Related papers: Reverse Brascamp-Lieb inequality and the dual Boll…
Let $A, B$ be positive definite $n\times n$ matrices. We present several reverse Heinz type inequalities, in particular \begin{align*} \|AX+XB\|_2^2+ 2(\nu-1) \|AX-XB\|_2^2\leq \|A^{\nu}XB^{1-\nu}+A^{1-\nu}XB^{\nu}\|_2^2, \end{align*} where…
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
We extend the main result in the previous paper of Zhang and the author relating the Milnor-Turaev torsion with the complex valued analytic torsion to the equivariant case.
Various results are proved giving lower bounds for the $m$th intrinsic volume $V_m(K)$, $m=1,\dots,n-1$, of a compact convex set $K$ in ${\mathbb{R}}^n$, in terms of the $m$th intrinsic volumes of its projections on the coordinate…
The aim of this work is to improve Wilker inequalities near the origin and {\pi}/2.
We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.
We will prove a reverse Rogers-Shephard inequality for log-concave functions. In some particular cases, the method used for general log-concave functions can be slightly improved, allowing us to prove volume estimates for polars of…
A Bell inequality defined for a specific experimental configuration can always be extended to a situation involving more observers, measurement settings or measurement outcomes. In this article, such "liftings" of Bell inequalities are…
In this short paper, we establish a variational expression of the Tsallis relative entropy. In addition, we derive a generalized thermodynamic inequality and a generalized Peierls-Bogoliubov inequality. Finally we give a generalized…
In this paper, we sharpen and generalize Carlson's double inequality for the arc cosine function.
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in complex Hilbert spaces are given. Applications for complex-valued functions are provided as well.
We analyse the recent claim that a violation of a Bell's inequality has been observed in the $B$--meson system [A. Go, {\em Journal of Modern Optics} {\bf 51} (2004) 991]. The results of this experiment are a convincing proof of quantum…
We give a very short proof of the Golden-Thompson inequality
We generalize the extension and trace results of Bj\"orn-Bj\"orn-Shanmugalingam \cite{BBS21} to the setting of complete noncompact doubling metric measure spaces and their uniformized hyperbolic fillings. This is done through a…
We consider a general way to obtain Pr\'ekopa-Leindler and Borell-Brascamp-Lieb type inequalities from Brunn-Minkowski type inequalities and provide numerous examples. We use the same heuristic to prove a discrete version of the…
The Bruss-Robertson inequality gives a bound on the maximal number of elements of a random sample whose sum is less than a specified value, and the extension of that inequality which is given here neither requires the independence of the…
The aim of this paper is threefold: a) Finding new direct and inverse results in the additive number theory concerning Minkowski sums of dilates. b) Finding a connection between the above results and some direct and inverse problems in the…
In this paper, we sharpen and generalize Carlson's double inequality for the arc cosine function.
We give a $L^2\times L^2 \rightarrow L^2$ convolution estimate for singular measures supported on transversal hypersurfaces in $\mathbb{R}^n$, which improves earlier results of Bejenaru, Herr & Tataru as well as Bejenaru & Herr. The arising…
New results related to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.