This paper reflects the renascence of sensitivity and parametric analysis in linear programming and extends single-parametric results to the case when there are multiple parameters in the objective function and in the right-hand side of equations. Multiparametric approach enables us to study more complex perturbation occurring in linear programs than the simpler sensitivity analysis does. Inter...

Let G be a connected semi-simple algebraic group of adjoint type over an algebraically closed field, and let G be the wonderful compactification of G. For a fixed pair (B, B−) of opposite Borel subgroups of G, we look at intersections of Lusztig’s G-stable pieces and the B−×B-orbits in G, as well as intersections of B ×B-orbits and B− ×B−-orbits in G. We give explicit conditions for such inters...

In this shot note we consider globally admissible inference rules. A rule r is globally admissible in a logic L if r is admissible in all logics with the finite model property which extend L. Here we prove a reduction theorem: we show that, for any modal logic L extending K4, a rule r is globally admissible in L iff r is admissible in all tabular logics extending L. The similar result holds for...

The usual Condorcet Criterion says that if an alternative is ranked ahead of all other alternatives by an absolute majority of voters, it should be declared the winner. The following partial extension of this criterion to other ranks is proposed: If an alternative is consistently ranked ahead of another alternative by an absolute majority of voters, it should be ahead in the final ranking. The ...

We add to the mounting evidence that the topological B model’s normalized holomorphic three-form has integral periods by demonstrating that otherwise the B2-brane partition function is ill-defined. The resulting Calabi-Yau manifolds are roughly fixed points of attractor flows. We propose here that any admissible background for topological strings requires a quantized (twisted) integrable pure s...

Let a(n; k) denote the number of combinatorial structures of size n with k components. One often has P n;k a(n; k)x y=n! = exp yC(x) , where C(x) is frequently the exponential generating function for connected structures. How does a(n; k) behave as a function of k when n is large and C(x) is entire or has large singularities on its circle of convergence? The Flajolet-Odlyzko singularity analysi...

We study Derrida’s generalized random energy model in the presence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic limit for all admissible values of parameters. We find that the fluctuations are described by a hierarchical structure which is obtained by a certain coarse-graining of the initial hierarchical structure ...

in this paper, we give a necessary condition for function in l^2with its dual to generate a dual shearlet tight frame with respect to admissibility.