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1

Rush, J. A. "A lower bound on packing density." Inventiones Mathematicae 98, no. 3 (1989): 499–509. http://dx.doi.org/10.1007/bf01393834.

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2

Erdahl, R. M., and B. Jin. "The lower bound method for reduced density matrices." Journal of Molecular Structure: THEOCHEM 527, no. 1-3 (2000): 207–20. http://dx.doi.org/10.1016/s0166-1280(00)00494-2.

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3

Weinberg, David H., Jordi Miralda‐Escude, Lars Hernquist, and Neal Katz. "A Lower Bound on the Cosmic Baryon Density." Astrophysical Journal 490, no. 2 (1997): 564–70. http://dx.doi.org/10.1086/304893.

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4

Chen, Geng. "Optimal density lower bound on nonisentropic gas dynamics." Journal of Differential Equations 268, no. 7 (2020): 4017–28. http://dx.doi.org/10.1016/j.jde.2019.10.017.

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5

Mowchenko, J. T. "A lower bound on channel density after global routing." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 8, no. 5 (1989): 574–77. http://dx.doi.org/10.1109/43.24886.

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6

Kozma, Robert Thijs, and Jenő Szirmai. "New horoball packing density lower bound in hyperbolic 5-space." Geometriae Dedicata 206, no. 1 (2019): 1–25. http://dx.doi.org/10.1007/s10711-019-00473-x.

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7

Yang, Seungho, Jinhyoung Lee, and Hyunseok Jeong. "Entropic Lower Bound for Distinguishability of Quantum States." Advances in Mathematical Physics 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/683658.

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For a system randomly prepared in a number of quantum states, we present a lower bound for the distinguishability of the quantum states, that is, the success probability of determining the states in the form of entropy. When the states are all pure, acquiring the entropic lower bound requires only the density operator and the number of the possible states. This entropic bound shows a relation between the von Neumann entropy and the distinguishability.
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8

KOBAYASHI, MITSUO. "A NEW SERIES FOR THE DENSITY OF ABUNDANT NUMBERS." International Journal of Number Theory 10, no. 01 (2014): 73–84. http://dx.doi.org/10.1142/s1793042113500814.

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A natural number n is called abundant if the sum of proper divisors of n exceeds n. In 1933 Behrend determined bounds for the natural density d𝒜 of abundant numbers, with subsequent improvements leading to the 1998 bounds of Deléglise, 0.2474 < d𝒜 < 0.2480. We present a new infinite series expression for the density of abundant numbers which can be used to calculate an improved lower bound.
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9

Rama, S. Kalyana, and Tapobrata Sarkar. "Holographic principle during inflation and a lower bound on density fluctuations." Physics Letters B 450, no. 1-3 (1999): 55–60. http://dx.doi.org/10.1016/s0370-2693(99)00114-8.

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10

Naudts, Jan. "Escort Density Operators and Generalized Quantum Information Measures." Open Systems & Information Dynamics 12, no. 01 (2005): 13–22. http://dx.doi.org/10.1007/s11080-005-0483-5.

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Parameterized families of density operators are studied. A generalization of the lower bound of Cramér and Rao is formulated. It involves escort density operators. The notion of ϕ-exponential family is introduced. This family, together with its escort, optimizes the generalized lower bound. It also satisfies a maximum entropy principle and exhibits a thermodynamic structure in which entropy and free energy are related by Legendre transform.
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11

Seong, Jin-Taek. "Theoretical Bounds on Performance in Threshold Group Testing Schemes." Mathematics 8, no. 4 (2020): 637. http://dx.doi.org/10.3390/math8040637.

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A threshold group testing (TGT) scheme with lower and upper thresholds is a general model of group testing (GT) which identifies a small set of defective samples. In this paper, we consider the TGT scheme that require the minimum number of tests. We aim to find lower and upper bounds for finding a set of defective samples in a large population. The decoding for the TGT scheme is exploited by minimization of the Hamming weight in channel coding theory and the probability of error is also defined. Then, we derive a new upper bound on the probability of error and extend a lower bound from convent
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12

Wang, Jin Ru, and Yuan Zhou. "The Lower Bound of Density Estimation for Biased Data in Sobolev Spaces." Advanced Materials Research 765-767 (September 2013): 744–48. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.744.

