Generalized Cycloidal Motion

1971 ◽  
Vol 93 (1) ◽  
pp. 131-139 ◽  
Author(s):  
D. Spragg ◽  
D. Tesar
Keyword(s):  
Design Methods ◽  
Important Special Case ◽  
Mechanical Advantage ◽  
Center Point ◽  
Wheel Rolling ◽  
Special Case

The motion coefficients and design methods for a wheel rolling externally or internally to a fixed wheel are given in Part I for linkage constraint satisfying up to 6 multiply separated positions. Part II provides design equations and graphical procedures in terms of the cubic circle and center point curves based on four symmetrical, multiply separated positions of the moving wheel. The important special case of an angular-circular transformer mechanism with constant mechanical advantage is treated in detail for four positions in Part III.

ON THE DENSITY OF HAUSDORFF DIMENSIONS OF BOUNDED TYPE CONTINUED FRACTION SETS: THE TEXAN CONJECTURE

2004 ◽  
Vol 04 (01) ◽  
pp. 63-76 ◽  
Author(s):  
OLIVER JENKINSON
Keyword(s):  
Hausdorff Dimension ◽  
Finite Subset ◽  
Continued Fraction ◽  
Cantor Set ◽  
Computational Method ◽  
Accurate Approximation ◽  
Natural Numbers ◽  
Important Special Case ◽  
The One ◽  
Special Case

Given a non-empty finite subset A of the natural numbers, let EA denote the set of irrationals x∈[0,1] whose continued fraction digits lie in A. In general, EA is a Cantor set whose Hausdorff dimension dim (EA) is between 0 and 1. It is shown that the set [Formula: see text] intersects [0,1/2] densely. We then describe a method for accurately computing dimensions dim (EA), and employ it to investigate numerically the way in which [Formula: see text] intersects [1/2,1]. These computations tend to support the conjecture, first formulated independently by Hensley, and by Mauldin & Urbański, that [Formula: see text] is dense in [0,1]. In the important special case A={1,2}, we use our computational method to give an accurate approximation of dim (E{1,2}), improving on the one given in [18].

Acceleration Analysis of Platform-Type Manipulators

1996 ◽  
Author(s):  
Maher G. Mohamed
Keyword(s):  
Stewart Platform ◽  
Algebraic Manipulation ◽  
Analysis Procedure ◽  
Compact Form ◽  
Numerical Examples ◽  
Acceleration Field ◽  
Center Point ◽  
Planar Manipulators ◽  
Acceleration Analysis ◽  
Special Case

Abstract The screw algebra is used to efficiently derive expressions in compact form for both the angular accelerations of the moving links and the linear accelerations of points on the links of platform-type manipulators. The analysis employs the property that the acceleration state of the manipulator platform can be determined by considering the acceleration states of the links of only one — any one — of the manipulator legs. The obtained expressions provide an ease in symbolic and algebraic manipulation. The analysis is then extended to specify the acceleration center point of ithe nstantaneous motion of the manipulator platform. The acceleration center point is then used in expressing the distribution of the acceleration field of the platform instant motion which is important in manipulator synthesis. The special case of planar manipulators is studied and simpler expressions are derived. Numerical examples are presented for the analysis of a 3-DOF planar platform-type and of a 6-DOF spatial “Stewart Platform” manipulators to illustrate the analysis procedure.

An Elementary Proof of Suslin Reciprocity

2005 ◽  
Vol 48 (2) ◽  
pp. 221-236 ◽  
Author(s):  
Matt Kerr
Keyword(s):  
Elementary Proof ◽  
Function Fields ◽  
Algebraic Cycles ◽  
Important Special Case ◽  
Special Case

AbstractWe state and prove an important special case of Suslin reciprocity that has found significant use in the study of algebraic cycles. An introductory account is provided of the regulator and norm maps on Milnor K2-groups (for function fields) employed in the proof.

