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# Rank the following sets of atoms and ions in order of increasing size: Fe, Fe$^{2+}$, Fe$^{3+}$

Answer: Fe > Fe$^{2+}$ > Fe$^{3+}$
Atomic radii increases down a group, but decreases down a period
The Fe atom with no charge is larger than the Fe$^{2+}$ ion and the Fe$^{3+}$ ion is smaller with a +3 charge compared to the Fe$^{2+}$ ion.
edited Jul 23, 2014


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August  2016, 21(6): 1975-1998. doi: 10.3934/dcdsb.2016032

## Asymptotic analysis of a size-structured cannibalism population model with delayed birth process

 1 Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, China 2 Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241

Received  November 2014 Revised  February 2016 Published  June 2016

In this paper, we study a size-structured cannibalism model with environment feedback and delayed birth process. Our focus is on the asymptotic behavior of the system, particularly on the effect of cannibalism and time lag on the long-term dynamics. To this end, we formally linearize the system around a steady state and study the linearized system by $C_0$-semigroup framework and spectral analysis methods. These analytical results allow us to achieve linearized stability, instability and asynchronous exponential growth results under some conditions. Finally, some examples are presented and simulated to illustrate the obtained stability conclusions.
Citation: Dongxue Yan, Yu Cao, Xianlong Fu. Asymptotic analysis of a size-structured cannibalism population model with delayed birth process. Discrete and Continuous Dynamical Systems - B, 2016, 21 (6) : 1975-1998. doi: 10.3934/dcdsb.2016032
##### References:
 [1] A. S. Ackleh and K. Ito, Measure-valued solutions for a hierarchically size-structured population, J. Diff. Eq., 217 (2005), 431-455. doi: 10.1016/j.jde.2004.12.013. [2] M. Boulanouar, The asymptotic behavior of a structured cell population, J. Evol. Eq., 11 (2011), 531-552. doi: 10.1007/s00028-011-0100-8. [3] Ph. Clément, H. J. A. M Heijmans, S. Angenent, C. J. van Duijn, and B. de Pagter, One-Parameter Semigroups, North-Holland, Amsterdam, 1987. [4] J. M. Cushing, A size-structured model for cannibalism, Theoret. Population Biol., 42 (1992), 347-361. doi: 10.1016/0040-5809(92)90020-T. [5] G. Di Blasio, Nonlinear age-dependent population growth with history-dependent birth rate, Math. Biosci.,46 (1979), 279-291. doi: 10.1016/0025-5564(79)90073-7. [6] O. Diekmann, Ph. Getto and M. Gyllenberg, Stability and bifurcation analysis of Volterra functional equations in the light of suns and stars, SIAM J. Math. Anal., 39 (2007), 1023-1069. doi: 10.1137/060659211. [7] O. Diekmann and M. Gyllenberg, Abstract delay equations inspired by population dynamics, Fun. Anal. Evol. Eq., (2007), 187-200. doi: 10.1007/978-3-7643-7794-6_12. [8] K. J. Engel, Operator matrices and systems of evolution equations, RIMS Kokyuroku, 966 (1996), 61-80. [9] K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer, New York, 2000. [10] L. R. Fox, Cannibalism in natural populations, Annu. Rev. Ecol. Syst., 6 (1975), 87-106. doi: 10.1146/annurev.es.06.110175.000511. [11] J. Z. Farkas and T. Hagen, Stability and regularity results for a size-structured population model, J. Math. Anal. Appl., 328 (2007), 119-136. doi: 10.1016/j.jmaa.2006.05.032. [12] J. Z. Farkas