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# Homework Help: Integrating a two variable equation

1. Aug 2, 2010

### groditi

1. The problem statement, all variables and given/known data

This is the problem I was given:

$$I_{n} = \int^{0}_{\infty}(1 + x^{2})^{-n} dx$$

I was told to "deduce that"

$$I_{n} = 2n(I_{n} - I_{n + 1})$$

so I can "Hence or otherwise show that"

$$\int^{0}_{\infty}(1 + x^{2})^{-4} dx = \frac{5\pi}{32}$$

2. Relevant equations

I don't even know what I am being asked to do. I have relegated myself to failing this problem. Originally, I figured I would just try to find the original function of the integrand and see if that left me somewhere that made more sense, but I can't find anything in my notes that explains how to solve this with two variables. I am not looking for an answer, but rather maybe a hint as to where I should be looking for an integration technique.

3. The attempt at a solution

The first thing that I gather is that I have to separate the parts, so I could do something like: if

$$z = 1 + x^{2}$$

then,

$$dz = 2x dx$$

and,

$$I_{n} = \int^{0}_{\infty}z(x)^{-n} dz$$

That obviously looks like something that came out of the chain rule, so I first go backwards on the power using $$\int a^{x} = \frac{a^{x+1}}{x+1}$$

which combined with the chain rule fives me,
$$\int z(x)^{-n} dz = \frac{z(x)^{1-n}}{1-n}$$

So far, so good. I know the integral of $$(1 + x^{2})$$ is $$(x + \frac{x^{3}}{3})$$

and here is where it all falls apart. I have no idea how to put those two parts together, and I don't know what to review / re-read to figure it out. Can anyone just at least tell me what kind of problem this is so I know what I am supposed to be searching for? As an econ student my calc background is very basic, we never had to deal with this sort of thing.

2. Aug 2, 2010

### Staff: Mentor

All of your limits of integration are upside-down. The integrals should look like this:
$$I_{n} = \int_0^{\infty}(1 + x^{2})^{-n} dx$$

This (above) isn't right. It looks like you just replaced dx with dz, but dz = 2x dx. That 2x has to come from somewhere.

Instead of an ordinary substitution like you tried, a trig substitution might be what is called for.

3. Aug 2, 2010

### rock.freak667

Try using integrating by parts with u=(1+x2)-n.

After which, you will need to use something along the lines of x= x+9-9

4. Aug 2, 2010

### groditi

Yikes. That was a latex typo, my apologies. Thank you for pointing out that dx error, i was under the impression that the 2xwould come from the derivative of $$x^{2}$$. I am learning this all from a set of notes and some videos, all by myself (no teacher or classmates) so it feels very overwhelming.

I thought about the trig substitution too. I remember that:
$$f(x) = tan^{-1}(x)$$
and
$$f'(x) = \frac{1}{1+x^{2}}$$

but I was unable tie that part together to n part. I get that $$\frac{1}{(1+x^{2})^{n}}$$ could just be expanded to $$(\frac{1}{(1+x^{2})})_{n} (\frac{1}{(1+x^{2})})_{n-1} \cdots (\frac{1}{(1+x^{2})})_{0}$$

but that still leaves me pretty confused.

At the core of it, I recognize that my calculus is poor. In fact, I have absolutely no clue what to do with the "n" term, I've never integrated something with two variables, so I don't know the special rules or formulas it takes to combine them. Looking through the notes I have on integrals, there's nothing with more than one variable in it, so I don't know where to look for more information. is that what they call partial differential equations? If I'm beyond help on this one, how about a suggestion for a textbook?

5. Aug 2, 2010

### rock.freak667

Think of 'n' as a constant rather than a variable. If you try integration by parts, it works out a bit easier than the trig. substitution IMO.

6. Aug 2, 2010

### vela

Staff Emeritus
Oftentimes, when you're asked to deduce a recurrence relation involving integrals, integration by parts, as rock.freak suggested, is a good place to start.


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# A car travelling with $\frac{5}{7}$ of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.

$17\frac{6}{7}$ km/hr

25 km/hr

30 km/hr

35 km/hr

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Non Deterministic Finite Acceptor (NFA):

An NFA is defined by the quintuple  M = (Q, ∑ , δ,  ${\mathbit{q}}_{\mathbf{0}}$, F)

Q  is a finite set of initial states.

is a finite set of symbols called the input alphabet.

Q is the initial state

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δ: Q X (Σ ∪ {λ}) → ${\mathbf{2}}^{\mathbf{Q}}$ or P(Q)

[It also has input alphabet λ i.e. it has moves for λ]

Language accepted by NFA (M) is the set of all strings accepted by M.

• ∀ω ∊ L, δ*(${q}_{0}$, ω) ∩ F ≠ ϕ (string ω accepted)
• ∀ω ∉ L, δ*(${\mathbit{q}}_{\mathbf{0}}$, ω) ∩ F = ϕ ( string ω rejected)


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Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CJM
Abstract view

# Bump Functions with Hölder Derivatives

We study the range of the gradients of a $C^{1,\al}$-smooth bump function defined on a Banach space. We find that this set must satisfy two geometrical conditions: It can not be too flat and it satisfies a strong compactness condition with respect to an appropriate distance. These notions are defined precisely below. With these results we illustrate the differences with the case of $C^1$-smooth bump functions. Finally, we give a sufficient condition on a subset of $X^{\ast}$ so that it is the set of the gradients of a $C^{1,1}$-smooth bump function. In particular, if $X$ is an infinite dimensional Banach space with a $C^{1,1}$-smooth bump function, then any convex open bounded subset of $X^{\ast}$ containing $0$ is the set of the gradients of a $C^{1,1}$-smooth bump function.


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# zbMATH — the first resource for mathematics

## Dubson, Alberto S.

Compute Distance To:
 Author ID: dubson.alberto-s Published as: Dubson, Alberto S.
 Documents Indexed: 8 Publications since 1978

#### Co-Authors

 7 single-authored 1 Brylinski, Jean-Luc 1 Kashiwara, Masaki

#### Serials

 4 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 3 Comptes Rendus de l’Académie des Sciences. Série I
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 7 Several complex variables and analytic spaces (32-XX) 5 Algebraic geometry (14-XX) 1 Measure and integration (28-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX)

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#### Cited by 45 Authors

 5 Massey, David Bradley 4 Dutertre, Nicolas 3 Aluffi, Paolo 3 de Góes Grulha, Nivaldo jun. 3 Yokura, Shoji 2 Laurent, Yves 2 Nabeshima, Katsusuke 2 Schürmann, Jörg 2 Seade, Jose Antonio 2 Tajima, Shinichi 2 Tibăr, Mihai-Marius 1 Barchini, Leticia 1 Berthelot, Pierre 1 Borho, Walter 1 Brylinski, Jean-Luc 1 Ernström, Lars 1 Evens, Sam 1 Fu, Joseph Howland Guthrie 1 Ginzburg, Victor 1 Goresky, Robert Mark 1 Hu, Haoyu 1 Illusie, Luc 1 Katz, Nicholas Michael 1 Laumon, Gérard 1 Malgrange, Bernard 1 McCrory, Clint G. 1 McGerty, Kevin 1 Mebkhout, Zoghman 1 Migliorini, Luca 1 Mirković, Ivan 1 Nadler, David 1 Ohmoto, Toru 1 Sabbah, Claude 1 Schapira, Pierre 1 Siesquén, Nancy Carolina Chachapoyas 1 Suwa, Tatsuo 1 Treumann, David 1 Vaquié, Michel 1 Verjovsky, Alberto 1 Wu, Lei 1 Yang, Enlin 1 Zaslow, Eric 1 Zhang, Xiping 1 Zhou, Peng 1 Zierau, Roger
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#### Cited in 28 Serials

 5 Duke Mathematical Journal 3 Transactions of the American Mathematical Society 2 Advances in Mathematics 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Inventiones Mathematicae 2 Manuscripta Mathematica 2 Proceedings of the Japan Academy. Series A 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Tohoku Mathematical Journal. Second Series 2 Topology and its Applications 1 Israel Journal of Mathematics 1 Compositio Mathematica 1 Publications Mathématiques 1 Journal of Algebra 1 Journal of Pure and Applied Algebra 1 Mathematische Annalen 1 Journal of the American Mathematical Society 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Journal of Mathematical Sciences (New York) 1 Selecta Mathematica. New Series 1 Transformation Groups 1 Milan Journal of Mathematics 1 Journal of Algebra and its Applications 1 Mathematics in Computer Science 1 Japanese Journal of Mathematics. 3rd Series 1 Journal of Singularities 1 Forum of Mathematics, Sigma
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#### Cited in 19 Fields

 35 Algebraic geometry (14-XX) 33 Several complex variables and analytic spaces (32-XX) 11 Manifolds and cell complexes (57-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Commutative algebra (13-XX) 4 Topological groups, Lie groups (22-XX) 3 Differential geometry (53-XX) 2 Nonassociative rings and algebras (17-XX) 2 Category theory; homological algebra (18-XX) 2 $$K$$-theory (19-XX) 2 Group theory and generalizations (20-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Associative rings and algebras (16-XX) 1 Partial differential equations (35-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Algebraic topology (55-XX)


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# Mathematical Sciences Research Institute

Home » Workshop » Schedules » Geometric classification

# Geometric classification

## Introductory Workshop: phenomena in high dimensions August 21, 2017 - August 25, 2017

August 23, 2017 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Monika Ludwig (Technische Universität Wien)
Location: MSRI: Simons Auditorium
Tags/Keywords
• Valuation

• Convex Body

• Sobolev space

• convex function

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

#### 9-Ludwig

Abstract

A fundamental theorem of Hadwiger classifies all rigid-motion invariant and continuous functionals on convex bodies (that is, compact convex sets) in ${\mathbb R}^n$ that satisfy the inclusion-exclusion principle, $$\operatorname{Z}(K)+ \operatorname{Z}(L) =\operatorname{Z}(K\cup L) +\operatorname{Z}(K\cap L)$$ for convex bodies $K$ and $L$ such that $K\cup L$ is convex. Under weak additional assumptions, such a functional $\operatorname{Z}$ is a finitely additive measure and hence Hadwiger's theorem is a counterpart to the classification of Haar measures. Hadwiger's theorem characterizes the most important functionals within Euclidean geometry, the $n+1$ intrinsic volumes, which include volume, surface area, and the Euler characteristic. In recent years, numerous further functions and operators defined on the space of convex bodies and more generally on function spaces were characterized by their properties. An overview of these results will be given:\\ \hspace*{16pt}\parbox{16pt}{(i)} Real and tensor valuations\\ \hspace*{16pt}\parbox{16pt}{(ii)} Minkowski valuation\\ \hspace*{16pt}\parbox{16pt}{(iii)} Valuations on function spaces.\\ The focus is on valuations that intertwine the SL$(n)$ and on connections to geometric functional analysis and analytic inequalities.


