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The proof of the Riemann hypothesis

Level of difficulty Hard

Hello dear Habrians, the text below outlines the proof of the Riemann hypothesis, which is awaiting verification at CMI (Clay mathematical institute). So let's get straight to the proof

2.6 If ƒ and g are power series with no constant term, then

T{1+f(s)] [1+ g(s)]} = T{1+f(s)+g(s)}.

Remark. Weakly analytic functions have a formal expansion as a power series near the origin. Formula 2.6 is just the linear approximation of this expansion (more precisely this is

on the branched double cover of the complex s-plane given by √5). This implies

2.6 T(3)T(s) or

2.7 √T(1+8)T(1+8/2)

which gives us the uniform constant 1/2 needed in 3.3 of section 3.

3. THE PROOF OF RH

In this section I will use the Todd function T(s) to prove RH. The proof will be by contradiction assume there is a zero & inside the critical strip but off the critical line. To prove RH, it is then sufficient to show that the existence of 6 leads to a contradiction..

Given b, take a = b in 2.1 then, on the rectangle Ka), T is a polynomial of degree k{a}.

(3.1)

F(s)T(1+((s+b)}-1

Consider the composite function of s, given by From its construction, and the hypothesis that ((b) = 0, it follows that 3.2 F is analytic at 80 and F(0) = 0. Now take fg F in 2.6 and we deduce the identity

3.3 F(s) 2F(s).

Since C is not of characteristic 2, it follows that F(s) is identically zero. 2.3 ensures that T is not the zero polynomial and so it is invertible in the field of meromorphic functions of s. The identity F(s)=0 then implies the identity ((s)= 0. This is clearly not the case and gives the required contradiction.

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Preserving Line Breaks and Skips in Markdown with React: A Practical Solution (marked.js)

Level of difficulty Easy

Markdown is widely used for its simplicity and readability. However, when it comes to handling line breaks as they appear in a TextArea input, developers often face challenges. In this article, we discuss a common problem encountered in rendering Markdown in React applications, particularly preserving line breaks, and provide a practical solution that we've found effective.

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Transitioning from JavaScript to TypeScript in React Projects: A Strategic Move for the Future

Level of difficulty Medium

In the dynamic world of software development, the choice of programming languages and tools can significantly impact the productivity and future-readiness of projects. My recent decision to transition our React project from JavaScript to TypeScript has sparked discussions, and I believe it's a story worth telling on a broader platform like Habr. Here, I want to delve into the rationale behind this move and the long-term benefits it presents.

TypeScript: A Steeper Curve for a Smoother Ride

TypeScript's reputation for complexity is not unwarranted, given its static typing and the need to master new concepts such as interfaces and generics. The setup and configuration require a meticulous approach. However, these hurdles are a small price to pay for the robustness and maintainability they introduce to your codebase. Drawing from my experiences with Angular, where TypeScript is employed by default, I've seen firsthand how TypeScript can elevate the quality of development, even if it demands a higher initial investment in learning and configuration.

The TypeScript Advantage in React Development

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Breaking Down Barriers: Building a Transparent DevOps Culture

Level of difficulty Medium

Numerous organizations across the globe are increasingly investing in DevOps to gain a competitive edge within their region. A survey echoes the same in the form of a depiction of the DevOps market size predicted to touch the enormous amount of $25.5 billion by 2028 at a CAGR of 19.7%. Not only this, even 86% of organizations have valued DevOps a lot.

Such an increase in DevOps adoption has spiked a concern over creating a healthy DevOps culture. This post sheds light on DevOps culture's meaning and how to cultivate it within your organization using proven strategies and modern DevOps tools.

What is a DevOps culture?

A DevOps culture is mainly focused on adopting values that take the DevOps principles and integrate them into relevant tools and methodologies. In other words, you can call it a bunch of values that emphasize creating an environment of constant communication and learning and a strong feedback structure.

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Artificial Intelligence and Machine Learning from the perspective

Hello, everyone! I'm Stanislav Kondrashov, and today I'd like to dive into the fascinating world of Artificial Intelligence (AI) and Machine Learning (ML). These are two of the most transformative technologies of our time, and they have the potential to reshape our world in numerous ways.

What is Artificial Intelligence?

