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  • Peter Birch added an answer in PRIME:
    Is there any explicit formula to find a generator of cyclic group Zp* given a prime p?

    Zp* = { 1, 2, ...... ..... ... p-1}, multiplication modulo p

    Peter Birch · Teesside University

    Yes - paper in preperation

  • Raid Amin added an answer in Running:
    What is the best statistics for small samples?

    Hello every one,

    I have 9 algorithms and 4 benchmarks, I only have the mean and standard deviation over all runs (the same number of runs), but I could not get them from the authors.

    Could anyone help me in choosing the best statistical test for:

    1.     Multiple comparison of all the 9 algorithms

    2.     Pairwise comparisons of my algorithm with each of the 8 remaining algorithms

    The numerical results I am aiming at comparing (and so analysing) are attached

    Thank you in advance

    Raid Amin · University of West Florida

    I would not insist on doing any statistical analysis of published results, especially when the authors seem not to be open to such an analysis by you.

    Addressing your question here, I would keep things simple. You can pool the sample variances to get an estimate of the random variability. Use Dunnett's test in which your algorithm is the control group.

    A basic Pareto Plot of the means, standard deviations, and coefficients of variation may be useful too.

  • Behnam Farid added an answer in Fourier Transform:
    What is the range of Fourier transform from continuous space to discrete space?

    Recently I read a paper where Fourier transformation is done from continuous k-space to discrete lattice space. The range is taken as ($-\pi$ to $\pi$).  Can you explain how  it can be done or any reference to that.

    Discretizing a Fourier integral on a regular mesh (at the points of a Bavais lattice in arbitrary dimension), the resulting function will become periodic with the periodicity that depends on the distance between the mesh points (these facts can be explicitly verified). Depending on the function under consideration, this approximation can accurately represent that exact function (that is the function calculated without discretizing the Fourier integral) over an interval (or domain) that is embedded in the domain of periodicity of the approximate function. For details, you may wish to consult Chapter 12 of the book Numerical Recipes (Cambridge University Press), by William H. Press et al.

  • Irina Pechonkina added an answer in Spirituality:
    If a crystal ball could tell you the truth about yourself, your life, the future or anything else, what would you want to know?

    Knowing ourselves is one of the major goals of our lives. Ancient Greek  considered it the utmost, ultimate target. Different branches of Sciences tried and partially succeeded to give certain answers. Spirituality offers also a lot, probably quite more than science. Our aspirations, prospects, perceptions, deepest hopes and accomplishments are mixed together in an ineffable blend, we use to call life.

    Sharing your thoughts on this quest would be an honest travel into ourselves, without indiscretion, but with the aim of giving each to another the very essence of our being.

    Irina Pechonkina · Math and Physical Lyceum

    Nothing. Unfortunately,many years ago I learned to analyze all the events and I had never mistaken in prognoses.We learned only on our own past mistakes to become wise.Romantic is always becoming to cynic. I can only pray for health of my sons, relatives, friends, students.

  • Rich Mcdonnell added an answer in References:
    The factors of global competitiveness of the national agro-industry?

    What are the factors of global competitiveness of the national agro-industry? Is there a model or models by which it can be determine and compare the competitiveness of this particular industry? I'm looking for literature references which specifically refer to this model or models.

    Rich Mcdonnell · Parker Hannifin Corporation


    You make some interesting points - but, many of which are at a much higher level than my particular focus and interest.

    That said, I look forward to what other contributors might care to comment on.



  • What techniques do we need to use to improve academic writing of students?

    the question is addressed to those who teach EAP to MA and PhD students.

    M. Laura Angelini · Catholic University of Valencia "San Vicente Martir"

    Hi Saltanat, 

    I agree with Aleksander. It has to be a tandem between student and teacher. I recommend the following book for help:

  • Luca Pietrogrande added an answer in Bone Fractures:
    Do orthopeadic surgeons make use of drill guides when drilling cannels in cortical bone for the placement of fracture fixatives?

    For the placement of screws and pins to stabilize complex bone fractures, some surgical procedures apply the drilling of holes through the cortical bone. Do surgeons make use of drill guides, and does anyone know which drilling angles can be applied without slipping sideways over the bone surface?

