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Constructing the demand function of a strictly convex preference relation
[article]

2016
*
arXiv
*
pre-print

We give conditions under which

arXiv:1611.02542v1
fatcat:vvxu4ip5pvaivkwbwwbpwhrfqa
*the*demand function*of*a strictly convex preference relation can be constructed. ... In*the*appendix we introduce Brouwer's*fan**theorem*(FT)*and**the*notion*of*a weakly (uniformly) continuous predicate,*and*we give a version*of**the*uniform continuity*theorem*for these predicates. ... If we are not interested in*uniqueness**of**maxima*, then we might suppose that ≻ only satisfies*the*weaker condition*of*being convex : for all x, y ∈ X*and*each t ∈ [0, 1], either (x + y)/2 x or (x + y)/ ...##
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Finding geodesics in a triangulated 2-sphere
[article]

2014
*
arXiv
*
pre-print

We apply

arXiv:1408.5949v2
fatcat:7h7zoypexfetvmhbf23nr5xnpi
*the*methods*of*thin position from knot theory to obtain a simple version*of**the*three geodesics*theorem*for*the*2-sphere [5]. ... In general these three geodesics may be unstable, corresponding, for example, to*the*three equators*of*an ellipsoid. ... Figure 6 . wheel,*fan*, planar lollipop,*and*their dual graphs 17.*Theorem*. Let T be a triangulation*of**the*2-sphere. Assume T with order O(T ) is in thin position. ...##
###
Page 527 of Mathematical Reviews Vol. 23, Issue 6B
[page]

1962
*
Mathematical Reviews
*

It
contains

*the*unknown maximum*of*density-contrast*and*is based on*maxima**of*|g”|*and*io'| to be deduced from observed g. . Kogbetliantz (Paris) Smith, R. A. ... 3023 51- f n ter- yyer ZOes Z0e8 y is*Fan*an lif.) 024 61- ‘ace ure His ‘is.) 025 39- ncy*and**and*ere*the*per 3 to ere in*and*nee*the*rth on- t to ller rk) 026 ible und )= ae 1/2, provided f"(z) <0*and*...##
###
Contingent solutions to the center manifold equation

1992
*
Annales de l'Institut Henri Poincare. Analyse non linéar
*

*the*map HE by

*the*Brouwer-Schauder-

*Fan*Fixed-Point

*Theorem*in locally convex spaces, i. e., a solution to

*the*equation (15). ...

*Existence*

*of*contingent solutions When cp is lipschitzian (

*and*thus, with linear growth), we denote by S~ (x, . )

*the*

*unique*solution to

*the*differential equation starting at x at time d. ... it is well known that when E converges to 0,

*the*solutions (xE ( . ), y£ ( . )) converges almost surely to a solution (x ( . ), y ( . )) to

*the*system

*of*differential (14) . ...

##
###
Page 1182 of Mathematical Reviews Vol. , Issue 93b
[page]

1993
*
Mathematical Reviews
*

These constructions depend on

*the**existence**of*primitive roots satisfying certain equations in finite fields.” 93b:94006 94A12 62E10 Iverson, Geoffrey J. (1-CA3-CG); Sheu, Ching*Fan*(1-CMU-PY) Characterizing ... It is then proven that*the*local*maxima**of**the*wavelet transform modulus detect*the*locations*of*irregular struc- 94 INFORMATION*AND*COMMUNICATION, CIRCUITS 1182 tures*and*provide numerical procedures ...##
###
Every contractible fan is locally connected at its vertex

1980
*
Transactions of the American Mathematical Society
*

We prove that each contractible

doi:10.1090/s0002-9947-1980-0574786-1
fatcat:4bj7agoa6rbsjonq7dkqmrvgjq
*fan*is locally connected at its vertex. It follows that every contractible*fan*is embeddable in*the*plane. This gives a solution to a problem raised by J. J. ... Charatonik*and*C. A. Eberhart. ...*The*author wishes to thank Professor A. Lelek for his encouragement*and*advice during*the*preparation*of*this paper. ...##
###
Some problems for typically real functions

1961
*
Canadian Journal of Mathematics - Journal Canadien de Mathematiques
*

For

doi:10.4153/cjm-1961-025-x
fatcat:ok6fsjieczacjl4magzp2ch7xe
*the*class S*of*normalized univalent functions in*the*unit circle*the*best known such problem is*of*course*the*problem*of*Gronwall (1) to determine*the**maxima**and**the*minima*of*|/(z)|*and*\f(z)\ for ... When f(x) is required to be increasing*the*solution*of**the*extremal problem is thus*uniquely*determined apart from its value at*the*point x = c.*THEOREM*1. ...##
###
Maximum norms of graphs and matrices, and their complements
[article]

