-
1
-
-
84973989029
-
Solution of the equation zexp(z)=a
-
Wright E.M. Solution of the equation zexp(z)=a. Proc. R. Soc. Edinb. A 1959, 65:193-203.
-
(1959)
Proc. R. Soc. Edinb. A
, vol.65
, pp. 193-203
-
-
Wright, E.M.1
-
3
-
-
0020072824
-
On the solution to the Michaelis-Menten equation
-
Beal S.L. On the solution to the Michaelis-Menten equation. J. Pharmacokinet. Biopharm. 1982, 10:109-119.
-
(1982)
J. Pharmacokinet. Biopharm.
, vol.10
, pp. 109-119
-
-
Beal, S.L.1
-
4
-
-
0001930735
-
Lambert's W function in Maple
-
Corless R.M., Gonnet G.H., Hare D.E.G., Jeffrey D.J. Lambert's W function in Maple. Maple Tech. Newslett. 1993, 9:12-22.
-
(1993)
Maple Tech. Newslett.
, vol.9
, pp. 12-22
-
-
Corless, R.M.1
Gonnet, G.H.2
Hare, D.E.G.3
Jeffrey, D.J.4
-
5
-
-
21444436092
-
On the Lambert W function
-
Corless R.M., Gonnet G.H., Hare D.E.G., Jeffrey D.J., Knuth D.E. On the Lambert W function. Adv. Comput. Math. 1996, 5:329-359.
-
(1996)
Adv. Comput. Math.
, vol.5
, pp. 329-359
-
-
Corless, R.M.1
Gonnet, G.H.2
Hare, D.E.G.3
Jeffrey, D.J.4
Knuth, D.E.5
-
6
-
-
0020900427
-
Computation of the explicit solution to the Michaelis-Menten equation
-
Beal S.L. Computation of the explicit solution to the Michaelis-Menten equation. J. Pharmacokinet. Biopharm. 1983, 11:641-657.
-
(1983)
J. Pharmacokinet. Biopharm.
, vol.11
, pp. 641-657
-
-
Beal, S.L.1
-
7
-
-
0000842764
-
Some applications of the Lambert W function to physics
-
Valluri S.R., Jeffrey D.J., Corless R.M. Some applications of the Lambert W function to physics. Can. J. Phys. 2000, 78:823-831.
-
(2000)
Can. J. Phys.
, vol.78
, pp. 823-831
-
-
Valluri, S.R.1
Jeffrey, D.J.2
Corless, R.M.3
-
8
-
-
0001951498
-
Analytical approximations for real values of the Lambert W-function
-
Barry D.A., Parlange J.Y., Li L., Prommer H., Cunningham C.J., Stagnitti F. Analytical approximations for real values of the Lambert W-function. Math. Comput. Simul. 2000, 53:95-103.
-
(2000)
Math. Comput. Simul.
, vol.53
, pp. 95-103
-
-
Barry, D.A.1
Parlange, J.Y.2
Li, L.3
Prommer, H.4
Cunningham, C.J.5
Stagnitti, F.6
-
9
-
-
79953741618
-
The Lambert W-function and some of their integrals: a case study of high-precision computation
-
Gautschi W. The Lambert W-function and some of their integrals: a case study of high-precision computation. Numer. Algor. 2011, 57:27-34.
-
(2011)
Numer. Algor.
, vol.57
, pp. 27-34
-
-
Gautschi, W.1
-
10
-
-
0000824932
-
Algorithm 743: a Fortran routine for calculating real values of the W-function
-
Barry D.A., Barry S.J., Culligan-Hensley P.J. Algorithm 743: a Fortran routine for calculating real values of the W-function. ACM Trans. Math. Softw. 1995, 21:172-181.
-
(1995)
ACM Trans. Math. Softw.
, vol.21
, pp. 172-181
-
-
Barry, D.A.1
Barry, S.J.2
Culligan-Hensley, P.J.3
-
11
-
-
0036704550
-
Explicit infiltration equations and the Lambert W-function
-
Parlange J.Y., Barry D.A., Haverkamp R. Explicit infiltration equations and the Lambert W-function. Adv. Water Resour. 2002, 25:1119-1124.
-
(2002)
Adv. Water Resour.
, vol.25
, pp. 1119-1124
-
-
Parlange, J.Y.1
Barry, D.A.2
Haverkamp, R.3
-
12
-
-
24644462768
-
Green-Ampt approximations
-
Barry D.A., Parlange J.Y., Li L., Jeng D.S., Crapper M. Green-Ampt approximations. Adv. Water Resour. 2005, 28:1003-1009.
