A bstract Three-loop ? -functions of the Minimal Supersymmetric Standard Model regularized by higher covariant derivatives are obtained for an arbitrary supersymmetric subtraction scheme. For this purpose we first calculate two-loop anomalous dimensions all MSSM chiral matter superfields defined in terms bare couplings. Then use NSVZ equations renormalization group functions couplings, which va...

The gradient flow of the Yang-Mills action acts pointwise on closed loops of gauge fields. We construct a topologically nontrivial loop of SU(2) gauge fields on S that is locally stable under the flow. The stable loop is written explicitly as a path between two gauge fields equivalent under a topologically nontrivial SU(2) gauge transformation. Local stability is demonstrated by calculating the...

We show that the four-loop four-point amplitudes of N = 5 supergravity are ultraviolet finite in four dimensions, contrary to expectations based on supersymmetry and duality-symmetry arguments. We explain why the diagrams of any covariant local formalism cannot manifestly exhibit the necessary cancellations for finiteness but instead require a new type of ultraviolet cancellation that we call a...

The paper studies the problem of nonlinear feedback control design of non-isothermal Continuously Stirred Tank Reactors (CSTR). The objective is to construct a feedback controller such that a desired equilibrium of the closed-loop dynamic is asymptotically stable and such that the closed-loop vector field is a conservative vector field of a particular type, i.e., a gradient system. Properties o...

Alam, act-A model-based controller generally works better w3th the model than vath the modelled plant due to the modelhng error This dtfference between the performances can be made small by selecting a model that ts accurate at the closed-loop relevant frequenoes In thts paper tt ts shown that an tteraUve approach of tdenttficatmn and control design can lead to a model that ts much better state...

We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various equivalences between global isometric immersion problems among different space forms and pseudoRiemannian space forms. As a corollary, we obtain a non-immersibili...

The task of implementing a supervisory controller is non-trivial, even though different theories exist that allow automatic synthesis of these controllers in the form of automata. One of the reasons for this discord is due to the asynchronous interaction between a plant and its controller in implementations, whereas the existing supervisory control theories assume synchronous interaction. As a ...