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Non-additive Bounded Sets of Uniqueness in ℤ n
[chapter]

2014
*
Lecture Notes in Computer Science
*

*In*this paper we compute the proportion

*of*

*non*-

*additive*

*sets*

*of*

*uniqueness*with respect to

*additive*

*sets*

*in*a given grid A ⊂

*Z*

*n*,

*in*the important case when d coordinate directions are employed. ... It turns out that d + 1 represents the minimal number

*of*directions one needs

*in*

*Z*

*n*(

*n*≥ d ≥ 3), under the requirement that such directions span a d-dimensional subspace

*of*

*Z*

*n*. ...

*Non*-

*additive*

*Bounded*

*Set*

*of*

*Uniqueness*

*In*this section we study

*non*-

*additive*

*sets*

*of*

*uniqueness*contained

*in*a given grid A,

*in*the important case when S contains the coordinate directions. ...

##
###
On the Non-additive Sets of Uniqueness in a Finite Grid
[chapter]

2013
*
Lecture Notes in Computer Science
*

Between these two opposite situations there are also the

doi:10.1007/978-3-642-37067-0_25
fatcat:clwlwfucobf7rjqtrwb4syne7m
*non*-*additive**sets**of**uniqueness*, which deserve interest*in*Discrete Tomography, since their*unique*reconstruction cannot be derived via the*additivity*... Discrete lattice*sets*which are*additive*with respect to a given*set*S*of*lattice directions are*uniquely*determined by X-rays*in*the direction*of*S. ...*Non*-*additive**Sets**of**Uniqueness*By means*of*Theorem 1 we can check if a*set**of*four directions S*uniquely*determines*bounded**sets**in*a grid A = {(i, j) ∈*Z*2 : 0 ≤ i < m, 0 ≤ j <*n*}. ...##
###
Representing Yosida-Hewitt decompositions for classical and non-commutative vector measures

2001
*
Expositiones mathematicae
*

Let m be a

doi:10.1016/s0723-0869(01)80024-4
fatcat:xjd647mynbhs3bsk4o5zq5mnqm
*bounded*, real valued measure on a field*of**sets*. Then, by the Yosida-Hewitt theorem, m has a*unique*decomposition into the sum*of*a countably*additive*and a singular measure. ... From this we obtain a simple formula for the countably*additive*part*of*a (strongly*bounded*) vector measure. ... Let*N*be the*set**of*natural numbers. Let Q(*N*) be the collection*of*all*non*-empty finite subsets*of**N*, and partially order Q(*N*) by*set*inclusion. ...##
###
Entropy Amplification Property and the Loss for Writing on Dirty Paper

2008
*
IEEE Transactions on Information Theory
*

The objective

doi:10.1109/tit.2008.917675
fatcat:d6ax67vn5jfcnolpsairyjy7lu
*of*this work is to show that even*in*the basic input-constrained*additive*state*setting*, Y = X + S +*Z*, the encoder is sometimes unable to use the SI efficiently if the receiver does not ... Thus almost 100 %*of*the available capacity is lost*in*WDP*in*the presence*of*difference-*set*noise. ... Acknowledgement The authors are indebted to Dave Forney for referring them to difference*set*theory. They also thank Yuval Kochman for simplifying the proof*of*Theorem 1. ...##
###
On approximately additive functions

2011
*
Journal of Mathematical Analysis and Applications
*

Note that F = k∈

doi:10.1016/j.jmaa.2011.02.048
fatcat:yelhhadjprh5lmhfs6erlm3goy
*N*kV 1 m > m 1 1 Remark 4 . 4*In*view*of*the example given*in*Remark 1, the*boundedness**of*C*in*Theorem 10 is necessary for the*uniqueness*and continuity*of*A. ... The example given*in*Remark 1 shows that the*boundedness**of*C is necessary for the*uniqueness**of*A*in*Proposition 8. ...##
###
On the local k-elasticities of Puiseux monoids
[article]

2018
*
arXiv
*
pre-print

If M is an atomic monoid and x is a nonzero

arXiv:1712.00837v3
fatcat:b33thyvcmrg6bch7gtvbqyhise
*non*-unit element*of*M, then the*set**of*lengths L(x)*of*x is the*set**of*all possible lengths*of*factorizations*of*x, where the length*of*a factorization is the ...*In*a recent paper, F. Gotti and C. O'Neil studied the*sets**of*elasticities R(P) := {L(x)/L(x) : x ∈ P}*of*Puiseux monoids P. ... Because many*of*the factorization-related questions on integral domains are independent*of*the ring*additive*structure,*in*the last few decades the study*of*the phenomenon*of**non*-*unique*factorization has ...##
###
Some Fubini Theorems on product σ-algebras for non-additive measures

2008
*
International Journal of Approximate Reasoning
*

Since the seminal paper

doi:10.1016/j.ijar.2007.02.007
fatcat:wa26dzmsgva7rgs2mb3fhgdqqu
*of*Ghirardato, it is known that Fubini Theorem for*non*-*additive*measures can be available only for functions defined as "slice-comonotonic". ... We give different assumptions that provide such Fubini Theorems*in*the framework*of*product r-algebras. ... Some Fubini Theorems on iterated integrals for*non*-*additive*measures on product r-algebras R*N*f dv ¼ P A;A finite mðAÞ Á min f ðAÞ. So*Z**Z*f dv 1 dv 2 ¼*Z**N**Z**N*f ð:; x 2 Þdv 2 ! ...##
###
Sharing a River with Downstream Externalities

2019
*
Games
*

*In*

*addition*, we show that this result holds true for numerous extensions

*of*our model. ... We consider the problem

*of*efficient emission abatement

*in*a multi polluter

*setting*, where agents are located along a river

*in*which net emissions accumulate and induce negative externalities to downstream ... For the grand coalition

*N*= S

*z*, the

*non*-cooperative core upper

*bounds*are satisfied. ...

