Uniform Domain Research Articles

Boundary behavior of superharmonic functions satisfying nonlinear inequalities in uniform domains

In a uniform domain Ω, we investigate the boundary behavior of positive superharmonic functions u satisfying the nonlinear inequality ―Δu(x) 0, α ∈ ℝ and p > 0, where Δ is the Laplacian and δ Ω (x) is the distance from a point x to the boundary of Ω. In particular, we present a Fatou type theorem concerning the existence of nontangential limits and a Littlewood type theorem concerning the nonexistence of tangential limits.

Validity of recent approaches for statistical nanoindentation of cement pastes

Abstract In this paper we proceed in the examination of different aspects of the application of statistical nanoindentation to hydrated cement pastes for determining the mechanical properties of the single phases. In particular, we evaluate the size of the uniform domains of hydration products in a volume of cement paste obtained by Focussed-Ion Beam Nanotomography and we show that the uniform domains are too small to origin separate peaks in the frequency plots. Finally, we show that the procedure of fitting the frequency plots by Gaussian distributions of different sizes is not robust and heavily relies on assumptions about the elastic properties of the different phases.

Nematic–nematic phase separation from uniform nematic domain in polymer LC and low-molecular-weight LC mixture showing network lattice formation in pinning stage

According to the well-defined phase diagram of a mixture of low-molecular-weight liquid crystal (LC) material and LC polymer, we investigated the LC/LC phase separation dynamics from the uniformly aligned nematic phase that was prepared by sandwiching it between rubbed cells with a thickness of 3 μm. Polymer compositions in the mixtures and decomposition temperatures varied from 28.3% to 34.4% and 14 to 21 °C, respectively. The phase separation proceeded in three stages in the following order; the early spinodal decomposition (SD) stage, later SD stage and pinning stage. In the final pinning stage, an ordered honeycomb network structure was formed wherein the low-molecular-weight LC-rich phases were accommodated within hollow microcells of the polymer LC-rich phase. The size of the network lattice was varied from 2 to 8 μm by varying the weight fraction of the mixtures and the decomposition temperature. Pinning lattice formation was discussed with respect to an interplay between orientational elasticity and anchoring effect on segregated domain boundaries, thus providing insights into nanoscopic self-organization in LC/LC segregation systems.

Magnetic Properties of Ni-Zn Ferrite Prepared with the Layered Precursor Method

We prepare NiZnFe2O4 soft magnetic ferrites with different molar ratios with the layered precursor method and investigate their magnetic properties. In the layered precursor, metal ions are scattered on the layer plate in a certain way on account of the effect of lowest lattice energy and lattice orientation. After high temperature calcinations, spinel ferrites with uniform structural component and single magnetic domain can be obtained, and the magnetic property is improved greatly. NiZnFe2O4 ferrites prepared have the best specific saturation magnetization of 79.15 emu·g−1, higher than that of 68 emu·g−1 prepared by the chemical co-precipitation method and that of 59 emu·g−1 prepared by the emulsion-gel method. Meanwhile the coercivity of NiZnFe2O4 ferrites prepared by layered precursor method is 14 kA·m−1, lower than that of 50 emu·g−1 prepared by the co-precipitation method and that of 59 emu·g−1 prepared by the emulsion-gel method.

Properties of superharmonic functions satisfying nonlinear inequalities in nonsmooth domains

In a uniform domain Ω, we present a certain reverse mean value inequality and a Harnack type inequality for positive superharmonic functions satisfying a nonlinear inequality -Δu(x) ≤ cδΩ(x)-αu(x)p for x ∈ Ω, where c > 0, α ≥ 0 and p > 1 and δΩ(x) is the distance from a point x to the boundary of Ω. These are established by refining a boundary growth estimate obtained in our previous paper (2008). Also, we apply them to show the existence of nontangential limits of quotients of such functions and to give an extension of a certain minimum principle studied by Dahlberg (1976).