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### Including Computing Systems in Engineering

 Short Title: Adv. Eng. Softw. Publisher: Elsevier Science Ltd., Oxford ISSN: 0965-9978 Online: http://www.sciencedirect.com/science/journal/09659978 Predecessor: Advances in Engineering Software and Workstations Comments: No longer indexed
 Documents Indexed: 740 Publications (1992–2012) References Indexed: 343 Publications with 9,268 References.
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### Authors

 7 Li, Shouyi 6 Hernández, Santiago 6 Zhao, Zhiye 5 Casteleiro, Manuel 5 Chen, Yaolong 5 Colominas, Ignasi 5 Kisi, Ozgur 5 Kita, Eisuke 5 Navarrina, Fermín 5 Yıldırım, Gürol 4 Bhasker, C. 4 Ferragut, Luis 4 Ganji, Davood Domiri 4 Montero, Gustavo 4 Seckin, Galip 3 Antunes do Carmo, José Simão 3 Bagci, Eyup 3 Bararnia, H. 3 Benhamadou, Mongi 3 Bilhan, Omer 3 Buglione, Luigi 3 Chen, Ting-Yu 3 Cobaner, Murat 3 çunkaş, Mehmet 3 Ebecken, Nelson Francisco Favilla 3 Ebrahim, R. Mohammad 3 Emiroglu, M. Emin 3 Farahani, Reza Zanjirani 3 Fontán, Arturo N. 3 García-Alonso, Fernando 3 Ghasemi, Erfan 3 Kamiya, Norio 3 Kara, Ilker Fatih 3 Kong, Liang 3 Kravanja, Stojan 3 Lai, Jiing-Yih 3 Laier, José Elias 3 Low, Kian Hsiang 3 Migallón, Violeta 3 Nassirharand, Amir 3 Noor, Ahmed Khairy 3 Ong, Hoon Liong 3 Onyejekwe, Okey Oseloka 3 Orsborn, Kjell 3 Özger, Mehmet 3 Penadés, José 3 Rama Mohan Rao, A. 3 Ramamurti, V. 3 Razmi, Jafar 3 Runesha, Hakizumwami B. 3 Senouci, Ahmed B. 3 Siarry, Patrick 3 Sirakoulis, Georgios Ch. 3 Soleimani, Soheil 3 Tanyildizi, Harun 3 Topping, Barry H. V. 3 Tsekouras, George E. 3 Villacampa, Yolanda 3 Wasfy, Tamer M. 3 Zhang, Xiaofei 2 Abran, Alain 2 Akhavan Niaki, Seyed Taghi 2 Akoz, Mevlut Sami 2 Ardiçlıoğlu, Mehmet 2 Asensio, Maria Isabel 2 Atiş, Cengiz D. 2 Baratta, Alessandro 2 Bessaou, Mourad 2 Bittnar, Zdenek 2 Cabaleiro, José Carlos 2 Carr, V. 2 Cascón, José Manuel 2 Cevik, Abdulkadir 2 Cha, Ju-Hwan 2 Chassiakos, Athanasios P. 2 Chen, Changnew 2 Commend, Stéphane 2 Cuillière, Jean-Christophe 2 Diaz, Jacobo 2 Dostál, Zdeněk 2 Dundar, Cengiz 2 Durany, José 2 Efe, Mehmet Onder 2 Escobar, José María 2 Fabian, Martin 2 Farajpour, Ismail 2 Fedorko, G. 2 Filiz, Hüzeyin 2 François, Vincent 2 Galiano, Vicente 2 Göğüş, M. Tolga 2 González-Vidosa, Fernando 2 González-Yuste, José María 2 González, Patricia 2 Gu, Zexu 2 Guo, Dahai 2 Guo, Yong-Ming 2 Guven, Aytac 2 Guzelbey, Ibrahim H. 2 Hájek, Jaroslav ...and 1,388 more Authors
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### Fields

 283 Computer science (68-XX) 213 Mechanics of deformable solids (74-XX) 152 Numerical analysis (65-XX) 98 Operations research, mathematical programming (90-XX) 75 Fluid mechanics (76-XX) 42 Partial differential equations (35-XX) 31 Biology and other natural sciences (92-XX) 28 Geophysics (86-XX) 17 Optics, electromagnetic theory (78-XX) 17 Systems theory; control (93-XX) 16 Classical thermodynamics, heat transfer (80-XX) 15 Statistics (62-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Ordinary differential equations (34-XX) 9 Information and communication theory, circuits (94-XX) 8 Mechanics of particles and systems (70-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 General and overarching topics; collections (00-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 History and biography (01-XX) 3 Potential theory (31-XX) 3 Approximations and expansions (41-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Mathematical logic and foundations (03-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral equations (45-XX) 2 Quantum theory (81-XX) 1 Combinatorics (05-XX) 1 Real functions (26-XX) 1 Probability theory and stochastic processes (60-XX)

