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In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert,…
The category of coherent sheaves over a noetherian scheme is very important for studying the properties of a given scheme. For noetherian schemes it is a well-known fact that the topology can be fully recovered from the corresponding…
We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…
We give necessary and sufficient conditions for the hull of a coherent sheaf to be coherent.
We characterise and investigate co-Higgs sheaves and associated algebraic and combinatorial invariants on toric varieties. In particular, we compute explicit examples.
In this note, we find a new inequality involving primes and deduce several Bonse-type inequalities.
Using the discriminant modular form and the Noether formula it is possible to write the admissible self-intersection of the relative dualising sheaf of a semistable hyperelliptic curve over a number field or function field as a sum, over…
Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison's inequality and several operator versions of Chebyshev's inequality. We also discuss well-known results around the matrix…
We view Dolbeault-Morse-Novikov cohomology H^{p,q}_\eta(X) as the cohomology of the sheaf \Omega_{X,\eta}^p of \eta-holomorphic p-forms and give several bimeromorphic invariants. Analogue to Dolbeault cohomology, we establish the…
Let $X$ be a compact connected CR manifold of dimension $2n-1, n\geq 2$ with a transversal CR $S^1$-action on $X$. We study the Fourier components of the Kohn-Rossi cohomology with respect to the $S^1$-action. By studying the Szeg\"o kernel…
In this technical note we describe a pair of results on heterotic compactifications. First, we give an example demonstrating that the usual statement of the anomaly-freedom constraint for perturbative heterotic compactifications (meaning,…
In this paper, we define the homological Morse numbers of a filtered cell complex in terms of relative homology of nested filtration pieces, and derive inequalities relating these numbers to the Betti tables of the multi-parameter…
We consider the problem of whether it is possible to improve the Novikov inequalities for closed 1-forms, or any other inequalities of a similar nature, if we assume, additionally, that the given 1-form is harmonic with respect to some…
In this note, we provide with a simple example to show a defect in the definition of the geometric mixing scale, and then introduce an improved scale, called as the strong geometric mixing scale. The main theorem in this note is the…
In this paper we study transversely holomorphic foliations of complex codimension one with some hypothesis on the transverse structure.
In this article, Bohr type inequalities for some complex valued harmonic functions defined on the unit disk are given. All the results are sharp.
This is a large audience version of our previous work (see math.AG/0301146) in which we prove the existence of an (exact) equivalence between the category of coherent analytic sheaves and the category of $\bar{\partial}$-coherent sheaves.…
The present paper is an extension of a previous paper written in collaboration with Markus Reineke dealing with quiver representations. The aim of the paper is to generalize the theory and to provide a comprehensive theory of…
We obtain some inequalities which are stronger than the Schur majorization inequalities.
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.