Complex Analysis - Science topic

Probability theory in number theory and complex analysis I have obtained some scientific conclusions and results. These are the finite or infinite condition of the existence of the uyechim for Gilbert's 10th problem, flaws in Bernstein's views on disinhibition (tetrahedral), and alternative annotations to it, determining the defects of the Byuffon problem, and alternative solutions to it, the specifying function detection algorithm for Fibonacci-type sequences. I would like to study at the doctoral (PHD) now. Can you give me some advice?

I do not know English very well, sorry for the shortcomings

Hello. I need some papers for analytic function with any operators

The energy operator ih∂/∂t and the momentum operator ihΔ or ih∂/∂x play a crucial role in the derivation of the Schrödinger equation, the Klein-Gordon equation, the Dirac equation, and other physics arguments.

The energy and momentum operators are not differential operators in the general sense; they do play a role in the derivation of the equations for the definition of energy and momentum.

However, we do not find any reasonable arguments or justifications for the use of such operators, and even their meaning can only be speculated from their names. It is used without explanation in textbooks.

The clues we found are:

1) In the literature [ Brown, L. M., A. Pais and B. Poppard (1995). Twentieth Centure Physics (I), Science Press.], "In March 1926, Schrödinger noticed that replacing the classical Hamiltonian function with a quantum mechanical operator, i.e., replacing the momentum p by a partial differentiation of h/2πi with position coordinates q and acting on the wave function, one also obtains the wave equation."

2) Gordon considered that the energy and momentum operators are the same in relativity and in non-relativism and therefore used in his relativistic wave equation (Gordon 1926).

(3) Dirac also used the energy and momentum operators in the relativistic equations with electron spins (Dirac 1928). Dirac called it the "Schrödinger representation", a self-adjoint differential operator or Hermitian operator (Dick 2012). (D).

Our questions are:

Why can this be used? Why is it possible to represent energy by time differential for wave functions and momentum by spatial differential for wave functions? Has this been historically argued or not?

Keywords: quantum mechanics, quantum field theory, quantum mechanical operators, energy operators, momentum operators, Schrödinger equation, Dirac equation.

The Introduction of complex numbers in physics was at first superficial but now they seem increasingly fundamental. Are we missing their true interpretation? What do you think?

I'm trying to solve the integral shown in the picture.

I'm using python libraries to plot the integrand (numpy and matplotlib.pyplot), as well as scipy.integrate library to solve the integral.

However, I'd like to see other suggestions or tips to solve this problem.

Any comment will be well appreciated.

Thanks, Pablo

From the earliest Pythagorean (~570BCE-~490BCE) view that "everything is number" [1], to the founder of modern physics, Galileo (1564-1642), who said "the book of nature is written in the language of mathematics" [2], to attempts by Hilbert (1862-1943) to mathematically "axiomatize" physics [3]，and to the symmetry principle [9], which today is considered fundamental by physics, Physics has never been separated from mathematics, but there has never been a definite answer as to the relationship between them. Thus Wigner (1902-1995) exclaimed [4]: "The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. gift which we neither understand nor deserve."

CN Yang, commenting on Einstein's "On the method of theoretical physics" [5], said, "Was Einstein saying that fundamental theoretical physics is a part of mathematics? Was he saying that fundamental theoretical physics should have the tradition and style of mathematics? The answers to these questions are no "[6]. So what is the real relationship between mathematics and physics? Is mathematics merely a tool that physics cannot do without? We can interpret mathematics as a description of physical behavior, or physics as operating according to mathematical principles, or they are completely equivalent, but one thing is unchangeable, all physics must ultimately be concretely embodied in its physical parameters, regardless of who dominates whom. We need to remember the essential question, "That is, we don't invent mathematical structures - we discover them, and invent only the notation for describing them"[7]. Mathematics is abstract existence, physics is reality. We cannot completely replace physical explanations with mathematical ones. For example, ask "How do light and particles know that they are choosing the shortest path [8]. The answer is that it is determined by the principle of least action. This is the correct mathematical answer, but not the final physical answer. The final physical answer should be, "Light and particles are not searching for shortest paths, they are creating and defining shortest paths". Why this can be so is because they are energy-momentum themselves. The ultimate explanation is just math*，if we can't boil it down to specific, well-defined, measurable physical parameters. Following Pythagoras' inspiring vision that the world can be built up from concepts, algorithms, and numbers [9]. When we discuss the relationship between math and physics, do we need first ask:

1) What are numbers? Shouldn't we first attribute numbers to "fundamental quantities" in mathematics and physics? Are scalars, vectors, and spinors complete expressions of such fundamental quantities? All other quantities are composites of these fundamental quantities, e.g., tensor.