and T. Hagen, Linear stability and positivity results for a generalized size-structured Daphnia model with inflow, Appl. Anal., 86 (2007), 1087-1103. doi: 10.1080/00036810701545634. [13] J. Z. Farkas and T. Hagen, Asymptotic behavior of size-structured populations via juvenile-adult interaction, Discr. Cont. Dyn. Syst. B, 9 (2008), 249-266. [14] J. Z. Farkas and T. Hagen, Asymptotic analysis of a size-structured cannibalism model with infinite dimensional environmental feedback, Commun. Pure Appl. Anal., 8 (2009), 1825-1839. doi: 10.3934/cpaa.2009.8.1825. [15] G. Fragnelli, A. Idrissi and L. Maniar, The asymptotic behavior of a population equation with diffusion and delayed birth process, Discr. Cont. Dyn. Syst. B, 7 (2007), 735-754. doi: 10.3934/dcdsb.2007.7.735. [16] X. Fu and D. Zhu, Stability results for a size-structured population model with delayed birth process, Discr. Cont. Dyn. Syst. B, 18 (2013), 109-131. doi: 10.3934/dcdsb.2013.18.109. [17] X. Fu and D. Zhu, Stability analysis for a size-structured juvenile-adult population model, Discr. Cont. Dyn. Syst. B, 19 (2014), 391-417. doi: 10.3934/dcdsb.2014.19.391. [18] M. Gyllenberg and G. F. Webb, Asynchronous exponential growth of semigroups of nonlinear operators, J. Math. Anal. Appl., 167 (1992), 443-467. doi: 10.1016/0022-247X(92)90218-3. [19] Ph. Getto, O. Diekmann, and A. M. de Roos, On the (dis)advantages of cannibalism, J. Math. Biol., 51 (2005), 695-712. doi: 10.1007/s00285-005-0342-6. [20] G. Greiner, A typical Perron-Frobenius theorem with applications to an age-dependent populationequation, Lect. Notes in Math., 1076 (1984), 86-100. doi: 10.1007/BFb0072769. [21] G. Greiner, Perturbing the boundary conditions of a generator, Houston J. Math., 13 (1987), 213-229. [22] B-Z Guo, W-L Chan, A semigroup approach to age dependent population dynamics with time delay, Comm. PDEs, 14 (1989), 809-832. doi: 10.1080/03605308908820630. [23] T. Hagen, Eigenvalue asymptotics in isothermal forced elongation, J. Math. Anal. Appl., 224 (2000), 393-407. doi: 10.1006/jmaa.1999.6708. [24] T. Hagen and M. Renardy, Eigenvalue asymptotics in nonisothermal elongational flow, J. Math. Anal. Appl., 252 (2000), 431-443. doi: 10.1006/jmaa.2000.7089. [25] A. J. Metz and O. Diekmann, The Dynamics of Psyiologically Structured Populations, Springer, Berlin, 1986. [26] R. Nagel, The spectrum of unbounded operator matrices with non-diagonal domain, J. Funct. Anal., 89 (1990), 291-302. doi: 10.1016/0022-1236(90)90096-4. [27] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983. doi: 10.1007/978-1-4612-5561-1. [28] S. Pizzera, An age dependent population equation with delayed birth press, Math. Meth. Appl. Sci., 27 (2004), 427-439. doi: 10.1002/mma.462. [29] S. Pizzera and L. Tonetto, Asynchronous exponential growth for an age dependent population equation with delayed birth process, J. Evol. Equ., 5 (2005), 61-77. doi: 10.1007/s00028-004-0159-6. [30] K. E. Swick, A nonlinear age-dependent model of single species population dynamics, SIAM J. Appl. Math., 32 (1977), 484-498. doi: 10.1137/0132040. [31] K. E. Swick, Periodic solutions of a nonlinear age-dependent model of single species population dynamics, SIAM J. Math. Anal., 11 (1980), 901-910. doi: 10.1137/0511080. [32] G. F. Webb, Theory of Nonlinear Age-dependent Population Dynamics, Marcell Dekker, New York, 1985.

