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## AM-42 - The Classic Transportation Problem

You are currently viewing an archived version of Topic The Classic Transportation Problem. If updates or revisions have been published you can find them at The Classic Transportation Problem.

The classic transportation problem concerns minimizing the cost of transporting a product from sources/supplies to destinations/demands. It is a network-flow problem that arises in industrial logistics and is often solved by linear programming (LP). The three inputs of the model are total units produced at each source, total units needed at each destination, and the cost to transport one unit from each source to each destination. And the objective is to minimize the total cost of transporting all units produced at sources to meet the demands at destinations. The problem solution includes three basic steps: 1) finding an initial basic feasible solution, 2) checking if the current solution is optimal (with the lowest costs), and improving the current solution through iteration. Solving such a problem relies strongly on the network data models, least-cost path algorithms, other functionalities in GIS. And an integrated framework is often adopted to utilize both GIS and non-GIS linear programming solvers to search for the optimal solution.

Author and Citation Info:

Song, Y. (2021). The Classic Transportation Problem. The Geographic Information Science & Technology Body of Knowledge (3rd Quarter 2021 Edition), John P. Wilson (ed.). DOI: 10.22224/gistbok/2021.3.5.

This entry was published on September 15, 2021.

This Topic is also available in the following editions:

• Song, Y. (2017). The Classic Transportation Problem. The Geographic Information Science & Technology Body of Knowledge (4th Quarter 2017 Edition), John P. Wilson (ed.). DOI: 10.22224/gistbok/2017.4.7.
• DiBiase, D., DeMers, M., Johnson, A., Kemp, K., Luck, A. T., Plewe, B., and Wentz, E. (2006). Approximating the Earth's shape with geoids. The Geographic Information Science & Technology Body of Knowledge. Washington, DC: Association of American Geographers. (2nd Quarter 2016, first digital)
Topic Description:

1. Definitions

Network: A network can be defined as a directed graph G = (V, A), where V is the set of vertices or nodes, and A is the set of arcs or links corresponding to the feasible routes between nodes. Each arc/link is often assigned with a weight reflecting the movement cost and some additional constraints such as flow capacities.

Linear Programming: A linear programming problem may be defined as a problem of maximizing/minimizing  a linear function subject to linear constraints. The constraints can be either equalities or inequalities. And the objective is to  find the optimal solution that minimizes/maximizes the linear function.

Industrial Logistics: In general, industrial logistics is the management of the resources between sources and destinations to meet the demands of the market. The resources include both physical items such as food and  equipment and abstract ones such as time and resources.

Heuristic: A heuristic trades optimality, completeness, accuracy, or precision for efficiency while solving a problem. Based on available information, a heuristic ranks the alternatives at each step to decide which direction to follow. For instance, a greedy heuristic selects a local optimum value at each stage, attempting to find a global optimum.

2. Modeling the Classic Transportation Problem

The classic transportation problem has long been an indispensable research problem in industrial and transportation logistics. The problem is driven by the need to transport a single commodity from sources (plants and factories) to destinations (warehouses and consumer markets). The total units produced at each source, the total units required by each destination, the cost to transport one unit from each source to each destination are assumed to be known. And the objective is to minimize the total cost of shipping units from sources to meet demands at destinations. The problem is also driven by the need to move people between activity locations such as home and office. The trip distribution step in the traditional four-step modeling is a classic transportation problem that aims to minimize the overall cost (e.g. travel distance or time) for people to move between activity locations (e.g. home and office).

Figure 1. Transporting a commodity from sources to destinations, Si and Dj denotes units supplied and units demanded. Source: author.

The number of units supplied by source i is Si, for i = 1,2, ... , m. The number of units required by destination j is Dj, for j = 1,2, ... , n. The cost of transporting one unit along the link from source i to destination j is cij, and the number of units transported along this link is xij. The total cost of transporting units from source i to all destinations {j} is:

Similarly, the total cost of transporting units to destinations j from all sources {i} is:

Thus, the classic transportation problem can be formulated as a linear equation:

Equation (3) represents the total transportation cost and is the objective function of the classic transportation problem. Equation (4) indicates that the total units shipped from source i should not exceed the available units Si at source i. Equation (5) indicates that the total units shipped to destination j should meet its demand Dj.

The network model above can be balanced or unbalanced. When the total supply at all resources, $\inline \sum _{i=1}^{m} \: S_i$ , is equal to the total demand at all destinations, $\inline \sum _{j=1}^{n} \: D_j$, the model is balanced. Otherwise, the model is unbalanced, with excess demand or excess supply. For the case of excessive demand, $\inline \sum _{i=1}^{m} \: S_i < \sum _{j=1}^{n} \: D_j$ , a dummy source is created to reflect the penalty cost, Dp, for each unit of unsatisfied demand. For the case of excess supply,  $\inline \sum _{i=1}^{m} \: S_i > \: \sum _{j=1}^{n} \: D_j$ , a dummy warehouse is created to reflect the storage cost, Ss, for each unit of surplus production.

The classic transportation problem can also be formulated as matrices. Figure 2 shows a balanced network model with m source and n destinations.

Figure 2. A balanced network model formulated as a matrix. Source: author.

3. Solving the Classic Transportation Problem

The classic transportation problem can be formulated using Equations (3) to (6), which are all linear equations. Hence, the problem can be structured as a linear program and solved using the simplex method. The three steps are 1) finding an initial basic feasible solution, 2) checking if the solution is optimal, and 3) continuing to improve the solution.

3.1 Finding an Initial Basic Feasible Solution

For the balanced transportation problem, the constraint set in Equation (4) and (5) is reformulated as (m + n) linear questions:

Therefore, one of the equations in the constraint set is redundant, and the total number of independent equations becomes (m + n − 1). This is because, if ai, i = 1, 2, ..., m and bj, j = 1, 2, ..., (n − 1) are specified, bn can be calculated as  $\inline b_n = \sum ^{m}_{i = 1} \: a_i - \sum ^{n-1}_{j = 1} \: b_j$ .  In a linear program, the basic variables are variables that are not zeros, and the number of basic variables in a basic feasible solution is the same as the number of independent constraint equations (Luenberger and Ye, 2015). Therefore, solutions to the balanced transportation problem should have  exactly (m + n − 1) basic variables; the remaining  (mn − (m + n − 1)) variables are non-basic variables and equal to zero.

Common methods to generate an initial basic feasible solution include 1) the northwest corner rule, 2) Vogel’s approximation method, and 3) Russell’s approximation method  (Hillier and Lieberman, 2010). Given the problem formulated as a matrix (see Figure 2), the northwest corner method simply starts with the northwest corner of the matrix and assigns x11 and sest its value as the smaller one of S1 and D1. Then, given the last assigned basic variable xij, select xi (j+1) as the next basic variable if source i has any supply left; otherwise, select x (i+1)j. The other two methods try to find a basic feasible solution that is closer to the optimal solution. The Vogel’s approximation method tries to reduce the risk of failing to allocate the cell with the lowest unit costs in a row or column. And the Russell’s approximation method selects the cells with the cost cij that is much smaller than the maximum cost in the row i and the maximum cost in the column j, that is, to minimize Δ ij = cijij. It takes a similar form as the simplex method in the next step for the optimality test.

Figure 3 is an example of the northwest corner rule. The method starts with the cell in the northwest corner from Source 1 to Destination 1, x11. Since the demand from the Destination 1 is 5 units and the supply from Source 1 is 8 units, the cell x11 takes the smaller value of 5 units. Since the first row has 3 units left at Source 1, we move one step to the east and processes the cell x12.The second column has a total demand of 9 units and Source 1 can provide 3 units of supply. Therefore, the cell x12 takes the value of 3 units which is smaller than 9 units. Now, Destination 2 needed 6 more units, so we move to the south and processethe cell x22. In each of the remaining iterations, the method moves one step to the east or south and the cell takes the smaller units remaining in its column and row. The process stops when it reaches the southeast corner of the matrix.

Figure 3. Finding an initial basic feasible solution using northwest corner rule. Source: author.

3.2 Check Optimality

Given the initial basic feasible solution, the next step is to check if the current solution is optimal. The optimization criteria can be formulated by defining two sets of shadow prices for the current solution {xij}: 1) a dispatch cost ui to transport one unit from source i to any destination, and 2) a reception cost vj to transport one unit to destination j from any source. These shadow prices should satisfy:

cij + ui = vj,      for xij > 0                                    (10)

Hence, the current solution is optimal if non-basic variables cannot offer lower costs at the destination (markets):

cij + ui  ≥ vj,      for xij = 0                                     (11)

These optimization criteria can be implemented by determining values of {ui} and {vi} based on Equation (10), calculating cost differences ∆cij = cij + uivj for all the non-basic variables, and checking whether all ∆cij is non-negative. Since the number of basic variables in the basic feasible solution is (m + n − 1) and the total number of shadow prices {ui} and {vj} is (m + n), we can always find a basic solution for {ui} and {vj}, and it is common to set u1 = 0. Figure 4 shows an example {ui} and {vj} given the initial basic feasible solution in Figure 3. The price difference ∆cij are placed on the left- bottom corner of each cell. Given the calculation result, the initial basic feasible solution is not optimal because the cost differences ∆c 13 , ∆c 14 and ∆c 32 are negative.

