一种有效制备2-氨基-3,5-二硝基-6-氯吡啶及其衍生物的方法

研究了2-氨基-3,5-二硝基-6-氯吡啶(4)及其衍生物的制备新方法.以廉价易得的2,6-二氯吡啶(1)为起始原料,通过硝化、氨化、硝化反应步骤得到中间体2-氨基-3,5-二硝基-6-氯吡啶(4),再与氨、叠氮化钠等亲核试剂反应分别得到2-氨基-3,5-二硝基吡啶-6-取代衍生物5~7.研究表明该方法具有原料便宜易得、后处理操作简单和产品纯度高等优点.     

Quantitative analysis of some system of integral equations

In this paper, we study the integrability of the non-negative solutions to the Euler-Lagrange equations associated with Weighted Hardy-Littlewood-Sobolev (HLS) inequality. We obtain the optimal integrability for the solutions. The integrability and the radial symmetry (which we derived in our earlier paper) are the key ingredients to study the growth rate at the center and the decay rate at infinity of the solutions. These are also the essential properties needed to classify all non-negative solutions. Some simple generalizations are also provided here.     

A necessary and sufficient condition for the nirenberg problem

We seek metrics conformal to the standard ones on Sⁿ having prescribed Gaussian curvature in case n = 2 (the Nirenberg Problem), or prescribed scalar curvature for n ≧ 3 (the Kazdan-Warner problem). There are well-known Kazdan-Warner and Bourguignon-Ezin necessary conditions for a function R(x) to be the scalar curvature of some conformally related metric. Are those necessary conditions also sufficient? This problem has been open for many years. In a previous paper, we answered the question negatively by providing a family of counter examples. In this paper, we obtain much stronger results. We show that, in all dimensions, if R(x) is rotationally symmetric and monotone in the region where it is positive, then the problem has no solution at all. It follows that, on S², for a non-degenerate, rotationally symmetric function R(θ), a necessary and sufficient condition for the problem to have a solution is that Rθ changes signs in the region where it is positive. This condition, however, is still not sufficient to guarantee the existence of a rotationally symmetric solution, as will be shown in this paper. We also consider similar necessary conditions for non-symmetric functions. ©1995 John Wiley & Sons, Inc.     

Synthesis of 2-Azido-4-nitroimidazole and Its Derivatives for High-Energy Materials

2-Azido-4-nitroimidazole and its derivatives have been synthesized for energetic material applications. The synthesized compounds were fully characterized by 1H, 13C NMR spectroscopy and elemental analysis. Most of them were determined by single crystal X-ray diffraction. The calculated densities of the compounds range between 1.71 and 1.92 g,cm-3. The calculated detonation pressures （P） for these derivatives fall in the range of 25.17 to 32.62 GPa and the detonation velocities （D） are distributed from 7.65 to 8.55 km·s-1.     

Pore-size tunable mesoporous zirconium organophosphonates with chiral L-proline for enzyme adsorption

Mesoporous zirconium organophosphonates with a tunable mesopore (pore diameter: from 4.8 to 16.3 nm) were synthesized through co-condensation of ZrCl4 and 1-phosphomethylproline (H3PMP) with the aid of organic additives in the presence of an anionic surfactant (sodium dodecyl sulfate) under weak acidic conditions. The organic additives, tetrahydrofuran, can effectively strengthen the assembly of ZrCl4 and H3PMP around the surfactant micelles through decreasing the hydrolysis and condensation rate of ZrCl4. The results of the N2 sorption isotherm and SEM image show that zirconium phosphate with a bimodal structure is formed by calcination of mesoporous zirconium organophosphonate. Mesoporous zirconium organophosphonates can effectively adsorb lysozyme (Lz) and papain, and the adsorption equilibrium for Lz can be reached within 30 min. The adsorption capacity for Lz and papain can reach as high as 438 and 297 mg/g, respectively. Furthermore, Lz adsorbed on mesoporous zirconium organophosphonates can retain its structural conformation as in its free state, and no leaching of Lz from the solid was observed when shaking the Lz-loaded solid in a buffer solution. Also, the existence of L-proline in the mesopore could help the adsorption of papain at a pH value lower than the pI of papain.     

An extension of the hardy-littlewood-pólya inequality

The Hardy-Littlewood-Pólya （HLP） inequality [1] states that if a∈l^p,b∈l^q and p>1,q>1,1/p + 1/q>1, λ=2-（1/p+1/q）,then Σ[（a_rb_s）/︱r-s︱^λ]（r≠s）≤C‖a‖_P‖b‖_q.In this article, we prove the HLP inequality in the case where λ= 1, p = q = 2 with a logarithm correction, as conjectured by Ding [2]:Σ[（a_rb_s）/︱r-s︱^λ]（r≠s,1≤r,s≤N）≤（2㏑N+1）‖a‖₂‖b‖₂.In addition, we derive an accurate estimate for the best constant for this inequality.     

Asymptotic radial symmetry and growth estimates of positive solutions to weighted Hardy–Littlewood–Sobolev system of integral equations

In this article, we study the asymptotics of the positive solutions of the Euler–Lagrange system of the weighted Hardy–Littlewood–Sobolev in R ⁿ $$\begin{array}{ll} u(x) = \frac{1}{|x|^{\alpha}}\int\limits_{R^{n}} \frac{v(y)^q}{|y|^{\beta}|x-y|^{\lambda}} dy,\\ v(x) = \frac{1}{|x|^{\beta}}\int\limits_{R^{n}} \frac{u(y)^p}{|y|^{\alpha}|x-y|^{\lambda}} dy.\end{array}$$ A new iterative method is introduced to obtain the optimal weighted local integrability of u(x). By this new method, we establish the asymptotic estimates of the solutions around the origin and near infinity. With these new estimates, we complete the study of the asymptotic behavior of the solutions. We believe this new iterative method and the new type of the weighted local estimates can be used in many other cases.