Ritz analysis of discontinuous beams using local trigonometric functions

The objective of the current paper is to present a Ritz-type analytical model for predicting the behavior of discontinuous beams such as thin-walled beams with cracks and multiply-stepped beams. The beam is discretized in the cracked as well as the un-cracked domains for a cracked thin-walled beam and in uniform beams for a multiple-stepped beam. A set of local trigonometric trial functions is used to define the twist angle for the cracked domain and the un-cracked domains, as well as to define the displacement field for uniform domains. A global equation system of unknown Ritz coefficients is derived by minimizing the Lagrangian functional or the total potential energy. In the present Ritz model, the interface continuity conditions between sub-domains are investigated and enforced into the global equation system using the condensation procedure or the Lagrange multipliers. Examples are presented to illustrate the effectiveness of the current model for free vibration and torsional analysis. Results obtained from the current model are found to agree well with those obtained using a detailed finite element method or with existing results in literature. The proposed model offers an efficient approach to reduce the modeling efforts and computational time required to analyze complex beams with cracks or multiple steps.

The Apollonian inner metric and uniform domains

In this paper we characterize uniform domains in terms of the Apollonian inner metric and the j-metric, thus providing solutions to two open problems given in [16]. We also discuss the relationships among uniform, A-uniform, Apollonian quasiconvex and quasi-isotropic domains (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Unions of John domains and uniform domains in real normed vector spaces

Let E be real normed vector spaces with the dimension at least 2. In this paper we study the following questions: When is the union of two John domains in E a John domain and when is the union of two uniform domains in E a uniform domain? 1. Introduction and main results Throughout the paper, we always assume that E denotes a real normed vector space with dimE ‚ 2 and that D is a proper subdomain in E. The norm of a vector z in E is written as jzj, and for any two points z1;z2 in E, the distance between them is denoted by jz1 i z2j, and the closed line segment with endpoints z1 and z2 by (z1;z2). For x 2 E and r > 0, we let B(x;r) denote the open ball in E with center x and radius r. For real numbers r and s, we use the notation: r ^ s = minfr;sg. John domains in Euclidean spaces R n were introduced by John (1) in connection with his work on elasticity. The term is due to Martio and Sarvas (3). Roughly speaking, a domain is a John domain if it is possible to travel from one point of the domain to another without going too close to the boundary. The precise definition is as follows. Definition 1.1. D is called a c-John domain if for every pair of points x1;x2 2 D there is a rectifiable arc ∞ joining them with '(∞(x1;x)) ^ '(∞(x2;x)) • c d(x) for all x 2 ∞, where c is a positive constant, ∞(xj;x) denotes the closed subarc of ∞ with endpoints xj and x (j = 1;2), '(∞(xj;x)) the arclength of ∞(xj;x). ∞ is called a c-John arc joining x1 and x2. See (4) for several characterizations of John domains. In the study of John do-

Some stability results under domain variation for Neumann problems in metric spaces

A famous result of Chenais (8) (1975) says that if ›n is a sequence of extension domains in R N that converges to › in the characteristic functions topology, then the weak solutions un for the problem (0.1) ( i¢un + un = f in ›n; @ un = 0 on @›n converge strongly to the solution u of the same problem in ›. It is also proved in (8) using the method of Calderon that an -cone condition is sucient to obtain uniform extension domains. In this paper we establish this result in a metric space framework, replacing the classical Sobolev space H 1 (›) by the Newtonian space N 1;2 (›). Moreover, using the latest results about extension domains contained in (2), and which rely on the techniques of Jones, we give weaker conditions on the domains for still getting stability of the Neumann problem. Finally we prove that the Neumann problem is stable for a sequence of quasiballs with uniform distortion constant that converge in a certain measure sense. The latter result gives a new existence theorem for some shape optimisation problems under quasiconformal variations.

Synthesis, Cocrystallization, and Microphase Separation of All-Conjugated Diblock Copoly(3-alkylthiophene)s

A series of all-conjugated diblock copoly(3-alkylthiophene)s with varying alkyl chain length, poly(3-butylthiophene)-b-poly(3-hexylthiophene) (P3BT-P3HT), poly(3-butylthiophene)-b-poly(3-dodecyl- thiophene) (P3BT-P3DDT), and poly(3-hexylthiophene)-b-poly(3-dodecylthiophene) (P3HT-P3DDT), were synthesized by modified Grignard metathesis polymerization. The obtained diblock copoly(3-alkyl- thiophene)s have well-controlled block ratios and molecular weights with narrow polydispersity indices. The diblock copoly(3-alkylthiophene)s comprised by the blocks with the alkyl side-chain length different by two carbon atoms (represented by P3BT-P3HT) have the ability of cocrystallizing into an uniform crystal domain, with the mutual interdigitation of the different side chains of the two blocks into a common interchain lamella. Other diblock copoly(3-alkylthiophene)s with the side chains different by more than two carbon atoms prefer to microphase separating into two crystal domains formed by the independent crystallization of each block. The AFM images revealed the characteristics of microphase-separated morphology in P3BT-P3DDT and P3HT-P3DDT diblock copoly(3-alkylthiophene)s.