3.3 Improving the Solution Through Iteration

If the current solution is not optimal, there is at least one non-basic variable xij = 0 with cost difference ∆cij < 0 that can reduce the overall transportation cost of the system.  A direct and possible method to improve the solution is to select the non-basic variable with the largest (in absolute term) negative ∆cij and increase its corresponding units xij as much as possible. For instance, the most negative difference is ∆c32 in Figure 4. After increasing x32 by ε unit, the sequence used to generate the initial basic feasible solution would be broken and we need to search for the two donor cells and one recipient cell in addition to cell (3, 2) that can complete a chain reaction. In our case, the donor cells (with basic variables) are (2, 2) and (3, 3) and the receipt cell is (2, 3). And we have x32 + ε, x22ε, x23 +  ε, and x33ε as the complete chain reaction. Hence, the ε takes the smaller value of x22 and x33 , which is 1. The total cost change can be calculated as, which is always negative:

ΔZ = (c32c22 + c23c33) × ε

= (c32 − (v2u2) + (v3u2) − (v3u3)) × ε                        (12)

= (c32 + u3v2) × ε = ∆cij × ε

Unless this current improved solution is optimal, we go to the next interaction.

Figure 4. Checking possible price reduction – initial transportation simplex tableau. Source: author.

Every linear program has a dual. Given the class transportation problem written as equations (3) to (6), its dual problem can be written using dual variables {ui} and {vj}:

The second and third steps in the transportation simplex method described above use this dual form to determine whether the solution in the current iteration is optimal and, if not, identify a better basic feasible solution.

4. The Classic Transportation Problem and GIS

Geographic information systems for transportation deal with information about and related to transportation systems and have been recognized as a major application of geographic information science (GIS) (Miller and Shaw, 2015). Major extensions to the formulations and solutions of the classic transportation problem are: 1) introducing intermediate transfer stops (a.k.a. hubs) (O’Kelly and Miller, 1994); 2) considering changes in supply and demand amounts and dynamic unit transportation costs (a.k.a. dynamic transportation problem) (Powell, et al. 1995);  3) including constraints to reflect network and loading capacities (Nahmias and Cheng 1993); and 4) setting multiple objectives beside minimizing shipping costs (Ulungu and Teghem 1994). These extensions correspond to real-world planning and operation scenarios and improve the practical merits of the basic model; however, they also bring great challenges, especially when dealing with large networks.

Regarding the classic transportation problem, GIS provides models and algorithms for collecting, managing, analyzing, and distributing spatial information. These include, but are not limited to, estimating supplies and demands, modeling and maintaining the transportation networks, calculating least-cost routes from sources to destinations for use in determining unit costs, and mapping the data and results. However, GIS has very limited capability to solve the optimization problem with linear programming by itself (Murray et al. 2019). An integrated framework is often adopted to utilize both GIS and non-GIS linear programming solvers to search for the optimal solution (Lei, et al. 2016).

Many existing software packages for optimization have linear programming solvers. Some packages require users to buy licenses such as LGO (Lipschitz-continuous Global Optimizer) and MINOPT (A Modeling Language and Algorithmic Framework for Linear, Mixed-Integer, Nonlinear, Dynamic, and Mixed-Integer Nonlinear Optimization). Some packages provide free versions with limited functions and full-versions upon purchase such as GAMS (General Algebraic Modeling System) and LINDO (Linear, Interactive, and Discrete Optimizer). Some are open-source packages free of charge such as AMPL (A Modeling Language for Mathematical Programming). For complex problems and large networks, the LP solvers typically apply heuristics to reduce computational complexity. And various algorithms have been employed to improve the formulation, solution, and evaluation process. For example, the network simplex algorithm based on graph theory and spanning-tree can more efficiently solve the minimum-cost flow problems than the simplex method described in Section 2. The CPLEX Optimizer by IBM (commercial), the NetworkX Python package, and additional software packages all include network simplex solvers. Some other examples include fuzzy and neuro-fuzzy methods, genetic algorithms, tabu search, and branch-and-bound approaches (Srivastava, 2007).

References:

Hillier, F. and Lieberman, G. (2010). Introduction to Operations Research. McGraw-Hill Education, 9th Edition.

Lei, T. L., Church, R. L., & Lei, Z. (2016). A unified approach for location-allocation analysis: integrating GIS, distributed computing, and spatial optimization. International Journal of Geographical Information Science, 30(3), 515–534.

Luenberger, D. G., and Ye, Y. (2015). Linear and Nonlinear Programming (Vol. 228). Springer.

Miller, H. J., and Shaw, S. L. (2001). Geographic Information Systems for Transportation: Principles and Applications. Oxford University Press on Demand.

Miller, H. J., and Shaw, S. L. (2015). Geographic Information Systems for Transportation in the 21st Century. Geography Compass, 9(4), 180-189.

Murray, A. T., Xu, J., Wang, Z., & Church, R. L. (2019). Commercial GIS location analytics: capabilities and performance. International Journal of Geographical Information Science, 33(5), 1106-1130

Nahmias, S., and Cheng, Y. (1993). Production and Operations Analysis (Vol. 2). Homewood, IL: Irwin.

O'Kelly, M. E., and Miller, H. J. (1994). The Hub Network Design Problem: A Review and Synthesis. Journal of Transport Geography, 2(1), 31-40.

Powell, W. B., Jaillet, P., and Odoni, A. (1995). Stochastic and Dynamic Networks and Routing. Handbooks in Operations Research and Management Science, 8, 141-295.

Srivastava, S. K. (2007). Green Supply-Chain Management: A State-Of-The-Art Literature Review. International Journal of Management Reviews, 9(1), 53-80.

Ulungu, E. L., and Teghem, J. (1994). Multi-objective combinatorial optimization problems: A survey. Journal of Multi-Criteria Decision Analysis, 3(2), 83-104.

Learning Objectives:
• Demonstrate how to model real-world transportation problems as linear programs.
• Define the classic transportation problem analytically using graphs,equations, and matrices.
• Distinguish between balanced and unbalanced problems, and explain why, if supply equals demand, there will always be a feasible solution.
• Delineate three major steps toward solving the classic transportation problem as a linear program and use simplex methods to get the optimal solution.
• Describe some main contributions of GIS to the classic transportation problem.
Instructional Assessment Questions:
• In the example provided in Figure 3, suppose that the demand of destination #3 increases from 2 units to 4 units, and there is a penalty cost of 1 for each unmet unit. Use the northwest corner method to find the initial feasible solution and use the simplex method to find the optimal solution for this unbalanced problem.
• Imagine that three local farms provide dairy supplies to five retail stores in a metropolitan area. Each farm has a limited supply, and each store has demands based on historical records. Model this classic transportation problem using graphs, equations, and matrices.
• Describe how the dual variables are used in the simplex method to determine the optimality of the current solution and search for the next better solution if needed. Please link the dual variables to the real-world scenario, which has production and market prices. Then, use the competition between suppliers to understand why the shadow price at each destination must be smaller than or equal to the shadow price at any source plus the transport cost from that source to this destination.


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# I Is the PBR Theorem valid?

1. Sep 6, 2017

### fanieh

https://en.wikipedia.org/wiki/PBR_theorem

"The theorem was first published as an arXiv preprint with Pusey as the principal author,[1] a subsequent version published in Nature Physics,[2] that states the theorem that either the quantum state corresponds to a physically real object and is not merely a statistical tool, or else all quantum states, including non-entangled ones, can communicate by action at a distance."

This is very fantastic claim. Since many believe quantum state is just statistical tool. Does it mean all quantum states, including non-entangled ones, can communicate by action at a distance? This can be easily proved or disproved. Since it seemed it couldn't, then the claim at Wikipedia appears not to be correct. Hope someone can edit it to give the right context. Thank you.

2. Sep 6, 2017

### Staff: Mentor

Its valid, but please read the entire paper - in particular note the assumptions (from the paper):
'One is that a system has a “real physical state” – not necessarily completely described by quantum theory, but objective and independent of the observer. This assumption only needs to hold for systems that are isolated, and not entangled with other systems. Nonetheless, this assumption, or some part of it, would be denied by instrumentalist approaches to quantum theory, wherein the quantum state is merely a calculational tool for making predictions concerning macroscopic measurement outcomes.'

That is the precise assumption many interpretations such as the ensemble reject or are silent on.

