Form Of Continuous Functions Research Articles

New Form Of Continuous Functions In Topological Spaces

New Form Of Continuous Functions In Topological Spaces

Collapse strength ratios for weak first-story buildings under soft soil intraslab earthquakes

Weak first-story buildings are susceptible to experience severe structural damage, and even collapse, during strong earthquakes as was evidenced during the September 19, 2017 (Mw = 7.1) intraslab earthquake that hit Mexico City. Such type of buildings are prone to exhibit a negative slope in their capacity curve due to weak first-story mechanism that might lead to dynamic instability during earthquake excitation. Therefore, this paper presents the main results of an investigation focused on evaluating the collapse strength ratios, Rc (i.e., the normalized lateral strength ratio in the onset of dynamic instability) of single-degree-of-freedom (SDOF) systems whose force-displacement nonlinear envelope (backbone) behavior is representative of that observed in existing multistory weak first-story buildings. Particularly, their envelope exhibit several levels of negative slope after a post-yield displacement ductility capacity. Median and dispersion of Rc ratios were obtained for degrading SDOF systems subjected to a set of 136 earthquake ground motions recorded in soft soil sites of Mexico City from instraslab earthquakes. Results of this investigation showed that Rc ratios depend on the normalized period of vibration with respect to the predominant period of the ground motion, T/Tg, the displacement ductility capacity, μc, and the negative slope after peak strength, αc. Additionally, the spectral trend of Rc ratios at soft soil sites is different to that reported for firm soil sites. A continuous functional form is introduced to obtain estimates of median Rc ratios for the preliminary seismic assessment of weak first-story buildings in this seismic environment.

Data-driven approach to characterize urban vitality: how spatiotemporal context dynamically defines Seoul’s nighttime

ABSTRACTThis study takes a data-driven approach to define urban nighttime by examining the spatiotemporal dynamics of urban vitality. Using micro-scale spatiotemporal analysis, this paper empirically provides a comprehensive, yet granular, picture of collective human behaviors in cities. Using Seoul, South Korea as a case study site, it prioritizes the spatiotemporal context in order to mitigate uncertain contextual effects inherent in such forms of data-driven analysis. Instead of leaving the data re-grouping up to researcher’s arbitrary decision, this paper employs a functional principal component analysis (FPCA) to systematically transform a set of discrete data to a continuous functional form. This paper applies FPCA on 24-hour-based dataset of pedestrian traffic in Seoul in order to make a data-driven extraction of principal components that characterize the city’s unique patterns of urban vitality. Extracting principal components allows for less statistically obvious phenomena to be measured that would have otherwise been hidden within the data. This approach proved successful in capturing nighttime vitality patterns that are eclipsed by the overwhelming trend of daytime patterns. Additionally, this paper compares differences between regions and seasons to examine what the differences can tell about the definition of nighttime.

Elastic analysis of variable profile and polar orthotropic FGM rotating disks for a variation function with three parameters

Analytical solutions are developed for the analysis of elastic polar orthotropic functionally graded annular disks rotating with constant angular velocity. The formulations are carried out by presuming a state of plane stress and small deformations. The elasticity moduli and thickness are varied radially by a nonlinear function controlled by three parameters, while the radial variation of density may be defined by any form of continuous function. Poisson’s ratios are taken to be constant. Annular disks having traction-free inner and outer surfaces, and annular disks mounted on a circular rigid shaft having traction-free outer surface are studied separately. The analytical solutions are verified numerically by the use of a computational model based on the nonlinear shooting method. An analysis that inspects the effects of the degree of orthotropy is presented. Elastic limit angular velocities are determined according to Hosford’s yield criteria. Stress, displacement and strain profiles are compared within the elastic range.

Signal and Noise Modeling of Microwave Transistors Using Characteristic Support Vector-based Sparse Regression

In this work, an accurate and reliable S- and Noise (N) - parameter black-box models for a microwave transistor are constructed based on the sparse regression using the Support Vector Regression Machine (SVRM) as a nonlinear extrapolator trained by the data measured at the typical bias currents belonging to only a single bias voltage in the middle region of the device operation do- main of (VDS/VCE, IDS/IC, f). SVRMs are novel learning machines combining the convex optimization theory with the generalization and therefore they guarantee the global minimum and the sparse solution which can be expressed as a continuous function of the input variables using a subset of the training data so called Support Vector (SV)s. Thus magnitude and phase of each S- or N- param- eter are expressed analytically valid in the wide range of device operation domain in terms of the Characteristic SVs obtained from the substantially reduced measured data. The proposed method is implemented successfully to modeling of the two LNA transistors ATF-551M4 and VMMK 1225 with their large operation domains and the comparative error-metric analysis is given in details with the counterpart method Generalized Regression Neural Network GRNN. It can be concluded that the Characteristic Support Vector based-sparse regression is an accurate and reliable method for the black-box signal and noise modeling of microwave transistors that extrapolates a reduced amount of training data consisting of the S- and N-data measured at the typical bias currents belonging to only a middle bias voltage in the form of continuous functions into the wide operation range.

