Axiomatic Digital Topology

The paper presents a new set of axioms of digital topology, which are easily understandable for application developers. They define a class of locally finite (LF) topological spaces. An important property of LF spaces satisfying the axioms is that the neighborhood relation is antisymmetric and transitive. Therefore any connected and non-trivial LF space is isomorphic to an abstract cell complex. The paper demonstrates that in an n-dimensional digital space only those of the (a, b)-adjacencies commonly used in computer imagery have analogs among the LF spaces, in which a and b are different and one of the adjacencies is the "maximal" one, corresponding to 3n\"i1 neighbors. Even these (a, b)-adjacencies have important limitations and drawbacks. The most important one is that they are applicable only to binary images. The way of easily using LF spaces in computer imagery on standard orthogonal grids containing only pixels or voxels and no cells of lower dimensions is suggested

Risk Rationing in China Rural Credit Markets

The purpose of this paper is to provide a specific test of Boucher, Carter et al. (2008) framework on risk rationing. The data were collected through a survey of 730 farm households in Shaanxi province conducted in November 2010. We compare factor associated with risk rationed, quantity rationed and price rationed farmers. Seemingly unrelated regressions are performed using risk rationing, quantity rationing and price rationing measure as the dependent variable and measures of demography, wealth, income, year of farming and risk aversion as independent variables. We apply seemingly unrelated regression, cluster analysis and cross tabulation in the study. According to a seemingly unrelated regression, we find existing risk rationing is due to risk-based behavior by borrowers. A cross tabulation results support the proposition by Boucher, Carter et al showing the financial wealthy is risk rationed and relatively land-poor is risk rationed. This paper is believed to be among the first empirical validation of the risk rationing theory.Risk rationing, credit market, china, Marketing, Risk and Uncertainty,

Understanding Hot-Electron Generation and Plasmon Relaxation in Metal Nanocrystals: Quantum and Classical Mechanisms

Generation of energetic (hot) electrons is an intrinsic property of any plasmonic nanostructure under illumination. Simultaneously, a striking advantage of metal nanocrystals over semiconductors lies in their very large absorption cross sections. Therefore, metal nanostructures with strong and tailored plasmonic resonances are very attractive for photocatalytic applications. However, the central questions regarding plasmonic hot electrons are how to quantify and extract the optically-excited energetic electrons in a nanocrystal. We develop a theory describing the generation rates and the energy-distributions of hot electrons in nanocrystals with various geometries. In our theory, hot electrons are generated owing to surfaces and hot spots. The formalism predicts that large optically-excited nanocrystals show the excitation of mostly low-energy Drude electrons, whereas plasmons in small nanocrystals involve mostly hot electrons. The energy distributions of electrons in an optically-excited nanocrystal show how the quantum many-body state in small particles evolves towards the classical state described by the Drude model when increasing nanocrystal size. We show that the rate of surface decay of plasmons in nanocrystals is directly related to the rate of generation of hot electrons. Based on a detailed many-body theory involving kinetic coefficients, we formulate a simple scheme describing the plasmon's dephasing. In most nanocrystals, the main decay mechanism of a plasmon is the Drude friction-like process and the secondary path comes from generation of hot electrons due to surfaces and electromagnetic hot spots. This latter path strongly depends on the size, shape and material of the nanocrystal, correspondingly affecting its efficiency of hot-electron production. The results in the paper can be used to guide the design of plasmonic nanomaterials for photochemistry and photodetectors.Comment: 90 pages, 21 figures, including Supplementary Informatio

Negative reflections of electromagnetic waves in chiral media

We investigate the reflection properties of electromagnetic/optical waves in isotropic chiral media. When the chiral parameter is strong enough, we show that an unusual \emph{negative reflection} occurs at the interface of the chiral medium and a perfectly conducting plane, where the incident wave and one of reflected eigenwaves lie in the same side of the boundary normal. Using such a property, we further demonstrate that such a conducting plane can be used for focusing in the strong chiral medium. The related equations under paraxial optics approximation are deduced. In a special case of chiral medium, the chiral nihility, one of the bi-reflections disappears and only single reflected eigenwave exists, which goes exactly opposite to the incident wave. Hence the incident and reflected electric fields will cancel each other to yield a zero total electric field. In another word, any electromagnetic waves entering the chiral nihility with perfectly conducting plane will disappear.Comment: 5 pages, 5 figure

