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.

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.

Substance P and its tachykinin NK1 receptor: a novel neuroprotective target for Parkinson's disease

Parkinson＇s disease （PD） is the most common motor neurode- generative disorder affecting approximately 4 million people worldwide. Although PD presents primarily with motor dysfunction, non-motor symptoms including cognitive decline, mood disorders, reduced olfaction and constipation are also of- ten present, with some of these non-motor symptoms even pre- senting prior to the onset of motor symptoms. It is well known that PD is largely caused by the gradual degeneration of dopa- minergic neurons within the substantia nigra pars compacta （SNc）, along with the presence of protein aggregates called Lewy bodies, which consist primarily of ct-synuclein and are found in the cytoplasm of surviving neurons. This ongoing cell loss and Lewy body pathology is not confined to the SNc, but is also seen in other brain regions implicated in PD pathogenesis such as the locus ceruleus.

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。

Shifting balance from neurodegeneration to regeneration of the brain: a novel therapeutic approach to Alzheimer's disease and related neurodegenerative conditions

Neurodegeneration is one of the biggest public health problems in modern society. Age-associated neurodegeneration, which is accelerated several-fold in Alzheimer＇s disease （AD） alone, is not only an enormous social and economic burden to the affected in- dividuals and their families, but is also a great scientific challenge. Currently 25-35 million people worldwide suffer from AD, the single largest cause of dementia in middle- to old-aged individuals. These numbers are projected to triple by 2050 if no treatment to prevent or reverse AD is developed.

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.

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.

Glyco-sphingo biology: a novel perspective for potential new treatments in Huntington's disease

Huntington＇s disease （HD） is the most common dominantly inherited neurodegenerative disorder, mainly characterized by the progressive striatal and cortical neurodegeneration and as- sociated motor, cognitive and behavioural disturbances （Zuccato et al., 2010）. The disease-causing mutation is an expansion of a GAG trinucleotide repeat （〉 36 repeats） encoding a polygluta- mine stretch in the N-terminal region ofhuntingtin （Htt） （Zuc- cato et al., 2010）, a ubiquitous protein whose function is still unclear （Zuccato et al., 2010）. Expansion of the polyQ stretch endows mutant Htt （mHtt） with toxic properties, and results in the development of a broad array of undesirable effects in both neuronal and non-neuronal cells （Zuccato et al., 2010）. Among all cellular dysfunctions and biochemical imbalances classically associated with HD, perturbed metabolism of （glyco） sphingolipids appears to play a crucial role in the pathogenesis of the disease. Over the last years, we and other have extensively contributed to these findings （Desplats et al., 2007;

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.

On The Northeast Regional Culture in Xiao Hong’s Novels

As the literary pride from the black land of northeast China,Xiao hong’s works show the unique regional culture of northeast China.With her meticulous brush strokes,she showed us the distinct geographical environment of the four seasons in north China,the strong local flavor and people’s sentiment,as well as the servility and ferocity of the people in the northeast.Xiao hong’s criticism of callous and ignorant servile characters and his praise of the consciousness of resistance and the indomitable life form,prompts us to think about the“national character”of northeast China and makes us feel the tragedy of society,the philosophy of life and the spirit of poets.

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.

Electromagnetic—Pure Gravity Connection via Hardy’s Quantum Entanglement

Pure gravity in eight dimensional super space possesses twenty degrees of freedom. Gauging these generalized coordinates in terms of a single self entangled Hardy type quantum particle we retrieve one hundred and thirty seven isometries corresponding to the well known value of the inverse electromagnetic fine structure constant. The deep implications of this thought provoking result are discussed in a general physical context.

The Racial Prejudice in City in Paul Auster’s Novels

In Auster’s novels,the racial prejudice occupies a vital part;the whites presently take a majority privileged position in the mainstream culture;both the blacks and Jews become the target of racial prejudice which is vividly embodied in City of Glass:The Graphic Novel,Ghosts,Man in the Dark,In the Country of Last Things.