Proof Of Identity Research Articles

PROOF WITHOUT WORDS: SINE DIFFERENCE IDENTITY

In this paper, we give a pictorial proof of sine difference identity.

Combinatorial Analysis of a Classic Card Trick

Summary We demonstrate how the analysis of Miraskill, a classic card trick by the legendary Canadian magician Stewart James (1908–1996), leads to a connection with the Legendre polynomials and provides a constructive proof of combinatorial identities that occur in quantum mechanics.

A geometric proof of the binomial identity

We give a geometric proof of the binomial identity for all natural n and real a,b. This work was inspired by the book [1], where the binomial identity for n = 3 and a,b > 0 is proved by breaking a cube C of size (a + b) × (a + b) × (a + b) into eight rectangular boxes and counting their volumes as follows.

A Natural Geometric Proof of the Length-Curvature Identity

Summary This note offers a natural geometric proof for the length-curvature identity for a C 2 function of two variables.

Personal Identity Proofing for E-Commerce: A Case Study of Online Service Users in the Republic of Korea

The rapid expansion of non-face-to-face e-commerce services in the Korea has significantly increased the importance of personal identity proofing (PIP) for verifying users in online transactions, such as payments, refunds, membership registrations, and access to age-restricted products. Currently, personal identity proofing agencies (PIPAs) indiscriminately provide all of a user’s personal information to internet service providers (ISPs), leading to substantial privacy concerns and preventing users from selectively disclosing only the necessary information. The objective of this paper is to enhance the safety, convenience, and security of PIP services by proposing a method that empowers users to control the personal information they disclose while enabling digital identity integration for both online and offline applications. To achieve this, an extensive overview and analysis of the current PIP systems in Korea is presented, including methods. The strengths and weaknesses of these systems are critically examined, revealing limitations in privacy protection, user convenience, and security. Based on this analysis, a new method is proposed that introduces differentiated levels of PIP means according to authentication strength, allowing for the minimal necessary disclosure of personal information. The proposed method aims to improve the stability and reliability of the PIP service environment by addressing current privacy concerns and enhancing user control over personal information. This approach can be applied to e-commerce services in Korea and other countries facing similar challenges, contributing to the development of safer and more reliable online services.

New Proofs of the Septic Rogers-Ramanujan Identities

New Proofs of the Septic Rogers-Ramanujan Identities

Principal–agent trust and adoption of digital financial services: Evidence from India

AbstractThe high reliance on cash is a lifestyle for many people, and their low proficiency with smartphone usage acts as an inertial barrier to using digital financial services (DFS). Given low financial or digital literacy, online banking transactions have to be promoted and mediated by DFS agents. This study examines the role of digital platforms, intermediaries such as banks, mobile money agents, payment banks, post offices, and the government's increasing use of digital technologies. This usage of digital platforms is based on the trust relationship between the principals, who are owners of their bank accounts, and agents of DFS, who are intermediaries. A linear probabilistic model is employed to determine the determinants behind the low adoption of DFS between the necessity and nonnecessity groups. We observe that demand‐side factors like education level, identity proof (documentation), and level of smartphone use proficiency increase the probability of a principal's involvement in a digital mode of payment. At the same time, supply‐side factors like digital infrastructure and trust deficit due to unviable commission incentives to DFS agents decrease the principal's likelihood of using digital platforms.

Dependent Ghosts Have a Reflection for Free

We introduce ghost type theory (GTT) a dependent type theory extended with a new universe for ghost data that can safely be erased when running a program but which is not proof irrelevant like with a universe of (strict) propositions. Instead, ghost data carry information that can be used in proofs or to discard impossible cases in relevant computations. Casts can be used to replace ghost values by others that are propositionally equal, but crucially these casts can be ignored for conversion without compromising soundness. We provide a type-preserving erasure procedure which gets rid of all ghost data and proofs, a step which may be used as a first step to program extraction. We give a syntactical model of GTT using a program translation akin to the parametricity translation and thus show consistency of the theory. Because it is a parametricity model, it can also be used to derive free theorems about programs using ghost code. We further extend GTT to support equality reflection and show that we can eliminate its use without the need for the usual extra axioms of function extensionality and uniqueness of identity proofs. In particular we validate the intuition that indices of inductive type—such as the length index of vectors—do not matter for computation and can safely be considered modulo theory. The results of the paper have been formalised in Coq.

Pfaffians are Pfine

Summary Pfaffians are less familiar functions on skew-symmetric matrices, and yet Donald Knuth claims they are more fundamental than determinants. We explore connections between determinants and Pfaffians. Along the way, the reader will encounter combinatorial proofs of identities for both matrix functions and play with permutations, matchings, Reidemeister moves, and game theory.

