Triangular Conditions Research Articles

L‐Type Calcium Current Reactivation Contributes to Arrhythmogenesis Associated with Action Potential Triangulation

The morphology of the mammalian cardiac action potential (AP) is an important factor in the susceptibility to drug-induced early afterdepolarizations (EADs) that may initiate torsade de pointes (TdP). AP triangulation has been shown to be an important predictor of drug-induced TdP. APs from guinea pig and rabbit left ventricular single myocytes were recorded using a microelectrode-recording technique. I(Ca-L) currents were recorded in ventricular myocytes of guinea pig and rabbit using patch-clamping technique. At a stimulus frequency of 0.5 Hz, guinea pig ventricular myocytes displayed a square-like AP, whereas rabbit ventricular myocytes exhibited a triangle-like AP. Dofetilide-induced EADs were observed only in rabbit ventricular myocytes. Under the guinea pig AP clamping condition, the normalized I(Ca-L) instant reactivation currents in guinea pig and rabbit myocytes at voltages of -40 mV were 0.13 +/- 0.01 and 0.14 +/- 0.01, respectively. However, when rabbit AP served as the first clamping voltage, the normalized I(Ca-L) reactivation currents at -40 mV in guinea pig and rabbit myocytes were 0.20 +/- 0.01, 0.21 +/- 0.01, respectively, indicating that the I(Ca-L) recovery from inactivation in the rabbit triangular AP condition was significantly faster than in the guinea pig square AP condition. Comparison of the voltage clamp using the triangular waveform with the square waveform further confirmed that triangulation accelerates I(Ca-L) recovery from inactivation. In rabbit ventricular myocardium, AP triangulation accelerates I(Ca-L) channel recovery from inactivation, leading to instability of the cell membrane potential during repolarization, which is capable of initiating TdP.

Application of feedback linearisation to the tracking and almost disturbance decoupling control of multi-input multi-output nonlinear system

The tracking and almost disturbance decoupling problem of multi-input multi-output nonlinear systems based on the feedback linearisation approach are studied. The main contribution of this study is to construct a controller, under appropriate conditions, such that the resulting closed-loop system is valid for any initial condition and bounded tracking signal with the following characteristics: input-to-state stability with respect to disturbance inputs and almost disturbance decoupling, that is, the influence of disturbances on the L2 norm of the output tracking error can be arbitrarily attenuated by changing some adjustable parameters. One example, which cannot be solved by the first paper of the almost disturbance decoupling problem on account of requiring some sufficient conditions that the nonlinearities multiplying the disturbances satisfy structural triangular conditions, is proposed to exploit the fact that the tracking and the almost disturbance decoupling performances are easily achieved by the proposed approach. To demonstrate the practical applicability, a famous half-car active suspension system has been investigated.

Using Copulas to Construct Bivariate Foreign Exchange Distributions with an Application to the Sterling Exchange Rate Index

We model the joint risk-neutral distribution of the euro-sterling and the dollar-sterling exchange rates using option-implied marginal distributions that are connected via a copula function that satisfies the triangular no-arbitrage condition. We then derive a univariate distribution for a simplified sterling effective exchange rate index. Our results indicate that standard parametric copula functions, such as the commonly used Normal and Frank copulas, fail to capture the degree of asymmetry observed in the data. We overcome this problem by using a non-parametric dependence function in the form of a Bernstein copula which is shown to produce a very close fit. We further give an example of how our approach can be used to price currency index options.

Semi-global stabilization of a class of uncertain nonlinear systems by linear output feedback

This brief deals with the problem of semi-global stabilization by output feedback for a class of uncertain nonlinear systems. Due to the presence of mismatched uncertainties and the lack of triangularity condition, the systems under consideration are not uniformly completely observable. In addition, the uncertain nonlinear dynamics of the systems are higher order, rather than linearly growing, in the unmeasurable states. All these make the systems not semi-globally stabilizable by the existing output feedback design schemes. In this brief, by extending the feedback domination design techniques proposed by Qian and Lin, a systematic design scheme is developed to construct linear output feedback controllers that semi-globally stabilize a general class of uncertain nonlinear systems under less restrictive conditions.

Crack growth in a new nickel-based superalloy at elevated temperature

Crack growth at elevated temperature has been examined in a new fine-grained nickel-based superalloy under triangular, fast-slow, slow-fast, dwell and sustained loading conditions at 650 and 725∘C. The effect of loading waveform seems to be minimal for base frequencies over 0.01 Hz with a mixture of time and cycle dependent crack growth observed for all but the fast-slow waveform, where the crack growth remained cycle-dependent and the crack growth rate mostly constant. For base frequencies less than 0.01 Hz, crack growth under dwell load clearly accelerated and the crack growth rates were comparable with those under sustained load. Creep contribution was found to be negligible while crack tip constraint may be relevant to the out-of-plane crack growth observed under predominantly sustained load conditions.

