An Optimal Estimate for the Anisotropic Logarithmic Potential

This paper introduces the new annulus body to establish the optimal lower bound for the anisotropic logarithmic potential as the complement to the theory of its upper bound estimate which has already been investigated. The connections with convex geometry analysis and some metric properties are also established. For the application, a polynomial dual log-mixed volume difference law is deduced from the optimal estimate.

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An Optimal Lower Bound for Hierarchical Universal Solutions for TSP on the Plane

Lecture Notes in Computer Science - Computing and Combinatorics ◽

10.1007/978-3-030-58150-3_18 ◽

2020 ◽

pp. 222-233

Author(s):

Patrick Eades ◽

Julián Mestre

Keyword(s):

Lower Bound ◽

Universal Solutions ◽

Optimal Lower Bound

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An optimal lower bound for the discrepancy of c-uniformly distributed functions modulo

Indagationes Mathematicae (Proceedings) ◽

10.1016/1385-7258(88)90004-2 ◽

1988 ◽

Vol 91 (1) ◽

pp. 21-28

Author(s):

Michael Drmota

Keyword(s):

Lower Bound ◽

Optimal Lower Bound

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On the Inf-Sup Constant of a Triangular Spectral Method for the Stokes Equations

Computational Methods in Applied Mathematics ◽

10.1515/cmam-2016-0011 ◽

2016 ◽

Vol 16 (3) ◽

pp. 507-522 ◽

Cited By ~ 4

Author(s):

Yanhui Su ◽

Lizhen Chen ◽

Xianjuan Li ◽

Chuanju Xu

Keyword(s):

Lower Bound ◽

Error Estimate ◽

Spectral Method ◽

Stokes Equations ◽

Necessary Condition ◽

Well Posedness ◽

Saddle Point Problems ◽

Numerical Examples ◽

Lbb Condition ◽

Optimal Lower Bound

AbstractThe Ladyženskaja–Babuška–Brezzi (LBB) condition is a necessary condition for the well-posedness of discrete saddle point problems stemming from discretizing the Stokes equations. In this paper, we prove the LBB condition and provide the (optimal) lower bound for this condition for the triangular spectral method proposed by L. Chen, J. Shen, and C. Xu in [3]. Then this lower bound is used to derive an error estimate for the pressure. Some numerical examples are provided to confirm the theoretical estimates.

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An optimal lower bound for nonregular languages

Information Processing Letters ◽

10.1016/0020-0190(94)90018-3 ◽

1994 ◽

Vol 52 (6) ◽

pp. 339 ◽

Cited By ~ 3

Author(s):

A. Bertoni ◽

Carlo Mereghetti ◽

Giovanni Pighizzini

Keyword(s):

Lower Bound ◽

Optimal Lower Bound

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Extreme Values of the Riemann Zeta Function on the 1-Line

International Mathematics Research Notices ◽

10.1093/imrn/rnx331 ◽

2017 ◽

Vol 2019 (22) ◽

pp. 6924-6932 ◽

Cited By ~ 5

Author(s):

Christoph Aistleitner ◽

Kamalakshya Mahatab ◽

Marc Munsch

Keyword(s):

Lower Bound ◽

Extreme Values ◽

Mean Square ◽

Self Similarity ◽

New Variant ◽

The Riemann Zeta Function ◽

Riemann Zeta ◽

The Mean ◽

Resonator Method ◽

Optimal Lower Bound

Abstract We prove that there are arbitrarily large values of t such that $|\zeta (1+it)| \geq e^{\gamma } (\log _{2} t +\log _{3} t) + \mathcal{O}(1)$. This essentially matches the prediction for the optimal lower bound in a conjecture of Granville and Soundararajan. Our proof uses a new variant of the “long resonator” method. While earlier implementations of this method crucially relied on a “sparsification” technique to control the mean-square of the resonator function, in the present paper we exploit certain self-similarity properties of a specially designed resonator function.

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An optimal lower bound on the number of variables for graph identification

COMBINATORICA ◽

10.1007/bf01305232 ◽

1992 ◽

Vol 12 (4) ◽

pp. 389-410 ◽

Cited By ~ 173

Author(s):

Jin-Yi Cai ◽

Martin F�rer ◽

Neil Immerman

Keyword(s):

Lower Bound ◽

Optimal Lower Bound

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An asymptotically optimal lower bound on the OBDD size of the middle bit of multiplication for the pairwise ascending variable order

Discrete Applied Mathematics ◽

10.1016/j.dam.2010.03.002 ◽

2010 ◽

Vol 158 (11) ◽

pp. 1195-1204 ◽

Cited By ~ 1

Author(s):

Martin Sauerhoff

Keyword(s):

Lower Bound ◽

Variable Order ◽

Asymptotically Optimal ◽

Optimal Lower Bound

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An optimal lower bound for turing machines with one work tape and a two-way input tape

Structure in Complexity Theory - Lecture Notes in Computer Science ◽

10.1007/3-540-16486-3_103 ◽

1986 ◽

pp. 249-264 ◽

Cited By ~ 7

Author(s):

Wolfgang Maass ◽

Georg Schnitger

Keyword(s):

Lower Bound ◽

Turing Machines ◽

Input Tape ◽

Optimal Lower Bound

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A Nearly Optimal Lower Bound on the Approximate Degree of AC^0

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) ◽

10.1109/focs.2017.10 ◽

2017 ◽

Cited By ~ 1

Author(s):

Mark Bun ◽

Justin Thaler

Keyword(s):

Lower Bound ◽

Optimal Lower Bound

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A note on the optimal lower bound pull-out capacity of inclined strip anchors in sand

Canadian Geotechnical Journal ◽

10.1139/t92-095 ◽

1992 ◽

Vol 29 (5) ◽

pp. 870-873 ◽

Cited By ~ 5

Author(s):

D. N. Singh ◽

P. K. Basudhar

Keyword(s):

Nonlinear Programming ◽

Finite Elements ◽

Lower Bound ◽

Key Words ◽

Excellent Agreement ◽

Limit Analysis ◽

Uplift Capacity ◽

Pull Out ◽

Predicted Values ◽

Optimal Lower Bound

A generalized procedure based on finite elements and nonlinear programming has been presented in this paper for finding the optimal lower bound pull-out capacity of inclined strip anchors in sands. The results obtained are compared with the values reported in the literature to validate the suggested method of analysis. The predicted values are found to be in excellent agreement with that of Meyerhof. Key words : limit analysis, lower bound, nonlinear programming, inclined anchors, uplift capacity.

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