Hybrid Digital Certificate Management System with QR Code and IoT Integrated on Hyperledger Fabric Blockchain

In contemporary society, management of physical documents such as educational certificates, identity proofs, vehicle registrations, and marriage certificates is an integral part of daily life. However, in present online world, there is a pressing need for digital transformation and the management of these documents. One significant challenge associated with this transformation is the susceptibility of original documents to replication or duplication. This vulner- ability is particularly concerning in the case of educational certificates, where fraud is prevalent. Fraudulent activities in the education sector can influence the proliferation of counterfeit educational and skill certificates, posing serious risks to society. For instance, individuals holding fraudulent degrees in professions such as engineering, medicine, law, and pharmacy may lack genuine competence, thereby posing substantial societal harm. To address the issue of certificate oversight and deter forgery, various approaches have been employed. Traditional methods typically involve the use of centralized databases or web servers for certificate storage, which introduces vulnerabilities because they represent single points of failure that leads to forgery and information loss. An optimal solution lies in the adoption of a Blockchain system that leverages a decentralized database structure to enhance data storage capacity and security. Blockchain technology has demonstrated disruptive potential and in- novative capabilities across multiple sectors because of its decentralized, transparent, and secure attributes. Its impact spans various domains, including banking, supply chain management, healthcare, education, and finance. Notably, in the education sector, Blockchain technology holds promise in enhancing security, transparency, and efficiency across different educational processes. In this study, we explore existing Blockchain oriented certificate management systems, critically analyze their limitations, and propose a novel hybrid educational certificate management model. The proposed model integrates Hyperledger Fabric, IoT, and 2D Barcode to develop a robust and secure framework for managing educational certificates.

Connections between two classes of generalized Fibonacci numbers squared and permanents of (0,1) Toeplitz matrices

By considering the tiling of an N-board (a linear array of N square cells of unit width) with new types of tile that we refer to as combs, we give a combinatorial interpretation of the product of two consecutive generalized Fibonacci numbers s n (where s n = ∑ i = 1 q v i s n − m i , s 0 = 1 , s n < 0 = 0 , where v i and m i are positive integers and m 1 < ⋯ < m q ) each raised to an arbitrary non-negative integer power. A ( w , g ; m ) -comb is a tile composed of m rectangular sub-tiles of dimensions w × 1 separated by gaps of width g. The interpretation is used to give combinatorial proof of new convolution-type identities relating s n 2 for the cases q = 2, v i = 1 , m 1 = M , m 2 = m + 1 for M = 0, m to the permanent of a (0,1) Toeplitz matrix with 3 nonzero diagonals which are − 2 , M−1, and m above the leading diagonal. When m = 1, these identities reduce to ones connecting the Padovan and Narayana's cows numbers.

A New (But Very Nearly Old) Proof of the Rogers-Ramanujan Identities

We present a new proof of the Rogers-Ramanujan identities. Surprisingly, all its ingredients are available already in Rogers seminal paper from 1894, where he gave a considerably more complicated proof.

Proof of some Littlewood identities conjectured by Lee, Rains and Warnaar

We prove a novel pair of Littlewood identities for Schur functions, recently conjectured by Lee, Rains and Warnaar in the Macdonald case, in which the sum is over partitions with empty 2-core. As a byproduct we obtain a new Littlewood identity in the spirit of Littlewood’s original formulae.

Proofs of some conjectural Hurwitz type identities for three squares due to Cooper and Hirschhorn

Let rs(n) denote the number of representations of n as the sum of s squares of integers. Hurwitz provided eleven cases in which the generating function of r3(an+b) is a simple infinite product. In 2004, Cooper and Hirschhorn proved eleven identities of Hurwitz, another twelve of the same sort and eighty infinite families of similar results by utilizing some q-series techniques. Moreover, they further conjectured eighty-two infinite families of Hurwitz type identities for r3(n). In this paper, we confirm these conjectural infinite families of Hurwitz type identities by using the theory of modular forms.

Candidate Authentication using OCR Techniques

This paper explores the application of Optical Character Recognition (OCR) techniques for authenticating candidates based on identity documents. As advancements in technology continue to redefine various industries, the integration of OCR into candidate authentication processes offers a streamlined and efficient solution. The aim is to design a system which gets the image of the identity proof and the details are being retrieved using the character segmentation which is done by a feature extraction optical character recognition algorithm (OCR). The authentication process encompasses document validation and implementation of security measures to safeguard against fraud.By combining YOLO object detection, Optical Character Recognition (OCR) and fuzzy matching technique ,this approach aims to enhance the accuracy and reliability of candidate authentication. This underscores the importance of a comprehensive authentication framework, incorporating both technological and procedural elements, to establish a robust and secure candidate authentication process in diverse contexts. Keywords: ID Verification,Optical Character Recognition (OCR), Text Extraction, YOLO,Object Detection,Image Segmentation, EasyOCR , Fuzzy Matching.

Socio-Economic and Health Consequences of COVID-19 on Indian Migrants: A Landscape Analysis.

