A Corollary for Nonsmooth Systems

In this note, two generalized corollaries to the LaSalle-Yoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right-hand sides. Lyapunov-based analysis methods are developed using differential inclusions to achieve asymptotic convergence when the candidate Lyapunov derivative is upper bounded by a negative semi-definite function

Dominant partition method

By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails

On reduction of differential inclusions and Lyapunov stability

In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions. The resulting reduced set-valued map is point-wise smaller (in the sense of set containment) than the original set-valued map. The corresponding reduced differential inclusion, defined by the reduced set-valued map, is utilized to develop a generalized notion of a derivative for locally Lipschitz candidate Lyapunov functions in the direction(s) of a set-valued map. The developed generalized derivative yields less conservative statements of Lyapunov stability theorems, invariance theorems, invariance-like results, and Matrosov theorems for differential inclusions. Included illustrative examples demonstrate the utility of the developed theory

Swimming in curved space or The Baron and the cat

We study the swimming of non-relativistic deformable bodies in (empty) static curved spaces. We focus on the case where the ambient geometry allows for rigid body motions. In this case the swimming equations turn out to be geometric. For a small swimmer, the swimming distance in one stroke is determined by the Riemann curvature times certain moments of the swimmer.Comment: 19 pages 6 figure

Spreading Rate-Dependent Variations in Crystallization Along the Global Mid-Ocean Ridge System

We investigate crustal accretion at mid-ocean ridges by combining crystallization pressures calculated from major element contents in mid-ocean ridge basalt (MORB) glasses and vapor-saturation pressures from melt inclusions and MORB glasses. Specifically, we use established major element barometers and pressures estimated from 192 fractional crystallization trends to calculate crystallization pressures from \u3e9000 MORB glasses across the global range of mid-ocean ridge spreading rates. Additionally, we estimate vapor-saturation pressures from \u3e400 MORB glasses from PETDB and \u3e400 olivine-hosted melt inclusions compiled from five ridges with variable spreading rates. Both major element and vapor-saturation pressures increase and become more variable with decreasing spreading rate. Vapor saturation pressures indicate that crystallization occurs in the lower crust and upper mantle at all ridges, even when a melt lens is present. We suggest that the broad peaks in major element crystallization pressures at all spreading rates reflects significant crystallization of on and off-axis magmas along the base of a sloping lithosphere. Combining our observations with ridge thermal models we show that crystallization occurs over a range of pressures at all ridges, but it is enhanced at thermal/rheologic boundaries, such as the melt lens and the base of the lithosphere. Finally, we suggest that the remarkable similarity in the maximum vapor-saturation pressures (∼3 kbars) recorded in melt inclusions from a wide range of spreading rates reflects a relatively uniform CO2 content of 50–85 ppm for the depleted upper mantle feeding the global mid-ocean ridge system

On Lorentz invariance and supersymmetry of four particle scattering amplitudes in SNR8S^N\R^8 orbifold sigma model

The $S^N\R^8$ supersymmetric orbifold sigma model is expected to describe the IR limit of the Matrix string theory. In the framework of the model the type IIA string interaction is governed by a vertex which was recently proposed by R.Dijkgraaf, E.Verlinde and H.Verlinde. By using this interaction vertex we derive all four particle scattering amplitudes directly from the orbifold model in the large $N$ limit.Comment: Latex, 23 page

A tabulation of pipe length to diameter ratios as a function of Mach number and pressure ratios for compressible flow

Computer programs and resulting tabulations are presented of pipeline length-to-diameter ratios as a function of Mach number and pressure ratios for compressible flow. The tabulations are applicable to air, nitrogen, oxygen, and hydrogen for compressible isothermal flow with friction and compressible adiabatic flow with friction. Also included are equations for the determination of weight flow. The tabulations presented cover a wider range of Mach numbers for choked, adiabatic flow than available from commonly used engineering literature. Additional information presented, but which is not available from this literature, is unchoked, adiabatic flow over a wide range of Mach numbers, and choked and unchoked, isothermal flow for a wide range of Mach numbers

The Gambling Functional Assessment (GFA): An Assessment Device For Identification of The Maintaining Variables of Pathological Gambling

The present paper describes the rationale and presents an assess-ment device for the identification of functional control of patholog-ical gambling behavior. It is suggested in this paper that only through identification of function and eventual treatment based on such function will interventions for the treatment of pathological gamblers become successful. A 20-item self-report format as-sessment is presented along with the scoring key for the instru-ment. Suggestions for future research on the psychometrics of the proposed instrument are presented along with implications for use in both research and clinical treatment facilities

The Googly Amplitudes in Gauge Theory

The googly amplitudes in gauge theory are computed by using the off shell MHV vertices with the newly proposed rules of Cachazo, Svrcek and Witten. The result is in agreement with the previously well-known results. In particular we also obtain a simple result for the all negative but one positive helicity amplitude when one of the external line is off shell.Comment: Latex file, 16 pages, 7 figures. Figures may bot display correctly in ps file. Pls use pdf file instea