For any vertex x in a connected graph G of order p ≥ 2, a set S of vertices of V is an x-detour set of G if each vertex v in G lies on an x-y detour for some element y in S. A connected x-detour set of G is an x-detour set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected x-detour set of G is the connected x-detour number of G and is denoted by cdx(...

We show how pattern formation in Faraday waves may be manipulated by varying the harmonic content of the periodic forcing function. Our approach relies on the crucial influence of resonant triad interactions coupling pairs of critical standing wave modes with damped, spatiotemporally resonant modes. Under the assumption of weak damping and forcing, we perform a symmetry-based analysis that reve...

In legged locomotion, the active forcing contributed by the leg can be considered to act in rotary and radial directions relative to the leg. Rotary forcing acting perpendicular to the leg, such as forcing due to hip torque, and radial forcing acting in the direction along the leg from foot to hip, are both present in animal locomotion. Given that these directions are orthogonal, simple rotary ...

To understand the regional impact of the atmospheric aerosols on the surface energy and water cycle in the southern Sierra Nevada characterized by extreme variations in terrain elevation, the authors examine the aerosol radiative forcing on surface insolation and snowmelt for the spring of 1998 in a regional climate model experiment. With a prescribed aerosol optical thickness of 0.2, it is fou...

Historical climate simulations of the period 1861–2000 using two new Geophysical Fluid Dynamics Laboratory (GFDL) global climate models (CM2.0 and CM2.1) are compared with observed surface temperatures. All-forcing runs include the effects of changes in well-mixed greenhouse gases, ozone, sulfates, black and organic carbon, volcanic aerosols, solar flux, and land cover. Indirect effects of trop...

The following notion of forcing was introduced by Grigorieff [2]: Let I ⊂ ω be an ideal, then P is the set of all functions p : ω → 2 such that dom(p) ∈ I. The usual Cohen forcing corresponds to the case when I is the ideal of finite subsets of ω. In [2] Grigorieff proves that if I is the dual of a p-point ultrafilter, then ω1 is preserved in the generic extension. Later, when Shelah introduced...

We present ocean model sensitivity experiments aimed at separating the influence of the projected changes in the ‘‘thermal’’ (near-surface air temperature) and ‘‘wind’’ (near-surface winds) forcing on the patterns of sea level and ocean heat content. In the North Atlantic, the distribution of sea level change is more due to the ‘‘thermal’’ forcing, whereas it is more due to the ‘‘wind’’ forcing...

[1] Estimation of parameters for land-surface models, along with their corresponding uncertainties, relies on the input data for the atmospheric forcing variables including atmospheric pressure, temperature, humidity, wind speed, precipitation, and incoming shortwave and longwave radiation. Most studies assume that forcing data are accurate and contain no random or systematic observational erro...

For a connected graph G = (V,E), a set S ⊆ E is called an edge-to-vertex geodetic set of G if every vertex of G is either incident with an edge of S or lies on a geodesic joining some pair of edges of S. The minimum cardinality of an edge-to-vertex geodetic set of G is gev(G). Any edge-to-vertex geodetic set of cardinality gev(G) is called an edge-to-vertex geodetic basis of G. A subset T ⊆ S i...

In a mechanical system x is the displacement and / is the time. We call g(x) a restoring force and ƒ(/) a forcing term. Throughout this paper f{t) will be periodic and when we speak of a periodic solution of (1) we always mean a solution having the same period as ƒ(/). If g(x) is simply a constant multiplied by x, equation (1) represents a linear oscillator. In this case the amplitude of the fo...