Thanks
Bill

3. Sep 6, 2017

### fanieh

I've been reading https://arxiv.org/pdf/1111.3328.pdf but I can't get the reason for the isolation.

Do you know why the assumption only needs to hold for systems that are isolated, and not entangled with other systems? What happens if the system is entangled with other systems. Why won't the PBR theorem no longer be valid?

4. Sep 6, 2017

### Staff: Mentor

Its been a while since I have gone into that theorem - it caused a big stir when released I think 6 years ago now and I don't recall the details too well - except what I posted because people sometimes ask - how can you maintain its not real anymore.

So I will have to wimp out and let someone with more current knowledge answer that one.

Thanks
Bill

5. Sep 7, 2017

### kith

The PBR theorem -under certain arguably weak assumptions- rules out that QM is a purely statistical theory about some underlying hidden variables which truly determine the physical state of a system.

In order to assess the significance of this, you should note that although some people vaguely hold such a view no currently popular interpretation is of this type. The Copenhagen interpretation denies that there are hidden variables and in the de-Broglie-Bohm theory (dBB), the wavefunction is not merely a statistical tool but influences the hidden variables.

The main influence of the PBR theorem on established interpretations is that it strengthens dBB against other conceivable hidden variable theories (HVTs). It proves that certain aspects of dBB are inevitable for HVTs and thus stands in the tradition of Bell's theorem (HVTs have to be non-local) and the Kochen-Specker theorem (HVTs have to be contextual).

For me, this leaves only one question about HVTs open: dBB is sometimes crticized for the fact that the wavefunction influences the hidden variables but not the other way round. I wonder if this is also inevitable for HVTs. (Maybe it is already known; I am no expert on these matters)

Last edited: Sep 7, 2017
6. Sep 7, 2017

### kith

Also check this blog post by Matt Leifer who discusses the PBR theorem by introducing the terminology of epistemic and ontic states which is often used in quantum foundations research.

7. Sep 7, 2017

### fanieh

Logic says the hidden variables (quantum potential or whatever) need to influence the wave function too.. what would it take to do this.. Demystifier? other Bohmians?

8. Sep 7, 2017

### DrChinese

Here is something Demystifier prepared a while back, pretty nice overview of PBR:

https://www.physicsforums.com/attachments/pbr-pdf.72453/

9. Sep 8, 2017

### vanhees71

What I still not get about this proof (as summarized nicely in @Demystifier 's slides as well as in the PBR paper) is that they somehow seem to prove the ontic nature of quantum states under the assumption that there's some hidden variable $\lambda$ that determines the QT probabilities, making these "ontic". Don't they just put what they claim to prove into this assumption? In standard minimally interpreted QT there's nothing like $\lambda$, and then isn't there again a loophole to the theorem in the sense that an epistemic interpretation of quantum state doesn't lead to a contradiction?

In my opinion minimally interpreted QT strongly suggests an epistemic interpretation of the quantum state, but as I tried to explain earlier in this thread, this doesn't imply non-objectivity either.

10. Sep 8, 2017

### Demystifier

Not exactly. They assume that there is some $\lambda$, but a priori it is not obvious that $\lambda$ can determine $\psi$. As I explained at page 15, the result is actually very surprising.

You are right, this interpretation is not ruled out by the PBR theorem. What is ruled out are some Einstein-like attempts to find a hidden-variable theory in which $\psi$ is eliminated completely. Roughly speaking, the PBR theorem tells: don't even try, you cannot find such a theory.

11. Sep 8, 2017

### Demystifier

Well, Bohmian hidden variables (that is, particle positions) do not inflence the wave function. And this is fully analogous to classical HJ theory where particle trajectories do not influence the S-function. So your logic is faulty.

12. Sep 8, 2017

### fanieh

In message #5, Kith last sentence was "For me, this leaves only one question about HVTs open: dBB is sometimes crticized for the fact that the wavefunction influences the hidden variables but not the other way round. I wonder if this is also inevitable for HVTs. (Maybe it is already known; I am no expert on these matters)"

If it was criticized.. this means some want the hidden variables to affect the wave function.. but in classical HJ theory, particle trajectories do not influence the S-function. So to avoid dBB being criticized, what should be the ontology such that the wave function can be influenced.. or if it can't be fixed within dBB.. can you please give example of another interpretation where the wave function can be influenced by a hidden variable such that the PBR theorem can apply? But then Kith mentioned "no currently popular interpretation is of this type".. so how do you cook up an interpretation which can support PBR theorem per Kith context? Many thanks.

13. Sep 8, 2017

### Demystifier

Yes, some people criticize the fact that dBB trajectories do not influence the wave function. All I can do about it to accuse them for hypocrisy, for why then they don't criticize the fact that classical trajectories do not influence the HJ S-function?

14. Sep 8, 2017

### vanhees71

Ok, then again a stupid question. What are dBB trajectories good for? AFAIK they are not (!) observable according to dBB.

15. Sep 8, 2017

### martinbn

But in the classical case they don't say that S-function influences the trajectories. And in dBB they say that.

16. Sep 8, 2017

### Demystifier

Of course they do (even if by using different words). Take a look at an analytical mechanics book again.

17. Sep 8, 2017

### Demystifier

That's the wrong question. The correct one is: Who are dBB trajectories good for? The answer is: They are good for (some of) those who think that there is a measurement problem in standard QM. Which, of course, excludes you.

This is analogous to atoms in 19th century, which were not observable at that time, but were still good for Boltzmann.

18. Sep 8, 2017

### martinbn

To me the wording is important. What words do they use and why don't the Bohmists use similar phrasing instead of influence? The thing is that for me the wave influences the trajectory sounds like the electric field influences the trajectory of a charged particle, which involves interaction between the particle and the field. And I have seen the pilot wave being compared to the electromagnetic field. If there is an interaction, the particle will influence the field as well, at least in principle.

19. Sep 8, 2017

### Demystifier

Actually, Bohmians rarely say "influence", except as a response to someone else who used the same word. Personally, I usually say "determine", in both the HJ theory and Bohmin mechanics.

20. Sep 8, 2017

### martinbn

Which is perfectly clear and unambiguous.

21. Sep 8, 2017

### Demystifier

Yes, some people use this analogy. I guess it's addressed to mathematically less sophisticated readers who are familiar with electromagnetic theory but not with HJ theory. For more sophisticated readers, the HJ analogy is much better.

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# Can a super land without flaps/spoilers?

Can the Airbus A380 or Boeing 787 land safely without flaps/slats/spoilers or thrust reversers?

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yeah they will come in overspeed and need a long runway to get to a stop – ratchet freak May 23 '14 at 18:54
Will this overspeed and slow braking (to avoid overheating the brakes) cause the tires to overheat and blow? Some tires can overheat on extended taxi durations, and this contemplates a much higher taxi speed. – Skip Miller May 23 '14 at 19:12
@SkipMiller if you "slow brake to avoid overheat", I would say that the chance of overheating is practically null, unless you are doing something else wrong. – Federico May 23 '14 at 19:21
For what it's worth, the Boeing 787 is not a "super." Its MTOW is less than even a 777 (all variants), let alone a 747. The 747 is still Boeing's heaviest aircraft. (A modified 747 was even used to carry 787 pieces, like its wings, around.) – dvnrrs May 23 '14 at 20:13
@SkipMiller, if you're landing with no flaps, then you have a LOT of energy to get rid of, and unless you have enough runway that the thrust reversers can get rid of most of it, then quite a bit of energy IS going into the brakes. So they're going to be hot. That's just what's going to happen with most no-flap landings. Braking "slowly" won't help much -- you have some amount of kinetic energy that needs to be absorbed by the brakes, so whether it's absorbed over 10 seconds or 30 seconds, it's all going into the brakes. If you have to land no-flap, then hot brakes is probably a given. – Ralph J Mar 16 '15 at 15:20

Even the largest commercial airliners are able to land without flaps, since flap failures do happen occasionally. See a report here where an A380 landed with no flaps. This was at the Auckland, New Zealand airport, where the runway is 3,635 m (11,926 ft) long.

The pilots have checklists to follow in the event of issues with flaps, which include information about what speeds they should fly with what amounts of flaps. They simply land at a higher than normal speed. The brakes can end up getting hotter than normal, so they may have to stop and let them cool or have them inspected by emergency services. The tires are designed to deflate with fusible plugs before high temperatures would cause them to blow.

Aircraft are also tested to make sure they can reject a takeoff at high weights (higher than normal landing weights) using no thrust reversers. Here is a video of the 747-8 doing this test.

