Related papers: Extended Derdzinski-Shen theorem for the Riemann t…

In this paper, we present some fixed point theorems for operator systems in the line of Krasnosel'skii's theorem in cones. The cone-compression and cone-expansion type conditions are imposed in a component-wise manner. Unlike related…

We develop some applications of certain algebraic and combinatorial conditions on the elements of Coxeter groups, such as elementary proofs of the positivity of certain structure constants for the associated Kazhdan--Lusztig basis. We also…

In two previous papers with Yi-Jen Lee, we defined and computed a notion of Reidemeister torsion for the Morse theory of closed 1-forms on a finite dimensional manifold. The present paper gives an a priori proof that this Morse theory…

We propose a notion of a ternary skew-symmetric covariant tensor of 3rd order, consider it as a 3-dimensional matrix and study a ten-dimensional complex space of these tensors. We split this space into a direct sum of two five-dimensional…

Exploiting particular features of classical groups, simple constructions are given for the irreducible constituents of the tensor square of the adjoint modules and the leading terms in higher tensor powers. This provides an independent…

In the paper, we give a Schur-Toponogov theorem in Riemannian geometry, which not only generalizes Schur's and Toponogov's theorem but also indicates their relation. Inspired by its proof, we also supply a new proof of Toponogov's theorem…

A new $Z$-eigenvalue inclusion theorem for tensors is given and proved to be tighter than those in [G. Wang, G.L. Zhou, L. Caccetta, $Z$-eigenvalue inclusion theorems for tensors, Discrete and Continuous Dynamical Systems Series B,22(1)…

Regular variation is a continuous-parameter theory; we work in a general setting, containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases. We give sequential versions of the main theorems, that is,…

We develop sufficient analytic conditions for recurrence and transience of non-sectorial perturbations of possibly non-symmetric Dirichlet forms on a general state space. These form an important subclass of generalized Dirichlet forms which…

In this paper we present a convergence theorem for continued fractions of the form $K_{n=1}^{\infty}a_{n}/1$. By deriving conditions on the $a_{n}$ which ensure that the odd and even parts of $K_{n=1}^{\infty}a_{n}/1$ converge, these same…

We suggest an extension of the gauge principle which includes tensor gauge fields. The extended non-Abelian gauge transformations of the tensor gauge fields form a new large group. On this group one can define field strength tensors, which…

Let $M$ be a Riemannian manifold with a polar action by the Lie group $G$, with section $\Sigma\subset M$ and generalized Weyl group $W$. We show that restriction to $\Sigma$ is a surjective map from the set of smooth $G$-invariant tensors…

In this paper, we study $L^p$-boundedness ($1<p\leq 2$) of the covariant Riesz transform on differential forms for a class of non-compact weighted Riemannian manifolds without assuming conditions on derivatives of curvature. We present in…

A new approach to the algebraic classification of second order symmetric tensors in 5-dimensional space-times is presented. The possible Segre types for a symmetric two-tensor are found. A set of canonical forms for each Segre type is…

We classify newforms with rational Fourier coefficients and complex multiplication for fixed weight up to twisting. Under the extended Riemann hypothesis for odd real Dirichlet characters, these newforms are finite in number. We produce…

Curvature tensors of higher-spin gauge theories have been known for some time. In the past, they were postulated using a generalization of the symmetry properties of the Riemann tensor (curl on each index of a totally symmetric rank-$n$…

The author constructs a theory of dagger formal schemes over $R$ and then defines the de Rham cohomology for flat dagger formal schemes $X$ with integral and regular reductions $\bar{X}$ which generalizes the Monsky-Washnitzer cohomology.…

For a noncommutative Orlicz space associated with a semifnite von Neumann algebra, a faithful normal semifnite trace and an Orlicz function satisfying $(\delta_2,\Delta_2)-$condition, an individual ergodic theorem is proved.

Using ideas from algebraic topology and statistical mechanics, we generalize Kirchhoff's network and matrix-tree theorems to finite CW complexes of arbitrary dimension. As an application, we give a formula expressing Reidemeister torsion as…

In this short note, we give a new proof of a theorem of Arezzo-Tian on the existence of smooth geodesic rays tamed by a special degeneration.