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Growth estimates for exp—log functions

1990
*
Journal of symbolic computation
*

This also provides another proof that the dominance problem

doi:10.1016/s0747-7171(08)80161-7
fatcat:yimpzqdqajhdfdf7wg5kvhe44y
*for**exp*-*log**functions*is Turing-reducible to the identity problem*for*constant terms. ...*Exp*-*log**functions*are those obtained from the constant 1 and the variable X by means of arithmetic operations and the*function*symbols*exp*() and logll. ... Firstly the identity problem*for**exp*-*log**functions*asks*for*a procedure to determine whether a given*exp*-*log*expression is identically zero. ...##
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New Insights into Modelling Bacterial Growth with Reference to the Fish Pathogen Flavobacterium psychrophilum

2020
*
Animals
*

In contrast with

doi:10.3390/ani10030435
pmid:32150847
pmcid:PMC7143051
fatcat:ssi7oqwsrnfyjotaaspyasfosi
*log*×*exp*and BAR,*log*× hyp can be easily manipulated mathematically allowing*for*simple algebraic expressions*for*time and microbial biomass at inflexion point, in addition to maximum ... The newly derived*functions*(*log*× hyp and*log*×*exp*), along with the Baranyi (BAR), simple logistic (*LOG*) and its modified form (MLOG) were evaluated based upon examination of residuals and measures of ... Using the parameter*estimates*from fitting*log*× hyp and*log*×*exp*to a given dataset, actual*growth*rate (Equation (9) ) can be calculated and plotted as a*function*of time. ...##
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Bayesian Inference of the Stochastic Gompertz Growth Model for Tumor Growth

2014
*
Communications for Statistical Applications and Methods
*

A stochastic Gompertz diffusion model

doi:10.5351/csam.2014.21.6.521
fatcat:xpxf5i25vvgenclrewi74dfmqi
*for*tumor*growth*is a topic of active interest as cancer is a leading cause of death in Korea. ... This likelihood is useful in providing a basis*for*the so-called continuous record or infill likelihood*function*and infill asymptotic. ... However, since Y t =*log*(X t /X 0 ), the probability density*function*of X t given X 0 = x 0 is f X t (x t |x 0 ) = 1 x t √ 2πσ 2 t*exp* (*log*( x t x 0 ) − m β ( 1 − e −βt ) + σ 2 ...##
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On the rate of growth of entire functions of fast growth

1963
*
Bulletin of the American Mathematical Society
*

The purpose of this note is to generalize the following well-known formula to give the order p and type a of an entire

doi:10.1090/s0002-9904-1963-10951-9
fatcat:on3xlnnbhvekjiqgddkee5aona
*function*/(s) = J^T-o a nZ n with M{r) =max| z |" r \f(z)\, that is [l; 2], ... X(3> is called the rank and i c<3> is called the title of the entire*function*. We call X( g > and / C( 3 > the rate of*growth*of the entire*function*of index q. Formulas*for*X (a) and K iq) . ... Consider f(x) =*exp*(q/p) x as a well defined solution of a simultaneous*functional*equation*exp*ltp] (f(x))=*exp*[tq] x (t = 0, ±1, ±2, • • • ) and*for*real r, define*exp*(r) (#) by uniform limit process ...##
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On the relation between maximum modulus, maximum term, and Taylor coefficients of an entire function

1985
*
Journal of Approximation Theory
*

*For*entire

*functions*of relatively slow

*growth*, a distinct increase of precision is achieved. Our approach originates in work by Hadamard. ... Relations are established between the quantities in the title in form of direct

*estimates*, instead of measuring the

*growth*of J" by its order, type, or some generalized order. ... In terms of the

*estimate*m(r) = O(A(r)) this means that we exclude

*functions*f

*for*which m(r) increases faster than

*exp*{a(

*log*r)*)

*for*some constant a > 0. ...

