Marine Tar Residues: a Review

Abstract Marine tar residues originate from natural and anthropogenic oil releases into the ocean environment and are formed after liquid petroleum is transformed by weathering, sedimentation, and other processes. Tar balls, tar mats, and tar patties are common examples of marine tar residues and can range in size from millimeters in diameter (tar balls) to several meters in length and width (tar mats). These residues can remain in the ocean envi-ronment indefinitely, decomposing or becoming buried in the sea floor. However, in many cases, they are transported ashore via currents and waves where they pose a concern to coastal recreation activities, the seafood industry and may have negative effects on wildlife. This review summarizes the current state of knowledge on marine tar residue formation, transport, degradation, and distribution. Methods of detection and removal of marine tar residues and their possible ecological effects are discussed, in addition to topics of marine tar research that warrant further investigation. Emphasis is placed on ben-thic tar residues, with a focus on the remnants of the Deepwater Horizon oil spill in particular, which are still affecting the northern Gulf of Mexico shores years after the leaking submarine well was capped

On polynomials approximating the solutions of nonlinear differential equations

Suppose that L(x) is a differential operator and R(t) a continuous function, and consider the differential equation (*) L(x) = R(t). Then a problem in approximation theory iswhether we can approximate a solution x(t) of (*) uniformlywith a sequence of polynomialsPnfor which we have ∥R(t)-L(pn)) ∥ ≦ ηn, where ∥. ∥ is a certain norm andrjna specific sequence of nonnegative constants. This is done here for a firstorder nonlinear differential operatorLand for two differentnorms, the uniform norm and theLpnorm (1≦p < +∞). © 1972, Pacific Journal of Mathematics