A host of nutrients are needed by cattle to support functions associated with life, and to grow, reproduce, and nourish their offspring (i.e., produce milk). A vast amount of resources have been expended to quantify the amounts of specific nutrients needed to perform these function so that economically efficient diets can be formulated. Feeding diets that provide adequate, but not excessive, am...

The Ray–Singer analytic torsion is the classical zeta-trace of a sum logarithm operators p-form Laplacians on de Rham complex. In this article, we examine residue-analytic torsion, defined using residue trace in place zeta function regularised trace.

Trace conditioning, a form of classical conditioning in which the presentation of the conditioned stimulus (CS) and the unconditioned stimulus (US) is separated in time by an interstimulus interval, requires an intact hippocampus. In contrast, classical conditioning procedures in which the CS and US are not separated by an interstimulus interval (i.e., delay conditioning procedures) typically d...

Trace conditioning, a form of classical conditioning in which the presentation of the conditioned stimulus (CS) and the unconditioned stimulus (US) is separated in time by an interstimulus interval, requires an intact hippocampus. In contrast, classical conditioning procedures in which the CS and US are not separated by an interstimulus interval (i.e., delay conditioning procedures) typically d...

Runtime Monitoring or Verification deals with traces. In its most simple form a monitoring system takes a trace produced by a system and a specification of correct behaviour and checks if the trace conforms to the specification. More complex applications may introduce notions of feedback and reaction. The notion that unifies the field is that we can abstract the runtime behaviour of a system by...

A host of nutrients are needed by cattle to support functions associated with life, and to grow, reproduce, and nourish their offspring (i.e., produce milk). A vast amount of resources have been expended to quantify the amounts of specific nutrients needed to perform these function so that economically efficient diets can be formulated. Feeding diets that provide adequate, but not excessive, am...

We study quadratic forms that can occur as trace forms qL/K of Galois field extensions L/K, under the assumption that K contains a primitive 4th root of unity. M. Epkenhans conjectured that qL/K is always a scaled Pfister form. We prove this conjecture and classify the finite groups G which admit a G-Galois extension L/K with a nonhyperbolic trace form. We also give several applications of thes...