Some weaker forms of continuous functions in topological spaces

In this paper, the study of \(g\omega\alpha\)-closed sets in topological spaces is continued, which are used to define and study some new spaces. Using \(g\omega\alpha\)-closed sets and \(g\omega\alpha\)-open sets, \(g\omega\alpha\)-continuous and \(g\omega \alpha^{*}\)-continuous functions are introduced and studied. It is found that these two classes of functions are weaker forms of continuous functions.

Analytical and Numerical Analysis of Functionally Graded Heat Conduction Based on Dirichlet Boundary Conditions.

An analytical and numerical solution for the one dimensional of heat conduction in a slab exposed to different temperature at both ends is presented. The distribution of heat throughout the transient direction obeys to functionally graded (FG) temperature based on Dirichlet boundary conditions. The variation of functionally graded temperature can be described by any form of continuous function. In this case, where the external heat fluxes are not directly definite based on the Dirichlet or mixed boundary conditions, the fluxes that concluded over the slab faces are free to vary until the equilibrium condition is reached. By numerically solving the resulting heat-conduction equation, the distribution of temperature which vary with time through the slab is obtained. The obtained analytical results are presented graphically and the influence of the gradient variation of the temperature on shape formed with changed time is investigated.

Discussion of “Improved Nonlinear Muskingum Model with Variable Exponent Parameter” by Said M. Easa

The discusser would like to thank the author for presenting an improved nonlinear Muskingum model with a variable exponent parameter and would like to draw attention to some points. The need to consider a variable exponent parameter for a nonlinear Muskingum model has been pointed out by the author. The variable exponent parameter accounts for the nonlinearity of flood wave and clearly produces better model performance than that with the constant exponent parameter. The author found that even a small number of inflow levels result in an improvement in model performance. As mentioned by the author, as the number of inflow levels increase, model performance improves, but the improvement was found to be small beyond five levels in different case studies. The variable exponent parameter proposed by the author accounts for the nonlinearity of flood wave in a disaggregate manner. When five inflow levels are used, the number of model parameters will be seven making it a highly overparameterized model. Additional parameters should not be added to a model unless the increased accuracy justifies the increase in model complexity. Also, model complexity can sometimes lead to an undesirable loss of predictive power. In a regression model, accuracy needs to be balanced against complexity, and slight improvements in accuracy do not compensate for the additional complexity. As it will be shown in this discussion, considering a suitable continuous functional form for exponent parameter of nonlinear Muskingum model results in a substantial improvement in model performance. The proposed general functional form has five parameters and thus will be comparable with the case of five inflow levels proposed by the author. The author and most of the previous researchers have used inaccurate explicit Euler’s method [Tung’s method (Tung 1985)] along with the manipulated discharge equation to get a better fit for observed data. This manipulation [using It−1 rather than It in Eq. (6) of the original paper] is not acceptable from a mathematical viewpoint. All explicit solution methods will produce similar results for small size of the time interval, Δt, but in practice for historical field data, the size of the time interval is fixed and may not be small enough, and thus a suitable solution method with sufficient accuracy should be used. As shown by Vatankhah (2010, 2014), fourth-order Runge-Kutta method is an accurate and suitable solution method among the explicit solution methods for solving the Muskingum model which will be used in this discussion.

Risks of Eosinophil-Related End-Organ Damage, Hematological Malignancies and Death Are Significantly Increased Even below Consensus Threshold Criteria for Blood Eosinophilia