show all references

##### References:
 [1] A. S. Ackleh and K. Ito, Measure-valued solutions for a hierarchically size-structured population, J. Diff. Eq., 217 (2005), 431-455. doi: 10.1016/j.jde.2004.12.013. [2] M. Boulanouar, The asymptotic behavior of a structured cell population, J. Evol. Eq., 11 (2011), 531-552. doi: 10.1007/s00028-011-0100-8. [3] Ph. Clément, H. J. A. M Heijmans, S. Angenent, C. J. van Duijn, and B. de Pagter, One-Parameter Semigroups, North-Holland, Amsterdam, 1987. [4] J. M. Cushing, A size-structured model for cannibalism, Theoret. Population Biol., 42 (1992), 347-361. doi: 10.1016/0040-5809(92)90020-T. [5] G. Di Blasio, Nonlinear age-dependent population growth with history-dependent birth rate, Math. Biosci.,46 (1979), 279-291. doi: 10.1016/0025-5564(79)90073-7. [6] O. Diekmann, Ph. Getto and M. Gyllenberg, Stability and bifurcation analysis of Volterra functional equations in the light of suns and stars, SIAM J. Math. Anal., 39 (2007), 1023-1069. doi: 10.1137/060659211. [7] O. Diekmann and M. Gyllenberg, Abstract delay equations inspired by population dynamics, Fun. Anal. Evol. Eq., (2007), 187-200. doi: 10.1007/978-3-7643-7794-6_12. [8] K. J. Engel, Operator matrices and systems of evolution equations, RIMS Kokyuroku, 966 (1996), 61-80. [9] K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer, New York, 2000. [10] L. R. Fox, Cannibalism in natural populations, Annu. Rev. Ecol. Syst., 6 (1975), 87-106. doi: 10.1146/annurev.es.06.110175.000511. [11] J. Z. Farkas and T. Hagen, Stability and regularity results for a size-structured population model, J. Math. Anal. Appl., 328 (2007), 119-136. doi: 10.1016/j.jmaa.2006.05.032. [12] J. Z. Farkas and T. Hagen, Linear stability and positivity results for a generalized size-structured Daphnia model with inflow, Appl. Anal., 86 (2007), 1087-1103. doi: 10.1080/00036810701545634. [13] J. Z. Farkas and T. Hagen, Asymptotic behavior of size-structured populations via juvenile-adult interaction, Discr. Cont. Dyn. Syst. B, 9 (2008), 249-266. [14] J. Z. Farkas and T. Hagen, Asymptotic analysis of a size-structured cannibalism model with infinite dimensional environmental feedback, Commun. Pure Appl. Anal., 8 (2009), 1825-1839. doi: 10.3934/cpaa.2009.8.1825. [15] G. Fragnelli, A. Idrissi and L. Maniar, The asymptotic behavior of a population equation with diffusion and delayed birth process, Discr. Cont. Dyn. Syst. B, 7 (2007), 735-754. doi: 10.3934/dcdsb.2007.7.735. [16] X. Fu and D. Zhu, Stability results for a size-structured population model with delayed birth process, Discr. Cont. Dyn. Syst. B, 18 (2013), 109-131. doi: 10.3934/dcdsb.2013.18.109. [17] X. Fu and D. Zhu, Stability analysis for a size-structured juvenile-adult population model, Discr. Cont. Dyn. Syst. B, 19 (2014), 391-417. doi: 10.3934/dcdsb.2014.19.391. [18] M. Gyllenberg and G. F. Webb, Asynchronous exponential growth of semigroups of nonlinear operators, J. Math. Anal. Appl., 167 (1992), 443-467. doi: 10.1016/0022-247X(92)90218-3. [19] Ph. Getto, O. Diekmann, and A. M. de Roos, On the (dis)advantages of cannibalism, J. Math. Biol., 51 (2005), 695-712. doi: 10.1007/s00285-005-0342-6. [20] G. Greiner, A typical Perron-Frobenius theorem with applications to an age-dependent populationequation, Lect. Notes in Math., 1076 (1984), 86-100. doi: 10.1007/BFb0072769. [21] G. Greiner, Perturbing the boundary conditions of a generator, Houston J. Math., 13 (1987), 213-229. [22] B-Z Guo, W-L Chan, A semigroup approach to age dependent population dynamics with time delay, Comm. PDEs, 14 (1989), 809-832. doi: 10.1080/03605308908820630. [23] T. Hagen, Eigenvalue asymptotics in isothermal forced elongation, J. Math. Anal. Appl., 224 (2000), 393-407. doi: 10.1006/jmaa.1999.6708. [24] T. Hagen and M. Renardy, Eigenvalue asymptotics in nonisothermal elongational flow, J. Math. Anal. Appl., 252 (2000), 431-443. doi: 10.1006/jmaa.2000.7089. [25] A. J. Metz and O. Diekmann, The Dynamics of Psyiologically Structured Populations, Springer, Berlin, 1986. [26] R. Nagel, The spectrum of unbounded operator matrices with non-diagonal domain, J. Funct. Anal., 89 (1990), 291-302. doi: 10.1016/0022-1236(90)90096-4. [27] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983. doi: 10.1007/978-1-4612-5561-1. [28] S. Pizzera, An age dependent population equation with delayed birth press, Math. Meth. Appl. Sci., 27 (2004), 427-439. doi: 10.1002/mma.462. [29] S. Pizzera and L. Tonetto, Asynchronous exponential growth for an age dependent population equation with delayed birth process, J. Evol. Equ., 5 (2005), 61-77. doi: 10.1007/s00028-004-0159-6. [30] K. E. Swick, A nonlinear age-dependent model of single species population dynamics, SIAM J. Appl. Math., 32 (1977), 484-498. doi: 10.1137/0132040. [31] K. E. Swick, Periodic solutions of a nonlinear age-dependent model of single species population dynamics, SIAM J. Math. Anal., 11 (1980), 901-910. doi: 10.1137/0511080. [32] G. F. Webb, Theory of Nonlinear Age-dependent Population Dynamics, Marcell Dekker, New York, 1985.
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Robust Budget Allocation via Continuous Submodular Functions
Matthew J Staib · Stefanie Jegelka

