We give conditions under which a function F (t, x, u, ψ0, ψ) satisfies the relation dF dt = ∂F ∂t + ∂F ∂x · ∂H ∂ψ − ∂F ∂ψ · ∂H ∂x along the Pontryagin extremals (x(·), u(·), ψ0, ψ(·)) of an optimal control problem, where H is the corresponding Hamiltonian. The relation generalizes the well known fact that the equality dH dt = ∂H ∂t holds along the extremals of the problem, and that in the auton...

The relationship between bilevel optimization and multiobjective optimization has been studied by several authors and there have been repeated attempts to establish a link between the two. We unify the results from the literature and generalize them for bilevel multiobjective optimization. We formulate sufficient conditions for an arbitrary binary relation to guarantee equality between the effi...

We develop normalisation by evaluation (NBE) for dependent types based on presheaf categories. Our construction is formulated in the metalanguage of type theory using quotient inductive types. We use a typed presentation hence there are no preterms or realizers in our construction, and every construction respects the conversion relation. NBE for simple types uses a logical relation between the ...

The relation between the two most important in mathematical physics first order systems of partial differential equations is among those topics which attract attention because of their general, even philosophical significance but at the same time do not offer much for the solution of particular problems concerning physical models. The Maxwell equations can be represented in a Dirac like form in...

Generalized measurements of an observable performed on a quantum system during a force protocol are investigated and conditions that guarantee the validity of the Jarzynski equality and the Crooks relation are formulated. In agreement with previous studies by M. Campisi, P. Talkner, and P. Hänggi [Phys. Rev. Lett. 105, 140601 (2010); Phys. Rev. E 83, 041114 (2011)], we find that these fluctuati...

We point out that a simple test of the mechanism of CP violation can be performed by a measurement of the CP asymmetries in exclusive and inclusive radiative rare decays. We show that the rate asymmetries ∆Γ = Γ(B → fγ)− Γ(B+ → f̄γ) for certain final states f can be predicted in a theoretically clean way. Some implications for b → sl+l− decays are discussed.

Figure 12: Example of interactions between equality constraints in a horizontal window. the window. The rst row of Figure 12 gives the values of n. The second row shows the equality constraints due to the symmetry of the corner and to the periodicity. The third row, nally, gives the equality constraints due to the symmetry of the image corner. It is clear form the second row that, for example, ...

We show that the intuitionistic first-order theory of equality has continuum many complete extensions. also study Vitali equivalence relation and there are intuitionistically precise versions it.