A Non-Iterative Problem-Dependent Formula for Stiff Dynamic Problems

A novel one-step formula is proposed for solving initial value problems based on a concept of eigenmode. It is characterized by problem dependency since it has problem-dependent coefficients, which are functions of the product of the step size and the initial physical properties to define the problem under analysis. It can simultaneously combine A-stability, explicit formulation and second order accuracy. A-stability implies no limitation on step size based on stability consideration. An explicit formulation implies no nonlinear iterations for each step. The second order accuracy with an appropriate step size can have a good accuracy in numerical solutions. Thus, it seems promising for solving stiff dynamic problems. Numerical tests affirm that it can have the same performance as that of the trapezoidal rule for solving linear and nonlinear dynamic problems. It is evident that the most important advantage is of high computational efficiency in contrast to the trapezoidal rule due to no nonlinear iterations of each step.

Krystyny Pisarkowej odkrywanie Malinowskiego

Krystyna Pisarkowa’s Discovering of Malinowski The article is concerned with the two-volume publication Językoznawstwo Bronisława Malinowskiego [Bronisław Malinowski’s Linguistics], edited by Krystyna Pisarek. Its first volume contains the editor’s thorough analysis of the linguistic achievements of this Polish-born British anthropologist, while the second volume includes translations of Malinowski’s works and a dictionary of the Kiriwina language. The linguistic importance of Malinowski’s works had been underestimated: his articles “Classificatory Particles in the Language of Kiriwina” (1920) and “The Problem of Meaning in Primitive Languages” (1923) were not included in the thirteen-volume collection of his writings (Dzieła [Works]). Pisarkowa, in turn, does recognize Malinowski’s contribution to linguistics and considers the following to be his unique achievements: (1) the discovery of the phatic function of speech (adopted by Roman Jakobson in his classification of language functions); (2) an explicit formulation of the principle of contextualism and the pragmatic aspect of word meaning; and (3) a precise description of the Kiriwina system of classificatory particles.

Numerical Modeling of the Degradation of the Normal Stress Under Large Number of Shearcycles

The evaluation of friction is an important element in the verification of stability and the determination of the bearing capacity of piles. In the case of cyclic stress, the soil-pile interface has a relaxation which corresponds to a fall in the horizontal stress which represents the normal stress at the lateral surface of the pile. This paper presents an explicit formulation to express the degradation of the normal stress after a large number of shear cycles as a function of cyclic parameters. In this study we are interested in the exploitation of the cyclic shear tests carried out by Pra-ai [1] with imposed normal rigidity (CNS) in order to demonstrate the phenomenon of falling of the normal stress. The approach presented in this paper consists in proposing a simple expression for estimating the degradation of normal stress as a function of cyclic shear parameters after a large number of cycles. The validation of this approach is verified by the application of this formulation to a real case where the comparison of the simulations made by this approach with those recorded on site shows the good adaptation of this approach to this type of problems.

Search Heuristics and Constructive Algorithms for Maximally Idempotent Integers

Previous work established the set of square-free integers n with at least one factorization n=p¯q¯ for which p¯ and q¯ are valid RSA keys, whether they are prime or composite. These integers are exactly those with the property λ(n)∣(p¯−1)(q¯−1), where λ is the Carmichael totient function. We refer to these integers as idempotent, because ∀a∈Zn,ak(p¯−1)(q¯−1)+1≡na for any positive integer k. This set was initially known to contain only the semiprimes, and later expanded to include some of the Carmichael numbers. Recent work by the author gave the explicit formulation for the set, showing that the set includes numbers that are neither semiprimes nor Carmichael numbers. Numbers in this last category had not been previously analyzed in the literature. While only the semiprimes have useful cryptographic properties, idempotent integers are deserving of study in their own right as they lie at the border of hard problems in number theory and computer science. Some idempotent integers, the maximally idempotent integers, have the property that all their factorizations are idempotent. We discuss their structure here, heuristics to assist in finding them, and algorithms from graph theory that can be used to construct examples of arbitrary size.

Social Sanction: Naked Parade and Vigilantism as Legal Violation Criminal Law Perspective and Human Rights

Naked parade and vigilantism are social sanctions or informal sanctions imposed by the community for acts deemed contrary to the local community's norms. These sanctions include vigilante action, which breaks the law. This paper aims to explain social sanctions (naked parade) from a legal perspective, particularly studied from human rights and criminal law. The study uses a normative approach so that the data sources include legal documents, references, and journals relevant to the problem being studied. The data analysis using consists of human rights principles and criminal law. The study results show that naked parade and vigilante as social sanction contradict human rights principles (liberty, non-discrimination, dignity, humanity, and equity). This act is also a criminal act, considering that the criminal law functions to protect the legal rights of individuals, the community, and the state. There is no explicit formulation of naked parade in the Penal Code (KUHP) or regulations outside the Penal Code. It is necessary to formulate it explicitly as an act that can be punished.

A Conforming A-FEM for Modeling Arbitrary Crack Propagation and Branching in Solids

In this paper, an improved conforming AFEM (C-AFEM) for efficient modeling of arbitrary crack propagation and branching is proposed and validated. An explicit formulation for branching cracks has been derived within the C-AFEM framework. The conjugate gradient method is integrated into the C-AFEM formulation to solve the local problem that consists of all elements traversed by single or multiple cracks. Multiple numerical evidences show that this new approach can substantially improve the modeling efficiency. The solution accuracy and numerical robustness are also significantly improved.

An Eigen-Based Theory For Structure-Dependent Integration Methods for Nonlinear Dynamic Analysis

An eigen-based theory for structure-dependent integration methods is constructed and it can provide the fundamental basis for the successful development of this type of integration methods. It is proved that a structure-dependent integration method can simultaneously combine unconditional stability and explicit formulation since it is proposed to accurately integrate low-frequency modes while no instability is guaranteed for high-frequency modes. In general, it is promising for solving inertial problems, where the total response is dominated by low-frequency modes. In addition, it can be explicitly and implicitly implemented for time integration although an explicit implementation is of practical significance since it can save many computational efforts due to the combination of unconditional stability and explicit formulation. A typical procedure to develop structure-dependent integration methods is constructed. In general, a coupled equation of motion for a multiple degree of freedom system can be decomposed into a set of uncoupled modal equations of motion by means of an eigen-decomposition technique. Next, an eigen-dependent integration method is developed to solve each modal equation of motion. Consequently, all the eigen-dependent integration methods are combined to form a structure-dependent integration method by employing a reverse procedure of the eigen-decomposition technique.

Pontryagin’s Maximum Principle for Optimal Control of Stochastic SEIR Models

In this paper, we study the necessary conditions as well as sufficient conditions for optimality of stochastic SEIR model. The most distinguishing feature, compared with the well-studied SEIR model, is that the model system follows stochastic differential equations (SDEs) driven by Brownian motions. Hamiltonian function is introduced to derive the necessary conditions. Using the explicit formulation of adjoint variables, desired necessary conditions for optimal control results are obtained. We also establish a sufficient condition which is called verification theorem for the stochastic SEIR model.