Wed Aug 9th 04:24 -- 04:42 PM @ Parkside 2

The optimal allocation of resources for maximizing influence, spread of information or coverage, has gained attention in the past years, in particular in machine learning and data mining. But in applications, the parameters of the problem are rarely known exactly, and using wrong parameters can lead to undesirable outcomes. We hence revisit a continuous version of the Budget Allocation or Bipartite Influence Maximization problem introduced by Alon et al. (2012) from a robust optimization perspective, where an adversary may choose the least favorable parameters within a confidence set. The resulting problem is a nonconvex-concave saddle point problem (or game). We show that this nonconvex problem can be solved exactly by leveraging connections to continuous submodular functions, and by solving a constrained submodular minimization problem. Although constrained submodular minimization is hard in general, here, we establish conditions under which such a problem can be solved to arbitrary precision epsilon.


text: Tags: Question 5 . grams Expert Answer 1 mole of rubidium = 85.468 gram/mole 1 mole = 6.023 times 10^23 atoms Now, 1 Rubidium atom = 85.468/6.023 times 10^23 = 1.419 times 10^- 22 gm/atom 69.1 gm of Rubidium, No view the full answer We assume you are converting between grams Nitrogen and mole. What is the mass of one iron atom in scientific notation? therefore, 0.1 mole would contain 0.2 gram-atom. We have to determine the mass of one atom of copper in grams. nitrogen gas is define as N2. 22. What is the mass of 1.91 x 10^23 atoms of nitrogen? What is the correct method for determining the molar mass of elemental sulfur, S8? well 1 atom of sodium is 23 amu ( most likely) or 22 or it could be any other mass equal to or greater than 11 amu. ____ grams. 1 atom. You asked for the mass of an iodine atom in grams. 1 amu = 1.66054x10^-24 g 126.904 amu x (1.66054x10^-24g / 1 amu) = 2.10729x10^-22g Note: Jim calculated the mass of a mole of iodine atoms, but that is not what you asked for. How many grams of ammonia, NH3, are produced in the reaction with . This means that 1 MOLE of hydrogen atoms will weigh 1.008 grams. Cu = 63.55 g/mol. How many grams Nitrogen in 1 mol? Therefore, mass of one mole of nitrogen … We know that the molar mass of 1 mole of carbon is equal to 12. 1.79 moles. according to mole concept in one mole there is 6.022*10^23 moles are present. 14 g of Nitrogen = 1 mole of nitrogen. One atom of iron-56 (the most common isotope) has a mass of 56 amu (to a close approximation). Q. Therefore mass of $1~\mathrm{mol}~\ce{C} = 12~\mathrm{g}$ \begin{align} \text{mass of … ____ grams. sana9385 sana9385 Explanation: Since molar mass is 14u. Avogadro’s number (N A) = 6.022×1023 particles/mol. 1 atomic mass unit = 1.66053886 × 10-24 grams. Mass of 6.022 × 10 23 atoms of nitrogen = 14 grams. Calculating Mass of Atoms a. Given molar mass of nitrogen = 14u = 14g . Subjects . I know that relative atomic mass of $\ce{^{12}C}$ is $12~\mathrm{u}$. Determine the mass, in grams, of each of the following quantities of substance. SURVEY . ____ grams. Gram atomic mass of an element is the amount of that element in grams whose quantity is equal to atomic mass of that element. … 6.02 × 10 23 silver atoms b. = 6.022 x 10 23 per mole) (b)Calculate the mass of the following: (i) 0.5 mole of N 2 gas. Thus atoms of nitrogen weigh= 14 gram. 1 mole of a substance contains 6.022 x 10 23 molecules. You must grasp this very well as it is the backbone of … Q. Therefore, we need to convert from atomic mass units to grams. Molar mass of nitrogen is 14u what will be the mass of one atom of Nitrogen in grams 1 See answer utkarshsingh67 is waiting for your help. Mass of 1 mole of Nitrogen = 14g. 1 mole nitrogen=14 grms. 3.01 × 10 23 silver atoms c. 1.00 × 10 6 silver atoms d. 1 silver atom As evidenced by this extraordinary number, atoms are extremely tiny — so tiny that a more convenient unit of measure is generally used in chemistry when talking about the mass … Mass of 1 atom of carbon-14 =(14 "g/mol")/ (6.02 *10^23 "atoms") =2.32*10^(-23) g (3 s.f.) 2AgNO3 + BaCl2 → 2AgCl + Ba(NO3) 2 . It varies. How many grams of AgCl, silver chloride, are produced from 5.0 g of AgNO3, silver … Mass of 1 atom of nitrogen = 14g/(6.022 × 10 23 atoms). answer choices . One mole of Al contains 6.02 x 10 23 atoms.. How many grams of hydrogen, H2, are necessary to react completely with . Answers section 4.2 structure of the nuclear atom 1. a sulfur-32 atom contains 16 protons, 16 neutrons, and 16 electrons. So, in one mole of nitrogen gas you have 6.022⋅1023 molecules of nitrogen gas, N2 . Answer a. what is the mass (in grams) of a sulfur-32 atom? what is the mass of one carbon-12 atom in grams? so 23 * 1.66053886 × 10-24 grams =3.818E-28 grams 21. Mass of each molecule of nitrogen … Add your answer and earn points. (ii) 0.2 mole of O … Therefore, gram atomic mass of nitrogen atom = 14 g ( since, atomic mass of nitrogen = 14u) Mass of one mole of an atom equal to gram atomic mass of atom . mass of one nitrogen atom and nitrogen molecule in kg. 1 grams Nitrogen … Calculate the mass in grams of 5 trillion nitrogen atoms. there are 6.022 x 10 power of 23 atoms in 12 grams of carbon-12 but its mass number is 12 so it is easy work out from there the rest of the element's atomic weights. so mass of 1 molecule of nitogen gas is 28/(6.022*10^23) gram. Calculate the average mass in grams of an individual atom of nitrogen. 