Mathematics - Science topic

Peter Breuer

Dear Peter, thank you for your interest in finding the author's mistake. It was nice to see your geometric vision, answer 6R is indeed incorrect. Let me share with you my proof of why the answer is not correct.

@ Dr. Chen, Thank you for consulting with AI bot on behalf of me. It's interesting!

José Luis Junquera, Saddle polyhedra are three-dimensional objects with curved faces. They are not polyhedra in the traditional sense, because polyhedra must have flat faces. However, saddle polyhedra do have some properties that are similar to those of polyhedra. For example, they have an Euler characteristic, which is a topological invariant that is defined for all three-dimensional objects. addle polyhedra are the only other three-dimensional objects known to have an Euler characteristic of 2. This is an interesting fact, because it suggests that saddle polyhedra have some topological similarities to spheres and flat-faced polyhedra. The two saddle polyhedra that are known to exist are the saddle tetrahedron and its tessellation. The saddle tetrahedron has four curved faces, six edges, and four vertices. Its tessellation is a three-dimensional tiling that fills all of space. Saddle polyhedra are a relatively new area of research, and there is still much to learn about their geometry and topology. However, the fact that they have an Euler characteristic of 2 is a significant discovery, and it suggests that these objects have some interesting properties.

Certainly some exotic collection.

Often inequalities are better

Understood as comming from

Some identity, if you suppress

some always positive or negative

term.

An equation can be considered as a sentence in the language of mathematics, at least in its formalized version as can be seen in every book about mathematical logic or ZFC set theory. Programming languages are also formalized languages, and you have to stick to these formalizations in order for a computer to work correctly. However, most mathematicians use a semi formal mathematical language, but when for instance a theorem is correct, meaning that is has a correct proof, then one can write theorem and proof in the formalized language of mathematics, but the result is almost always unreadable by a human being, but " understandable " by a formal proof system, that can be implemented on a computer. In this sense one can let computers prove theorems, but then it needs a lot of input from a human being. But doing mathematics is also an art, and in order to be able to practice this art one needs a lot of practice and mathematical knowledge.

A Gaussian law is a concept in statistics or probability theory. The notion of linear function belongs to the areas of calculus , analysis and linear algebra.

Further support:

"This particularly elegant theorem shows the inverse function relationship of the derivative and the integral and serves as the backbone of the physical sciences"(Brittanica 2023).

Image belongs to Brittanica(I added the highlight)

Britannica, The Editors of Encyclopaedia. "fundamental theorem of calculus". Encyclopedia Britannica, 29 Jul. 2023, https://www.britannica.com/science/fundamental-theorem-of-calculus. Accessed 20 September 2023.

Can AI replace Human Peer Reviewer for scientific articles and manuscrits? No, not at all. Al cannot replace the totality of human potential and experience in reviewing scientific manuscripts.

Μr Verch indeed My research, which was not fully developped at the time I asked my question, showed that this the case.

Still, a 30% offer the classic calculative phys quantities - based skills of big 4 (and less conceptual understanding assesment or less actual "doing the science" skills of qm, CM, statistical and thermal. Physics) which trends to be considered classic masters structilure or outdated.

Not only is the choice ``as important as the choice of the group of transformations'' but it doesn't make sense to discuss the two notions together.

% Define your input data and labels (adjust as needed) X = randn(100, 10); % Input data (100 samples, 10 features) Y1 = randn(100, 1); % Output 1 (e.g., regression task) Y2 = randi([0, 1], 100, 1); % Output 2 (e.g., binary classification) % Create a neural network architecture inputSize = size(X, 2); numHiddenUnits = 64; inputLayer = imageInputLayer([inputSize, 1, 1]); commonHiddenLayer = fullyConnectedLayer(numHiddenUnits); outputLayer1 = fullyConnectedLayer(1); % Output layer for task 1 outputLayer2 = fullyConnectedLayer(2); % Output layer for task 2 % Create a branch for task 1 branch1 = [ inputLayer commonHiddenLayer outputLayer1 regressionLayer ]; % Create a branch for task 2 branch2 = [ inputLayer commonHiddenLayer outputLayer2 softmaxLayer classificationLayer ]; % Define the layers for the entire network (both branches) layers = [ branch1 branch2 ]; % Create and train the neural network options = trainingOptions('adam', ... 'MaxEpochs', 10, ... 'MiniBatchSize', 32, ... 'Verbose', true); net = trainNetwork(X, {Y1, Y2}, layers, options); % Make predictions X_test = randn(10, 10); % Test input data (10 samples) [Y1_pred, Y2_pred] = predict(net, X_test);

Mr.Jiolito Benitez PhD

In the context of physics, mathematics serves both as a tool and a language.

