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One of the central themes in the philosophy of formal sciences (or mathematics) is the debate between realism (sometimes misnamed Platonism) and nominalism (also called "anti-realism"), which has different versions.
In my opinion, what is decisive in this regard is the position adopted on the question of whether objects postulated by the theories of the formal sciences (such as the arithmetic of natural numbers) have some mode of existence independently of the language that we humans use to refer to them; that is, independently of linguistic representations and theories. The affirmative answer assumes that things like numbers or the golden ratio are genuine discoveries, while the negative one understands that numbers are not discoveries but human inventions, they are not entities but mere referents of a language whose postulation has been useful for various purposes.
However, it does not occur to me how an anti-realist or nominalist position can respond to these two realist arguments in philosophy of mathematics: first, if numbers have no existence independently of language, how can one explain the metaphysical difference, which we call numerical, at a time before the existence of humans in which at t0 there was in a certain space-time region what we call two dinosaurs and then at t1 what we call three dinosaurs? That seems to be a real metaphysical difference in the sense in which we use the word "numerical", and it does not even require human language, which suggests that number, quantities, etc., seem to be included in the very idea of ​​an individual entity.
Secondly, if the so-called golden ratio (also represented as the golden number and related to the Fibonacci sequence) is a human invention, how can it be explained that this relationship exists in various manifestations of nature such as the shell of certain mollusks, the florets of sunflowers, waves, the structure of galaxies, the spiral of DNA, etc.? That seems to be a discovery and not an invention, a genuine mathematical discovery. And if it is, it seems something like a universal of which those examples are particular cases, perhaps in a Platonic-like sense, which seems to suggest that mathematical entities express characteristics of the spatio-temporal world. However, this form of mathematical realism does not seem compatible with the version that maintains that the entities that mathematical theories talk about exist outside of spacetime. That is to say, if mathematical objects bear to physical and natural objects the relationship that the golden ratio bears to those mentioned, then it seems that there must be a true geometry and that, ultimately, mathematical entities are not as far out of space-time as has been suggested. After all, not everything that exists in spacetime has to be material, as the social sciences well know, that refer to norms, values or attitudes that are not. (I apologize for using a translator. Thank you.)
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Indeed, that is a possibility. Perhaps what we call numbers are labels in a language, as a kind of names that do not really name anything that is literally beyond human language and representations, or that are a way of referring to systems, scales , etc. of which they are a part, mere nodes of a conceptual structure. Some authors have argued that numbers are only signs, signs that are part of representational and notational systems that have proven to be effective, useful instruments to be applied to parts of reality, which are improved and refined over time. However, I believe that it is necessary to take into account the fact that not every system, model or scale works, and this perhaps reveals that there are structural characteristics of the reality to which they are applied that are imposed as limits, that constrain what can be work and what doesn't, and this perhaps means that, although they do not literally describe abstract entities (numbers or geometric figures, for example) as we imagine them, mathematical systems and theories somehow express that which is beyond the representations themselves. You can't use just any geometry to build a house or to explain why Mercury "wobbles" when it's at perihelion, and that suggests that mathematical systems, mathematized theories and models are human creations but they could not be totally arbitrary, so that, even in a metaphorical or indirect way, it should not be ruled out that they represent structural characteristics of the world to which they are applied that is beyond human constructs. We must not forget that we humans perceive in three dimensions, we listen less than dogs, we believe that colors are in things and, to an important extent, we elaborate our theories and build our image of the world accordingly ("the human is the measure of all things" said Protagoras), but there seems to be more and more evidence that, at least the macroscopic physical world is not three-dimensional, so we may never really know what lies beyond us and our representations and to that mystery we must add that of why some models and mathematical theories work and others do not. Greetings.
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I extracted the DNA from tissue (25 mg) and made the elution in 100 micro liter of an elution buffer, then made a real time PCR for CMV. Now when calculating the copy number of the viral load, is it calculated as copu number per micro liter or per mg?
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This paper might be of help to you
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hi 
I am working on dam and reservoir interacrion and the order of numbers in fluid mass matrix is E-7 which seems very little 
aany one that remmember whats th order of numbers in mass matrix for a 120 meter rservoir ?
it is a big help for me 
best regard
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The mass matrix M(p) describes the generalized mass and inertia of the system as a function of the vehicle pose. Contributions to this matrix can be determined for each rigid body by using algebraic manipulations to rearrange the kinetic co- energy (3.11) into the quadratic form (3.16), for which the mass matrix is then obvious.The mass matrix for the fuselage body is found by rearranging the energy and has the same form as that found in conventional aircraft equations of motion [1, 2]. The mass matrix is(3.19)׀׀Mp=׀׀m0I00which is a diagonal matrix with the mass and inertia tensor along the block diagonal. The mass matrix for the first linkage (i = 1, e.g. the wings) is given in (3.20), and should a second linkage (i = 2, e.g. the four-bar mechanism, tail surface, etc.) need to be modeled, the mass matrix is given in (3.21). Each mass matrix has along its block diagonal the scalar mass, the inertia relative to the fuselage center of mass, and the inertia of the linkage. Off-diagonal terms represent inertial couplings within the system. The total mass matrix of the system is a summation of the mass matrices of each rigid body.View chapterPurchase book
Models and model adjustments Alvar M. Kabe, Brian H. Sako, in Structural Dynamics Fundamentals and Advanced Applications, 2020 1.2.4 Bar finite element The mass and stiffness matrix coefficients for a uniform bar element are available from the Bernoulli-Euler beam element mass and stiffness matrices; see Eqs. (1.2-14) and (1.2-51). Since there is no coupling between the longitudinal coordinates, u1 and v1, and the lateral and rotational coordinates, u2, v2, u6, and v6, the coefficients associated with u1 and v1 are the values that yield the sought-after matrices(1.2-62)[mbar]=ρl420[1407070140][kbar]=AEl[1−1−11]View chapterPurchase book
Vibrations of structures Carl T.F. Ross BSc, PhD, DSc, CEng, FRINA, MSNAME, in Advanced Applied Finite Element Methods, 1998 8.4.4 Torque bar The mass matrix for a prismatic torque bar is now derived. From Fig. 8.3, the angle of twist ϕ is given by 📷Sign in to download full-size imageFig. 8.3.ϕ=[(1−ξ) Ξ]{ϕ1ϕ2}=[N]{ui}where ξ=x/l, but as the rotational displacement, at any point, varies with r(8.50)[m]=∫vol[N]Trρ[N]r d(vol) ϕ1ϕ2=ρIxl6[2112]ϕ1ϕ2,where Ix = 2nd polar moment of are of the cross-section of the torque bar about its centroid and in the direction of the x axis.View chapterPurchase book