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I've never heard about the designed-in tire deflation, is there an article I can read? – CGCampbell May 23 '14 at 19:52
@CGCampbell Check this video out youtube.com/watch?v=qc_v6tXsv6g (same as posted above). At the end of the test they mention and show the deflation of the tires due to heat. – sandy May 23 '14 at 20:55
PBS had a multivolume video series (4 or 5 tapes) on the design, construction, and testing of the 777. The torture tests of brake overheating caused the fusible plugs to blow, so that fire crews wouldn't be endangered by exploding tires. – Phil Perry May 23 '14 at 22:34
@PhilPerry I think this clip is from that series, but I liked the newer one better. youtube.com/watch?v=9nA7B-JWt3M – fooot May 23 '14 at 23:05
@PhilPerry Unlike the A340-600 RTO test, where the tires did explode. Some selected quotes: "It's not an important fire." "Bring the stairs." "Bring the stairs, now!" – reirab Jul 27 '15 at 20:33

Specific information can be difficult to come by, and each airline may have their own guidance on the subject. I wasn't able to find anything for the 787, but for the according to one 777 crew handbook I found, flaps up landing was not part of certification:

All Flaps and Slats Up Landing
The probability of both leading and trailing edge devices failing to extend is extremely remote. System reliability and design have reduced the need for some traditional non-normal landing procedures. As a result, an all flaps up landing NNC was not required for airplane certification and does not appear in the AFM or in the QRH.

Basically this means that a demonstration of a no-flaps landing was not required during certification, so no specific guidance appears in the official handbook, and the manufacturer makes no claim that it can be done safely.

None of the Boeing 787 handbooks I found had official procedures for a flaps-up landing either.

That doesn't mean that it can't be done, but pilots are "on their own" so to speak, and the airplane may not be usable afterward.[see note]

But the basic procedure you'd expect them to follow is somewhere along these lines:

• Attempt to troubleshoot flaps first (best to avoid the problem altogether)
• Remove excess fuel (either dump or burn)
• Pick suitable airport considering runway length, altitude, and safety gear (e.g. EMAS)
• Declare emergency and prepare airport (ready the fire trucks, etc)
• Approach above no-flaps stall speed and touchdown as close to the start of the runway as possible
• Engage brakes, spoilers, and thrust-reversers as appropriate
• Write a book.

[note] "If you can walk away from a landing, it's a good landing. If you use the airplane the next day, it's an outstanding landing."

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A minor nitpick: Remove the excess fuel (either dump or burn) after picking a suitable airport ;) – dooburt May 25 '14 at 10:48
@dooburt as long as you're nitpicking, declare an emergency first, otherwise you've got to follow your original fight plan. The order isn't strict. – tylerl May 25 '14 at 15:03
that was a given - hence the ;) on the end. Written in humour. A comprehensive list nonetheless. +1. – dooburt Jun 4 '14 at 8:37

Any aircraft can land without those devices. I would say that the Gimli Glider is a nice example, with no power it could not extend its flaps/slats.

They are used, as @ratchetfreak notes in the comments, to reduce the touchdown speed and, as a consequence, the runway length needed to reach a stop or taxiing velocity.

To be noted, also, that a safe landing is mostly defined by the vertical velocity at tochdown, usually in the order of 1-3 feets per second. See for example this accident report where it states

mild touchdown rates [...] less than 5 feet per second

Since the vertical component is the relevant parameter for a safe landing, and given that without flaps/slats the forward velocity will be larger than usual, the aircraft will have to approach with a shallower angle than the usual 3°.

Absence of thrust reversers, as you might imagine, will only affect the braking process.

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The Shuttle Landing Facility's 15,000 foot runway isn't always available... any info on the A380's landing distance without flaps/slats/reversers? Is it indeed feasible on "normal" runways at large airports? – dvnrrs May 23 '14 at 19:40
@dvnrrs I edited the answer to include a famous example. I have no data for the A380, sadly. – Federico May 23 '14 at 19:41
Didn't the Gimli Glider get stopped by having its nose gear collapse? – dvnrrs May 23 '14 at 20:10
@dvnrrs yes, but the touchdown went fine – Federico May 23 '14 at 20:24
@dvnrrs - the landing gear didn't collapse, it was never locked down properly in the first place – Jon Story Dec 23 '15 at 12:59


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var ch_selected=Math.floor((Math.random()*ch_queries.length)); Thus the root mean square speed is {eq}v \approx 468\,{\rm{m/s}} {/eq} Become a member and unlock all Study Answers. A verb root (also known as the root form of a verb or the base form of a verb) is the version listed in the dictionary. Gynecology : gynec OLOGY (jin e kol’ o jee) n. Study of minerals Ok. The study of the diseases of women 12. Root Mean Square, RMS is defined as the square root of mean square where mean square is the arithmetic mean of the squares of numbers. LAB 3: STUDY OF ROOTS INTRODUCTION The plant root system makes up the major part of the plant body, both in terms of function and bulk (W1). Choose from 500 different sets of term:hem = root meaning blood (3) flashcards on Quizlet. This study resource helps in understanding the origins and root meaning of the ancient language. Learn root mean square with free interactive flashcards. Many English words are formed by taking basic words and adding combinations of prefixes and suffixes to them. There seems to be an endless list of them. Choose from 500 different sets of term:bibl = root meaning book (2) flashcards on Quizlet. The word root ‘geo’ comes from the Greek word ge- that means ‘Earth’. ch_color_text = "0D3700"; A basic word to which affixes (prefixes and suffixes) are added is called a root word because it forms the basis of a new word. In order to accomplish this, the roots must grow into new regions of the soil (W2). In its simplest form, the term root architecture refers to the spatial configuration of a plant's root system. Definition of root in the Idioms Dictionary. origin applies to the things or persons from which something is ultimately derived and often to the causes operating before the thing itself comes into being. What is/ lies at the root of the problem is their lack of interest. English : The best site for the Students to learn English online. This page explains the various forms of verbs and has examples of verb roots as well as an interactive exercise. The root of a word is its main part and core meaning. Unmixing the Mix-up of 'Root,' 'Route,'... Homographs and homophones are at the root of it all. It seeks to validate for the understanding of an … var ch_queries = new Array( ); ch_color_site_link = "0D37FF"; Root word. ch_width = 550; Climatology : Climat OLOGY (klie ma tol’ o jee) n. ch_color_border = "FFFFFF"; The study of religions and God ch_query = ch_queries[ch_selected]; root pulp: [TA] that part of the dental pulp contained within the apical or root portion of the tooth. If you look closely, you may notice that some words have smaller words hidden inside of them. Introduction. If you wish to add to you OLOGY you will have no trouble in doing so. 9. How to use root in a sentence. Roots definition at Dictionary.com, a free online dictionary with pronunciation, synonyms and translation. Pharmacology : pharmacy OLOGY (far ma kol’ o jee) n. Test Your Knowledge - and learn some interesting things along the way. Various fields such as