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Adaptive $$r$$ and $$h-r$$ algorithms for boundary elements. Zbl 0770.65077
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A finite-difference scheme for mixed boundary value problems of arbitrary-shaped elastic bodies. Zbl 0953.74614
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2000
A multipopulation genetic algorithm aimed at multimodal optimization. Zbl 1011.68115
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2002
Evaluation of singular integrals in the symmetric Galerkin boundary element method. Zbl 1073.65108
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2004
The second generation of self-organizing adaptive penalty strategy for constrained genetic search. Zbl 1075.90081
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2004
Parallel EFG algorithm for heat transfer problems. Zbl 1079.80504
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2005
Neuro-fuzzy approach in estimating Hazen-Williams friction coefficient for small-diameter polyethylene pipes. Zbl 1272.76188
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2009
A new tool in electrostatics using a really-coded multipopulation genetic algorithm tuned through analytical test problems. Zbl 1003.68572
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2001
GAUSS: an online algorithm selection system for numerical quadrature. Zbl 1003.68581
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2002
Large-scale application of some modern CSM methodologies by parallel computation. Zbl 1003.68539
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2000
Computation of sensitivity derivatives of Navier-Stokes equations using complex variables. Zbl 1003.68536
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2000
A methodology for VLSI implementation of cellular automata algorithms using VHDL. Zbl 1003.68562
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2001
Implementation of sub-structuring within an object-oriented framework. Zbl 0984.68529
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2001
Coupling of adaptively refined dual mixed finite elements and boundary elements in linear elasticity. Zbl 1074.65529
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1995
Solution of the Falkner-Skan wedge flow by HPM-Padé method. Zbl 1376.76055
Bararnia, H.; Ghasemi, E.; Soleimani, Soheil; Ghotbi, Abdoul R.; Ganji, D. D.
2012
Stochastic subset optimization incorporating moving least squares response surface methodologies for stochastic sampling. Zbl 1239.62148
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2012
A faster circle-sweep Delaunay triangulation algorithm. Zbl 1239.68075
2012
Ant colony algorithm for traffic signal timing optimization. Zbl 1239.90025
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2012
Analysis of the dynamics of rigid blocks using the theory of distributions. Zbl 1239.74060
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2012
GeoPDEs: a research tool for isogeometric analysis of PDEs. Zbl 1246.35010
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2011
Application of homotopy analysis method to solve MHD Jeffery-Hamel flows in non-parallel walls. Zbl 1316.76078
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2011
Optimizing reserve capacity of urban road networks in a discrete network design problem. Zbl 1239.90014
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2011
Performance analysis and optimization strategies for a D3Q19 lattice Boltzmann kernel on nVIDIA GPUs using CUDA. Zbl 1308.76221
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2011
Computer modelling of wire strands and ropes. I: Theory and computer implementation. Zbl 1459.74004
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2011
Free vibration analyses of Timoshenko beams with free edges by using the discrete singular convolution. Zbl 1231.74168
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2011
Parallel computing techniques applied to the simultaneous design of structure and material. Zbl 1308.74126
Coelho, Pedro G.; Cardoso, João B.; Fernandes, Paulo R.; Rodrigues, Hélder C.
2011
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2011
A parallel strategy for the multiparametric analysis of structures with large contact and friction surfaces. Zbl 1392.74068
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2011
Binary collision of drops in simple shear flow at finite Reynolds numbers: geometry and viscosity ratio effects. Zbl 1356.76375
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2011
Integrating rotation from angular velocity. Zbl 1343.65095
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2011
Solution of free vibration equation of elastically supported Timoshenko columns with a tip mass by differential transform method. Zbl 1231.70018
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2011
Strategic design of competing supply chain networks with foresight. Zbl 1211.90034
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2011
Formulation of the Audze-Eglais uniform Latin hypercube design of experiments for constrained design spaces. Zbl 1416.62449
Fuerle, Fabian; Sienz, Johann
2011
Fast, curvature-based prediction of rolling forces for porous media based on a series of detailed simulations. Zbl 1373.74030
Wiederkehr, T.; Klusemann, B.; Müller, Heinrich; Svendsen, B.
2011
Implementation of the Arlequin method into ABAQUS: basic formulations and applications. Zbl 1332.74049
Qiao, H.; Yang, Q. D.; Chen, W. Q.; Zhang, C. Z.
2011
A graph theoretic-based heuristic algorithm for responsive supply chain network design with direct and indirect shipment. Zbl 1214.90016
Pishvaee, Mir Saman; Rabbani, Masoud
2011
Numerical solutions of the one-phase classical Stefan problem using an enthalpy Green element formulation. Zbl 1229.80009
Onyejekwe, Okey Oseloka; Onyejekwe, Ogugua N.
2011
Double chains quantum genetic algorithm with application to neuro-fuzzy controller design. Zbl 1222.68248
Li, P. C.; Song, K. P.; Shang, F. H.
2011
On a Galerkin boundary node method for potential problems. Zbl 1226.65100
Li, Xiaolin; Zhu, Jialin
2011
Efficient stochastic structural analysis using Guyan reduction. Zbl 1332.74024
Panayirci, H. M.; Pradlwarter, H. J.; Schuëller, G. I.
2011
Use of artificial neural networks for prediction of discharge coefficient of triangular labyrinth side weir in curved channels. Zbl 1332.76037
Bilhan, Omer; Emiroglu, M. Emin; Kisi, Ozgur
2011
A hybrid data-fusion system using modal data and probabilistic neural network for damage detection. Zbl 1412.74073
Jiang, Shao-Fei; Fu, Chun; Zhang, Chunming
2011
Combining temporal partitioning and temporal placement techniques for communication cost improvement. Zbl 1220.68027
Ouni, Bouaoui; Ayadi, Ramzi; Mtibaa, Abdellatif
2011
Parameter sensitivity study of the Nelder-Mead simplex method. Zbl 1220.65071
Wang, Peter C.; Shoup, Terry E.
2011
Friction and wear studies between cylinder liner and piston ring pair using Taguchi design method. Zbl 1219.62187
Kapsiz, Murat; Durat, Mesut; Ficici, Ferit
2011
Parametric optimisation in a 2-D cellular automata model of fundamental seismic attributes with the use of genetic algorithms. Zbl 1416.86017
Georgoudas, I. G.; Sirakoulis, G. Ch.; Scordilis, E. M.; Andreadis, I.
2011
Irregular stock cutting system based on AutoCAD. Zbl 1231.65046
Weng, Wei-Chu; Kuo, Hsin-Chuan
2011
1D unified mathematical model for environmental flow applied to steady aerated mixed flows. Zbl 1408.76382
Kerger, F.; Erpicum, S.; Dewals, B. J.; Archambeau, P.; Pirotton, M.
2011
Using a computational domain and a three-stage node location procedure for multi-sweeping algorithms. Zbl 1231.65045
Ruiz-Gironés, E.; Roca, X.; Sarrate, J.
2011
Simulated wave-driven ANN model for typhoon waves. Zbl 1283.76051
Chang, Hsien-Kuo; Liou, Jin-Cheng; Liu, Shen-Jung; Liaw, Shyne-Ruey
2011
Comprehensive aircraft configuration design tool for integrated product and process development. Zbl 1206.65044
Azamatov, Abdulaziz; Lee, Jae-Woo; Byun, Yung-Hwan
2011
Fractional differential equations in electrochemistry. Zbl 1177.78041
Oldham, Keith B.
2010
Block aggregation of stress constraints in topology optimization of structures. Zbl 1303.74033
París, J.; Navarrina, F.; Colominas, I.; Casteleiro, M.
2010
Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two-opposite edges. Zbl 1406.74269
Civalek, Ömer; Korkmaz, Armağan; Demir, Çiğdem
2010
The quadratic MITC plate and MITC shell elements in plate bending. Zbl 1195.74184
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2010
Approximate traveling wave solutions for coupled Whitham-Broer-Kaup shallow water. Zbl 1372.76078
Ganji, D. D.; Rokni, Houman B.; Sfahani, M. G.; Ganji, S. S.
2010
A study of multiscale wavelet-based elements for adaptive finite element analysis. Zbl 1182.65169
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2010
A modified Pareto genetic algorithm for multi-objective build-to-order supply chain planning with product assembly. Zbl 1231.90397
Che, Z. H.; Chiang, C. J.
2010
A parameter-tuned genetic algorithm for multi-product economic production quantity model with space constraint, discrete delivery orders and shortages. Zbl 1187.90121
Reza Pasandideh, Seyed Hamid; Akhavan Niaki, Seyed Taghi; Yeganeh, Jalil Aryan
2010
PARFES: A method for solving finite element linear equations on multi-core computers. Zbl 1205.65139
Fialko, S.
2010
Multi-objective aggregate production planning with fuzzy parameters. Zbl 1231.90395
2010
Alternating two-stage methods for consistent linear systems with applications to the parallel solution of Markov chains. Zbl 1184.65039
Migallón, Héctor; Migallón, Violeta; Penadés, Jose
2010
A parameter free continuous ant colony optimization algorithm for the optimal design of storm sewer networks: constrained and unconstrained approach. Zbl 1182.65087
Afshar, M. H.
2010
Boundary point method for linear elasticity using constant and quadratic moving elements. Zbl 1303.74037
Ma, Hang; Zhou, Juan; Qin, Qing-Hua
2010
Cloud theory-based simulated annealing approach for scheduling in the two-stage assembly flowshop. Zbl 1201.90086
2010
Improved group-theoretical method for eigenvalue problems of special symmetric structures, using graph theory. Zbl 1180.65044
Kaveh, A.; Nikbakht, M.
2010
Automatic LEFM crack propagation method based on local Lepp-Delaunay mesh refinement. Zbl 1423.74815
Azócar, David; Elgueta, Marcelo; Rivara, María Cecilia
2010
Single- and multi-objective shape design of Y-noise barriers using evolutionary computation and boundary elements. Zbl 1182.65097
Greiner, David; Aznárez, Juan J.; Maeso, Orlando; Winter, Gabriel
2010
A mesh-geometry based method for coupling 1D and 3D elements. Zbl 1346.74165
Bournival, Sylvain; Cuillière, Jean-Christophe; François, Vincent
2010
Behavior of micro-polar flow due to linear stretching of porous sheet with injection and suction. Zbl 1346.76192
Bararnia, H.; Ghasemi, E.; Domairry, G.; Soleimani, S.
2010
Efficient solution for Galerkin-based polynomial chaos expansion systems. Zbl 1205.65025
Panayirci, H. M.
2010
An efficient genetic algorithm to maximize net present value of project payments under inflation and bonus-penalty policy in resource investment problem. Zbl 1194.90057
Shahsavar, Moslem; Niaki, Seyed Taghi Akhavan; Najafi, Amir Abbas
2010
A new mechanism for maintaining diversity of Pareto archive in multi-objective optimization. Zbl 1197.65063
Hájek, Jaroslav; Szöllös, András; Šístek, Jakub
2010
Strategic design of competing centralized supply chain networks for markets with deterministic demands. Zbl 1188.91074
Rezapour, Shabnam; Farahani, Reza Zanjirani
2010
Parallel discrete element simulation of poly-dispersed granular material. Zbl 1381.74234
Kačianauskas, Rimantas; Maknickas, Algirdas; Kačeniauskas, Arnas; Markauskas, Darius; Balevičius, Robertas
2010
Predicting discharge capacity of triangular labyrinth side weir located on a straight channel by using an adaptive neuro-fuzzy technique. Zbl 1423.76335
Emiroglu, M. Emin; Kisi, Ozgur; Bilhan, Omer
2010
Genetic algorithms and finite element coupling for mechanical optimization. Zbl 1303.74035
Corriveau, Guillaume; Guilbault, Raynald; Tahan, Antoine
2010
Optimal trajectory planning for industrial robots. Zbl 1379.70012
Gasparetto, A.; Zanotto, V.
2010
Artificial neural network approaches for prediction of backwater through arched bridge constrictions. Zbl 1406.74003
Pinar, Engin; Paydas, Kamil; Seckin, Galip; Akilli, Huseyin; Sahin, Besir; Cobaner, Murat; Kocaman, Selahattin; Akar, M. Atakan
2010
Inverse analysis FOR two-dimensional structures using the boundary element method. Zbl 1425.74203
Ferreira, M. D. C.; Venturini, W. S.
2010
Topology optimization of three-dimensional load-bearing structures using boundary elements. Zbl 1307.74059
Bertsch, Christine; Cisilino, Adrián P.; Calvo, Néstor
2010
Usage of artificial intelligence methods in free flowing gated closed conduits for estimation of oxygen transfer efficiency. Zbl 1307.76069
Baylar, A.; Batan, M.
2010
Solving PDEs in non-rectangular 3D regions using a collocation finite element method. Zbl 1187.65130
Sewell, Granville
2010
Modelling solute transport in soil columns using advective-dispersive equations with fractional spatial derivatives. Zbl 1381.76349
San Jose Martinez, F.; Pachepsky, Y. A.; Rawls, W. J.
2010
PyPnetCDF: a high level framework for parallel access to netCDF files. Zbl 1185.68110
Galiano, Vicente; Migallón, Héctor; Migallón, Violeta; Penadés, Jose
2010
On the improvements of the particle swarm optimization algorithm. Zbl 1182.65089
Chen, Ting-Yu; Chi, Tzu-Ming
2010
On the viscoelastic beam subjected to moving mass. Zbl 1423.74503
Mofid, M.; Tehranchi, A.; Ostadhossein, A.
2010
Generation of structured meshes in multiply connected surfaces using submapping. Zbl 1182.65186
Ruiz-Gironés, E.; Sarrate, J.
2010
Application of two different neural network techniques to lateral outflow over rectangular side weirs located on a straight channel. Zbl 1346.76122
Bilhan, Omer; Emiroglu, M. Emin; Kisi, Ozgur
2010
Navigation of mobile robots in the presence of obstacles. Zbl 1381.70022
Abiyev, R.; Ibrahim, D.; Erin, B.
2010
Development and validation of a numerical topology optimization scheme for two and three dimensional structures. Zbl 1372.74071
Taggart, D. G.; Dewhurst, P.
2010
Bézier-PARSEC: an optimized aerofoil parameterization for design. Zbl 1372.76015
Derksen, R. W.; Rogalsky, Tim
2010
Comparing numerical methods for response of beams with moving mass. Zbl 1312.74061
Bulut, Hasan; Kelesoglu, Omer
2010
An elasto-viscoplastic analysis of direct extrusion of a double base solid propellant. Zbl 1425.74096
Kalaycioglu, Baris; Dirikolu, M. Husnu; Çelik, Veli
2010
ANN-based GA for generating the sizing curve of stand-alone photovoltaic systems. Zbl 1189.78045
2010
Hybrid one-way delay estimation for networked control system. Zbl 1185.93008
Xu, Wenjun; Zhou, Zude; Liu, Quan
2010
A mixed integer linear program and tabu search approach for the complementary edge covering problem. Zbl 1187.65070
2010
Rapid low fidelity turbomachinery disk optimization. Zbl 1279.76021
Gutzwiller, David P.; Turner, Mark G.
2010
Genetic heritage evolution by stochastic transmission in the optimal design of water distribution networks. Zbl 1184.90028
Bolognesi, Andrea; Bragalli, Cristiana; Marchi, Angela; Artina, Sandro
2010
Numerical modelling of fatigue crack initiation of martensitic steel. Zbl 1279.74039
Glodež, S.; Jezernik, N.; Kramberger, J.; Lassen, T.
2010
A solution to the fundamental linear complex-order differential equation. Zbl 1185.34003
2010
Comparison of an ANN approach with 1-D and 2-D methods for estimating discharge capacity of straight compound channels. Zbl 1423.86009
Unal, Burhan; Mamak, Mustafa; Seckin, Galip; Cobaner, Murat
2010
Effective thermal emission on TFT-LCD TV panels for improving image quality. Zbl 1375.80020
Chu, Chung-Yi; Pan, Min-Chun
2010
Buckling analysis of laminated composite plates with an elliptical/circular cutout using FEM. Zbl 1423.74344
Komur, M. Aydin; Sen, Faruk; Ataş, Akın; Arslan, Nurettin
2010
An adaptive parametric interpolator for trajectory planning. Zbl 1182.65021
Wang, Xin; Wang, Junwei; Rao, Zhi
2010
An alternative scheme for the corner-corner contact in the two-dimensional discontinuous deformation analysis. Zbl 1423.74658
Bao, Huirong; Zhao, Zhiye
2010
Shape and discrete sizing optimization of timber trusses by considering of joint flexibility. Zbl 1423.74735
Šilih, S.; Kravanja, S.; Premrov, M.
2010
Wave-current interactions over bottom with appreciable variations in both space and time. Zbl 1423.76057
Antunes do Carmo, José Simão
2010
Modeling of transfer length of prestressing strands using genetic programming and neuro-fuzzy. Zbl 1423.74493
2010
Base sliding and dynamic response of landfills. Zbl 1178.86005
Zania, Varvara; Psarropoulos, Prodromos N.; Tsompanakis, Yiannis
2010
Artificial neural network-based kinematics Jacobian solution for serial manipulator passing through singular configurations. Zbl 1355.70005
Hasan, Ali T.; Ismail, N.; Hamouda, A. M. S.; Aris, Ishak; Marhaban, M. H.; Al-Assadi, H. M. A. A.
2010
On the use of a SIMD vector extension for the fast evaluation of boundary element method coefficients. Zbl 1303.76097
Iemma, Umberto
2010
Development of an object-oriented finite element program with adaptive mesh refinement for multi-physics applications. Zbl 1406.74640
Nie, J. H.; Hopkins, D. A.; Chen, Y. T.; Hsieh, H. T.
2010
A CAE-integrated distributed collaborative design system for finite element analysis of complex product based on SOOA. Zbl 1183.65016
Yu, Jiaqing; Cha, Jianzhong; Lu, Yiping; Xu, Wensheng; Sobolewski, M.
2010
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### Cited in 270 Journals