Crack growth in a new nickel-based superalloy at elevated temperature

Crack growth mechanisms at elevated temperature have been examined in a new nickel-based superalloy. Scanning electron microscopy has been used to identify the fracture modes in specimens tested under triangular, fast-slow, slow-fast, dwell and sustained loading conditions at 650 and 725°C. A model has been developed considering a predominant oxidation-driven crack growth mechanism, as revealed from the SEM analysis. An oxidation sensitive time has been adopted to characterise the rate-dependent crack growth, together with an Arrehenius relationship to take account of the influence of temperature. The model predictions have been compared with the experimental results.

PBW bases for a class of braided Hopf algebras

We prove the existence of a basis of Poincaré–Birkhoff–Witt type for braided Hopf algebras R generated by a braided subspace V ⊂ P ( R ) if the braiding on V fulfills a triangularity condition. We apply our result to pointed Hopf algebras with abelian coradical and to Nichols algebras of low dimensional simple U q ( sl 2 ) -modules.

Robust adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems via small-gain approach

This paper presents a novel robust adaptive fuzzy tracking controller (RAFTC) for a wide class of perturbed strict-feedback nonlinear systems with both unknown system and virtual control gain nonlinearities. For unknown system nonlinearities, two types for them are included: one naturally satisfies the “triangularity condition” and may possess a class of unstructured uncertain functions which are not linearly parameterized, while the other is partially known and consists of parametric uncertainties and known “bounding functions”. The Takagi–Sugeno type fuzzy logic systems are used to approximate unknown system nonlinearities and a systematic design procedure is developed for synthesis of RAFTC by combining the backstepping technique and generalized small-gain approach. The algorithm proposed is highlighted by three advantages: (i) the semi-global uniform ultimate bound of RAFTC in the presence of perturbed uncertainties and unknown virtual control gain nonlinearities can be guaranteed, (ii) the adaptive mechanism with minimal learning parameterizations is obtained and (iii) the possible controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques can be removed. Performance and limitations of proposed method are discussed and illustrated with simulation results.

Cross-Hedging with Currency Options and Futures

This paper develops an expected utility model of a multinational firm facing exchange rate risk exposure to a foreign currency cash flow. Currency derivative markets do not exist between the domestic and foreign currencies. There are, however, currency futures and options markets between the domestic currency and a third currency to which the firm has access. Since a triangular parity condition holds among these three currencies, the available, yet incomplete, currency futures and options markets still provide a useful avenue for the firm to indirectly hedge against its foreign exchange risk exposure. This paper offers analytical insights into the optimal cross-hedging strategies of the firm. In particular, the results show the optimality of using options in conjunction with futures in the case of currency mismatching, even though cash flows appear to be linear.

Orthogonal Embeddings of Linear Time-Varying Systems

Given a contractive linear system T which is represented as a causal linear contractive operator on a Hilbert space H, we study the question: When does there exist an isometric or unitary causal extension of T to H⊕H? Here causality is formulated as a lower triangularity condition and we assume the same causality structure for the extension. This question is often referred to as the generalized Darlington synthesis problem for linear time-varying systems.

Cross-hedging with Currency Options and Futures

This paper develops an expected utility model of a multinational firm facing exchange rate risk exposure to a foreign currency cash flow. Currency derivative markets do not exist between the domestic and foreign currencies. There are, however, currency futures and options markets between the domestic currency and a third currency to which the firm has access. Since a triangular parity condition holds among these three currencies, the available, yet incomplete, currency futures and options markets still provide a useful avenue for the firm to indirectly hedge against its foreign exchange risk exposure. This paper offers analytical insights into the optimal cross-hedging strategies of the firm. In particular, the results show the optimality of using options in conjunction with futures in the case of currency mismatching, even though cash flows appear to be linear.

Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems

This paper presents a robust adaptive neural control design for a class of perturbed strict feedback nonlinear system with both completely unknown virtual control coefficients and unknown nonlinearities. The unknown nonlinearities comprise two types of nonlinear functions: one naturally satisfies the "triangularity condition" and can be approximated by linearly parameterized neural networks, while the other is assumed to be partially known and consists of parametric uncertainties and known "bounding functions." With the utilization of iterative Lyapunov design and neural networks, the proposed design procedure expands the class of nonlinear systems for which robust adaptive control approaches have been studied. The design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. Leakage terms are incorporated into the adaptive laws to prevent parameter drifts due to the inherent neural-network approximation errors. It is proved that the proposed robust adaptive scheme can guarantee the uniform ultimate boundedness of the closed-loop system signals.. The control performance can be guaranteed by an appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach.

Borromini's Plans for Sant'Ivo alla Sapienza

Drawings are communicators of ideas that need to be considered not only very carefully and precisely, but also in the context of their purpose and audience. In the specific case of Francesco Borromini9s plans for the church of Sant9Ivo alla Sapienza (1638-1667), additional information on the earliest designs is extracted from the famous bee plan through its comparison with a new, accurate survey of the constructed building, another newly identified plan fragment, and contemporary historic documents. While a straightforward chronological comparison is sufficient to read the earliest drawings, from before 1640, the drawings of the 1660 period, when arranged only by date, do not at first reveal a coherent order. The complete chronology and typological comparison of the early and late plans, including analysis of variations in plan sizes and geometric construction, strongly suggest that the church9s form originated from a hexagon, but the building itself and Borromini9s depictions of it were later changed in response to pressures from structural problems and changes in patronage to emphasize tripartite and triangular conditions in spatial form and iconography. In the late period, Borromini deliberately falsified certain specific drawings, both because he wanted to obscure certain conditions and also to portray the building in idealized terms that would enhance his reputation.

