Verification of the Landau Equation and Hardy’s Inequality

We prove the L estimate for the isotropic version of the homogeneous landau problem, which was explored by M. Gualdani and N. Guillen. As shown in a region of the smooth potentials range under values of the interaction exponent (2), a weighted Poincaré inequality is a natural consequence of the traditional weighted Hardy inequality, which in turn implies that the norms of solutions propagate in the L1 space. Now, the L estimate is based on the work of De Giorgi, Nash, and Moser, as well as a few weighted Sobolev inequalities.

A Survey of English Translation Studies of Lu You’s Poetry Based on the Data Analysis of Domestic Academic Journals (2001-2022)

This article presents a comprehensive analysis of the current state of research on the English translation of Lu You’s poetry, utilizing a data sample comprising research papers published in the CNKI Full-text Database from 2001 to 2022. Employing rigorous longitudinal statistical methods, the study examines the progress achieved over the past two decades. Notably, domestic researchers have displayed considerable interest in the study of Lu You’s English translation works since 2001. The research on the English translation of Lu You’s poetry reveals a diverse range of perspectives, indicating a rich body of scholarship. However, several challenges persist, including insufficient research, limited translation coverage, and a noticeable focus on specific poems such as “Phoenix Hairpin” in the realm of English translation research. Consequently, there is ample room for improvement in the quality of research output on the English translation of Lu You’s poems, as well as its recognition within the academic community. Building on these findings, it is argued that future investigations pertaining to the English translation of Lu You’s poetry should transcend the boundaries of textual analysis and encompass broader theoretical perspectives and research methodologies. By undertaking this shift, scholars will develop a more profound comprehension of Lu You’s poetic works and make substantive contributions to the field of translation studies. Thus, this article aims to bridge the gap between past research endeavors and future possibilities, serving as a guide and inspiration for scholars to embark on a more nuanced and enriching exploration of Lu You’s poetry as well as other Chinese literature classics.

An Investigation into the Case of Multi-interpretation in Poetry Translation

In translating poems, it is very common that different people have quite different versions of the same poem. This paper therefore intends to expound upon the underlying factors from the perspective of Hermeneutics,by exploring the relationship between the textual meaning and the textual significance of a poem, as well as the relationship between the author's intention and the textual intention of a poem, aiming to explain the key element in translating poems—multi-interpretation.

Reasons of Taoism in Robert Bly's Poetry

Bly's preference of Taoist thoughts to Western philosophy and ideology in his poetry has its deeper reasons. It is his secluded life attitude and his poetics construction that promote him to learn from the ancient Chinese poetry which contains adequate Taoist ideas.

NEW WEIGHTED MULTILINEAR OPERATORS AND COMMUTATORS OF HARDY-CESàRO TYPE

This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesaro oper- ators （with symbols in central BMO spaces） are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.

GRADIENT ESTIMATES FOR SOLUTIONS TO QUASILINEAR ELLIPTIC EQUATIONS WITH CRITICAL SOBOLEV GROWTH AND HARDY POTENTIAL

This note is a continuation of the work[17].We study the following quasilinear elliptic equations- △pu-μ/｜x｜p ｜u｜p-2 u=Q（x）｜u｜Np/N-p -2u,x∈R N,where 1 〈 p 〈 N,0 ≤ μ 〈（（N-p）/p）p and Q ∈ L∞（RN）.Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.

Weighted Composition Operators between Hardy Spaces on the Unit Ball

We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the operator from H^1 to H^1 is compact if and only if it is weakly compact. Meanwhile, we get the analogue on the Bergman spaces.

双曲Hardy空间中的Sσ—函数与gλ,σ—函数

本文在双曲Ｈａｒｄｙ空间Ｈｐσ（１≤ｐ＜∞）中引进分别类似于调和分析中Ｓ函数与ｇλ函数的Ｓσ函数与ｇλ，σ函数．证明当ｆ∈Ｈｐσ时，Ｓσ（ｆ）与ｇλ。

Experimentally testing Hardy's theorem on nonlocality with entangled mixed states

Hardy＇s theorem on nonlocality has been verified by a series of experiments with two-qubit entangled pure states.However,in this paper we demonstrate the experimental test of the theorem by using the two-photon entangled mixed states.We first investigate the generic logic in Hardy＇s proof of nonlocality,which can be applied for arbitrary two-qubit mixed polarization entangled states and can be reduced naturally to the well-known logic tested successfully by the previous pure state experiments.Then,the optimized violations of locality for various experimental parameters are delivered by the numerical method.Finally,the logic argued above for testing Hardy＇s theorem on nonlocality is demonstrated experimentally by using the mixed entangled-photon pairs generated via pumping two type-I BBO crystals.Our experimental results shows that Hardy＇s proof of nonlocality can also be verified with two-qubit polarization entangled mixed states,with a violation of about 3.4 standard deviations.