Introduction

2020 ◽  
pp. 1-6
Author(s):  
Peter Scholze ◽  
Jared Weinstein
Keyword(s):  
Moduli Spaces ◽  
Function Fields ◽  
Number Fields ◽  
Important Special Case ◽  
Langlands Correspondence ◽  
Key Innovation ◽  
Perfectoid Spaces ◽  
Definition Of ◽  
Special Case

This introductory chapter provides an overview of Drinfeld's work on the global Langlands correspondence over function fields. Whereas the global Langlands correspondence is largely open in the case of number fields K, it is a theorem for function fields, due to Drinfeld and L. Lafforgue. The key innovation in this case is Drinfeld's notion of an X-shtuka (or simply shtuka). The Langlands correspondence for X is obtained by studying moduli spaces of shtukas. A large part of this course is about the definition of perfectoid spaces and diamonds. There is an important special case where the moduli spaces of shtukas are classical rigid-analytic spaces. This is the case of local Shimura varieties. Some examples of these are the Rapoport-Zink spaces.

On the Hyperplane Sections Through two Given Points of an Algebraic Variety

1970 ◽  
Vol 22 (1) ◽  
pp. 128-133 ◽  
Author(s):  
Wei-Eihn Kuan
Keyword(s):  
Simple Proof ◽  
Hyperplane Section ◽  
Rational Points ◽  
Infinite Field ◽  
Important Special Case ◽  
Irreducible Curve ◽  
Irreducible Variety ◽  
Dimension 2 ◽  
Hyperplane Sections ◽  
Special Case

1. Let k be an infinite field and let V/k be an irreducible variety of dimension ≧ 2 in a projective n-space Pn over k. Let P and Q be two k-rational points on V In this paper, we describe ideal-theoretically the generic hyperplane section of V through P and Q (Theorem 1) and prove that the section is almost always an absolutely irreducible variety over k1/pe if V/k is absolutely irreducible (Theorem 3). As an application (Theorem 4), we give a new simple proof of an important special case of the existence of a curve connecting two rational points of an absolutely irreducible variety [4], namely any two k-rational points on V/k can be connected by an irreducible curve.I wish to thank Professor A. Seidenberg for his continued advice and encouragement on my thesis research.

scholarly journals Deception through Half-Truths

2020 ◽  
Vol 34 (06) ◽  
pp. 10110-10117
Author(s):  
Andrew Estornell ◽  
Sanmay Das ◽  
Yevgeniy Vorobeychik
Keyword(s):  
Polynomial Time ◽  
Transition Function ◽  
Np Hard ◽  
Fundamental Issue ◽  
Fake News ◽  
False Information ◽  
Important Special Case ◽  
Bayes Network ◽  
Special Case

Deception is a fundamental issue across a diverse array of settings, from cybersecurity, where decoys (e.g., honeypots) are an important tool, to politics that can feature politically motivated “leaks” and fake news about candidates. Typical considerations of deception view it as providing false information. However, just as important but less frequently studied is a more tacit form where information is strategically hidden or leaked. We consider the problem of how much an adversary can affect a principal's decision by “half-truths”, that is, by masking or hiding bits of information, when the principal is oblivious to the presence of the adversary. The principal's problem can be modeled as one of predicting future states of variables in a dynamic Bayes network, and we show that, while theoretically the principal's decisions can be made arbitrarily bad, the optimal attack is NP-hard to approximate, even under strong assumptions favoring the attacker. However, we also describe an important special case where the dependency of future states on past states is additive, in which we can efficiently compute an approximately optimal attack. Moreover, in networks with a linear transition function we can solve the problem optimally in polynomial time.

