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Technology has positive impacts on various aspects of our social life. Creating a globally connected system allows comfort of access to a variety of resources and services. In addition, technology like Internet has been thriving ground for innovation and creativity. One such creation is Blockchain. The Blockchain technology provided many existing and emerging technologies ultimate Frisbee. With its enduring properties and decentralized architecture, it is taking spotlight in many services. Like healthcare industry, supply chain services and government sectors. One such future application of the Blockchain is E Voting. We aim of such application would be to provide a decentralized architecture to run and support a voting scheme that is fair, open and independently verifiable. The protocol has been designed to deliver fundamental e-voting properties as well as offer the outstanding peer-to-peer characteristics of blockchain, which will make sure that voting is open, fair and unable to get tempered.

Children's Fractional Knowledge elegantly tracks the construction of knowledge, both by children learning new methods of reasoning and by the researchers studying their methods. The book challenges the widely held belief that children's whole number knowledge is a distraction from their learning of fractions by positing that their fractional learning involves reorganizing not simply using or building upon their whole number knowledge. This hypothesis is explained in detail using examples of actual grade-schoolers approaching problems in fractions including the schemes they construct to relate parts to a whole, to produce a fraction as a multiple of a unit part, to transform a fraction into a commensurate fraction, or to combine two fractions multiplicatively or additively. These case studies provide a singular journey into children's mathematics experience, which often varies greatly from that of adults. Moreover, the authors' descriptive terms reflect children's quantitative operations, as opposed to adult mathematical phrases rooted in concepts that do not reflect and which in the classroom may even suppress youngsters' learning experiences. Highlights of the coverage: Toward a formulation of a mathematics of living instead of being Operations that produce numerical counting schemes Case studies: children's part-whole, partitive, iterative, and other fraction schemes Using the generalized number sequence to produce fraction schemes Redefining school mathematics This fresh perspective is of immediate importance to researchers in mathematics education. With the up-close lens onto mathematical development found in Children's Fractional Knowledge, readers can work toward creating more effective methods for improving young learners' quantitative reasoning skills.

Voting system using blockchain aims at providing the facility to cast vote from anywhere. It has the workability to allow casting of vote from any remote location. The election is held in full confidentiality that security is maintained in such a manner that voter can vote only if he logs into the system by entering the correct username and password. Voter will get the username and secret password to cast his vote. The voter will log into the system using his unique ID, they will then give his/her vote which will be stored into block-chain. Internet voting focuses on security, privacy, and secrecy issues, as well as challenges for stakeholder involvement and observation of the process. A new approach is proposed for voting system to prevent manipulation of the votes. Block chain overcomes the drawbacks of the previous voting system. It increases the security by not allowing the hacker to affect the rest of the nodes in the block chain. Voters can effectively submit their vote without revealing their identity or political preferences to the public. Counting votes becomes easy for the official since only one vote can be casted by each voter. no fake accounts can be created by anyone.

The interconnection between the Liouville–Weyl fractional integral and the Lambert function is studied. The class of modified Abel equations of the first kind is solved. A new integral formula for the Gamma function and possibly new transform pairs for the Laplace and Mellin transform have been found. <br />

Electoral processes using electronic devices allow voters to cast electronically. Devices such as personal computers, Direct Record Machines (DRE) voting machines, and smartcards, among others, in conjunction with private nets or the Internet have been the main tools to implement electronic voting systems (e-voting). Some years ago, mobile devices had not been considered due to their storage restrictions and low computational power; however, nowadays the technology in these devices has advanced and it is possible to implement complicated applications that offer security services such as confidentiality and authentication. In this paper, a reliable and efficient e-voting system for Android Smartphone is implemented. The e-voting proposed herein is composed of three entities: the authentication server (AS), the voting server (VS) and the voter (V) which runs on an Android Smartphone. Two short messages, between V and AS, are necessary to generate an electronic ballot. In order to cast a vote, one more message containing the ballot is sent from V to VS. Bilinear pairing functions are used to verify the signatures contained in the electronic ballot. Each ballot has short lengths, implying improvements in transmission times. Additionally, considering that the most costly operations such as bilinear pairing are not performed in V, the results obtained in tests show that the e-voting system is efficient.