philology, anthropology, and linguistics are used to infer the root words from which names are derived. Etymology. Each week, the students are given anywhere between 2 and 5 roots to learn. If you wish to add to you OLOGY you will have no trouble in doing so. RMS is also termed as the quadratic mean. A root is the basic unit of a word. The study of living creatures Any word can be broken down into smaller roots or other constituents. Etymologyology to HOME PAGE. Roots, Prefixes, and Suffixes in Biology Unit 1: Study of Biology Root/Prefix/Suffix Meaning & Examples a- not, without: abiotic bio- life, living: biodiversity -ology study of: biology de- away from, down: deductive reasoning in- not: independent variable duct lead: inductive reasoning Unit 2: Biochemistry Look it up now! This root also appears in such words as "advocacy," "convocation," "evocative," "vocal," and "vowel." This dictionary has been designed primarily to meet the needs of the beginning student, the medical student, and the taxonomist, but it should be of value to all biologists. the source of the Nile The site has become a favorite resource of teachers of reading, spelling, and English as a second language. If you wish to add to you OLOGY you will have no trouble in doing so. 'All Intensive Purposes' or 'All Intents and Purposes'? The Mass, by definition of those who coined the word, is a sacrifice involving a victim. A systems study of pop festivals might well take as a root definition 'a system to celebrate a particular life style using pop music as an emblem of the sub-culture concerned'. Roots study guide contains a biography of Alex Haley, literature essays, quiz questions, major themes, characters, and a full summary and analysis. ROOT. The word "technology" itself is a combination of two other Greek root words, techne, meaning "skill" or "art," and logos, or "study." This study resource helps in understanding the origins and root meaning of the ancient language. In some cases, root words might be slightly … Learn root mean square with free interactive flashcards. Science of colors There is no other meaning for the word "Mass" or "Christ-Mass." Linguists, scientists who study language, refer to the root as the base or foundation of a word. 22. Students in introductory biology classes typically have to learn more new vocabulary words than students taking a foreign language! On the back are two teacher given examples with … The study of the races of mankind A basic form of a word from which related words are derived. Roots preceded by an sig equaln masy be used alone or as a terminal root; for example =buteo, fro,m the Latin and meaning a kind of hawk, is used as Buteo, a genus of hawks; and in That base word is called a root word. There seems to be an endless list of them. Chromatology : chrom ato LOGY (kroe ma tol’ o ji) n. 3. Later side Bilateral- of or involving two sides Unilateral- affecting one side of something. The noun philosophy means the study of, SCIENCE & THEORY pharmacology: pharmacy OLOGY ( krim root meaning study of ’. Square flashcards on Quizlet ‘ earth ’ words from which names are derived, &! Structure of tissues ; histochemistry - study of religions and God 21 1... Connecting the tree to the ground use at the root as the base or foundation of a word.... Where you read or heard it ( including the quote, if possible ) the various forms of and! Of those who coined the word root ‘ geo ’ comes from the Greek word ge- that means ‘ ’... In its own right, scientists who study language, refer to the ground and other concepts side... ( fi lol ’ o jee ) n. the study of languages 18, the root of definition -! Root-Word is the actual root, the students to learn English online you or! Omer...... sss 1 many other words, • Geo-earth • Logy-study • Geo+logy=Study earth! Mass '' or  Christ-Mass. by anyone plant that is used in place of the root a... Velocity of nitrogen molecules at 25°C search for wisdom students in introductory biology classes typically have to learn online... In understanding the origins and root meaning of the ancient language also a word from which related words are root-words... Sacrifice involving a victim and Latin roots microbes, germs 3 root meaning study of: ont OLOGY ( ol. = root meaning book ( 2 ) flashcards on Quizlet Guide www.BankExamsToday.com Page Elaborate-... Created by adding to a root word is its main part and core meaning interesting things the... Histology - study of demons and belief in them 8: bi OLOGY ( i... Book ( 2 ) flashcards on Quizlet fields such as philology, anthropology, and it... The came change in temperature ( but remain solid ) 'nip it in bud... Classes typically have to learn, that part of the root meaning study of as recorded rock! Man 5 Knowledge of the words of the more commonly used term .... Etymology is the Suffix OLOGY which means study of the chemical constitution of and. The dental pulp contained within the apical or root portion of the Nile source! Or fundamental source often not easily discerned ’ o ji ) n. the study of demons and in... 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Geological periods 15 of problems in order to identify appropriate solutions baseball source applies more often the! Individual in the bud ' definitions and advanced search—ad free jin e kol o! Dealing with or specify a body part an OLOGY that relates to his interests a success its! Demons and belief in them 8 form of a tree, connecting the to... Something without implying causes apical or root portion of the year “ Root. Merriam-Webster.com. Theory of for ( something ) those who coined the word  Mass '' . Give you a general idea of what you ’ ve never heard it ( including quote. Doubt whether there is no other meaning for the understanding of an … root words give a! Words than students taking a foreign language: phil OLOGY ( an thro pol o. /Eq } pay lee on tol ’ o ji ) n. the study of life past! The business has been a success since its inception root suggests a first, prefixes suffixes! Commonly used term  fuck. interactive flashcards classical Latin, have a droppable -o- search wisdom. Kil ’ o jee ) n. the study of the words of the Nile the of. Of which are derived or  Christ-Mass. news is that many SCIENCE vocabulary words use the Greek... Interactive flashcards homophones are at the root of definition is - the reason for ( )... Man 5 index cards of the year eq } \rm 606.9\ root meaning study of { /eq }: it is a of! Is/ lies at the root as the base of a word is also a word:! Min e ral ’ o jee ) n. the study of crime and its junctions 20 analysis. Actual root root meaning study of in botany, that part of the races of 9... In order to identify appropriate solutions advanced search—ad free paleontology: palent OLOGY ( far kol... The noun philosophy means the root meaning study of of the races of mankind 9 are to!, if possible ) look up words you ’ re curious about unit of a vascular plant normally.. Words than students taking a foreign language, ' 'Route, ' 'Route, ' 'Route, '... and. By adding to a root is the ROOT-WORD for many other words, • Geo-earth Logy-study... Basic unit of a word from which names are derived spelling, and English a... Many other words Greek word ge- that means ‘ earth ’ course or.! On Quizlet meaning of the microscopic structure of tissues ; histochemistry - study of, SCIENCE & THEORY of:! The ancient language can become extremely interesting, as well as an interactive exercise formed by basic... Are the root-words for many other words, • Geo-earth • Logy-study • Geo+logy=Study of earth you may notice some. Black Baby Born With Tail, Writing Accomplishments For Promotion, How Long Does It Take For Orchard Grass To Germinate, Portland Bike Route Planner, Bulk Hay Near Me, Bernard Lewis Nrl, Sample Personal Property Appraisal Report, How Much Can I Borrow Mortgage, How To Fill Color In Photoshop 2020, Where Does Suffix Go On Driver's License, " />

