exact Maximal Convergence in Capacity and Zero Distribution of Rational Approximants

Let E be a compact, connected set in \(\mathbb {C}\) with regular, connected complement, and let f be meromorphic on E with maximal Green domain \(E_{\rho (f)}\) of meromorphy, \(\rho (f) < \infty \). We investigate rational approximations \(r_{n,m_n}\) of f on E with numerator degree \(\le n\) and denominator degree \(\le m_n\) where \(m_n = o(n)\) as \(n \rightarrow \infty \) and $$\begin{aligned} \underset{n \rightarrow \infty }{\lim \sup } \, \Vert f - r_{n,m_n}\Vert ^{1/n}_{\partial E} \le \frac{1}{\rho (f)}. \end{aligned}$$ If \(\{r_{n,m_n}\}_{n \in \Lambda }\) is maximally convergent in capacity to f on \(E_{\rho (f)}\) for some \(\Lambda \subset \mathbb {N}\), then this subsequence converges exactly to f on \(E_{\rho (f)}\) if f has a branch point on the boundary of \(E_{\rho (f)}\). Moreover, the exact convergence in capacity implies that the normalized zero distributions of \(r_{n,m_n}\) converge weakly to the equilibrium measure of \(\overline{E}_{\rho (f)}\) as \(n \rightarrow \infty \), at least for a subsequence of \(\mathbb {N}\).

Efficient n-point iterative methods with memory for solving nonlinear equations

In this paper, we proposed a family of n-point iterative methods with and without memory for solving nonlinear equations. The convergence order of the new n-point iterative methods without memory is 2n requiring n+1 functional evaluations in per full iteration, which implies that the new n-point iterative methods without memory are optimal according to Kung-Traub conjecture. Based on the n-point methods without memory, the n-point iterative methods with memory are obtained by using n+1self-accelerating parameters. The maximal convergence order of the new n-point iterative methods with memory is (2n+1?1+22(n+1)+1)/2$(2^{n+1}-1+\sqrt {2^{2(n+1)}+1} )/2$, which is higher than any existing iterative methods with memory. Numerical examples are demonstrated to confirm theoretical results.

Almost everywhere $${(C, \alpha, \beta &gt; 0)}$$ ( C , α , β &gt; 0 ) -summability of the Fourier series of functions on the 2-adic additive group

We investigate Cesaro summability of bivariate integrable functions on the 2-adic group. We prove the a.e. convergence of 2-adic Cesaro means \({\sigma^{\alpha, \beta}_{n, m} f \rightarrow f}\) as \({n, m \rightarrow \infty}\) for functions \({f \in\,L\,{\rm log}^{+}\,L(\mathbb{I}^2)}\) and \({\alpha, \beta > 0}\). Then it is shown that this convergence result can not be improved in the Pringsheim sense, that is, \({L\,{\rm log}^{+}\,L}\) is the maximal convergence space for \({\sigma^{1, 1}_{n, m}}\) when there are no conditions for the indices except that they tend to infinity. We prove that for all measurable functions \({\delta : [o, \infty) \rightarrow [o, \infty)}\) for which \({{\rm lim}_{t \rightarrow \infty} \delta(t) = 0}\) there is a function \({f \in\,L\,\log^{+}\,L\, \delta(L)}\) with lim sup \({|\sigma_{2^{n_{1}}, 2^{n_{2}}} f(x)| = +\infty}\) a.e. as \({{\rm min}\,\{n_{1}, n_{2}\} \rightarrow \infty}\).

Microwave radiation of solar active regions before X flares according to the RATAN-600 observations in 2011

The evolution of the microwave radiation from four active regions, where strong X-ray flares (X-class, GOES) occurred in 2011, has been studied. Daily multiwavelength RATAN-600 radio observations of the Sun in the 1.6–8.0 cm range have been used. It has been indicated that the radiosource above the photospheric magnetic field neutral line (above the region with the maximal convergence of the fields opposite in sign) becomes predominant in the structure of the active region microwave radiation one to two days before a powerful flare as in the eruptive events previously studied with RATAN-600. The appearance of such a radiosource possibly reflects the current sheet formation in the corona above the active region. The energy necessary for a flare is stored in the magnetic field of active region, which can be considered as a factor for predicting a powerful flare.

Finding the pseudogradient of the objective function in procedures for estimation of interframe deformations of images

In the recursive estimate of parameters of interframe geometric deformations of digital images, calculating the pseudogradient from a local sample and current estimates of deformation parameters to be measured involves finding derivatives in terms of finite differences. The maximal convergence rate of estimates of the deformation parameters can be achieved when using the most informative readings of images in a local sample. Under this approach, there exist optimal values of increments in the parameters and basic axes, depending on the mismatch between estimates and correlation properties of the image. The performance of the procedures may be increased if the increments are optimized at each iteration. The potential accuracy of estimation of the parameters, as given by the Cramer-Rao inequality, serves as an optimality criterion when calculating the pseudogradient of the objective function. It is shown that the condition of maximum of information can be reduced to the condition of maximization of the ratio of the expectation of the pseudogradient to its mean square deviation. Application of optimized values of increments enables one to reduce considerably (up to several times) the computational cost with the same accuracy of estimation.