Optimum Receiver-Side Tuning Capacitance for Capacitive Wireless Power Transfer

This paper reveals the optimum capacitance value of a receiver-side inductor-capacitor (LC) network to achieve the highest efficiency in a capacitive power-transfer system. These findings break the usual convention of a capacitance value having to be chosen such that complete LC resonance happens at the operating frequency. Rather, our findings in this paper indicate that the capacitance value should be smaller than the value that forms the exact LC resonance. These analytical derivations showed that as the ratio of inductor impedance divided by plate impedance increased, the optimum Rx capacitance decreased. This optimum capacitance maximized the TX-to-RX transfer efficiency of a given set of system conditions, such as matching inductors and coupling plates.

Quadratic Forms over a ∈ Local Field

This chapter presents various results about quadratic forms over a field complete with respect to a discrete valuation. The discussion is based on the assumption that K is a field of arbitrary characteristic which is complete with respect to a discrete valuation ν‎ and uses the usual convention that ν‎(0) = infinity. The chapter starts with a notation regarding the ring of integers of K and the natural map from it to the residue field, followed by a number of propositions regarding an anisotropic quadratic space. These include an anisotropic quadratic space with residual quadratic spaces, an unramified quadratic space of finite dimension, unramified finite-dimensional anisotropic quadratic forms over K, unramified anisotropic quadratic forms and a bilinear form, and a round quadratic space over K. The chapter concludes with a theorem that there exists an anisotropic quadratic form over K, unique up to isometry, and is non-singular.

Summarizing a group of 14C dates on the historical time scale: with a worked example from the Late Neolithic of Bavaria

There is a large gap between the fact of a radiocarbon determination and the archaeological answer to the question to which it relates. The first part of the gap is addressed by calibration, that turns a measure of 14C activity into an estimate of a calendar date. Here is a contribution to the second part, by which a set of calibrated dates is made to provide a calendar range for the archaeological events under study.This note follows ANTIQUITY's usual convention, under which uncalibrated determinations are given in lower-case, b.p., and calibrated dates in small capitals, BP, BC or AD.

Some continuity properties of linear transformations in normed spaces

Let X and Y be normed spaces and let L(X, Y) denote the set of linear transformations (henceforth called “operators”) T with domain a linear subspace D(T) of X and range R(T) contained in Y. The restriction of T to a subspace E is denoted by T/E; by the usual convention T|E = T|E∩ D(T). For a given linear subspace E the family of infinite dimensional ssubspaces of E is denoted by (E). An operator Tis said to have a certain property ℙ ubiquitously if every E ∈ (X) contains an F ∈(E) for which T|F has property ℙ For example, T is ubiquitously continuous if each E ∈(X) contains an F∈ (E) for which T|F is continuous. In the present note we shall characterize ubiquitous continuity, isomorphy, precompactness and smallness. A subspace of X is called a principal subspace if it is closed and of finite codimension in X. The restriction of an operator to a principal subspace will be called a principal restriction. The symbol T will always denote an arbitrary operator in L(X, Y).

High-precision radiocarbon chronometry of ancient Egypt, and comparisons with Nubia, Palestine and Mesopotamia

Radiocarbon dating began in archaeology with ancient Egypt, for it was to the securely dated materials from Egypt that Willard Libby naturally turned when his new radiocarbon method needed verification from reliable historical sources. With this paper the reverse process begins: verifying and correcting the conventional chronology for Egypt and neighbouring regions by calibrated radiocarbon.This paper compares calibrated radiocarbon dates against historical dates in a manner not well covered by ANTIQUITY's usual convention. So in this paper only uncalibrated radiocarbon dates are denoted by ‘b.p.’, historical dates are denoted by ‘BC’, and calibrated radiocarbon dates by ‘Cal BC’ or simply ‘BC’ when the meaning is clear from the context.

Higher Derivations and the Jordan Canonical Form of the Companion Matrix

The purpose of this note is to give a basis with respect to which the companion matrix of an equation (over a field of any characteristic) is in Jordan canonical form.Let k be a field. Define a k-linear map Di:k[X]→k[X] by where the integer is the binomial coefficient n!;/i!;(n —i)!;. We adopt the usual convention that if i>9 or j<0. Then D=(D0, D1D2,…) is a higher derivation (see [1, p. 192]).

Some computations for m-dimensional partitions

1. It was known to Euler that p(n), the number of unrestricted partitions of n into non-increasing integral parts, is generated bywith the usual convention that p(0) = 1.

On non-dissipative Markov chains

Consider a Markov chain with an enumerable infinity of states, labelled 0, 1, 2, …, whose one-step transition probabilities pij are independent of time. ThenI write and, departing slightly from the usual convention,Then it is known ((1), pp. 324–34, or (6)) that the limits πij always exist, and that

On the decimal representation of integers

Let r be any fixed integer with, r≥ 2; then, given any positive integer n, we can find* integers αk(r, n) (k = 0, 1, 2, …) such thatwhere, subject to the conditionsthe integers αk(r, n) are uniquely determined, and, in fact, clearlyαk(r, n) = [n/rk] − r[n/rk+1](square brackets denoting integral parts, according to the usual convention).