IntroductionBlood eosinophilia may arise from clonal intrinsic disorders or reactive extrinsic conditions. The eosinophilic granulocytes (eosinophils) may have diverse physiological functions and cause organ involvement. A dose-dependent relation between eosinophilia and risks of end-organ damage has not been described and it is not known whether numbers below internationally used threshold criteria for eosinophilia in adults (<0.5x109/L) may pose increased risks of eosinophil-related outcomes. Also, eosinophilia may represent an early paraclinical sign of hematological malignant disease (Andersen et al, Am J Hematol 2013), but the change in risks as a continuous function of the numbers of eosinophils has not been investigated.The aim of the study was, by the use of routine blood samples from a comprehensive primary care cohort, to investigate the effect of eosinophils on risks of experiencing end-organ damage and to explore the continuous functional form of the known effect on risks of hematological malignancies and death in search of prognostic cutoffs. MethodsFrom the Copenhagen Primary Care Differential Count (CopDiff) database, we identified 359.950 individuals with at least one differential cell count (DIFF) from 2000-2007. From these, one DIFF was randomly chosen from each individual. From the Danish Cancer Registry and the Danish Civil Registration System we ascertained hematological malignancies and death within three years following the DIFF. From the Danish National Patient Register we ascertained cardiological, neurological, skin, gastrointestinal and respiratory disease within three years following the DIFF. Furthermore we computed Charlson's comorbidity Index (CCI) within three years before the DIFF. Using multivariate logistic regression, the odds ratio between the eosinophil count and the three-year incidence of the outcome was calculated as a restricted cubic spline (Desquilbet et al, Stat Med 2010) and adjusted for previous eosinophilia, sex, age, year, month, CRP, previous cancer and CCI. ResultsIn the total cohort of 359.950 individuals from a primary care setting there was an equal sex-distribution and a mean age of 48.3 years. 345.544 individuals had eosinophils within the reference interval whereas 14.406 individuals (4%) exhibited eosinophilia. Risks for all outcomes were significantly increased above, but also below the consensus threshold criteria for eosinophilia. The lowest risk for hematologic cancer was found at an eosinophil count of 0.17 x109/L – which we set to be the baseline eosinophil count for all spline figures (figures 1-7). The lowest risk for benign disease and death was found at a similar eosinophil count. Risks for all outcomes increased for counts >0.17 x109/L and plateaued around 1.0x109/l. Risks for many outcomes also significantly increased for eosinophil counts < 0.17 x109/l up to a level of risk comparable to severe eosinophilia. [Display omitted] ConclusionIn this study on almost 400.000 individuals, we demonstrate that eosinophils may increase the risk of end-organ damage as well as malignant hematological disease and death even within the limits of consensus normal range. This observation possibly explains why a relationship between eosinophilia and organ damage or prognosis has been difficult to demonstrate previously. In the normal range below 0.17 x109/L a suspected phenomenon of extravasation is probable which converts to a prognostic factor for end-organ damage, death and hematological cancer which is also a novel observation. Apparently, a protective effect of low number of eosinophils in respiratory disease indicates that eosinophils may be causal in these disease entities and this needs to be investigated further. A plateau of ORs around 1x109/l has clinical impact for treating patients with primary eosinophilia because the risks of complications do not increase proportionally and suggests that in severe eosinophilia only a minor part of the eosinophil population leaves the blood stream to cause organ damage. More to be presented at ASH. Disclosures:No relevant conflicts of interest to declare.

Variational iteration method to solve moving boundary problem with temperature dependent physical properties

In this paper, variational iteration method is used to solve a moving boundary problem arising during melting or freezing of a semi infinite egion when physical properties (thermal conductivity and specific heat) of the two regions are temperature dependent. The Result is compared with result obtained by exact method (when thermal conductivity and specific heat in two regions are temperature independent) and semi analytical method (When thermal conductivity and specific heat are temperature dependent) and are in good agreement. We obtain the solution in the form of continuous functions. The method performs extremely well in terms of efficiency and simplicity and effective for solving the moving boundary problem.

Pasting Lemmas for g-Continuous Functions

The Pasting Lemma for continuous functions plays a key role in algebraic topology. Several mathematicians have established pasting lemmas for some stronger and weaker forms of continuous functions. In this paper we prove pasting lemmas for rg-continuous, gp-continuous, gc-irresolute, and gpr-continuous functions.

Direct and inverse one-phase Stefan problem solved by the variational iteration method

In this paper, solutions of one-phase direct and inverse Stefan problems are presented. The direct problem consists in a calculation of temperature distribution and of a function which describes the position of the moving interface, whilst the inverse problem consists in a calculation of temperature distribution as well as in the reconstruction of the function which describes the temperature distribution on the boundary, when the position of the moving interface is known. The proposed solution is based on the variational iteration method, after the application of which we obtain the solution in the form of continuous functions.