The COVID-19 pandemic has hugely affected the world and human lives, the economy, and lifestyles. The pandemic control measures, such as lockdowns, forced many people to migrate from their destination to their source in various states, leading to increased vulnerability of migrants. The present review aimed to explore the different health, economic, and social impacts on internal migrants of India during the pandemic. The publications on internal migration and COVID-19 from India were retrieved from PubMed and Google Scholar using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. A total of 159 articles were extracted, of which 28 were reviewed. The articles published after March 1, 2020, were included in the review, irrespective of the design. Out of 28 articles, only half were original studies; the rest were either perspective, opinion, and review studies or editorial and commentary papers. Depression, anxiety, and stress due to job loss and lockdown were the major health issues documented. There was livelihood disturbance due to loss of income, such as inability to pay rent, loans, borrowing from relatives, and fear of its consequences. The migrants also faced stigma and discrimination from the villagers. The review also highlighted that although the government implemented various schemes to help the migrants, the majority were left out due to the non-availability of identity proof and ration cards. The safeguarding measures for these unregistered migrants must be facilitated to access health, economic, and social protection. Although various publications have focused on the mental health of the migrants, the socio-ecological aspects have been least explored, which calls for further studies. The literature on the impact of COVID-19 on other vulnerable populations like women and children and access to healthcare services is also scant, which needs to be explored further.

Quality control of allergen products with mass spectrometry part I: Positioning within the EU regulatory framework.

Mass spectrometry (MS) has advanced greatly and many of its applications are ready for utilization within regulatory procedures and could significantly contribute to overcome challenges in standardization of allergen products. It seems sensible to discuss MS within the regulatory framework, before addressing technical questions. While the application to purified proteins is well established from product development to manufacturer's release analytics, its application to complex products such as allergen products is still under development. It needs to be determined where it can complement or replace established methods or where MS offers limited improvement. Despite its technical appeal and versatility, currently MS is mentioned in regulatory guidelines only as one possible measurement method. For example, no specific MS method is given in the European Pharmacopoeia. We discuss applications of MS within the EU regulatory framework. This includes their advantages and disadvantages and their positioning between research, characterization, manufacturer's release analytics and official batch testing. We discuss the qualitative detection of single and multiple allergens as proof of identity, qualitative to semi-quantitative protein profiles for batch to batch consistency testing, and quantification of allergens to state mass units of allergens. MS may also facilitate standardization of allergen products, reference products and reference standards.

Функциональный метод доказательства тождеств

The elements of the mathematical analysis course occupy a significant place in the school mathematics course. When teaching the elements of mathematical analysis, students acquire a mathematical apparatus that can be effectively used in solving many problems of mathematics, physics and engineering. The use of mathematical analysis methods makes it possible to solve a number of problems, the solution of which is impossible or difficult by elementary methods. Note that the possibilities of mathematical analysis methods are not limited to such tasks. Thus, the language of derivatives and integrals allows us to formulate many laws of nature strictly. In addition, the use of elements of mathematical analysis in solving problems of school mathematics allows you to learn more deeply the basic concepts of the theory being studied. But school textbooks and textbooks pay little attention to these issues. This article also examines the proof of identities using mathematical analysis methods. The article is relevant for specialists, teachers, students, students involved in school mathematics.

Enhancing Security and Flexibility in the Industrial Internet of Things: Blockchain-Based Data Sharing and Privacy Protection

To address the complexities, inflexibility, and security concerns in traditional data sharing models of the Industrial Internet of Things (IIoT), we propose a blockchain-based data sharing and privacy protection (BBDSPP) scheme for IIoT. Initially, we characterize and assign values to attributes, and employ a weighted threshold secret sharing scheme to refine the data sharing approach. This enables flexible combinations of permissions, ensuring the adaptability of data sharing. Subsequently, based on non-interactive zero-knowledge proof technology, we design a lightweight identity proof protocol using attribute values. This protocol pre-verifies the identity of data accessors, ensuring that only legitimate terminal members can access data within the system, while also protecting the privacy of the members. Finally, we utilize the InterPlanetary File System (IPFS) to store encrypted shared resources, effectively addressing the issue of low storage efficiency in traditional blockchain systems. Theoretical analysis and testing of the computational overhead of our scheme demonstrate that, while ensuring performance, our scheme has the smallest total computational load compared to the other five schemes. Experimental results indicate that our scheme effectively addresses the shortcomings of existing solutions in areas such as identity authentication, privacy protection, and flexible combination of permissions, demonstrating a good performance and strong feasibility.

Leveraging zero knowledge proofs for blockchain-based identity sharing: A survey of advancements, challenges and opportunities

Identity sharing systems, regardless of their architectural models, share common vulnerabilities. These systems compel users to divulge personal information and furnish proof of identity for accessing services, leaving them susceptible to data breaches that can culminate in identity theft and jeopardize online data security. While blockchain technology offers a potential remedy, delivering enhanced security, immutability, and traceability, it simultaneously raises pertinent concerns surrounding privacy and transparency. The integration of zero-knowledge proof (ZKP) technology has emerged as a promising solution, particularly in enhancing privacy within the transparent blockchain ecosystem. Our paper conducts an exhaustive survey of the existing literature, with a particular focus on the assimilation of ZKP technology into blockchain for the secure sharing of user identities. We undertake a critical evaluation of the advancements achieved in this domain, pinpoint the formidable challenges that must be confronted, and uncover nascent opportunities for further exploration. Our contribution transcends the realms of mere summarization and analysis; we go a step further by offering recommendations drawn from real-world case studies and delineating future research directions.