Artificial Intelligence is the concept of creating machines or computer systems that can perform tasks that typically require human intelligence. These tasks include problem-solving, speech recognition, decision-making, language understanding, and more. AI systems aim to mimic human cognitive functions, and they come in various forms, from basic rule-based systems to advanced machine learning models.

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Detecting the Undetectable: An Experiment on AI Text Rewriting

Level of difficulty Medium

The Significance of AI Detectors

In an era of unprecedented technological advancement, Artificial Intelligence (AI) has permeated almost every facet of our lives, including content creation and academic research. With the advent of sophisticated AI writing algorithms, the risks of plagiarism, data duplication, and intellectual property theft have significantly increased. It has resulted in the developing and popularizing of AI-powered plagiarism detectors—tools designed to identify copied or suspiciously similar content. Platforms like Copy Leaks, ZeroGpt, and Sherlock AI Detector use complex algorithms to scan vast swathes of online content, providing an invaluable service in safeguarding the integrity of academic, journalistic, and creative works.

Experiment Objective and Methodology

The integrity and originality of scholarly work form the cornerstone of academic integrity, a foundational tenet underpinning higher education and scientific research. With the advent of increasingly sophisticated artificial intelligence (AI) algorithms capable of generating human-like textual content, the sanctity of this cornerstone is imperiled. Consequently, the capacity to discern between original human-authored texts and AI-rewritten ones has metamorphosed into a pressing yet relatively unexplored technological and ethical imperative. This experiment aims to rigorously scrutinize the performance of extant AI text detection algorithms in identifying rewritten scholarly content. By doing so, we aim to assess the current vulnerabilities in the system and provide empirically informed recommendations to bolster the mechanisms safeguarding academic probity. The implications of this research extend beyond academia, resonating across sectors where the authenticity of textual content is pivotal. 

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What Is Base64 and Why It Is Important?

Level of difficulty Easy

In the world of computers and digital communication, data is everything. Data is constantly sent and stored, from text messages to photographs shared on social media. However, data in its raw form is not always straightforward to work with. This is when Base64 comes into play. In this post, we will look at what Base64 is, how it works, and why it is significant in the world of computing.

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Guide to Generating iOS Certificates and Profile Files for App Development

Level of difficulty Easy

Guide to G

Introduction: Currently, many companies use H5 frameworks for app development, and among these H5 frameworks, uniapp is the most mature. Therefore, hbuilderx has become the preferred choice for developers. However, packaging an app requires a certificate. So how do we obtain this certificate? Generating an Apple certificate is relatively complex, so here I will focus on the process of generating an iOS certificate.

Currently, many companies use H5 frameworks for app development, and among these H5 frameworks, uniapp is the most mature. Therefore, hbuilderx has become the preferred choice for developers. However, packaging an app requires a certificate. So how do we obtain this certificate?

Generating an Apple certificate is relatively complex, so here I will focus on the process of generating an iOS certificate:

If you don’t have an Apple Developer account yet, you need to register for one in the Apple Developer Center. The tutorial for registering an Apple Developer account is as follows: Tutorial for Registering an Apple Developer Account (in Chinese).

Once you have the Apple Developer account, you can follow the steps below to create the certificate.

First, let’s create a p12 certificate. The process for creating a p12 certificate is as follows:

1.Log in to the Apple Developer backend and click on the “certificates” menu to enter the certificate management page. Click on the blue plus sign on the right side to start creating a certificate. When creating the certificate, choose the “iOS Distribution Ad Hoc and App Store” type, which includes both real device testing and distribution types (ad hoc for testing, app store for distribution). Please do not choose the “Apple” or “Dev” types of certificates, as they cannot be used for cloud packaging in hbuilderx.

2.During the creation of the certificate, it will ask us to provide a csr file, as shown in the image.

3.Switch to Appuploader.

Appuploader home — A tool improve iOS development efficiency such as submitting IPA to App Store and managing iOS certificates.

Use the function of generating iOS certificates in Appuploader to create this .p12 file, as shown in the image. After generating the .p12 file, download it to your local computer.

Go back to the Apple Developer Center. The .p12 certificate generated by appuploader will be synchronized back. You can then use appuploader to generate the p12 format Apple certificate.
With the above steps, the p12 packing certificate has been generated.