-
(2005)
Adv. Water Resour.
, vol.28
, pp. 1003-1009
-
-
Barry, D.A.1
Parlange, J.Y.2
Li, L.3
Jeng, D.S.4
Crapper, M.5
-
13
-
-
0037015350
-
Kinetics of multilayer Langmuirian adsorption
-
Vinokurov I.A., Kankare J. Kinetics of multilayer Langmuirian adsorption. Langmuir 2002, 18:6789-6795.
-
(2002)
Langmuir
, vol.18
, pp. 6789-6795
-
-
Vinokurov, I.A.1
Kankare, J.2
-
14
-
-
77957894990
-
Coincidences in chemical kinetics: surprising news about simple reactions
-
Yablonsky G.S., Constales D., Marin G.B. Coincidences in chemical kinetics: surprising news about simple reactions. Chem. Eng. Sci. 2010, 65:6065-6076.
-
(2010)
Chem. Eng. Sci.
, vol.65
, pp. 6065-6076
-
-
Yablonsky, G.S.1
Constales, D.2
Marin, G.B.3
-
15
-
-
77955869437
-
The utility of the Lambert function W[aexp(a-bt)] in chemical kinetics
-
Williams B.W. The utility of the Lambert function W[aexp(a-bt)] in chemical kinetics. J. Chem. Educ. 2010, 87:647-651.
-
(2010)
J. Chem. Educ.
, vol.87
, pp. 647-651
-
-
Williams, B.W.1
-
16
-
-
78751646785
-
Alternate solutions for two particular third order kinetic rate laws
-
Williams B.W. Alternate solutions for two particular third order kinetic rate laws. J. Math. Chem. 2011, 49:328-334.
-
(2011)
J. Math. Chem.
, vol.49
, pp. 328-334
-
-
Williams, B.W.1
-
17
-
-
34247495526
-
Explicit reformulation of the Colebrook-White equation for turbulent flow friction factor calculation
-
Sonnad J.R., Goudar C.T. Explicit reformulation of the Colebrook-White equation for turbulent flow friction factor calculation. Ind. Eng. Chem. Res. 2007, 46:2593-2600.
-
(2007)
Ind. Eng. Chem. Res.
, vol.46
, pp. 2593-2600
-
-
Sonnad, J.R.1
Goudar, C.T.2
-
18
-
-
65249099599
-
Efficient resolution of Colebrook equation
-
Clamond D. Efficient resolution of Colebrook equation. Ind. Eng. Chem. Res. 2009, 48:3665-3671.
-
(2009)
Ind. Eng. Chem. Res.
, vol.48
, pp. 3665-3671
-
-
Clamond, D.1
-
19
-
-
77955355825
-
New approach to the nonlinear analysis of a chemostat with impulsive state feedback control
-
Sun K., Kasperski A., Tian Y., Chen L. New approach to the nonlinear analysis of a chemostat with impulsive state feedback control. Int. J. Chem. React. Eng. 2010, 8:A99.
-
(2010)
Int. J. Chem. React. Eng.
, vol.8
-
-
Sun, K.1
Kasperski, A.2
Tian, Y.3
Chen, L.4
-
20
-
-
0003518480
-
-
John Wiley & Sons, New York
-
Segel I.H. Enzyme Kinetics 1993, John Wiley & Sons, New York.
-
(1993)
Enzyme Kinetics
-
-
Segel, I.H.1
-
22
-
-
0031582628
-
Closed-form solution for time-dependent enzyme kinetics
-
Schnell S., Mendoza C. Closed-form solution for time-dependent enzyme kinetics. J. Theor. Biol. 1997, 187:207-212.
-
(1997)
J. Theor. Biol.
, vol.187
, pp. 207-212
-
-
Schnell, S.1
Mendoza, C.2
-
23
-
-
0032899689
-
Parameter estimation using a direct solution of the integrated Michaelis-Menten equation
-
Goudar C.T., Sonnad J.R., Duggleby R.G. Parameter estimation using a direct solution of the integrated Michaelis-Menten equation. Biochim. Biophys. Acta 1999, 1429:377-383.
-
(1999)
Biochim. Biophys. Acta
, vol.1429
, pp. 377-383
-
-
Goudar, C.T.1
Sonnad, J.R.2
Duggleby, R.G.3
-
24
-
-
0035812906
-
Explicit oxygen concentration expression for estimating extant biodegradation kinetics from respirometric experiments
-
Goudar C.T., Ellis T.G. Explicit oxygen concentration expression for estimating extant biodegradation kinetics from respirometric experiments. Biotechnol. Bioeng. 2001, 75:74-81.
