We consider multidimensional gravitational models with a nonlinear scalar curvature term and form fields in the action functional. In our scenario it is assumed that the higher dimensional spacetime undergoes a spontaneous compactification to a warped product manifold. Particular attention is paid to models with quadratic scalar curvature terms and a Freund-Rubin-like ansatz for solitonic form ...

In odd-dimensional spaces, gauge invariance permits a Chern-Simons mass term for the gauge fields in addition to the usual Maxwell-Yang-Mills kinetic energy term. We study the Casimir effect in such a (2+1)-dimensional Abelian theory. For the case of parallel conducting lines the result is the same as for a scalar field. For the case of circular boundary conditions the results are completely di...

A model of scalar turbulent advection in compressible flow is analytically investigated. It is shown that, depending on the dimensionality d of space and the degree of compressibility of the smooth advecting velocity field, the cascade of the scalar is direct or inverse. If d . 4 the cascade is always direct. For a small enough degree of compressibility, the cascade is direct again. Otherwise i...

We demonstrate the existence of a secular back-reaction on inflation using a simple scalar model. The model consists of a massless, minimally coupled scalar with a quartic self-interaction which is a spectator to Λ-driven inflation. To avoid problems with coincident propagators, and to make the scalars interact more like gravitons, we impose a covariant normal ordering prescription which has th...

in this paper, by modifying cheng-yau$'$s technique to complete hypersurfaces in $s^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [h. li, hypersurfaces with constant scalar curvature in space forms, {em math. ann.} {305} (1996), 665--672].

2. Direct Adaptive Control of Scalar Plant. Let us begin with a simple scalar adaptive system, ẋp(t) = apxp(t) + kpu(t) (1) where xp(t) ∈ R is the plant state, u(t) ∈ R is the control input, ap ∈ R is an unknown scalar and only the sign of kp ∈ R is known. For the direct adaptive controller we choose a reference model as ẋm(t) = amxm(t) + kmr(t)− l(x(t)− xm(t)). (2) All of the parameter above a...

Motivated in part by string theory, we consider the idea that the standard ΛCDM cosmological model might be modified by the effect of a long-range scalar dark matter interaction. The variant of this widely-discussed notion considered here is suggested by the Brandenberger-Vafa [1] picture for why we perceive three spatial dimensions. In this picture there may be at least two species of dark mat...

There has been some evidence that the fine structure “constant” α may vary with time. We point out that this variation can be described by a scalar field in some supergravity theory in our toy model, for instance, the N = 8 extended supergravity in four dimensions which can be accommodated in M-theory. Email address: [email protected],[email protected] There exists a lot of analysis about the obser...

There has been some evidence that the fine structure “constant” α may vary with time. We point out that this variation can be described by a scalar field in some supergravity theory in our toy model, for instance, the N = 8 extended supergravity in four dimensions which can be accommodated in M-theory. Email address: [email protected],[email protected] There exists a lot of analysis about the obser...

Let Y be a binary random variable and X a scalar. Let β̂ be the maximum likelihood estimate of the slope in a logistic regression of Y on X with intercept. Further let x̄0 and x̄1 be the average of sample x values for cases with y = 0 and y = 1, respectively. Then under a condition that rules out separable predictors, we show that sign(β̂) = sign(x̄1− x̄0). More generally, if xi are vector valued the...