On the projection and macphail constants ofl n p spaces

We prove that the projection and Macphail constants ofl _n ^p (1≦p≦2) are asymptotically equivalent ton ^1/2 andn ^−1/2 respectively. We also obtain some relations linking certain parameters of general finite dimensional real Banach spaces. This note is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Prof. J. Lindenstrauss, to whom the author wishes to express his thanks and appreciation.     

Electrochemical methods for analysing and controlling charge transfer at the electrode–tissue interface

There have been rapid advances in the development of new materials for use in electrode–tissue interfacing. The development of conducting polymers, conducting hydrogels, carbon nanotubes, graphene and other conducting materials has provided a rich landscape for controlling charge transfer at the electrode–tissue interface and hence to monitor and manipulate cell behaviour. These materials have been used in tissue-engineered constructs to direct and control cell proliferation, growth and differentiation. However, their translation to clinical devices has been less successful. In this review, the use of electroanalytical techniques to develop an understanding of charge transfer at the electrode–tissue interface is discussed. In particular, the impact of solution and electrode conditions on charge injection capacity is demonstrated. The importance of standardised testing methods and the correlation of electrochemical and electrophysiological performance show the limitations of empirical studies and help define key electrode properties for clinical devices. The development of a sound theoretical basis for charge transfer at this increasingly important interface is being advocated to improve clinical outcomes and device lifetime and reduce power usage.     

EBC-232 and 323: A Structural Conundrum Necessitating Unification of Five In Silico Prediction and Elucidation Methods

Structurally unique halimanes EBC-232 and EBC-323, isolated from the Australian rainforest plant Croton insularis, proved considerably difficult to elucidate. The two diastereomers, which consist an unusual oxo-6,7-spiro ring system fused to a dihydrofuran, were solved by unification and consultation of five in silico NMR elucidation and prediction methods [i.e., ACDLabs, olefin strain energy (OSE), DP4, DU8+ and TD DFT CD]. Structure elucidation challenges of this nature are prime test case examples for empowering future AI learning in structure elucidation.     

Determination of work functions near melting points of refractory metals by using a direct-current arc

A direct-current arc in argon at atmospheric pressure was used to determine effective work functions of refractory metals, including tantalum, tungsten, molybdenum, and niobium. The procedure is experimentally advantageous because surface cleanliness of the specimen is not critical, high vacuum is not required, and the anode-cathode spacing is not critical. The experimental procedure involves striking an arc to a metal wire cathode to form a melted ball having an emitting area defined by its diameter. The literature melting point of the metal is taken as the emitting temperature. By using these parameters and the known arc current, effective work functions were calculated from the Richardson-Dushman equation. The calculated work functions agree with recommended handbook values to within about 0.1 V and have typical repeatabilities of 0.02 V. By varying the arc current, Richardson plots can be made over a temperature range from a few hundred degrees below the melting point to about 50° over the melting point of the test metal. A Richardson plot over this temperature range is presented for tantalum.     

Self-avoiding walk in five or more dimensions I. The critical behaviour

We use the lace expansion to study the standard self-avoiding walk in thed-dimensional hypercubic lattice, ford5. We prove that the numberc _n ofn-step self-avoiding walks satisfiesc _n ~A ⁿ , where is the connective constant (i.e. =1), and that the mean square displacement is asymptotically linear in the number of steps (i.e.v=1/2). A bound is obtained forc _n(x), the number ofn-step self-avoiding walks ending atx. The correlation length is shown to diverge asymptotically like (^––Z)^1/2. The critical two-point function is shown to decay at least as fast as x^–2, and its Fourier transform is shown to be asymptotic to a multiple ofk ^–2 ask0 (i.e. =0). We also prove that the scaling limit is Gaussian, in the sense of convergence in distribution to Brownian motion. The infinite self-avoiding walk is constructed. In this paper we prove these results assuming convergence of the lace expansion. The convergence of the lace expansion is proved in a companion paper.Supported by the Nishina Memorial Foundation and NSF grant PHY-8896163.Supported by NSERC grant A9351     

Construction of the Incipient Infinite Cluster for Spread-out Oriented Percolation Above 4 + 1 Dimensions

 We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ ^d × ℤ₊, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ ⁿ (E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n)  ℤ ^d × ℤ₊, summing this probability over x  ℤ ^d , and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ_∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n ⁻¹, we prove existence of a limiting measure ℚ_∞, with ℚ_∞ = ℙ_∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension of the cluster of the origin, under ℙ_∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented percolation to super-Brownian motion, for d+1 > 4+1. Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002 RID="*" ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl     

Maps Preserving Zeros of xy*

For a prime ring A with involution, we explore the characterization of additive bijective maps φ: A → A such that φ(x)φ(y)* = 0 whenever xy* = 0. In particular, we show that if A is prime, unital, and generated by nontrivial idempotents, then there is a *-monomorphism g of A into Q, and an element r ∈ A such that φ(x) = rg(x) for all x ∈ A.     

Xe对NO(X)微分截面和非弹性散射中的碰撞诱导旋转准直

本文对NO(X)-Xe碰撞系统在碰撞能量为519 cm^-1,测量了完全?-双峰分解的微分截面和碰撞引起的旋转准直力矩. 同时结合初始量子态选择,使用六极杆的非均质电场,借助量子态分辨的测量,利用(1+1'')共振增强的多光子电离和速度离子成像. 结果显示,微分截面以及偏振相关的微分截面均显示与从头算势能面上进行的量子力学散射计算[J. K?os etal. J. Chem. Phys. 137, 014312 (2012)]一致. 通过与准经典轨迹、硬壳势能的量子力学散射以及运动近端模型的比较,评估了势能对所测微分截面和碰撞引起的旋转准直力矩的影响.