-
(2001)
Biotechnol. Bioeng.
, vol.75
, pp. 74-81
-
-
Goudar, C.T.1
Ellis, T.G.2
-
25
-
-
5644245248
-
Progress curve analysis for enzyme and microbial kinetic reactions using explicit solutions based on the Lambert W function
-
Goudar C.T., Harris S.K., McInerney M.J., Suflita J.M. Progress curve analysis for enzyme and microbial kinetic reactions using explicit solutions based on the Lambert W function. J. Microbiol. Methods 2004, 59:317-326.
-
(2004)
J. Microbiol. Methods
, vol.59
, pp. 317-326
-
-
Goudar, C.T.1
Harris, S.K.2
McInerney, M.J.3
Suflita, J.M.4
-
26
-
-
73849130978
-
Explicit solution of the integrated 1-exp equation for predicting accumulation and decline of concentrations for drugs obeying nonlinear saturation kinetics
-
Keller F., Hartmann B., Czock D. Explicit solution of the integrated 1-exp equation for predicting accumulation and decline of concentrations for drugs obeying nonlinear saturation kinetics. Ther. Drug Monit. 2009, 31:783-785.
-
(2009)
Ther. Drug Monit.
, vol.31
, pp. 783-785
-
-
Keller, F.1
Hartmann, B.2
Czock, D.3
-
27
-
-
80051782020
-
An alternative explicit model expression equivalent to the integrated Michaelis-Menten equation and its application to nonlinear saturation pharmacokinetics
-
Goličnik M. An alternative explicit model expression equivalent to the integrated Michaelis-Menten equation and its application to nonlinear saturation pharmacokinetics. Ther. Drug Monit. 2011, 33:362-365.
-
(2011)
Ther. Drug Monit.
, vol.33
, pp. 362-365
-
-
Goličnik, M.1
-
28
-
-
79952447939
-
Explicit analytic approximations for time-dependent solutions of the generalized integrated Michaelis-Menten equation
-
Goličnik M. Explicit analytic approximations for time-dependent solutions of the generalized integrated Michaelis-Menten equation. Anal. Biochem. 2011, 411:303-305.
-
(2011)
Anal. Biochem.
, vol.411
, pp. 303-305
-
-
Goličnik, M.1
-
29
-
-
78649909547
-
Evaluation of enzyme kinetic parameters using explicit analytic approximations to the solution of the Michaelis-Menten equation
-
Goličnik M. Evaluation of enzyme kinetic parameters using explicit analytic approximations to the solution of the Michaelis-Menten equation. Biochem. Eng. J. 2011, 53:234-238.
-
(2011)
Biochem. Eng. J.
, vol.53
, pp. 234-238
-
-
Goličnik, M.1
-
30
-
-
0020464815
-
Kinetics of hydrogen consumption by rumen fluid, anaerobic digestor sludge, and sediment
-
Robinson J.A., Tiedje J.M. Kinetics of hydrogen consumption by rumen fluid, anaerobic digestor sludge, and sediment. Appl. Environ. Microbiol. 1982, 44:1374-1384.
-
(1982)
Appl. Environ. Microbiol.
, vol.44
, pp. 1374-1384
-
-
Robinson, J.A.1
Tiedje, J.M.2
-
31
-
-
0021211264
-
m and the rate of endogenous substrate production R from substrate depletion data
-
m and the rate of endogenous substrate production R from substrate depletion data. Microb. Ecol. 1984, 10:165-178.
-
(1984)
Microb. Ecol.
, vol.10
, pp. 165-178
-
-
Robinson, J.A.1
Characklis, W.G.2
-
32
-
-
42249109511
-
Kinetics of propionate conversion in anaerobic continuously stirred tank reactors
-
Nielsen H.B., Mladenovska Z., Ahring B.K. Kinetics of propionate conversion in anaerobic continuously stirred tank reactors. Environ. Technol. 2008, 29:151-160.
-
(2008)
Environ. Technol.
, vol.29
, pp. 151-160
-
-
Nielsen, H.B.1
Mladenovska, Z.2
Ahring, B.K.3
-
33
-
-
80051794283
-
Accurate kinetic parameter estimation during progress curve analysis of systems with endogenous substrate production
-
Goudar C.T. Accurate kinetic parameter estimation during progress curve analysis of systems with endogenous substrate production. Biotechnol. Bioeng. 2011, 108:2499-2503.
-
(2011)
Biotechnol. Bioeng.