 184 Computer Methods in Applied Mechanics and Engineering 117 Engineering Analysis with Boundary Elements 81 Advances in Engineering Software 79 International Journal for Numerical Methods in Engineering 53 Computational Mechanics 53 Applied Mathematical Modelling 50 Mathematical Problems in Engineering 47 Computers & Mathematics with Applications 44 Applied Mathematics and Computation 33 Journal of Computational Physics 31 Engineering Computations 31 Structural and Multidisciplinary Optimization 27 Journal of Computational and Applied Mathematics 21 Computers & Operations Research 19 International Journal of Production Research 17 International Journal of Computer Mathematics 16 European Journal of Operational Research 16 Archives of Computational Methods in Engineering 15 Acta Mechanica 15 Applied Numerical Mathematics 15 Journal of Vibration and Control 14 Computers and Fluids 13 International Journal of Computational Methods 12 European Journal of Mechanics. A. Solids 10 Numerical Algorithms 10 Nonlinear Dynamics 9 International Journal of Computational Fluid Dynamics 9 Abstract and Applied Analysis 9 International Journal of Structural Stability and Dynamics 8 Meccanica 8 Applied Mathematics and Mechanics. (English Edition) 8 Journal of Global Optimization 8 Communications in Numerical Methods in Engineering 8 Journal of Mathematical Chemistry 8 Optimization and Engineering 8 Inverse Problems in Science and Engineering 8 Acta Mechanica Sinica 8 International Journal for Computational Methods in Engineering Science and Mechanics 8 International Journal of Applied and Computational Mathematics 7 International Journal for Numerical Methods in Fluids 7 Fuzzy Sets and Systems 7 Kybernetes 7 Mathematics and Computers in Simulation 7 SIAM Journal on Scientific Computing 7 Computational and Applied Mathematics 7 International Journal of Theoretical and Applied Finance 7 Communications in Nonlinear Science and Numerical Simulation 7 Journal of Computational Acoustics 7 Boundary Value Problems 7 Journal of Industrial and Management Optimization 6 International Journal of Heat and Mass Transfer 6 Numerical Methods for Partial Differential Equations 6 Mathematical and Computer Modelling 6 Advances in Difference Equations 6 Advances in Applied Mathematics and Mechanics 5 International Journal for Numerical and Analytical Methods in Geomechanics 5 International Journal of Solids and Structures 5 Wave Motion 5 Computing 5 Mechanics Research Communications 5 Journal of Scientific Computing 5 Annals of Operations Research 5 European Journal of Mechanics. B. Fluids 5 International Journal of Fracture 5 Optimization Letters 5 Advances in Mathematical Physics 4 Journal of Fluid Mechanics 4 Journal of the Franklin Institute 4 Chaos, Solitons and Fractals 4 Automatica 4 Information Sciences 4 Journal of Optimization Theory and Applications 4 Numerische Mathematik 4 Opsearch 4 Theoretical Computer Science 4 Asia-Pacific Journal of Operational Research 4 Applied Mathematics Letters 4 Archive of Applied Mechanics 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Computational Optimization and Applications 4 International Journal of Numerical Methods for Heat & Fluid Flow 4 Advances in Computational Mathematics 4 Complexity 4 Mathematics and Mechanics of Solids 4 Multibody System Dynamics 4 Mathematical and Computer Modelling of Dynamical Systems 4 Discrete Dynamics in Nature and Society 4 International Journal of Nonlinear Sciences and Numerical Simulation 4 Journal of Applied Mathematics 4 International Journal for Numerical Methods in Biomedical Engineering 4 Computational Methods for Differential Equations 3 Mathematical Methods in the Applied Sciences 3 BIT 3 Journal of Non-Newtonian Fluid Mechanics 3 Pattern Recognition 3 Continuum Mechanics and Thermodynamics 3 Numerical Linear Algebra with Applications 3 International Transactions in Operational Research 3 Optimization Methods & Software 3 Computational Geosciences ...and 170 more Journals
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### Cited in 46 Fields

 653 Numerical analysis (65-XX) 631 Mechanics of deformable solids (74-XX) 260 Operations research, mathematical programming (90-XX) 251 Fluid mechanics (76-XX) 195 Partial differential equations (35-XX) 107 Ordinary differential equations (34-XX) 100 Computer science (68-XX) 65 Systems theory; control (93-XX) 60 Biology and other natural sciences (92-XX) 43 Classical thermodynamics, heat transfer (80-XX) 39 Calculus of variations and optimal control; optimization (49-XX) 39 Geophysics (86-XX) 36 Probability theory and stochastic processes (60-XX) 34 Real functions (26-XX) 29 Mechanics of particles and systems (70-XX) 27 Optics, electromagnetic theory (78-XX) 27 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 26 Integral equations (45-XX) 26 Statistics (62-XX) 25 Operator theory (47-XX) 20 Harmonic analysis on Euclidean spaces (42-XX) 19 Approximations and expansions (41-XX) 12 Statistical mechanics, structure of matter (82-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 9 Combinatorics (05-XX) 9 Functions of a complex variable (30-XX) 9 Dynamical systems and ergodic theory (37-XX) 8 Information and communication theory, circuits (94-XX) 7 Quantum theory (81-XX) 6 Potential theory (31-XX) 6 Functional analysis (46-XX) 5 Special functions (33-XX) 5 Difference and functional equations (39-XX) 3 History and biography (01-XX) 2 Sequences, series, summability (40-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Nonassociative rings and algebras (17-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Relativity and gravitational theory (83-XX) 1 Mathematics education (97-XX)


text:
# More on 'Number of Tiers' Discussion

Tim Bass (@NANOG-LIST) nanog at dune.silkroad.com
Sun Apr 14 18:03:46 UTC 1996

Michael,

There is little doubt that the 'existing operational ecology'
is a very suboptimal paradigm (4,5, or whatever-level). It is
suboptimal for IPv4 and extremely suboptimal for IPv6.