Modal analysis of an undamped MDoF system Jimin He, Zhi-Fang Fu, in Modal Analysis, 2001 Example 5.4 The mass and stiffness matrices of the 4DoF system in Example 5.1 are respectively:[M]=[1000010000100001]kgand[K]=[2000−100000−10002000−100000−10002000−100000−10002000]N/mand the mode shape matrix is:[Ψ]=[0⋅37363−0⋅36180−0⋅44721−0⋅827060⋅60455−0⋅223610⋅276391⋅338210⋅604550⋅223610⋅27639−1⋅338210⋅373630⋅36180−0⋅447210⋅82706]Therefore, the modal mass matrix can be calculated as:[⋅mi.]=[Ψ]T[M][Ψ]=[1⋅0101700000⋅3618000000⋅5527900000⋅94966]According to equation (5.7), the mass-normalized mode shape matrix of the 4DoF system becomes:[Φ]=[0⋅37363−0⋅36180−0⋅44721−0⋅827060⋅60455−0⋅223610⋅276391⋅338210⋅604550⋅223610⋅27639−1⋅338210⋅373630⋅36180−0⋅447210⋅82706][1⋅0101700000⋅3618000000⋅5527900000⋅94966]−1/2=[0⋅37175−0⋅60150−0⋅60150−0⋅371750⋅60150−0⋅371750⋅371750⋅601500⋅601500⋅371750⋅37175−0⋅601500⋅371750⋅60150−0⋅601500⋅37175]This mass-normalized mode shape matrix can be used to verify equations (5.40 and 41).View chapterPurchase book
Model checks Alvar M. Kabe, Brian H. Sako, in Structural Dynamics Fundamentals and Advanced Applications, 2020 Problem 4.9 Given the mass and stiffness matrices of an unconstrained system[m]=[200020001][k]=[2−20−24−20−22]compute the circular frequencies squared, mode shapes, inertia relief matrix, and flexibility matrix, [Ge]; and then show that [Ge][m][ϕr]=[0] and that the inertia relief matrix multiplied by [m][ϕr] is also equal to a null matrix.View chapterPurchase book
Multi-degree-of-freedom systems Alvar M. Kabe, Brian H. Sako, in Structural Dynamics Fundamentals and Advanced Applications, 2020 Problem 6.1 For the given mass and stiffness matrices solve the eigenvalue problem by first inverting the mass matrix. Also, normalize the resulting mode shapes to unit modal mass. What is the relationship between the trace (sum of the diagonal elements) of [D] and the sum of the eigenvalues?[m]=[3001][k]=[4−2−24](−λ[I]+[D]){ϕ}={0}and[D]=[m]−1[k]View chapterPurchase book
CASIMIR—a human body model for the analysis of seat vibrations Alexander Siefert, Jörg Hofmann, in DHM and Posturography, 2019 4.1 Condensation of the occupied seat To integrate the occupied seat into an MBS analysis, a condensation of the system matrix of the detailed model has to be performed. In Abaqus, the substructure technique enables to condense a system to the relevant DOF. Because of the linearization of the system at the operational point, the variation of properties in the frequency range is not considered.The internal forces {I¯R} of the condensed system result from the equation of motion, see Eq. (10.3), of the defined DOF.(10.3){I¯R}=[M¯]{q¯R}+[C¯]{q˙R}+[K¯]{qR}EquationofmotionforcondensedsystemThe reduced mass matrix [M¯], the reduced damping matrix [C¯], and the reduced stiffness matrix [K¯] represent the substructure. The first step is the choice of the DOF to be considered in the substructure. This step is crucial as it defines the information handed over to the MBS calculation. In the case of a ride comfort analysis, these are the global eigenmodes relevant for the transmissibility. Further relevant points for the assessment must be considered. Accordingly, nodes of the seat structure, the seat surface, and the human body are chosen. The following list shows a general overview of the locations, which should be considered; see also Fig. 10.11: 📷Sign in to download full-size imageFigure 10.11. Exemplary nodes for generation of the substructure.•Fixation points at the seat rail•Structural locations of underframe and backrest•Rear and bottom suspension system•A-side of the upholstery cushion and backrest•Center of gravity of thighs, pelvis, lumbar spine, and torsoIn the next step, the reproduction of the dynamic properties should be checked. Accordingly, a natural frequency analysis is performed for the MBS solver, here Simpack, and for the FE solver, here Abaqus. If the nodes for the substructure are chosen correctly, the resonance frequencies and the mode shapes should correlate very well. Based on the correlation, it can be stated that the substructure reproduces the linearized properties of the detailed model very well and thus the condensation is v for the occupied seat.View chapterPurchase book
Pendulum model Timothy M. Barrows, Jeb S. Orr, in Dynamics and Simulation of Flexible Rockets, 2021 Linearized quasi-steady mass matrix for the pendulum model The above mass matrix must be recomputed at each time step. For some applications, such as a frequency domain analysis tool, this is undesirable. This section describes how to create a quasi-steady mass matrix. We can write
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Dears, please help me.
Could you prove that for any big number N there exists a composite Fermat number F_k such
that F_k > N?
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Fermat numbers are odd numbers.
I think you are confused with Fibonacci numbers where F3n even numbers.
Best wishes
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Im supposed to synthesize Ni0.9Co2O4 and Ni0.95Co2O4. I'm gonna use the salts Ni(NO3)2 and Co(NO3)2 but Im confused what the numbers 0.9 and 0.95 next to the nickel means and how to start this calculation. 
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NiCo2O4 is synthesized by the hydro-thermal route in the presence of urea.
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If corresponding factorials and triangular numbers are added, the results form the sequence of numbers, {2, 5, 12, 34, 135, 741, 5068, 40356, ...}, which I call factoriangular numbers. In the list of the first few factoriangular numbers, I found three Fibonacci numbers: 2, 5 and 34. Aside from these three, are there other Fibonacci numbers in the sequence of factoriangular numbers?
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Now it is a a complete useful answer.
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Dear all,
Hello!
How the size of individual cell can be measured by a typical SSC vs FSC graph without using a reference (known size beads or cells)? Although from a typical SSC vs FSC graph, we can find out relative size and complexity of the cells belonging to a particular population, how can we measure the cell size by using the numbers appears on the graph axis and the number below the graph (x1000 or so)?
Thanks
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Hi Mohammad! I also agree that you should use size reference beads. Can you please link the papers you are talking about?
PS: does anyone have a good protocol for cell size measurement with beads?
Best regards,
Gabriele
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To me, an Erdös number seems like a harmless piece of trivia, akin to having the same astrological sign as some celebrity or sleeping in the same hotel room that a famous person had once slept in. I realize that a network of linked Erdös numbers may have interesting topological properties, but other than that, do they show anything of general significance?
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If E(x) represents Erdős number, then
E(x): H→R
is a mapping, where H is the set of all human beings, and N is the set of nonnegative integers.
H is an increasing variable set with time.
The solution of E(x)=0 has a solution x ∈ K where K is the set of all humans who are not co-authors with Erdős and not any co-author of any co-author of Erdős up to any order!
K is a nonempty set almost all elements in H are in K except a very few.
E(x)=1 has a few numbers of solutions, that is x∈C, where C is the set of co-authors of Erdős and the cardinal number of C is 511.
Now I raise the following question:
Assume that r >1 a positive integer. Is E(x) = r solvable?
In other words Is E(x) onto?
Another important question: What is E(Erdős)?
If the answer is E(Erdős) = 0 because Erdős is not a co-author of himself.
But on the other hand: Erdős is a co-author with some Erdős co-authors, and then E(Erdős) is not zero !
Is it a paradox like that of Russell's paradox?