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In this paper, we consider the density estimation problem from independent and identically distributed (i.i.d.) biased observations. We study the lower bound of convergence rates of density estimation over Sobolev spaces WrN(NN+) under the Lp risk by using Fanos lemma.
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13

Hirsch, Jonas, та Michele Marini. "Lower bound for the perimeter density at singular points of a minimizing cluster in ℝN". ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 1. http://dx.doi.org/10.1051/cocv/2019005.

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In this paper, we study the blow-ups of the singular points in the boundary of a minimizing cluster lying in the interface of more than two chambers. We establish a sharp lower bound for the perimeter density at those points and we prove that this bound is rigid, namely having the lowest possible density completely characterizes the blow-up.
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14

Chen, Senming, and Changjiang Zhu. "A lower bound for the density of the steady Navier–Stokes equations." Applied Mathematics Letters 98 (December 2019): 88–94. http://dx.doi.org/10.1016/j.aml.2019.05.043.

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15

Ouyang, Yu Hua, and Xiang Dong Jia. "Asymptotic Performance Analysis of Two-Way Opportunistic Relaying Channels." Applied Mechanics and Materials 347-350 (August 2013): 1419–24. http://dx.doi.org/10.4028/www.scientific.net/amm.347-350.1419.

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The work interests in the two-way opportunistic relaying (TWOR) system in which the analog network coding (ANC) employed. For the TWOR-ANC, we first present the traditional max-min best relay selection scheme as well as the corresponding closed-form analytical expressions for the cumulative distribution function (CDF) and the probability density function (PDF) of the end-to-end SNR. Then, to simplify the analysis of system performance, by using the approximation of the modified Bessel function of the second kind, , we obtain the performance bounds of the TWOR-ANC system. The analytical results
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16

Lovejoy, William S. "Bounds on the Optimal Age-at-First-Capture for Stochastic, Age-Structured Fisheries." Canadian Journal of Fisheries and Aquatic Sciences 43, no. 1 (1986): 101–7. http://dx.doi.org/10.1139/f86-011.

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This paper addresses the problem of optimally exploiting an age-structured fishery with stochastic, density-dependent recruitment; stochastic dynamics; and cohort-dependent prices, costs, catchabilities, and survival rates. Sufficient conditions are derived for an age-at-first-capture to be a necessary component of the optimal management regime, and a lower bound on this critical age is calculated. The method consists of replacing the stochastic, density-dependent model with more traditional (stochastic, density-independent and deterministic, density-independent) models which yield lower bound
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17

MARIN, L. "DYNAMICAL BOUNDS FOR STURMIAN SCHRÖDINGER OPERATORS." Reviews in Mathematical Physics 22, no. 08 (2010): 859–79. http://dx.doi.org/10.1142/s0129055x10004090.

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The Fibonacci Hamiltonian, that is a Schrödinger operator associated to a quasiperiodical Sturmian potential with respect to the golden mean has been investigated intensively in recent years. Damanik and Tcheremchantsev developed a method in [10] and used it to exhibit a non trivial dynamical upper bound for this model. In this paper, we use this method to generalize to a large family of Sturmian operators dynamical upper bounds and show at sufficently large coupling anomalous transport for operators associated to irrational number with a generic diophantine condition. As a counterexample, we
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18

Ghasemi Naraghi, Mehdi, and Yousef Alipouri. "Minimum variance lower bound estimation with Gaussian Process models." Transactions of the Institute of Measurement and Control 40, no. 6 (2017): 1799–807. http://dx.doi.org/10.1177/0142331217690802.

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In this paper, we utilize the probability density function of the data to estimate the minimum variance lower bound (MVLB) of a nonlinear system. For this purpose, the Gaussian Process (GP) model has been used. With this model, given a new input and based on past observations, we naturally obtained the variance of the predictive distribution of the future output, which enabled us to estimate MVLB as well as estimation uncertainty. Also, an advantage of the proposed method over others is its ability to estimate MVLB recursively. The application of this method to the real-life dynamic process (e
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19

Duong, Quang-huy, Heri Ramampiaro, Kjetil Nørvåg, and Thu-lan Dam. "Density Guarantee on Finding Multiple Subgraphs and Subtensors." ACM Transactions on Knowledge Discovery from Data 15, no. 5 (2021): 1–32. http://dx.doi.org/10.1145/3446668.