##
###
Page 234 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 63, Issue 4
[page]

1957
*
American Mathematical Society. Bulletin of the American Mathematical Society
*

Each

*non*-negative Baire measure ¢ on @® has a*unique*decomposition ¢=¢c+¢p into a*non*-negative Baire measure ¢c¢ identically zero on Baire*sets**of*the first category, plus a Baire measure ¢p minimal on ... Using the complex methods introduced*in*previous papers the following typical result is obtained: The two conditions (i) f(*z*)=e*) >. _, saz*/*n*!=o(1) as*z*@, |*z*| —Rez=O(1), (ii) S07_, svse=0(*N*?) ...##
###
Robust Control of Linear Systems With Disturbances Bounded in a State Dependent Set

2011
*
IEEE Transactions on Automatic Control
*

This technical note examines attractiveness and minimality

doi:10.1109/tac.2011.2141330
fatcat:hg7izqt7gbdztmxcpvdsr7eyyu
*of*invariant*sets*for linear systems subject to*additive*disturbances confined*in*a state-dependent*set*. ...*In*many practical applications, the disturbance may evolve*in*a compact*set*while being generated by a dynamic process with a given model and*bounded*input. ... Rakovic for his help, constructive comments, and suggestion*of*several steps*in*this development. ...##
###
On Statistical Methods in the Theory of Almost-Periodic Functions

1933
*
Proceedings of the National Academy of Sciences of the United States of America
*

Let pi, (P2, ... be a sequence

doi:10.1073/pnas.19.5.549
pmid:16587784
pmcid:PMC1086065
fatcat:j4woyco7hvgrnh6ovcuw2wkqxu
*of*monotone absolutely*additive**set*functions*of*uniformly*bounded*variation*in*J: (-M < x _ Ml; -M < y < M) converging to the monotone absolutely*additive**set*function so ... From a continuum*of*monotone absolutely*additive**set*functions (T(E)*of*uniformly*bounded*variation it is possible to select a sequence Ipo,(E) I such that as*n*becomes infinite (p"(R) approaches the limit ...##
###
Non-commutative automorphisms of bounded non-commutative domains

2016
*
Proceedings of the Royal Society of Edinburgh. Section A Mathematics
*

We establish rigidity (or

doi:10.1017/s0308210515000748
fatcat:2vtlmfkj6ffupg7dan77ftiy5u
*uniqueness*) theorems for*non*-commutative (NC) automorphisms that are natural extensions*of*classical results*of*H. Cartan and are improvements*of*recent results. ... We apply our results to NC domains consisting*of*unit balls*of*rectangular matrices. ... Unless an*additional*hypothesis*of*continuity (or*boundedness*) is added, nc-functions can behave badly. Example 3. ...##
###
Some Aspects in n-dimensional almost Periodic functions iii

2011
*
Revista de Matemática: Teoría y Aplicaciones
*

For this functions we find some

doi:10.15517/rmta.v11i2.241
fatcat:ywkqc55anze2tfgjkb4imxo2nq
*uniqueness**sets**in*R and R*n*. The paper finishes analizing the relation*of*this functions and the function sinc. ... The properties*of*almost periodical functions and some new results have been published*in*[CA1], [CA2] and [CA3]*In*this paper we show some new definitions*in*order to analize some singularities. ... The above statements can be formulated*in*R*N*, for example: {sin(*n*),*n*∈*Z**N*} is dense*in*[−1, 1]. Definition 1 Let G be any discreet*non*trivial*additive*group*of*R*N*. ...##
###
An Addition Theorem and Its Arithmetical Application

2000
*
Journal of Number Theory
*

Almost arithmetical multiprogressions appear as

doi:10.1006/jnth.2000.2521
fatcat:uqqsvpu7evhitm4btsljrxblna
*sets**of*lengths*in*rings*of*algebraic integers, and the*addition*theorem will be applied to an arithmetical situation again. Academic Press ... We prove an*addition*theorem stating that arbitrary sumsets*of*such*sets*are*of*the same type again. ... The best tool investigated so far for describing the*non*-*uniqueness*is the system*of**sets**of*lengths. We briefly recall some terminology. ...##
###
On stochastic set functions. I

1956
*
Acta Mathematica Hungarica
*

*Boundedness*

*of*

*sets*

*of*quantiles Let

*Z*be an arbitrary

*set*and ξ

*z*(

*z*∈

*Z*) a family

*of*random variables. Denote by Q(λ,

*z*) a λ-quantile

*of*the variable ξ

*z*. ... If the quantiles Q(λ,

*z*) can be chosen

*in*such a way that the

*set*{Q(λ,

*z*),

*z*∈

*Z*} is

*bounded*from below (from above), then we have If the quantiles Q(λ,

*z*) can be chosen

*in*such a way that the

*set*{Q( ... choice

*of*the quantiles Q(λ,

*z*) does not matter as

*in*this case the

*boundedness*(unboundedness)

*of*the

*sets*{Q(λ,

*z*),

*z*∈

*Z*} with a special choice

*of*the quantiles Q(λ,

*z*) implies the

*boundedness*

*of*the ...

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