##
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BMOA estimates and radial growth of B_ϕ functions
[article]

2008
*
arXiv
*
pre-print

BMO

arXiv:0807.5131v1
fatcat:gxdes2d4czbrtfj757qpf2wp4i
*estimates*and the radial*growth*of Bloch*functions*have been studied by B. Korenblum [3]. The present paper contains some natural generalizations of these results. ... The space BMOA is the space of*functions*f ∈ H 1*for*which Mathematics Subject Classification: Primary 30E20, 30D50. 0 Key words and phrases: Bloch space, BMOA*estimates*, radial*growth*of*functions*. ... Korenblum*for*the Bloch space B are generalized*for*B φ . Note that the*function**log*(1 − z) ∈ B , however*log*2 (1 − z) / ∈ B. ...##
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Statistical Weight Kinetics Modeling and Estimation for Silica Nanowire Growth Catalyzed by Pd Thin Film

2011
*
IEEE Transactions on Automation Science and Engineering
*

Model

doi:10.1109/tase.2010.2070493
fatcat:2guhwzp6zrh2rbqwljyzreyrfa
*estimation*and comparison are conducted using both maximum likelihood*estimation*(MLE) and Bayesian approaches. ... We investigate six different weight kinetics models in predicting weight changes during*growth*. ... The*log*-likelihood*function**for*model 5 is: L 5 (θ, σ 2 1 , σ 2 2 ) = N i=1 {I t≤t0 [− 1 2*log*(σ 2 1 ) − 1 2σ 2 1 (y i − α 1*exp*(α 2 /t i )) 2 ] + I t>t0 [− 1 2*log*(σ 2 2 ) − 1 2σ 2 2 (y i − at i − b) ...##
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Generalized n-Laplacian: boundedness of weak solutions to the Dirichlet problem with nonlinearity in the critical growth range

2014
*
Open Mathematics
*

∈ L Φ(Ω) is a non-trivial continuous

doi:10.2478/s11533-013-0329-2
fatcat:3cabsarvajbslo6ne34bta2qvm
*function*and µ ≥ 0 is a small parameter. ... such that the space W 01 L Φ(Ω) is embedded into an exponential or multiple exponential Orlicz space, the nonlinearity f(x, t) has the corresponding critical*growth*, V(x) is a continuous potential, h ... Acknowledgements The author would like to thank Professors Andrea Cianchi, Pavel Drábek and Stanislav Hencl*for*fruitful discussions. ...##
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On Determining the Growth of Meromorphic Solutions of Algebraic Differential Equations Having Arbitrary Entire Coefficients

1973
*
Nagoya mathematical journal
*

In this paper, we treat the problem of determining the rate of

doi:10.1017/s0027763000015270
fatcat:oqds5ynognfk5iqez4ceujsf64
*growth*of meromorphic*functions*on the plane, which are solutions ofnthorder algebraic differential equations whose coefficients are arbitrary ... entire*functions*(i.e., equations of the form,Ω(z,y,dy/dz,• • •,dny/dzn) —0, whereΩis a polynomial iny,dy/dz,• • •,dny/dznwhose coefficients are arbitrary entire*functions*ofz.) ... ) (r +*log*+ N(r, y 0 ) +*log*+ N(r, Hence, in any case, the*growth*of a solution y Q can be*estimated*in terms of the counting*functions*N(r,y 0 ) and N(r,l/y Q )*for*the poles and zeros respectively, ...##
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On the Use of the Gompertz Model to Predict Microbial Thermal Inactivation Under Isothermal and Non-Isothermal Conditions

2011
*
Food Engineering Reviews
*

The versatility of the Gompertz model in describing kinetics with different shapes, varying from a

doi:10.1007/s12393-010-9032-2
fatcat:uqdqwgqdkbb3pnpr27fszenhdi
*log*-linear tendency till a complete sigmoidal shape, makes it attractive*for*predictive purposes, both ... In this field, the use of mathematical models that describe the microorganisms' kinetics in such conditions is an important tool*for*convenient design, control and optimization of efficient processes. ... [15] also proposed a modification*for*the Gompertz equation, as follows:*log*N ¼ A þ C*exp*Àexp ÀBðt À MÞ ½ f g ð3Þ and considered:*Growth*rate ¼ BC e ð4Þ lag ¼ M À 1 B ð5Þ Generation time ¼ 24 Â logð2Þ ...##
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Growth/survival of Salmonella enteritidis on fresh poultry and fish stored under vacuum or modified atmosphere

