‎In this work we prove Malliavin differentiability for the solution to an SDE with locally Lipschitz and semi-monotone drift‎. ‎To prove this formula‎, ‎we construct a sequence of SDEs with globally Lipschitz drifts and show that the $p$-moments of their Malliavin derivatives are uniformly bounded‎.

A nonlocal analogue of the biharmonic operator with involution-type transformations was considered. For corresponding equation involution, we investigated solvability boundary value problems a fractional-order having derivative Hadamard-type. First, involution type were The properties matrices these investigated. As applications considered transformations, questions about problem for studied. M...

The hermitian level of composition algebras with involution over a ring is studied. In particular, it is shown that the hermitian level of a composition algebra with standard involution over a semilocal ring, where two is invertible, is always a power of two when finite. Furthermore, any power of two can occur as the hermitian level of a composition algebra with nonstandard involution. Some bou...

Theorem 1.1. There exists a holomorphic map σ of C of the form ξ → λξ + O(2), η → λη + O(2), with λ not a root of unity and |λ| = 1, such that σ is reversible by an antiholomorphic involution and by a formal holomorphic involution, and is however not reversible by any C-smooth involution of which the linear part is holomorphic. In particular, the σ is not reversible by any holomorphic involution.

The thymus is the organ devoted to T-cell production. The thymus undergoes multiple rounds of atrophy and redevelopment before degenerating with age in a process known as involution. This process is poorly understood, despite the influence the phenomenon has on peripheral T-cell numbers. Here we have investigated the FVB/N mouse strain, which displays premature thymic involution. We find multip...

The main goal of this paper is to propose an approach inverse spectral problems for functional-differential operators (FDO) with involution. For definiteness, we focus on the second-order FDO involution-reflection. Our based reduction problem matrix form and solution Sturm-Liouville operator by developing method mappings. obtained contains weight, which causes qualitative difficulties in study ...

A Lipschitz map f between the metric spaces X and Y is called a Lipschitz quotient map if there is a C > 0 (the smallest such C, the co-Lipschitz constant, is denoted coLip(f), while Lip(f) denotes the Lipschitz constant of f) so that for every x ∈ X and r > 0, fBX(x, r) ⊃ BY (f(x), r/C). Thus Lipschitz quotient maps are surjective maps which by definition have the property ensured by the open ...

We show that over a field of characteristic 2 a central simple algebra with orthogonal involution that decomposes into a product of quaternion algebras with involution is either anisotropic or metabolic. We use this to define an invariant of such orthogonal involutions in characteristic 2 that completely determines the isotropy behaviour of the involution. We also give an example of a non-total...

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a carefull analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate th...

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a careful analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate the...