Stabilization of the Electroweak Scale in 3-3-1 Models

One way of avoiding the destabilization of the electroweak scale through a strong coupled regime naturally occurs in models with a Landau-like pole at the TeV scale. Hence, the quadratic divergence contributions to the scalar masses are not considered as a problem anymore since a new nonperturbative dynamic emerges at the TeV scale. This scale should be an intrinsic feature of the models and there is no need to invoke any other sort of protection for the electroweak scale. In some models based on the $SU(3)_C\otimes SU(3)_W\otimes U(1)_{X}$ gauge symmetry, a nonperturbative dynamics arise and it stabilizes the electroweak scale.Comment: 10 pages. Version with some improvements and corrections in the tex

Dimension on Discrete Spaces

In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by means of axioms, and the axioms are based on an obvious geometrical background. This work presents some discrete models of n-dimensional Euclidean spaces, n-dimensional spheres, a torus and a projective plane. It explains how to construct new discrete spaces and describes in this connection several three-dimensional closed surfaces with some topological singularities It also analyzes the topology of (3+1)-spacetime. We are also discussing the question by R. Sorkin [19] about how to derive the system of simplicial complexes from a system of open covering of a topological space S.Comment: 16 pages, 8 figures, Latex. Figures are not included, available from the author upon request. Preprint SU-GP-93/1-1. To appear in "International Journal of Theoretical Physics

Experience versus Talent Shapes the Structure of the Web

We use sequential large-scale crawl data to empirically investigate and validate the dynamics that underlie the evolution of the structure of the web. We find that the overall structure of the web is defined by an intricate interplay between experience or entitlement of the pages (as measured by the number of inbound hyperlinks a page already has), inherent talent or fitness of the pages (as measured by the likelihood that someone visiting the page would give a hyperlink to it), and the continual high rates of birth and death of pages on the web. We find that the web is conservative in judging talent and the overall fitness distribution is exponential, showing low variability. The small variance in talent, however, is enough to lead to experience distributions with high variance: The preferential attachment mechanism amplifies these small biases and leads to heavy-tailed power-law (PL) inbound degree distributions over all pages, as well as over pages that are of the same age. The balancing act between experience and talent on the web allows newly introduced pages with novel and interesting content to grow quickly and surpass older pages. In this regard, it is much like what we observe in high-mobility and meritocratic societies: People with entitlement continue to have access to the best resources, but there is just enough screening for fitness that allows for talented winners to emerge and join the ranks of the leaders. Finally, we show that the fitness estimates have potential practical applications in ranking query results

Intrinsic Spin Hall Effect in the presence of Extrinsic Spin-Orbit Scattering

Intrinsic and extrinsic spin Hall effects are considered together on an equal theoretical footing for the Rashba spin-orbit coupling in two-dimensional (2D) electron and hole systems, using the diagrammatic method for calculating the spin Hall conductivity. Our analytic theory for the 2D holes shows the expected lowest-order additive result for the spin Hall conductivity. But, the 2D electrons manifest a very surprising result, exhibiting a non-analyticity in the Rashba coupling strength $\alpha$ where the strictly extrinsic spin Hall conductivity (for $\alpha = 0$) cannot be recovered from the $\alpha \to 0$ limit of the combined theory. The theoretical results are discussed in the context of existing experimental results.Comment: 5 pages, 2 figure

Effect of processing condition and composition on the microhardness of Cu-(2.5-10)vol.%Al₂O₃ nanocomposite powder particles produced by high energy mechanical milling

Nanostructured Cu-(2.5-10vol.%)Al₂O₃ nanocomposites were produced using high energy mechanical milling. For the as-milled Cu- Al₂O₃ composite powder particles having Al₂O₃ volume fractions of 2.5% and 5%, the increase in average microhardness is significant with the increase of milling time from 12 hours to 24 hours. With the increase of the content of Al₂O₃ nanoparticles the microhardness increases and in the range of 255HV-270HV. The milled nanocomposite powders were heat treated at 150, 300, 400 and 500°C for 1 hour, respectively, to determine the thermal stability of the powder particles as a function of annealing temperature. The average microhardness increased/decreased for the Cu- Al₂O₃ composites after annealing at 150°C due to the dislocation density, while increasing the annealing temperature to 300°C and 400°C the average microhardness almost remained mostly unchanged. Further increasing the annealing temperature to 500°C causes significant decrease in average microhardness due to reduction in dislocation density and coarsening of Cu grains of the Cu- Al₂O₃ composite powders produced after 24 hours of milling. This paper is to report and discuss the changes of the microhardness of the material, caused by the compositions and processing conditions, used to fabricate the Cu-(2.5-10)vol.% Al₂O₃ nanocomposite powders