The International Monetary Fund has long been a prominent institutional site of disagreement between rich and poor countries over how national preferences are to be aggregated for purposes of arriving at and implementing collective decisions. At the core of this disagreement is a fundamental problem that is both theoretical and practical: how best to reconcile the principle of sovereign equality with the fact of wide power asymmetries among members. More powerful states who contribute the bulk of the IMF's resources have successfully insisted that the Fund's weighted voting system reflect their position in the international power hierarchy, while their less powerful counterparts who use those resources call for votes to be distributed in closer debate spills over into disputes over how the actual distribution of votes has evolved, with developing countries recurrently expressing their dissatisfaction with voting weights they view as too small – individually and collectively – to permit meaningful participation in the IMF's internal governance. These differences over the IMF's decision process translate into divergent preferences between more and less developed countries on particular policy issues, such as the amount of IMF resources, the role and content of IMF conditionality, and use of Special

"In this article, we give su cient conditions for the existence, uniqueness and Ulam{Hyers stability of solutions for a coupled system of two-point nabla fractional di erence boundary value problems subject to anti-periodic boundary conditions, using the vector approach of Precup [4, 14, 19, 21]. Some examples are included to illustrate the theory."

Conventional electronic voting systems use a centralized scheme. A central administration of these systems manages the entire voting process and has partial or total control over the database and the system itself. This creates some problems, accidental or intentional, such as possible manipulation of the database and double voting. Many of these problems have been solved thanks to permissionless blockchain technologies in new voting systems; however, the classic consensus method of such blockchains requires specific computing power during each voting operation. This has a significant impact on power consumption, compromises the efficiency and increases the system latency. However, using a permissioned blockchain improves efficiency and reduces system energy consumption, mainly due to the elimination of the typical consensus protocols used by public blockchains. The use of smart contracts provides a secure mechanism to guarantee the accuracy of the voting result and make the counting procedure public and protected against fraudulent actions, and contributes to preserving the anonymity of the votes. Its adoption in electronic voting systems can help mitigate part of these problems. Therefore, this paper proposes a system that ensures high reliability by applying enterprise blockchain technology to electronic voting, securing the secret ballot. In addition, a flexible network configuration is presented, discussing how the solution addresses some of the security and reliability issues commonly faced by electronic voting system solutions.

Frontmatter -- Preface -- Contents -- Introduction: economics with memory -- Part I: Concept of memory -- 1 Concept of memory in economics -- Part II: Concepts of economics with memory -- 2 Concepts of marginal values with memory -- 3 Marginal values of noninteger order in economic analysis -- 4 Deterministic factor analysis of processes with memory -- 5 Elasticity for processes with memory -- 6 Multiplier for processes with memory -- 7 Accelerator for processes with memory -- 8 Duality of multipliers and accelerators with memory -- Part III: Linear models of economics with memory -- 9 Model of natural growth with memory -- 10 Model of growth with constant pace and memory -- 11 Harrod–Domar growth model with memory -- 12 Dynamic intersectoral Leontief models with memory -- 13 Market price dynamics with memory effects -- 14 Cagan model of inflation with memory -- Part IV: Nonlinear models of economics with memory -- 15 Model of logistic growth with memory -- 16 Kaldor-type model of business cycles with memory -- 17 Solow models with power-law memory -- 18 Lucas model of learning with memory -- 19 Self-organization of processes with memory -- Part V: Advanced models: distributed lag and memory -- 20 Multipliers and accelerators with lag and memory -- 21 Harrod–Domar model with memory and distributed lag -- 22 Dynamic Keynesian model with memory and lag -- 23 Phillips model with distributed lag and memory -- Part VI: Advanced models: discrete time approach -- 24 Discrete accelerator with memory -- 25 Comparison of discrete and continuous accelerators -- 26 Exact discrete accelerator and multiplier with memory -- 27 Logistic map with memory from economic model -- Part VII: Advanced models: generalized memory -- 28 Economics model with generalized memory -- Part VIII: Instead of conclusion -- 29 Fractional calculus in economics and finance -- 30 Future directions of economics with memory -- Bibliography -- Index