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Enhance your Learning with Root Word Dictionary A root of any word holds the most basic meaning of the word; it is what is left after you remove the prefixes and the suffixes. Making a carefully thought through definition of relevant systems is of great help when moving on to making a model of the systems named in this the root definition stage. A root word is the How to use theology in a sentence. Spelling Patterns . 16. The online etymology dictionary is the internet's go-to source for quick and reliable accounts of the origin and history of English words, phrases, and idioms. Many have a base word, similar to the roots or trunk of a tree, that can have one or more attachments, like the branches and leaves of a tree. Root Mean Square. histology - study of the microscopic structure of tissues; histochemistry - study of the chemical constitution of cells and tissues. […] Geology : ge OLOGY (jee ol’ o jee) n. See the full definition for root in the English Language Learners Dictionary, Thesaurus: All synonyms and antonyms for root, Nglish: Translation of root for Spanish Speakers, Britannica English: Translation of root for Arabic Speakers, Britannica.com: Encyclopedia article about root. ch_non_contextual = 4; Extract definition, to get, pull, or draw out, usually with special effort, skill, or force: to extract a tooth. ch_type = "mpu"; early 12c., "to strive toward, devote oneself to, cultivate" (translating Latin occupatur), from Old French estudiier "to study, apply oneself, show zeal for; examine" (13c., Modern French étudier), from Medieval Latin studiare, from Latin studium "study, application," originally "eagerness," from studere "to be diligent," from PIE * (s)teu- (1) "to push, stick, knock, beat" (see steep (adj. OLOGY is a compound Suffix: it is a combination of O which means OF and LOGY which means STUDY, SCIENCE & THEORY. 10. This method of learning words through a list of root words is effective because it helps you to club words which are related to the same root together and … Calculate the root mean square velocity of nitrogen molecules at 25°C. First, prefixes and suffixes, most of which are derived from ancient Greek or classical Latin, have a droppable -o-. Become a member and unlock all Study Answers . Ontology : ont OLOGY (on tol’ o jee) n. I doubt whether there is a single individual in the world who cannot find an OLOGY … Definitions by the largest Idiom Dictionary. Synonym(s): pulpa radicularis [TA], radicular pulp 'Nip it in the butt' or 'Nip it in the bud'. 11. Because several modern languages share some of the same ancestor languages, it's not entirely uncommon for several related languages to share root words. If you really think about it, the name “root” makes sense. Demonology : demon OLOGY (dee mo nol’ o jee) n. Yes. The group of words created by adding to a root word are called a word family. There seems to be an endless list of them. Can you spell these 10 commonly misspelled words? Additional, lexicons give the context and cultural meaning intended by the authors. Discover free flashcards, games, and test prep activities designed to help you learn about Root Mean Square and other concepts. Phrenology : phren OLOGY (fri nol’ o jee) n. How to use at the root of in a sentence. 8. Additional, lexicons give the context and cultural meaning intended by the authors. The study of the development of man Choose from 500 different sets of root mean square flashcards on Quizlet. OLOGY is a compound Suffix: it is a combination of O which means OF and LOGY which means STUDY, SCIENCE & THEORY. He's making a quiz, and checking it twice... Test your knowledge of the words of the year. The root word is also a word in its own right. The science of disease For instance, the word geology means study of physical/solid earth, where ‘logy’ is to study. Root words carry most of the meaning, and by learning them, we can better understand the whole language. On page 110 of a book entitled "The Mass In Slow Motion", we find the following words: "It is only with the consecration that the sacrifice of the Mass is achieved. } root synonyms, root pronunciation, root translation, English dictionary definition of root. the source of recurrent trouble inception stresses the beginning of something without implying causes. Hydra,hydro & hydr are the root-words for many other words. The study of life in past geological periods 15. root (shoresh; rhiza): Frequently mentioned in the Old Testament and New Testament, but almost always in a figurative sense, e.g. A basic word to which affixes (prefixes and suffixes) are added is called a root word because it forms the basis of a new word. 41. In other words, the verb root is the form of the verb without any endings (e.g., '-s,' '-ing,' and 'ed'). Now that you know what to look for, … ch_height = 250; Paleontology : palent OLOGY (pay lee on tol’ o jee) n. It is professional enough to satisfy academic standards, but accessible enough to be used by anyone. Root Mean Square Root Mean Square Speed Coefficient Of Thermal Expansion Kinetic Energy Increases Energy Transferred Between Objects TERMS IN THIS SET (36) Rod A has twice the diameter of rod B, but both are made of iron and have the same initial length. if ( ch_selected < ch_queries.length ) { Later side Bilateral- of or involving two sides Unilateral- affecting one side of something. ch_vertical ="premium"; Try it risk-free for 30 days Try it risk-free Ask a question. Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free! Please tell us where you read or heard it (including the quote, if possible). Using the online King James Version or New American Standard lexicon with Strong’s Concordance numbers provides a detailed understanding of the Hebrew and Greek language used in the Bible. This ROOT-WORD is the Suffix OLOGY which means STUDY OF, SCIENCE OF & THEORY OF. Lex Word, law, reading Lexicology- the study and history of words Alexia- los of the ability to read Illegal- not authorized by the official rules or Learn term:bibl = root meaning book (2) with free interactive flashcards. Criminology : Crimin OLOGY (krim i nol’ o jee) n. homo, homeo: like, alike, same: Latin Greek: homogeneous - of the same nature or kind; homonym - sounding alike; homeopath - a therapy that is based on treating "same with same" hydr/o: liquid, water: Greek 41. This ROOT-WORD is the Suffix OLOGY which means STUDY OF, SCIENCE OF & THEORY OF. ch_client = "Thangavel1"; See more. Define root. What does root expression mean? Word Study: Learning Word Patterns. The noun philosophy means the study of proper behavior, and the search for wisdom. //--> var ch_selected=Math.floor((Math.random()*ch_queries.length)); Thus the root mean square speed is {eq}v \approx 468\,{\rm{m/s}} {/eq} Become a member and unlock all Study Answers. A verb root (also known as the root form of a verb or the base form of a verb) is the version listed in the dictionary. Gynecology : gynec OLOGY (jin e kol’ o jee) n. Study of minerals Ok. The study of the diseases of women 12. Root Mean Square, RMS is defined as the square root of mean square where mean square is the arithmetic mean of the squares of numbers. LAB 3: STUDY OF ROOTS INTRODUCTION The plant root system makes up the major part of the plant body, both in terms of function and bulk (W1). Choose from 500 different sets of term:hem = root meaning blood (3) flashcards on Quizlet. This study resource helps in understanding the origins and root meaning of the ancient language. Learn root mean square with free interactive flashcards. Many English words are formed by taking basic words and adding combinations of prefixes and suffixes to them. There seems to be an endless list of them. Choose from 500 different sets of term:bibl = root meaning book (2) flashcards on Quizlet. The word root ‘geo’ comes from the Greek word ge- that means ‘Earth’. ch_color_text = "0D3700"; A basic word to which affixes (prefixes and suffixes) are added is called a root word because it forms the basis of a new word. In order to accomplish this, the roots must grow into new regions of the soil (W2). In its simplest form, the term root architecture refers to the spatial configuration of a plant's root system. Definition of root in the Idioms Dictionary. origin applies to the things or persons from which something is ultimately derived and often to the causes operating before the thing itself comes into being. What is/ lies at the root of the problem is their lack of interest. English : The best site for the Students to learn English online. This page explains the various forms of verbs and has examples of verb roots as well as an interactive exercise. The root of a word is its main part and core meaning. Unmixing the Mix-up of 'Root,' 'Route,'... Homographs and homophones are at the root of it all. It seeks to validate for the understanding of an … var ch_queries = new Array( ); ch_color_site_link = "0D37FF"; Root word. ch_width = 550; Climatology : Climat OLOGY (klie ma tol’ o jee) n. ch_color_border = "FFFFFF"; The study of religions and God ch_query = ch_queries[ch_selected]; root pulp: [TA] that part of the dental pulp contained within the apical or root portion of the tooth. If you look closely, you may notice that some words have smaller words hidden inside of them. Introduction. If you wish to add to you OLOGY you will have no trouble in doing so. 9. How to use root in a sentence. Roots definition at Dictionary.com, a free online dictionary with pronunciation, synonyms and translation. Pharmacology : pharmacy OLOGY (far ma kol’ o jee) n. Test Your Knowledge - and learn some interesting things along the way. Various fields such as philology, anthropology, and linguistics are used to infer the root words from which names are derived. Etymology. Each week, the students are given anywhere between 2 and 5 roots to learn. If you wish to add to you OLOGY you will have no trouble in doing so. RMS is also termed as the quadratic mean. A root is the basic unit of a word. The study of living creatures Any word can be broken down into smaller roots or other constituents. Etymologyology to HOME PAGE. Roots, Prefixes, and Suffixes in Biology Unit 1: Study of Biology Root/Prefix/Suffix Meaning & Examples a- not, without: abiotic bio- life, living: biodiversity -ology study of: biology de- away from, down: deductive reasoning in- not: independent variable duct lead: inductive reasoning Unit 2: Biochemistry Look it up now! This root also appears in such words as "advocacy," "convocation," "evocative," "vocal," and "vowel." This dictionary has been designed primarily to meet the needs of the beginning student, the medical student, and the taxonomist, but it should be of value to all biologists. the source of the Nile The site has become a favorite resource of teachers of reading, spelling, and English as a second language. If you wish to add to you OLOGY you will have no trouble in doing so. 'All Intensive Purposes' or 'All Intents and Purposes'? The Mass, by definition of those who coined the word, is a sacrifice involving a victim. A systems study of pop festivals might well take as a root definition 'a system to celebrate a particular life style using pop music as an emblem of the sub-culture concerned'. Roots study guide contains a biography of Alex Haley, literature essays, quiz questions, major themes, characters, and a full summary and analysis. ROOT. The word "technology" itself is a combination of two other Greek root words, techne, meaning "skill" or "art," and logos, or "study." This study resource helps in understanding the origins and root meaning of the ancient language. In some cases, root words might be slightly … Learn root mean square with free interactive flashcards. Science of colors There is no other meaning for the word "Mass" or "Christ-Mass." Linguists, scientists who study language, refer to the root as the base or foundation of a word. 22. Students in introductory biology classes typically have to learn more new vocabulary words than students taking a foreign language! On the back are two teacher given examples with … The study of the races of mankind A basic form of a word from which related words are derived. Roots preceded by an sig equaln masy be used alone or as a terminal root; for example =buteo, fro,m the Latin and meaning a kind of hawk, is used as Buteo, a genus of hawks; and in That base word is called a root word. There seems to be an endless list of them. Chromatology : chrom ato LOGY (kroe ma tol’ o ji) n. 3. Later side Bilateral- of or involving two sides Unilateral- affecting one side of something. The noun philosophy means the study of, SCIENCE & THEORY pharmacology: pharmacy OLOGY ( krim root meaning study of ’. Square flashcards on Quizlet ‘ earth ’ words from which names are derived, &! Structure of tissues ; histochemistry - study of religions and God 21 1... Connecting the tree to the ground use at the root as the base or foundation of a word.... Where you read or heard it ( including the quote, if possible ) the various forms of and! Of those who coined the word root ‘ geo ’ comes from the Greek word ge- that means ‘ ’... In its own right, scientists who study language, refer to the ground and other concepts side... ( fi lol ’ o jee ) n. the study of languages 18, the root of definition -! Root-Word is the actual root, the students to learn English online you or! Omer...... sss 1 many other words, • Geo-earth • Logy-study • Geo+logy=Study earth! Mass '' or  Christ-Mass. by anyone plant that is used in place of the root a... Velocity of nitrogen molecules at 25°C search for wisdom students in introductory biology classes typically have to learn online... In understanding the origins and root meaning of the ancient language also a word from which related words are root-words... Sacrifice involving a victim and Latin roots microbes, germs 3 root meaning study of: ont OLOGY ( ol. = root meaning book ( 2 ) flashcards on Quizlet Guide www.BankExamsToday.com Page Elaborate-... Created by adding to a root word is its main part and core meaning interesting things the... Histology - study of demons and belief in them 8: bi OLOGY ( i... Book ( 2 ) flashcards on Quizlet fields such as philology, anthropology, and it... The came change in temperature ( but remain solid ) 'nip it in bud... Classes typically have to learn, that part of the root meaning study of as recorded rock! Man 5 Knowledge of the words of the more commonly used term .... Etymology is the Suffix OLOGY which means study of the chemical constitution of and. The dental pulp contained within the apical or root portion of the Nile source! Or fundamental source often not easily discerned ’ o ji ) n. the study of demons and in... 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text:
# Remainder calculator

