A generalized Hausdorff dimension for functions and sets

Let E be a compact subset of the n-dimensional unit cube, 1_n, and let C be a collection of convex bodies, all of positive n-dimensional Lebesgue measure, such that C contains bodies with arbitrarily small measure. The dimension of E with respect to the covering class C is defined to be the number

d_C(E) = sup(β:H_{β, C}(E) > 0),

where H_{β, C} is the outer measure

inf(Ʃm(C_i)^β:UC_i Ↄ E, C_i ϵ C) .

Only the one and two-dimensional cases are studied. Moreover, the covering classes considered are those consisting of intervals and rectangles, parallel to the coordinate axes, and those closed under translations. A covering class is identified with a set of points in the left-open portion, 1’_n, of 1_n, whose closure intersects 1_n - 1’_n. For n = 2, the outer measure H_{β, C} is adopted in place of the usual:

Inf(Ʃ(diam. (C_i))^β: UC_i Ↄ E, C_i ϵ C),

for the purpose of studying the influence of the shape of the covering sets on the dimension d_C(E).

If E is a closed set in 1₁, let M(E) be the class of all non-decreasing functions μ(x), supported on E with μ(x) = 0, x ≤ 0 and μ(x) = 1, x ≥ 1. Define for each μ ϵ M(E),

d_C(μ) = lim/c → inf/0 log ∆μ(c)/log c , (c ϵ C)

where ∆μ(c) = v/x (μ(x+c) – μ(x)). It is shown that

d_C(E) = sup (d_C(μ):μ ϵ M(E)).

This notion of dimension is extended to a certain class Ӻ of sub-additive functions, and the problem of studying the behavior of d_C(E) as a function of the covering class C is reduced to the study of d_C(f) where f ϵ Ӻ. Specifically, the set of points in 1₁,

(*) {d_B(F), d_C(f)): f ϵ Ӻ}

is characterized by a comparison of the relative positions of the points of B and C. A region of the form (*) is always closed and doubly-starred with respect to the points (0, 0) and (1, 1). Conversely, given any closed region in 1₂, doubly-starred with respect to (0, 0) and (1, 1), there are covering classes B and C such that (*) is exactly that region. All of the results are shown to apply to the dimension of closed sets E. Similar results can be obtained when a finite number of covering classes are considered.

In two dimensions, the notion of dimension is extended to the class M, of functions f(x, y), non-decreasing in x and y, supported on 1₂ with f(x, y) = 0 for x · y = 0 and f(1, 1) = 1, by the formula

d_C(f) = lim/s · t → inf/0 log ∆f(s, t)/log s · t , (s, t) ϵ C

where

∆f(s, t) = V/x, y (f(x+s, y+t) – f(x+s, y) – f(x, y+t) + f(x, t)).

A characterization of the equivalence d_C1(f) = d_C2(f) for all f ϵ M, is given by comparison of the gaps in the sets of products s · t and quotients s/t, (s, t) ϵ C_i (I = 1, 2).

Feedback communication using orthogonal signals

This research is concerned with block coding for a feedback communication system in which the forward and feedback channels are independently disturbed by additive white Gaussian noise and average power constrained. Two coding schemes are proposed in which the messages to be coded for transmission over the forward channel are realized as a set of orthogonal waveforms. A finite number of forward and feedback transmissions (iterations) per message is made. Information received over the feedback channel is used to modify the waveform transmitted on successive forward iterations in such a way that the expected value of forward signal energy is zero on all iterations after the first. Similarly, information is sent over the feedback channel in such a way that the expected value of feedback signal energy is also zero on all iterations after the first. These schemes are shown to achieve a lower probability of error than the best one-way coding scheme at all rates up to the forward channel capacity, provided only that the feedback channel capacity be greater than the forward channel capacity. These schemes make more efficient use of the available feedback power than existing feedback coding schemes, and therefore require less feedback power to achieve a given error performance.

The global optimization of phase-incoherent signals

The problem of global optimization of M phase-incoherent signals in N complex dimensions is formulated. Then, by using the geometric approach of Landau and Slepian, conditions for optimality are established for N = 2 and the optimal signal sets are determined for M = 2, 3, 4, 6, and 12.

