Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.     

Channel-Supermodular Entropies: Order Theory and an Application to Query Anonymization

This work introduces channel-supermodular entropies, a subset of quasi-concave entropies. Channel-supermodularity is a property shared by some of the most commonly used entropies in the literature, including Arimoto–Rényi conditional entropies (which include Shannon and min-entropy as special cases), k-tries entropies, and guessing entropy. Based on channel-supermodularity, new preorders for channels that strictly include degradedness and inclusion (or Shannon ordering) are defined, and these preorders are shown to provide a sufficient condition for the more-capable and capacity ordering, not only for Shannon entropy but also regarding analogous concepts for other entropy measures. The theory developed is then applied in the context of query anonymization. We introduce a greedy algorithm based on channel-supermodularity for query anonymization and prove its optimality, in terms of information leakage, for all symmetric channel-supermodular entropies.     

一类混合单调算子的不动点定理

运用锥理论与迭代方法,讨论了在较弱条件下一类混合单调算子的不动点的存在唯一性,所得结果是某些已有结果的本质改进和推广.     

拟树图按第二大无符号拉普拉斯特征值排序

A connected graph G=(V,E) is called a quasi-tree graph if there exists a vertex v_0∈V(G) such that G-v_0 is a tree.In this paper,we determine all quasi-tree graphs of order n with the second largest signless Laplacian eigenvalue greater than or equal to n-3.As an application,we determine all quasi-tree graphs of order n with the sum of the two largest signless Laplacian eigenvalues greater than to 2 n-5/4.     

Antiferromagnetic Ordering in TmCu2

Intermetallic compound TmCu₂ crystalizes in the orthorhombic structure, orders antiferromagnetically (AF) and exhibits four different AF phases below T _N = 6.5 K. In all these phases the Tm magnetic moment is parallel to the b-axis. The ground-state AF1 (T < 3.4 K) corresponds to the squared-up AF structure with propagation vector ₀₁ = (5/8, 0, 0) and magnetic unit cell 8a × b × c. Narrow phases AF2 and AF3 (3.3 K < T < 3.7 K and 3.6 K < T < 4.6 K) are 'spin-slip'-derivatives from the AF1 structure, yielding propagation vectors ₀₂ = (0.633, 0, 0.02) and ₀₃ = (0.618, 0, 0), respectively. The phase AF4 (4.4 K < T < T _N) is then incommensurate transversal spin-wave with the propagation ₀₄ = (0.64, 0, 0). The co-existence of AF phases indicates the first-order transitions between them.     

Tetrachloroferrate (III) Salts of BDH-TTP [2,5-Bis(1,3-dithiolan-2-ylidene)-1,3,4,6-tetrathiapentalene] and BDA-TTP [2,5-Bis(1,3-dithian-2-ylidene)-1,3,4,6-tetrathiapentalene]: Crystal Structures and Physical Properties

Three FeCl₄ salts based on non-tetrathiafulvalene (TTF) donors, 2,5-bis(1,3-dithiolan-2-ylidene)-1,3,4,6-tetrathiapentalene (BDH-TTP) and 2,5-bis(1,3-dithian-2-ylidene)-1,3,4,6-tetrathiapentalene (BDA-TTP), have been prepared and characterized as κ-(BDH-TTP)₂FeCl₄, β-(BDA-TTP)₂FeCl₄, and (BDA-TTP)₃FeCl₄ · PhCl. The κ-(BDH-TTP)₂FeCl₄ salt, with a room-temperature conductivity (σ_rt) of 39 S cm⁻¹, is metallic down to 1.5 K, and its magnetic susceptibility obeys the Curie-Weiss law with a Curie constant (C) of 4.25 emu K mol⁻¹ and a Weiss constant (θ) of 0.041 K. β-(BDA-TTP)₂FeCl₄ exhibits metallic behavior (σ_rt=9.4 S cm⁻¹) with a sharp metal-to-insulator (MI) transition (T_MI=113 K) and antiferromagnetic ordering with the Néel temperature of near 8.5 K, whereas the solvated (BDA-TTP)₃FeCl₄ · PhCl salt is a semiconductor with a thermal activation energy of 0.11 eV (σ_rt=2.0× 10⁻² S cm⁻¹) and exhibits Curie-Weiss behavior (C=4.42 emu K mol⁻¹, θ=−0.35 K).     

Partial Results in Δ 3 0 -Categoricity in Linear Orderings and Boolean Algebras

The notion of ₃ ⁰ -categoricity in linear orderings and Boolean algebras is examined. We provide a proof for the fact that there are uncountably many relatively ₃ ⁰ -categorical linear orderings, and furnish a proof of another fact which suggests that the (unrelatively) ₃ ⁰ -categorical linear orderings may be very difficult to classify. In stark contrast to these results for linear orderings, a complete classification of the relatively ₃ ⁰ -categorical Boolean algebras is given.     

Influence of surface ordering on the wetting of structured liquids

The substrate is shown to induce substantial ordering in diblock copolymer thin films above the bulk order-disorder transition (ODT) where, thermodynamically, a phase mixed state is favored. Initially, uniform films reorganize to form a hierarchy of transient surface patterns and stable film thicknesses that depend on the initial film thickness and on the substrate. Self-consistent field calculations of the free energy of the system for different situations, depending on the relative tendency for the different block components to be attracted to the substrate and/or free surface, provide an explanation of the formation of the stable film thicknesses. A continuum picture proposed earlier by Brochard et al.rovides an explanation of the wetting characteristics of this system. In some cases the ordering destabilizes the film so that dewetting occurs (wetting autophobicity), whereas in other cases the surface ordering results in a kinetic stabilization of a film that would otherwise dewet. Received 3 August 2001 and Received in final form 1 November 2001     

Nanoparticle ordering by dewetting of Co on SiO2

Most metals on SiO₂ have a finite contact angle and are therefore subject to dewetting during thermal processing. The resulting dewetting morphology is determined primarily by nucleation and growth or instabilities. The dewetting mechanism implies a disordered spatial arrangement for homogeneous nucleation, but an ordered one for instabilities such as spinodal decomposition. Here, we show that the morphology of laser-melted ultrathin Co film (4-nm thick) can be attributed to dewetting via an instability. Dewetting leads to breakup of the continuous Co film into nanoparticles with a monomodal size distribution with an average particle diameter of 75 nm±23 nm. These nanoparticles have short-range order (SRO) of 130 nm in their separation. This result has important implications for nanomanufacturing with a robust spacing or size selection of nanoparticles in addition to spatial ordering.     

The effect of low intra-sublattice repulsion on phase diagram of YBa2Cu3O6+x : A Monte Carlo simulation study

We report the results of Monte Carlo simulation of the phase diagram and oxygen ordering in YBa₂Cu₃O_6+x for low intra-sublattice repulsion. At low temperatures, apart from tetragonal (T), orthorhombic (OI) and ‘double cell’ ortho II phases, there is evidence for two additional orthorhombic phases labelled here asOI andOIII. At high temperatures, there was no evidence for the decomposition of theOI phase into theT andOI phases. We find qualitative agreement with experimental observations and cluster-variation method results.