The Experts below are selected from a list of 162 Experts worldwide ranked by ideXlab platform

V.b. Bajic - One of the best experts on this subject based on the ideXlab platform.

  • Algebraic conditions for stability of linear singular Systems
    1991. IEEE International Sympoisum on Circuits and Systems, 1991
    Co-Authors: V.b. Bajic
    Abstract:

    Stability properties of arbitrary solutions of linear singular Systems are considered. Solution properties of Nonhomogeneous Systems are investigated on the basis of properties of an associated homogeneous System. The relationship of Nonhomogeneous and homogeneous singular Systems in terms of stability is investigated and clarified. Algebraic conditions for stability and boundedness of linear singular Systems are derived in terms of conditions on System matrices. The algebraic conditions are independent of the System index and smoothness of the forcing term in the Nonhomogeneous System.

Carmela Currò - One of the best experts on this subject based on the ideXlab platform.

  • Wave features of a hodograph-like transformation for quasilinear hyperbolic Systems
    Zeitschrift für Angewandte Mathematik und Physik, 1990
    Co-Authors: Carmela Currò
    Abstract:

    We study the properties of a variables transformation for a 2×2 quasilinear hyperbolic Nonhomogeneous System of first order, related to wave propagation. The considered variables transformation transforms characteristic curves of the original System, into characteristic curves of the transformed System. We make use of this property to study the propagation of weak discontinuities (acceleration waves) compatible with the quasilinear System (1.1). Finally a special class of rate-type media is considered and asymptotic solutions are investigated.

  • Wave features of a hodograph-like transformation for quasilinear hyperbolic Systems
    Zeitschrift für angewandte Mathematik und Physik ZAMP, 1990
    Co-Authors: Carmela Currò
    Abstract:

    We study the properties of a variables transformation for a 2×2 quasilinear hyperbolic Nonhomogeneous System of first order, related to wave propagation. The considered variables transformation transforms characteristic curves of the original System, into characteristic curves of the transformed System. We make use of this property to study the propagation of weak discontinuities (acceleration waves) compatible with the quasilinear System (1.1). Finally a special class of rate-type media is considered and asymptotic solutions are investigated. Si studiano le proprietà di una trasformazione di variabili per un sistema quasilineare iperbolico del primo ordine non omogeneo. La trasformazione considerata trasforma curve caratteristiche del sistema originale in curve caratteristiche del sistema trasformato. Utilizzando queste proprietà si studia la propagazione delle onde di discontinuità (onde di accelerazione) compatibile con il sistema quasilineare iperbolico considerato e si cercano soluzioni asintotiche.

Christian Constanda - One of the best experts on this subject based on the ideXlab platform.

  • The Newtonian Potential
    Springer Monographs in Mathematics, 2014
    Co-Authors: Christian Constanda
    Abstract:

    The Nonhomogeneous System ( 3.8)—that is, $$\begin{aligned} A(\partial _x)u(x)+g(x)=0,\quad x\in S^+\,\, \mathrm{or}\,\,x\in S^-, \end{aligned}$$ where \(A(\partial _x)\) is defined by ( 3.9)—can be reduced to its homogeneous version if we know a particular solution of it. Our aim is to construct such a solution and to determine conditions under which this solution has all the required smoothness properties.

  • the Nonhomogeneous System
    2011
    Co-Authors: Gavin R Thomson, Christian Constanda
    Abstract:

    System (1.10) is not straightforward to analyze because of the Nonhomogeneous term on the right-hand side. In this chapter we construct a particular solution of the System in terms of a domain potential whose kernel is the matrix of fundamental solutions for the operator \({\rm A}^\omega (\partial _x )\) introduced in Chapter 2.

Mette S Olufsen - One of the best experts on this subject based on the ideXlab platform.

  • persistent instability in a Nonhomogeneous delay differential equation System of the valsalva maneuver
    Bellman Prize in Mathematical Biosciences, 2019
    Co-Authors: Benjamin E Randall, Nicholas Z Randolph, Mette S Olufsen
    Abstract:

    Abstract Delay differential equations are widely used in mathematical modeling to describe physical and biological Systems, often inducing oscillatory behavior. In physiological Systems, this instability may signify (i) an attempt to return to homeostasis or (ii) System dysfunction. In this study, we analyze a nonlinear, nonautonomous, Nonhomogeneous open-loop neurological control model describing the autonomic nervous System response to the Valsalva maneuver (VM). We reduce this model from 5 to 2 states (predicting sympathetic tone and heart rate) and categorize the stability properties of the reduced model using a two-parameter bifurcation analysis of the sympathetic delay (Ds) and time-scale (τs). Stability regions in the Ds τs-plane for this Nonhomogeneous System and its homogeneous analog are classified numerically and analytically, identifying transcritical and Hopf bifurcations. Results show that the Hopf bifurcation remains for both the homogeneous and Nonhomogeneous Systems, while the Nonhomogeneous System stabilizes the transition at the transcritical bifurcation. This analysis was compared with results from blood pressure and heart rate data from three subjects performing the VM: a control subject exhibiting sink behavior, a control subject exhibiting stable focus behavior, and a patient with postural orthostatic tachycardia syndrome (POTS) also exhibiting stable focus behavior. Results suggest that instability caused from overactive sympathetic signaling may result in autonomic dysfunction.

