A new operational matrix based on Bernoulli polynomials

In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized to transform the differential equation to a matrix equation which corresponds to a system of algebraic equations with unknown Bernoulli coefficients. This method can be used for many problems such as differential equations, integral equations and so on. Numerical examples show the method is computationally simple and also illustrate the efficiency and accuracy of the method

Dimensionality-driven spin-flop transition in quasi-one-dimensional PrBa2Cu4O8

In the quasi-one-dimensional cuprate PrBa$_2$Cu$_4$O$_8$, the Pr cations order antiferromagnetically at 17 K in zero field. Through a combination of magnetic susceptibility, torque magnetometry, specific heat and interchain transport measurements, the anisotropic temperature-magnetic field phase diagram associated with this ordering has been mapped out. A low-temperature spin-flop transition in the Pr sub-lattice is found to occur at the same magnetic field strength and orientation as a dimensional crossover in the ground state of the metallic CuO chains. This coincidence suggests that the spin reorientation is driven by a change in the anisotropic Rudermann-Kittel-Kasuya-Yosida (RKKY) interaction induced by a corresponding change in effective dimensionality of the conduction electrons.Comment: 8 pages, 8 figure

Tracking probabilistic truths: a logic for statistical learning

We propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty and represent the agent’s beliefs about probability, we consider a plausibility map, associating to each possible distribution a plausibility ranking. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds (or more generally, truth in all the worlds that are plausible enough). We consider two forms of conditioning or belief update, corresponding to the acquisition of two types of information: (1) learning observable evidence obtained by repeated sampling from the unknown distribution; and (2) learning higher-order information about the distribution. The first changes only the plausibility map (via a ‘plausibilistic’ version of Bayes’ Rule), but leaves the given set of possible distributions essentially unchanged; the second rules out some distributions, thus shrinking the set of possibilities, without changing their plausibility ordering.. We look at stability of beliefs under either of these types of learning, defining two related notions (safe belief and statistical knowledge), as well as a measure of the verisimilitude of a given plausibility model. We prove a number of convergence results, showing how our agent’s beliefs track the true probability after repeated sampling, and how she eventually gains in a sense (statistical) knowledge of that true probability. Finally, we sketch the contours of a dynamic doxastic logic for statistical learning.publishedVersio

Numerical Modeling of Bistun Rock Slope Behavior in Grouting Using Discrete Element Method

The discrete element method is an established method for considering discontinuous deformation behavior of joint systems. This paper provides a description of this algorithm used to model coupled hydraulic and mechanical effects of joints on rock mass behavior. The paper also describes Bistun rock slope stability analysis using empirical (SMR) and numerical (D.E.) methods. The behavior of the rock slope and rock blocks containing Bistun epigraph in grouting and groundwater flow has successfully simulated using UDEC (Universal Distinct Element Code) program. Finally, results have been presented and discussed on slope stability condition and grouting pressure

Shear deformation theories for elastic buckling of fluid-infiltrated porous plates: An analytical approach

In this paper, Reddy's higher-order and Mindlin's first-order plate theories are used for buckling analysis of porous rectangular plates subjected to various types of mechanical loading. The condition of the internal pores is considered to be either free of or saturated by fluid. Biot's theory of poroelasticity is thereby employed to model the behaviour of fluid. Distribution of pores is assumed to vary through the thickness according to an asymmetric distribution. For each displacement field considered, five highly coupled partial differential equations are derived by means of variational principle. These systems of equations are first decoupled through an efficient method, and then solved analytically for Levy-type boundary conditions. Accuracy of the approach is examined by comparing the obtained results with those available in literature. Eventually, comprehensive parametric studies are provided to investigate the effects of geometrical parameters, boundary conditions, loading conditions, porosity coefficient and pore fluid compressibility on the buckling response of the system. The results suggest that a structure with higher equivalent rigidity is met, when its corresponding internal pores are saturated by fluid. The results of the current work can be considered as a benchmark for future studies

Comparison of the pregnancy outcomes between the medical and surgical treatments in tubal ectopi pregnancy

Background: Various treatments have been proposed to treat ectopic pregnancy, but their impact on future pregnancies is still the subject of controversy. Objective: The aim of this study is to compare the medical and surgical treatment methods and their impact on the subsequent fertility results and complications in women with a history of ectopic pregnancy. Materials and Methods: In this analytical, cross-sectional study, 370 women with the history of ectopic pregnancy, (treared with single dose of methotrexate or salpingectomy by laparotomy), that referred to Al-Zahra Hospital, Rasht, Guilan between 2009 to 2013 were enrolled. 147 women responded to the phone call. The age, the number of women that needed to drug for pregnancy, fertility rate and the fertility outcomes were studied. Result: 147 women responded to the call and between them, 114 women tried to get pregnant again after the ectopic pregnancy treatment. They were agreed to the participate in the study. The mean age of the patients was 28.56±5.63 yr. The fertility rates in the medical and the surgical groups were 56.6 and 47.61, respectively (p=0.141). There were no significant differences in the poor consequences of pregnancy among the two groups; ectopic pregnancy (p=0.605), miscarriage (p=0.605), and prematuredelivery (p=0.648). 15.1 in the medicinal group and two patients 12.5 in the surgical group had received fertility treatment in order to get pregnant (p=0.135). There was no significant difference in two groups. Conclusion: It seems that surgical treatment depending on the underlying variables of each patient, can be used such as medical treatment, without worrying about its effect on fertility. © 2018, Research and Clinical Center for Infertitlity. All rights reserved