    Any cues related to tools and procedures are very welcome.

    Luca Pietrogrande · University of Milan

    I agree with you the only reason to do not use a guide drill is indolence.

    The use of a drill guide always makes easier to drill the bone.

    Nonetheless if you want to make a hole with a sharp angle it is necessary sometimes to have a very sharp point to make, without any motorized rotation, an initial little perforation.

  • Jan Grzegorek added an answer in Crime:
    Is there a bigger crime in mathematics than "divide by 0"?

    We know that not checking the value of the divisor for 0 leads to such 'absurdum' as the following 'proof':

    Let us have x=0 hence giving a true equation x=2*x which we can simplify dividing both side over x getting: 1=2 which I belie is not true :) since we overlooked to give up the division operations since the divisor (x) was assumed to be 0.

    However, the "0 division" is a kind of definite (hence "death") phenomena.  Even a very very small divisor: 0.0000000000000000000000000000000000000000001 still can be used. So, my question is if you know any other "no case" which is similar to it but evidently different in nature (no division is involved :)

    [Pls hit the green ^ if you like it]

    Jan Grzegorek · University of Warsaw

    Good question. I think that that biggest crime


  • Pedro Correia added an answer in Well Logging:
    I would like suggestions for articles that approach correlations between well logs and seismic attributes, can anyone help me?

    I'm looking for the applicability and case studies of seismic amplitude x well properties and acoustic impedance x well properties relationship and correlation. Thank you foward

    Pedro Correia · Technical University of Lisbon

    Hi Romario,

    The relation between seismic velocities and acoustic impedance is typically given by using wavelet convolution transformation.

    Seismic inversion relies on this. You have a trace of acoustic impedance and from there you 1) calculate the reflectivity trace, 2) wavelet convolute the refletivity into 3) synthetic seismic. From this point you can calculate, for example, the correlation between the real seismic trace and the synthetic seismic trace.

    Typically you use the information on the wells (real-data) to calibrate your wavelet (it's never perfect but it's an approximation nevertheless). Than you try to make an estimation (simulation) model of acoustic impedance in you reservoir. Finally you wavelet convolve that model into synthetic seismic and compare it to the real one.

    This is how geostatistical seismic inversion works (well at least most of the methods).

    The important point is that you should first build your synthetic seismic from well log acoustic impedance and only than proceed with comparing it to the real seismic.

  • What happen, electrochemically speaking, when the membrane of a PEMFC is drying ?

    Hi, I am curious to know which are the chemical processes happening in the membrane when this one is drying, thus leading to a voltage degradation and irreversible failure.

    Soichi Michel-Aimé Fukuhara · Institut Franche-Comté Electronique Mécanique Thermique et Optique Sciences et Technologies

    Thank you everyone for your answers. So, M. Bandarenka, if I understand correctly, the drying process will block the hydrophilic pathways which are the ones used by protons (or the easiest one). Combined this to M. Massonnat's answer, it means, that the energy to produce the same electrical power is higher. However, what cause the depolymerisation of the superstructure ? Why drying process depolymerize the membrane ? Thank you again to everyone

  • Dannielle S. Green added an answer in ANOVA:
    In asymmetrical ANOVA, fixed and orthogonal, which term is the Control vs others tested over?

    I have an experiment with two fixed and orthogonal factors (dose and concentration) and one control. I thought I knew how to do it, but have found contrasting literature on how to carry out the asymmetrical anova and most papers do not declare the details of how the analyses were done. Also most of the papers refer to designs with random factors, such as those in Glasby and Underwood etc and mine are all fixed. I have carried out two separate anovas, (1) one way with all treatments including control and (2) two way with dose x concentration without control. When I construct the asymmetrical anova from the two analyses, I am not sure whether to test control vs others against the res from analysis (1) or from the combined residual from (1) and (2). Any suggestions?

    Dannielle S. Green · Trinity College Dublin

    Hi Salvatore, thanks for your response. I am using R.

  • Fairouz Bettayeb added an answer in Men:
    When you hear the words "black and white" what ideas that run in your mind?

    "black and white" are two opposite words include for example the white men and black men it indicates the color of the skin, "black and white" also indicates the good and evil, love and hate, peace and war ........

