Determination of the Minimum Departure Interval between Trains with same High-Speed at the Relatively Initial Station

2014 ◽  
Vol 587-589 ◽  
pp. 1737-1740
Author(s):  
Jing Jing Shao ◽  
Lei Shan Zhou ◽  
Zi Xi Bai ◽  
Yong Feng Shang
Keyword(s):  
High Speed ◽  
Operational Efficiency ◽  
High Density ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Research Focus ◽  
High Speed Railway ◽  
High Speed Trains ◽  
Necessary And Sufficient

Chinese high-speed railway is in a boom and making train diagram with high-density trains to relieve capacity intense and improve operational efficiency has become the research focus. Different kinds of station intervals between adjacent trains are the basis for the train diagram. According to the situation in which trains with different speed run on the same line and the proportion of high-speed trains is much larger than that of middle-speed trains, this paper raises principles and methods to determine the minimum departure interval between trains with same speed at the relatively initial station. The minimum departure interval between trains with same speed at the relatively initial station is a necessary and sufficient condition for making train diagram since there is no overtaking between same-speed trains.

5.—The Uniform Asymptotic Stability of Certain Linear Differential-difference Equations

1976 ◽  
Vol 74 ◽  
pp. 71-79
Author(s):  
R. Datko
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Difference Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniform Asymptotic Stability ◽  
Linear Ordinary Differential Equations ◽  
Linear Differential ◽  
Necessary And Sufficient

SynopsisA necessary and sufficient condition is developed for determination of the uniform stability of a class of non-autonomous linear differential-difference equations. This condition is the analogue of the Liapunov criterion for linear ordinary differential equations.

On the Modulii of Analytic Functions

1970 ◽  
Vol 13 (3) ◽  
pp. 325-327 ◽  
Author(s):  
Malcolm J. Sherman
Keyword(s):  
Analytic Functions ◽  
Point Of View ◽  
Sufficient Condition ◽  
Two Dimensional ◽  
Necessary And Sufficient Condition ◽  
Concrete Form ◽  
Norm Equality ◽  
Image Position ◽  
Necessary And Sufficient

The problem to be considered in this note, in its most concrete form, is the determination of all quartets f1, f2, g1, g2 of functions analytic on some domain and satisfying*where p > 0. When p = 2 the question can be reformulated in terms of finding a necessary and sufficient condition for (two-dimensional) Hilbert space valued analytic functions to have equal pointwise norms, and the answer (Theorem 1) justifies this point of view. If p ≠ 2, the problem is solved by reducing to the case p = 2, and the reformulation in terms of the norm equality of lp valued analytic functions gives no clue to the answer.

scholarly journals When Does a Dual Matrix Have a Dual Generalized Inverse?

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1386
Author(s):  
Firdaus E. Udwadia
Keyword(s):  
Explicit Expression ◽  
Generalized Inverse ◽  
Sufficient Conditions ◽  
Generalized Inverses ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Real Matrices ◽  
Explicit Expressions

This paper deals with the existence of various types of dual generalized inverses of dual matrices. New and foundational results on the necessary and sufficient conditions for various types of dual generalized inverses to exist are obtained. It is shown that unlike real matrices, dual matrices may not have {1}-dual generalized inverses. A necessary and sufficient condition for a dual matrix to have a {1}-dual generalized inverse is obtained. It is shown that a dual matrix always has a {1}-, {1,3}-, {1,4}-, {1,2,3}-, {1,2,4}-dual generalized inverse if and only if it has a {1}-dual generalized inverse and that every dual matrix has a {2}- and a {2,4}-dual generalized inverse. Explicit expressions, which have not been reported to date in the literature, for all these dual inverses are provided. It is shown that the Moore–Penrose dual generalized inverse of a dual matrix exists if and only if the dual matrix has a {1}-dual generalized inverse; an explicit expression for this dual inverse, when it exists, is obtained irrespective of the rank of its real part. Explicit expressions for the Moore–Penrose dual inverse of a dual matrix, in terms of {1}-dual generalized inverses of products, are also obtained. Several new results related to the determination of dual Moore-Penrose inverses using less restrictive dual inverses are also provided.

Determination of the semi-nice dimensions

1985 ◽  
Vol 97 (1) ◽  
pp. 79-88 ◽  
Author(s):  
C. T. C. Wall
Keyword(s):  
Sufficient Condition ◽  
Jet Space ◽  
Necessary And Sufficient Condition ◽  
Stable Maps ◽  
Necessary And Sufficient

As the culmination of a notable sequence of papers, Mather [6] gave a necessary and sufficient condition that stable maps were dense in C∞(N, P): it is that the dimensions n and p satisfy the condition n <σ(n, p), where σ(n, p) is the codimension (in a sufficiently large jet space) of the set of jets in Jr(n, p) whose classification (for ℋ-equivalence) ‘involves moduli’.

scholarly journals On the area of surfaces

1919 ◽  
Vol 96 (674) ◽  
pp. 71-81 ◽  
Keyword(s):  
Integral Formula ◽  
Curved Surface ◽  
General Nature ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Definition Of ◽  
Necessary And Sufficient

The necessary and sufficient condition that a curve should possess a length, this length being given by the usual integral formula, is well known. The curve being defined by the equations x = x ( u ), y = y ( u ), the condition is that x ( u ) and y ( u ) should be expressible as integrals with respect to u . It may seem scarcely credible that no corresponding theorem is known with regard to the area of a surface. Such is, however, the case. And what is more surprising, no one has hitherto succeeded in giving such a definition of the area of a curved surface as permits of a determination of a sufficient condition of a general nature that the surface should possess an area, this area being given by the integral formula known to hold in the simplest cases.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

Sign in / Sign up

Export Citation Format

Share Document