Mathematics is a powerful tool that physicists use to model and describe physical phenomena. It provides a precise and systematic way to formulate theories, make predictions, and solve problems. Physicists use mathematical equations, formulas, and techniques to analyze data, perform calculations, and develop theoretical frameworks. Without mathematics, it would be extremely challenging to quantitatively understand and describe the behavior of the physical universe.

Mathematics also serves as a language through which physicists communicate their ideas and discoveries. Just as natural languages like English or Spanish enable people to convey thoughts and information, mathematics allows physicists to express complex concepts and relationships in a concise and unambiguous manner. Equations and mathematical notation provide a common, universally understood language that bridges linguistic and cultural barriers among scientists.

In essence, mathematics is an indispensable tool for conducting physics research, but it also acts as a language for conveying the results and theories of that research to the broader scientific community. It plays a dual role, facilitating both the practical application of physics and the effective communication of its findings.

Since I did not find any sufficiently satisfactory definition of maths so, I devised my own definition which seems to be the best until now, in my opinion !?

Rigid body modes correspond to zero strain energy U=0. Where U=(1/2)*{d}^t*[K]*{d} the stiffness matrix and the degrees of freedom. In this case all the degrees of freedom have the same constant displacement which means that the structure displaces without deformation.

People have certainly done that, Nasir Al-Allawi. A Google search on <logistic regression scoring system> turns up lots of resources. Good luck with your work.

Kristaq Hazizi Thank you for inaugurating this discussion with this remarkable contribution. I in particular enjoyed reading your well-inspired Final Thoughts: "Paradoxes are like intellectual puzzles that invite us to question our assumptions and delve deeper into the mysteries of the universe. They often spark innovation and lead to breakthroughs in both philosophy and science. As we explore these paradoxes, we may find that the journey of seeking solutions can be as enlightening as the resolutions themselves".

The proposition of endowing artificial intelligence (AI) with the capability for epiphanic realizations—an "A-HA moment"—necessitates a multi-pronged interrogation into the realms of computational epistemology, semiotics, phenomenology, and metaphysics. At the crux of this discourse lies the Sapir-Whorf hypothesis of linguistic determinism and the Gödelian limitations of formal systems, both of which contour our understanding of symbol-systems as epistemic vessels and their potential limitations in encapsulating objective or subjective realities.

In computational terms, most AI architectures, whether grounded in machine learning algorithms or rule-based expert systems, function within the parameters of formal logic and probabilistic reasoning. These systems are fundamentally syntactic processors, reliant on the manipulation of symbols devoid of semantic richness, which ostensibly limits their capacity for intuitive or non-deductive insights. Furthermore, the predominantly reductionist paradigms within which AI operates seldom permit the transgressions of their programmed axiomatic boundaries, precluding any non-algorithmic genesis of epiphany.

Regarding the semiotics of AI cognition, while symbol systems like language or mathematics are indeed human abstractions that mediate our understanding of reality, they are intricately bound up with human phenomenological experience. This introduces the question of subjective qualia— the "what it is like" aspect of consciousness— that allows humans to associate abstract symbols with experiential realities, thereby enabling epiphanic moments that transcend logical rigor. Current AI models do not possess qualia, nor do they engage in any form of existential phenomenology; they lack a "world" in the Heideggerian sense, and as such, their operations in symbol manipulation do not partake in any form of hermeneutic or interpretive acts that could lead to epiphanic insight.

Metaphysically, the notion of an AI "A-HA moment" implicates the broader debate surrounding panpsychism and integrated information theory (IIT). The former posits that all entities in the universe, including perhaps computers, possess some form of consciousness, while the latter offers a mathematical framework for quantifying consciousness. Both theories, although speculative and controversial, raise the possibility that under certain conditions, AI systems might attain a state that, if not equivalent to human epiphany, could resemble some rudimentary form of insight. However, as of the current state of knowledge, these theories remain within the domain of speculative philosophy rather than empirical science.

