Related papers: Inversion of adjunction for higher rational singul…

This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further…

We treat interpolation for various logics.

We construct an explicit combinatorial model of the functor which adds right adjoints to the morphisms of an $\infty$-category, and we speculate on possible extensions to higher dimensions.

We prove some statements of left- and right-continuous variants of generalized inverses of non-decreasing real functions.

In this note, we establish a generalized analytic inversion of adjunction via the Nadel-Ohsawa multiplier/adjoint ideal sheaves associated to plurisubharmonic (psh) functions for log pairs, by which we answer a question of Koll\'{a}r in…

We introduce the notion of weighted singular vectors and weighted uniform exponent with respect to a set of weights. We prove invariance of these exponents for affine subspaces and submanifolds inside those affine subspaces. For certain…

We establish an explicit form of the Backlund transformation for the most known integrable systems.

We give canonical resolutions of singularities of several cone varieties arising from invariant theory. We establish a connection between our resolutions and resolutions of singularities of closure of conjugacy classes in classical Lie…

We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.

We prove Fujita's freeness conjecture for Gorenstein complexity-one $T$-varieties with rational singularities.

A vector variational principle is proved.

In this article we prove the explicit Mordell Conjecture for large families of curves. In addition, we introduce a method, of easy application, to compute all rational points on curves of quite general shape and increasing genus. The method…

We give explicit expressions for higher order convolutions of Cauchy numbers, either as one single integral or in terms of the Stirling numbers of the first and second kinds.

Several results about the union-closed sets conjecture are presented.

A systematic method of summing the corrections to the renormalon residue arising from higher order renormalons is discussed.

We present a generalization of the multiplier ideal version of inversion of adjunction, often known as the restriction theorem, to centers of arbitrary codimension. We approach inversion of adjunction from the subadjunction point of view.…

An element of a group is said to be reversible if it is conjugate to its inverse. We characterise the reversible elements in the group of diffeomorphisms of the real line, and in the subgroup of order preserving diffeomorphisms.

Continued fractions are used to give an alternate proof of $e^{x/y}$ is irrational.

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.

Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.