Generalized Huygens types inequalities for Bessel and modified Bessel functions

In this paper, we present a generalization of the Huygens types inequalities involving Bessel and modified Bessel functions of the first kind

On the Wilker and Huygens-type inequalities

Chen and Cheung [C.-P. Chen, W.-S. Cheung, Sharpness of Wilker and Huygens type inequalities, J. Inequal. Appl. 2012 (2012) 72, \url{http://dx.doi.org/10.1186/1029-242X-2012-72}] established sharp Wilker and Huygens-type inequalities. These authors also proposed three conjectures on Wilker and Huygens-type inequalities. In this paper, we consider these conjectures. We also present sharp Wilker and Huygens-type inequalities.Comment: 18 pages, 0 figure

Extension of Huygens type inequalities for Bessel and modified Bessel Functions

In this paper, new sharpened Huygens type inequalities involving Bessel and modified Bessel functions of the first kinds are establishe

A proof of two conjectures of Chao-Ping Chen for inverse trigonometric functions

In this paper we prove two conjectures stated by Chao-Ping Chen in [Int. Trans. Spec. Funct. 23:12 (2012), 865--873], using a method for proving inequalities of mixed trigonometric polynomial functions

New trigonometric and hyperbolic inequalities

The aim of this paper is to prove new trigonometric and hyperbolic inequalities, which constitute among others refinements or analogs of famous Cusa-Huygens, Wu-Srivastava, and related inequalities. In most cases, the obtained results are sharp.Comment: 12 page

A subtly analysis of Wilker inequality

The aim of this work is to improve Wilker inequalities near the origin and {\pi}/2.Comment: 6 page

Extension of Frame's type inequalities to Bessel and modified Bessel functions

Our aim is to extend some trigonometric inequalities to Bessel functions. Moreover, we extend the hyperbolic analogue of these trigonometric inequalities. As an application of these results we present a generalization of Cusa-type inequality to modified Bessel function. Our main motivation to write this paper is a recent publication of Chen and S\'andor, which we wish to complement

Sharp Cusa type inequalities for trigonometric functions with two parameters

Let $\left( p,q\right) \mapsto \beta \left( p,q\right)$ be a function defined on $\mathbb{R}^{2}$. We determine the best or better $p,q$ such that the inequality% \begin{equation*} \left( \frac{\sin x}{x}\right) ^{p}<\left( >\right) 1-\beta \left( p,q\right) +\beta \left( p,q\right) \cos ^{q}x \end{equation*}% holds for $x\in \left( 0,\pi /2\right)$, and obtain a lot of new and sharp Cusa type inequalities for trigonometric functions. As applications, some new Shafer-Fink type and Carlson type inequalities for arc sine and arc cosine functions, and new inequalities for trigonometric means are established.Comment: 29 page

A Method of Proving a Class of Inequalities of Mixed Trigonometric Polynomial Functions

In this article we consider a method of proving a class of inequalities of the form (1). The method is based on the precise approximations of the sine and cosine functions by Maclaurin polynomials of given order. By using this method we present new proofs of some inequalities from the articles C.-P. Chen, W.-S. Cheung [J. Inequal. Appl. 2012:72 (2012)] and Z.-J. Sun, L. Zhu [ISRN Math. Anal. (2011)]

Overcoming the EPR paradox

Quantum experiments detect particles, but they reveal information about wave properties. No matter how quanta are detected, they always express the local net state of the corresponding wave-function. The mechanism behind this process is still a mystery. However, quantum wave-functions evolve like classical waves. If they determine all the observations, why do they entail "weird" phenomena? In particular, why do they produce conceptual problems, such as the EPR paradox? It turns out that all the major interpretations in quantum mechanics are particle-based ontologies. Variables of fundamental interest, such as momentum and position, are assumed to reflect the input states of discrete entities, even when their evolution is predicted by wave equations. Here I show that a whole class of microscopic phenomena, including entanglement, can be interpreted without contradictions if the variables of quantum mechanics are actually treated as wave properties. The main recommendation is to assume that sharp spectral states are transient outcomes of superposition, rather than permanent input components.Comment: 10 pages, 4 figures, 1 good solutio