A graph efficiency multiproduct model of corn/livestock farming: Accounting for nitrate pollution

This paper estimates a non-parametric production frontier for a population of 117 corn/livestock farms in the Corn Belt region in 1987, employing a hyperbolic graph efficiency approach. There are 7 outputs, 39 variable inputs, 4 fixed inputs, and one bad input (residual nitrogen). Three graph efficiency models are estimated. A profit maximization model is specified to estimate a production frontier constrained only by the fixed factors. Two other models involving tax constraints are also estimated. One involves a tax directly on nitrogen and the other involves a tax directly on residual nitrogen, making the disposal of residual nitrogen costly. The nitrogen tax constraint is more effective in reducing residual nitrogen loadings and causes a larger reduction in income than the residual tax constraint.     

A “Multiplicative Coboundary” theorem for some sequences of random matrices

Schmidt(¹⁰) showed that if the family of distributions of the partial sums of a strictly stationary random sequence is tight, then that random sequence is a coboundary. Here an analog of that result is proved for some sequences of random matrices, with partial sums replaced by matrix products.     

Z 3-Graded exterior differential calculus and gauge theories of higher order

We present a possible generalization of the exterior differential calculus, based on the operator d such that d³=0, but d²0. The entities dx ⁱ and d² x ^k generate an associative algebra; we shall suppose that the products dx ⁱ dx ^k are independent of dx ^k dx ⁱ , while theternary products will satisfy the relation: dx ⁱ dx ^k dx ^m =jdx ^k dx ^m dx ⁱ =j ²dx ^m dx ^m dx ⁱ dx ^k , complemented by the relation dx ⁱ d² x ^k =jd² x ^k dx ⁱ , withj:=e^2i/3.We shall attribute grade 1 to the differentials dx ⁱ and grade 2 to the second differentials d² x ^k ; under the associative multiplication law the grades add up modulo 3.We show how the notion ofcovariant derivation can be generalized with a 1-formA so thatD:=d+A, and we give the expression in local coordinates of thecurvature 3-form defined as :=d² A+d(A ²)+AdA+A ³.Finally, the introduction of notions of a scalar product and integration of theZ ₃-graded exterior forms enables us to define the variational principle and to derive the differential equations satisfied by the 3-form . The Lagrangian obtained in this way contains the invariants of the ordinary gauge field tensorF _ik and its covariant derivativesD _i F _km .     

Synthesis and Structure of Perfluorocongressane

Perfluorocongressane was synthesized using elemental fluorine and characterized by mass spectra, (19)F NMR, and X-ray crystallography.     

Jumps of Minimal Degrees Below 0'

We show that there is a degree a REA in and low over 0' suchthat no minimal degree below 0' jumps to a degree above a. Wealso show that every nonlow recursively enumerable degree boundsa nonlow minimal degree.     

The algebra of directed complexes

The theory of directed complexes is a higher-dimensional generalisation of the theory of directed graphs. In a directed graph, the simple directed paths form a subset of the free category which they generate; if the graph has no directed cycles, then the simple directed paths constitute the entire category. Generalising this, in a directed complex there is a class of split subsets which is contained in and generates a free -category; when a simple loop-freeness condition is satisfied, the split sets constitute the entire -category. The class of directed complexes is closed under the natural product and join constructions. The free -categories generated by directed complexes include the important examples associated to cubes and simplexes.     

Synthesis, crystal structure, and properties of MnNCN, the first carbodiimide of a magnetic transition metal

Synthesis, single-crystal structure determination, and magnetic properties are reported for manganese carbodiimide, MnNCN. The presumably unstable but inert phase adopts the trigonal system (R3m) with a = 3.3583(4) A, c = 14.347(2) A, V = 140.13(3) A3, and Z = 3. Divalent manganese is octahedrally coordinated by nitrogen atoms at 2.26 A, and the NCN(2-) unit adopts the linear [N=C=N](2-) carbodiimide shape with two C=N double bonds of 1.23 A. MnNCN contains high-spin Mn(II) with five unpaired electrons and behaves like an antiferromagnet with an ordering temperature below 30 K.