The New qd Algorithms

Acta Numerica ◽  
1995 ◽  
Vol 4 ◽  
pp. 459-491 ◽  
Author(s):  
Beresford N. Parlett
Keyword(s):  
Singular Values ◽  
Eigenvalues And Eigenvectors ◽  
Triangular Factorization ◽  
Matrix Computation ◽  
Important Special Case ◽  
Singular Vectors ◽  
Tridiagonal Matrices ◽  
Recent Origin ◽  
Special Case

Let us think about ways to find both eigenvalues and eigenvectors of tridiagonal matrices. An important special case is the computation of singular values and singular vectors of bidiagonal matrices. The discussion is addressed both to specialists in matrix computation and to other scientists whose main interests lie elsewhere. The reason for hoping to communicate with two such diverse sets of readers at the same time is that the content of the survey, though of recent origin, is quite elementary and does not demand familiarity with much beyond triangular factorization and the Gram-Schmidt process for orthogonalizing a set of vectors. For some readers the survey will cover familiar territory but from a novel perspective. The justification for presenting these ideas is that they lead to new variations of current methods that run a lot faster while achieving greater accuracy.

scholarly journals On the number of excursion sets of planar Gaussian fields

2020 ◽  
Vol 178 (3-4) ◽  
pp. 655-698
Author(s):  
Dmitry Beliaev ◽  
Michael McAuley ◽  
Stephen Muirhead
Keyword(s):  
Plane Wave ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Gaussian Fields ◽  
Important Special Case ◽  
Level Densities ◽  
Excursion Sets ◽  
Nodal Set ◽  
Different Types ◽  
Special Case

Abstract The Nazarov–Sodin constant describes the average number of nodal set components of smooth Gaussian fields on large scales. We generalise this to a functional describing the corresponding number of level set components for arbitrary levels. Using results from Morse theory, we express this functional as an integral over the level densities of different types of critical points, and as a result deduce the absolute continuity of the functional as the level varies. We further give upper and lower bounds showing that the functional is at least bimodal for certain isotropic fields, including the important special case of the random plane wave.

A representation for discrete distributions by equiprobable mixtures

1980 ◽  
Vol 17 (01) ◽  
pp. 102-111 ◽  
Author(s):  
Arthur V. Peterson ◽  
Richard A. Kronmal
Keyword(s):  
Random Variables ◽  
Discrete Distribution ◽  
Discrete Distributions ◽  
Important Special Case ◽  
Discrete Random Variables ◽  
Special Case

We obtain a representation of an arbitrary discrete distribution with n mass points by an equiprobable mixture of r distributions, each of which has no more than a (≧2) mass points, where r is the smallest integer greater than or equal to (n – 1)/(a – 1). An application to the generation of discrete random variables on a computer is described, which has as an important special case Walker's (1977) alias method.

scholarly journals On the inverses of Kasami and Bracken–Leander exponents

2020 ◽  
Vol 88 (12) ◽  
pp. 2597-2621
Author(s):  
Lukas Kölsch
Keyword(s):  
Algebraic Degree ◽  
Binary Representation ◽  
Important Special Case ◽  
Kasami Function ◽  
Special Case

Abstract We explicitly determine the binary representation of the inverse of all Kasami exponents $$K_r=2^{2r}-2^r+1$$ K r = 2 2 r - 2 r + 1 modulo $$2^n-1$$ 2 n - 1 for all possible values of n and r. This includes as an important special case the APN Kasami exponents with $$\gcd (r,n)=1$$ gcd ( r , n ) = 1 . As a corollary, we determine the algebraic degree of the inverses of the Kasami functions. In particular, we show that the inverse of an APN Kasami function on $${\mathbb {F}}_{2^n}$$ F 2 n always has algebraic degree $$\frac{n+1}{2}$$ n + 1 2 if $$n\equiv 0 \pmod 3$$ n ≡ 0 ( mod 3 ) . For $$n\not \equiv 0 \pmod 3$$ n ≢ 0 ( mod 3 ) we prove that the algebraic degree is bounded from below by $$\frac{n}{3}$$ n 3 . We consider Kasami exponents whose inverses are quadratic exponents or Kasami exponents. We also determine the binary representation of the inverse of the Bracken–Leander exponent $$BL_r=2^{2r}+2^r+1$$ B L r = 2 2 r + 2 r + 1 modulo $$2^n-1$$ 2 n - 1 where $$n=4r$$ n = 4 r and r odd. We show that the algebraic degree of the inverse of the Bracken–Leander function is $$\frac{n+2}{2}$$ n + 2 2 .

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