Existence of three weak solutions for a perturbed anisotropic discrete Dirichlet problem

In this paper, we study the existence of at least three distinct solutions for a perturbed anisotropic discrete Dirichlet problem. Our approach is based on recent variational methods for smooth functionals defined on reflexive Banach spaces. Some examples are presented to demonstrate the application of our main results.     

Multiple periodic solutions for non-linear difference systems involving the p-Laplacian

Using the three critical points theorem, Clark's theorem and the Morse theory, multiple periodic solutions for non-linear difference systems involving the p-Laplacian are obtained by variational methods.     

三标度AHP法在核应急决策中的应用

核事故发生时,采取正确的应急决策可以减轻事故的后果和危害.考虑到核应急决策的多目标性和模糊性,并针对传统AHP法的不足,利用三标度AHP法建立了多层次应急决策评估模型.模型较大程度的减小了评价的主观性,具有操作性强、稳定性好的特点.将模型与模糊层次模型计算结果进行比较,二者对方案的优劣排序是一致的.但模型在对最优方案的取舍上分辨率较高,对核应急决策具有实际的指导意义.     

A novel multi‐detection technique for three‐dimensional reciprocal‐space mapping in grazing‐incidence X‐ray diffraction

A new scattering technique in grazing‐incidence X‐ray diffraction geometry is described which enables three‐dimensional mapping of reciprocal space by a single rocking scan of the sample. This is achieved by using a two‐dimensional detector. The new set‐up is discussed in terms of angular resolution and dynamic range of scattered intensity. As an example the diffuse scattering from a strained multilayer of self‐assembled (In,Ga)As quantum dots grown on GaAs substrate is presented.     

The interaction of three fields in ECE theory: The inverse Faraday effect

The simultaneous interaction of three fundamental fields is illustrated in Einstein Cartan Evans (ECE) theory with reference to the effect of gravitation on the inverse Faraday effect. The three-field interaction in this case is that of the fermionic, electromagnetic and gravitational fields. The interaction of the first two is developed in a well-defined semi-classical approximation of the ECE wave equation and the effect of gravitation incorporated through the index reduced canonical energy momentum density T. The exercise is repeated using the ECE wave equations and a general rule developed for the effect of gravitation on the fermionic, electromagnetic weak and strong fields.     

Remote preparation of an entangled two-qubit state with three parties

We present a scheme for probabilistic remote preparation of an entangled two-qubit state with three parties from a sender to either of two receivers. The quantum channel is composed of a partially entangled two-qubit state and a partially entangled three-qubit state. We calculate the successful total probabilities of the scheme in general and particular cases, respectively. We also calculate total classical communication cost in a general case and two particular cases, respectively.     

Extraordinary transport behavior of gases in isothermally annealed poly(4‐methyl‐1‐pentene) membranes

Poly(4‐methyl‐1‐pentene) (PMP) membranes were modified through isothermal annealing to investigate the change of their crystalline structure and rigid and mobile amorphous fractions (RAF and MAF), assuming a three‐phase model, affected the gas transport behavior. The crystalline structure was characterized by wide‐angle X‐ray diffraction (WAXD) and small‐angle X‐ray scattering (SAXS) techniques, and the free volume properties were analyzed by positron annihilation lifetime spectroscopy. Compared with the pristine membrane, the annealed membranes show higher crystallinity; the crystals undergo partial structural change from form III to form I. The lamellar crystal thickness, rigid amorphous fraction thickness, and long period in the lamellar stacks increase with crystallinity. The annealed PMP membranes exhibit higher permeability due to the increase in larger size free volumes in MAF and higher selectivity due to the increase in smaller size free volumes in RAF, respectively. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2368–2376     

Topological identification of the first uninodal 8‐connected lsz MOF built from 2,2′‐difluorobiphenyl‐4,4′‐dicarboxylate pillars and cadmium(II)–triazolate layers

Using polynuclear metal clusters as nodes, many high‐symmetry high‐connectivity nets, like 8‐connnected bcu and 12‐connected fcu , have been attained in metal–organic frameworks (MOFs). However, construction of low‐symmetry high‐connected MOFs with a novel topology still remains a big challenge. For example, a uninodal 8‐connected lsz network, observed in inorganic ZrSiO₄, has not been topologically identified in MOFs. Using 2,2′‐difluorobiphenyl‐4,4′‐dicarboxylic acid (H₂L) as a new linker and 1,2,4‐triazole (Htrz) as a coligand, a novel three‐dimensional Cd^II–MOF, namely poly[tetrakis(μ₄‐2,2′‐difluorobiphenyl‐4,4′‐dicarboxylato‐κ⁵O¹,O^1′:O^1′:O⁴:O^4′)tetrakis(N,N‐dimethylformamide‐κO)tetrakis(μ₃‐1,2,4‐triazolato‐κ³N¹:N²:N⁴)hexacadmium(II)], [Cd₆(C₁₄H₆F₂O₄)₄(C₂H₂N₃)₄(C₃H₇NO)₄]_n, (I), has been prepared. Single‐crystal structure analysis indicates that six different Cd^II ions co‐exist in (I) and each Cd^II ion displays a distorted [CdO₄N₂] octahedral geometry with four equatorial O atoms and two axial N atoms. Three Cd^II ions are connected by four carboxylate groups and four trz⁻ ligands to form a linear trinuclear [Cd₃(COO)₄(trz)₄] cluster, as do the other three Cd^II ions. Two Cd₃ clusters are linked by trz⁻ ligands in a μ_1,2,4‐bridging mode to produce a two‐dimensional Cd^II–triazolate layer with (6,3) topology in the ab plane. These two‐dimensional layers are further pillared by the L²⁻ ligands along the c axis to generate a complicated three‐dimensional framework. Topologically, regarding the Cd₃ cluster as an 8‐connected node, the whole architecture of (I) is a uninodal 8‐connected lsz framework with the Schläfli symbol (4²²·6⁶). Complex (I) was further characterized by elemental analysis, IR spectroscopy, powder X‐ray diffraction, thermogravimetric analysis and a photoluminescence study. MOF (I) has a high thermal and water stability.     

A thermally stable three‐dimensional cobalt(II) coordination polymer based on the V‐shaped ligand 4‐(4‐carboxyphenoxy)isophthalate

A new cobalt(II) coordination polymer (CP), poly[[bis[μ₆‐4‐(4‐carboxylatophenoxy)benzene‐1,3‐dicarboxylato‐κ⁶O¹:O¹:O³:O^3′:O⁴:O^4′]bis(1,10‐phenanthroline‐κ²N,N′)tricobalt(II)] 0.72‐hydrate], {[Co₃(C₁₅H₇O₇)₂(C₁₂H₈N₂)₂]·0.72H₂O}_n, (I), is constructed from Co^II ions and 4‐(4‐carboxyphenoxy)isophthalate (cpoia³⁻) and 1,10‐phenanthroline (phen) ligands. Based on centrosymmetric trinuclear [Co₃(phen)₂(COO)₆] secondary building units (SBUs), the structure of (I) is a three‐dimensional CP with a (3,6)‐connected net and point symbol (4².6)₂(4⁴.6².8⁷.10²). The positions of four [Co₃(phen)₂(COO)₆] SBUs and four cpoia³⁻ ligands reproduce a Chinese‐knot‐shaped arrangement along the ab plane. (I) has been characterized by single‐crystal X‐ray diffraction, IR spectroscopy, powder X‐ray diffraction (PXRD) and thermostability analysis. It shows a good thermal stability from room temperature to 673 K. In addition, the temperature dependence of the magnetic properties was measured.