Now, let me teach you how to generate the profile file required for packaging:

1.Enter the Apple Developer Center and click on “Identifiers” to create an app ID (package name). After creating it, it should look like the image below. Note that the format of the package name is typically in the format of a Java package name: com.xxxxxx.yyy.

2.If you have already created the app ID from the previous step, you can then enter the “profiles” menu to start creating the profile file.

3.When creating the profile file, choose “

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How to deploy a Healthcare Application on AWS EC2

Level of difficulty Medium

AWS provides a full range of services designed specifically to satisfy the specific requirements of the HealthCare industry. This tutorial is going to show how to set up a HealthCare application on Amazon EC2.

One of the foundational features of AWS is Amazon Elastic Compute Cloud (EC2), which offers scalable computational capacity in the cloud. On EC2 instances, HealthCare applications may be quickly scaled and deployed, guaranteeing high availability. Here is an example of a HealthCare application being deployed on EC2:

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How to build an Electron desktopCapturer screen picker dialog

Level of difficulty Easy

Since Electron's desktopCapturer API doesn't provide a desktop picker dialog, you need to implement it yourself.

Disclaimer: I don't want to focus on the UI part, so you can use whatever you prefer, such as React, Vue, etc. You can find a simple HTML UI layout in my index.html file.

Firstly, we need to go to our main.js file and import the modules we are going to use:

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How to switch codesign certificates on Electron App for Mac (OSX)

Level of difficulty Medium

When you have an electron app that originally was distributed with a certificate for an individual developer. And you would like to sign the next update to that app with a certificate from your organization. It will break an auto-update installation process because codesign requirements aren't met.

So, to prevent this issue, your next app version should include information about both certificates (old and new). All future app versions can be signed with the new certificate, and the auto-update process will not be disrupted.

See the example below.

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10 things you may be asked about at UX Designer job interview

Level of difficulty Easy

Any job interview is quite a stressful event, especially if you’ve graduated just recently and don’t have enough experience in communicating with hiring managers. Another problem is, interviews may be conducted differently in different companies: for example, employers may ask various specific questions depending on the position you are applying for, so there is no way to get 100% prepared for anything you may be asked. However, the list of general questions that HRs usually go through before switching to more specific ones are usually pretty standard, and they are aimed at getting to know you as a person and a professional. We’ve collected a list of a few most common topics that you’re most likely to be asked to talk about at a UX designer job interview — let’s discuss them.

Basic info about yourself

The question “Tell us about yourself” is the basis of any job interview. It allows recruiters to understand who they’re talking to and why you’re applying for this job. Here you are expected to present yourself in a concise, but effective manner by telling about your education and working experience, what inspires you professionally and why you would like to pursue a career in UX.

Basic knowledge of UX design

No matter how many degrees you have or how high your experience level is, your recruiters need to evaluate your knowledge of UX design as a whole. But keep in mind that a job interview is not an exam, so here you are expected not to recite the textbook definitions learned by heart, but rather share your personal understanding of UX and your role as a designer in general. Consider talking about how you define UX, what creates value in the design, what are the necessary parts of a UX design process, what are the current trends in UX. You might also be asked to explain the difference between UI and UX to see how you understand the role of each in the development process.

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Hightech Fun Arduino Projects that Anyone can Male

Level of difficulty Easy

Smart dust bins are the perfect DIY project that blends the senses with the latest technology. With the aid of sensors and microcontrollers you can build a garbage bin that opens automatically when you move by it. It closes when you have got rid of your trash.

The procedure of creating the project is simple, which makes it an the perfect DIY project for kids.

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A Quick Guide on How to Optimize Apps for Foldable Smartphones?

Level of difficulty Medium

The App Development industry is rapidly evolving with innovations and advancements. Gone are the days when phones were only used for calls and messages. Now with advanced technological developments, the use of mobile has also revolutionized. This has considerably changed after the introduction of smartphones and foldable devices. It has, over time, emerged as one of the most promising solutions for all needs. Users can do almost anything with these advanced devices, from multi-screen functionality to personalized use. So, how are the apps optimized and designed for these foldable devices? This blog details a complete analysis of the same for your better understanding...

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