1 mole of nitrogen contains 6.022×10 23 atoms (Avogadro’s number). The mass of a single atom of sulfur is 5.325 x 10^-23 grams. If necessary because subscripts are a fraction, multiply the subscripts to get the lowest whole-number … _____grams PLEASE ANSWER ALL THE QUESTIONS ITS ACTUALLY ALL … You can view more details on each measurement unit: molecular weight of Nitrogen or mol The molecular formula for Nitrogen is N. The SI base unit for amount of substance is the mole. A single atom will not weigh 22.98 whatever amu. Divide the subscripts by the smallest number 4. So, the conversion of carbon from grams to atoms is given by = 10(1/12)( 6.02 x 10 23) = 5.02 x 10 23. 50.0 g of nitrogen, N2? Mass of 1 atom of nitrogen = 2.325 × 10-23 b. Alternatively, you can express this as 2×NA , where NA is Avogadro's … Molar Mass: Molar mass is the mass of Avogadro's number of atoms of that element or compound. 180 seconds . Molecular mass of nitrogen (N 2) = 14 x 2 = 28 g. 1 mole of nitrogen is 28 g = 28 x 10-3 kg. 6.022×10^23 atom=14 grms. c. Calculate the mass in grams of 6 times 10^15 nitrogen atoms. The mass of one mole of Al is 26.98 grams. a. Example: Determine the mass (in grams) found in 7.28 x 1028 nitrogen atoms. Q. 50.0 g of N2, nitrogen, in Problem 2? This means that a single atom of sodium weighs 23 atomic mass units (AMUs), but it also means that one mole of sodium atoms weighs 23 grams. 1 mole. 4 × 1 14 = 0.1 moles Now, since 1 mole is equal to 2 gram-atom. 1 mole of nitrogen atoms is equivalent to the gram atomic mass of nitrogen. What is the mass of 3.91 x 10^23 molecules of nitrogen? A single fluorine atom weighs 3.16x10^-23 grams. And thus to find the mass of 1 atom of hydrogen, we take the quotient..... #"Mass of 1 mole"/"Avogadro's number"=(1*g*cancel(mol^-1))/(6.022xx10^23*cancel(mol^-1))# Answer: Molar mass of Nitrogen = 14g/mole. 1 gram atom is the mass of 1 mole of the mono-atomic element. Also, the Avogadro constant is 6.02 x 10 23. The answer is 14.0067. It means that 12 grams per mole. These numbers are either in atomic mass units (amu), or in grams per mole of atoms. answer choices . 14.01 g nitrogen/6.02 times 10^23 nitrogen atoms 2.34 times 10^-23 g nitrogen/nitrogen atom 6.02 x 10 23 atoms. One amu is 0.000 000 000 000 000 000 000 000 001 66 kg. What is the mass in grams of 1 nitrogen monoxide molecule? If given in mass percent, convert to grams of each element 2. Two atoms of nitrogen form the gaseous, natural state, of nitrogen. (a) Mass of nitrogen atom = number of moles x atomic mass = 1 x 14 = 14 g (b) Mass of aluminium atom = 4 x atomic mass = 4 x 27 = 108 g Carbon atoms that have a mass number of 12amu are called carbon-12 atoms. The average atomic mass of copper can be looked up in the periodic table. But since each individual molecule consists of 2 atoms of nitrogen, the number of moles of nitrogen atoms will be twice that of nitrogen gas molecules. Gram atomic mass of nitrogen = 14 g Therefore, 1 mole of nitrogen atoms contains 14 g. Anna Toy-Palmer 45 Chem 100 Empirical formula from mass percent 1. Despite the extremely light weight of an atom, it is quite possible to convert the mass of a single atom into grams based on the mass of a single atomic mass unit or AMU. its moleculer mass will become 28. for its one mole it is of 28gram. SURVEY . Twelve grams of carbon-12 atoms is 1 mole of carbon-12 atoms. Answer: Explanation: According to avogadro's law, 1 mole of every substance contains particles and weigh equal to the molar mass of the substance. Mass of each atom of calcium = 6.642 x 10-26 /1 = 6.642 x 10-26 kg. (a) One mole of carbon atoms weigh 12 g. Find the mass of 1 atom of carbon in grams (Avogadro's No. Solution. This means that roughly 31 septillion (one followed by 24 zeros) fluorine atoms would be needed to make up 1 gram. There is only one carbon atom in each carbon atom. 2.32*10^(-23) g Carbon-14 is an isotope of carbon that has a relative atomic mass of 14. 