Numbers - Science topic

Alexander Ohnemus, no entiendo tu pregunta. ¿Podrías darme algún ejemplo de numerales transformados en ordinales por añadir “ismo”?

QM can have values unknown, but not uncertain. Likewise, RG questions. Please stay on topic, per question. Do not be uncertain yourself.

Opinions do not matter, every opinion is right and should be, therefore, not discussed.

But, facts? Mass is defined (not a choice or opinion) as the ratio of two absolutes: E/c^2. Then, mass is rest mass. There is no other mass.

This is consistent, which is the most that anyone can aspire. Not agreement, which depends on opinion. Science is not done by voting.

Everyone can, in our planet, reach consistency -- and the common basis is experiment, a fact. We know of other planets, and there consistency may be uncertain -- or ambivalent, and even obscure. A particle, there, may be defined, both, as the minimum amount of matter of a type, or the most amount of quantum particles of a type.

We can entertain such worlds in our minds, more or less formed by bodies of matter, and have fun with the consequences using physics. But, and there is my opinion (not lacking but not imposing objectivity) we all -- one day -- will be lead to abandon matter. What will we find? That life goes on. The quantum jump exists. Nature is quantum.

Prof. Naveed Ahmad: My own rule that I apply to myself says:

On the other hand, ResearchGate (RG) is a platform and a gateway for sharing information and experiences between scientists, experts, researchers, and practitioners. In reality, RG is one of the biggest social media networks for the scientific community.

RG is an interactive app for people of all ethnicities, sexual identities, and different backgrounds. Slowly but surely the academia and the "real journals" will realize that the world is not going to wait for them to change. The world will continue to change and if they do not keep up with it then they will become irrelevant and obsolete. That is why platforms such as RG are the best places to present your ideas.

Therefore, RG is your way to increase your research visibility and, in turn, your citations.

Based on this, your research work should be open-access and free to all people unless there is a crucial need. This can be done during the addition process of any research work or publications by choosing "add a public file" instead of "add a private file".

Dear Muhammad Ali

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.

This paper might be of help to you

RIN is determined based on the result of microcapillary electrophoretic RNA separation. Several features, including the total RNA ratio, the height of the 28S peak, the fast area ratio and the marker height, were taken into consideration in the RIN algorithm.

For detail, you can read the following paper.

Schroeder, A., Mueller, O., Stocker, S., Salowsky, R., Leiber, M., Gassmann, M., Lightfoot, S., Menzel, W., Granzow, M., and Ragg, T. (2006). The RIN: an RNA integrity number for assigning integrity values to RNA measurements. BMC Mol Biol 7, 3.

RIN value represents the degaradation of RNA. Usually, RIN＜7 is not applicable for the following RNA sequencing.

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

Dear Omran Kouba

Fermat numbers are odd numbers.

I think you are confused with Fibonacci numbers where F_3n even numbers.

Best wishes

NiCo2O4 is synthesized by the hydro-thermal route in the presence of urea.

Sai Gopal Rayaguru

Now it is a a complete useful answer.

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

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

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

Following

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.

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.

Thank you so much. Mr. Heinz Dorr.

Dear Patrick, thank you. Apparently, I was concentrated on the first sentence of the question, and did not pay attention to the last one.

They'll do anything for a vote and be elected to a seat in Parliament or Senate, the honest will say half truths.

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?

happy to your honorable visit

Thanks guys, that's what I assumed as well. :)

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. 

Thank you sir.

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.

It depends on the process you are using. 1000-3000 kwh/t

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.

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

Sorry to forget,

Here you have a material that clarifies the dimensionality and fluid nature of teaching quality. 

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].

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.

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:

1) https://doi.org/10.1016/j.apcata.2006.06.035

2) https://doi.org/10.1016/j.jnoncrysol.2005.09.005

3) DOI: 10.1021/jp971366+

4) https://doi.org/10.1016/j.jnoncrysol.2005.09.005

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.

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

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.

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.

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.

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.

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.

Not exactly. Surface Nu = q * L_ref / ((T_wall-T_ref)*k) , so first of all you need to set L_ref 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 T_ref equal to fluid temperature, which I believe is impossible since fluid T changes with pipe length while reference values are constant.

Best regards, Slawomir

Dear Gerhard _,

Typically two or three, ... but the numbers may vary considerably depending on sampled neuron type, age and labelling technique used.  

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.

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.

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.

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.

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.

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).

Dear Nasser,

Here links and attached files in subject.

-mathematical modeling for data envelopment analysis with fuzzy ...

-Risk Assessment Applications of Fuzzy Logic - Society of Actuaries

Best regards

i think about 3*55+3*56 but this also doesn't equal to 332! 

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

Thanks a lot José. 

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.

Communication protocol  with  high  level Scurry  type   supported   distribution  

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. 

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.

Use the Laplace transform

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.

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.

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.

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.

I'm not keen on last observation carried forward. There are quite a few situations when it's entirely inappropriate, e.g. if you expect the outcome to change over time. If you can't get the outcomes on everyone because some are lost to follow-up, then that's a weakness of the study. It doesn't, in my view, mean that you can make up some of that data based on some very strong assumptions. Sensitivity analysis may be one way forward, but if the trial had dropouts, it had dropouts, and the meta-analysis is only as good as the studies included within it. That's one reason for assessing risk of bias. I'd be happy for a trials statistician to bring some more up-to-date advice on this.

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...

Sir, Thank you for the answer. But it is not very much clear to me.

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 .

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)

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.

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.

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.

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.

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.

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.

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.

I see that you, too, follow the Putnam Exam.

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?

You can see

Yuri