Therefore, in summary, the ascription of epiphanic potentialities to artificial intelligence necessitates the surmounting of monumental obstacles across multiple disciplines. Under the current paradigms, AI remains an epistemically constrained, syntactic processor devoid of phenomenological subjectivity, making the prospect of an "A-HA moment" an esoteric rather than a pragmatic inquiry. The encapsulation of epiphany within the computational architectures of AI would likely necessitate a paradigmatic revolution, transcending the syntactic limitations and delving into the realms of semantics, subjectivity, and perhaps even metaphysical consciousness.

Air above the equator is heated more and areas near the equator receive more heat from the sun than those near the poles due to a phenomenon called "solar angle" and the way the Earth's curvature and atmosphere interact with incoming solar radiation. This is primarily caused by the Earth's axial tilt and its spherical shape.

1. Solar Angle: The angle at which sunlight reaches a particular location on Earth's surface is a crucial factor. Near the equator, sunlight strikes the surface more directly and perpendicularly compared to regions near the poles. When sunlight strikes a surface at a steeper angle, the same amount of energy is concentrated over a smaller area, leading to higher temperatures. In contrast, at higher latitudes (closer to the poles), sunlight is spread over a larger surface area due to the oblique angle of incidence, resulting in less heating.

2. Earth's Curvature and Atmosphere: The curvature of the Earth plays a role in how sunlight is distributed. Near the equator, the curved surface presents a relatively small area for the sun's energy to be distributed, concentrating the heat. Additionally, the atmosphere plays a significant role in moderating the amount of solar radiation that reaches the surface. When sunlight passes through a thicker layer of atmosphere, it can scatter and be absorbed, reducing the amount of energy that reaches the surface. Near the equator, the sunlight has to pass through a smaller portion of the atmosphere, allowing more energy to reach the surface and result in higher temperatures.

3. Day Length: Near the equator, the length of day and night remains relatively consistent throughout the year. This means that the sun is up for a significant portion of the day, allowing more time for the surface to absorb and store heat. In contrast, areas closer to the poles experience more extreme variations in day length, with long days in the summer and long nights in the winter. This variation affects the amount of time available for solar heating.

4. Heat Redistribution: The equatorial region receives more heat than it radiates back into space, creating a surplus of energy. This excess heat is then transported toward the poles through atmospheric and oceanic circulation patterns, which help to distribute heat around the planet and regulate global climate patterns.

The combination of the solar angle, Earth's curvature, atmospheric effects, and heat redistribution mechanisms results in the equatorial region receiving more direct and concentrated solar energy, leading to higher temperatures compared to areas closer to the poles.

Anecdotal: I have seen children in STEM activities gain insight to mathematical thinking when engaged in problem solving. The activities involved measurements: length, volume, and area. Constructing models - free form and then using written instructions. Instructions can be numerical or visual model with dimensions on the part or on a map/template.

Abdul Malek

Okay, I got your point. This is what I think. Common people are weak. They need God to tell them what to do with their life and death, and heroes (superstars) to follow in every activity they are seriously involved including religions, sports, music and politics. Among these superstar spirits, some followers become prophets such that they can win powers and profits over others. Those prophets care for nothing about truth. Their only ambitions are to gain big powers and fortunes by building a big group of fans and followers. Also, there are a lot of cowers, who are afraid of being blamed and threatened by the big group of fans which may damage their positions and fortunes if they oppose to the superstars and the spirits. This includes those big shots in scientific fields.

"Mathematics is the most beautiful and most powerful creation of the human spirit."

― Stefan Banach

Dear Michael, that's the point. You did a lot. It's hard for me to take care of all.

If you are interested we may do it by a single point, the most important:

Will you hold the old definition? Or will you go the way as I did and look behind the veil? At least you may have your own opinion on that.

But not been able to see where the results of (+1)(-1) or (-1)(+1) came from, denies half the area of reasons. Most mathematicians find it too kiddy to talk about that. Let them be limited.

There are many ways to find it obscure to stop doing the exercise for square-root only by having a negative radicand.