    Fairouz Bettayeb · Centre de Recherche Scientifique et Technique en Soudage et Contrôle

    Only two nice colors

  • How can we discover patterns?

    A powerful method for finding new patterns is to take the abstract patterns that we directly observe and look at them by themselves. In this case, lets move beyond the vegetable origins of Fibonacci numbers and just think about the Fibonacci sequence as an interesting entity in its own right.

    For example the cone flower and the sunflower both display natures signature of dual, locking spirals.

    Dejenie A. Lakew · John Tyler Community College

    Patterns are nature's way of displaying itself. We humans either discover or imitate patterns in nature such as  foliages of things described by Fibonacci sequence or we create patterns of our own imaginary patterns. These are patterns I created to promote the collateral existence of  mathematics and art. 

  • Maxwell Akaba added an answer in Entrepreneurship:
    Do you really feel that Generation (Gen X, Y or Z) affects preference for entrepreneurship?

    I am conducting a research on preference of Gen Y people for entrepreneurship.

    I need support for the literature.


    Maxwell Akaba · Runel Oil Ltd and associated companies,Ghana


    I am sure you have a very important issue to investigate. May be with some collaboration I may provide an African perspective to this important study, if your study is multicultural and global in character. This may be a world need, in fact.

    The African societal and cultural values are changing(Munroe and Munroe, 1972; Akaba et al.2015), and will change more with time and space (Appaduria, 1990). It will make very interesting a study to find out how the African cohorts affect society and world geopolitics  over a period ,and compare these with others world wide. It may also be a good idea to do projections for Gen Z, in the African perspective, in relation to other regional and international building blocks.

    From the above a global, as well as regional predictions, can be made, possibly on behavior patterns to expect in future, product and services needs of generation Z can also be forecast,. as well as changes in political and managerial systems that will suit them.

    Kindly let me know whether a collaboration is possible. This answer is to attempt to broaden the scope a bit for you


    Appadurai, A. (1990), ‘Disjuncture and difference in the global cultural economy.” In: Global Culture: Nationalism, Globalization, and Modernity. Featherstone, M. (ed). London:
    Sage, pp. 295–310.

    Munroe, R.L. & Munroe, R.H. (1972) ‘Obedience among children in an East African society’. Journal of Cross-Cultural Psychology, 3(4), pp. 395–399.

  • Prashant Motwani asked a question in Abaqus:
    How to Define Loading Protocol in ABAQUS for Cyclic loading?

    I have attached the experimental protocol for the test. My questions is

    1) should I give this as it is in the tabular column while defining amplitude

    2) what should i give the time period value in the step function

  • Are all economic relationships non-linear?

    Keynes given the theory of price and wage sticky-ness and ascribed it to asymmetry of human expectations and behaviors.

    Many other behavioral economists such as Shiller, Kahnemann and Taversky they are also of the non-linear or asymmetric behavior as people respond more to negative than to similar positive. In this connection one more famous line is companies are slow to hire and fast to fire.

    As most of movements in variables of economics whether macro-economics or international economics is due to collective response of human beings. Thus, nonlinear testing or threshold or some regime switching models must be used more frequently than linear models in research papers. But reverse happens. What are the reasons for more papers on linear testing in empirical studies?

    Yoshinori Shiozawa · Osaka City University

    Roman Matkovsky sees only one side of a coin. 

    When we want to analyze "regime switching" or phase transition and even some other catastrophic events, it is evident we should make and use non-linear models, because linear models do not show these phenomena. But, some important questions in economics have a reversed relation. One of such cases is price theory. 

    Rajesh Sharma started explanation of his question by this phrase: 

    Keynes given [sic] the theory of price and wage sticky-ness and ascribed it to asymmetry of human expectations and behaviors. 

    Price and wage stickiness is one of major concerns of New Keynesians. Let us examine the neoclassical price theory. I confine my argument on price theory of industrial products. Prices of financial assets behave extremely differently. Wages are more complicated, because it is partly determined by power relations and is not an easy object of economic analysis. 