Best wishes
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Hi i have 3 PDE5 inhibitor drugs im looking to compare to each other in a systematic review & meta analysis
All 3 drugs have trial results comparing them to placebo ( no head to head trails)
what statistical method would be best to compare all 3 to see which is the most effective ?
thanks
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Hi,
if you want just compare results of several studies you can calculate the effect size for each study and then compare them.
you can choose the appropriate effect size index based on the analyses presented in the studies included in your review
claudio
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Hi im currently doing a systematic review and meta-analysis for the first time, and i do not entirely understand how to effectively compare 3 PDE5 inhibitor drugs against each other for my data analysis ?
Would you construct a forest plot with all studies from all 3 drugs against placebo and see which had the greatest effect?
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Following
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Hi I am currently doing a systematic review and meta analysis comparing 3 PDE5 inhibitors for the treatment of erectile dysfunction, the studies are alll interventio vs placebo, however some
are flexible dosage and some are fixed dosage, how would I incorporate these dosages in a forest plot? Would I pool them all together? Or have two seperate forest plots, one competing fixed dosage and one comparing flexible dosage? Also I second question is would a traditional meta analysis or a network meta analysis Work best for my review? Bare in mind all trails compare against placebo
thanks
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For the first question: perform subgroup analysis according to the treatment doses. Further, conduct metaregression.
For the second question: network meta-analysis could be conducted but at first perform traditional meta-analysis then network meta-analysis to compare between 3 PDE5 inhibitors.
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Dear everone,
I have a simple question about the definition of doping concentrations.
For example, one presents his/her doping formula for a complex crystal as:
ABmCn:X. Then the author states that the doping  concentration of X is 5 %.
My question is:
The percentage (5%) of the doping centration is relative to the number of atoms of the whole formula (ABmCn), or the element it replaced, such as the number m for atom B, assumed that the authors use atomic percentage ?
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In a general accepted way the concentration x% refer to the ratio of mass of the entire system and the mass of the doping material. Another definition refers to the ratio of the number of atoms.
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Hi.
When i do a modal test on any structures.
So, How many can i select number of measurement points? 
How can i select locations to put sensors? 
And, the end, what does they depend on?
Thank you.
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Thank you so much. Mr. Heinz Dorr.
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Here a(x) and b(x)  satisfy b(x)=a(1/x), c(x) and d(x) satisfy d(x)=c(1/x), where the coefficients of polynomials a(x),b(x),c(x),d(x) belong to Fq. Then how to count the number of solutions (a(x),c(x)) in Fq.
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Dear Patrick, thank you. Apparently, I was concentrated on the first sentence of the question, and did not pay attention to the last one.
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number of facets
dangel bonds
active facets 
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They'll do anything for a vote and be elected to a seat in Parliament or Senate, the honest will say half truths.
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We know that the number of aftershocks epends on the main shock magnitude.What is the relative number of aftershocks for each magnitude?
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I just read that in Time Dependent Model, the definition of foreshock, mainshock and aftershock is not necessary. In this model, every event is potentially triggered by all the previous events and every event can trigger subsequent events according to their relative time-space distance. What do you say about Stochastic models of earthquake clustering?
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if the plant extract gives effect
as much does not isolate the material responsible for this effect??
there is a large number of researches that are limited to the extract only
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happy to your honorable visit
many thank's
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Imagine n number of samples, in each of which I measure the expression of proteins A and B. The expression is not given as numbers, but rather classified in 4 categories (weak, medium, strong, very strong). What I want to test for is whether the expression of protein A correlates with the expression of B across all samples. What is the correct statistical test for that?
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Thanks guys, that's what I assumed as well. :)
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This would allow easy manipulation of plasmids for cloning.
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I think Singh's answer needs some elaboration. It is true that there are some plasmids whose copy number can be increased by the addition of antibiotics, normally in the situation where the antibiotics affect the mode of replication control for that plasmid. Or in some cases by stopping cellular protein synthesis which allows some (but not all) plasmids to continue to replicate. This is rarely used any longer although was fairly common a few decades ago before the construction of high copy number plasmids. 
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On what basis we can say theoritical plates are more for capillary coloumn
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Thank you sir.
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I use AlleleID 6 to design primers. Recently when I enter the accession number of a gene, I encounter an error indicating that the accession number is not in the correct format.
Does any one know how the problem can be solved?
Thanks
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Thank You All
I want AlleleID to download the sequence directly using the Accession number, because this way, the exon information will be automatically downloaded. This is important because I am going to design exon-junction primers.
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Either crystals or fibrils, spray-drying or freeze-drying or else?
I just need a rough number. Thank you.
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It depends on the process you are using. 1000-3000 kwh/t
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Hi,
I am using IBM-SPSS V24. I am experiencing a weird problem. When I copy any variable from 1 data set to another, the copying seems to work fine; but it reduces (and in some variables increases) the number of valid cases. For instance,  in the original data set, I have 1028 valid cases. But when I copy it to a new data set the number of cases reduces to 978.
The data set is in this form, i.e., 1=Yes, and 2=0. 
Any help in this regard would be highly appreciated.
Thank you.
Mustunsir
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No, it's all SPSS. And unfortunately, I am unable to make sense of the date that copying adds or drops. I have 6000 sample size in total. And I am copying from one SPSS file to another.
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The fundamental defects Zeno's Paradox have disclosed are inside mathematics; just see the “debates” in newly discovered modern version of Zeno's Paradox---------Harmonic Series Paradox:
1, Are those Un--->0 items in Harmonic Series infinitesimals?
2, If they are not, what are they and what is infinitesimal?
3, If they are, are they potential infinitesimals or actual infinitesimals, why?
4, if they are potential infinitesimals, how to have numerical cognition to them; if they are actual infinitesimals, how to have numerical cognition to them?
5, what kind of mathematical tool limit theory is? Does it treat “potential infinite related number forms” or “actual infinite related number forms”?
6, Can we produce infinite items each bigger than 1/2, or 100, or 1000000, or 1000000000000000000,…by brackets-placing rule with limit theory from Un--->0 items in Harmonic Series and change Harmonic Series into an infinite series with infinite items each bigger than any positive constants (such as 100000000000000000000000000000)?
Since antiquity, no one in the world with the standard or non-standard or some future new “former languages” within the theatrical frame of present classical “potential infinite--actual infinite” related science and mathematics are unable to answer such questions self-justificationaly!
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First change the series into one that will smaller term by term.
So if it diverges you can be sure that the original series also diverges.
Change the denominator 3 into 4, the denominators 5, 6, 7 into 8,
the denominators 9 through 15 into 16, and so on, so you are summing terms
1/2+1/2+......which must diverge. The number of terms summed
go as 2, 4, 8, ..... This would not be the only way to do it.
Hope this finally clears up doubts
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How bioanalyzer determine the RIN of RNA sample?
Why in some cases the RIN appears as not applicable? What could happened?
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I believe the RNA integrity number (RIN) is inferred based on the ratio of ribosomal RNAs (18S and 28S in human samples).
What is your sample of interest? If it's not a total cell extract, the RIN value is not relevant. Also, if you're using non-mammalian material, the RIN may be off. 