The method is the following: The signals are assumed to be equally probable and to have equal energy, and thus are represented by points ṡ_i, i = 1, 2, …, M, on the unit sphere S₁ in C^N. If W_ik is the halfspace determined by ṡ_i and ṡ_k and containing ṡ_i, i.e. W_ik = {ṙϵC^N:| ≥ | ˂ṙ, ṡ_k˃|}, then the Ʀ_i = ∩/k≠i W_ik, i = 1, 2, …, M, the maximum likelihood decision regions, partition S₁. For additive complex Gaussian noise ṅ and a received signal ṙ = ṡ_ie^jϴ + ṅ, where ϴ is uniformly distributed over [0, 2π], the probability of correct decoding is P_C = 1/π^N ∞/ʃ/0 r^2N-1e^-(r2+1)U(r)dr, where U(r) = 1/M M/Ʃ/i=1 Ʀ_i ʃ/∩ S₁ I₀(2r | ˂ṡ, ṡ_i˃|)dσ(ṡ), and r = ǁṙǁ.

For N = 2, it is proved that U(r) ≤ ʃ/C_α I₀(2r|˂ṡ, ṡ_i˃|)dσ(ṡ) – 2K/M. h(1/2K [Mσ(C_α)-σ(S₁)]), where C_α = {ṡϵS₁:|˂ṡ, ṡ_i˃| ≥ α}, K is the total number of boundaries of the net on S₁ determined by the decision regions, and h is the strictly increasing strictly convex function of σ(C_α∩W), (where W is a halfspace not containing ṡ_i), given by h = ʃ/C_α∩W I₀ (2r|˂ṡ, ṡ_i˃|)dσ(ṡ). Conditions for equality are established and these give rise to the globally optimal signal sets for M = 2, 3, 4, 6, and 12.

Surface water temperature of Windermere. Monthly and yearly totals of degree-days centigrade and monthly mean temperatures, 1933 to 1975

The surface temperature of Windermere has been recorded by the staff of the Freshwater Biological Association on every weekday (with a few minor exceptions) since 11 January 1933. This publication presents this information in a form which can easily be used by individual research workers. There are 43 tables (1 for each year, 1933-1975) which give the data, expressed as degree-days centigrade. The tables show for each month the number of degree-days above each temperature from 0 degree C to the highest recorded, at 1 degree C intervals. Mean temperatures are obtained by dividing the number of degree-days over 0 degree C by the relevant number of days. The advantage of degree-days rather than mean temperatures is that degree-days are additive so data for any desired periods may be combined quickly and simply. Seasonal results for spring, summer, autumn and winter are presented in tabular form, as are selected totals for comparisons between years. Further tables give the mean temperature in each month of the year, and the frequency distributions of monthly mean temperatures.

Friction and heat transfer coefficients in smooth and rough pipes with dilute polymer solutions

Measurements of friction and heat transfer coefficients were obtained with dilute polymer solutions flowing through electrically heated smooth and rough tubes. The polymer used was "Polyox WSR-301", and tests were performed at concentrations of 10 and 50 parts per million. The rough tubes contained a close-packed, granular type of surface with roughness-height-to-diameter ratios of 0.0138 and 0.0488 respectively. A Prandtl number range of 4.38 to 10.3 was investigated which was obtained by adjusting the bulk temperature of the solution. The Reynolds numbers in the experiments were varied from =10,000 (Pr= 10.3) to 250,000 (Pr= 4.38).

Friction reductions as high as 73% in smooth tubes and 83% in rough tubes were observed, accompanied by an even more drastic heat transfer reduction (as high as 84% in smooth tubes and 93% in rough tubes). The heat transfer coefficients with Polyox can be lower for a rough tube than for a smooth one.

The similarity rules previously developed for heat transfer with a Newtonian fluid were extended to dilute polymer solution pipe flows. A velocity profile similar to the one proposed by Deissler was taken as a model to interpret the friction and heat transfer data in smooth tubes. It was found that the observed results could be explained by assuming that the turbulent diffusivities are reduced in smooth tubes in the vicinity of the wall, which brings about a thickening of the viscous layer. A possible mechanism describing the effect of the polymer additive on rough pipe flow is also discussed.