2013
*
arXiv
*
pre-print

In this paper, we mainly study

arXiv:1302.1239v1
fatcat:ql5ss4df2nhtvg3wsnzohcsgr4
*the*trace norm*of**the*adjacency matrix*of*a graph, also known as*the*energy*of*graph. We give*the*maximum trace norms for*the*graph*and*its complement. ... In*the*last section*the*same questions are studied for Ky*Fan*norms. ... Acknowledgement This work was done while*the*second author was vistiting*the*University*of*Memphis. ...##
###
Page 4685 of Mathematical Reviews Vol. , Issue 90H
[page]

1990
*
Mathematical Reviews
*

Let

*the*class T have a*unique*mode at*the*point x = 0.*The*authors prove two limit*theorems*that show*the*relationships between Q*and*its two subclasses. ... There*exist*various bivariate*and*multivariate asymptotic (or sta- ble) distributions*of*extremes whose margins can be Gumbel, Fréchet or Weibull distributions*of*extremes (*maxima*or minima), mutually ...##
###
Page 6380 of Mathematical Reviews Vol. , Issue 2000i
[page]

2000
*
Mathematical Reviews
*

By applying our earlier results together with

*the**Fan*-Glicksberg fixed-point*theorem*, we prove some ex- istence results for implicit variational inequalities*and*implicit quasi-variational inequalities ... For*the*coincidence-type equation («) Lx = Nx, where L, F: X — X x Y*and*X, Y are partially ordered Banach spaces, a*theorem*is obtained which states that, under some additional conditions,*the**existence*...##
###
Page 3742 of Mathematical Reviews Vol. , Issue 84i
[page]

1984
*
Mathematical Reviews
*

(Russian)
Limit

*theorems*for random processes*and*statistical inference, pp. 6-19, 217, “*Fan*”, Tashkent, 1981. ... Author’s summary: “A quick*and*elementary proof*of*inequalities for*the*moments*of**the**maxima**of*Brownian motion stopped at an arbitrary time is given, together with a precise computation*of**the*constants ...##
###
Maximum Properties and Inequalities for the Eigenvalues of Completely Continuous Operators

1951
*
Proceedings of the National Academy of Sciences of the United States of America
*

*FAN*always solvable

*uniquely*for

*the*integer y since (i) 01(Xx)/d is an integer, (ii) X/d is prime to r/d. ...

*Of*course, any power

*of*a linear substitution is linear. But

*the*property

*of*

*the*last

*theorem*is not characteristic

*of*exponential

*and*linear substitutions. ... always solvable

*uniquely*for

*the*integer y since (i) 01(Xx)/d is an integer, (ii) X/d is prime to r/d. ...

##
###
Do constraints facilitate or inhibit creative problem solving: A theoretical explanation of two seemingly contradictory experimental studies

2012
*
2012 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS)
*

In this paper, we provide a theoretical explanation

doi:10.1109/nafips.2012.6291043
fatcat:okjde7c6mjduvc2qz4jrrmlcd4
*of*these two seemingly contradictory experimental results. ... that a natural*unique**existence**theorem*is equivalent to*the**fan**theorem*. ... " that contains*the**theorem*about*the*computability*of**unique*solutions. ...##
###
Stability of localized structures in non-local reaction-diffusion equations

1998
*
Methods and Applications of Analysis
*

These eigenvalues are shown to interlace

doi:10.4310/maa.1998.v5.n4.a2
fatcat:szrkovoffjbyjerp7t2vm45hb4
*the*eigenvalues*of*a related local Sturm-Liouville operator. An oscillation*theorem*for*the*corresponding non-local eigenfunctions also is established. ...*The*stability*of*non-homogeneous, steady state solutions*of*a scalar, non-local reaction-diffusion equation is considered. ... Kriegsmann constructs a locally*unique*1-pulse using*the*method*of*matched asymptotic expansions. Locally*unique*n-pulse solutions*of*(3.1) also*exist*[1] . ...##
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Distribution Endpoint Estimation Assessment for the use in Metaheuristic Optimization Procedure

2018
*
MENDEL
*

In

doi:10.13164/mendel.2018.1.093
fatcat:5g4qar5vabbp7bvrjv4lq3q3qy
*the*following paper, we give a short review*of**the*recent endpoint estimators derived on*the*basis*of*extreme value theory,*and*compare them by simulations. ... We discuss also*the*difficulties in their application*and*suitability*of**the*estimators for various optimization instances. ... -iii.)*of*various art with*unique*global*maxima*.*The*particular models are listed below. ...
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