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Dense subregion (subgraph & subtensor) detection is a well-studied area, with a wide range of applications, and numerous efficient approaches and algorithms have been proposed. Approximation approaches are commonly used for detecting dense subregions due to the complexity of the exact methods. Existing algorithms are generally efficient for dense subtensor and subgraph detection, and can perform well in many applications. However, most of the existing works utilize the state-or-the-art greedy 2-approximation algorithm to capably provide solutions with a loose theoretical density guarantee.
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20

Kozma, Robert Thijs, and Jenő Szirmai. "New Lower Bound for the Optimal Ball Packing Density in Hyperbolic 4-Space." Discrete & Computational Geometry 53, no. 1 (2014): 182–98. http://dx.doi.org/10.1007/s00454-014-9634-1.

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21

Hislop, Peter D., and Peter Müller. "A lower bound for the density of states of the lattice Anderson model." Proceedings of the American Mathematical Society 136, no. 08 (2008): 2887–93. http://dx.doi.org/10.1090/s0002-9939-08-09361-1.

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22

Lellis, Camillo De, and Matteo Focardi. "Density lower bound estimates for local minimizers of the 2d Mumford–Shah energy." Manuscripta Mathematica 142, no. 1-2 (2013): 215–32. http://dx.doi.org/10.1007/s00229-012-0601-y.

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23

Kang, Kyu Ho. "The predictive density simulation of the yield curve with a zero lower bound." Journal of Empirical Finance 33 (September 2015): 51–66. http://dx.doi.org/10.1016/j.jempfin.2015.06.002.

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24

Buckley, Jenni M., Danny C. Leang, and Tony M. Keaveny. "Sensitivity of Vertebral Compressive Strength to Endplate Loading Distribution." Journal of Biomechanical Engineering 128, no. 5 (2006): 641–46. http://dx.doi.org/10.1115/1.2241637.

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The sensitivity of vertebral body strength to the distribution of axial forces along the endplate has not been comprehensively evaluated. Using quantitative computed tomography-based finite element models of 13 vertebral bodies, an optimization analysis was performed to determine the endplate force distributions that minimized (lower bound) and maximized (upper bound) vertebral strength for a given set of externally applied axial compressive loads. Vertebral strength was also evaluated for three generic boundary conditions: uniform displacement, uniform force, and a nonuniform force distributi
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25

Atserias, Albert, Ilario Bonacina, Susanna F. De Rezende, Massimo Lauria, Jakob Nordström, and Alexander Razborov. "Clique Is Hard on Average for Regular Resolution." Journal of the ACM 68, no. 4 (2021): 1–26. http://dx.doi.org/10.1145/3449352.

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We prove that for k ≪ 4√ n regular resolution requires length n Ω( k ) to establish that an Erdős–Rényi graph with appropriately chosen edge density does not contain a k -clique. This lower bound is optimal up to the multiplicative constant in the exponent and also implies unconditional n Ω( k ) lower bounds on running time for several state-of-the-art algorithms for finding maximum cliques in graphs.
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26

DASS, BAL KISHAN, and POONAM GARG. "BOUNDS FOR CODES CORRECTING/DETECTING REPEATED LOW-DENSITY BURST ERRORS." Discrete Mathematics, Algorithms and Applications 04, no. 04 (2012): 1250048. http://dx.doi.org/10.1142/s1793830912500486.

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This paper presents lower bound on the number of parity-check digits required for linear codes that correct m-repeated low-density burst errors of length b (fixed) with weight w or less (w ≤ b). An upper bound on the number of parity-check digits required for linear codes that are capable of detecting such m-repeated low-density bursts has also been derived.
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27

Moustrou, Philippe. "On the density of cyclotomic lattices constructed from codes." International Journal of Number Theory 13, no. 05 (2017): 1261–74. http://dx.doi.org/10.1142/s1793042117500695.