2) Do mathematics and physics have to have these fundamental quantities in common before we can further discuss the consistency between their theorems? That is, the unification of mathematics and physics must begin with the unification of fundamental quantities.

3) Where do these fundamental quantities come from in physics? In what way are they represented?

--------------------------------

Notes：

* And then what do imaginary numbers in physics correspond to? [10][11]

--------------------------------

References：

[1] McDonnell, J. (2017). The Pythagorean World: Why Mathematics Is Unreasonably Effective In Physics Springer.

[2] Kosmann-Schwarzbach, Y. (2011). The Noether Theorems. The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century. Y. Kosmann-Schwarzbach and B. E. Schwarzbach. New York, NY, Springer New York: 55-64.

Einstein, A. (1934). "On the method of theoretical physics." Philosophy of science 1(2): 163-169.

[3] Corry, L. (2004). David Hilbert and the axiomatization of physics (1898-1918): From Grundlagen der Geometrie to Grundlagen der Physik, Springer.

[4] Wigner, E. P. (1990). The unreasonable effectiveness of mathematics in the natural sciences（1960）. Mathematics and Science, World Scientific: 291-306. 【这个说法本身可能是存在问题的，不是数学在物理学中的有效性，而是不能够区分物理学准则和数学算法。】

[5] Einstein, A. (1934). "On the method of theoretical physics." Philosophy of science 1(2): 163-169.

[6] Yang, C. N. (1980). "Einstein's impact on theoretical physics." Physics Today 33(6): 42-49.

[7] Russell, B. (2010). Principles of mathematics （1903）, Routledge.

[8] https://www.researchgate.net/post/NO4_How_do_light_and_particles_know_that_they_are_choosing_the_shortest_path

[9] Wilczek, F. (2006). "The origin of mass." Modern Physics Letters A 21(9): 701-712.

[10] Chian Fan, e. a. (2023). "How to understand imaginary numbers (complex numbers) in physics." from https://www.researchgate.net/post/NO6_How_to_understand_imaginary_numbers_complex_numbers_in_physics.

[11] Baylis, W. E., J. Huschilt and J. Wei (1992). "Why i?" American Journal of Physics 60(9): 788-797. 【复数、虚数、波函数】

Here by "surface" I mean a projective variety of dimension 2 (over an algebraically closed field k, as in Ch.1 of Hartshorne).

My question is:

Given a positive integer n >0, can we define a (possibly singular) surface S in n-dimensional projective space P^n, such that S does not admit an embedding into any P^m for m < n ?

That is, I am asking for a constructive proof, an effective algorithm taking as input n, that generates the set of homogenous polynomials defining such a surface.

How does this relate to the number and degrees of the homogenous polynomials required to define S ?

I am analysing complex survey data in stata. Tests like lrtest, AIC or BIC are not supported by svy and thus I could not use any of these to compare successive models for improvment. I have read about using the wald test. Is something available to test the overall model and so be able to compare successive models? I would really appreciate if someone out there could suggest a way out...

Best regard's

Dear researchers, which are the general contours L understood from the sentence: ‘L is a vertical contour cutting the real z-axis between 0 and 1 in complex analysis?’ I have seen a integral that I am studying about, but my intention is to adjust the contour for my problem based on that sentence. My integral:

integral on contour L of (z^-a)/(sin(pi*z))^2 dz under z as complex value.

My concern is to define the best structure of L if applies.