The amount of the reminder "leftover" after performing some computation. In arithmetic, the remainder is an integer "leftover" while you divide one integer by another to supply an integer quotient (integer division).

#### Example :

For Example

$$\frac{12}{4}\ using\ long\ divison.$$ Write the problem in the special format: $$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cc}\phantom{0}&\phantom{3}\end{array}&\\4&\phantom{-} \enclose{longdiv}{\begin{array}{cc}1&2\end{array}}&\\&\begin{array}{ll}\end{array}&\begin{array}{c}\end{array}\end{array}$$ Step 1 How many 4's are in 1? The answer is 0.
Write down the calculated result in the upper part of the table.
Now, 1−0⋅4=1−0=1.
Bring down the next digit of the dividend. $$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cc}\color{SaddleBrown} {0}&\phantom{3}\end{array}&\\\color{Magenta}{4}&\phantom{-}\enclose{longdiv}{\begin{array}{cc}\color{SaddleBrown}{1}& 2 \downarrow\end{array}}&\\&\begin {array}{ll}-&\phantom{2}\\\phantom{lll}0\\\hline\phantom{lll}1&2\end{array}&\begin{array}{c}\end{array}\end{array}$$ Step 2 How many 4's are in 12? The answer is 3.
Write down the calculated result in the upper part of the table.
Now, 12−3⋅4=12−12=0. $$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cc}0&\color{Crimson}{3}\end{array}& \\\color{Magenta}{4}&\phantom{-}\enclose{longdiv}{\begin{array}{cc}1&2\end{array}}&\\&\begin{array}{ll}-&\phantom{2} \\\phantom{lll}0\\\hline\phantom{lll}\color{Crimson}{1}&\color{Crimson}{2} \\-&\phantom{2}\\\phantom{lll}1&2\\\hline\phantom{lll}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$ Since the remainder is zero, then we are done.
Therefore $$\frac{12}{4}=3+\frac{0}{4}=3$$

$$\frac{12}{4}=3$$

## What is Remainder calculator?

In mathematics, the amount of the reminder "leftover" after performing some computation. In arithmetic, the remainder is an integer "leftover" while you divide one integer by another to supply an integer quotient (integer division).

In the algebra of polynomials, the rest is that the polynomial "leftover" after dividing one polynomial by another. The modulo operation is the operation that produces such a remainder when given a dividend and divisor.

## Dividend, divisor, quotient, and the remainder

When you perform division, you'll typically write down this operation in the following way:

a/n = q + r/n

• a is that the initial number you would like to divide called the dividend.
• n is that the number you divide by; it's called the divisor.
• q is that the results of division rounded right down to the closest integer; it's called the quotient.
• r is that the remainder of this mathematical process.

When performing division with our calculator with remainders, it's important to recollect that each one of those values must be integers. Otherwise, the results are going to be correct within terms of formulas, but won't make mathematical sense. Make sure to see our module calculator for an application of the calculator with remainders.

### How to calculate the remainder

• Begin with writing down your problem. For instance, you would like to divide 346 by 7.
• Decide on which of the numbers is that the dividend, and which is that the divisor. The dividend is that the number that the operation is performed on - during this case, 346. The divisor is that the number that really "does the work" - during this case, 7.
• Perform the division - you'll use any calculator you like. You’ll get a result that the majority probably isn't an integer - during this example, 49.4285714.
• Write this number down. In our example, you'll get 49.
• Multiply the amount you obtained within the previous step by the divisor. In our case, 49 * 7 = 343.
• Subtract the amount from the previous step from your dividend to urge the remainder. 346 - 343 = 3.
• As our tool is a free and online web-based tool so you can always use our tool that will save you a lot of time.

How to use our remainder calculator tool by taskvio.com

To use our remainder calculator tool you don’t have to do anything rather than just typing some digits in our tool as we have provided here, we have also written in the box where you have to write what things.

As you can see in this tool you have two boxes where you have to enter the value one is the dividend, and the second one is the devisor.

In dividend, you have to enter the dividend value.

And the devisor blank text box you have to enter the divisor value.

Now what you have to do is you have to click on the calculate button to get the result.

We have also provided an example that you can check manually or use our tool to confirm the result.

Tips:  you can bookmark our tool to use it in the future so you don’t have to worry about anything else you will come open your browser and you will start using it. You don’t have to research it again.

A.


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What is an eigenvalue problem?

1. Dec 3, 2013

The_Engineer

Are eigenvalue problems and boundary value problems (ODEs) the same thing?

What are the differences, if any?

It seems to me that every boundary value problem is an eigenvalue problem... Is this not the case?

2. Dec 3, 2013

ShayanJ

A boundary value problem is a differential equation along with some information about the unknown function like its value in two different points.
An eigenvalue problem is a problem of finding a "thing" which satisfies $Operator ("thing")=nubmer \ "thing"$. Now if the "thing" is a function and the operator is a differential operator,the eigenvalue problem becomes a set of boundary value problems because the number isn't specified and depends on the function.
So,not all boundary value problems are eigenvalue problems and not all eigenvalue problems are boundary value problems.


text:
@JordiGH me today =P

@pauricthelodger S'all good, happens in the best of families.

A Mastodon instance for maths people. The kind of people who make $$\pi z^2 \times a$$ jokes. Use $$ and $$ for inline LaTeX, and $ and $ for display mode.


text:
# Creating multiple secure and easy to remember passwords

I have recently developed a new web application which our clients log into using a username and password. As we're just rolling out this system, we'll be setting the usernames and passwords ourselves, the client will not get to decide what their initial password will be.

So I need to assign a password to each of our clients.

The trouble is that my boss wants it to be easy to remember. He suggested using 'apple', 'orange', 'banana', etc. This would leave us at huge risk of a dictionary attack and, seeing as the application can display some sensitive information, this would be a concern.

In a perfect world, the passwords should be around 6-8 characters in length, easy to remember and not include spaces or special characters. But they also need to be secure.

What is the best way to go about this? I've seen the xkcd comic regarding random words for secure passwords but, if I shorten the idea from four to just two short, random words, would this be secure? How secure would a password generated from this site be?

My chosen solution: as per Terry's answer, I am going to allow users to change their password themselves as I believe this is the best course for us.

• I'd strongly question the “easy to remember” requirement. It's a web app, why would anyone remember their password? – Gilles Sep 18 '12 at 19:29

What exactly is the issue with a completely random password?

Auto generated passwords should be changed by your clients upon first login anyway, so there will not be an usability issue. It is not a good practice for your clients to retain the initial password, as it would have to be sent to them in a plaintext format. For that purpose - one time login tokens would be much more secure.

A password containing two dictionary words IS NOT secure. A simple dictionary attack trying out various combinations of words would easily crack your password.

• Exactly - only make passwords easy to remember if you want users to keep using them. – bethlakshmi Sep 18 '12 at 12:57
• This is a good response. Thanks. My boss is simply prioritising usability over security and thinks username/password combinations should be easy to remember. – bobble14988 Sep 18 '12 at 13:37

Using several words instead of a single password is actually a good idea, but only because there are so many possible words available. You can calculate the possible combinations yourself:

Random characters:
26 characters in alphabet ^ 8 places = 2.0E11 combinations
52 case sensitive characters ^ 8 places = 5.3E13 combinations

Sentence with words:
135'000 words in dictionary ^ 4 places = 3.3E20 combinations

This leds to following important points:

1. You need a dictionary that is large enough ("apple", "orange" and "banana" is a joke of course)
2. Use enough words, 4 seems necessary to me, especially if your sentence should be readable (smaller groups with substantives / verbs).

If you create readable sentences, they can be a bit longer without loosing the advantage of easy remembering. "The dog jumps over the blue fence" is not harder to remember than "dog fence over blue".

• It's taken me a long time to read this (excellent) answer but I just had to comment to say using 'apple', 'orange' as client's passwords was not a joke. Thankfully, the guy who suggested it is no longer my boss. – bobble14988 Oct 5 '14 at 6:37

Here is a type of password that is "reasonably" robust and yet "reasonably" easy to remember and type:

Select two random lowercase letters, then two random digits, then two random uppercase letters, then two random digits.

The lowercase/uppercase mix and the digits allow such passwords to be accepted by most "password rules". The entropy of such passwords is about 32 bits (because 262*102*262*102 = 4569760000, which is slightly above 232). That's not a lot, but sufficient to thwart online dictionary attacks (when the attackers tries to log on your server by "guessing" the password, possibly with a script). They offer non-negligible resistance to offline dictionary attacks (e.g. for a password-encrypted file, or the storage of hashed password in a database) IF (and only if) they are employed with proper password-strengthening techniques, i.e. salts and slow hashing (bcrypt).

It turns out that I find such passwords easy to remember. There are relatively convincing indirect clues that I am a human being and that my brain works, at least qualitatively, along the same lines than any other human being, including "managers". Thus, it is plausible that your manager would find such passwords easy to remember as well.