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Recently, Venkatesh improved the best known lower bound for lattice sphere packings by a factor [Formula: see text] for infinitely many dimensions [Formula: see text]. Here, we prove an effective version of this result, in the sense that we exhibit, for the same set of dimensions, finite families of lattices containing a lattice reaching this bound. Our construction uses codes over cyclotomic fields, lifted to lattices via Construction A. We also prove a similar result for families of symplectic lattices.
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28

Randall, Greg C., Kameron R. Hansen, Brian Jackson, and David T. Fullwood. "Lower-bound dislocation density mapping in microcoined tantalum using high-resolution electron backscatter diffraction." Materials Characterization 153 (July 2019): 318–27. http://dx.doi.org/10.1016/j.matchar.2019.04.033.

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29

Chen, Geng, Ronghua Pan, and Shengguo Zhu. "A polygonal scheme and the lower bound on density for the isentropic gas dynamics." Discrete & Continuous Dynamical Systems - A 39, no. 7 (2019): 4259–77. http://dx.doi.org/10.3934/dcds.2019172.

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30

Riba, J. "A Performance Lower Bound for Quadratic Timing Recovery Accounting for the Symbol Transition Density." IEEE Transactions on Signal Processing 52, no. 11 (2004): 3278–88. http://dx.doi.org/10.1109/tsp.2004.836536.

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31

Brustein, Ram, and A. J. M. Medved. "Proof of a universal lower bound on the shear viscosity to entropy density ratio." Physics Letters B 691, no. 2 (2010): 87–90. http://dx.doi.org/10.1016/j.physletb.2010.06.018.

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32

Brown, Lawrence D., and Roger H. Farrell. "A Lower Bound for the Risk in Estimating the Value of a Probability Density." Journal of the American Statistical Association 85, no. 412 (1990): 1147–53. http://dx.doi.org/10.1080/01621459.1990.10474988.

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33

Lin, Yuan, and L. B. Freund. "An lower bound on receptor density for stable cell adhesion due to thermal undulations." Journal of Materials Science 42, no. 21 (2007): 8904–10. http://dx.doi.org/10.1007/s10853-007-1720-9.

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34

Esposito, Luca. "Density lower bound estimate for local minimizer of free interface problem with volume constraint." Ricerche di Matematica 68, no. 2 (2018): 359–73. http://dx.doi.org/10.1007/s11587-018-0407-7.

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35

Tenzer, Robert, Ahmed Abdalla, and Peter Vajda. "The spherical harmonic representation of the gravitational field quantities generated by the ice density contrast." Contributions to Geophysics and Geodesy 40, no. 3 (2010): 207–23. http://dx.doi.org/10.2478/v10126-010-0009-1.

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The spherical harmonic representation of the gravitational field quantities generated by the ice density contrastWe derive the expressions for computing the ice density contrast stripping corrections to the topography corrected gravity field quantities by means of the spherical harmonics. The expressions in the spectral representation utilize two types of the spherical functions, namely the spherical height functions and the newly introduced lower-bound ice functions. The spherical height functions describe the global geometry of the upper topographic bound. The spherical lower-bound ice funct
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36

Lumban Gaol, Irvan, and Charles O. P. Marpaung. "Risk Assessment of Power Generated from a Wind Turbine in Different Climate Cities in Indonesia." International Journal of Smart Grid and Sustainable Energy Technologies 2, no. 1 (2019): 97–102. http://dx.doi.org/10.36040/ijsgset.v2i1.223.

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In this paper, a risk analysis based on Monte Carlo Simulation has been used to examine the power generated from a wind turbine. There are five cities are selected based on the wind speed to be examined the power density generated from the wind turbine. The cities are Kupang, Tanjung Pinang, Krinci, Kotabaru, and Pontianak. Among the five cities, Kupang has the highest wind speed, while Pontianak has the lowest wind speed. In this study, the wind speed is assumed to be an unspecified parameter or a random variable. The Monte Carlo Simulation is run by using a software @RISK. The results show t
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37

Sun, Jianwei, John P. Perdew, and Adrienn Ruzsinszky. "Semilocal density functional obeying a strongly tightened bound for exchange." Proceedings of the National Academy of Sciences 112, no. 3 (2015): 685–89. http://dx.doi.org/10.1073/pnas.1423145112.