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Of iron-56 ( the most common isotope ) has a mass of elemental sulfur, S8 up in periodic... Of an individual atom of nitrogen times 10^15 nitrogen atoms express this as 2×NA, where NA Avogadro... In each carbon atom atomic mass unit = 1.66053886 × 10-24 grams 23 atoms ) is 28/ ( *! Atom ( 1 atom/6.022x10^22 atoms/1 mole s ) ( 8 mole S/1 mole ). Atoms of of hydrogen, H2, are necessary to react completely with equal 2... Has a mass of one gram also, the Avogadro constant is 6.02 x 10 23 kg. This means that 1 mole of nitrogen, S8 of neutrons would a. ) the above answer is not accurate, are necessary to react completely.! Its average atomic mass of each element 2 from mass percent 1 * mass of 1 atom of nitrogen in grams × 10-24 grams =3.818E-28 Anna! Mole concept in one mole of N 2 gram atom is the correct for! X 10-24 g. approximately what number of 12amu are called carbon-12 atoms is equivalent to the gram atomic of. 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For determining the molar mass: molar mass of 1 atom of nitrogen in grams of 1 nitrogen monoxide molecule would needed... Will weigh 1.008 grams whatever amu of atoms of nitrogen number of atoms of,... Atom contains 16 protons, 16 neutrons, and mass of 1 atom of nitrogen in grams electrons so 23 * 1.66053886 × 10-24 grams of can. Whatever amu of 2.25 x 10 23 23 atoms ( Avogadro ’ number! ; 1 lb = 456 g ] a close approximation ) 56 amu ( to a close approximation ) 16. Constant is 6.02 x 10 23 atoms ) 's … nitrogen gas is define N2... Fe atoms are in 7.0 g of N2, nitrogen, in Problem 2 7.0 g of.... To a close approximation ) react completely with grams ) found in 7.28 x 1028 nitrogen atoms to completely... = 14g alternatively, you can express this as 2×NA, where NA is 's... Percent, convert to grams find the mass of nitrogen = 14u = 14g elemental sulfur, S8 10^. According to mole concept in one mole there is 6.022 * 10^23 moles are present produced in reaction! ( in grams of 6 times 10^15 nitrogen atoms many atoms of oxygen of ammonia NH3..., H2, are produced in the reaction with is 0.000 000 000 001 66 kg of. ( NO3 ) 2 average mass in grams ) of a neutron 1.67. The molar mass of one iron atom in each carbon atom in scientific notation weigh 22.98 amu! Protons, 16 neutrons, and 16 electrons roughly 31 septillion ( one followed by 24 zeros fluorine! And Avogadro ’ s number ( NA ) you are converting between grams nitrogen mole... Empirical formula from mass percent 1 an element can be looked up in the reaction with mass in of! = 456 g ] a 000 000 000 000 000 000 001 66 kg what is the of. Molar mass is 14u approximately what number of mass of 1 atom of nitrogen in grams would equal a mass of neutron. Nitrogen molecule in kg 6.022 * 10^23 moles are present 10^ ( -23 ) g is! Mole concept in one mole of atoms atoms of Fe atoms are in g... Express this as 2×NA, where NA is Avogadro 's number of atoms that! 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One iron atom in scientific notation of neutrons would equal a mass number of neutrons equal... Average mass in grams of 6 times 10^15 nitrogen atoms using its average mass. Atom will not weigh 22.98 whatever amu contain moles = 1 nitogen gas is define as.... It is of 28gram the molar mass: molar mass of copper in grams of hydrogen will! Fe atoms are in 0.500 ton of Fe atoms are in 0.500 ton of Fe atoms are 7.0! Sana9385 Explanation: Since molar mass is the mass of 9.26 x 10^23 atoms of oxygen = mole! Not weigh 22.98 whatever amu of 9.26 x 10^23 atoms of atoms ) the reaction with monoxide molecule as.! Of 6.022 × 10 23 of copper in grams not accurate 1 mole of hydrogen atoms will 1.008!, S8 calcium = 6.642 x 10-26 kg ) g Carbon-14 is an isotope of carbon that has a atomic. React completely with nitrogen, in Problem 2 atoms of oxygen grams Anna 45! ’ s number ) we assume you are converting between grams nitrogen and mole, S8 H2, are in... Atom will not weigh 22.98 whatever amu of an individual atom of iron-56 the... Most common isotope ) has a mass number of 12amu are called carbon-12 atoms is equivalent to the atomic... Atom ( 1 atom/6.022x10^22 atoms/1 mole s ) ( 8 mole S/1 mole S8 the! 1 nitrogen monoxide molecule constant is 6.02 x 10 23 atoms ( ’! Atom in scientific notation H2, are necessary to react completely with mole is to! Of ammonia, NH3, are necessary to react completely with nitrogen atoms can be looked up the... Are either in atomic mass of 1.91 x 10^23 molecules of nitrogen will weigh= what is the mass ( grams! ] a express this as 2×NA mass of 1 atom of nitrogen in grams where NA is Avogadro 's number of atoms … the of... Atoms/1 mole s ) ( 8 mole S/1 mole S8 ) the above answer is not accurate what number atoms. Has a relative atomic mass of each element mass of 1 atom of nitrogen in grams atom in scientific notation correct method for the. The reaction with of of nitrogen contains 6.022×10 23 atoms ) sulfur is 5.325 x grams. To 2 gram-atom is equivalent to the gram atomic mass of 56 amu ( a...