Best regards,

Carlos Lopez

Snakemake is a versatile workflow management system that can be applied to various fields, including plant pathology. In plant pathology, Snakemake can streamline and automate complex analysis pipelines, making research more efficient and reproducible. Here's a brief overview of how Snakemake is used in plant pathology:

1. **Automated Analysis Pipelines**: Plant pathologists often deal with diverse datasets, such as DNA/RNA sequences, microscopy images, and phenotypic data. Snakemake enables researchers to create automated pipelines that handle data preprocessing, quality control, analysis, and visualization. This automation reduces manual errors and ensures consistent analysis across different samples.

2. **Bioinformatics Workflows**: Snakemake is particularly useful in plant pathology for managing bioinformatics workflows. It can integrate various tools and software packages for tasks like sequence alignment, variant calling, and phylogenetic analysis. Researchers define rules that describe dependencies and data transformations, allowing complex analyses to be executed seamlessly.

3. **Reproducibility and Traceability**: Snakemake ensures reproducibility by capturing all dependencies and steps in a workflow. Researchers can easily reproduce their analyses by rerunning the same Snakemake script. This is crucial in plant pathology, where accurate and reproducible results are essential for understanding disease mechanisms and developing mitigation strategies.

4. **Iterative Studies**: Plant pathologists often conduct iterative studies to investigate disease progression or response to treatments. Snakemake simplifies these studies by automating repetitive tasks and adjusting the workflow as new data or hypotheses emerge.

5. **Data Integration and Visualization**: Snakemake can incorporate data integration and visualization steps in the workflow. For instance, it can merge multiple types of data (genomic, transcriptomic, and phenotypic) to provide a comprehensive view of plant-pathogen interactions.

6. **Customized Analysis**: Snakemake allows researchers to customize their analysis pipelines based on the specific needs of their plant pathology studies. This flexibility ensures that the workflow is tailored to address research questions effectively.

7. **Parallel Processing**: Large-scale plant pathology studies often involve analyzing extensive datasets. Snakemake's parallel processing capabilities enable researchers to distribute tasks across multiple processors or compute nodes, significantly reducing analysis time.

8. **Collaboration and Sharing**: Snakemake workflows can be easily shared with collaborators, making it simpler to collaborate on complex analyses. This promotes knowledge sharing and accelerates research progress.

In summary, Snakemake plays a vital role in plant pathology by automating and streamlining analysis pipelines, enhancing reproducibility, and facilitating complex bioinformatics workflows. Its flexibility, parallel processing capabilities, and user-friendly syntax make it a valuable tool for researchers studying plant-pathogen interactions, disease mechanisms, and mitigation strategies.

A friend of mine majors in math. He is confused about the symbol ℘ appearing in Complex Analysis written by Elias M. Stein and Rami Shakarchi. He tells me that it can be considered as "P" in some essays, relating to Weierstrass's elliptic function. I am really interested in what ℘ is. It seems to be quite different from the normal alphabet "P". Is it merely a symbol? Or an alphabet? Or something else? Please tell me. My friend and I are both eager to know more about it. Thank you!

Complex numbers are involved almost everywhere in modern physics, but the understanding of imaginary numbers has been controversial.

In fact there is a process of acceptance of imaginary numbers in physics. For example.

1) Weyl in establishing the Gauge field theory

After the development of quantum mechanics in 1925–26, Vladimir Fock and Fritz London independently pointed out that it was necessary to replace γ by −iħ 。“Evidently, Weyl accepted the idea that γ should be imaginary, and in 1929 he published an important paper in which he explicitly defined the concept of gauge transformation in QED and showed that under such a transformation, Maxwell’s theory in quantum mechanics is invariant.”【Yang, C. N. (2014). "The conceptual origins of Maxwell’s equations and gauge theory." Physics today 67(11): 45.】

【Wu, T. T. and C. N. Yang (1975). "Concept of nonintegrable phase factors and global formulation of gauge fields." Physical Review D 12(12): 3845.】

2) Schrödinger when he established the quantum wave equation

In fact, Schrödinger rejected the concept of imaginary numbers earlier.