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Because of its useful accuracy and efficiency, density functional theory (DFT) is one of the most widely used electronic structure theories in physics, materials science, and chemistry. Only the exchange-correlation energy is unknown, and needs to be approximated in practice. Exact constraints provide useful information about this functional. The local spin-density approximation (LSDA) was the first constraint-based density functional. The Lieb–Oxford lower bound on the exchange-correlation energy for any density is another constraint that plays an important role in the development of generali
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38

He, Ling-Bing, Jie Ji, and Ling-Xuan Shao. "Lower bound for the Boltzmann equation whose regularity grows tempered with time." Kinetic & Related Models 14, no. 4 (2021): 705. http://dx.doi.org/10.3934/krm.2021020.

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<p style='text-indent:20px;'>As a first step towards the general global-in-time stability for the Boltzmann equation with soft potentials, in the present work, we prove the quantitative lower bounds for the equation under the following two assumptions, which stem from the available energy estimates, i.e. (ⅰ). the hydrodynamic quantities (local mass, local energy, and local entropy density) are bounded (from below or from above) uniformly in time, (ⅱ). the Sobolev regularity for the solution grows tempered with time.</p>
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39

Sakurai, Yohei. "Comparison Geometry of Manifolds with Boundary under a Lower Weighted Ricci Curvature Bound." Canadian Journal of Mathematics 72, no. 1 (2018): 243–80. http://dx.doi.org/10.4153/s0008414x1800007x.

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AbstractWe study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound. We consider a curvature condition in which the weighted Ricci curvature is bounded from below by the density function. Under the curvature condition and a suitable condition for the weighted mean curvature for the boundary, we obtain various comparison geometric results.
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40

Newey, Whitney K., and James L. Powell. "Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions." Econometric Theory 6, no. 3 (1990): 295–317. http://dx.doi.org/10.1017/s0266466600005284.

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We consider the linear regression model with censored dependent variable, where the disturbance terms are restricted only to have zero conditional median (or other prespecified quantile) given the regressors and the censoring point. Thus, the functional form of the conditional distribution of the disturbances is unrestricted, permitting heteroskedasticity of unknown form. For this model, a lower bound for the asymptotic covariance matrix for regular estimators of the regression coefficients is derived. This lower bound corresponds to the covariance matrix of an optimally weighted censored leas
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41

Thomas, Peter J. "A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process." Journal of Applied Probability 48, no. 02 (2011): 420–34. http://dx.doi.org/10.1017/s0021900200007968.

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We prove that the first passage time density ρ(t) for an Ornstein-Uhlenbeck processX(t) obeying dX= -βXdt+ σdWto reach a fixed threshold θ from a suprathreshold initial conditionx0> θ > 0 has a lower bound of the form ρ(t) >kexp[-pe6βt] for positive constantskandpfor timestexceeding some positive valueu. We obtain explicit expressions fork,p, anduin terms of β, σ,x0, and θ, and discuss the application of the results to the synchronization of periodically forced stochastic leaky integrate-and-fire model neurons.
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42

Freund, L. B. "A lower bound on implant density to induce wafer splitting in forming compliant substrate structures." Applied Physics Letters 70, no. 26 (1997): 3519–21. http://dx.doi.org/10.1063/1.119219.

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43

Angilella, G. G. N., N. H. March, F. M. D. Pellegrino, and R. Pucci. "Proposed lower bound for the shear viscosity to entropy density ratio in some dense liquids." Physics Letters A 373, no. 10 (2009): 992–98. http://dx.doi.org/10.1016/j.physleta.2009.01.025.

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44

Thomas, Peter J. "A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process." Journal of Applied Probability 48, no. 2 (2011): 420–34. http://dx.doi.org/10.1239/jap/1308662636.