  • persistent instability in a Nonhomogeneous delay differential equation System of the valsalva maneuver
    arXiv: Dynamical Systems, 2019
    Co-Authors: Benjamin E Randall, Nicholas Z Randolph, Mette S Olufsen
    Abstract:

    Delay differential equations (DDEs) are widely used in mathematical modeling to describe physical and biological Systems. Delays can impact model dynamics, resulting in oscillatory behavior. In physiological Systems, this instability may signify (i) an attempt to return to homeostasis or (ii) System dysfunction. In this study, we analyze a nonlinear, nonautonomous, Nonhomogeneous open-loop neurological control model describing the autonomic nervous System response to the Valsalva maneuver. Unstable modes have been identified as a result of parameter interactions between the sympathetic delay and time-scale. In a two-parameter bifurcation analysis, we examine both the homogeneous and Nonhomogeneous Systems. Discrepancies between solutions result from the presence of the forcing functions which stabilize the System. We use analytical methods to determine stability regions for the homogeneous System, identifying transcendental relationships between the parameters. We also use computational methods to determine stability regions for the Nonhomogeneous System. The presence of a Hopf bifurcation within the System is discussed and solution types from the sink and stable focus regions are compared to two control patients and a patient with postural orthostatic tachycardia syndrome (POTS). The model and its analysis support the current clinical hypotheses that patients suffering from POTS experience altered nervous System activity.

Li Yang - One of the best experts on this subject based on the ideXlab platform.

  • A study on the forming conditions of basalts in seamounts of the South China Sea
    Chinese Journal of Geochemistry, 1994
    Co-Authors: Li Zhaolin, Qin Shecai, Pang Xuebin, Liang Dehua, Teng Yunye, Li Yang
    Abstract:

    Volcanic rocks in seamounts of the South China Sea consist mainly of alkali basalt, tholeiitic basalt, trachyandesitic pumice, dacite, etc. Inclusions in the minerals of the volcanic rocks are mainly amorphous melt inclusions, which reflects that the volcanic rocks are characterized by submarine eruption and rapid cooling on the seafloor. Furthermore, fluid-melt inclusions have been discovered for the first time in alkali basalts and mantle-derived xenoliths. indicating a process of differentiation between magma and fluid in the course of mantle partial melting. Alkali basalts and inclusions may have been formed in this Nonhomogeneous System.

  • A study on the forming conditions of basalts in seamounts of the South China Sea
    Chinese Journal of Geochemistry, 1994
    Co-Authors: Li Zhaolin, Qin Shecai, Pang Xuebin, Liang Dehua, Teng Yunye, Qiu Zhili, Li Yang
    Abstract:

    Volcanic rocks in seamounts of the South China Sea consist mainly of alkali basalt, tholeiitic basalt, trachyandesitic pumice, dacite, etc. Inclusions in the minerals of the volcanic rocks are mainly amorphous melt inclusions, which reflects that the volcanic rocks are characterized by submarine eruption and rapid cooling on the seafloor. Furthermore, fluid-melt inclusions have been discovered for the first time in alkali basalts and mantle-derived xenoliths. indicating a process of differentiation between magma and fluid in the course of mantle partial melting. Alkali basalts and inclusions may have been formed in this Nonhomogeneous System. Rock-forming temperatures of four seamounts were estimated as follows: the Zhongnan seamount alkali basalt 1155 ∼ 1185 °C; the Xianbei seamount alkali basalt 960 ∼ 1200 °C; tholeiitic basalt 1040 ∼ 1230 °C; the Daimao seamount tholeiitic basalt 1245 ∼ 1280 °C; and the Jianfeng seamount trachyandestic pumice 880 ∼ 1140 °C. Equilibrium pressures of alkali basalts in the Zhongnan and Xianbei seamounts are 13.57 and 8.8 × 10^8 Pa, respectively. Pyroxene equilibrium temperatures of mantle xenoliths from the Xianbei seamount were estimated at 1073 ∼ 1121 °C, and pressures at (15.58 ∼ 22.47)×10^8Pa, suggesting a deep-source (e.g. the asthenosphere) for the alkali basalts.