【Yang, C. N. (1987). Square root of minus one, complex phases and Erwin Schrödinger.】

【Kwong, C. P. (2009). "The mystery of square root of minus one in quantum mechanics, and its demystification." arXiv preprint arXiv:0912.3996.】

【Karam, R. (2020). "Schrödinger's original struggles with a complex wave function." American Journal of Physics 88(6): 433-438.】

The imaginary number here is also related to the introduction of the energy and momentum operators in quantum mechanics：

Recently @Ed Gerck published an article dedicated to complex numbers:

Our question is, is there a consistent understanding of the concept of imaginary numbers (complex numbers) in current physics? Do we need to discuss imaginary numbers and complex numbers ( dual numbers) in two separate concepts.

_______________________________________________________________________

2023-06-19 补充

On the question of complex numbers in physics, add some relevant literatures collected in recent days.

1) Jordan, T. F. (1975). "Why− i∇ is the momentum." American Journal of Physics 43(12): 1089-1093.

2）Chen, R. L. (1989). "Derivation of the real form of Schrödinger's equation for a nonconservative system and the unique relation between Re (ψ) and Im (ψ)." Journal of mathematical physics 30(1): 83-86.

3) Baylis, W. E., J. Huschilt and J. Wei (1992). "Why i?" American Journal of Physics 60(9): 788-797.

4）Baylis, W. and J. Keselica (2012). "The complex algebra of physical space: a framework for relativity." Advances in Applied Clifford Algebras 22(3): 537-561.

5）Faulkner, S. (2015). "A short note on why the imaginary unit is inherent in physics"; Researchgate

6）Faulkner, S. (2016). "How the imaginary unit is inherent in quantum indeterminacy"; Researchgate

7）Tanguay, P. (2018). "Quantum wave function realism, time, and the imaginary unit i"; Researchgate

8）Huang, C. H., Y.; Song, J. (2020). "General Quantum Theory No Axiom Presumption: I ----Quantum Mechanics and Solutions to Crisises of Origins of Both Wave-Particle Duality and the First Quantization." Preprints.org.

9）Karam, R. (2020). "Why are complex numbers needed in quantum mechanics? Some answers for the introductory level." American Journal of Physics 88(1): 39-45.

The conventional choice of lagging vs leading angle to represent the phase difference between voltage and current in AC circuits is somewhat arbitrary.

The standard convention of a lagging current (or leading voltage) likely arose from the historical analysis of resistive-inductive circuits, where current naturally lags the voltage.

However, for a capacitive circuit, the current leads the voltage. There is no inherent reason why we must adhere to the historical convention of having current lag voltage in all cases. An alternative convention could just as well designate current leading voltage for inductive circuits and lagging for capacitive circuits. While this alternative is not commonly used, it was firstly introduced by Steinmetz by 1900 in its book "THEORY AND CALCULATION ALTERNATING CURRENT PHENOMENA" [1], page 21, but then it was neglected in favour of the current interpretation. To me, it sounds more natural the Steinmetz interpretation for several reasons.

What do you think?

[1] http://www.survivorlibrary.com/library/theory_and_calculation_of_alternating_current_phenomena_1900.pdf.

It finally has occurred to me that there is a similarity between i = √-1 and √2. They are each linearized representations of essentially quadratic values. We use the former in complex numbers and include the latter in the real number system as an irrational number. Each has proved valuable and is part of accepted mathematics. However, an irrational number does not exist as a linear value because it is indeterminate – that is what non-ending, non-repeating decimal number means: it never can exist. Perhaps we need an irrational number system as well as a complex number system to be rigorous.

The sense of this observation is that some values are essentially quadratic. An example is the Schrödinger Equation which enables use of a linearized version of a particle wave function to calculate the probability of some future particle position, but only after multiplying the result by its complex conjugate to produce a real value. Complex number space is used to derive the result which must be made real to be real, i.e., a fundamentally quadratic value has been calculated using a linearized representation of it in complex number space.

Were we to consider √-1 and √2 as similarly non-rational we may find a companion space with √2 scaling to join the complex number space with √-1 scaling along a normal axis. For example, Development of the algebraic numbers a + b√2 could include coordinate points with a stretched normal axis (Harris Hancock, Foundations of the Theory of Algebraic Numbers).