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I wish to get away from opinion polls and vague expressions such as good or poor. I am looking for a precise job evaluation, preferably using numbers. With this I could than compare one teacher to another and show exactly why they scored differently.
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Sorry to forget,
Here you have a material that clarifies the dimensionality and fluid nature of teaching quality. 
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What is the domain and co-domain (range) of the inverse function of arcsin: is it all real numbers or from -1 to 1?
Yes, it is the sin(x), but is x from minus infinite to plus infinite, or just from -pi/2 to pi/2?
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Dear Toso,
arcsin maps  [-1, 1] on [-pi/2, pi/2],
The inverse function is the sin restricted to the interval [-pi/2, pi/2] with co-domain [-1, 1].
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Antimicrobial resistance and genes on plasmids
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Dear Adnan,
You could determine the number of different plasmids carried by a bacterial isolate using a number of techniques depending on the nature of your isolate and the plasmids. If the plasmids are reasonably small and high copy number, then DNA samples can be assessed by gel electrophoresis. In order not to be confused by plasmid supercoiling you could try digesting the DNA sample with restriction enzymes likely to cut only once. However, if you had many different plasmids each with multiple cut sites, the banding profile will look very complex. You could attempt to obtain a draft genomic sequence using a NGS technique, but this approach is expensive and plasmid DNA may to be well-represented in the total DNA sample. As suggested by Bhoj R Singh, you could try a PCR approach targeting known plasmid replication, maintenance or transfer functions, and use theses as a measure of the number of different plasmids present. However, there are a lot of examples of plasmids having multiple replicons etc. which will confuse the issue.
As you are looking at antibiotic resistances, have you considered transforming or conjugating another host bacteria with your isolates? It may be possible to determine how many plasmids there are based on the diversity of transformants or transconjugates you can recover. This will also mean that you have isolated single plasmids in your host which would mean that subsequent analysis is easier. However, this approach requires that you have a host bacterium that is phylogenetically close to your isolates, as transformation, conjugation, plasmid replication and maintenance are all sensitive to host range issues.
Regards, Andrew.
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How to quantified the silanol number in Mesoporous material like (SBA-15, MCM-41, SBA-16, KIT-6)?
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Hi Chandran,
There are several techniques, such as TGA, XPS, FTIR and 29Si NMR. As Christian mentioned, 29Si NMR spectroscopy is one of them. See the following references:
3) DOI: 10.1021/jp971366+
Reference 1 also shows titration and XPS, while references 2 and 3 adds Near-IR, and reference 4 adds thermogravimetry and FTIR. Additionally, this paper: DOI: 10.1021/jp9008724, show studies in Mid- and Near-FTIR of silanol groups. 
A simple way, is the TGA analysis of adsorbed amines. This paper: DOI: 10.1021/acsami.6b15507, and references therein, describes well the procedure. Adsorbed amines will undergo hofmann-elimination reaction, which are proton dependent, and seems to be independent of the acid site strength. Therefore the amount of desorbed amine at certain temperature range can be correlated to amount of hydroxyl groups in the materials. The paper also discuss some considerations and possible variations.
The best technique to choose will depend on the characteristics of your material.
Best Regards,
Alexandre.
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The hadoop mapreduce based approach is linearly scalable i.e. the time efficiency improves as number of processors increases. What is the theoretical limit for increasing number of processors in a cluster?
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When it comes to mathematics for Map reduce. There are two basic properties that are required for any operation to be performed using Map Reduce as follows: 1) Catamorphism  and 2) Monoid - a combination of two properties existence of neutral element and associativity. Now none from both of these imply to a mathematical model for predicting optimal number of nodes for processing data on map reduce.
To answer your question: linear scalability of Map Reduce over what? By growing data set size or by growing number of nodes (or processors). If data set size is fixed, then optimal number of nodes may be found out experimentally. Also, since your data set size is fixed, if size of data set is quite less few nodes should be enough. Also, it depends on which nodes your data is present. Say you have 10 nodes, and after inserting some 1TB data, this data is stored on only 5 nodes than other nodes would not take part into the Map Reduce job concerning that data by using the property of existence of neutral elements.
Hope this helps
Regards
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Many Academician and researchers think that number, quality and citation does not matter. But another school of thought relates quality of a paper to number of citation. What can be some successful strategies to increase the number of citations?
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The idea of sharing knowledge and personal research through a scientific online platform seams perfect to me. (not at all unethical...) After all, isn't communication one of the main tasks of an honest scientific researcher ???
My beautiful country, Portugal, is small and far from the rest of Europe. As an Anatomist, I find that my research, although fundamental, as a basic science in Medicine, still reaches a rather restricted audience... In this sense, the chance to reach wider inter nation audiences to communicate my work online, is very important. I am thankful to RG for this chance to reach and communicate...
I wouldn't worry much for the number of citations to my work. But I do care to communicate as widely as possible, worldwide, when I believe my research can be useful.
Best wishes, Maria
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I would be very grateful if you could direct me to publicly available dataset for clustering and/or classification with/without known class membership. Variables (attributes) should be continuous (no categorical/binary); and number of observation should be greater than number of variables.  Number of variables less than 100 would be preferable.
Thanks
Michael
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Kaggle?  They have a lot of great data.  Titanic dataset is fun, they also have a pretty descent Imbd scrape.  I use them sometimes in my analytics class.
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I want to analysis streamflow variation with rainfall in small catchment ( around 150 km^2) . I have 30 yers monthly rainfall data and 10 years monthly streamflow data. These streamflow data are the only avaliable data in this station.there are no other streamflow gauging stations within the catchment.
I want to know how to proceed with these avaliable data? Waht are the method availables?
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I have difficulty imagining the availability of only monthly data.  A monthly reading of a stream height or flow is not sufficient in most circumstances.  If you have only monthly data summaries, perhaps the raw hourly or daily data has been lost with time.  Monthly data with just rainfall and streamflow can help determine water balance as the remainder of rainfall minus streamflow is evapotranspiration and any deep seepage losses.  You might try dividing tims of year between dormant season and growing season.  There are various hydrologic tools, models, techniques to apply with limited data, such as SCS soil curve numbers of hydrologic response.  
A difficulty with monthly data may includ some months with high rainfall on last day, with most of the storm runoff from that storm occurring in next month.  So you may have a few months where rainfall and runoff totals appear unusual.
If you have any other stream and rainfall gauges in the same physiographic vicinity, even at some distance, with greater detail of readings, you might try to correlate.  Hydrologists learn tools in school, but also learn from reading hydrologic studies of catchment experiments and in consultation with other hydrologists.   
Without knowing more about your needs or intent, it is difficult to suggests the options.  I am concerned though that one reading a month for streamflow is sufficient for anything unless flow has almost no variation.
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Someone can recommend me different decisions to reduce the amount of items of a psychological scale
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Dear Researcher! You can use the techniques of Exploratory factor analysis and Confirmatory factors analysis for psychological scale validation and reduction of number of items.
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My name is SUsan Smith and I have been identified incorrectly ....could you fix this?  I am attached to a number of papers dealing with Telomeres and this has nothing to do with me.