BOUNDEDNESS OF STEIN'S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES

Let （X, d,μ） be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L^2（X）. Assume that the semigroup e^-tL generated by L satisfies the Davies-Gaffney estimates. Also, assume that L satisfies Plancherel type estimate. Under these conditions, we show that Stein＇s square function Gδ（L） arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces HL^p（X） to L^p（X） for all 0 〈 p ≤ 1.

Sylvia Plath And Her Poetry Viewed In Psychological Aspect

Sylvia Plath is a major representative of the American confessional poetry. Her idiosyncratic poetry and her suicide in1963 aroused an intensive interest and study on her and her poems that hasn't subsided until now. This paper tries to explore the so-called Sylvia Plath myth and analyzes the various factors that molded her extreme psychology, theme and style by Lacanian psychoanalytic approach.

AN IMPROVED HARDY'S INEQUALITY

In this paper we shall extend Hardy＇s inequality associated with Fourier trans- form to the strip n（2-p） ≤σ〈 n＋p（N＋ 1） where N = [n（1/p- 1）], the greatest integer not exceeding n（1/p - 1）.

The relation between Hardy's non-locality and violation of Bell inequality

We give an analytic quantitative relation between Hardy＇s non-locality and Bell operator. We find that Hardy＇s non-locality is a sufficient condition for the violation of Bell inequality, the upper bound of Hardy＇s non-locality allowed by information causality just corresponds to Tsirelson bound of Bell inequality and the upper bound of Hardy＇s non- locality allowed by the principle of no-signaling just corresponds to the algebraic maximum of Bell operator. Then we study the CabeUo＇s argument of Hardy＇s non-locality （a generalization of Hardy＇s argument） and find a similar relation between it and violation of Bell inequality. Finally, we give a simple derivation of the bound of Hardy＇s non-locality under the constraint of information causality with the aid of the above derived relation between Hardy＇s non-locality and Bell operator.

A HEAT KERNEL VERSION OF HARDY’S THEOREM FOR THE LAGUERRE HYPERGROUP

In this article, we prove a heat kernel version of Hardy＇s theorem for the Laguerre hypergroup.

HEAT KERNELS AND HARDY'S UNCERTAINTY PRINCIPLE ON H-TYPE GROUPS

This article obtains an explicit expression of the heat kernels on H-type groups and then follow the estimate of heat kernels to deduce the Hardy＇s uncertainty principle on the nilpotent Lie groups.

On Some Integral Inequalities of Hardy-Type Operators

In recent time, hardy integral inequalities have received attentions of many researchers. The aim of this paper is to obtain new integral inequalities of hardy-type which complement some recent results.

Poet Zang Kejia Talks About Mao Zedong’s Poetry—Commemorating Mao Zedong’s Centenary

ZANG Kejla was already a well-known fi-gure in Chinese literary circles during the1930s.Mao Zedong used to invite him tothe Qingzheng Hall to talk about poetry and edita few pieces,and the two became good friends.AsMao’s 100th birthday approached,I visited thepoet to talk with him about the late chairman’spoetry.Mao Zedong is a name known across theworld.A great revolutionary,politician and mili-tary scientist,he was also a poet at heart.Someforeign observers once wondered that“a poet hadcreated a new China.”His pieces have a veryrevolutionary flavor that recount to his readers

A MATHEMATICAL PROOF OF A PROBABILISTIC MODEL OF HARDY'S INEQUALITY

In this paper using an argument from [1] , we prove one of the probabilistic version of Hardy＇s inequality.

Rebellious Spirit in Shelley’s Poetry

雪莱的诗歌反映了他争取平等和自由的反叛思想。诗歌中揭示了他对上层阶级的诅咒 。

Resolution of Hardy’s Paradox within Spacetime Physics and the Ithaca Interpretation of Quantum Mechanics

By religiously adhering to physics in spacetime and taking the final verdict of N.D. Mermin’s Ithaca interpretation of quantum mechanics seriously, Hardy’s paradox is completely resolved. It is then concluded that logical and mathematically consistent physical theories must be put in spacetime related formalism such as noncommutative geometry and E-infinity theory to avoid quantum paradoxes. At a minimum, we should employ the philosophy behind consistent quantum interpretation such as that of the famous Ithaca interpretation of D. Mermin.