1996
*
Letters in Applied Microbiology
*

The essential oil and packing treatments had remarkable delaying effects on the

doi:10.1111/j.1472-765x.1996.tb00044.x
pmid:8987452
fatcat:ptctoi56xjgk3atrphf5hbgfre
*growth*of S. typhimurium. ... The structural identifiability properties of the Baranyi model were analyzed in fitting the effect of oregano and thyme essential oils on*growth*of Salmonella typhimurium in rainbow trout stored under ... These parameters can be*estimated*as following (Toğrul and Arslan, 2004) : n n i=1 1 =*log**log*/*log*×100*exp*,i pre,i*exp*,i MPE N N N (8) n i=1 pre,i*exp*,i 1 = n*log**log*MBE N N (9) n n i=1 1/2*exp*,i ...##
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USING NONLINEAR FIXED AND MIXED MODELS WITH SWITCHING FUNCTIONS TO ALLOW FOR HORMESIS IN GROWTH OF ESCHERICHIA COLI

2007
*
Conference on Applied Statistics in Agriculture
*

Classic bacterial

doi:10.4148/2475-7772.1112
fatcat:6ry6sohh2rai3dwbse6bow5b3i
*growth*curves display an increase in optical density over time. In this paper, we use the logistic*function*to model*growth*in optical density of E. coli over time. ... We examine several switching*functions*that allow*for*the effect of hormesis and compare the ability of nonlinear fixed and mixed models to detect the presence of hormesis. ... These changes can be described by logistic or*log*-logistic regression models. The models provide such*estimates*as maximum optical density, maximum rate of*growth*, and time to maximum rate of*growth*. ...##
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Growth estimates of entire functions with the help of their relative L^{∗}-types and relative L^{∗}- weak types

2018
*
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
*

In this paper we attempt to prove some results related to the

doi:10.31801/cfsuasmas.443685
fatcat:ycr5n4seabditjl63x2azpwe34
*growth*rates of entire*functions*on the basis of relative L -type and relative L -weak type of an entire*function*with respect to another entire ...*function*. ... 1 inf*log**log*M f (r)*log*re L(r) : An entire*function**for*which L -order and L -lower order are the same is said to be of regular L -*growth*. ...##
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Nonlinear Growth Models for Modeling Oil Palm Yield Growth

2005
*
Journal of Mathematics and Statistics
*

This study provided the basic needs of parameters

doi:10.3844/jmssp.2005.225.232
fatcat:dbtfmrrfszhdpagegvdsws5qne
*estimation**for*nonlinear*growth*model such as partial derivatives of each model, determination of initial values*for*each parameter and statistical tests ... This study found that the Gompertz, logistic,*log*-logistic, Morgan-Mercer-Flodin and Chapman-Richard*growth*models have the ability*for*quantifying a*growth*phenomenon that exhibit a sigmoid pattern over ... The parameter*estimates**for*the logistic, Gompertz, negative exponential, monomolecular and Morgan-Mercer-Flodin*growth**functions*are all statistically significant at the 5% level. ...##
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Nonlinear Growth Models for Modeling Oil Palm Yield Growth

2005
*
Journal of Mathematics and Statistics
*

This study provided the basic needs of parameters

doi:10.3844/jmssp.2005.225.233
fatcat:wo2pec46zndhhg3dfeb2g6zapa
*estimation**for*nonlinear*growth*model such as partial derivatives of each model, determination of initial values*for*each parameter and statistical tests ... This study found that the Gompertz, logistic,*log*-logistic, Morgan-Mercer-Flodin and Chapman-Richard*growth*models have the ability*for*quantifying a*growth*phenomenon that exhibit a sigmoid pattern over ... The parameter*estimates**for*the logistic, Gompertz, negative exponential, monomolecular and Morgan-Mercer-Flodin*growth**functions*are all statistically significant at the 5% level. ...
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