Kamoun and Klienrock were specific ) and Tanenbaum in his latest
and greatest third edition agreed ) that a ln(N) hierarchical
superstructure is optimal for large networks.  They also
conclude that path-length is 'not a real problem', just to be
complete.

BTW, and please do not take this in a negative way and I
offer my apologies for the following diatribe:

\begin{diatribe}

Documenting 'the way things are' is nice for 'informational
and historical' purposes.  But, building new paradigms and
structures on top of highly suboptimal and outdated architectures
just added to the problem and does little to move society
toward progress.

Using the 'information RFC' logic below; we could easily apply
the same logic to humankind.  Crime, hatred, envy, greed, selfishness,
etc. is 'the way human society exists' suboptimal and problematic.
Why strive to build a better 'human network' when the 'informational
human RFC' (IHRFC maybe ;-) clearly documents a very suboptimal
civilization.

Anyway, as I once had to learn and still learn every day, _opinions_
are not unique and everyone has at least five thousand of them,
making _opinions_ noise with knowledge.  Doing the background research,
going back to the body of knowledge in the field and adding
foundation to vision and opinion significantly decreases the
noise level.

\end{diatribe}

Just think how effective NANOG or any group could be if all the working
members took the time to learn the body of background knowledge
others have left around as 'clues'.

Best Regards,

Tim

>
> On Sun, 14 Apr 1996, Tim Bass wrote:
>
> > The simple idea for illumination in this post is simply; It is not A Good
> > Idea to propose a concrete, structured four-level superstructure
> > for the Internet  (and we have not begin to look at IPv6, BTW).
>
> Not proposing a 4-level hierarchical routing technology.
> Just describing the existing operational ecology using a 4-level metaphor
> as a proposed informational RFC.
>
> Have a look at http://www.sidhe.memra.com/rough.txt if you want to see
> the rough draft.
>


text:
# Writing to many cells from many controls' respective value

I have this program on Excel VBA, that implements a userform in order to simplify input and to create control charts from the data input analyze the data and send emails if certain conditions are met.

My problem is that everything works properly but after running line by line I noticed that when filling up the corresponding cells in excel with the user input on the userform the macro takes long to execute each line.

I am wondering if any of you have a different method of doing this that would reduce the time it takes to run through all these lines.

Function completeData(mo As String)

Dim row As Integer
row = moRow(mo)
DataHistory

'Tag Information
Worksheets("Data").Cells(row, 2).value = ComboBox1.value 'set UPC
Worksheets("Data").Cells(row, 4).value = TextBox2.value 'set DateCured
Worksheets("Data").Cells(row, 5).value = TextBox48.value 'set DateTested
Worksheets("Data").Cells(row, 41).value = ComboBox2.value 'set Grinder
Worksheets("Data").Cells(row, 42).value = ComboBox3.value 'set Metal
Worksheets("Data").Cells(row, 43).value = ComboBox4.value 'set Press
Worksheets("Data").Cells(row, 44).value = ComboBox5.value 'set Clock
Worksheets("Data").Cells(row, 45).value = ComboBox6.value 'set Oven

'weight 0min Wheels
Worksheets("Data").Cells(row, 15).value = TextBox3.value
Worksheets("Data").Cells(row + 1, 15).value = TextBox4.value
Worksheets("Data").Cells(row + 2, 15).value = TextBox5.value

'Before Thikness
''''FirstWheel
Worksheets("Data").Cells(row, 6).value = TextBox6.value
Worksheets("Data").Cells(row, 7).value = TextBox7.value
Worksheets("Data").Cells(row, 8).value = TextBox8.value
Worksheets("Data").Cells(row, 9).value = TextBox9.value
''''SecondWheel
Worksheets("Data").Cells(row + 1, 6).value = TextBox10.value
Worksheets("Data").Cells(row + 1, 7).value = TextBox11.value
Worksheets("Data").Cells(row + 1, 8).value = TextBox12.value
Worksheets("Data").Cells(row + 1, 9).value = TextBox13.value
''''ThirdWheel
Worksheets("Data").Cells(row + 2, 6).value = TextBox14.value
Worksheets("Data").Cells(row + 2, 7).value = TextBox15.value
Worksheets("Data").Cells(row + 2, 8).value = TextBox16.value
Worksheets("Data").Cells(row + 2, 9).value = TextBox17.value

'Balance
Worksheets("Data").Cells(row, 11).value = TextBox18.value
Worksheets("Data").Cells(row + 1, 11).value = TextBox19.value
Worksheets("Data").Cells(row + 2, 11).value = TextBox20.value

'weight 0min Material
Worksheets("Data").Cells(row, 19).value = TextBox21.value
Worksheets("Data").Cells(row + 1, 19).value = TextBox22.value
Worksheets("Data").Cells(row + 2, 19).value = TextBox23.value

'After 5min
'''Wheels
Worksheets("Data").Cells(row, 16).value = TextBox24.value
Worksheets("Data").Cells(row + 1, 16).value = TextBox25.value
Worksheets("Data").Cells(row + 2, 16).value = TextBox26.value
'''Metal
Worksheets("Data").Cells(row, 20).value = TextBox27.value
Worksheets("Data").Cells(row + 1, 20).value = TextBox28.value
Worksheets("Data").Cells(row + 2, 20).value = TextBox29.value
'checkSpallin 5 min
If CheckBox1.value = True Then Worksheets("Data").Cells(row, 12).value = "Y"
If CheckBox2.value = True Then Worksheets("Data").Cells(row + 1, 12).value = "Y"
If CheckBox3.value = True Then Worksheets("Data").Cells(row + 2, 12).value = "Y"

'Grinding from 5min to 10min metal initial weight
Worksheets("Data").Cells(row, 21).value = TextBox30.value
Worksheets("Data").Cells(row + 1, 21).value = TextBox31.value
Worksheets("Data").Cells(row + 2, 21).value = TextBox32.value

'After 10min
'''Wheels
Worksheets("Data").Cells(row, 17).value = TextBox33.value
Worksheets("Data").Cells(row + 1, 17).value = TextBox34.value
Worksheets("Data").Cells(row + 2, 17).value = TextBox35.value
'''Metal
Worksheets("Data").Cells(row, 22).value = TextBox36.value
Worksheets("Data").Cells(row + 1, 22).value = TextBox37.value
Worksheets("Data").Cells(row + 2, 22).value = TextBox38.value
'checkSpallin 10 min
If CheckBox4.value = True Then Worksheets("Data").Cells(row, 13).value = "Y"
If CheckBox5.value = True Then Worksheets("Data").Cells(row + 1, 13).value = "Y"
If CheckBox6.value = True Then Worksheets("Data").Cells(row + 2, 13).value = "Y"

'Grinding from 10min to 15min metal initial weight
Worksheets("Data").Cells(row, 23).value = TextBox39.value
Worksheets("Data").Cells(row + 1, 23).value = TextBox40.value
Worksheets("Data").Cells(row + 2, 23).value = TextBox41.value

'After 15min
'''Wheels
Worksheets("Data").Cells(row, 18).value = TextBox42.value
Worksheets("Data").Cells(row + 1, 18).value = TextBox43.value
Worksheets("Data").Cells(row + 2, 18).value = TextBox44.value
'''Metal
Worksheets("Data").Cells(row, 24).value = TextBox45.value
Worksheets("Data").Cells(row + 1, 24).value = TextBox46.value
Worksheets("Data").Cells(row + 2, 24).value = TextBox47.value
'checkSpallin 15 min
If CheckBox7.value = True Then Worksheets("Data").Cells(row, 14).value = "Y"
If CheckBox8.value = True Then Worksheets("Data").Cells(row + 1, 14).value = "Y"
If CheckBox9.value = True Then Worksheets("Data").Cells(row + 2, 14).value = "Y"

End Function

Like I said, it works but it takes long to finish. Essentially this is what is consuming time. I don't know what to implement to make it run faster. Any ideas are welcome.