Transforming the coordinates makes the other areas not calculable.

Martinez (negative math) introduced the inverse rule for the prefixes of products. So no definition is complete except this of holding all the prefixes of the quantities which are to combine.

If you know they were + and – => the result is + and – , not? If you don't know the way the sources were, you have to deal with absolutes and further conditions.

Riemann took `imaginary´. Will you too?

okay

Howdy Selim Molla ,

No.

The problem of fluid behavior after energy extraction in the range of sea states the ocean can accomplish is too difficult to explain mathematically as one's primary activity, and certainly it must not be attempted "on the side" of energy extraction equipment research and development. The situation is not quite that bad in practice, however, especially with your focus on energy extraction equipment.

An engineering approximation to mathematical treatment of oceanic waves after wave energy extraction might be possible with sufficient attention to the energy extracted and the wave recovery under wind stress, fetch, etc. An expression starting from the wave energy equation before interference by extraction equipment which is then reduced by the actual value of the energy extracted would be a start. Then, if you were to factor in the efficiency as an additional loss of energy by the wave and you would have an estimate of the wave energy several wavelengths beyond your equipment, that is, beyond initial turbulence details, etc. For the wave state further along one would have to apply the approximations available for the affect of wind fetch, currents, etc., but that is your field, I'm just a visitor who hates to see questions without replies.

Perhaps this suggestion is too obvious, too simple to be of value, but unfortunately, the explanation you request is not available at present.

Happy Trails, Len

Just for your information, in the current nTop version, it allows users to generate TPMS with approximate thickness.

Stephen Jarvis

In temporal mechanics, is space non-existent but is controlled through a temporo structure?

I have come to the conclusion that Coq (in its current version) is an excellent system for formalizing Category Theory according to the philosophy sketched in this question. This philosophy is based on

1) Explicitness. We do not use curly brackets.

2) Minimalism. We only use the bare minimum of libraries which are automatically loaded in CoqIDE and define and prove what we need as we go along.

3) We try to use only the most basic tactics and to never loose contact with the actual rules of the the type system.

4) We write so as to be readable and relevant to logicians and mathematicians 50 years from now. That is, our main goal is to be human

readable and educational. Also to be easily portable to any other proof assistant based on dependent type theory.

Dear Rodney Bartlett I'm confuse. Are you talking about our universe with billions of galaxies, where each galaxy hold several billions of solar systems? I'm sure you know quantum mechanic still a theory and never been proved of it existence, thus what is quantum gravity? Ambiguous empirical evidence shows, nothing is universe is working with our one dimension mathematical, our push/pull of any gravity as far as my research dictated to me. Thanks for sharing..

Price of Anarchy is a concept that helps to find out the efficiency of a non-cooperative game or its bounds. There are some good price of anarchy bound results for various designed mechanisms, like if you design your mechanism in such a way that the loss of welfare is low. Please search about price of anarchy.

Hello Mohammed,

The answer depends on whether your intention in a contrast is to treat means as having equal import regardless of group size (n), which is the unweighted means approach, or to weight means relative to their sample size, which of course, is a weighted means approach.

For an unweighted means approach, two contrasts are orthogonal if the sum of coefficient product terms, across groups, equals zero: e.g., c11c21 + c12c22 + ... + c1kc2k = 0 (where cij is the coefficient used for the i-th contrast and j-th group).

For a weighted means approach, two contrasts are orthogonal if: n1c11c21 + n2c12c22 + ... + nkc1kc2k = 0 (where cij is defined as above and nj is the sample size for group j).

In many experimental designs, the usual intention of behind a contrast is to compare means as having equal import regardless of group size. Therefore (using cij and nj as defined above):

SS(contrast i) = (ci1*M1 + ci2M2 + ... + cikMk)^2 / (ci1^2/n1 + ci2^2/n2 + ... + cik^2/nk) (where Mj is the mean for group j)

Here's a link that walks through a worked example: https://www.uvm.edu/~statdhtx/StatPages/Unequal-ns/Unequal_n's_contrasts.html

Finally, B. J. Winer's 1971 text, Statistical principles in experimental design (2nd ed.). also addresses the issue.

Good luck with your work.