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Yes you remove the publications following the instructions given above. Next time  when RG asks you to accept publications by Susan Smith check for the titles of the publications. If those are yours, then only say yes, otherwise no. Another Susan cannot upload her papers in your contributions.
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I want to support a qualitative study with some rudimentary number based analysis. My data comprises 10 variables, each having a perceptual range from 1 (least different from ideal) to 7 (most different from ideal). Thanks!
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It sounds like you want to see if the bulk of responses are different than the default "ideal" value of 1.
One statistical test you can use in this case is One-sample Wilcoxon Signed-rank Test.  But this test has some assumptions about the distribution of the data.  An alternate (less-powerful) test is the Sign Test for One-sample Data.
These tests are discussed here:
I assume you want to conduct this test for each of the variables separately.
Practically speaking, since your default "ideal" value is at the end of the scale, I think testing if responses are different than this is cooking the books a little bit, kind of like a push poll, or leading the witness.
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How to i find nusselt number in Ansys fluent.
When i click wall fluxes >> Surface nusselt number ina pipe . the plot shows weird values of surface nusselt number of 1e5 at entrance and 2e4 around developed flow in pipe for air which i know i wrong , please tell me about this. 
Thanks
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Not exactly. Surface Nu = q * Lref / ((Twall-Tref)*k) , so first of all you need to set Lref in Reference Values equal to your pipe diameter if you didn't do it already. However, there is also bad news, because to obtain pipe Nu you would have to set your Tref equal to fluid temperature, which I believe is impossible since fluid T changes with pipe length while reference values are constant.
Best regards, Slawomir
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What formula should be used to convert grain size number (G) into the grain size in µm?
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Dear Gerhard ,
 Thank you very march for your  details answer 
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Based on some images, it looks like there can be variability in the exact number, but does anyone know of any literature that describes the diversity of neuronal nucleoli and gives exact numbers for how many nucleoli per neuron among different cell types? Thanks!!
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Typically two or three, ... but the numbers may vary considerably depending on sampled neuron type, age and labelling technique used.  
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The completion of genome sequences from human and mice suggested a regulatory role of space (Chorobiology) in controlling biological phenomena and activities.  Consequently fundamental constants of mathematics such as π, the ratio of a circle's circumference to its diameter, should have a role in describing properties and establishing control in biology.
The Greek mathematician Archimedes who found π, developed a rigorous approach to approximating π. Archimedes observed that polygons drawn inside and outside a circle would have perimeters somewhat close to the circumference of the circle.
While π is an infinite number (never ending No), it relates to a symmetric geometrical image, the circle, but intriguingly Archimedes used polygons to measure the circumference of the circle.
What could be the meaning or the role of π in the control of signal transduction? And why π is an infinite number?
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pi (π), in mathematics, the ratio of the circumference of a circle to its diameter. The symbol for pi is π. The ratio is the same for all circles and is approximately 3.1416. It is of great importance in mathematics not only in the measurement of the circle but also in more advanced mathematics in connection with such topics as continued fractions, logarithms of imaginary numbers, and periodic functions. Throughout the ages progressively more accurate values have been found for π; an early value was the Greek approximation 31/7, found by considering the circle as the limit of a series of regular polygons with an increasing number of sides inscribed in the circle. About the mid-19th cent. its value was figured to 707 decimal places and by the mid-20th cent. an electronic computer had calculated it to 100,000 digits. Although it has now been calculated to some 2.6 trillion digits, the exact value of π cannot be computed. It was shown by the German mathematician Johann Lambert in 1770 that π is irrational and by Ferdinand Lindemann in 1882 that π is transcendental; i.e., cannot be the root of any algebraic equation with rational coefficients. The important connection between π and e, the base of natural logarithms, was found by Leonhard Euler in the famous formula e i π = - 1, where i = - 1art/square-root-of-negative-1.gif the square root of negative 1.
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I was looking for examples of first order sentences written in the language of fields, true in Q (field of rational numbers) and C (field of complex numbers) but false in R (field of real numbers). I found the following recipe to construct such sentences. Let a be a statement true in C but false in R and let b be a statement true in Q but false in R. Then the statement z = a \/ b is of course true in Q and C, but false in R. 
Using this method, I found the following z:=
(Ex x^2 = 2) ---> (Au Ev v^2 = u)
which formulated in english sounds as "If 2 has a square-root in the field, then all elements of the field have square roots in the field." Of course, in Q the premise is false, so the implication is true. In C both premise and conclusion are true, so the implication is true. In R, the premise is true and the conclusion false, so the implication is false. Bingo.
However, this example is just constructed and does not really contain too much mathematical enlightment. Do you know more interesting and more substantial (natural) examples? (from both logic and algebraic point of view)
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Something algebraic, implicitly talking about ordering:
"for every nonzero number x, x or -x is a square but not both."
This holds in R (it is essentially an axiom of real closed fields) but not in Q or C (x=2 is a counterexample for both). Now you can take the logical negation.
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There are some papers which give the overall complexity of finding all maximum matchings of a Tree/graph.....But I need Number of max matchings, not all the matchings.
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There are estimates for the number of perfect matchings in some families of graphs. For example, for planar graphs, or for regular graphs. General estimations usually have poor quality.
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Hi everyone,
I need to perform a topic analysis on various corpora of documents and I need a procedure that can be applied to all of these corpora independently in a standard way. 
These are the characteristics of the corpora:
  • the number of documents in each corpus will hardly be more the 500 and most of the times is around 50;
  • documents are generally very shot (from 20 to 200 words most fo the times);
  • each corpus is independent and analyses will never be done merging corpora, but only performed within each corpus;
  • the language of documents will be homogeneous within each corpus, but it may vary between corpora;
  • the number of topics is unknown a priori, and topics will be different in every corpus.
 Specifically, I’m looking for a procedure that:
  • automatically detects the best number of recurrent topic in each corpus, but that it is also able to take into account that some documents may have “peculiar” topics that are not represented in any other document. These are not of interest and may be seen as a kind of “residuals”. If these peculiar, single-document topics are identified as further topics by the model it is fine too;
  • gives for every document a % for all the identified recurrent topics, plus a % that is “residual” from them. Otherwise, also the single-document topics have to be identified and scored in each document.
if I understand the LDA models well, they don’t allow this “residual” part and the sum of the %-score of the topics is always 1. Moreover, they are not good in identifying single-document topics and the result for these “outcast” documents is somehow a uniform score for all the topics, even though none of them is truly present in the document.
Are there other topic analysis models that better fit with my task or I misunderstood the LDA models?
Thank you very much!
Massimiliano
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I do not think topic analysis on a collection of 50 documents would give robust and stable results since LDA is generally an ill-posed task which has many solutions. Why can't you perform some soft clustering to detect "outliers" with peculiar topics. I am not an expert in topic modelling but the authors of this work suggest a general model that embraces LDA and PLSA (though I do not know whether it is used in practice). If I understand them properly, you could regularize the model to enforce the topics to be as diverse as possible but that is by no means a "black-box" procedure.