磷酸盐激光玻璃的化学机械抛光

从磷酸盐激光玻璃的成分和结构出发,分析了其化学机械抛光(CMP)机制。通过实验验证了磷酸盐激光玻璃对抛光液pH值具有较强的选择性,在微酸性和中性条件下磷酸盐激光玻璃具有较高的抛光效率,在抛光液中添加pH值调节添加剂会保持抛光环境的酸碱性从而影响抛光效率和抛光质量。通过对pH值和抛光剂浓度的控制获得了均方根(RMS)优于0.6 nm的磷酸盐激光玻璃的超光滑表面。

Community Turnover of Wood-Inhabiting Fungi across Hierarchical Spatial Scales

For efficient use of conservation resources it is important to determine how species diversity changes across spatial scales. In many poorly known species groups little is known about at which spatial scales the conservation efforts should be focused. Here we examined how the community turnover of wood-inhabiting fungi is realised at three hierarchical levels, and how much of community variation is explained by variation in resource composition and spatial proximity. The hierarchical study design consisted of management type (fixed factor), forest site (random factor, nested within management type) and study plots (randomly placed plots within each study site). To examine how species richness varied across the three hierarchical scales, randomized species accumulation curves and additive partitioning of species richness were applied. To analyse variation in wood-inhabiting species and dead wood composition at each scale, linear and Permanova modelling approaches were used. Wood-inhabiting fungal communities were dominated by rare and infrequent species. The similarity of fungal communities was higher within sites and within management categories than among sites or between the two management categories, and it decreased with increasing distance among the sampling plots and with decreasing similarity of dead wood resources. However, only a small part of community variation could be explained by these factors. The species present in managed forests were in a large extent a subset of those species present in natural forests. Our results suggest that in particular the protection of rare species requires a large total area. As managed forests have only little additional value complementing the diversity of natural forests, the conservation of natural forests is the key to ecologically effective conservation. As the dissimilarity of fungal communities increases with distance, the conserved natural forest sites should be broadly distributed in space, yet the individual conserved areas should be large enough to ensure local persistence.

Reciclado de polvo inconel 718 y evolución de las propiedades de los componentes fabricados con los mismos.

[ES]El objetivo de este trabajo ha sido la determinación de un proceso para la reutilización del polvo metálico desperdiciado durante el proceso de aporte por láser. El polvo necesita ser inyectado para ser fundido directamente sobre el aporte pero un alto porcentaje de las partículas golpean el área no fundida y directamente rebotan fuera de la zona de aporte. La eficiencia de las partículas depositadas puede bajar hasta el 40 % dependiendo de la configuración y del tamaño del punto de aporte. El material utilizado ha sido la superaleación de níquel Inconel 718 debido a su potencial aplicación en procesos de fabricación aditiva. Después del primer uso, el polvo es recolectado y tamizado. La fracción indeseada es magnéticamente segregada y la parte limpia es nuevamente tamizada para obtener datos y de nuevo mezclada para estar lista para la reutilización. No ha sido añadido polvo nuevo a la fracción recuperada y este procedimiento ha sido repetido 5 veces. Los test experimentales muestran que el material depositado presenta resultados similares a aquellos obtenidos con polvo nuevo. La implementación de este proceso permite la mejora de la eficiencia final reduciendo tanto costes como residuos materiales.

Preparation of Y1.84La0.16O3 nanopowders by oxalate co-precipitation method

Nanopowder of Y(1.84)mLa(0.16)O(3) was prepared by oxalate co-precipitation method. The powder was characterized by TG-DTA, XRD and TEM. The results show that the precursor is Re-2 (NO3)(2) (C2O4)(2)center dot 2H(2)O (Re=Y, La), and the Y1.84La0.16O3 nanopowders produced by calcining the precursor at 1000 degrees C for 4 h are 20 similar to 40 nm spherical particles and well dispersed. The powders were with high sintering activity and could be fabricated to transparent ceramic without additive at 1450 similar to 1550 degrees C in H-2 atmosphere for 3 hours. The total transmission of the transparent ceramic could reach 80%.