• There is no reason for this code to take a second to execute. Does the Data worksheet contain a lot of formulas? Please post the code for moRow(mo).
– user109261
Aug 22, 2016 at 16:21
• What's DataHistory doing? You'll want to include it in your post, since it might be where your bottleneck is. What code is caling this function? Is it called in a loop? This definitely looks like a Code Review question, but it will need a bit more context to be meaningfully answered. Aug 22, 2016 at 16:23
• moRow finds row, DataHistory is meant to set a record for the combobox. That said, those two lines take O(1) to execute, what is taking long is each line after 'Tag Information. @Mikegrann thank you for your array recommendation. I'll take a look at that.
– Jorge Vargas Moreno
Aug 22, 2016 at 16:27
• The rest of the code also executes in constant time. That doesn't mean it's the part slowing you down. Direct assignments into cell values are slow, but Thomas is right when he says that it shouldn't take nearly as long as described for a single run. Look at your other procedures again for possible slowdowns. Aug 22, 2016 at 16:31
• A With ... End With statement would not only clean up the code but improve its execution time. edit Since you are not returning a value, this would be better as a Sub rather than a Function.
– user66882
Aug 22, 2016 at 16:35

## 3 Answers

The first thing to do is to switch off calculation, sheet events and screen updating before you write anything to a worksheet, and restore it when you're done: that way you won't have Excel try to re-calculate the entire workbook whenever you write to a cell.

Next, name things, starting with the "Data" sheet. Select the worksheet in the Project Explorer (Ctrl+R), then bring up the Properties toolwindow (F4) and type DataSheet under the sheet's (name) property.

Then you can do this:

With DataSheet
.Cells(...).Value = ...
.Cells(...).Value = ...
.Cells(...).Value = ...
.Cells(...).Value = ...
.Cells(...).Value = ...
.Cells(...).Value = ...
.Cells(...).Value = ...
...
End With

In the form's designer (F7), give each control a meaningful name. For example ComboBox1 contains a UPC code, so it should be named SelectedUPC.

The problem with this is that you already have tons of code referring to these controls, and renaming ComboBox1 to SelectUPC would break your code, because ComboBox1 would be left referring to nothing.

You'll need tools to do this cleanly. Fortunately Rubberduck can help with this refactoring:

You could right-click on a control, select Rubberduck > Rename (or right-click a ComboBox1 identifier reference in the code, select Rubberduck > Refactor > Rename), then specify SelectedUPC as the new name, and then...

Rubberduck renames the associated event handler(s) and in-code identifier references for you - so there's no excuse for having meaningless identifiers anywhere anymore.

DISCLAIMER I'm heavily involved with the Rubberduck project.

Speaking of naming, it's not clear at all what moRow means to be doing, nor who is calling that function, or even why it needs to be a Function.

Procedures that don't return a value should be Sub procedures; a Sub procedure executes a sequence of operations; a Function procedure computes a value and returns it to the caller.

Also, module members in VBA are implicitly Public, which means completeData (which should be CompleteData to be PascalCase like all other VBA procedures) is a public member of that UserForm.

I'd strongly recommend reading up on VBA UserForm best practices, and restructure your code so that the form doesn't "run the show": the form should be there only to provide the rest of the code with user input, not to actually perform the worksheet manipulations - a form's code-behind should only be concerned about the form and its controls; a form that knows about a worksheet, plainly knows (and does) too many things.

I'd also suggest you define an enum to name each column of your "Data" sheet, so instead of this:

With DataSheet
.Cells(row, 2).Value = SelectedUPC.Value

You would have that:

With DataSheet
.Cells(row, DataSheetColumns.UPC).Value = SelectedUPC.Value

All that's needed is a simple declaration:

Private Enum DataSheetColumns
UPC = 2
DateCured = 4
DateTested = 5
...
End Enum

That makes it much easier to read the rest of the code, and seeing DataSheetColumns.UPC being assigned to SelectedClock.Value looks much more wrong than if it's column 44 being assigned: making wrong code look wrong is even more important than writing code that "works".

You are writing to a lot of cells one at a time, which can be slow. Your output doesn't go into a single block of cells, which is too bad, but you can still make it faster by building an array wherever possible and dumping this array into the sheet in one shot.

For example, this block

'Before Thikness
''''FirstWheel
Worksheets("Data").Cells(row, 6).value = TextBox6.value
Worksheets("Data").Cells(row, 7).value = TextBox7.value
Worksheets("Data").Cells(row, 8).value = TextBox8.value
Worksheets("Data").Cells(row, 9).value = TextBox9.value
''''SecondWheel
Worksheets("Data").Cells(row + 1, 6).value = TextBox10.value
Worksheets("Data").Cells(row + 1, 7).value = TextBox11.value
Worksheets("Data").Cells(row + 1, 8).value = TextBox12.value
Worksheets("Data").Cells(row + 1, 9).value = TextBox13.value
''''ThirdWheel
Worksheets("Data").Cells(row + 2, 6).value = TextBox14.value
Worksheets("Data").Cells(row + 2, 7).value = TextBox15.value
Worksheets("Data").Cells(row + 2, 8).value = TextBox16.value
Worksheets("Data").Cells(row + 2, 9).value = TextBox17.value

can be streamlined like this:

'Before Thikness
Dim vOutput As Variant
ReDim vOutput(1 To 3, 1 To 4)
''''FirstWheel
vOutput(1, 1) = TextBox6.value
vOutput(1, 2) = TextBox7.value
vOutput(1, 3) = TextBox8.value
vOutput(1, 4) = TextBox9.value
''''SecondWheel
vOutput(2, 1).value = TextBox10.value
vOutput(2, 2) = TextBox11.value
vOutput(2, 3) = TextBox12.value
vOutput(2, 4) = TextBox13.value
''''ThirdWheel
vOutput(3, 1) = TextBox14.value
vOutput(3, 2) = TextBox15.value
vOutput(3, 3) = TextBox16.value
vOutput(3, 4) = TextBox17.value
''''Dump to worksheet
Worksheets("Data").Cells(row, 6).Resize(3, 4).Value = vOutput

Do this wherever there are blocks of output.

At the same time, follow the suggestions to turn off screen updating and automatic calculations.

Option Explicit

Function completeData(mo As String)

Application.ScreenUpdating = False

Dim row As LongPtr

row = moRow(mo)

...rest of code

Application.ScreenUpdating = True

End Function

• Your answer could really benefit from some explanation as to what you are suggesting and why. Aug 29, 2016 at 10:57
• What's the LongPtr for? What's the rationale behind it? What if the code needs to run on 32-bit Office? Please take a minute to edit your answer to clarify - a code dump is scarcely a well-received answer on this site. Aug 29, 2016 at 14:31
• LongPtr is a long integer pointer data type. it helps the macro to run a bit quicker for integer values such as row numbers. I am not sure if this is a problem on 32 bit office. Though I have found Long Integer Pointer LongPtr to be useful for running through rows in large text file counts and also large excel worksheets quicker than the integer data type. Using non-variant data types where possible speeds up the macro.
– R2D2
Oct 30, 2016 at 22:00


text:
A 10 meters long ladder is leaned against a wall and a 1 meter times 1 meter big box, as the picture illustrates. The width of the ladder is negligible. How high up on the wall does the ladder reach?

2. Look at the similar triangles.
(1 Blue dot and 2 red dots) and the triangle (1 Blue dot and 2 black dots).

Thus,
$\frac{h-1}{1}=\frac{h}{w}$

And, by Pythagorean theorem,
$w^2+h^2=100$

Now you can solve

3. This gives me a fourth order equation. I don't know how to solve them.

4. Originally Posted by TriKri
This gives me a fourth order equation. I don't know how to solve them.
Take hackers equations and turn them into an interative scheme:

$
w_n=\frac{h_n-1}{h_n}
$

$
h_{n+1}=\sqrt{100-w_n^2}
$

Now put $h_0=9.9$, $h_1=9.93794$, $h_2=9.93799$, $h_3=9.93799$.

So $h \approx 9.93799$

(we choose an initial guess of $h=9.9$ by doing a rough drawing of the
arrangement and measuring the approximate height, but a rough guess of 9 will have
added just one more iteration to get this level of accuracy)

The scheme also produces an approimate value for $w\approx 1.11188$

RonL

5. I would like to note that there is technically another solution: h = 1.11188 m, which the diagram (sort of) rules out. In this case the ladder is nearly horizontal rather than vertical. (I rarely take diagrams as being "to scale" or in the correct orientation unless I have to.)

-Dan

6. Originally Posted by CaptainBlack
Take hackers equations and turn them into an interative scheme:

$
w_n=\frac{h_n}{h_n-1}
$

$
h_{n+1}=\sqrt{100-w_n^2}
$

Now put $h_0=9.9$, $h_1=9.959509$, $h_2=9.959454$, $h_3=9.959454$.

So $h \approx 9.959454$

(we choose an initial guess of $h=9.9$ by doing a rough drawing of the
arrangement and measuring the approximate height, but a rough guess of 9 will have
added just one more iteration to get this level of accuracy)

RonL
Nice! But that's cheating!

7. Originally Posted by TriKri
Nice! But that's cheating!
In what way, I could have guessed the solution anyway I wanted.

By the way for some reason the iterative solution appears to be wrong,
that I will have to look into

Fixed now. Note the value of w produced is topsquarks other solution.