A three-space with Rational – Irrational – Imaginary axes would clarify that linearization requires a closing operation to restore the result to the Rational number axis, where reality resides.

[Note: most people do not think like I do, and almost everyone is happy about that: please read openly, exploringly, as if there might be something here. (Yes, my request is based on experience!) Tens of thousands of pages in physics and mathematics literature from popular exposition to journal article lie behind this inquiry, should you wish to consider that.]

Consider the class of real elementary functions defined on a real interval I. These

are real analytic functions. How can we characterise their power series ? That is, what

can we say about their coeficients, the structure of the series of their coeficients ?

For instance there are coeficients a(n) given by rational functions in n , or given by combinations of rational functions and factorials functions, computable coeficients, coeficients given by recurrence relations, etc.

It is easy to give an example of a real analytic function which is not elementary. Just solve the equation x'' - tx = 0 using power series. This equation is known not to have any non-trivial elementary solution, in fact it has no Liouville solution (indefinite integrals of elementary functions).

How do you plot complex analysis graphs on the Geogebra platform?

How do you find books, information, and articles about it?

The attached image is the introduction of part D - Complex Analysis from [Kreyszig, E. (2009). Advanced engineering mathematics, 10th edition.]. At the end of the introduction, the author explains why complex analysis is important in three points. I am having difficulty understanding point (3), my questions are: 1- How studying analytic functions as functions of a complex variable leads to a deeper understanding of their properties? 2- How studying analytic functions as functions of a complex variable leads to interrelations in complex that have no analog in real calculus. I am grateful to anyone who could or tried to answer my questions and if possible provide examples to get a full understanding.

Is the Poincaré Conjecture relatively easy to prove for the case of simply connected real analytic 3- manifolds ?

I want to know the complexity analysis (Time and Space ) of the algorithm of multi-task learning deep neural network-based compared to the conventional algorithms.

Consider the powerful central role of differential equations in physics and applied mathematics.

In the theory of ordinary differential equations and in dynamical systems we generally consider smooth or C^k class solutions. In partial differential equations we consider far more general solutions, involving distributions and Sobolev spaces.

I was wondering, what are the best examples or arguments that show that restriction to the analytic case is insufficient ?

What if we only consider ODEs with analytic coeficients and only consider analytic solutions. And likewise for PDEs. Here by "analytic" I mean real maps which can be extended to holomorphic ones. How would this affect the practical use of differential equations in physics and science in general ? Is there an example of a differential equation arising in physics (excluding quantum theory !) which only has C^k or smooth solutions and no analytic ones ?

It seems we could not even have an analytic version of the theory of distributions as there could be no test functions .There are no non-zero analytic functions with compact support.

Is Newtonian physics analytic ? Is Newton's law of gravitation only the first term in a Laurent expansion ? Can we add terms to obtain a better fit to experimental data without going relativistic ?

Maybe we can consider that the smooth category is used as a convenient approximation to the analytic category. The smooth category allows perfect locality. For instance, we can consider that a gravitational field dies off outside a finite radius.

Cosmologists usually consider space-time to be a manifold (although with possible "singularities"). Why a manifold rather than the adequate smooth analogue of an analytic space ?

Space = regular points, Matter and Energy = singular points ?

Hi, in a paper, I found the equation.

f(x)=(x+a-ib)^-1 - (x-a-ib)^-1

And, I'm going to get the answer.

integral[ Im[f(x)] ] = ?

(integrate from 0 to infinity)

I am analyzing the squeal of simple brake using Abaqus and I tried to find the unstable frequencies using complex frequency which caused the squealing noise; however, all of the modes have nearly zero dampings (lie on the imaginary axis) and the pairs of modes which become coupled and formed a stable/unstable pair couldn't be found. I attach the brake model in the comment. How can I found some unstable frequencies using Abaqus?

Conformal mapping is a powerful tool to solve 2D boundary value problems that would would otherwise not be able to be solved analytically

Have these ideas been extended to 3D applications? Can someone point me to a suitable reference?