Nd3+掺杂的氧化镧钇透明激光陶瓷的光谱性能研究

Nd3+-doped Y2-2x La-2x O-3 (x = 0.08) transparent ceramics were fabricated by conventional fabrication process. Spectroscopic properties of the samples were investigated. The absorption band of Nd3+ : Y1.84La0.16O3 was broad covering the wavelength range 780-850 nm. When doped with 1.5at% Nd3+, the cross sections of the sample at 820 nm and laser diode pumped 808 nm were 1.81 x 10(-20) cm(2) and 1.54 x 10(-20) cm(2), respectively. The strongest emission peak of the sample was centered at 1078 mn with long fluorescent lifetime, broad emission bandwidth and high quantum efficiency. Because of the additive La2O3, the spectroscopic quality parameter (X-Nd) of matrix was' decreased from 1.6 to 0.46, thus the fluorescence branch ratio of F-4(3/2) - (4) I-11/2 transition was increased to 56.82%. These properties of Nd3' : Y1.84La0.16O3 transparent ceramic are benefitial to achieve high efficient laser output and ultrashort modelocked pulse.

Investigation of the spectroscopic properties of (Y0.92-xLa0.08Ndx)(2)O-3 transparent ceramics

The spectroscopic properties of (Y0.92-xLa0.08Ndx)(2)O-3 transparent ceramics were investigated. According to three intensity parameters (Omega(2),Omega(4),Omega(6)) fitted by the Judd-Ofelt theory, the spectroscopic quality parameter (X-Nd), branching ratio (beta(J,J')), and quantum efficiency (eta) of Nd3+ were determined. It was found that X-Nd of the host, owing to the additive La2O3, was decreased from 1.6 to 0.46; thus beta(J,11/2) was increased from 46% to 56.82%. A figure of merit of the specimens was discussed and compared with Nd:YAG transparent ceramic. (c) 2007 Optical Society of America.

Er^3＋／Yb^3＋共掺的氧化镧钇透明陶瓷的光谱性能研究

采用传统无压烧结工艺制备了Er^3＋／Yb^3＋共掺的氧化镧钇透明陶瓷并对其光谱性能进行了研究．样品具有较大的吸收和发射截面．La2O3的添加使样品的荧光寿命（τs）与玻璃接近，当Yb^3＋和Er^3＋的掺杂量分别为5at％和0．5at％时，测得τs=9．65ms．这种荧光寿命长、发射截面大和线宽窄的特性有利于微型、可集成化和大功率激光输出的实现．

光学表面的标量散射理论

简要论述了标量散射理论的研究进展做,着重介绍了Beckman的一维标量散射理论和几种典型的多层膜散射模型-非相关表面粗糙度模型、附加表面粗糙度模型和非相关体内不均匀模型,比较了这些模型在中心波长为632.8nm的11层高反膜的散射特性.结果表明,非相关体内的不均匀性引起反射能带边缘散射,反射能带内的散射主要由附加表面粗糙度引起.理想粗糙度对膜系反射带内的散射影响很小,对反射带边缘几乎无影响.预测了标量散射理论的应用领域及前景.

Effects of process on microstructure and properties of translucent Dy-alpha-SiAlON sintered at lower temperatures

Hot pressing (HP) at higher sintering temperature has been a traditional and prevalent technique for the fabrication of alpha-SiAlON. In order to prepare translucent SiAlON more easily, LiF was used as a non-oxide sintering additive to lower the sintering temperature to <= 1650 degrees C. As a result, all of the samples possessed a good hardness and fracture toughness. At the same time, the lower temperature sintered samples showed a higher optical transmittance in the range of 2.5-5.5 mu m wavelength (0.5 mm in thickness). The maximum infrared transmission reached 68% at a wavelength of 3.3 mu m. The present work shows that the sintering process has a strong effect on microstructure and property of alpha-SiAlON. To be exact, a lower sintering temperature and longer holding time can produce some fully-developed microstrcture, which is beneficial for the optical transmittance. (C) 2008 The Ceramic Society of Japan. All rights reserved.

Proposal and validation of methodologies for the categorisation of continuous variables in the development of prediction models

158 p.