RonL

8. I solved it without using numerical methods.
It is a bit tricky.

The ladder is 10m long and let at the point of contact with the box, it is divided into x(the upper part) and y(the lower part).{x+y=10}
You see that
$\frac{1}{x^2}+\frac{1}{y^2}=1$
$x^2 +y^2=x^2y^2$
$(x+y)^2=(xy)^2+2xy$
Let xy=b
$100=b^2+2b$
$b^2+2b-100=0$
since b is positive
$b(=xy)=\sqrt{101}-1$
$x(10-x)=\sqrt{101}-1$
solving for x, we get
$x=5\pm \sqrt{24-\sqrt{101}}$
Since we are looking for maximum height,
we have
$x=5+ \sqrt{24-\sqrt{101}}$
$h=\sqrt{x^2-1}+1$

Keep Smiling
Malay

9. Wow, impressive! How did you know you should solve it like this? Is it some kind of standard equation in some branch of mathematics? I'm just wondering because I haven't read enough with math to be able to solve it myself... ^_^

10. Originally Posted by TriKri
Wow, impressive! How did you know you should solve it like this? Is it some kind of standard equation in some branch of mathematics? I'm just wondering because I haven't read enough with math to be able to solve it myself... ^_^

It just striked me.
I haven't studied fourth order equations, was trying to use the cube(its all sides are equal)

Keep Smiling
Malay

11. That's some ladder problem. I didn't know it could get this hard :-P Man, my math class is wimpy XD

12. Originally Posted by benzi455
That's some ladder problem. I didn't know it could get this hard :-P Man, my math class is wimpy XD

Have you showed them malaygoel's solution?

13. Originally Posted by malaygoel
It just striked me.
I haven't studied fourth order equations, was trying to use the cube(its all sides are equal)

Keep Smiling
Malay
The cube? I haven't heard of that before, but not strange, regardning what I said before...

I was trying to make the equation more general by puting the sides of the bow to a and b, but I couldn't solve it you'r way since I couldn't get only xy left in the equation and no x or y. But I'm still impressed. Is this the way to solve third order equations?

14. Originally Posted by TriKri
Is this the way to solve third order equations?
Yes!

It was first made by Italian mathematicians: Tartalia, Cardano. I think they kept it secret.

I have memorized the original method for solving 3rd order equations . And can up with my own which is simpler but not always works, 2 nights ago when I was falling asleep I was thinking about a techinique that will make my solution always workable did not try it yet.

Maybe, I will post it for thee.

15. Originally Posted by ThePerfectHacker
Yes!

It was first made by Italian mathematicians: Tartalia, Cardano. I think they kept it secret.

I have memorized the original method for solving 3rd order equations . And can up with my own which is simpler but not always works, 2 nights ago when I was falling asleep I was thinking about a techinique that will make my solution always workable did not try it yet.

Maybe, I will post it for thee.
Trikri!!
i mistyped it.
I want to say I was trying use the square.
i don't know how to solve cubic equations.

Keep Smiling
Malay


text:
With the school year starting, I can’t keep up with the one-post-a-day frequency anymore. Still, I want to keep plowing ahead towards class field theory.

Today’s main goal is to show that under certain conditions, we can always extend valuations to bigger fields. I’m not aiming for maximum generality here though.

Dedekind Domains and Extensions

One of the reasons Dedekind domains are so important is

Theorem 1 Let ${A}$ be a Dedekind domain with quotient field ${K}$, ${L}$ a finite separable extension of ${K}$, and ${B}$ the integral closure of ${A}$ in ${L}$. Then ${B}$ is Dedekind. (more…)


text:
# countable intersection of closed convex bounded subsets reflexive banach space is non empty.

If $X$ is a reflexive Banach space and $(C_n), n \in \mathbb{N}$ is a sequence of closed convex bounded sets with $C_{n+1}$ contained in $C_n$ for all $n \in \mathbb{N}$. How does one show that the countable intersection of $C_n$ for $n \in \mathbb{N}$ is not the empty set?

-
How does one mark some answers as correct? – nada Jun 10 '12 at 18:43

If $x_n \in C_n$, Eberlein-Shmulyan says some subsequence has a weak limit point $x$. Show that $x$ is in all the $C_n$. – Robert Israel Jun 10 '12 at 22:00


text:
# Looking for an equation expressed algebriacally that answers the following

1. Jun 28, 2009

### seasnake

Given an XY graph where the horizontal line is X and the vertical line is Y and their intersection is zero, if A = 0,1 (a horizontal line one increment above the X axis), I want to know the formula that correctly expresses the value of B if B started at 0,0 and always approaches infinite A at a uniformly constant rate.

2. Jun 28, 2009

### Mentallic

a.k.a. The Cartesian Plane. Probably the most widely known and frequently used coordinate system in Mathematics

Everything is very clear cut, until...
You just said "A= 0, 1", a notation I would have interpreted as the point (0, 1) but then you say "(a horizontal line one increment above the X axis)" which is the line y= 1. In either case, what do you mean by "approaches infinite A"? A is NOT "infinite". Do you mean "is asymptotic to y= 1 as x goes to infinity"? And what do you mean by "approaches at a uniformly constant rate"? That d(y-1)/dx= constant? That's impossible. Any solution to that is linear and cannot be asymptotic to y= 1. d(y-1)/dx= constant*(y-1) is possible. Calling the constant rate $\alpha$, any solution to that is of the form
$$y=1+ Ce^{\alpha x}$$
which approaches y= 1 at constant rate $\alpha< 0$.


text:
Math and Arithmetic
Algebra
Calculus

# What is the answer to Evaluate e to the x sinx dx?

###### Wiki User

Evaluate the integral?

Use integration by parts.

uv - int v du

u = e^x

du = e^x

dv = sinx

v = -cosx

int e^x sinx dx

-e^x cosX - int -cosx e^x

-e^x cosx + sinx e^x + C

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## Related Questions

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### How do you differentiate sine squared x?

Using the Chain Rule :derivative of (sinx)2 = 2(sinx)1 * (derivative of sinx)d/dx (Sinx)2 = 2(sinx)1 * [d/dx (Sinx)]d/dx (Sinx)2 = 2(sinx) * (cosx)d/dx (Sinx)2 = 2 (sinx) * (cosx)d/dx (Sinx)2 = 2 sin(x) * cos(x)

### What is the derivative of the square root of 1-sinx?

√(1-sinx)=(1-sinx)1/2Chain rule: d/dx(ux)=x(u)x-1*d/dx(u)d/dx(1-sinx)1/2=(1/2)(1-sinx)1/2-1*d/dx(1-sinx)d/dx(1-sinx)1/2=(1/2)(1-sinx)-1/2*d/dx(1-sinx)-The derivative of 1-sinx is:d/dx(u-v)=du/dx-dv/dxd/dx(1-sinx)=d/dx(1)-d/dx(sinx)d/dx(1-sinx)1/2=(1/2)(1-sinx)-1/2*[d/dx(1)-d/dx(sinx)]-The derivative of 1 is 0 because it is a constant.-The derivative of sinx is:d/dx(sinu)=cos(u)*d/dx(u)d/dx(sinx)=cos(x)*d/dx(x)d/dx(1-sinx)1/2=(1/2)(1-sinx)-1/2*[0-(cos(x)*d/dx(x))]-The derivative of x is:d/dx(xn)=nxn-1d/dx(x)=1*x1-1d/dx(x)=1*x0d/dx(x)=1*(1)d/dx(x)=1d/dx(1-sinx)1/2=(1/2)(1-sinx)-1/2*[0-(cos(x)*1)]d/dx(1-sinx)1/2=(1/2)(1-sinx)-1/2*[0-(cos(x))]d/dx(1-sinx)1/2=(1/2)(1-sinx)-1/2*[-cos(x)]d/dx(1-sinx)1/2=(-cosx)/[2√(1-sinx)]

### Find the exact value of the area under the first arch of fx x sinx The first arch is between x 0 and the first positive x-intercept?

First, find the upper limit of integration by setting xsin(x)=0. It should be pi. Then use integration by parts to integrate xsin(x) from 0 to pi u=x dv=sinx dx du=dx v=-cosx evaluate the -xcosx+sinx from 0 to pi the answer is pi ps webassign sucks

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= cos(x)-(cos3(x))/3 * * * * * Right numbers, wrong sign! Int(sin3x)dx = Int(sin2x*sinx)dx = Int[(1-cos2x)*sinx]dx = Int(sinx)dx + Int[-cos2x*sinx]dx Int(sinx)dx = -cosx . . . . . (I) Int[-cos2x*sinx]dx Let u = cosx, the du = -sinxdx so Int(u2)du = u3/3 = 1/3*cos3x . . . . (II) So Int(sin3x)dx = 1/3*cos3x - cosx + C Alternatively, using the multiple angle identities, you can show that sin3x = 1/4*[3sinx - sin3x] which gives Int(sin3x)dx = 1/4*{1/3*cos(3x) - 3cosx} + C

### How do you prove that the derivative of csc x is equals to -csc x cot x?

d/dx cscx = d/dx 1/sinx = d/dx (sinx)-1= -(sinx)-2 cosx = -cosx/sin2x = -1/sinx.cosx/sinx = -cscx cotx I suggest you copy this out onto paper so it is more clear. The / signs make it harder to see what is happening compared to horizontal divide lines.

### What is the integral of sin x cubed?

Int(sin3x)dx = Int(sin2x*sinx)dx = Int[(1-cos2x)*sinx]dx = Int(sinx)dx + Int[-cos2x*sinx]dx Int(sinx)dx = -cosx . . . . . (I) Int[-cos2x*sinx]dx Let u = cosx, the du = -sinxdx so Int(u2)du = u3/3 = 1/3*cos3x . . . . (II) So Int(sin3x)dx = 1/3*cos3x - cosx + C Alternatively, using the multiple angle identities, you can show that sin3x = 1/4*[3sinx - sin3x] which gives Int(sin3x)dx = 1/4*{1/3*cos(3x) - 3cosx} + C

### Integral of xex dx?

let u = x du=dx let dv= e^x v=e^x ∫ xe^(x)dx = xe^x - ∫ e^(x)dx = xe^x - e^x = e^x ( x-1 ) + c

### Limit x approaches 0 sinx divide x equals 1 evaluate limit x approaches 0 cos2x-1 divide x?

== == Cos2x - 1 = [1 - 2sin2 x] - 1 = - 2sin2 x; so [Cos2x - 1] / x = -2 [sinx] [sinx / x] As x approaches 0, sinx / x app 1 while 2 sinx app 0; hence the limit is 0.