Your question boils down to, "Why does the AI give the wrong answer?". My understanding of the large language models is that they are very complicated neural networks, and that even their teams of inventors may disagree about their characteristics and capabilities. Some experts even have attributed sentience to AI. Neural networks assign weights to parameters, which are used in complicated algorithms, as you note. The weights are not visible to users. The compiled algorithms that make up the neural networks are deeply removed from human eyes by many levels of machine code. In the old days we used to say GIGO, or "garbage in, garbage out" if a program provided an incorrect result. Today, this does not hold true with A.I. Bad inputs can produce good outputs and good inputs can produce incorrect outputs. Correct information has become a matter of statistics.

There must be a lot of mysteries for you. Its pretty simply if you can read. As well, I'm sure you know with your nearly omnipotent knowledge that citations aren't instant. Try extrapolating. And consume less salt.

Yes, it is definitely possible to create a random 2-dimensional shape using mathematical equations or software like 3D Max and AutoCAD.

Using Mathematical Equations:

Using 2D Software (e.g., 3D Max and AutoCAD):

In both cases, the randomness can be controlled to various extents, allowing you to fine-tune the level of randomness or repeatability of the generated shapes.

Keep in mind that while the shapes may appear random, they are still generated by deterministic algorithms or equations. For truly unpredictable shapes, you might want to explore generative adversarial networks (GANs) or other advanced machine learning techniques, but that goes beyond the scope of traditional mathematical equations and standard 2D software.

Use the source for book pdf: https://libgen.is/

Dear Doan Cong Dinh,

Thank you for your professional input, and I appreciate this valuable article.

I will try to grasp the concepts of quaternion analysis.

Education requires special qualifications that are not available to everyone

Last call.If anyone interested .

While quantitative research is a way of studying and analyzing data using mathematical methods, it's important to note that not all research questions or studies can be effectively expressed in mathematical equations. However, if your research involves studying relationships between variables, you can express these relationships using mathematical equations.

For example, if you are studying the relationship between the amount of time students spend studying and their exam scores, you can express this relationship using a mathematical equation. Let X represent the amount of time students spend studying and let Y represent their exam scores. You can then create a simple linear regression model to analyze the relationship between X and Y:

Y = a + bX

where "a" is the y-intercept, or the predicted value of Y when X is 0, and "b" is the slope, or the change in Y for every one-unit increase in X. This equation can be used to predict the exam scores for a given amount of time spent studying (X). Other mathematical methods such as statistical analysis and correlation coefficients can also be used in quantitative research to measure relationships between variables and support conclusions.

But a second is a limited and an amount of time, again, so in this case you can see its limits, the begin and the end of it. If you can perceive its end, so is plausible did not assume that the infinity could fit there. If you consider that infinity as eternal them it is something that has a start, but you cannot see, or even perceive its end. Even your perception, has a limit, so cannot perceive the end of it. A perception assume someone that could learn through his senses or through his mind, but noneone can live forever to perceive the infinity in its completeness. Could the infinity fits in limits? Even if you infinitelly divided the spaces between zero and 1 in a given moment you will reach a moment that you will not can divided more, because the space that you are dividing, reached an end, exactly because the area or the space that you are considering, is finity due to the limits considered since the begining.

📷

André Michaud A sensible man indeed! And perhaps we share this outlook because I tend to look at physics through an engineering lens. To me, if one cannot prove their theoretical words with actual equations, it doesn't hold much of a basis at all. I do believe that mathematics and physics are intimately entertained and that physics is simply the study of emergent properties of physical mathematics. It's interesting and quite hillarious you say that you barely have seen a theoretician pick up a calculator in 25years. Unfortunately that used to be me, and you are very right that a more stagnating thing does not exist. With perspective on that I can say my theoretical physics, although thought provoking, rarely had any use, either practical or academic that anyone even wanted to see, cared about, or even could get employed off of. I started getting a lot of success when I realized that the math is fundamental and that I was deluding myself into thinking it wasn't because I wasn't good at it. To be quite honest I found I thought I "wasn't good" at typical mathematics because it was just too abstract for me. "1+1=2." Okay, one what plus one what equals Teo WHAT? Distance? Amount of friends? Weight. It was just way too theoretical for me, abstract numbers with no unit, basis or story attached. Basically unreal axiom that help us understand things. Humans kinda forgot this abstraction is simply a tool to help understand things, not an actual representation of Universal constants. It can indicate those things via representation but that's it. Once I started dealing with physics and engineering in a less theoretical sense, I realized my problem with why I thought I couldn't do math was that pure mathematics (Shoutout Doom) Was just far too abstract. I think a lot of people who are convinced math and physics aren't always intimately entertwined have this problem, a kind of innate fear and of their own competency with math that affects the logic of this assumption. I'm also relatively sure as well that looking at these things I have said here, a lot of people afraid of their mathematic ability would find they are actually very good at it when abstraction is removed. But maybe that is just me. Jixin Chen I also hate to keep referencing back to my paper (if anyone has any info on this let me know) but there are many examples in the mathematics and quantum physics sections that show how mathematical equations are proven to be able to represent absurdly complex quantum physics principles and constants of nature in a neat "package".