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A q-ary necklace of length n is an equivalence class of q-coloured strings of length n under rotation. The number is
Nq(n)=(1/n) \sum_{i|n}\varphi(n/i) q^i
For example q=3, n=3,  N3(3)=11
000 000 000
001 100 010
002 200 020
011 101 110
012 201 120
021 102 210
022 202 220
112 211  121
122 212 221
111 111 111
222 222 222
But if the first bit must take modulo 2, then the answer is 4. For example
001
002
011
122
Here 210=010, 001=201 , 000=200 and so on. Note: the first bit must take modulo 2.
What is the number of Necklaces in length n and beading of q different colors with the first bit taking modulo 2?
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I do not know, whether it will be helpful for you, but I proposed some method. In any way, I would be glad to hear any comments.
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What are the defferences between RAxML and Baysian analysis in term of modeling, how we know the number of replicates in RAxML
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Basically, RAxML uses Maximum Likelihood methods for analysis while Bayesian Inferences uses methods from Bayesian Statistics. Both are probabilistic methods, but Maximum Likelihood, used by RAxML is basically a method the calculate the probability associated to every tree possibly to your data, and chooses the tree with the higher probability (likelihood).
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When normalized fuzzy weights are multiplying the fuzzy numbers so that the resulting fuzzy numbers go outside the range of possible values for a number. This certainly happen because the sum of the upper-bounds of the fuzzy weights are > 1. What do you suggest to tackle this problem (i.e. to emphasize the resulting fuzzy numbers to be inside the range of possible values)?
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Dear Researchers,
I hope this question finds you well.
In the attached LINGO window, I'd like to know the mean of the highlighted number of nonlinear variables.
My model is nonlinear and the non-linearity is in the set of constraints, namely, one binary variable multiplied by continuous variable. 
Thank you in advance.
Best Regards,
Mahmoud
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i think about 3*55+3*56 but this also doesn't equal to 332! 
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i saw in a paper that u(3,1) has one s-boson and three p-boson. i want to get a general reception about all lie algebras. could any one help me please?
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Dear Tadeusz
thanks alot for your book. i read it as soon as possible but could you please tell me about my question simply?
i want some simple books to learn Lie algebra and topology basically . for example Frankel book about topology is very good case . could you please introduce me some others?
thanks again
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I'm looking for the theoretical model !!
Dean flows, microchannels, derivation of analytical solution to dean flows
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Thanks a lot José. 
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There are three number line in mathematics:
1. Real Number Line.
2. Imaginary Number Line.
3. Circular Number Line.
1 subset 2 subset 3.
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Dear Doctor Yadav,
If X is any set, then Card (X ) less than of Card (P(X)) less than of Card(P(P(X))) less than of ...
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In interval arithmetic, for an interval I= [a, b] we define -I = [-b, -a]. But, it does not satisfy the arithmetic formula like I + J -I = I and more specifically, I - I != [0,0]. It creates a whole lot of problems.
A question comes to mind as how authentic this arithmetic is? Can we call this as something other than arithmetic? Will it be simply another algebraic system which satisfies certain properties?
In this case, when intervals are reduced to singleton sets or numbers by making the end points meet, will it be same as normal arithmetic of numbers?
Can some some source material be linked for reference!
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If '+' and '-' are supposed to be inverse operations to each other then I+J-I should be equal to J. However, it may be that the manner in which we define '-' operation it is not the inverse of '+'. Then is '-' is just an operation but not the inverse of '+' !
Now the question is: The set of all intervals over the set of real numbers is not a group.
Now let us come to the multiplication operation. In this case it seems to be a group.
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Please can someone give me a reference on the distribution of Pisot numbers on the real line.
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Communication protocol  with  high  level Scurry  type   supported   distribution  
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Which multilevel inverter topology have least number of switches to generate maximum level?
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You always have interesting questions, I had that questions to, some years ago, what I think, after reviewing many references, is that multilevel converters that aims to reduce the number of transistors again traditional topologies, usually have different blocking voltage in transistors, that means they generate many levels with few switches, but their maximum voltage is limited to the voltage in some transistors, some transistors block few volts and other block high voltage, sometimes the output voltage, and traditional multilevel converters such as diode clamped, flying capacitor and cascaded bridges, and now the modular multilevel inverter, are designed to have the same voltage in all transistors. My conclusions where, reduced-switches multilevel inverters should not be compare with traditional high voltage multilevel converters, it would be unfair, for low voltage and getting many levels, you may use reduced-switches topologies, but they have to compete with the traditional full bridge with an LC filter, the modular multilevel converter is the only topology that have being used to high voltage in the practice, even for power transmission. 
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In the papers given in the links below, we define factoriangular number (Ftn) as the sum of corresponding factorial and triangular number, that is, Ftn = n! + Tn where Tn = n(n+1)/2. Notice that Ft1 = 2T1 = 2 and Ft3 = 2T3 = 12. Aside from 2 and 12, is there any other factoriangular number that is twice a triangular number?
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Dear George,
In Case 1, (k-2p-1)|(2p)! does not imply k-2p-1 ≤ 2p.
In fact, we have k-2p-1=1*2*...*(p-1)*(p+1)*...*2p>2p for p>1.
Similarly, in Case 2 (k-2p-1)|(2p+1)! does not imply k-2p-1 ≤ 2p+1.
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Factoriangular numbers (denoted by Ftn) are formed by adding corresponding factorials and triangular numbers, that is Ftn = n! + Tn, where Tn is the nth triangular number. The closed form of the exponential generating function of the sequence of factoriangular numbers can be easily derived from the exponential generating functions of n! and of Tn (see the link below). How about the closed form of the ordinary generating function of such sequence?
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Use the Laplace transform
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There are many relationships or connections between factorials and triangular numbers that can be found in the literature, both old and new. In a recent study on factoriangular numbers (sums of corresponding factorials and triangular numbers), we unintentionally found that n! = T(n-1)!+n - T(n-1)! - Tn where Tk is the kth triangular number. Curious on this, can you help us find older literature that also mentioned the stated relationship between factorials and triangular numbers?
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Factorials are not relevant here. For any numbers m and n one has the identity
mn = T(m+n) - T(m) - T(n), where T(x) = x(x+1)/2
Of course, one can use m=n! as well.
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I'm currently working on PORTFOLIO Optimization for my research paper. I used GA to solve a multi-objective problem but instead of using binary number as a gene indicator/ chromosome I used real number. Then I normalized it for the weights to be equal to 1. Is it ok to use real numbers instead of binary numbers?
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Charlene Mae De vera Galang
If you use real number you will get more search space as compared to the binary one.
please go through the my publication for more detail or use the Goldberg's book.
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One solution to the Diophantine equation 8n! + (2n + 1)2 = m2 is n = 6, m = 77. What are the other positive integer solutions to the said equation?
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Taking the given equation, m2 = (2n + 1)2 + 8·n!, we may try to see if some kind of approximation might help to for large n. Stirling's formula would give, for n >> 1: n! ≈√(2·π·n)·nn·exp(-n). So: m2 ≈ (2n+1)2 + √ [27·π·n2n+1·exp(-2n)]. Then, since m must be integer, m2 should be a square number. We may want to take a few close square numbers, and give then a try with the selected n. Although n= 6 is not much larger than the unit, we may want to try with this number, as other possible integer solutions seem hard to find. For n = 6, last formula yields m2 ≈ 5690. A few close square numbers are: {5476, 5625, 5776, 5929}. It is found that the last number solves the equation; being therefore m = √5929 = 77. Hopefully, for higher n, this kind of search strategy may perform somewhat better, and it might be possible to restrict the set of square numbers to be checked, possibly to just the nearest pair. If a solution is not found for a given n, it seems reasonable to move to next integer. Of course, it would be still quite challenging to deal with arithmetics of very large integers while verifying possible solutions ― if indeed they can be found.
