We study the vanishing neighbourhood of non-isolated singularities of functions on singular spaces by associating a general linear function. We use the carrousel monodromy in order to show how to get a better control over the attaching of thimbles. For one dimensional singularities, we prove obstructions to integer (co)homology groups and to the eigenspaces of the monodromy via monodromies of n...

We prove a few cases of a conjecture on the invariance of cohomological support loci under derived equivalence by establishing a concrete connection with the related problem of the invariance of Hodge numbers. We use the main case in order to study the derived behavior of fibrations over curves.

The literature surrounding the Bell numbers is vast: see, for example, Comtet [1, Chapter 5]. Close cousins of the Bell numbers are the Uppuluri-Carpenter numbers (sometimes called the complementary Bell numbers); they count the excess of the number of set partitions of {1, . . . , n} into an even number of blocks over the number of partitions into an odd number of blocks. They are the integer ...

The purpose of this note is to propose and motivate a conjecture on the behavior of cohomological support loci for topologically trivial line bundles under derived equivalence, to verify it in the case of surfaces, and to explain further developments. The reason for such a conjecture is the desire to understand the relationship between the cohomology groups of (twists of) the canonical line bun...

We consider a family of slightly extended version of the Raynaud’s surfaces X over the field of positive characteristic with Mumford-Szpiro type polarizations Z, which have Kodaira non-vanishing H(X,Z) 6= 0. The surfaces are at least normal but smooth under a special condition. We compute the cohomologies H(X,Z) for i, n ∈ Z and study their (non-)vanishing. Finally, we give a fairly large famil...

In this article, continuous and discontinuous integral controllers for multiple-input multiple-output (MIMO) systems are designed a large class of nonlinear systems, which (partially) feedback linearizable. These arbitrary positive or negative degree homogeneity derived by combining Lyapunov function obtained from the implicit (ILF) method with some extra explicit terms. Discontinuous able to s...

Abstract We study the effect of quantum decoherence on inflationary cosmological perturbations. This process might imprint specific observational signatures revealing nature mechanism being related to longstanding issue quantum-to-classical transition fluctuations. Several works have investigated statistical properties primordial In particular, it has been shown that cosmic leads corrections cu...