Hello,

I would like to prove that the type of coordination bond between copper and oxygen is dsp2 in the following complex structure. So I used NBO analysis, but there seems to be no related information. I wonder if there is anything else that needs to be applied.

I will receive all the advice with thanks. I also attached a file that used NBO analysis (.log).

Thank you.

Hello

Can someone help me to solve this?

Because I really don't know about these problems and still can't solve it until now

But I am still curious about the solutions

Hopefully you can make all the solutions

Sincerely

Wesley

We have 2 groups (total 8 participants, 4 in each group with 2 male and 2 female) of participants (one group on one end of the continuum and the other on the other end) with a score on a variable (Continuum). After applying intervention 1, we applied intervention 2 on both groups. Are we going to use paired samples t-test separately for both groups thrice (Once with pre-test score and intervention 1 and second time with pre-test score and intervention 2 and third time with intervention 1 and intervention 2)? How are we going to analyse this experimental data?

How to work properly in the development of an integral like the Abel Plana defined on this image:

I am interested in to have a set of steps for attacking the problem of developing the integral and to determine a criterion of convergence for any complex value s, I mean, when the integral could have some specifical behavior at, for example, s=1/2 + i t where I am interested in to study it.

I am interested in the proper evaluation of that integral only with formal steps into complex analysis.

The Abel PLana formula appears also on https://en.wikipedia.org/wiki/Abel%E2%80%93Plana_formula

Best regards

Carlos López

I have docked my dna and ligand and then save the best-docked structure in the form of pdb then I take the coordinates of my ligand and form the .itp and .gro file using PRODRG software. It gives me topol.top file then I add coordinates of ligand (.gro) file in DNA.gro file and increase the total no. of atoms and also added ligand.itp in topol.top and also added ligand 1 in molecules in topol.top even after this my solv.gro file of DNA and ligand does not show any interaction. i am not able to form ions.tpr file. i have attached solv.gro file.

Hi,

I'm a new user of MatLab and I want an objective way to identify how complicated an image is according to it's color variation. I can't use entropy() because it's for grayscale image. How can I do that?

Thanks!

Dear fellow researchers,

In your expert opinion, do you think the Riemann Hypothesis is true? The first billion zeros have been computed and they all verify this hypothesis. However, we have previously seen patterns hold until a very large number than break (There is a conjecture that holds for n<10^40). Do you think there is any reason to believe that it might be false?

How many more years do you predict it will take before the Riemann Hypothesis is solved?

Do you think we are close or does it seem that we are still very far?

Can anyone help me prove using Contour Integration that the value of integral log(1+z)/z from limit -1 to +1 is pi^2/4?

I would like to know the advantages in terms of complexity in the analysis (which software is easier to use). Also, I want to know wich software is more reliable for the analysis of mechanism.

I am attempting to solve the limit which involves the Reimann Function zeta

Lim [(zeta(1-z)zeta(1-zc))/(zeta(z)zeta(zc))]=1

as z tends to get closer to a root of the Reimann Function Zeta written here as zeta.

Here zc in the equation means the conjugate of the complex number z.

How to prove or where to find the integral inequality (3.3) involving the Laplace transforms, as showed in the pictures here? Is the integral inequality (3.3) valid for some general function $h(t)$ which is increasing and non-negative on the right semi-axis? Is the integral inequality (3.3) a special case of some general inequality? I have proved that the special function $h(t)$ has some properties in Lemma 2.2, but I haven't prove the integral inequality (3.3) yet. Wish you help me prove (3.3) for the special function $h(t)$ in Lemma 2.2 in the pictures.

As we know, the Cauchy integral formula in the theory of complex functions holds for a complex function which is analytic on a simply connected domain and continuous on its boundary. This formula appears in many textbooks on complex functions.

My question is: where can I find a generalization of the Cauchy integral formula for a complex function which is analytic on a multiply connected domain and continuous on its boundary?

Basic knowledge of Complex Analysis and Nevanlinna value distribution theory.

What is the physical meaning of the adiabatic coupling constant g?

Conformal Mapping is used to solve 2D electrostatic phenomena, but what are the steps to follow, and how one get to know about which mapping function should use to map?