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There have been three suspended questions in present classical set theory ever since:
1, the definition of set------should the definition of set concern the nature of elements inside the set? How we distinguish different sets(Such as Odd Number Set and Natural Number Set)?  Will the nature of elements inside the set decide the existing state of the set as well as its relationship with other set?
But, it is “the different natures of the elements in real number set and natural number set” that make Cantor proved the different cardinalities between the two sets.
2, how to judge whether a set belongs to “potential infinite set” or “actual infinite set” or both “potential infinite set” and “actual infinite set”? What kind of nature do the elements have inside “potential infinite set” or “actual infinite set” or both “potential infinite set” and “actual infinite set”?
3, can we have many different bijection proofs with different result between two infinite sets? If we can, what conclusion should people choose in front of two opposite results, why?
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1. You can understand the nature of elements of a set by its definition only. For example. collection of boys in a class is a set. So, here the nature of the set is that its elements are all boys. To distinguish sets, we have to understand the nature of elements. In even number set all elements are even, that means divisible by 2, whereas in odd number set elements are not divisible by 2.
2. I am not sure about it, but if you consider both infinity as the meaning of unbounded, none of our existing theory would fail. If any of our theory would fail due to this fact, human will think of new base or new definition. Necessity is the mother of invention. I think there is no necessity so far. (may be I am wrong)
3. The nature of infinite set is that it can have bijective map with its own subset. So, there is no harm in it. Also, they are not contradicting anything, as you have not provided any bijective map between N and Q, that map is not a bijective map between N and Q, instead it is a map between N and a subset of Q. Also, I would like to add one more point, if there are more than one bijection, they wont produce any opposite results at all. By seeing this point, I remember a joke. A school kid come and say to her mom that maths teacher is wrong, because yesterday she said 4+5=9, and then 6 + 3 = 9. Today she says that 7+2=9. If you consider "opposite results" with this you will definitely feel the argument is not correct.
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in conducting meta-analysis 
how can i deal with dropouts in clinical trials.
when can i use intention to treat analysis?
what about if the original trial not reporting the cause of dropouts?
for example 
in one trial included in meta-analysis
- number of participants  randomized: 36
- number of participants evaluated at 1 year: 24 (14 group 1 ; 10 group 2)
appreciate your time and efforts
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Drop-outs in clinical trials assume importance if they are due to lack of efficacy and/or adverse events. The general principle is that each and every patient included in a clinical trial should be accounted for. In the case referred to, it is mentioned that No. of participants randomized. Does it mean all were treated?
Intention to treat  (ITT) analysis may be used if the dataset includes some patients for whom there are incomplete data. ITT analysis allows inclusion of such patients provided they have received at least one dose of the drug and there is at least one post-treatment observation/value which can be carried forward.
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Let factorials be added to their corresponding triangular numbers resulting to a sequence of numbers {2, 5, 12, 34, 135, 741, ...}, which I call factoriangular numbers in my recent papers. Let T(n) be the nth triangular number. Notice that 741 = 6! + T(6) = T(38). Are there other numbers that are both factoriangular and triangular?
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To Stephen: not really. The power of 2 in n! is [n/2] + [n/(2^2)] + [n/(2^3)] +.... . For n = 6, this power is 3 + 1 = 4 and not 6-1 = 5. Indeed 720 = 16 x 45.
On the question: we know that all numbers which are not powers of 2 have different representations as difference of non-consecutive triangular numbers:
Because of this, I think that a proof for the finitude of solutions to our questions could be very hard. On the other hand, it would be really remarkable and surprizing if one had infinitely many solutions...
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For declaration of a primer to be used for the purpose of barcoding, what is the number of individuals to be screened for that region?
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Sir, Thank you for the answer. But it is not very much clear to me.
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Let the set of all repunits (repeated units) i.e., 1,11,111,... is X.
=> X = { Rn : n belongs to postive integer }
(Repunit of n defined by Rn. 1 is R!. 11 is R2, etc....)
Generally is not satisfy closed property.
  1. Under what condition or when X satisfy closed property?
  2. For which n, R2n+1 is prime?
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Yes dear Srinivasan, put the second "word" just next the first one. In French we call it juxtaposition, I think the terminology is the same in English .
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In meta-analysis, is there any restrictions on the number of studies to perform subgroup analysis? i.e, what is the minimum number of studies to be included in the subgroup analysis?
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There is no accepted minimum number of studies that are required for a meta-analysis. However, in different refernces you can find different minimum number of studies. For example:
• Cochrane handbook: a minimum of 10 studies
(no reason for the number)
• At least 6-10 studies for a continuous study-level
variable when the sizes of the included studies
are moderate or large (Fu et al., 2011)
• For a categorical subgroup variable, each
subgroup should have a minimum of 4 studies (Fu
et al., 2011)
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I have a sequence of n numbers in a computer game, I want to move m solders randomly based on this sequence. for example 
n={1,2,3}
and m=3
we get the following solution:
s1={1}, s2: {2,3}, s3={} or 
s1={1,2,3}, s2: {},s3={}, or 
s1={3,2,1}, s2: {},s3={}, or
s1={3,2}, s2: {}, s3={1}, or
s1={1}, s2: {2}, s3={3}, or
s1={3}, s2: {2}, s3={1}, or
s1={}, s2: {23}, s3={1}, or ...
for n=3 and m=3 I counted 60 different ways if I was not wrong, what is the formula to find the number of all possible solutions?
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You can see it in this way:
You have three distinguishable containers s1,...,s3 and 3 distinguishable numbers to put in them, being the order important inside every container.
So your different options can be identified with the number of ways we can order the 3 numbers on a line, with 2 indistinguishable markers added to tag where one container finishes and the following one starts.
For example, your option s1={1},s2={2,3},s3={} is identified with the string 1|23| (the number one in the first container, the numbers 2,3 in the second one, the third one empty), while your option s1={}, s2={}, s3={3,1,2} is identified with the string ||312.
So, the number of options you have is the same as all the possible orderings of 3 distinguishable numbers and 2 indistinguishable markers, or (3+2)!/2! = 5!/2! = 60.
In the general case you will have n numbers and m-1 markers, and hence you will have (n+m-1)!/(m-1)! options.
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HI,
1.I read about stereo tactic radio surgery physics , but i don't understand what is the important different between external beam radio therapy and srs.
except the stereo tactic techniques which is required for fixing skull and narrowing beam which aided to intracranial target volume?
I have many question for example:
I don't know how we can flat this narrow beam in different arc? it is the same  procedures which is done in external therapy by filter?
2. In the gamma knife system we need to how many source ? the number of  ports is equal the number of source?or more?
Thanks in advance.