    Imagine Marshallian demand and supply curve explanation. There are many varieties of neoclassical price theories, but the essence is explained by this textbook level price theory. It normally supposes that cost function is S-shaped. This is a typical non-linear relation. However, in this case, this observation (or more correctly belief) is not based on real cost measuring. There are a few attempts for this and, as I have written about Joel Dean in my previous post, the obtained results tell that cost function is linear rather than any quadratic or cubic functions. 

    Why, then, do many economists believe that cost curve of is S-shaped? Where was this belief born? The reason is simple. It was the “necessity of a theory” and not an observation of the reality. Basic assumption of the neoclassical price theory is that there are supply and demand functions which are (only) dependent of prices. S-shaped cost function was the most convenient way to explain how supply function is obtained or defined from firms' profit maximizing behavior. 

    All readers must know this. A firm produces and supplies its product at such a quantity that the marginal cost becomes equal to the price of the product. This explanation requires that marginal cost is rising at the actual level of production. Dean's measurements and other knowledge of cost accounting show that cost is constant for a wide range of production levels (or linear if you like). Here, "cost" means direct cost. If we take into account fixed cost, depreciation or general administrative expenses, the average cost is decreasing. In other words, the firms are operating at increasing returns to scale. 

    If this is true, the standard neoclassical price theory loses its foundation. Price and marginal cost do not determine the firm's supply quantity. Consequently, the supply function, which is the sum of each firm's supply, is not defined. This is a catastrophe for believers of the neoclassical price theory and they denied with their all efforts that cost function is not linear but distinctly S-shaped. 

    Please note that small deviation from linear cost curve does not change the problem very much. What is necessary is the sufficiently big rise of the marginal cost (to become comparable with the price) at the actual operating range of production. Most often made apologies were like this one: the cost rises when it approaches the production full capacity. They are not valid, because majority of modern firms are operating sufficiently below the full capacity, if it exists. Almost all firms would be happy to produce and supply 30% or 40 % more than present supply volume at the present price. If the demand is expected to continue for a long period, they will extend their supply by two or three or even ten times at the constant price. 

    Neoclassical price theory is totally flawed and the S-shape reasoning is necessary for its validity. To believe that linearity is always an approximation is too naïve in economics. This kind of naïveness helped for a longtime the survival of a flawed theory. Economists should be more methodologically skeptical.

  • Pedro Correia added an answer in Trend Analysis:
    Is there any good software for trend graph?

    Dear scientists,

    I'm conducting a Joinpoint trend analysis project, but I got a problem with graphing task. I used Joinpoint Regression program to 'draw' a trend graph, but the quality is not as good as my expectation. Could you please give me some suggestions?

    p/s: free software are more preferable.

    Thank you in advance!

    Pedro Correia · Technical University of Lisbon

    Hi Nguyen,

    There are a lot of free software around to do this. For points and graphs plots I would advise:

    1) SOFA: http://www.sofastatistics.com/home.php (statistics software)

    2) SciEnPlot: http://2dscience.com/ (data analysis and visualization)

    3) SciDAVis: http://scidavis.sourceforge.net/ (data analysis and visualization)

    4) Online charts: http://www.onlinecharttool.com/ (chart web software)

    If you are whiling to give it a try at some basic programming (the result will be as good as your effort):

    a) matplotlib: http://matplotlib.org/ (plotting python library)

    b) D3: http://d3js.org/ (plotting javascript library)

    c) seaborn: http://stanford.edu/~mwaskom/software/seaborn/ (plotting python library)

    d) R: http://www.r-project.org/ (very high-level programming language)

    e) Bokeh: http://bokeh.pydata.org/en/latest/ (basically D3 for python)

    Than you have actual graph software:

    *1) gephi: http://gephi.github.io/

    *2) network-X: https://networkx.github.io/

    All of the above are free. And there are many more out there (for instance every spreadsheet software is able to do what you seem to want).

  • Ahed Jumah Alkhatib asked a question in Violence:
    What do you think about schoolchildren violence and lead exposure?

    I am planning to conduct a new study about schoolchildren violence and lead exposure.

    Any suggestion, recommendations are welcome

  • Mohammad Aboonajmi asked a question in Innovation:
    What kind of innovations have motivated the course of human history?

    What  kind of innovations have motivated the course of human history?

  • Does anyone know of good resources that explain the development of the idea of statistical significance?

