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

Matthew Hendtlass
2016 arXiv   pre-print
We give conditions under which 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)/  ...

### Finding geodesics in a triangulated 2-sphere [article]

Abigail Thompson
2014 arXiv   pre-print
We apply the methods of thin position from knot theory to obtain a simple version of the three geodesics theorem for the 2-sphere .  ...  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

Jean-Pierre Aubin, Guiseppe Da Prato
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

Lex G. Oversteegen
1980 Transactions of the American Mathematical Society
We prove that each contractible 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

James A. Jenkins
1961 Canadian Journal of Mathematics - Journal Canadien de Mathematiques
For 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]

Vladimir Nikiforov, Xiying Yuan
2013 arXiv   pre-print
In this paper, we mainly study 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

K. Fan
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

Karen Villaverde, Olga Kosheleva, Martine Ceberio
2012 2012 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS)
In this paper, we provide a theoretical explanation 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

Amitabha Bose, Gregory A. Kriegsmann
1998 Methods and Applications of Analysis
These eigenvalues are shown to interlace 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  .  ...

### Distribution Endpoint Estimation Assessment for the use in Metaheuristic Optimization Procedure

Jan Holesovky
2018 MENDEL
In 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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