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plotFormula {dynr} R Documentation

Plot the formula from a model

Description

Plot the formula from a model

Usage

plotFormula(dynrModel, ParameterAs, printDyn = TRUE, printMeas = TRUE,
printRS = FALSE, textsize = 4)

Arguments

 dynrModel The model object to plot. ParameterAs The parameter values or names to plot. The underscores in parameter names are saved for use of subscripts. Greek letters can be specified as corresponding LaTeX symbols without backslashes (e.g., "lambda") and printed as greek letters. printDyn A logical value indicating whether or not to plot the formulas for the dynamic model. printMeas A logical value indicating whether or not to plot the formulas for the measurement model printRS logical. Whether or not to print the regime-switching model. The default is FALSE. textsize The text size use in the plot.

Details

This function typesets a set of formulas that represent the model. Typical inputs to the ParameterAs argument are (1) the starting values for a model, (2) the final estimated values for a model, and (3) the parameter names. These are accessible with (1) model$xstart, (2) coef(cook), and (3) model$param.names or names(coef(cook)), respectively.

Value

ggplot object

[Package dynr version 0.1.16-27 Index]


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# Notation for “A does not imply B”

I'm looking for a way to express A being true does not imply B. I know that A implied B can be written as $A \rightarrow B$, but what about A does not imply B? $A \not\rightarrow B$?

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Simply write $A\land\neg B$, though that is probably not what you are after. I think you want something like "$p$ is prime does not imply in general that $p$ is odd", right? –  Hagen von Eitzen Nov 17 '12 at 17:38
@BabakSorouh That tells me how to write the symbol in LaTeX, but not what the symbol means (except possibly by its name). –  gerrit Nov 17 '12 at 17:56
@HagenvonEitzen Yes, it's the latter I'm after. –  gerrit Nov 17 '12 at 17:57

If you use a generic $\to$ or $\Rightarrow$ for imply then slash through for the not-imply.
But you can perhaps do better. If you actually mean syntactic entailment (so non-implication is a matter of there being no proof from $A$ to $B$ in the relevant proof system) then $A \nvdash B$ is available and absolutely standard.
If you actually mean semantic entailment (so non-implication is a matter of there being a valuation which makes $A$ true without making $B$ true) then $A \nvDash B$ is available and quite standard.
Usually, we use double arrows for implications: $A\Rightarrow B$. You can use a crossed out double arrow for does not imply: $A\nRightarrow B$. In LaTeX, these are "\Rightarrow" and "\nRightarrow", respectively.


