相关论文: Ky Fan inequalities

We review several inequalities concerning Gaussian measures - isoperimetric inequality, Ehrhard's inequality, Bobkov's inequality, S-inequality and correlation conjecture.

The nature of dark matter and the origin of the baryon asymmetry are two of the deepest mysteries of modern particle physics. In the absence of hints regarding a possible solution to these mysteries, many approaches have been developed to…

Several inequalities are presented which, in part, generalize inequalities by Weinstein and Weiss, giving rise to new lower bounds for the Bayes risk under squared error loss.

Homotopy coherence has a considerable history, albeit also by other names. We provide a brief semi-historical survey providing some links that may not be common knowledge.

In this paper, the Authors establish a new identity for differentiable functions. By the well-known H\"older and power mean inequality, they obtain some integral inequalities related to the convex functions and apply these inequalities to…

Certain basic inequalities between intrinsic and extrinsic invariants for a submanifold in a (k, m)-contact space form are obtained. As applications we get some results for invariant submanifolds in a (k,m)-contact space form.

A critical discussion of our knowledge about extragalactic cosmic rays and magnetic fields is attempted. What do we know for sure? What are our prejudices? How do we confront our models with the observations? How can we assess the…

Quantum Fano inequality (QFI) in quantum information theory provides an upper bound to the entropy exchange by a function of the entanglement fidelity. We give various Fano-like upper bounds to the entropy exchange and QFI is a special case…

We overview series of multiqubit Bell's inequalities which apply to correlation functions. We present conditions that quantum states must satisfy to violate such inequalities.

We present a regularized version of H\"{o}lder-Brascamp-Lieb inequalities studied by Bennett, Carbery, Christ, and Tao. These inequalities lead to a generalization of the multilinear Kakeya inequality.

Gender inequalities in science have long been observed globally. Studies have demonstrated it through survey data or published literature, focusing on the interests of subjects or authors; few, however, examined the manifestation of gender…

In this report, we aim to exemplify concentration inequalities and provide easy to understand proofs for it. Our focus is on the inequalities which are helpful in the design and analysis of machine learning algorithms.

The increasing application of Artificial Intelligence and Machine Learning models poses potential risks of unfair behavior and, in light of recent regulations, has attracted the attention of the research community. Several researchers…

The open problems and the most recent developments in flavour physics are briefly reviewed. Particular attention is devoted to the current "anomalies" in the CKM picture and their possible interpretation in beyond-the-Standard-Model…

An interplay between the sum of certain series related to Harmonic numbers and certain finite trigonometric sums is investigated. This allows us to express the sum of these series in terms of the considered trigonometric sums, and permits…

Over the last decades, the distribution of income and wealth has been deteriorating in many countries, leading to increased inequalities within and between societies. This tendency has revived the interest in the subject greatly, yet it…

In this paper, the authors establish some inequalities involving the Psi and $k$-Gamma functions. The procedure utilizes some monotonicity properties of some functions associated with the Psi and $k$-Gamma functions.

In this paper, we give a new inequality for convex functions of real variables, and we apply this inequality to obtain considerable generalizations, refinements, and reverses of the Young and Heinz inequalities for positive scalars.…

We give a necessary and sufficient condition for a generalized Bott manifold to be Fano or weak Fano. As a consequence we characterize Fano Bott manifolds.

The article is devoted to remarkable interrelation between the norm estimates for $k$-plane transforms in weighted and unweighted $L^p$ spaces and geometric integral inequalities for cross-sections of measurable sets in $\mathbb{R}^n$. We…