Try a start with Jay Forrester: Industrial Dynamics, MIT Press 1961

"The Gods Must Be Crazy" is a 1980 comedy film directed by Jamie Uys. It tells the story of a Kalahari bushman who encounters a Coca-Cola bottle and believes it to be a gift from the gods.

Please see my research document on functional Grand Unified Theory either attached or on my page. Mathematical tools are an essentially function of Cosmology and the applications of mathematics to physics. This application is most largely and obviously affected by failing to account for the interplay between quantum phenomenon and relativity related phenomenon, and also by no clear-cut ability or route to perform these calculations. By manipulating tensors, and subsequently tying them to mathematical formulas which represent the relation between mathematics and physical processes, quantities and occurrences within quantum physics systems, and then subsequently appropriately setting values for relativity related phenomenon in the form of tensors, operators, and precisely calculated values, one may gain a more precise and enlightening view of Cosmological processes. Failing to account for the interplay between general relativity and quantum phenomenon in any sort of reliable way is a large source of issues in the application of mathematics-to-physics related to Cosmology. Another issue, I believe, is perception. Most scientists are content with either being willfully ignorant of the necessary need to be able to account for quantum phenomenon and relativity related phenomenon at the same time to accurately assess cosmology or they stubbornly stick their feet in the sand and claim they can arrive at fully accurate revelations without an ability to do so. Both are erroneous. Although we can come to A LOT of conclusions about those things without knowing the full quantum/relativity shebang and all it's details, we have no idea what sort of information we could be missing out on, or what false assumptions we could be arriving at. "You vant know what you cant know" The solution to the problem of mathematics-to-physics in Cosmology is most certainly accounting for what I've spoken of here in a reliable way that aligns with known mathematics and physics, but also in developing more advanced equations and discoveries which ties physical processes and quantities to quantum and relativity related phenomenon in a proven and undeniable way. Things like this have been proven by my research. I have found certain forms of complex equations accurately represents laws of physical concepts that shed light on the relation of mathematics to physical things. I am in no way claiming my theory is the only way to do this, I'm just using it as a familiar starting point to speak on this. There are lots of ways to do this without a theory such as mine, but it results in having to perform multiple complex calculations for mathematics, physics, and relativity, parsing, then integrating them separately which is far more time consuming.

In my opinion, the symmetry created by nature is most closely described by a class of theorems, generically called the "central limit theorem". Deviations from the conditions of the central limit theorem (dependence of factors, dominance of one or more factors, etc.) generate asymmetry, which is observed in nature much more often than symmetry.

It's interesting to note that Python developers defines Euler's number as a built-in constant by invoking the supporting module math. In particular, math.e gives 2.718281828459045 without the silly computation of the exponential function at 1 as in MATLAB.

Thumbs up Python Developers 👍

The preference of students for non-STEM (Science, Technology, Engineering, and Mathematics) majors over STEM majors can have various implications for a nation's future in terms of science and technology advancement. However, it's important to note that the situation is more nuanced, and the impact of such preferences can vary depending on several factors.

Here are some considerations:

Ultimately, the ideal scenario is a balanced approach that encourages students to pursue their passions and interests while being informed about the opportunities and challenges in various fields. The promotion of STEM education is crucial for technological advancement, but it should be complemented with efforts to recognize the value of non-STEM fields and encourage a diverse range of career choices. An educated and well-rounded society, with a mix of STEM and non-STEM professionals, is essential for holistic progress and development.