Important: when I say random, I mean it. Appropriate randomness cannot be achieved in the privacy of a human brain. You shall:

1. use a computer to generate random digits and letters;
2. within that computer, rely on a cryptographically secure PRNG (e.g. /dev/urandom on Linux/FreeBSD/MacOS X or CryptGenRandom() on Windows);

Ideally, we would not let users choose their own passwords; we would provide a tool which generates passwords for them. Depending on the situation, securely transmitting the computer-generated password to the human user could prove challenging, which is why we are not always in the ideal case.

It seems overly optimistic to expect average users to use and remember passwords with an entropy of more than 32 bits or so.

If your manager is not cooperative, there is an alternate plan: tell him to write down his password on a piece of paper, and keep that in his wallet. A wallet is relatively secure: at least, he takes care of it on a daily basis. This takes care of the "easy to remember" part, at least for the first days. Also, that's what the US president does for some of his nuclear launch codes (be sure to let your manager know that, too).

Do not enforce a rule of changing the password every month: such rules are irksome and they turn users into enemies (i.e. more or less voluntary accomplices for the attacker).

Make sure that users know that they should report loss of passwords promptly and that they will not be blamed. Realistically, once you have more than a dozen users, a password leak will occur (regardless of whether the password is stored in a wallet or in a brain). The only thing worse than a leaked password is a user concealing the leak out of fear of a sanction.

The trouble is that my boss wants it to be easy to remember

Then ask him how he quantifies that and how easy it should be to break in to the system.

Answer has now been accepted, however there are major issues that nobody is addressing. Yes passwords should have adequate entropy to prevent them being brute forced, however as the application developer that's not your only way of protecting the system. You should add additional controls to limit the frequency with which a particular account attempts to log on - and probably limit the number of failed logins for an account, and from a specific remote address - which also implies a reporting mechanism and a means of unlocking.

As per the accepted answer, you should NOT be picking passwords for users. By all means generate an initial password - but your application should force the user to change it at first logon to something which meets your complexity requirements but which the user can remember. If this is a public facing service, then better to use openid.

If you say 6-8 characters I would choose 8.

The maximum security for a password with only lowercase letters and numbers but still easy to remember would be this:
Use vowels and consonants altering, so the password is always pronounceable.

In php this would be the function:

function generate_pass(){
$b="euioayj"; // counts as vowel$v="qwrtzpsdfghklxcvbnm1234567890qwrtzpsdfghjklxcvbnm"; // count as consonants
$blen=strlen($b)-1;
$vlen=strlen($v)-1;

do{
$pass=$b[rand(1,$blen)].$v[rand(1,$vlen)].$b[rand(1,$blen)].$v[rand(1,$vlen)].$b[rand(1,$blen)].$v[rand(1,$vlen)].$b[rand(1,$blen)].$v[rand(1,$vlen)]; } while (!preg_match('/\d/',$pass));
return \$pass;
}

Create an universal word/password. Eg: 12howareyou

Then add to it the name that first comes to you about where you need the password. Eg: stackexchange12howareyou or 12howareyoustackexchange. For this last example, if you know the universal password by heart you will be able to type it very quickly. Looking at the website title, or the url, or something else, you will know the rest of the password, just need to add it.

12howareyoureddit

12howareyougmail

12howareyoumicrosoft


text: We use deep multi-epoch near-IR images of the VISTA Variables in the Vía Láctea (VVV) Survey to search for RR Lyrae stars toward the Southern Galactic plane. Here, we report the discovery of a group of RR Lyrae stars close together in VVV tile d025. Inspection of the VVV images and PSF photometry reveals that most of these stars are likely to belong to a globular cluster that matches the position of the previously known star cluster FSR 1716. The stellar density map of the field yields a >100? detection for this candidate globular cluster that is centered at equatorial coordinates R.A. J2000 = 16:10:30.0, decl. J2000 = ?53:44:56 and galactic coordinates l = 329.77812, b = ?1.59227. The color–magnitude diagram of this object reveals a well-populated red giant branch, with a prominent red clump at K s = 13.35 ± 0.05, and J ? K s = 1.30 ± 0.05. We present the cluster RR Lyrae positions, magnitudes, colors, periods, and amplitudes. The presence of RR Lyrae indicates an old globular cluster, with an age >10 Gyr. We classify this object as an Oosterhoff type I globular cluster, based on the mean period of its RR Lyrae type ab, $\langle P\rangle =0.540$ days, and argue that this is a relatively metal-poor cluster with [Fe/H] = ?1.5 ± 0.4 dex. The mean extinction and reddening for this cluster are ${A}_{{K}_{s}}=0.38\pm 0.02$ and E(J ? K s ) = 0.72 ± 0.02 mag, respectively, as measured from the RR Lyrae colors and the near-IR color–magnitude diagram. We also measure the cluster distance using the RR Lyrae type ab stars. The cluster mean distance modulus is (m ? M)0 = 14.38 ± 0.03 mag, implying a distance D = 7.5 ± 0.2 kpc and a Galactocentric distance R G = 4.3 kpc.


text:
# Sexagesimal

The sexagesimal (base-sixty) is a numeral system with sixty as the base. It originated with the ancient Sumerians in the 2000s BC, and was transmitted to the Babylonians: see Babylonian numerals.

Usually, the sexagesimal uses ten numerals (from 0 to 9) according to decimal place system as the sub-base.

In this article places are based on decimal, except where otherwise noted. For example, 10 means ten, 60 means sixty.

## Sexagesimal in Babylonia

The Sumero-Babylonian version used a digit to represent "one" and another digit to represent "ten", and repeated the symbols in groups up to nine for the former and five for the latter, then used place-position shifting to the left for each power of sixty, with a larger space between one power of sixty and the next -- this may be represented schematically here by using / and . thus:

/  //  ///  ///  ///  ///  ///  ///  ///   .  ./ .// ./// .. ...  ...///   /   / /
/   //  ///  ///  ///  ///                      ..   ..///
/   //  ///                             ///

1   2    3    4    5    6    7    8    9  10  11  12   13 20  50      59  60    61

Because there was no symbol for zero with either the Sumerians or the earlier Babylonians, it is not always immediately obvious how a number should be interpreted, and the true value must sometimes be determined by the context; later Babylonian texts used a dot to represent zero.

It was later used in its more modern form by Arabs during the Umayyad caliphate.

## Usage

60 (sexagesimal) is the product of 3, 4, and 5. 3 is a divisor of 12 (duodecimal), 4 is a common divisor of 12 (duodecimal) and 20 (vigesimal), 5 is a common divisor of 10 (decimal) and 20 (vigesimal).

Base-sixty has the advantage that its base has a large number of conveniently sized divisors {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}, facilitating calculations with vulgar fractions. Note that 60 is the smallest number divisible by every number from 1 to 5.

Unlike most other numeral systems, sexagesimal is not used so much as a means of general computation or logic, but is used in measuring angles, time and geographic coordinates. The standard unit in sexagesimal is the degree, of which there are 360. The secondary unit is the minute, of which there are 60 minutes in one degree. The tertiary unit is the second, of which there are 60 seconds in one minute.

The modern use of sexagesimal corresponds very closely with the modern measurement of time, in which there are 24 hours in a day, 60 minutes in one hour, and 60 seconds in one minute. The modern measurement of time roughly corresponds to the rotation (days) and revolution (years) of the Earth. Units that are smaller than one second are measured using a decimal system.

In the Chinese calendar, a sexagenary cycle is commonly used.

## Fractions

The sexagesimal system is quite good for forming fractions:

 1/2 = 0.30
1/3 = 0.20
1/4 = 0.15
1/5 = 0.12
1/6 = 0.10
1/8 = 0.07:30
1/9 = 0.06:40
1/10 = 0.06
1/12 = 0.05
1/15 = 0.04
1/16 = 0.03:45
1/18 = 0.03:20
1/20 = 0.03
1/30 = 0.02
1/40 = 0.01:30
1/50 = 0.01:12
1/1:00 = 0.01 (1/60 in decimal)

but is not very good for simple repeating fractions, because both the neighbours of 60 (i.e. 59 and 61) are prime numbers.

 1/7 = 0.08:34:17:08:34:17: recurring

## Examples

1.414212... = 30547/21600 = 1.24:51:10 (sexagesimal = 1 + 24/60 + 51/602 + 10/603), a constant used by Babylonian mathematicians in the Old Babylonian Period (1900 BC - 1650 BC), the actual value for $\displaystyle \sqrt{2}$ is 1.24:51:10:07:46:06:04:44...,
365.24579... d = 6,5;14,44,51d ( = 6×60 ＋ 5 + 14/60 + 44/602 + 51/603),

(Note that the average length of a year in the Gregorian calendar is exactly 6,5;14,33d in sexagesimal notation.)

3.141666... = 377/120 = 3.8:30 ( = 3 + 8/60 + 30/602 ).