scholarly journals Tame combing and almost convexity conditions

2010 ◽  
Vol 269 (3-4) ◽  
pp. 879-915 ◽  
Author(s):  
Sean Cleary ◽  
Susan Hermiller ◽  
Melanie Stein ◽  
Jennifer Taback
Keyword(s):  
Almost Convexity ◽  
Convexity Conditions

scholarly journals Sharp Rank-One Convexity Conditions in Planar Isotropic Elasticity for the Additive Volumetric-Isochoric Split

2021 ◽  
Vol 143 (2) ◽  
pp. 301-335
Author(s):  
Jendrik Voss ◽  
Ionel-Dumitrel Ghiba ◽  
Robert J. Martin ◽  
Patrizio Neff
Keyword(s):  
Differential Inequalities ◽  
Two Dimensional ◽  
Ellipticity Condition ◽  
One Dimensional ◽  
Suitable Sense ◽  
Precise Analysis ◽  
Rank One ◽  
Isotropic Elasticity ◽  
Convexity Conditions

AbstractWe consider the volumetric-isochoric split in planar isotropic hyperelasticity and give a precise analysis of rank-one convexity criteria for this case, showing that the Legendre-Hadamard ellipticity condition separates and simplifies in a suitable sense. Starting from the classical two-dimensional criterion by Knowles and Sternberg, we can reduce the conditions for rank-one convexity to a family of one-dimensional coupled differential inequalities. In particular, this allows us to derive a simple rank-one convexity classification for generalized Hadamard energies of the type $W(F)=\frac{\mu }{2} \hspace{0.07em} \frac{\lVert F \rVert ^{2}}{\det F}+f(\det F)$ W ( F ) = μ 2 ∥ F ∥ 2 det F + f ( det F ) ; such an energy is rank-one convex if and only if the function $f$ f is convex.

scholarly journals The Loop Shortening Property and Almost Convexity

2003 ◽  
Vol 102 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Murray J. Elder
Keyword(s):  
Almost Convexity

scholarly journals Some Janowski Type Harmonic q-Starlike Functions Associated with Symmetrical Points

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 629 ◽  
Author(s):  
Muhammad Arif ◽  
Omar Barkub ◽  
Hari Srivastava ◽  
Saleem Abdullah ◽  
Sher Khan
Keyword(s):  
Differential Operator ◽  
Harmonic Functions ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Partial Sums ◽  
Circular Region ◽  
Necessary And Sufficient ◽  
New Criterion ◽  
Symmetrical Points ◽  
Convexity Conditions

The motive behind this article is to apply the notions of q-derivative by introducing some new families of harmonic functions associated with the symmetric circular region. We develop a new criterion for sense preserving and hence the univalency in terms of q-differential operator. The necessary and sufficient conditions are established for univalency for this newly defined class. We also discuss some other interesting properties such as distortion limits, convolution preserving, and convexity conditions. Further, by using sufficient inequality, we establish sharp bounds of the real parts of the ratios of harmonic functions to its sequences of partial sums. Some known consequences of the main results are also obtained by varying the parameters.

scholarly journals Rational Growth and Almost Convexity of Higher-Dimensional Torus Bundles

2017 ◽  
Vol 2019 (13) ◽  
pp. 4004-4046
Author(s):  
Corey Bregman
Keyword(s):  
Unit Circle ◽  
Dimensional Torus ◽  
Torus Bundle ◽  
Generating Set ◽  
Growth Series ◽  
Torus Bundles ◽  
Almost Convex ◽  
Higher Dimensional ◽  
Finite Index Subgroup ◽  
Almost Convexity

AbstractGiven a matrix $A\in SL(N,\mathbb{Z})$, form the semidirect product $G=\mathbb{Z}^N\rtimes_A \mathbb{Z}$ where the $\mathbb{Z}$-factor acts on $\mathbb{Z}^N$ by $A$. Such a $G$ arises naturally as the fundamental group of an $N$-dimensional torus bundle which fibers over the circle. In this article, we prove that if $A$ has distinct eigenvalues not lying on the unit circle, then there exists a finite index subgroup $H\leq G$ possessing rational growth series for some generating set. In contrast, we show that if $A$ has at least one eigenvalue not lying on the unit circle, then $G$ is not almost convex for any generating set.

scholarly journals CONVEX REPLICA SYMMETRY BREAKING FROM POSITIVITY AND THERMODYNAMIC LIMIT

2004 ◽  
Vol 18 (04n05) ◽  
pp. 585-591 ◽  
Author(s):  
PIERLUIGI CONTUCCI ◽  
SANDRO GRAFFI
Keyword(s):  
Symmetry Breaking ◽  
Covariance Matrix ◽  
Thermodynamic Limit ◽  
Matrix Elements ◽  
Replica Symmetry ◽  
Replica Symmetry Breaking ◽  
Random Energy Model ◽  
Random Energy ◽  
The Matrix ◽  
Convexity Conditions

Consider a correlated Gaussian random energy model built by successively adding one particle (spin) into the system and imposing the positivity of the associated covariance matrix. We show that the validity of a recently isolated condition ensuring the existence of the thermodynamic limit forces the covariance matrix to exhibit the Parisi replica symmetry breaking scheme with a convexity conditions on the matrix elements.

scholarly journals ON NONRELATIVISTIC $Q\bar Q$ POTENTIAL VIA THE WILSON LOOP IN GALILEAN SPACETIME

2011 ◽  
Vol 26 (23) ◽  
pp. 1719-1724 ◽  
Author(s):  
HARYANTO M. SIAHAAN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wilson Loop ◽  
Quantum Field ◽  
Nonrelativistic Quantum ◽  
Dynamical Exponent ◽  
Galilean Symmetry ◽  
Convexity Conditions

We calculate the static Wilson loop from string/gauge correspondence to obtain the [Formula: see text] potential in nonrelativistic quantum field theory, i.e. CFT with Galilean symmetry. We analyze the convexity conditions13 for [Formula: see text] potential in this theory, and obtain restrictions for the acceptable dynamical exponent z.

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