Shape programming of a magnetic elastica

We consider a cantilever beam which possesses a possibly non-uniform permanent magnetization, and whose shape is controlled by an applied magnetic field. We model the beam as a plane elastic curve and we suppose that the magnetic field acts upon the beam by means of a distributed couple that pulls the magnetization towards its direction. Given a list of target shapes, we look for a design of the magnetization profile and for a list of controls such that the shapes assumed by the beam when acted upon by the controls are as close as possible to the targets, in an averaged sense. To this effect, we formulate and solve an optimal design and control problem leading to the minimization of a functional which we study by both direct and indirect methods. In particular, we prove that minimizers exist, solve the associated Lagrange-multiplier formulation (besides non-generic cases), and are unique at least for sufficiently low intensities of the controlling magnetic fields. To achieve the latter result, we use two nested fixed-point arguments relying on the Lagrange-multiplier formulation of the problem, a method which also suggests a numerical scheme. Various relevant open question are also discussed.

PURE BENDING OF ELASTIC CURVE OF A BEAM

The problem of pure bending of an elastic curved beam with a given moment M is considered. It is proved that the values of stresses and strains found in this paper depend on the value of the Poisson's ratio μ. An exact analytical solution to this problem is obtained with the determination of unambiguous expressions for stresses and deformations.

Verification Plan Using Neural Algorithm Blockchain Smart Contract for Secure P2P Real Estate Transactions

Blockchain and artificial intelligence are the most important keywords in the Fourth Industrial Revolution. This study sought to apply these core technologies to future validated algorithms that make real estate transactions secure to come up with an encryption algorithm. In addition, the real estate transaction is being paid a large fee by the middlemen, the real estate agent. Furthermore and recently, P2P (peer-to-peer) real estate exchange is used a lot. However, these P2P real estate exchanges also have problems that have not been identified by each other between landlords and tenants. In particular, a research model was established to compare and verify the PBFT (practical Byzantine fault tolerance) algorithm of Hyperledger through the blockchain agreement process. Subsequently, a process for verifying the real estate contract was established. Through VM (virtual machine) research methodology for the verification of blockchain real estate contracts, ElGamal communication was provided to prove quantum cryptography. We also automated lightweight encryption test verification tools and blockchain smart contract VM (virtual machine) models using artificial intelligence. Verification was performed through a reservation server and a monitoring server using a test verification tool for network-based lightweight security IoT (Internet of things) GW (gateway). It presents important ECP (elastic curve program) and elastic curve Qu-Vanstone (ECQV) models among the main functions of the blockchain smart contract, and it is equipped with quantum-based encryption algorithm. In addition, the necessary UML (unified modeling language) source code and performance data were calculated according to the actual experimental environment, and the average value for blockchain for administrative or government authorized assets—4000 TPS (transaction per second) were tested. In the future, we want to use this technology for real estate transactions.

Tratado Prático Sobre Funções de Singularidade: Modelamento de Cargas em Vigas de Concreto Armado

<p>Present treatise deals with applications of singularity functions from a broad perspective in civil engineering, extending its use to hyperstatics, and deepening mathematical questions little explored before. The content is presented through examples discussed in detail, giving to the reader a clear and objective reading. Original mathematical formulations are developed, such as the Macaulay-Serpa series. The treatise is extended to the calculation of hyperstatic porticoes and to the modeling of triangular loads. In this context, the theory appears as an important instrument for the analysis of ruptures in reinforced concrete beams. For the accomplishment of this treatise, an exhaustive search of bibliographical references was made, showing that the existent literature on the subject, mostly of foreign origin, is quite limited.</p><p class="-1"><strong>Key words: </strong>Singularity functions, reinforced concrete, hyperstatics, discontinuous loading, elastic curve.</p><p class="-1">==================================================================================== </p><p>O presente tratado versa sobre aplicações das funções de singularidade numa ampla perspectiva da engenharia civil, estendendo seu uso à hiperestática e aprofundando questões matemáticas pouco exploradas anteriormente. O conteúdo é apresentado através de exemplos discutidos em detalhes, proporcionando ao leitor uma leitura clara e objetiva. Formulações matemáticas originais são desenvolvidas, como a série Macaulay-Serpa. O tratado é estendido ao cálculo de pórticos hiperestáticos e à modelagem de cargas triangulares. Nesse contexto, a teoria aparece como um instrumento importante para a análise de rupturas em vigas de concreto armado. Para a realização deste tratado, foi feita uma busca exaustiva das referências bibliográficas, mostrando que a literatura existente sobre o assunto, principalmente de origem estrangeira, é bastante limitada.</p><p class="-1"><strong>Palavras-Chave: </strong>Funções de singularidade, concreto armado, hiperestática, carga descontínua, curva elástica. </p>