    I am looking for information on the history of the development of statistical significance formulae, the mathematical calculations and why they were chosen.

    I would also like to learn the same about effect size.


    William Harper · The University of Western Ontario

    The text Statistics  (especially the 1979 first edition)by Freedman, Pisani, and Purvis provides a good review of the development of the idea of statistical significance.

  • Paras Patel added an answer in Binary Liquids:
    Does a Refractive Index show anomaly in Liquid Binary Mixtures?
    Much thanks.
    Paras Patel · Hemchandracharya North Gujarat University, Patan, India


    You can use vibro viscometer for viscosity less than 1cp.

    and If it is not possible you can use ubbelohde type viscometer having range 2cp. first you calculate it's A and B constant and then use. it's gives better result. it's my person experience.

  • What should be done for becoming the Emily Wolf or Max Born????

    I changed the filed in Physics from Semiconductor Physics to Optics(Nano-Resolution Optics). Now what should i do to become good in Optics??? My which areas of physics should be Powerful??? Life is learning so i can take open courses kindly share your experiences????

    Kaleem Ullah · Nanjing University of Science and Technology

    Thank you very much. Yes you are right mathematics is very necessary for the optics can you refer me any paper or easy and good book for diffraction mathematics?????

  • Michael Patriksson added an answer in Websites:
    How much time does it take the reviewing process journals?

    Dear ALL,

    I would like to have an idea about how much time does it take the reviewing process journals.

    I didn't find the information in many journal's websites. (Eg. Published in  inderscience, emerald group publishing...)

    Michael Patriksson · Chalmers University of Technology

    The problem is that plenty of those journals that state that the review process is very fast also are those that are not serious, but earn a lot of money from their publication fees.

    It is - I'm afraid - to some degree a question if you can wait longer in order to have a good paper published in a good journal, or if you simply want it published fast. You pay the price of a longer time before publication - and even a possible rejection - since the prestige in publishing in a good journal is that high. 

    I for one would choose the good journal first of all, because you then know that you will be treated fairly, correctly, and scientifically maturely. Fast journals often don't pay attention to the important technical details in your paper - they simply see the profit that they get from your publication. (So an erroneous paper can often be published in such a journal, as the desire to make a profit is more important than to publish good papers.)

  • What is philosophy of mathematics? What is it for?

    Philosophy of physics once placed a significant role to solve defects in the foundation of physics disclosed by paradoxes; it is hopefully that philosophy of mathematics will do the same.

    The infinite related paradoxes have been troubling us for such a long time------the fundamental defects are not only mathematics and not only philosophy. Is it the faults of our not having been done enough on “philosophy of mathematics”?

    Do we need both theoretical and applied “philosophy of mathematics”?

    Is it too much requirements for “philosophy of mathematics”?

    Geng Ouyang · MinNan Normal University

    Dear Mr. H Chris Ransford, I agree with you that people have been talking about “philosophy of mathematics” in different situations and different times.

    But I think what we are doing in this thread is different from previous, we are driven and powered by the newly discovered infinite related Harmonic Series Paradox and we have very clear target------we hope to solve some of the infinite related fundamental defects in our mathematics through the discussions here.

    Sincerely yours, Geng   

  • Maysam Molana added an answer in Heat Transfer:
    Does anyone have the experience dealing with earth-sheltered buildings, from the simulation aspects or the psychological ones?

    I need to find any researches about people's acceptability and reactions to live in an earth-sheltered construction.

    Another aspect, is to find a suitable simulation program which can calculate the heat transfer effect with different soil thicknesses around the building.

    Maysam Molana · Shahid Chamran University of Ahvaz

    Dear Heba,

    It seems that your study is so interesting and comprehensive. By your comment about details, I am so eager to know about any proceedings. 

    I read your well organised questionnaire and hope to be a suitable approach.

    I did some unpublished studies about underground buildings and hot and relative humid regions such as Ahvaz, Iran for educational function. Please see the attachment for more detail of a good research in this field. 

    Feel free to contact me if you want. 

  • Shrish Bajpai asked a question in MATLAB:
    How can create training data from hyperspectral images for supervised learning process in matlab & do the training process through matlab or R?

    I do not know how to create a training set from images & learning through R or matlab.