New gTLDs – Pandora's Box is open

In a world with over 1.6 billion Internet users, the expansion of generic Top-Level Domains (gTLDs) continues to be a key issue for legal right holders and Internet users generally. Originally, expansion of gTLDs was largely motivated by the recognition that there is a conflict between domain names and trademark owners with similar marks, which belong to different geographical locations, or to different goods and/or services classification. This expansion has, in the past, been relativity ‘controllable’. However, in June 2008, the board of the Internet Cooperation for Assigned Names and Numbers (ICANN) approved the concept of introducing new gTLDs in unlimited numbers. This development is significant to legal right holders in many ways, and is expected to create further controversy in an unsettled area of law, that of property rights over domain names and their relationship with other legal rights. This paper reviews the manner in which ICANN is handling the expansion of gTLDs from a legal right holders' perspective. The paper will examine the application of the Uniform Domain Name Dispute Resolution Policy (UDRP), arguing that over the past 10 years the UDRP has exhibited significant inconsistencies in the making of decisions and that the issues of interpretation of the policy and the use of precedent can only be resolved by a unitary appeal procedure. ICANN's new proposal of introducing a Uniform Rapid Suspension System (URS) is still pending consideration and it is unknown at this juncture whether this will be used in conjunction with the UDRP or otherwise.

On potentials in generalized Hölder spaces over uniform domains in ℝ n

We show that Riesz-type potential operators of order α over uniform domains Ω in ℝn map the subspace \(H_{0}^{\lambda }(\Omega )\) of functions in Holder space Hλ(Ω) vanishing on ∂Ω, into the space Hλ+α(Ω), if λ+α≤1. This is proved in a more general setting of generalized Holder spaces with a given dominant of continuity modulus. Statements of such a kind are known for instance for the whole space ℝn or more generally for metric measure spaces with cancellation property. In the case of domains in ℝn when the cancellation property fails, our proofs are based on a special treatment of potential of a constant function.

A Unified Architecture for the Accurate and High-Throughput Implementation of Six Key Elementary Functions

This paper presents a unified architecture for the compact implementation of several key elementary functions, including reciprocal, square root, and logarithm, in single-precision floating-point arithmetic. The proposed high-throughput design is based on uniform domain segmentation and curve fitting techniques. Numerically accurate least-squares regression is utilized to calculate the polynomial coefficients. The architecture is optimized by analyzing the trade-off between the size of the required memory and the precision of intermediate variables to achieve the minimum 23-bit accuracy required for single-precision floating-point representation. The efficiency of the proposed unified data path is demonstrated on a common field-programmable gate array.

Polar switching in the smectic-AdPAphase composed of asymmetric bent-core molecules

We have studied mesogenic properties in the smectic- A(d)P(A) phase of an asymmetric bent-core liquid crystal by means of polarizing optical microscopy, second-harmonic generation (SHG), electro-optical (EO), and dielectric measurements. In homeotropically aligned cells, EO switching is clearly observed from a schlieren texture with both four- and two-brush defects to a uniform bright domain under the application of very low in-plane electric field below 1 V/microm. The phase is SHG active under an electric field, i.e., SHG gradually increases without a threshold and saturates with the increasing field. In homogeneous cells, by applying triangular wave field at saturated voltage, the splitting of the polarization switching current peak is observed, indicating that the mesophase is antiferroelectric. The dielectric studies indicate a Debye-type relaxation of the transverse dipoles associated with the rotation of the molecules about their long axis. The dc bias-dependent dielectric relaxation time and the dielectric strength suggest that a field-induced antiferroelectric-ferroelectric phase transition occurs continuously beyond 1.2 V/microm and is reversible. The field-dependent texture observation is consistent with the dielectric measurements. Two possible models are proposed to interpret the continuous phase transition.

