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It is of great significance to sort specific types of cells through a fast and efficient technology in biomedical research and clinical applications. In this study, commercial hollow glass beads were modified with 3-aminopropyltriethoxysilane (ATPES) and hyaluronic acid (HA) sequentially, which can capture HeLa cells with nearly 100% efficiency within 10min. The beads can specifically recognize and sort HeLa cells from a cell coculture of HeLa and L-929 depending on their strong buoyancy and good affinity with cancer cells. The job provides a facile, quick and low-cost cell sorting method, which has potential application in the fields of specific and efficient cell isolation.

It is proved in this article, that in the framework of Riemannian geometry, the existence of large sets of antipodes (i.e. farthest points) for diametral points of a smooth surface has very strong consequences on the topology and the metric of this surface. Roughly speaking, if the sets of antipodes of diametral points are closed curves, then the surface is nothing but the real projective plane.

We obtain sharp volume bound for a conic 2-sphere in terms of its Gaussian curvature bound. We also give the geometric models realizing the extremal volume. In particular, when the curvature is bounded in absolute value by $1$, we compute the minimal volume of a conic sphere in the sense of Gromov. In order to apply the level set analysis and isoperimetric inequality as in our previous works, we develop new analytical tools to treat regions with vanishing curvature.

The percolation phenomena on two-dimensional square lattice is considered. The quotient χ of connectivity length ξ^> above percolation threshold p_c and ξ^< below p_c at the same small distance Δp is discussed. The results of two different algorithms and programs and agreement with theoretical/mathematical predications is presented, in contrast to previous contradictory Monte Carlo simulation results.

In the context of (2+1)–dimensional gravity, we use holonomies of constant connections which generate a q–deformed representation of the fundamental group to derive signed area phases which relate the quantum matrices assigned to homotopic loops. We use these features to determine a quantum Goldman bracket (commutator) for intersecting loops on surfaces, and discuss the resulting quantum geometry.

Experiments reveal the existence of metallic bands at surfaces of metals and insulators. The bands can be doped externally. We review properties of surface superconductivity that may set up in such bands at low temperatures and various means of superconductivity defection. The fundamental difference as compared to the ordinary superconductivity in metals, besides its two-dimensionality lies in the absence of the center of space inversion. This results in mixing between the singlet and triplet channels of the Cooper pairing.

This letter deals with the experimental observation of oscillations in the infrared reflectance from Nb ultra-thin films deposited on α-type SiO₂ substrates. P-polarized reflectance (R_p) measurements are made using a tunable p-polarized CO₂ waveguide laser using wavelengths between 9.2 and 10.4 μm. Several Nb/SiO₂ quantum wells were specially made by the RF sputtering technique. Tailored thicknesses run between 5.5 and 55 Å. Because of the strong influence from the chosen substrate, IR reflectivity was fitted to the optical response of our metal-substrate system by using the three-oscillator model and numerical calculations on the basis of the local field calculation for a single metallic quantum well. Although quantum size effects are well studied in semiconductor compounds, there are only a few studies of this effect in metallic films where the present investigation has its most important contribution.

Oscillations in the infrared reflectance from metallic ultrathin films are described as consequence of quantum size effects. In this contribution, we present experimental evidence of such oscillations for Nb ultrathin films deposited on α-type SiO₂ substrates. Also, it is shown how substrates influence the size effects and the amplitude but not the period of oscillations. Because of the strong influence from the chosen substrate due to absorption, IR reflectivity was fitted to the optical response of our metal-substrate and bare-substrate system by using the three-oscillator model and numerical calculations on the basis of the local field calculation for a single metallic quantum well. Although quantum size effects are well studied in semiconductor compounds, there are few studies of this effect in metallic films where the present investigation has its most important contribution. Measurements for p-polarized reflectance (R_p) are made using a tunable p-polarized CO₂ waveguide laser using wavelengths from the p-branch (9.4 to 9.7 μm) and R-branch (10.0 to 10.4 μm). Nb/SiO₂ ultrathin films were assembled by a conventional RF sputtering technique and tailored thicknesses were deposited from 5.5 to 55 Å.

In this paper, we show the interest of the 3D discrete surface notion for the extraction of object contours. We introduce some notions related to surfaces of 18-and 26-connected objects in 3D discrete images, and a new sequential algorithm to extract the surface and contours of 26-connected objects. Then, we present a PRAM related algorithm to construct the successor function of the surface graph. The complexity of the algorithm is O(log N) for an N×N×N image, with N³ processors.

In Ref. 6, two similar characterizations of discrete surfaces of ℤ³ are proposed which are called strong 18-surfaces and strong 26-surfaces. The proposed characterizations consist in some natural global properties of surfaces. In this paper, we first give local necessary conditions for an object to be a strong 26-surface. An object satisfying these local properties is called a near strong 26-surface. Then we construct continuous analogs for near strong 26-surfaces and, using the continuous Jordan Theorem, we prove that the necessary local conditions previously introduced in fact give a complete local characterization of strong 26-surfaces: the class of near strong 26-surfaces coincides with the class of strong 26-surfaces.

We derive explicit differential equations for dynamical systems defined on generic surfaces applying elliptic and automorphic function theory to make uniform the surfaces in the upper half of the complex plane with the hyperbolic metric. By modifying the definition of the standard theta series we will determine general meromorphic systems on a fundamental domain in the upper half plane the solution trajectories of which "roll up" onto an appropriate surface of any given genus.

We consider the theory and applications of bivariate fractal interpolation surfaces constructed as attractors of iterated function systems. Specifically, such kind of surfaces constructed on rectangular domains have been used to demonstrate their efficiency in computer graphics and image processing. The methodology followed is based on the labeling used for the vertices of the rectangular domain rather than on the constraints satisfied by the contractivity factors or the boundary data.