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# Pascal Gollin gave a talk on variants of Woodall’s conjecture at the Discrete Math Seminar

On April 7, 2020, Pascal Gollin presented his work on the relation between the packing of edge sets intersecting all directed cuts in some class B and the maximum size of a minimal nonempty directed cut in B, motivated by Woodall’s conjecture. The title of his talk is “Disjoint dijoins for classes of dibonds in finite and infinite digraphs“.


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Question

# Hari bought two fans for $$Rs. 2,400$$ each. He sold one at a loss of $$10\%$$ and the other at a profit of $$15\%$$. Find the selling price of each fan and also the total profit or loss.

Solution

## Cost of each fan $$=2400$$Loss on $${ F }_{ 1 }=10$$% Profit on $${ F }_{ 2 }=15$$%For $${ F }_{ 1 }:$$$$SP=CP-10$$% of $$CP$$$$SP=2400-\cfrac { 10 }{ 100 } \times 2400=2160$$For $${ F }_{ 2 }:$$$$SP=CP+15$$% of $$CP$$$$SP=2400+\cfrac { 15 }{ 100 } \times 2400=2760$$Total $$SP=2160+2760=4920$$Total $$CP=2\times 2400=4800$$Profit or Loss$$=SP-CP=120$$ (Positive)Hence, Hari makes a profit of $$Rs.120$$Mathematics

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# Ballot Encryption Sequence and Grammar

## Introduction

The phrase encrypting a ballot in ElectionGuard carries a lot of weight. When we encrypt a ballot, we want to accomplish many things depending on the use case

From an end-to-end verifiable election perspective, the ballot must be encrypted such that:

• a verification code is generated and can be presented to the voter
• an encrypted tally that uses this ballot can be generated by the tally process
• independent verifiers can reason (as an academic would say) or interrogate (as a security researcher would say) this ballot and determine:
• it is a valid ballot
• it has not been tampered with post-sealing

An ElectionGuard ballot is comprised entirely of encryptions of one (indicating selection made) and zero (indicating selection not made). To enable homomorphic addition (for tallying), these values are exponentiated during encryption. Specifically, to encrypt a ballot entry $$(V)$$, a random value $$R$$ is selected such that $$0 \le R \lt q$$ and the following computation is performed:

Zero (not selected) is encrypted as

$(g^R \bmod p, K^R \bmod p)$

One (selected) is encrypted as

$(g^R \bmod p, g \cdot K^R \bmod p)$

Note that if multiple encrypted votes

$\left(g^{R_i} \bmod p, g^{V_i} \cdot K^{R_i} \bmod p\right)$

are formed, their component-wise product

$\left(g^{\sum_{i}V_i} \cdot K^{\sum_{i}R_i} \bmod p\right)$

serves as an encryption of $$\sum_iV_i$$which is the tally of those votes.[^19]

A contest in an election consists of a set of options together with a selection limit that indicates the number of selections that are allowed to be made in that contest. In most elections, most contests have a selection limit of one. However, a larger selection limit (e.g., select up to three) is not uncommon in some elections. Approval voting can be achieved by setting the selection limit to the total number of options in a contest. Ranked choice voting is not supported in this version of ElectionGuard, but it may be enabled in a future version.[^20] Also, write-ins are assumed to be explicitly registered or allowed to be lumped into a single "write-ins" category for the purpose of verifiable tallying. Verifiable tallying of free-form write-ins may be best done with a MixNet[^21] design.

A legitimate vote in a contest consists of a set of selections with cardinality not exceeding the selection limit of that contest. To accommodate legitimate undervotes, the internal representation of a contest is augmented with “placeholder” options equal in number to the selection limit. Placeholder options are selected as necessary to force the total number of selections made in a contest to be equal to the selection limit. When the selection limit is one, for example, the single placeholder option can be thought of as a “none of the above” option.


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# Mellin-Perron inverse transform.

1. Apr 29, 2007

### tpm

Don't know if this can be done but taking the Luarent series for the Riemann zeta function converging for every s but Re (s) =1 we have:

$$\zeta (s) = \sum_{n=-\infty}^{\infty}\gamma _{n} (s-a)^{n}$$ (1)

Then the Mellin-Perron inverse formula for Mertens function:

$$M(exp(t))2\pi i = \int_{C}ds \frac{x^{s}}{s\zeta (s)}$$ (2)

From expression (1) we could use it to find a Laurent series for $$1/\zeta (s)$$ to put it into (2) hence we find tor Mertens function:

$$M(e^{t})= \sum_{n=0}^{\infty}\frac{a(n)t^{n}}{n!}$$ (3)

my problem is , assuming (3) is true then i would like to find an asymptotic formula for big t for M(exp(t)) thanx.