General conditions for bounded relative error in simulations of highly reliable Markovian systems

We establish a necessary condition for any importance sampling scheme to give bounded relative error when estimating a performance measure of a highly reliable Markovian system. Also, a class of importance sampling methods is defined for which we prove a necessary and sufficient condition for bounded relative error for the performance measure estimator. This class of probability measures includes all of the currently existing failure biasing methods in the literature. Similar conditions for derivative estimators are established.

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Syarat Perlu dan Cukup untuk Keterbatasan Potensial Riesz di Ruang Morrey Klasik

Jurnal Natur Indonesia ◽

10.31258/jnat.14.3.227-229 ◽

2013 ◽

Vol 14 (3) ◽

pp. 227

Author(s):

Mohammad Imam Utoyo ◽

Basuki Widodo ◽

Toto Nusantara ◽

Suhariningsih Suhariningsih

Keyword(s):

Characteristic Function ◽

Morrey Space ◽

Necessary Conditions ◽

Riesz Potential ◽

Necessary Condition ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Research Results ◽

Necessary And Sufficient

This script was aimed to determine the necessary conditions for boundedness of Riesz potential in the classical Morrey space. If these results are combined with previous research results will be obtained the necessary and sufficient condition for boundedness of Riesz potential. This necessary condition is obtained through the use of characteristic function as one member of the classical Morrey space.

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ON THE FINITENESS PROBLEM FOR AUTOMATON (SEMI)GROUPS

International Journal of Algebra and Computation ◽

10.1142/s021819671250052x ◽

2012 ◽

Vol 22 (06) ◽

pp. 1250052 ◽

Cited By ~ 22

Author(s):

ALI AKHAVI ◽

INES KLIMANN ◽

SYLVAIN LOMBARDY ◽

JEAN MAIRESSE ◽

MATTHIEU PICANTIN

Keyword(s):

Decision Problem ◽

Decision Procedure ◽

Necessary Condition ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Mealy Automata ◽

Necessary And Sufficient ◽

New Criteria

This paper addresses a decision problem highlighted by Grigorchuk, Nekrashevich, and Sushchanskiĭ, namely the finiteness problem for automaton (semi)groups. For semigroups, we give an effective sufficient but not necessary condition for finiteness and, for groups, an effective necessary but not sufficient condition. The efficiency of the new criteria is demonstrated by testing all Mealy automata with small stateset and alphabet. Finally, for groups, we provide a necessary and sufficient condition that does not directly lead to a decision procedure.

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The necessary and sufficient condition for clustering of nodes based on the signs of connections in generalized signed networks

International Journal of Modern Physics B ◽

10.1142/s0217979219500863 ◽

2019 ◽

Vol 33 (10) ◽

pp. 1950086

Author(s):

Qi Wang ◽

Yinhe Wang ◽

Zilin Gao ◽

Lili Zhang ◽

Wenli Wang

Keyword(s):

Clustering Algorithms ◽

Necessary Condition ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Signed Networks ◽

Clustering Problem ◽

Structural Hole ◽

Signed Network ◽

Necessary And Sufficient ◽

Sufficient And Necessary Condition

This paper investigates the clustering problem for the generalized signed networks. By rigorous derivations, a sufficient and necessary condition for clustering of the nodes in generalized signed networks is proposed in this paper. In order to obtain this condition, the concept of friends group is first introduced for the nodes based on their links’ sign. Then, the unprivileged network is also defined in this paper by employing the concepts of structural hole and broker. Compared with the existing clustering algorithms, the outstanding advantage in this paper is that only the positive or negative (especially, or zero) sign of the links is required regardless of their density or sparsity. We have proved mathematically that a generalized signed network is classifiable if and only if it is an unprivileged network. Finally, two examples associated with numerical simulations are proposed to generate the unprivileged networks.

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Summability methods based on the Riemann Zeta function

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171288000067 ◽

1988 ◽

Vol 11 (1) ◽

pp. 27-36

Author(s):

Larry K. Chu

Keyword(s):

Zeta Function ◽

Riemann Zeta Function ◽

Necessary Condition ◽

Real Sequence ◽

Necessary And Sufficient Condition ◽

Summability Methods ◽

The Riemann Zeta Function ◽

Riemann Zeta ◽

Summability Matrix ◽

Necessary And Sufficient

This paper is a study of summability methods that are based on the Riemann Zeta function. A limitation theorem is proved which gives a necessary condition for a sequencexto be zeta summable. A zeta summability matrixZtassociated with a real sequencetis introduced; a necessary and sufficient condition on the sequencetsuch thatZtmapsl1tol1is established. Results comparing the strength of the zeta method to that of well-known summability methods are also investigated.