, vol.108
, pp. 2499-2503
-
-
Goudar, C.T.1
-
34
-
-
36448991175
-
One-compartment model with Michaelis-Menten elimination kinetics and therapeutic window: an analytical approach
-
Tang S., Xiao Y. One-compartment model with Michaelis-Menten elimination kinetics and therapeutic window: an analytical approach. J. Pharmacokinet. Pharmacodyn. 2007, 34:807-827.
-
(2007)
J. Pharmacokinet. Pharmacodyn.
, vol.34
, pp. 807-827
-
-
Tang, S.1
Xiao, Y.2
-
35
-
-
84856375867
-
Explicit reformulations of the Lambert W-omega function for calculations of the solutions to one-compartment pharmacokinetic models with Michaelis-Menten elimination kinetics
-
Goličnik M. Explicit reformulations of the Lambert W-omega function for calculations of the solutions to one-compartment pharmacokinetic models with Michaelis-Menten elimination kinetics. Eur. J. Drug Metab. Pharmacokinet. 2011, 36:121-127.
-
(2011)
Eur. J. Drug Metab. Pharmacokinet.
, vol.36
, pp. 121-127
-
-
Goličnik, M.1
-
36
-
-
0031194188
-
Theoretical analysis of protein concentration determination using biosensor technology under conditions of partial mass transport limitation
-
Christensen L.L.H Theoretical analysis of protein concentration determination using biosensor technology under conditions of partial mass transport limitation. Anal. Biochem. 1997, 249:153-164.
-
(1997)
Anal. Biochem.
, vol.249
, pp. 153-164
-
-
Christensen, L.L.H.1
-
37
-
-
0030890210
-
Kinetic analysis of protein antigen-antibody interaction limited by mass transport on an optical biosensor
-
Myszka D.G., Morton M., Doyle L., Chaiken I.M. Kinetic analysis of protein antigen-antibody interaction limited by mass transport on an optical biosensor. Biophys. Chem. 1997, 64:127-137.
-
(1997)
Biophys. Chem.
, vol.64
, pp. 127-137
-
-
Myszka, D.G.1
Morton, M.2
Doyle, L.3
Chaiken, I.M.4
-
38
-
-
0037008090
-
Determination of active concentrations and association and dissociation rate constants of interacting biomolecules: an analytical solution to the theory for kinetic and mass transport limitations in biosensor technology and its experimental verification
-
Sigmundsson K., Masson G., Rice R., Beauchemin N., öbrink B. Determination of active concentrations and association and dissociation rate constants of interacting biomolecules: an analytical solution to the theory for kinetic and mass transport limitations in biosensor technology and its experimental verification. Biochemistry 2002, 41:8263-8276.
-
(2002)
Biochemistry
, vol.41
, pp. 8263-8276
-
-
Sigmundsson, K.1
Masson, G.2
Rice, R.3
Beauchemin, N.4
öbrink, B.5
-
39
-
-
32944474840
-
Kinetics of antigen binding to antibody microspots: strong limitations by mass transport to the surface
-
Kusnezow W., Syagailo Y.V., Rüffer S., Klenin K., Sebald W., Hoheisel J., Gauer C., Goychuk I. Kinetics of antigen binding to antibody microspots: strong limitations by mass transport to the surface. Proteomics 2006, 6:794-803.
-
(2006)
Proteomics
, vol.6
, pp. 794-803
-
-
Kusnezow, W.1
Syagailo, Y.V.2
Rüffer, S.3
Klenin, K.4
Sebald, W.5
Hoheisel, J.6
Gauer, C.7
Goychuk, I.8
-
40
-
-
79151472202
-
Asymptotic of conduction velocity restitution in models of electrical excitation in the heart
-
Simitev R.D., Biktashev V.N. Asymptotic of conduction velocity restitution in models of electrical excitation in the heart. Bull. Math. Biol. 2011, 73:72-115.
-
(2011)
Bull. Math. Biol.
, vol.73
, pp. 72-115
-
-
Simitev, R.D.1
Biktashev, V.N.2
-
41
-
-
79551680642
-
A continuum constitutive model for the active behavior of skeletal muscle
-
Ehret A.E., Böl M., Itskov M. A continuum constitutive model for the active behavior of skeletal muscle. J. Mech. Phys. Solids 2011, 59:625-636.
-
(2011)
J. Mech. Phys. Solids
, vol.59
, pp. 625-636
-
-
Ehret, A.E.1
Böl, M.2
Itskov, M.3
-
42
-
-
67650502852
-
Upscaling of the advection-diffusion-reaction equation with Monod reaction
-
Heße F., Radu F.A., Thullner M., Attinger S. Upscaling of the advection-diffusion-reaction equation with Monod reaction. Adv. Water Resour. 2009, 32:1336-1351.