Is there any web reference or Book?

I want to solve Poisson's Equation in 2D geometry, please provide some good reference or Book for this.

Thank You in advance...

See for example   the paper arXiv:1001.1805v1 [math.CV] 12 Jan 2010,

The Schwarz Lemma at the

Boundary by Steven G. Krantz. In this paper the author explores versions of the Schwarz lemma

at a boundary point of a domain (not just the disc). Estimates on

derivatives of the function, and other types of estimates as well, are considered.The author reviews recent results of several authors, and present some new theorems as well

It seems that  this question is related to  Q1. Is there a version of Jack's lemma for hyperbolic domains in space?.

I'm working on a project and I wanted to know the Time and Space complexity Analysis of MOEAs. I have searched the google scholar but there isn't any valuable information on this matter. please help me and let me know if there is a good comparative study or article on this subject.

thanks

Consider I am using multiple KDE bandwidths for my data and I would like to find out what the 'best-fit-model' would be. Is there anything like AIC for glm that I could use to accomplish this? I have used AUC and complexity analysis outlined in papers like Silva et al. 2018, but my Reviewer 2 has notified me that AUC isn't sufficient for this. After running the analysis on several nonsensical smoothing values I tend to agree.

Any assistance is appreciated.

Decision Trees are extremely fast in classification. However, they are slow in construction during learning phase. Is there any paper on complexity analysis of Multiway Split, Multi-Class Decision tree?

Compute nontrivial zeros of Riemann zeta function is an algebraically complex task. However, if someone able to prove such an iterative formula can be used to get all approximate nontrivial using an iterative formula, then its value is limitless.How ever to prove such an iterative formula is kind of a huge challenge. If somebody can proved such a formula what kind of impact will produce to Riemann hypothesis? . Also accuracy of approximately calculated non trivial accept as close calculation to non trivial zeros ?

Here I have been calculated and attached first 50 of approximate nontrivial using an iterative such formula that I have been proved. Also it is also can be produce millions of none trivial zeros. But I am very much voirie about its appearance of its accuracy !!. Are these calculations Is ok?

Is there any transformation from fuzzy to the real or complex domain??

Can anyone please tell me about the complexity analysis in terms of Big oh of various image denoising techniques? Or I want to know how much time image denoising techniques are required for its operation...(Big oh notation)

Whenewer someone say that TMS, or complexity analysis or machine learning is 'novel methodology' I wander how long simething could be perceived as novel. In case if TMS even more than 30 years seems not to be enough. What do you think, what are the factors importannt in this issue?

Dear Professor, I have read your paper and it is very interesting to be used in the deformation analysis. But for this complex analysis, is there any supporting documents that can help us understand clearly on how he formula may work to the data until the output?

Thank you Sir

Time Series Analysis of 3D Coordinates Using Nonstochastic O...

I have a paper accepted recently subject to some corrections but not sure how to address one of the comments says ": " I think the authors should add a content about the complexity analysis of the fuzzy multi-objective model ". You help would be much appreciated.

complexity analysis tools

More general, I want to get an algebra of holomorphic fuctions on n-dimesional complex ball as qoutient of algebra of holomorphic fuctions on C^k. I know there exists Remmert-Bishop-Narasimhan-Wiegmann embedding theorem, but it does not provide us any explicit representation of complex ball as closed submanifold.

Some news about state of the art about Steve Smale 21^th century problems; in particular, I'm interested on "Mean Value Problem" (not inserted in original Smale's 1998 list, but formulated by Smale already in 1981, see Addenda in attached paper). Gianluca

if u be a harmonic function in sobolev space W^(1,p) (Omega) with zero trace (i.e; T(u)=0) and  {Laplace operator} (u) =0, then u identically zero.

The quadratic term of a Taylor expansion of a multivariate scalar valued function can be expressed in terms of the Hessian. Is there a similar form for vector valued functions, in the sense that all partial derivatives can be arranged in a matrix or tensor?

Is the series in the picture convergent? If it is convergent, what is the sum of the series?

