Coordinate transform invariance

A four-dimensional operator is shown to contain the operator-generators for rotation, scale, reflections, and boosts. The hypothesis is advanced that a physical system changes under this operator by at most a complex phase factor due to invariance against the choice of menial frame. A canonical transform gives a simple relation between space-time and energy-momentum. The basic conserved quantity is a four-dimensional angular momentum and/or coupling constant. The differential of this function contains a second-order differential product which is constrained as a power series in the independent variable. The analysis explores the consequences of the model and shows its degree of correspondence to the standard models.     

Communication Roles, Perceived Effectiveness, and Satisfaction in an Environmental Management Program

Earlier research has shown a relationship between various forms of structural centrality and perceived leadership and role satisfaction in small experimental groups. The limited amount of research on this topic in naturally occurring social networks has yielded results that often conflict with one another. Different results have generally been attributed to possible differences in task environments. This paper examines the relationship between two types of structural centrality and perceived influence, role satisfaction, and perceived effectiveness in an environmental resource management program. Findings in this paper suggest that the observed differences in relationships between the network and other variables is partly a function of global network properties (e.g., marginality of subgroups) and related task environments. This revised version was published online in August 2006 with corrections to the Cover Date.     

Investigation by EPR and ENDOR spectroscopy of the novel 4Fe ferredoxin fromPyrococcus furiosus

The hyperthermophilic archaeonPyrococcus furiosus contains a four-Fe ferredoxin (Pf- Fd) that differs from most other 4Fe-Fd’s in that its [Fe₄S₄] cluster is anchored to protein by only three cysteinyl residues.Pf- Fd also is of interest because in its reduced form, [Fe₄S₄]⁺, the cluster exhibits bothS = 1/2 andS = 3/2 spin states. Addition of excess cyanide ion converts the cluster exclusively to anS = 1/2 state (g₁ = 2.09, g₂ = 1.95, g₃ = 1.92), however dialysis restores the EPR signal of native reduced protein indicating that the cluster is not irreversibly altered by cyanide. Both the native protein and protein in the presence of excess cyanide ion (Pf- Fd 4Fe-CN) were investigated here using the techniques of electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) spectroscopy. In particular,Pf- Fd 4Fe-CN was investigated using¹³CN^? and C¹⁵N^? ligands.¹³C and¹⁵N ENDOR indicated that a single cyanide ion bound directly, with the cluster showing an unusually small contact interaction (a_iso(¹³C)～ ?3 MHz, a_iso(¹⁵N) ～ 0). This is in contrast to cyanide bound to monomeric low-spin Fe(III)-containing proteins such as transferrin and myoglobin, for which the¹³C hyperfine coupling has a large isotropic component (a_iso(¹³C) ≈ ?30 MHz). This small contact interaction is not due to low spin density of Fe, as⁵⁷Fe ENDOR of the singly and triply labeledPf- Fd 4FeCN isotopologs, [⁵⁷FeFe₃S₄]⁺ and [Fe⁵⁷Fe₃S₄]⁺, show hyperfine coupling characteristic for [Fe₄S₄]⁺ clusters, particularly for the Fe to which cyanide binds. Thus, the low spin density on¹³C is not due to low spin density on the Fe ion to which it binds. Further theoretical work is needed to explain the contrast between the strong electronic effect of cyanide ion binding with the low spin density on the ligand.     

Some variations on Kac's formula for Brownian motion

We show that under suitable conditions $$\begin{gathered} E_x f\left\{ {a + \int_0^t \beta \left[ {b + \int_0^s {\alpha \left( {X_r } \right)dr, c + s, X_s } } \right]ds, b + \int_0^t {\alpha \left( {X_s } \right)ds, c + t, X_t } } \right\} \hfill \\ = e^{tG} f\left[ {a, b, c, x} \right] \hfill \\ \end{gathered} $$ whereX _t is a Brownian motion andG is the generator of a (C ₀) contraction semigroupe ^tG.