The extension of some Orlicz space results to the theory of optimal measure

2013 ◽  
Vol 286 (8-9) ◽  
pp. 760-771 ◽  
Author(s):  
Nutefe Kwami Agbeko ◽  
Sever Silvestru Dragomir
Keyword(s):  
Orlicz Space ◽  
Optimal Measure

Analysis and Optimization of the Static and Dynamic Characteristics of Head Frame

2011 ◽  
Vol 418-420 ◽  
pp. 2055-2059 ◽  
Author(s):  
Yu Lin Wang ◽  
Na Jin ◽  
Kai Liao ◽  
Rui Jin Guo ◽  
Hu Tian Feng
Keyword(s):  
Machine Tool ◽  
Dynamic Characteristics ◽  
Maximum Stress ◽  
Dynamic Performance ◽  
Mode Shapes ◽  
Cnc Machine ◽  
Static And Dynamic Characteristics ◽  
Maximum Deformation ◽  
Improvement Measures ◽  
Optimal Measure

The head frame is a key component which plays a supportive and accommodative role in the spindle system of CNC machine tool. Improving the static and dynamic characteristics has profound significance to the development of machine tool and product performance. The simplified finite element modal is established with ANSYS to carry out the static and modal analysis. The results showed that the maximum deformation of the head frame was 0.0066mm, the maximum stress was 3.94Mpa, the deformation of most region was no more than 0.0007mm, which all verified that the head frame had a good stiffness and deforming resistance; several improvement measures for dynamic performance were also proposed by analyzing the mode shapes, and the 1st order natural frequency increased 7.33% while the head frame mass only increased 1.58% applying the optimal measure, which improved the dynamic characteristics of the head frame effectively.

Second-order Riesz Transforms and Maximal Inequalities Associated with Magnetic Schr ödinger Operators

2015 ◽  
Vol 58 (2) ◽  
pp. 432-448 ◽  
Author(s):  
Dachun Yang ◽  
Sibei Yang
Keyword(s):  
Hardy Space ◽  
Orlicz Space ◽  
Orlicz Function ◽  
Second Order ◽  
Riesz Transforms ◽  
Muckenhoupt Weights ◽  
Schrodinger Operator ◽  
Magnetic Schrödinger Operator ◽  
Maximal Inequalities ◽  
Reverse Hölder

AbstractLet be a magnetic Schrödinger operator on ℝn, wheresatisfy some reverse Hölder conditions. Let be such that ϕ(x, ·) for any given x ∊ ℝn is an Orlicz function, ϕ( ·, t) ∊ A∞(ℝn) for all t ∊ (0,∞) (the class of uniformly Muckenhoupt weights) and its uniformly critical upper type index . In this article, the authors prove that second-order Riesz transforms VA-1 and are bounded from the Musielak–Orlicz–Hardy space Hµ,A(Rn), associated with A, to theMusielak–Orlicz space Lµ(Rn). Moreover, we establish the boundedness of VA-1 on . As applications, some maximal inequalities associated with A in the scale of Hµ,A(Rn) are obtained

scholarly journals Some spectral formulas for functions generated by differential and integral operators in Orlicz spaces

2021 ◽  
Vol 13 (2) ◽  
pp. 326-339
Author(s):  
H.H. Bang ◽  
V.N. Huy
Keyword(s):  
Fourier Transform ◽  
Orlicz Space ◽  
Differential Operators ◽  
Orlicz Spaces ◽  
Integral Operators ◽  
Young Function ◽  
The Fourier Transform

In this paper, we investigate the behavior of the sequence of $L^\Phi$-norm of functions, which are generated by differential and integral operators through their spectra (the support of the Fourier transform of a function $f$ is called its spectrum and denoted by sp$(f)$). With $Q$ being a polynomial, we introduce the notion of $Q$-primitives, which will return to the notion of primitives if ${Q}(x)= x$, and study the behavior of the sequence of norm of $Q$-primitives of functions in Orlicz space $L^\Phi(\mathbb R^n)$. We have the following main result: let $\Phi $ be an arbitrary Young function, ${Q}({\bf x} )$ be a polynomial and $(\mathcal{Q}^mf)_{m=0}^\infty \subset L^\Phi(\mathbb R^n)$ satisfies $\mathcal{Q}^0f=f, {Q}(D)\mathcal{Q}^{m+1}f=\mathcal{Q}^mf$ for $m\in\mathbb{Z}_+$. Assume that sp$(f)$ is compact and $sp(\mathcal{Q}^{m}f)= sp(f)$ for all $m\in \mathbb{Z}_+.$ Then $$ \lim\limits_{m\to \infty } \|\mathcal{Q}^m f\|_{\Phi}^{1/m}= \sup\limits_{{\bf x} \in sp(f)} \bigl|1/ {Q}({\bf x}) \bigl|. $$ The corresponding results for functions generated by differential operators and integral operators are also given.

scholarly journals Extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with Orlicz norm

2021 ◽  
Vol 41 (5) ◽  
pp. 629-648
Author(s):  
Fatiha Boulahia ◽  
Slimane Hassaine
Keyword(s):  
Orlicz Space ◽  
Extreme Points ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Orlicz Norm ◽  
Amemiya Norm

In the present paper, we give criteria for the existence of extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with Orlicz norm. Some properties of the set of attainable points of the Amemiya norm in this space are also discussed.

scholarly journals Searching for the bottom of the ego well: Failure to uncover ego depletion in Many Labs 3

2017 ◽  
Author(s):  
Miguel A. Vadillo ◽  
Natalie Gold ◽  
Magda Osman
Keyword(s):  
Stroop Task ◽  
Secondary Task ◽  
Large Scale ◽  
Limited Resource ◽  
Ego Depletion ◽  
Self Control ◽  
Significant Evidence ◽  
Heated Debate ◽  
The Subject ◽  
Optimal Measure

According to a popular model of self-control, willpower depends on a limited resource that can be depleted when we perform a task demanding self-control. Over the last five years, the reliability of the empirical evidence supporting this model has become the subject of heated debate. In the present study, we reanalysed data from a large-scale study –Many Labs 3– to test whether performing a depleting task has any effect on a secondary task that also relies on self-control. Although we used a large sample of more than 2,000 participants for our analyses, we did not find any significant evidence of ego-depletion: Persistence on an anagram solving task (a typical measure of self-control) was not affected by previous completion of a Stroop task (a typical depleting task in this literature). Our results suggest that persistence in anagram solving may not be an optimal measure to test depletion effects.

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