Precautionary Governance and the Limits of Scientific Knowledge: A Democratic Framework for Regulating Nanotechnology

I. INTRODUCTION II. A PRINCIPLE IN SEARCH OF MEANING: THE NORMATIVE FLUIDITY OF THE PRECAUTIONARY PRINCIPLE A. Introduction: On the Pragmatic Nature of the Precautionary Principle B. The Normative Fluidity of the Precautionary Principle: A Close Look 1. The Hazard Condition 2. The Knowledge Condition 3. The Prescriptive Dimension III. FROM AMBIVALENCE TO POLITICS: THE PRECAUTIONARY PRINCIPLE AS A POLITICAL FRAMEWORK FOR REGULATING RISKS A. Why Politics: Legitimacy, Reflexivity and Creativity B. The Politics of Precaution: Generic Building Blocks 1. The Hazard Condition 2. The Knowledge Condition 3. The Prescriptive Dimension IV. RE-POLITICIZING THE GOVERNANCE OF RISK: FIVE CHALLENGES IN THE DEMOCRATIZATION OF RISK REGULATION IN THE CONTEXT OF NANOTECHNOLOGY A. Extending the Horizon of Civic Participation: From the Regulation of Risks to the Governance of Innovation and Scientific Policy B. Changing the Institutional Framework of Doing Nanoscience: Science Shops Mediating Agents C. E-deliberation 1. Multi-layered Participation--Confronting the Attraction Problem 2. Using Computer Supported Argumentation and Collaborative Decisionmaking Systems D. Risk Visualization E. De-Biasing the Decisionmaking Process V. BRINGING DEMOCRACY INTO THE PRECAUTIONARY PRINCIPLE: CONCLUDING REMARKS I. INTRODUCTION Nanotechnology presents regulators with a difficult challenge. Nanomaterials and nanoprocesses involve deep uncertainties regarding their potential benefits and health and environmental risks, reflecting the embryonic state of the underlying science. These uncertainties are exacerbated by the fact that nanotechnology is not a uniform domain, but encompasses a broad range of technologies and products, including bionanotechnology, supramolecular chemistry, nanostructured materials, and self-assembly nanoprocesses. (1) Given these uncertainties, there have been various calls to use the precautionary principle (PP) a governing principle in the regulation of nanotechnology. Thus, for example, the Intergovernmental Forum on Chemical Safety (IFCS) recommended in September 2008 that the precautionary principle be used as one of the general principles of risk management throughout the life cycle of manufactured (2) A recent joint statement by several environmental NGOs notes similarly that It]he Precautionary Principle must be applied to nanotechnologies because scientific research to-date suggests that exposure to at least some nanomaterials, nanodevices, or the products of nanobiotechnology is likely to result in serious harm to human health and the environment. (3) Drawing on the PP, many environmental groups have called for a moratorium on the sale (and even research) of products containing nanomaterials, arguing that the research to date is insufficient to guarantee the safety of nanoproducts, and that whatever safety research has been conducted has not been properly disseminated to the public. (4) The need to apply a precautionary strategy in the regulation of nanotechnology has also been recognized by legal scholars, (5) advisory bodies (6) and 'regulators. (7) These calls rest on several assumptions: * There is plausible support for the claim that nanotechnology is possibly risky, and is risky in novel and non-uniform ways. (8) * There is an expanding gap between the pace at which new products containing nanomaterials are being developed and the generation of relevant environmental, health and safety data. This gap also reflects the fact that current methods of risk assessment are not necessarily appropriate for the evaluation of nanomaterials. …

Optimal and robust design of brain-state-in-a-box neural associative memories

This paper presents a new optimization approach to the design of associative memories via the brain-state-in-a-box (BSB) neural network. The optimization approach proposed in this paper provides the large and uniform domains of attraction of the prototype patterns, the large robustness margin for the weight matrix of the perturbed BSB neural network, the asymptotic stability of the prototype patterns, and the global stability of the BSB neural network. Based on some known qualitative properties of the BSB neural network and theoretical results presented in this paper, a synthesis method of the BSB-based associative memory is established. The synthesis method presented in this paper is given in the form of a linear matrix inequality-based optimization problem, which can be efficiently solved by a readily available software. Design examples are given to demonstrate the applicability of the proposed method and to compare with the existing synthesis methods.