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Trying to add value to Hanno's answer, a major difference between stereotactic radiosurgery (SRS) and external bean radiation therapy (EBRT) is the dose delivered in the number of fractions. SRS delivers what will results as an ablative dose (e.g. 15-20Gy) in generally a single fraction whilst EBRT may deliver 40-80Gy over 16-20-35 fractions. Radiologically the SRS delivers a dose equivalent to something around 100-120Gy in a 2Gy fractionated approach all over a 1hour single visit session. 
SRS is also generally employed on small lesions up to about 0.3cm-3cm max diameter (dose is adjusted according to size) rather than e.g. EBRT for a lung lesions ~8cm sphere.
The 201 beams from the 201 Co-60 sources (although I believe now the number of sources have been reduced in the new Elekta Pefextion) can be collimated in size or "switched" off. The old gamma knife had a collimator piece that had to be loaded into the machine after each port was appropriately loaded, I have attached a few photos of got back in 94 of a unit in the UK. The newer gamma knife does the collimation internally.
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Hybrid metaheuristic with data minning ?
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Blum Blum Shub (B.B.S.) is a pseudorandom number generator proposed in 1986 by Lenore Blum, Manuel Blumand Michael Shub.[1]
Blum Blum Shub takes the form:
x_{n+1} = x_n^2 \bmod M
where M=pq is the product of two large primes p and q. At each step of the algorithm, some output is derived fromxn+1; the output is commonly either the bit parity of xn+1 or one or more of the least significant bits of xn+1.
The seed x0 should be an integer that is co-prime to M (i.e. p and q are not factors of x0) and not 1 or 0.
The two primes, p and q, should both be congruent to 3 (mod 4) (this guarantees that each quadratic residue has one square root which is also a quadratic residue) and gcd(φ(p-1), φ(q-1)) should be small (this makes the cycle length large).
An interesting characteristic of the Blum Blum Shub generator is the possibility to calculate any xi value directly (viaEuler's Theorem):
x_i = \left( x_0^{2^i \bmod \lambda(M)} \right) \bmod M
where \lambda is the Carmichael function. (Here we have \lambda(M) = \lambda(p\cdot q) = \operatorname{lcm}(p-1, q-1)).
nteger factorization problem is one of the most important parts in the world of cryptography. The security of the widely-used public-key cryptographic algorithm, RSA [1], and the Blum Blum Shub cryptographic pseudorandom number generator [2] heavily depend on the presumed difficulty of factoring a number to its prime constituents. As the size of the number to be factored gets larger, the difficulty of the problem increases enormously. This fact has led to the development of many different algorithms to attack bigger number within polynomial time.
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In the fuzzy system,once we fix the input variables and corresponding to MFs, are the rules of the fuzzy system been fixed?For example ,threre are 2 input variables and corresponding to 4 MFs in each input. So how many rules in total, 8 or 16? And I have some findings in a paper of ANFIS presented in the picture? I want to know why is that? Thanks a lot!!!
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Initially you should consider 16 rules. But the main issue is: How many MF's do we need to represent each input variable ?? If you have data, a clustering procedure should be applied in this case in order to determine a suitable number of cluster related to each input. Each cluster can be represented by a MF.
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Regarding type of variables(discrete and continuous) which is the best for for large problem instances:
First: A very large and NP-hard MILP formulation with large number of discrete(binary) variables and small number of continuous variables (and also fewer number of homogeneous constraints).
Second: A very large and NP-hard MILP formulation with fewer number of discrete(integer) variables and large number of continuous variables (and also larger number of heterogenous constraints).
1).both formulations are equivalent, 2).both formulations are not tight, 3).degree of complexity of both is very high, 4).the problem shoud be solved with exact methods for large instances, 5).both expected to be  intractable for very large instances.
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I am just giving you a tentative answer from my point of view. A complexity analysis woudl have to be made to support (or not) the argument:
I have this idea that the complexity of integer programming, which makes it a hard problem, is connected to the combinatorial explosion of possibilities (for example) 0 or 1) for each variable, which is exponential-like in the worst case. Unlike with continuous (particularly convex) functions you usually have no easy way of using continuity to go incrementally towards the solution. We might be left with "possibilities enumeration" procedures, like heuristics that try to exclude many possibilities to be faster.
So as as a rule of thumb I would try to get away as much as possible from discrete variables, since I have this idea that these are the ones that probably increase complexity the most. So I would go for your 2nd formulation.
I am not sure this reasoning makes sense in your case.
Kind regards.
Fernando.
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The question is about monophonic number of graph and relation to dominating set of graph.
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yeah sorry,
just like the geodetic number of a graph, there is something like monophonic number of a graph. which means set of vertices of a graph such that every other vertex of grah G lies on monophonic path joining two vertices from that set.
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We call a certain day 2015-12-1 "H" and another day 2015-12-10 "b", "H" ends at 2015-12-1 but has no beginning; and "b" with a beginning at 2015-12-10 and infinitely going up.
Now the problem is: where did 2015-12-1 and 2015-12-10 came from? In mathematics, those "cuts" are called: infinite, super infinite, super super infinite, super super super infinite, super super super super infinite.
Can we really have such infinite, super infinite, super super infinite, super super super infinite, in our mathematics?
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Dear Geng, the problem is extremely nice, and i remember an observation made by my prof. of analytical geometry, about the train from X station.
"When the train arrive in the station X an infinite passengers come down from the train, another infinite passengers come up in the train and inside the train, remain an other infinite passengers."
I'm sorry, but your question make me remember his lighty memory.
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Let q be an odd positive integer, and let Nq denote the number of integers a such that 0 < a < q/4 and gcd(a, q) = 1. How do I see that Nq is odd if and only if q is of the form pk with k a positive integer and p a prime congruent to 5 or 7 modulo 8?
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I see that you, too, follow the Putnam Exam.
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Can you give me meterials relating natural gas field development? How do I choose the optimal number of wells?
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With massive fracturing the spacing can be much further apart but then you need excellent seismic input to try and see which package of fractures you are draining.
Medhdi has given you excellent advice on initial stages. I would follow his advice. 
Is this an academic exercise at A&M or is this an actual field development in Kuwait?
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What is the partition of repunit? Is It possible to find the general formula for partition of repunit?
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I need these measurement for the diversity analysis of population of vectors
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The (vector) norm not the suitable measure in this problem.
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I need publications on method ABN created by Jaime Martinez Montero, thanks a lot 
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You can read something experiences about it in http://algoritmosabn.blogspot.com.es
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Result: The number of compositions of 2n, say c_1+c_2+...c_k=2n, satisfy that Sum_(i=1..j) c_i <2j for all j=1..k is equal to C(2n-1, n), i.e., the number 2n-1 choose n.
E.g., when n=2, C(3, 2)=3 because we can write 4=1+1+1+1=1+1+2=1+2+1.
Is there an easy way to prove it directly?
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To Ricky,
Just to clarify... your example is for n=2, so 2n=4 and you found 3 compositions with the formula C(3,2). Looks like C(2n-1,n) instead of C(2n+1, n+1). Tried it too for n=3 and it gives C(5,3)=10 compositions. With no + signs to make it short : 111111, 11112, 11121, 1113, 11211, 1122, 1131, 12111, 1212 and 1221.