### How do you differentiate x sinx with respect to x?

You should apply the chain rule d/dx(x.sin x) = x * d/dx(sin x) + sin x * d/dx(x) = x * cos x + sin x * 1 = x.cos x + sin x

### What is the derivative of y equals -3xsinx - 1.5x to the 2 plus 5x when x equals pi?

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### Verify that Cos theta cot theta plus sin theta equals csc theta?

It's easiest to show all of the work (explanations/identities), and x represents theta. cosxcotx + sinx = cscx cosx times cosx/sinx + sinx = csc x (Quotient Identity) cosx2 /sinx + sinx = csc x (multiplied) 1-sinx2/sinx + sinx = csc x (Pythagorean Identity) 1/sinx - sinx2/sinx + sinx = csc x (seperate fraction) 1/sinx -sinx + sinx = csc x (canceled) 1/sinx = csc x (cancelled) csc x =csc x (Reciprocal Identity)

### Integral of 1 divided by sinx cosx?

Integral of [1/(sin x cos x) dx] (substitute sin2 x + cos2 x for 1)= Integral of [(sin2 x + cos2 x)/(sin x cos x) dx]= Integral of [sin2 x/(sin x cos x) dx] + Integral of [cos2 x/(sin x cos x) dx]= Integral of (sin x/cos x dx) + Integral of (cos x/sin x dx)= Integral of tan x dx + Integral of cot x dx= ln |sec x| + ln |sin x| + C

### How do you differentiate x sinx with respect to y?

If you actually mean "... with respect to x", and that y is equal to this function of x, then the answer is:y = x sin(x)∴ dy/dx = sin(x) + x cos(x)

### What is the derivative of the square root of 2 raised to the power of cos x?

The derivative of 2^x is 2^x * ln2 so the derivative of 2^cosx * ln2 multiplied by d/dx of cox, which is -sinx so the derivative of the inside function is -sinx * 2^cosx *ln2. As to the final question, using the chain rule, d/dx (2^cosx)^0.5 will equal half of (2^cosx)^-0.5 * -sinx * 2^cosx * ln2

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cos(xx)?d/dx(cosu)=-sin(u)*d/dx(u)d/dx(cos(xx))=-sin(xx)*d/dx(xx)-The derivative of xx is:y=xx ;You have to use implicit derivation because there is no formula for taking the derivative of uu.lny=lnxxlny=xlnx-The derivative of lnx is:d/dx(lnu)=(1/u)*d/dx(u)-d/dx(uv)= u*dv/dx+v*du/dxTherefore:(1/y)*dy/dx=x*[(1/x)*d/dx(x)]+lnx(d/dx(x))-The derivative of x is:d/dx(xn)=nxn-1d/dx(x)=1*x1-1d/dx(x)=1*x0d/dx(x)=1*(1)d/dx(x)=1(1/y)*dy/dx=x*[(1/x)*(1)]+lnx(1)(1/y)*dy/dx=x*[(1/x)]+lnx(1/y)*dy/dx=(x/x)+lnx(1/y)*dy/dx=1+lnxdy/dx=y(1+lnx) ;Multiply y to both sidesdy/dx=xx(1+lnx) ;y=xx, so replace the y with xxd/dx(cos(xx))=-sin(xx)*[xx*(1+lnx)]d/dx(cos(xx))=-(1+lnx)*xx*sin(xx)(cosx)x?Again with the implicit derivation:y=(cosx)xlny=x*ln(cosx)(1/y)*dy/dx=x[d/dx(lncosx)]+lncosx(d/dx(x))(1/y)*dy/dx=x[(1/cosx)*(-sinx)(1)]+lncosx(1) ;The derivative of lncosx is (1/cosx)*d/dx(cosx). The derivative of cosx is (-sinx)*d/dx (x). The derivative of x is 1.(1/y)*dy/dx=x[(1/cosx)*(-sinx)]+lncosx(1/y)*dy/dx=x[-tanx]+lncosx(1/y)*dy/dx=-xtanx+lncosxdy/dx=y(-xtanx+lncosx) ;Multiply both sides by ydy/dx=(cosx)x(-xtanx+lncosx) ;y=(cosx)x, replace all y's with (cosx)xdy/dx=(cosx)x(-xtanx+lncosx)=(cosx)x-1(cosx*lncosx-xsinx)

### What is sin 3x in terms of sin x?

given the identity sin(x+y)=sinx cosy + siny cosxsin2x = 2 sinx cosx andsin(2(x)+x) = sin 2x cos x + sinx cos 2xusing the last two identities givessin3x= 2 sinx cosx cosx + sinx cos2xfactoring the sinx we havesin3x = sinx(2cosx cosx+cos2x)which satisfies the requirement.However, we can simplify further since cos 2x = cosx cosx - sinx sinx (a well known identity)sin3x = sinx (2cosx cosx +cosx cosx - sinx sinx)so sin3x= sinx(3cosx cosx - sinx sinx)or sin 3x = 3.cosÂ²x.sinx - sinÂ³x* * * * *Good, but not good enough. The answer was required in terms of sin, not a mixture of sinx and cosx. Easily recitified, though, since cos²x = 1 - sin²xTherefore sin3x = 3*(1-sin²x)*sinx - sin³x= 3sinx - 3sin³x - sin³x= 3sinx - 4sin³x

### How do you integrate sin x to the power of 2n?

I will assume that we are taking d/dx, not d/dn. There are two ways to interpret what you asked. First way is (sinx)^(2n). Second way is sin(x^(2n)). First answer: 2n(sinx)^(2n-1)(cosx)=2ncosx(sinx)^(2n-1). Second answer: cos(x^(2n))(2nx^(2n-1)).

### How do you integrate x power e power x?

{xe^x dx integrate by parts let f(x) = x so f'(x) = 1 and g(x) = e^x so g'(x) = e^x so.. f(x)*g(x) - {(g(x)*f'(x)) dx therefore xe^x - {(e^x * 1) dx so.. xe^x - e^x + C factorize so... (x-1)e^x + C

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# Summation of natural number set with power of $m$ [duplicate]

Who knows about the summation of this series: $$\sum\limits_{i=1}^{n}i^m$$ where $m$ is constant and $m\in \mathbb{N}$?

thanks

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# Why does portfolio optimization require a positive-definite covariance matrix?

Why does the portfolio optimization mean-variance model require the covariance matrix to be positive-definite? Does this requirement have to do with the need to be able to invert the matrix during optimization?

How is positive-definiteness achieved? Does it happen because all matrix elements (variance and covariance) are non-negative? In which cases do asset returns fail to make the covariance matrix positive definite? are there any known work-arounds when this happens

To supplement the other answer, yes there are optimization reasons for the covariance matrix being symmetric positive definite (SPD). All positive definite matrices are invertible and its inverse is also positive definite.

This guarantees a unique global minimum in a quadratic optimization problem (MVO).

Lots of material available on the topic: https://www.cis.upenn.edu/~cis515/cis515-12-sl14.pdf

• A follow up question for you: when the solution is not unique, it just means there is a set of solutions (portfolios), not just one. How to mathematically characterise this set? I have never seen this clearly explained in finance books. – noob2 Aug 14 at 14:35
• Here's my guess. If you have a perfectly correlated, identical time series which causes a 0 eigenvalue and thus not a positive definite matrix, the resulting set of portfolio solutions will be cases where the weights for the identical assets can vary as long as they add up to a certain weight since it doesn't matter which you allocate to. – Quantoisseur Aug 14 at 15:51
• Yes, that is correct – Quantoisseur Aug 14 at 16:10
• A zero eigenvalue can happen easily. A negative eigenvalue is theoretically impossible in a true covariance matrix (variance is always positive) but a slight negative could show up because of roundoff error. – noob2 Aug 14 at 16:12
• @Quantoisseur I have run into zero eigenvalues when one "basket" asset is a linear combination of other assets (e.g., EUR and ECU used to be linear combinations of pre-EUR currencies for a while). The optimal portfolio is not unique because you may be indifferent to holding the basket or its components that replicate it. – Dimitri Vulis Aug 14 at 17:04

Positive definite matrix $$A$$ is defined as $$x^TAx > 0$$ for all vectors $$x$$.

Since a term $$w^T\Sigma w$$ in Markowitz (and other models as well) expresses variance in returns, it is a measure of dispersion. Any measure of dispersion has to be positive (or maybe zero but it is a case where there is no uncertainty and hence no risk). Negative dispersion is meaningless.


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# A Lemma in complex function theory II

Abstract : In this sequel to the previous paper with the same title, we prove a similar result as in part I, but which holds for $\vert f(z)\vert^k$, where $k>0$ is any real number.
Document type :
Journal articles
Domain :

Cited literature [2 references]

https://hal.archives-ouvertes.fr/hal-01104341
Contributor : Romain Vanel Connect in order to contact the contributor
Submitted on : Friday, January 16, 2015 - 4:40:43 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Saturday, September 12, 2015 - 6:30:26 AM

### File

12Article2.pdf
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### Citation

R Balasubramanian, K Ramachandra. A Lemma in complex function theory II. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 1989, Volume 12 - 1989, pp.6 - 13. ⟨10.46298/hrj.1989.109⟩. ⟨hal-01104341⟩

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