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We prove that the first passage time density ρ(t) for an Ornstein-Uhlenbeck process X(t) obeying dX = -β Xdt + σdW to reach a fixed threshold θ from a suprathreshold initial condition x0 > θ > 0 has a lower bound of the form ρ(t) > kexp[-pe6βt] for positive constants k and p for times t exceeding some positive value u. We obtain explicit expressions for k, p, and u in terms of β, σ, x0, and θ, and discuss the application of the results to the synchronization of periodically forced stochastic leaky integrate-and-fire model neurons.
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45

Nguyen, Quoc Khanh, Stefano Serra-Capizzano, and Eddie Wadbro. "On using a zero lower bound on the physical density in material distribution topology optimization." Computer Methods in Applied Mechanics and Engineering 359 (February 2020): 112669. http://dx.doi.org/10.1016/j.cma.2019.112669.

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46

Politis, Konstadinos, and Markos V. Koutras. "SOME NEW BOUNDS FOR THE RENEWAL FUNCTION." Probability in the Engineering and Informational Sciences 20, no. 2 (2006): 231–50. http://dx.doi.org/10.1017/s0269964806060141.

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In the literature, most of the bounds for the renewal function U(x) corresponding to a lifetime distribution F are given in terms of the first two moments of F only. The best general upper bound of this type is the one given in Lorden (1970). In the present article, we show that improved bounds can be obtained if one exploits the specific form of the distribution F. We derive a bound that improves upon Lorden's, at least on an interval [0,a) with a ≤ ∞, and we give both sufficient and necessary conditions for this improvement to hold uniformly for x ≥ 0. Refined upper as well as lower bounds a
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47

KOPPELMAN, DAVID M. "A LOWER BOUND ON THE AVERAGE PHYSICAL LENGTH OF EDGES IN THE PHYSICAL REALIZATION OF GRAPHS." Parallel Processing Letters 06, no. 01 (1996): 137–43. http://dx.doi.org/10.1142/s0129626496000145.

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The stereo-realization of a graph is the assignment of positions in Cartesian space to each of its vertices such that vertex density is bounded. A bound is derived on the average edge length in such a realization. It is similar to an earlier reported result, however the new bound can be applied to graphs for which the earlier result is not well suited. A more precise realization definition is also presented. The bound is applied to d-dimensional realizations of de Bruijn graphs, yielding an edge length of Ω((1−2−d)rn/d/(2n)), where r is the radix (number of distinct symbols) and n is the numbe
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48

Tjulin, A., A. I. Eriksson, and M. André. "Localization of wave fields in lower hybrid cavities." Annales Geophysicae 22, no. 8 (2004): 2951–59. http://dx.doi.org/10.5194/angeo-22-2951-2004.

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Abstract. We investigate lower hybrid wave trapping in cylindrically symmetric density depletions in the electrostatic approximation. Our investigation is inspired by previous observations of such trapping by spacecraft in the auroral region at altitudes up to about 2000km, and the recent discovery of this phenomenon at altitudes above 20000km in the inner magnetosphere. No particular shape is assumed for the density depletion, which need not be strictly zero outside some value of the radial coordinate r. Important previously known properties concerning parabolic density depletions extending t
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49

NAGY, DÁNIEL T. "On the Number of 4-Edge Paths in Graphs With Given Edge Density." Combinatorics, Probability and Computing 26, no. 3 (2016): 431–47. http://dx.doi.org/10.1017/s0963548316000389.

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We investigate the number of 4-edge paths in graphs with a given number of vertices and edges, proving an asymptotically sharp upper bound on this number. The extremal construction is the quasi-star or the quasi-clique graph, depending on the edge density. An easy lower bound is also proved. This answer resembles the classic theorem of Ahlswede and Katona about the maximal number of 2-edge paths, and a recent theorem of Kenyon, Radin, Ren and Sadun about k-edge stars.
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50

Rybin, Pavel, Kirill Andreev, and Victor Zyablov. "Error Exponents of LDPC Codes under Low-Complexity Decoding." Entropy 23, no. 2 (2021): 253. http://dx.doi.org/10.3390/e23020253.

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Abstract:
This paper deals with the specific construction of binary low-density parity-check (LDPC) codes. We derive lower bounds on the error exponents for these codes transmitted over the memoryless binary symmetric channel (BSC) for both the well-known maximum-likelihood (ML) and proposed low-complexity decoding algorithms. We prove the existence of such LDPC codes that the probability of erroneous decoding decreases exponentially with the growth of the code length while keeping coding rates below the corresponding channel capacity. We also show that an obtained error exponent lower bound under ML de
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