Hedging with mismatched currencies

This article presents a model of a risk‐averse multinational firm facing risk exposure to a foreign currency cash flow. Forward markets do not exist between the firm's own currency and the foreign currency, but do exist for a third currency. Because a triangular parity condition holds among these three currencies, the available forward markets, albeit incomplete, provide a useful avenue for the firm to indirectly hedge against its foreign exchange rate risk exposure. This article offers analytical insights into the optimal cross‐hedging strategies of the firm. In particular, the results show that separate unbiasedness of the forward markets does not necessarily imply a perfect full hedge that eliminates the entire foreign exchange rate risk exposure of the firm. The optimal cross‐hedging strategies depend largely on the firm's marginal utility function and on the correlation of the random spot exchange rates. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19:859–875, 1999

Robust control of uncertain nonlinear systems via measurement feedback

The authors consider the problem of robust control via measurement feedback for a class of uncertain nonlinear systems. Usual assumptions like triangularity conditions and global Lipschitzness used in previous work on this topic are not imposed. The key tool employed in the constructive control design procedure is the recent small (nonlinear) gain theorem which has already proved very powerful in solving diverse control problems.

Global stabilization of MIMO minimum-phase nonlinear systems without strict triangular conditions

An extension of backstepping to a class of multivariable minimum-phase nonlinear systems is proposed. The systems are assumed to be in a special interlaced form which includes a lower triangular form as a special case. The extension involves the recursive application of backstepping and augmentation.

Robust output tracking of nonlinear systems with mismatched uncertainties

The problem of robust output tracking for a class of uncertain nonlinear systems which do not satisfy the conventional matching condition is considered. The main assumption on the uncertainty is that the triangularity condition is satisfied. Based on backstepping method and input/output linearization approach, we propose a class of non-adaptive state feedback controllers which can guarantee exponential stability of the tracking error for the uncertain nonlinear systems first. Next, adaptive control laws are developed so that no prior knowledge of the bounds on the uncertainties is required. By updating these upper bounds, we design a class of adaptive robust controllers. It is shown that under the proposed adaptive robust control the tracking error of the controlled system converges to zero as time approaches infinity.

Backstepping dynamic compensator design for the PMAC servo-drive

In the paper the robust tracking control design of high performance PMAC servo-drive based on exact feedback linearization and extended with integrator backstepping is presented. The feedback system is globally asymptotically stable in the sense of the Lyapunov direct method for a class of parameter perturbations and disturbances without affecting the relative degree and satisfying strict triangularity conditions (STC). The proposed n-th order dynamic compensator significantly extends the class of nonlinear uncertainties acting in the entire electromechanical system for which stable servo-drive operation is preserved. The physical bounds of control signals and states are also considered.

The hidden angular momenta of Racah and -jcoefficients

The Racah formula for the SU(2) 6-j coefficient is usually considered as a pure combinatorial formula. A physical interpretation is found for this formula and, more generally, for combinatorial formulae of the 3n-j coefficients. Angular momenta are associated with the points of the finite projective geometry PG where triangular conditions appear as collinearities of points. A 3n-j coefficient corresponds to a subset of PG so that some of the angular momenta are hidden for the 3n-j. The combinatorial formula of the 3n-j is interpreted as the summation over these hidden angular momenta of a highly symmetric `full -J symbol'.

Precision motion control of a magnetic suspension actuator using a robust nonlinear compensation scheme

This paper presents a robust nonlinear compensation algorithm for realizing large travel in magnetic suspension systems suffering from parameter variations and external disturbance forces. A geometric feedback linearization technique that utilizes the complete nonlinear description of the electromagnetic field distribution is employed to obtain large travel. Robustness to uncertainties in the feedback linearized system is achieved through the development of a discrete-time delay-control-based compensation algorithm. In comparison to previous developments, the new scheme removes the constraints of triangularity conditions in compensation of unmatched uncertainties. The performance of this algorithm is experimentally investigated on a magnetic suspension system. In each of the experiments, the controller is designed using the approximate nonlinear model of the system, which is significantly different from the actual plant model. For a fixed set of gains, the robust nonlinear controller accurately stabilizes the system for a large range of ball positions. In trajectory tracking performance evaluation, the controller provides tracking accuracies that are of the same order of magnitude as the accuracy of the position sensor. Finally, when the suspended ball is impressed with an external disturbance force, the controller provides adequate model regulation and rejection of disturbance forces, demonstrating high stiffness control. The experimental results, therefore, verify the consistent performance of the algorithm in realizing large travel in spite of parameter variations and external disturbances.