For example, we have a sequence,

S={-1,-1,1,1,0,-1,-1,-1,-1,-1,-1,-1,0,0,1,-1,1,1,0,-1,0,1,-1,1,-1,-1,1,1,0,-1,0,-1,0,0,-1,-1,0,-1,1,0,1,1,-1,0,0,1,-1,1}

Can we use, Berlekamp–Massey algorithm to find the linear complexity of the given sequence?

Thanks in advance.

Analytical Solution

In Magnetic measurements., VSM parameter results are given following with Ms = 2.5110 x10-3 emu/g ; Mr = -4.0825 x10-3 emu/g and Hc = 477.34 G. Can anyone import your advice.

Hi,

I'm wondering about any Applications of Theory of Nevanlinna in Other Disciplines, such as Physics.

Any Papers, Theses and books are important to me.

Best regards

  I think, the old Markushevich's book on Analytic Functions is a good source of techniques and results in general. However, many particular cases may not fit those frames and may require specific analysis.

Best regards, Boyan.

What is the best or simplest reference, which says that a bounded subharmonic function can be extended over a condimension 2 subset?

Hi, 

In Statistical signal processing, lot of research is based on complex analysis. Many techniques and methods are transformed to complex domain. Whereas complex information is only important in form of magnitude and phase. So whats the difference in using magnitude information or real and imaginary information of the data?  Why is phase important? What the difference of the signal that is added with phase information and without phase information?

Appreciate your comments

Let f(x)+g(x) = h(x). Here, h(x) is minimum at the points(a1,a2,...,ak). For which condition , we can say that f(x) is also minimum at the points(a1,a2,...,ak)?

Thanks in advance for your idea and please give any reference

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I am interested in using conformal maps for image distortion and I am looking for software environments that can do this. So far I came up with:

1) SeamlessMaker, a commercial stand alone program for image filtering etc., that has some conformal maps for selection: http://www.hypatiasoft.fr/

2) ComplexMapStill.jar, a free stand alone Java implementation by Christian Mercat with some predefined maps and the possibility to define new ones: https://karczmarczuk.users.greyc.fr/TEACH/InfoGeo/Work/ComplexMapStill.jar

3) ImageForwardTransformation[] in Mathematica: http://community.wolfram.com/groups/-/m/t/854405?p_p_auth=TLh6kMXL

Are there other implementations

1) in other programming languages: C/C++, Python, ...

2) in commercial Math environments: Maple, MathLab, ...

3) in free Math environments: Scilab, Octave, ...

For my art processes  I would ideally need  a command line program that takes a path to an input image, a description of a conformal map and a path for the resulting output image so that this could be called from my own scripts. But a batch process within a Math environment would also be useful.

What are completely monotonic functions on an interval $I$? See the picture 1.png

What is the Bernstein-Widder theorem for completely monotonic functions on the infinite interval $I=(0,\infty)$? See the picture 1.png

My question is: is there an anology on the finite interval $I=(a,b)$ of the Bernstein-Widder theorem for completely monotonic functions on the infinite interval $I=(0,\infty)$? In other words, if $f(x)$ is a completely monotonic function on the finite interval $I=(a,b)$, is there an integral representation like (1.2) in the picture 1.png for the completely monotonic function $f(x)$ on the finite interval $(a,b)$?

The answer to this question is very important for me. Anyway, thank everybody who would provide answers and who would pay attention on this question.

if i have a model like this;

proc logistic data=name;

where disease in (0,1);

class sex race presents education wealth region / param=ref;

model disease (event='1') = age sex race presents education wealth region age*education wealth*region region*education;

run;

How do I get the odds ratio for each of these;

age

sex

race

presents

education

wealth

region

age*education

wealth*region

region*education

using the oddratio statement in proc logistic? Since the variable region is invoved in two different interaction.

thanks

In two-dimensional case, we can follow Kohn's definition of type by using holomorphic tangent vector field and the Levi function to define infinite type(cite H. Kang, Holomorphic automorphisms of certain class of domains of infinite type, Tohoku Math. J. (2) 46 (1994), 435–442. MR 95f:32041).  But when we consider in higher dimensions, can we still use this method to define infinite type?