Modeling adhesion-independent cell migration

A two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modeled as an elastic curve, subject to an internal pressure force. Net polymerization or depolymerization in the cortex is modeled via local addition or removal of material, driving a cortical flow. The model takes the form of a fully nonlinear degenerate parabolic system. An existence analysis is carried out by adapting ideas from the theory of gradient flows. Numerical simulations show that these simple rules can account for the behavior observed in experiments, suggesting a possible mechanical mechanism for adhesion-independent motility.

Elastic strips with null and pseudo-null directrix

The solution of the variational problem which gives elastic strips in Minkowski [Formula: see text]-space is separately obtained for elastic strips with null and pseudo-null directrix. First, critical points of the modified Sadowsky functional (which depends on the modified torsion) for elastic strips with null directrix are characterized by three Euler–Lagrange equations. A connection is established between elastic curves on the two-dimensional null cone and elastic strips with null directrix. Then conservation laws of elastic strips with null directrix in Minkowski 3-space are given. Second, equilibrium equations for elastic strips with pseudo-null directrix are determined and solved. It is also shown the tangent and the binormal of a critical curve of the Sadowsky functional correspond to a null elastic curve in de Sitter 2-space and a spacelike elastic curve in the two-dimensional null cone, respectively. Finally, two conservation laws for elastic strips with pseudo-null directrix are derived.

Online Signature Verification Based on a Single Template via Elastic Curve Matching

Person verification using online handwritten signatures is one of the most widely researched behavior-biometrics. Many signature verification systems typically require five, ten, or even more signatures for an enrolled user to provide an accurate verification of the claimed identity. To mitigate this drawback, this paper proposes a new elastic curve matching using only one reference signature, which we have named the curve similarity model (CSM). In the CSM, we give a new definition of curve similarity and its calculation method. We use evolutionary computation (EC) to search for the optimal matching between two curves under different similarity transformations, so as to obtain the similarity distance between two curves. Referring to the geometric similarity property, curve similarity can realize translation, stretching and rotation transformation between curves, thus adapting to the inconsistency of signature size, position and rotation angle in signature curves. In the matching process of signature curves, we design a sectional optimal matching algorithm. On this basis, for each section, we develop a new consistent and discriminative fusion feature extraction for identifying the similarity of signature curves. The experimental results show that our system achieves the same performance with five samples assessed with multiple state-of-the-art automatic signature verifiers and multiple datasets. Furthermore, it suggests that our system, with a single reference signature, is capable of achieving a similar performance to other systems with up to five signatures trained.

THE CLASSICAL BERNOULLI-EULER ELASTIC CURVE IN A MANIFOLD

In this study, we describe the classical Bernoulli-Euler elastic curve in a manifold by the property that the velocity vector field of the curve is harmonic. Then, a condition is obtained for the elastic curve in a manifold. Finally, we give an example which provides the condition mentioned in this paper and illustrate it with a figure.

Blockchain-based Multi-Purpose Authentication Method for Anonymity and Privacy

Various applications using smart contract, a leading application technology of blockchain, are being rapidly introduced to the industrial sector. As a result, services in various fields are actively being developed. Currently, most of the services are offered on a variety of platforms, not blockchain-based. If these services are linked to prepaid features that provide anonymity in smart contracts, a more diverse service scenario could be created. In this paper, we propose scenarios that provide certification for various purposes based on smart contracts. It provides a scenario that provides the privacy of the contract signed by the customer while retaining the anonymity provided by blockchain. Smart contracts register keys that do not give a clue to guess the encoding keys and deliver hash functions of the child keys that change each time with authentication parameters.In addition, the master seed that can generate these authentication parameters is designed to be kept only by the user and the service provider to be able to verify them. It is proposed by considering both a single service provider transaction and a smart contract authentication model that is shared with a large number of service providers. To generate these child keys, we proposed a mechanism to use the method of generation of child keys based on the Elastic Curve Cryptography public-key method. Various attack scenarios were analyzed to complement the scenario and the efficiency of the proposed mechanism was analyzed. In addition, differences and excellence were compared by organizing scenarios that had the same purpose as scenarios in the relevant study