A Unified Approach to Reflexivization in Semitic and Romance

AbstractThe paper proposes a unified analysis of reflexivization, applicable equally to Semitic languages and to Romance languages. We contrast our account with previous ones that have distinguished between reflexivization of the sort found in Semitic, which is clause-bound, can be the input to nominalization, and is sensitive to the semantics of the verb, and reflexivization of the sort found in Romance which applies across clauses, is not the input to nominalization and is insensitive to the semantics of the verb. These analyses take reflexivization of the Semitic type to be a "lexical" operation, and Romance reflexivization to be a "syntactic" operation, though in both cases, reflexivization is characterized as an operation applying to the thematic roles of the verb. Consonant with the view that all valence changing operations apply to a uniform domain, we argue that reflexivization in Semitic and in Romance can be given a uniform analysis as an operation of exactly the same type in exactly the same local domain. The "syntactic" residue found in Romance can be shown not to be reflexivization at all, but to be better analyzed as anaphoric binding. The confusion is due to the syncretism between reflexive morphology and reflexive anaphors, in turn the result of a language change whereby pronouns morphologize. We address the issues which have precluded Romance reflexive clitics from being analyzed as anaphors.

On unique extension of time changed reflecting Brownian motions

Let $D$ be an unbounded domain in $\RR^d$ with $d\geq 3$. We show that if $D$ contains an unbounded uniform domain, then the symmetric reflecting Brownian motion (RBM) on $\overline D$ is transient. Next assume that RBM $X$ on $\overline D$ is transient and let $Y$ be its time change by Revuz measure ${\bf 1}_D(x) m(x)dx$ for a strictly positive continuous integrable function $m$ on $\overline D$. We further show that if there is some $r>0$ so that $D\setminus \overline {B(0, r)}$ is an unbounded uniform domain, then $Y$ admits one and only one symmetric diffusion that genuinely extends it and admits no killings. In other words, in this case $X$ (or equivalently, $Y$) has a unique Martin boundary point at infinity.

Magnesium-induced lipid bilayer microdomain reorganizations: implications for membrane fusion.

Interactions between dipalmitoylphosphatidylcholine (DPPC) and dipalmitoylphosphatidylserine (DPPS), combined both as binary lipid bilayer assemblies and separately, under the influence of divalent Mg2+, a membrane bilayer fusogenic agent, are reported. Infrared vibrational spectroscopic analyses of the lipid acyl chain methylene symmetric stretching modes indicate that aggregates of the two phospholipid components exist as domains heterogeneously distributed throughout the binary bilayer system. In the presence of Mg2+, DPPS maintains an ordered orthorhombic subcell gel phase structure through the phase transition temperature, while the DPPC component is only minimally perturbed with respect to the gel to liquid crystalline phase change. The addition of Mg2+ induces a reorganization of the lipid domains in which the gel phase acyl chain planes rearrange from a hexagonal configuration toward a triclinic, parallel chain subcell. Examination of the acyl chain methylene deformation modes at low temperatures allows a determination of DPPS microdomain sizes, which decrease upon the addition of DPPC-d62 in the absence of Mg2+. On adding Mg2+, a uniform DPPS domain size is observed in the binary mixtures. In either the presence or absence of Mg2+, DPPC-d62 aggregates remain in a configuration for which microdomain sizes are not spectroscopically measurable. Analysis of the acyl chain methylene deformation modes for DPPC-d62 in the binary system suggests that clusters of the deuterated lipids are distributed throughout the DPPS matrix. Light scattering and fluorescence measurements indicate that Mg2+ induces both the aggregation and the fusion of the lipid assemblies as a function of the ratio of DPPS to DPPC. The structural reorganizations of the lipid microdomains within the DPPS-DPPC bilayer are interpreted in the context of current concepts regarding lipid bilayer fusion.

Anomalous uniform domain in a twisted nematic cell constructed from micropatterned surfaces

We have discovered an optically uniform type of domain that occurs in twisted nematic (TN) cells that are constructed from substrates chemically patterned with stripes via microcontact printing of self-assembled monolayers; such domains do not occur in TN cells constructed from uniform substrates. In such a cell, the azimuthal anchoring at the substrates is due to the elastic anisotropy of the liquid crystal rather than the conventional rubbing mechanism. A model is presented that predicts the relative stability of the twisted and anomalous states as a function of the material and design parameters.