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369
Edge Isoperimetric Problems on Graphs
 Bolyai Math. Series
"... We survey results on edge isoperimetric problems on graphs, present some new results and show some applications of such problems in combinatorics and computer science. 1 Introduction Let G = (V G ; EG ) be a simple connected graph. For a subset A ` VG denote I G (A) = f(u; v) 2 EG j u; v 2 Ag; ` G ..."
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Cited by 22 (6 self)
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We survey results on edge isoperimetric problems on graphs, present some new results and show some applications of such problems in combinatorics and computer science. 1 Introduction Let G = (V G ; EG ) be a simple connected graph. For a subset A ` VG denote I G (A) = f(u; v) 2 EG j u; v 2 Ag
Generalized Isoperimetric Problem
, 1997
"... In this paper the differential equations describing the minimal length curves satisfying the integral constraining relations of a general type are obtained. Moreover, an additional necessary condition supplementing Pontryagin maximum principle for the generalized isoperimetric problem is established ..."
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Cited by 2 (0 self)
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In this paper the differential equations describing the minimal length curves satisfying the integral constraining relations of a general type are obtained. Moreover, an additional necessary condition supplementing Pontryagin maximum principle for the generalized isoperimetric problem
Isoperimetric Problems in Discrete Spaces
 Bolyai Soc. Math. Stud
, 1994
"... This paper is a survey on discrete isoperimetric type problems. We present here as some known facts about their solutions as well some new results and demonstrate a general techniques used in this area. The main attention is paid to the unit cube and cube like structures. Besides some applications o ..."
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Cited by 30 (5 self)
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This paper is a survey on discrete isoperimetric type problems. We present here as some known facts about their solutions as well some new results and demonstrate a general techniques used in this area. The main attention is paid to the unit cube and cube like structures. Besides some applications
NONLOCAL ISOPERIMETRIC PROBLEMS
"... Abstract. We characterize the volumeconstrained minimizers of a nonlocal free energy given by the difference of the tperimeter and the sperimeter, with s smaller than t. Exploiting the quantitative fractional isoperimetric inequality, we show that balls are the unique minimizers if the volume is ..."
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is sufficiently small, depending on t − s, while the existence vs. nonexistence of minimizers for large volumes remains open. We also consider the corresponding isoperimetric problem and prove existence and regularity of minimizers for all s, t. When s = 0 this problem reduces to the fractional isoperimetric
ON A NONLOCAL ISOPERIMETRIC PROBLEM ON THE
"... Abstract. In this article we analyze the minimization of a nonlocal isoperimetric problem (NLIP) posed on the 2sphere. After establishing the regularity of the free boundary of minimizers, we characterize two critical points of the functional describing (NLIP): the single cap and the double cap. W ..."
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Abstract. In this article we analyze the minimization of a nonlocal isoperimetric problem (NLIP) posed on the 2sphere. After establishing the regularity of the free boundary of minimizers, we characterize two critical points of the functional describing (NLIP): the single cap and the double cap
Generalized Isoperimetric Problem
 Journal of Mathematical Systems, Estimation, and Control
, 1997
"... In this paper the differential equations describing the minimal length curves satisfying the integral constraining relations of a general type are obtained. Moreover, an additional necessary condition supplementing Pontryagin maximum principle for the generalized isoperimetric problem is established ..."
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In this paper the differential equations describing the minimal length curves satisfying the integral constraining relations of a general type are obtained. Moreover, an additional necessary condition supplementing Pontryagin maximum principle for the generalized isoperimetric problem
Periodic Phase . . . Isoperimetric Problems
, 2006
"... We consider two well known variational problems associated with the phenomenon of phase separation: the isoperimetric problem and minimization of the Cahn–Hilliard energy. The two problems are related through a classical result in Γconvergence and we explore the behavior of global and local minimiz ..."
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We consider two well known variational problems associated with the phenomenon of phase separation: the isoperimetric problem and minimization of the Cahn–Hilliard energy. The two problems are related through a classical result in Γconvergence and we explore the behavior of global and local
Recent advances in isoperimetric problems
"... The origin of isoperimetric problems is lost in the beginning of the history of Mathematics. We know that Greek mathematicians treated the isoperimetric properties of the circle and the sphere, the last of which can be formulated in two equivalent ways: (i) among all bodies of the same volume, the r ..."
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Cited by 1 (0 self)
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The origin of isoperimetric problems is lost in the beginning of the history of Mathematics. We know that Greek mathematicians treated the isoperimetric properties of the circle and the sphere, the last of which can be formulated in two equivalent ways: (i) among all bodies of the same volume
The Isoperimetric Problem For Pinwheel Tilings
 Communication in Mathematical Physics
, 1994
"... In aperiodic "pinwheel" tilings of the plane there exist unions of tiles with ratio (area)/(perimeter) 2 arbitrarily close to that of a circle. Such approximate circles can be constructed with arbitrary center and any sufficiently large radius. The existence of such circles follows from ..."
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Cited by 11 (0 self)
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Research supported in part by an NSF Mathematical Sciences Postdoctoral Fellowship and Texas ARP Grant 003658037 I. Introduction and Statement of Results The classic isoperimetric problem in the plane, which asks for the curve of least length enclosing some fixed area, has stimulated much important
Asymptotical Isoperimetric Problem
"... Let X and Y be two finite sets. Let ρ: X × Y → [0, +∞) be a distortion measure. The distortion measure defined on the power sets ρn: X n ×Y n → [0, +∞) is given by the formula ρn(x n,y n) = 1 n n∑ ρ(xi,yi) (1) where x n = (x1,...,xn) and y n = (y1,...,yn) (∀i, xi ∈ X and yi ∈ Y) are elements of the ..."
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of the power sets X n, Y n, respectively. Let A ⊂ X n. The dneighbor of A is defined by i=1 Γ d (A) = {y n ∈ Y n: ∃x n ∈ A s.t. ρn(x n,y n) ≤ d}. (2) Define Gn(M,d) = min{Γ d (A)  : A  ≥ M}. (3) The isoperimetric problem is to determine this function and to find subsets A of X n for which the minimum
Results 1  10
of
369