Exogenous agents that target transmembrane domains of proteins

Although membrane proteins account for approximately one third of all proteins encoded in the human genome, the functions and structures of their transmembrane domains are much less understood than the water-soluble regions. A major hurdle in studying these transmembrane domains is the lack of appropriate exogenous agents that can be used as specific probes. Despite the daunting challenges, major strides have recently been made in targeting the transmembrane domains of a variety of membrane proteins. High affinity and selectivity have been achieved in model biophysical systems, membranes of bacteria, and mammalian cells.     

Induction of Ring‐Shaped Calcium Oxalate Patterns by Boundaries between Liquid Expanded Phase and Liquid Condensed Phase in Langmuir‐Blodgett Film

The formation of calcium oxalate kidney stones was related to injuries of renal epithelial membranes. The liquid condensed (LC) domains in Langmuir‐Blodgett (LB) film of dipalmitoylphosphatidylcholine (DPPC) were used as a model system to induce crystal growth of urinary mineral calcium oxalate monohydrate (COM). The circular defective boundaries between the LC and liquid expanded (LE) phases of the DPPC monolayer could provide much more nucleating sites for crystallization of COM crystals. It induced ring‐shaped or solid circular patterns of COM crystals on hydrophobic quartz substrates depending on the crystallization time.     

A remark on irregularity of the -Neumann problem on non-smooth domains

It is an observation due to J. J. Kohn that for a smooth bounded pseudoconvex domain in there exists such that the -Neumann operator on maps (the space of -forms with coefficient functions in -Sobolev space of order ) into itself continuously. We show that this conclusion does not hold without the smoothness assumption by constructing a bounded pseudoconvex domain in , smooth except at one point, whose -Neumann operator is not bounded on for any .

     

INITIAL-OBLIQUE DERIVATIVE PROBLEMS FOR NONLINEAR PARABOLIC SYSTEMS WITH MEASURABLE COEFFICIENTS

This paper deals with some initial-oblique derivative boundary value problems for nonlinear nondivergent parabolic systems of several second order equations with measurable coefficients in multiply connected domains. Firstly, a priori estimates of solutions for the initial-boundary value problems are given, and then by using the above estimates of solutions and the Leray-Schauder theorem, the existence and uniqueness of solutions for the problems are proved.     

Geometry and Growth Rate of Frobenius Numbers of Additive Semigroups

Linear combinations x ₁ a ₁ ⋯ x _n a _n of n given natural numbers a _s (with nonnegative integral coefficients x _s ) attain all the integral values, starting from some integer N(a), called the Frobenius number of vector a (provided that the integers a _s have no common divisor, greater than 1). The growth rate of N(a) with the large value of σ = ta ₁ ⋯ a _n depends peculiarly from the direction α of the vector a = σα. The article proves the lower bound of order and the upper bound of order σ ². Both orders are reached from some directions α. The averaging of N(a) along all directions, performed for σ = 7, 19, 41 and 97, provides the values, confirming the rate σ ^p for some p between 3/2 and 2 (for n = 3), excluding neither 3/2 nor 2, for the asymptotic behaviour at large σ. One gets check p ≈ 1, 66 for σ between 100 and 200. These unexpected results, based on some strange relations of the Frobenius numbers to the higher-dimensional continued fractions geometry, lead to many facts of this arithmetic trubulence theory, discussed in this article both as theorems and as conjectures. ^★ Partially supported by RFBR grant 05-01-00104.     

Hyperbolic uniformization of Fermat curves

The ground-breaking research on the uniformization of curves was conducted at the beginning of the last century. Nevertheless, there are few examples in the literature of algebraic curves for which an explicit uniformization is known. In this article we obtain an explicit uniformization of the Fermat curves F _N , for each . The results presented here are based in part on an earlier study of the second author [6] in which each Riemann surface F _N (ℂ) was described as a quotient of the complex disk by a Fuchsian group Γ. 2000 Mathematics Subject Classification Primary—11F03, 11F06; Secondary—11F30 This work was partially supported by MCYT BFM2000-0627 and BMF2003-01898.     

Large time behavior of anisotropic electromagnetic/elasticity equations in exterior domains

We find uniform rates of decay of the total energy of the coupled system of anisotropic electromagnetic/elasticity model in exterior domains provided mild dissipative effects are present. The decay of the total energy is of polynomial type. The conclusions of this paper improve previous results on the subject.     

Two-Person Second-Order Games,Part 2: Restructuring Operations to Reach a Win-Win Profile

In Part 1 of the paper, using habitual domains theory and finite Markov chain theory, we have introduced a new model for describing the evolution of the states of mind of players over time, the two-person second-order game. The concepts of focal mind profile as well as the solution concept of win-win mind profile have been introduced as solution concepts for these games. In Part 2 of the paper, we address the problem of restructuring a game where the focal profile (1,1) is not reachable or is not a win-win profile into a game where the profile (1,1) is a reachable win-win profile. Precisely, under some reasonable assumptions, we derive the possibility theorem that it is always possible to reach a win-win mind profile in a two-person second-order game. Moreover, we provide practical operations for restructuring games for reaching a win-win profile. This research was partially supported by the National Science Council, Taiwan, NSC96-2416-H009-013.     

Periodic Schur functions and slit discs

A simply connected domain is called a slit disc if minus a finite number of closed radial slits not reaching the origin. A slit disc is called rational (rationally placed) if the lengths of all its circular arcs between neighboring slits (the arguments of the slits) are rational multiples of 2π. The conformal mapping of onto , (0)=0, ^′(0)>0, extends to a continuous function on mapping it onto . A finite union E of closed non-intersecting arcs e_k on is called rational if for every k, ν_E(e_k) being the harmonic measures of e_k at ∞ for the domain . A compact E is rational if and only if there is a rational slit disc such that . A compact E essentially supports a measure with periodic Verblunsky parameters if and only if for a rationally placed . For any tuple (α₁,…,α_g+1) of positive numbers with ∑_kα_k=1 there is a finite family of closed non-intersecting arcs e_k on such that ν_E(e_k)=α_k. For any set and any >0 there is a rationally placed compact such that the Lebesgue measure |EE^*| of the symmetric difference EE^* is smaller than .