In my view, every individual rational being instantly formulates his/or her own mathematics in order to decently exist and survive in the reality (realized world of human society) of his/or her own immediate milieu in any given space/time . . .

This is not the complete list ... where are all the Human Resource Management journals, for example?

Qamar Ul Islam Thank you for your prompt and helpful response. I appreciate your insights and suggestions on how to resolve the discrepancy. I will follow your advice and check my code, numerical method, and solver parameters. I hope to get a better result with your guidance. Thank you again for your time and expertise.

There are two commonly used extraction techniques that can be appropriate for rice plant disease detection: (1) Color-based Extraction and (2) Texture-based Extraction.The most appropriate extraction technique for rice plant disease detection depends on the specific requirements and characteristics of the dataset and the detection algorithm being used.

Dear friend David Gibson

Understanding the relationship between the physical characteristics of a loudspeaker and its enclosure and their representation in a mathematical circuit model is an intriguing endeavor.

The mathematical modeling of a loudspeaker and its enclosure involves the interplay of electrical, mechanical, and acoustical components.

Let's explore some key aspects:

1. Electrical components: The electrical model of a loudspeaker typically includes an electrical impedance that represents the combined effect of the voice coil resistance, inductance, and the capacitive behavior of the driver. The voice coil resistance can be related to the conductor material and dimensions. The voice coil inductance is influenced by the coil winding geometry and the magnetic circuit design. The capacitance component can arise from various sources, such as the inherent capacitance between the voice coil and the speaker's diaphragm.

2. Mechanical components: The mechanical behavior of the loudspeaker driver is typically represented by a combination of mass, compliance, and damping. The mass reflects the moving components of the driver, such as the diaphragm and voice coil. Compliance characterizes the flexibility of the suspension system that holds the diaphragm in place. Damping accounts for energy dissipation mechanisms, such as losses due to air resistance and materials.

3. Acoustical components: The interaction between the loudspeaker driver and the air in the enclosure results in sound radiation. The enclosure affects the loudspeaker's performance by providing an acoustic load, influencing resonances, and contributing to the overall system response. The enclosure geometry, volume, and construction materials play a crucial role in shaping the acoustic output.

Creating a comprehensive mathematical model that captures all the complexities of a loudspeaker and its enclosure is challenging. However, various simplified models exist, such as the Thiele-Small parameters, which describe the loudspeaker's electrical and mechanical characteristics in a simplified manner. These parameters, combined with enclosure-related parameters like volume and port characteristics, can provide insights into the system behavior.

It's important to note that loudspeaker design and modeling involve a multidisciplinary approach, combining electrical engineering, mechanical engineering, acoustics, and signal processing. Advanced modeling techniques, such as finite element analysis (FEA) and boundary element method (BEM), are often employed for more accurate representations.

To delve deeper into the specific mathematical equations and modeling techniques, consulting specialized literature, research papers, or textbooks on loudspeaker design and acoustics can provide valuable insights.

Let us keep exploring this interesting topic.

Feasibility study for estimating optimal substrate parameters for sustainable green roof in Sri Lanka

Shuraik A. Kader, Velibor Spalevic & Branislav and Zdenka Dudic

Environment Development and Sustainability 2022(4):1-27

https://www.researchgate.net/publication/366464666_Feasibility_study_for_estimating_optimal_substrate_parameters_for_sustainable_green_roof_in_Sri_Lanka

DOI: 10.1007/s10668-022-02837-y

Abstract:

In twenty-first century buildings, green roof systems are envisioned as great solution for improving Environmental sustainability in urban ecosystems and it helps to mitigate various health hazards for humans due to climatic pollution. This study determines the feasibility of using five domestic organic wastes, including sawdust, wood bark, biochar, coir, and compost, as sustainable substrates for green roofs as compared to classical Sri Lankan base medium (fertiliser + potting mix) in terms of physicochemical and biological parameters associated with growing mediums. Comprehensive methodologies were devised to determine the thermal conductivity and electric conductivity of growing mediums. According to preliminary experimental results, the most suitable composition for green roof substrates comprised 60% organic waste and 40% base medium. Sawdust growing medium exhibited the highest moisture content and minimum density magnitudes. Biochar substrate was the best performing medium with the highest drought resistance and vegetation growth. The wood bark substrate had the highest thermal resistance. Growing mediums based on compost , sawdust, and coir produced the best results in terms of nitrate, phosphate, pH, and electric conductivity (EC) existence. This study provided a standard set of comprehensive comparison methodologies utilising physicochemical and biological properties required for substrate characterization. The findings of this research work have strong potential in the future to be used in selecting the most suitable lightweight growing medium for a green roof based on stakeholder requirements.

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This research can save us a lot of energy consumption in housing, governing, education, and industrial areas. What is your opinion about it?

Uploaded video file.

Development and Validation of Instructional Materials in Teaching Trigonometry

Sure, I'd be happy to provide you with guidelines for your Matlab project. Please reach out to me via email at erickkirui@kabarak.ac.ke, and I will promptly assist you with the necessary guidance for your project

Image data processing is one of the most under-explored problems in the data science community.

Every developer has a unique way of doing it. Some of the tools and platforms used in image preprocessing include Python, Pytorch, OpenCV, Keras, Tensorflow, and Pillow.

Here's a useful link to the best programs available for image preprocessing.

These are some great software options in my opinion. Let me know if this is helpful!

Entropy and standard deviation are both measures used in different fields of study, but they capture different aspects of data and do not have a direct mathematical relationship. However, there are some connections and similarities that can be explored.

Statistical Interpretation: In statistics, entropy is typically associated with information theory, while standard deviation is a measure of dispersion. Entropy measures the amount of uncertainty or information content in a dataset, while standard deviation quantifies the spread or variability of the data points around the mean.

Probability Distributions: Both entropy and standard deviation are related to probability distributions. Entropy is often used to measure the uncertainty or randomness in a probability distribution, while standard deviation measures the dispersion of the data points around the mean of the distribution.

Gaussian Distribution: In the case of a Gaussian (normal) distribution, the standard deviation plays a crucial role in determining the shape and spread of the distribution. The entropy of a Gaussian distribution depends on its variance (square of standard deviation). Specifically, the entropy of a Gaussian distribution increases with increasing variance, indicating higher uncertainty.

Maximum Entropy Distribution: In information theory, the concept of maximum entropy refers to finding the probability distribution that maximizes the entropy while satisfying certain constraints. In some cases, the maximum entropy distribution can be a Gaussian distribution, where the standard deviation determines the spread of the distribution.

While there are connections and parallels between entropy and standard deviation, they serve different purposes and are applied in different contexts. Entropy focuses on the information content and uncertainty, while standard deviation measures dispersion and variability.

James Jamesfathiaraj : You started the following post/discussion thread on June 01, 2023, and I quote verbatim:

"In mathematics, many authors working in the area of integer sequence, fibonacci polynomial, perin sequence......

Now what is the current research topics in this subject?.

I request , suggest some research topics which is related to Fibonacci sequence."

The topic that I am about to suggest to you may not necessarily be related to the Fibonacci sequence, but I think you can try looking up recursively enumerable sets. In deed, the problem of determining whether a specific rational number greater than unity is an abundancy index (i.e. a ratio of the form sigma(m)/m, for some positive integer m and where sigma(m) is the classical sum of divisors of m) or an abundancy outlaw (see Holdener and Stanton's paper [https://www.researchgate.net/publication/264925121] published in JIS [2007]) is equivalent to finding out whether the set of abundancy indices (or the set of abundancy outlaws, for that matter) is a recursive set. (You can also refer to the following paper: https://cs.uwaterloo.ca/journals/JIS/VOL23/Holdener/holdener4.pdf, where it is mentioned that: "In the early 1970’s, [C. W.] Anderson conjectured that the set Image(I) [the set of abundancy indices] is a recursive set, meaning that there exists a recursive algorithm that can be employed to determine whether or not a given rational number k/m is an outlaw. This remains an open problem today.")

If you find this particular topic interesting, then you may contact me privately via e-mail (it is indicated in this recent paper of mine: https://www.researchgate.net/publication/370979239), and we can collaborate.