Current Issue : October - December Volume : 2016 Issue Number : 4 Articles : 7 Articles
We study the L2-gain analysis problem for a class of discrete-time switched systems with time-varying delays. A mode-dependent average dwell time (MDADT) approach is applied to analyze the L2-gain performance for these discrete-time switched delay systems. Combining a multiple Lyapunov functional method with the MDADT approach, sufficient conditions expressed in form of a set of feasible linear matrix inequalities (LMIs) are established to guarantee the L2-gain performance. Finally, a numerical example will be provided to demonstrate the validity and usefulness of the obtained results....
Factor analysis models with continuous and ordinal responses are a useful tool for assessing relations between the latent\nvariables and mixed observed responses. These models have been successfully applied to many different fields, including\nbehavioral, educational, and social-psychological sciences. However, within the Bayesian analysis framework, most developments\nare constrained within parametric families, of which the particular distributions are specified for the parameters of interest. This\nleads to difficulty in dealing with outliers and/or distribution deviations. In this paper, we propose a Bayesian semiparametric\nmodeling for factor analysis model with continuous and ordinal variables. A truncated stick-breaking prior is used to model\nthe distributions of the intercept and/or covariance structural parameters. Bayesian posterior analysis is carried out through\nthe simulation-based method. Blocked Gibbs sampler is implemented to draw observations from the complicated posterior. For\nmodel selection, the logarithm of pseudomarginal likelihood is developed to compare the competing models. Empirical results are\npresented to illustrate the application of the methodology....
A design strategy of optimal output regulators for dual-rate discrete-time systems, whose output sampling period is an integer\nmultiple of the input updating period, is proposed. At first, by using the discrete lifting technique, the dual-rate discrete-time\nsystem is converted to a single-rate augmented system in form and the lifted state-space model is constructed. Correspondingly,\nthe performance index of the original system is modified to the performance index of the single-rate augmented system. And\nthe original problem is transformed into an output regulation problem for the augmented system. Then, according to the optimal\nregulator theory, an optimal output regulator for the dual-rate discrete-time system is derived. In the meantime, the existence\nconditions of the optimal output regulator are discussed. Finally, a numerical example is included to illustrate the effectiveness of\nthe proposed method....
We consider the optimal control problem for a mathematical model describing steady flows of a nonlinear-viscous incompressible\nfluid in a bounded three-dimensional (or a two-dimensional) domain with impermeable solid walls. The control parameter is the\nsurface force at a given part of the flow domain boundary. For a given bounded set of admissible controls, we construct generalized\n(weak) solutions that minimize a given cost functional....
With the advantages of good low-speed torque capability and excellent instant response performance, twin-screw superchargers\nhave great potential in the automobile market, but the noise of these superchargers is the main factor that discourages their use.\nTherefore, it is important to study their noise mechanism and methods of reducing it. This study included a transient numerical\nsimulation of a twin-screw supercharger flow field with computational fluid dynamics software and an analysis of the pressure field\nof the running rotor. The results showed that overcompression was significant in the compression end stage of the supercharger,\nresulting in a surge in airflow to a supersonic speed and the production of shock waves that resulted in loud noise. On the basis of\nthese findings, optimization of the supercharger is proposed, including expansion of the supercharger exhaust orifice and creation\nof a slot along the direction of the rotor spiral normal line at the exhaust port, so as to reduce the compression end pressure, improve\nthe exhaust flow channel, and weaken the source of the noise. Experimental results showed that the noise level value of the improved\ntwin-screw supercharger was significantly lower at the same speed than the original model, with an average decrease of about 5 dB\n(A)....
Let Ã?© be a bounded domain in a real Euclidean space. We consider the equation du(t, x)/dt = C(x)u(t, x) + âË?«Ã?© K(x, s)u(t, s)ds +\n[f(u)](t, x (t > 0; x âË?Ë? Ã?©), where C(.) and K(ââ?¹â?¦, ââ?¹â?¦) are matrix-valued functions and f(.) is a nonlinear mapping. Conditions for the\nexponential stability of the steady state are established. Our approach is based on a norm estimate for operator commutators....
Did any physics experts expect SUPERRELATIVITY paper, a physics revolution producing the\nEINSTEIN-RODGERS RELATIVITY EQUATION, producing the HAWKING-RODGERS BLACK HOLE\nRADIUS, and producing the STEFAN-BOLTZMANN-SCHWARZSCHILD-HAWKING-RODGERS BLACK\nHOLE RADIATION POWER LAW, as the author gave a solution to The Clay Mathematics Instituteââ?¬â?¢s\nvery difficult problem about the Navier-Stokes Equations? The Clay Mathematics Institute in May\n2000 offered that great $million prize to the first person providing a solution for a specific statement\nof the problem: ââ?¬Å?Prove or give a counter-example of the following statement: In three space\ndimensions and time, given an initial velocity field, there exists a vector velocity and a scalar\npressure field, which are both smooth and globally defined, that solve the Navier-Stokes Equations.ââ?¬Â\nDid I, the creator of this paper, expect SUPERRELATIVITY to become a sophisticated conversion\nof my unified field theory ideas and mathematics into a precious fluid dynamics paper to\nhelp mathematicians, engineers and astro-physicists? [1]. Yes, but I did not expect such superb\nequations that can be used in medicine or in outer space! In this paper, complicated equations for\nmulti-massed systems become simpler equations for fluid dynamic systems. That simplicity is\nwhat is great about the Navier-Stokes Equations. Can I delve deeply into adding novel formulae\ninto the famous Schwarzschildââ?¬â?¢s equation? Surprisingly, yes I do! Questioning the concept of reversibility\nof events with time, I suggest possible 3-dimensional and 4-dimensional co-ordinate\nsystems that seem better than what Albert Einstein used, and I suggest possible modifications to\nMaxwellââ?¬â?¢s Equations. In SUPERRELATIVITY, I propose that an error exists in Albert Einsteinââ?¬â?¢s Special\nRelativity equations, and that error is significant because it leads to turbulence in the universeââ?¬â?¢s\nfluids including those in our human bodies. Further, in SUPERRELATIVITY, after I create\nSchwarzschild-based equations that enable easy derivation of the Navier-Stokes Equations, I suddenly\ncreate very interesting exponential energy equations that simplify physics equations, give a\nmathematical reason for turbulence in fluids, give a mathematical reason for irreversibility of\nevents with time, and enable easy derivation of the Navier-Stokes Equations. Importantly, my new\nexponential Navier-Stokes Equations are actually wave equations as should be used in Fluid Dynamics.\nThrilled by my success, I challenge famous equations by Albert Einstein and Stephen\nHawking [2] [3]....
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