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THE FINITE SUM OF THE PRODUCTS OF TWO TOEPLITZ OPERATORS

Journal of the Australian Mathematical Society ◽

10.1017/s1446788708000128 ◽

2009 ◽

Vol 86 (1) ◽

pp. 45-60 ◽

Cited By ~ 2

Author(s):

XUANHAO DING

Keyword(s):

Toeplitz Operator ◽

Finite Rank ◽

Toeplitz Operators ◽

Necessary Condition ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Finite Rank Perturbation ◽

Sum Of Products ◽

Finite Sum ◽

Necessary And Sufficient

AbstractWe consider in this paper the question of when the finite sum of products of two Toeplitz operators is a finite-rank perturbation of a single Toeplitz operator on the Hardy space over the unit disk. A necessary condition is found. As a consequence we obtain a necessary and sufficient condition for the product of three Toeplitz operators to be a finite-rank perturbation of a single Toeplitz operator.

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On Modelling AM/AM and AM/PM Conversions via Volterra Series

International Journal of Electronics and Telecommunications ◽

10.1515/eletel-2016-0036 ◽

2016 ◽

Vol 62 (3) ◽

pp. 267-272

Author(s):

Andrzej Borys ◽

Wiesław Sieńko

Keyword(s):

Power Amplifiers ◽

Transfer Functions ◽

Volterra Series ◽

Polynomial Coefficient ◽

Necessary Condition ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Nonlinear Transfer ◽

Necessary And Sufficient ◽

Nonzero Polynomial

Abstract In this paper, we present the expressions, not published up to now, that describe the AM/AM and AM/PM conversions of communication power amplifiers (PAs) via the Volterra series based nonlinear transfer functions. Furthermore, we present a necessary and sufficient condition of occurrence of the nonzero values of AM/PM conversion in PAs. Moreover, it has been shown that Saleh’s approach and related ones, which foresee nonzero level of AM/PM conversion, are not models without memory. It has been also shown that using a polynomial description of a PA does not lead to a nonzero AM/PM conversion. Moreover, a necessary condition of occurrence of an AM/AM conversion in this kind of modelling is existence of at least one nonzero polynomial coefficient associated with its odd terms of degree greater than one.

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Some results concerning frames in Banach spaces

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.38.2007.80 ◽

2007 ◽

Vol 38 (3) ◽

pp. 267-276 ◽

Cited By ~ 3

Author(s):

S. K. Kaushik

Keyword(s):

Finite Number ◽

Banach Spaces ◽

Necessary Condition ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Linearly Independent ◽

Banach Frame ◽

Minimal Sequence ◽

Definition Of ◽

Necessary And Sufficient

A necessary and sufficient condition for the associated sequence of functionals to a complete minimal sequence to be a Banach frame has been given. We give the definition of a weak-exact Banach frame, and observe that an exact Banach frame is weak-exact. An example of a weak-exact Banach frame which is not exact has been given. A necessary and sufficient condition for a Banach frame to be a weak-exact Banach frame has been obtained. Finally, a necessary condition for the perturbation of a retro Banach frame by a finite number of linearly independent vectors to be a retro Banach frame has been given.

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Analysing Willerding’s formula for solving the planar three point resection problem

Journal of Applied Geodesy ◽

10.1515/jag-2018-0037 ◽

2019 ◽

Vol 13 (1) ◽

pp. 27-31

Author(s):

Gerhard Heindl

Keyword(s):

Mathematical Problem ◽

Autonomous Robot ◽

Necessary Condition ◽

Sufficient Condition ◽

Robot Localization ◽

Necessary And Sufficient Condition ◽

Necessary And Sufficient

Abstract The main mathematical problem in the planar three point resection problem of surveying is to find a necessary and sufficient condition that a point on a plane is uniquely determined if the directions from that point to three given points are known only up to an unknown offset. It will be shown in this paper that such a condition is the applicability of Willerding’s formula for computing the point in question, and that this condition is equivalent to the well-known necessary condition that the four considered points are not located on a circle or a line. Because of this result, the easy evaluation and the short derivation of Willerding’s formula, it can be expected, that this formula will be widely used in surveying, and also for autonomous robot localization.

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On An Affine Connection Which Admits A Volume-Like Form

Canadian Mathematical Bulletin ◽

10.4153/cmb-1990-077-6 ◽

1990 ◽

Vol 33 (4) ◽

pp. 482-488 ◽

Cited By ~ 1

Author(s):

D. P. Chi ◽

Y. D. Yoon

Keyword(s):

Affine Connection ◽

Riemannian Metric ◽

Necessary Condition ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Riemannian Connection ◽

Cech Cohomology ◽

Necessary And Sufficient

AbstractA necessary and sufficient condition to obtain a volumelike form from an affine connection is given in terms of the Čech cohomology, after the volume-like form is naturally defined without a Riemannian metric. A necessary condition for an affine connection to be a Riemannian connection for some metric is also given.

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