We review the construction known as the Nahm transform in a generalized context, which includes all the examples of this construction already described in the literature. The Nahm transform for translation invariant instantons on R is presented in an uniform manner. We also analyze two new examples, the first of which being the first example involving a four-manifold that is not hyperk”ahler.

 In this paper, we aresupposed to introduce the definitions of n-fold commutative, andimplicative hyper K-ideals. These definitions are thegeneralizations of the definitions of commutative, andimplicative hyper K-ideals, respectively, which have been definedin [12]. Then we obtain some related results. In particular wedetermine the relationships between n-fold implicative hyperK-ideal and n-fol...

in this paper, we aresupposed to introduce the definitions of n-fold commutative, andimplicative hyper k-ideals. these definitions are thegeneralizations of the definitions of commutative, andimplicative hyper k-ideals, respectively, which have been definedin [12]. then we obtain some related results. in particular wedetermine the relationships between n-fold implicative hyperk-ideal and n-fold...

We propose a new method to construct degenerate $3$-$(\alpha,\delta)$-Sasakian manifolds as fiber products of Boothby-Wang bundles over hyperk\"ahler manifolds. Subsequently, we study homogeneous $3$-$(\alpha, \delta)$-Sasakian and prove that no non-trivial compact examples exist well there is exactly one family nilpotent Lie groups with this geometry, the quaternionic Heisenberg groups.

A taut contact sphere on a 3-manifold is a linear 2-sphere of contact forms, all defining the same volume form. In the present paper we completely determine the moduli of taut contact spheres on compact left-quotients of SU(2) (the only closed manifolds admitting such structures). We also show that the moduli space of taut contact spheres embeds into the moduli space of taut contact circles. Th...

In this article we give a uniform proof why the shift map on Floer homology trajectory spaces is scale smooth. This works for various homologies, periodic, Lagrangian, Hyperk\"ahler, elliptic or parabolic, and uses Hilbert space valued Sobolev theory.

We derive a local ansatz for generalized K\"ahler surfaces with nondegenerate Poisson structure and biholomorphic $S^1$ action which generalizes the classic Gibbons-Hawking invariant hyperK\"ahler manifolds, allows choice of one arbitrary function. By imposing K\"ahler-Ricci soliton equation, or equivalently equations type IIB string theory, construction becomes rigid, we classify all complete ...

We prove the existence of Bridgeland stability conditions on Kuznetsov components Gushel-Mukai varieties, and describe structure moduli spaces semistable objects in these categories even-dimensional case. As applications, we construct a new infinite series unirational locally complete families polarized hyperk\"{a}hler varieties K3 type, characterize Hodge-theoretically when component an variet...

Abstract Background and Aims hyperkaliemia is highly prevalent among chronic kidney disease (CKD) patients its management determinant to allow the maintenance of therapies demonstrated cardiovascular renal benefit. Attitude towards variable different guidelines also clinicians. The aim this study was analyze nephrologist response K serum levels > 5.5 mmol/l in out-patient setting. Method...