Day of week effects on diurnal ozone/NOx cycles and transportation emissions in Southern California

Diurnal cycles of ground-level ozone and its precursor NOx concentrations stem from and reflect complex temporal patterning of many underlying factors, including transportation emissions. Investigating the complexity of diurnal ozone/NOx cycles at a finer temporal resolution allows a better understanding of ozone dynamics and helps in designing ozone control strategies. This study applied functional data analysis techniques to hourly resolved ozone and NOx measurement data from the 1997 Southern California Ozone Study. Functional analysis of variance on diurnal ozone/NOx cycles for urban and rural monitoring sites confirmed, in a new continuous functional form, the ozone weekend effect. Functional data analysis also allows for a direct examination of day-of-week effects on ozone formation/destruction rates. Comparisons of Sunday ozone rates to those on weekdays demonstrate earlier, faster, and longer duration of ozone accumulation on Sunday. The results are further interpreted from the transportation emissions perspective using hourly resolved weigh-in-motion traffic data.

Variational eigenstrain analysis of synchrotron diffraction measurements of residual elastic strain in a bent titanium alloy bar

Most procedures for experimental stress evaluation rely on the measurement of elastic strain followed by point-wise calculation of stress based on continuum elasticity assumptions despite the fact that the real purpose of the investigation is to characterise the state of stress everywhere in the object to the greatest possible detail. Using the example of residual elastic strain measurements in a bent titanium alloy bar taken by means of high energy synchrotron X-ray diffraction, an interpretation technique is here introduced based on the variational eigenstrain analysis. An analytical framework is presented for the solution of the direct problem of eigenstrain, that is, the calculation of residual elastic strain distribution within an inelastically bent beam containing a known distribution of eigenstrain. An inverse problem about closest matching between the model and experiment is then cast in a form that allows determination of the underlying eigenstrain distribution from a single noniterative solution of linear system. Subsequently the complete stress state can be reconstructed everywhere within the object in the form of continuous functions. The value of the approach lies in the fact that subsequent deformation modelling can be carried out with the effects of residual stresses (and their evolution) naturally incorporated. The extension of this approach to more complex geometrics within the framework of the finite element method is briefly discussed.

The adaptive integration method for calculating general free energy functions

We describe a new adaptive sampling method for computing free energies for a wide variety of applications. The method is both simple and accurate. Results for thermodynamic quantities are obtained with this method in the form of continuous functions.

SOME REMARKS ON QUASI AND WEAKLY QUASI CONTINUOUS FUNCTIONS

Since N. Levin [1] in 1961 defined the weakly continuous function, there is a lot of weakened forms of continuous function. In this paper we consider two forms of the weakened form of continuous function and study the some properties of them.

A note on θ‐generalized closed sets

The purpose of this note is to strengthen several results in the literature concerning the preservation of θ‐generalized closed sets. Also conditions are established under which images and inverse images of arbitrary sets are θ‐generalized closed. In this process several new weak forms of continuous functions and closed functions are developed.

Linear interpolation of histograms

A prescription is defined for the interpolation of probability distributions that are assumed to have a linear dependence on a parameter of the distributions. The distributions may be in the form of continuous functions or histograms. The prescription is based on the weighted mean of the inverses of the cumulative distributions between which the interpolation is made. The result is particularly elegant for a certain class of distributions, including the normal and exponential distributions, and is useful for the interpolation of Monte Carlo simulation results which are time-consuming to obtain.

Monte Carlo entropic sampling for the study of metastable states and relaxation paths

We present a continuous extension of the recent Monte Carlo entropic method for sampling a density of states restricted in dimensionless macroscopic parameters. The method performs a random walk through a two-dimensional macrostate space and provides complete information in the form of continuous functions of the system's coupling constants. For the example of an Ising system, we project relaxation paths from Monte Carlo Metropolis dynamic over the two-dimensional state space and compare them with a ``most probable path'' associated with the equilibrium distribution, derived from the density of states. We observe a close agreement between them in the stochastic regime, i.e., before the system escapes from the metastable state. We establish a Markovian macroscopic dynamic over the two macroscopic parameters and we discuss it with respect to the Metropolis microscopic dynamic.

Functional forms for technical change functions

In this paper we examine the four properties of technical change functions introduced by Sato [1980, 1981], paying particular attention to the composition property. We show by way of examples that two of the properties are independent, but that a third is a necessary consequence of two others. A theorem providing a necessary condition for the composition property is stated and proved. Finally, we identify the general continuous functional form of technical change functions for which the efficiency of factor i is independent of the quantities of all factors j ≠ i. Noting an unappealing characteristic of a member of this class of transformations, we propose an additional property for technical change functions and note that it is independent of the others.