-
(2009)
Adv. Water Resour.
, vol.32
, pp. 1336-1351
-
-
Heße, F.1
Radu, F.A.2
Thullner, M.3
Attinger, S.4
-
43
-
-
79951834948
-
Estimating reaction rate coefficients within a travel-time modeling framework
-
Gong R., Lu C., Wu W.M., Cheng H., Gu B., Watson D., Jardine P.M., Brooks S.C., Criddle C.S., Kitanidis P.K., Luo J. Estimating reaction rate coefficients within a travel-time modeling framework. Groundwater 2011, 49:209-218.
-
(2011)
Groundwater
, vol.49
, pp. 209-218
-
-
Gong, R.1
Lu, C.2
Wu, W.M.3
Cheng, H.4
Gu, B.5
Watson, D.6
Jardine, P.M.7
Brooks, S.C.8
Criddle, C.S.9
Kitanidis, P.K.10
Luo, J.11
-
44
-
-
39549121697
-
An analytical solution of capillary rise restrained by gravity
-
Fries N., Dreyer M. An analytical solution of capillary rise restrained by gravity. J. Colloid Interface Sci. 2008, 320:259-263.
-
(2008)
J. Colloid Interface Sci.
, vol.320
, pp. 259-263
-
-
Fries, N.1
Dreyer, M.2
-
45
-
-
76049109673
-
Explicit analytical solutions for liquid infiltration into capillary tubes: dynamic and constant contact angle
-
Hilpert M. Explicit analytical solutions for liquid infiltration into capillary tubes: dynamic and constant contact angle. J. Colloid Interface Sci. 2010, 344:198-208.
-
(2010)
J. Colloid Interface Sci.
, vol.344
, pp. 198-208
-
-
Hilpert, M.1
-
46
-
-
77951252785
-
Calculating activation energy of amorphous phase with the Lambert W function
-
Zhang L., Xing D., Sun J. Calculating activation energy of amorphous phase with the Lambert W function. J. Therm. Anal. Calorim. 2010, 100:3-10.
-
(2010)
J. Therm. Anal. Calorim.
, vol.100
, pp. 3-10
-
-
Zhang, L.1
Xing, D.2
Sun, J.3
-
47
-
-
77955056463
-
Radial capillary transport from an infinite reservoir
-
Conrath M., Fries N., Zhang M., Dreyer M.E. Radial capillary transport from an infinite reservoir. Transp. Porous Media 2010, 84:109-132.
-
(2010)
Transp. Porous Media
, vol.84
, pp. 109-132
-
-
Conrath, M.1
Fries, N.2
Zhang, M.3
Dreyer, M.E.4
-
48
-
-
79960837614
-
Solution for the critical thickness models of dislocation generation in epitaxial thin films using the Lambert W function
-
Belgacem C.H., Fnaiech M. Solution for the critical thickness models of dislocation generation in epitaxial thin films using the Lambert W function. J. Mater. Sci. 2011, 46:1913-1915.
-
(2011)
J. Mater. Sci.
, vol.46
, pp. 1913-1915
-
-
Belgacem, C.H.1
Fnaiech, M.2
-
49
-
-
70549111547
-
A copper electrolysis cell model including effects of the ohmic potential loss in the cell
-
Pohjoranta A., Mendelson A., Tenno R. A copper electrolysis cell model including effects of the ohmic potential loss in the cell. Electrochim. Acta 2010, 55:1001-1012.
-
(2010)
Electrochim. Acta
, vol.55
, pp. 1001-1012
-
-
Pohjoranta, A.1
Mendelson, A.2
Tenno, R.3
-
52
-
-
79953047475
-
Exact and approximate solutions for the decades-old Michaelis-Menten equation: progress-curve analysis through integrated rate equations
-
Goličnik M. Exact and approximate solutions for the decades-old Michaelis-Menten equation: progress-curve analysis through integrated rate equations. Biochem. Mol. Biol. Educ. 2011, 39:117-125.
-
(2011)
Biochem. Mol. Biol. Educ.
, vol.39
, pp. 117-125
-
-
Goličnik, M.1
-
53
-
-
84864373167
-
An explicit solution for progress-curve analysis in systems characterized by endogenous substrate production, Microb.
-
(in press) doi:10.1007/s00248-011-9996-3
-
C.T. Goudar, An explicit solution for progress-curve analysis in systems characterized by endogenous substrate production, Microb. Ecol. (in press) doi:10.1007/s00248-011-9996-3.
-
Ecol.
-
-
Goudar, C.T.1
|