A robust and efficient surface intersection algorithm that is implementable in floating point arithmetic, accepts surfaces algebraic or otherwise and which operates without human supervision is critical to boundary representation solid modeling. To the author's knowledge, no such algorithms has been developed. All tolerance-based subdivision algorithms will fail on surfaces with sufficiently small intersections. Algebraic techniques, while promising robustness, are presently too slow to be practical and do not accept non-algebraic surfaces. Algorithms based on loop detection hold promise. They do not require tolerances except those associated with machine associated with machine arithmetic, and can handle any surface for which there is a method to construct bounds on the surface and its Gauss map. Published loop detection algorithms are, however, still too slow and do not deal with singularities. We present a new loop detection criterion and discuss its use in a surface intersection algorithms. The algorithm, like other loop detection based intersection algorithms, subdivides the surfaces into pairs of sub-patches which do not intersect in any closed loops. This paper presents new strategies for subdividing surfaces in a way that causes the algorithms to run quickly even when the intersection curve(s) contain(s) singularities.

We consider the question of which right-angled Artin groups contain closed hyperbolic surface subgroups. It is known that a right-angled Artin group A(K) has such a subgroup if its defining graph K contains an n-hole (i.e. an induced cycle of length n) with n ≥ 5. We construct another eight "forbidden" graphs and show that every graph K on ≤ 8 vertices either contains one of our examples, or contains a hole of length ≥ 5, or has the property that A(K) does not contain hyperbolic closed surface subgroups. We also provide several sufficient conditions for a right-angled Artin group to contain no hyperbolic surface subgroups.

We prove that for one of these "forbidden" subgraphs P₂(6), the right-angled Artin group A(P₂(6)) is a subgroup of a (right-angled Artin) diagram group. Thus we show that a diagram group can contain a non-free hyperbolic subgroup answering a question of Guba and Sapir. We also show that fundamental groups of non-orientable surfaces can be subgroups of diagram groups. Thus the first integral homology of a subgroup of a diagram group can have torsion (all homology groups of all diagram groups are free Abelian by a result of Guba and Sapir).

We introduce an equivalence relation, called stable equivalence, on knot diagrams and closed generically immersed curves on surfaces. We give bijections between the set of abstract knots, the set of virtual knots, and the set of the stable equivalence classes of knot diagrams on surfaces. Using these bijections, we define concordance and link homology for virtual links. As an application, it is shown that Kauffman's example of a virtual knot diagram is not equivalent to a classical knot diagram.

In a paper of Menasco and Reid, it is conjectured that there exist no hyperbolic knots in S³ for which the complement contains a closed embedded totally geodesic surface. In this note, we show that one can get "as close as possible" to a counter-example. Specifically, we construct a sequence of hyperbolic knots {K_n} with complements containing closed embedded essential surfaces having principal curvatures converging to zero as n tends to infinity. We also construct a family of two-component links for which the complements contain closed embedded totally geodesic surfaces of arbitrarily large genera. In addition, we prove that a closed embedded surface with sufficiently small principal curvatures is not only quasi-Fuchsian (a result of Thurston's), but it is also either acylindrical or the boundary of a twisted I-bundle.

Goldman [2] and Turaev [4] found a Lie bialgebra structure on the vector space generated by non-trivial free homotopy classes of loops on an orientable surface. Chas [1] by the aid of the computer, found a negative answer to Turaev's question about the characterization of the classes with cobracket zero as multiples of simple classes, in every surface of negative Euler characteristic and positive genus. However, she left open Turaev's conjecture, namely if, for genus zero, every class with cobracket zero is a multiple of a simple class. The aim of this paper is to give a positive answer to this conjecture.

Turaev proves a formula for the Dijkgraaf–Witten invariants of surfaces in terms of projective representations by using the state sum invariant technique from quantum topology. In this paper, we present another proof of Turaev's theorem by using classical method of characters and representation theory. A version of Turaev's formula for surfaces with boundary is also given.

Our goal is to systematically compute the $ℂP^2$-genus of as many prime knots up to 8-crossings as possible. We obtain upper bounds on the $ℂP^2$-genus via coherent band surgery. We obtain lower bounds by obstructing homological degrees of potential slice discs. The obstructions are pulled from a variety of sources in low-dimensional topology and adapted to $ℂP^2$. There are 27 prime knots and distinct mirrors up to 7-crossings. We now know the $ℂP^2$-genus of all of these knots. There are 64 prime knots and distinct mirrors up to 8-crossings. We now know the $ℂP^2$-genus of all but 6 of these knots, where the $ℂP^2$-genus was not determined explicitly, it was narrowed down to 2 possibilities. As a consequence of this work, we show an infinite family of knots such that the $ℂP^2$-genus of each knot differs from that of its mirror.

In this paper we study isotopy classes of closed connected orientable surfaces in the standard $3$-sphere. Such a surface splits the $3$-sphere into two compact connected submanifolds, and by using their Heegaard splittings, we obtain a $2$-component handlebody-link. In this paper, we first show that the equivalence class of such a 2-component handlebody-link up to attaching trivial $1$-handles can recover the original surface. Therefore, we can reduce the study of surfaces in the $3$-sphere to that of $2$-component handlebody-links up to stabilizations. Then, by using $G$-families of quandles, we construct invariants of $2$-component handlebody-links up to attaching trivial $1$-handles, which lead to invariants of surfaces in the $3$-sphere. In order to see the effectiveness of our invariants, we will also show that our invariants can distinguish certain explicit surfaces in the $3$-sphere.