Open Interval Research Articles

On the backward stochastic differential equation with generator f(y)|z|2

In this paper, we consider the backward stochastic differential equation (BSDE) with generator f(y)|z|2, where the function f is defined on an open interval D and locally integrable. The existence and uniqueness of bounded solutions and Lp(p≥1) solutions of such BSDEs are obtained. Some comparison theorems and a converse comparison theorem of such BSDEs are established. As an application, we give a probabilistic interpretation of viscosity solution of quadratic PDEs.

On solutions for a class of fractional Kirchhoff-type problems with Trudinger–Moser nonlinearity

In this paper, we prove the existence of at least three nontrivial solutions for the following class of fractional Kirchhoff-type problems: [Formula: see text] where [Formula: see text] is a constant, [Formula: see text] is a bounded open interval, [Formula: see text] is a continuous potential, the nonlinear term [Formula: see text] has exponential growth of Trudinger–Moser type, [Formula: see text] and [Formula: see text] denotes the standard Gagliardo seminorm of the fractional Sobolev space [Formula: see text]. More precisely, by exploring a minimization argument and the quantitative deformation lemma, we establish the existence of a nodal (or sign-changing) solution and by means of the Mountain Pass Theorem, we get one nonpositive and one nonnegative ground state solution. Moreover, we show that the energy of the nodal solution is strictly larger than twice the ground state level. When we regard [Formula: see text] as a positive parameter, we study the behavior of the nodal solutions as [Formula: see text].

Modeling successive birth interval of women in Ethiopia: application of parametric shared frailty and accelerated failure time model

BackgroundBoth short and long birth intervals are associated with many risk factors and about 29% of births are short birth intervals in Ethiopia. The purpose of this study is to model the birth intervals of adult women aged 15–49 years using accelerated failure time and shared frailty models in order to analyze the birth intervals of Ethiopian women.MethodsThe data was obtained from the 2016 Ethiopian Demographic and Health Survey (EDHS). Accelerated failure time with different baseline and shared frailty models are used for the analysis to identify important demographic and socio-economic factors affecting the length of birth intervals and correlates of the birth intervals respectively.ResultsThe data consists of 9147 women, of which about 7842 (85.5%) are closed interval and the rest of 1323(14.5%) are open interval. Accelerated failure time (AFT) result revealed that women education level, husbands education level, age at first birth, marital status, religion and family wealth index are significant factors affecting birth interval of women in Ethiopia.ConclusionWomen with closely spaced births tend to have larger family sizes when compared with women with longer inter-birth interval. Longer successive birth interval tends to reduce the total fertility rate of women. Furthermore, improvements in socio-economic status and level of education of women associate with reduced fertility, improved maternal and child wellbeing, and longer birth interval.

Analytic properties of sextet polynomials of hexagonal systems

In this paper we investigate analytic properties of sextet polynomials of hexagonal systems. For the pyrene chains, we show that zeros of the sextet polynomials \(P_n(x)\) are real, located in the open interval \((-3-2\sqrt{2},-3+2\sqrt{2})\) and dense in the corresponding closed interval. We also show that coefficients of \(P_n(x)\) are symmetric, unimodal, log-concave, and asymptotically normal. For general hexagonal systems, we show that real zeros of all sextet polynomials are dense in the interval \((-\infty ,0]\), and conjecture that every sextet polynomial has log-concave coefficients.

Optimal Economic Growth Models with Nonlinear Utility Functions

We study a class of finite horizon optimal economic growth problems with nonlinear utility functions and linear production functions. By using a maximum principle in the optimal control theory and employing the special structure of the problems, we are able to explicitly describe the unique solution via input parameters. Economic interpretations of the obtained results and an open problem about the case where the total factor productivity falls into a bounded open interval defined by the growth rate of labor force, the real interest rate, and the exponent of the utility function are also expressed.

Convergence analysis of gradient-based iterative algorithms for a class of rectangular Sylvester matrix equations based on Banach contraction principle

We derive an iterative procedure for solving a generalized Sylvester matrix equation AXB+CXD = E, where A,B,C,D,E are conforming rectangular matrices. Our algorithm is based on gradients and hierarchical identification principle. We convert the matrix iteration process to a first-order linear difference vector equation with matrix coefficient. The Banach contraction principle reveals that the sequence of approximated solutions converges to the exact solution for any initial matrix if and only if the convergence factor belongs to an open interval. The contraction principle also gives the convergence rate and the error analysis, governed by the spectral radius of the associated iteration matrix. We obtain the fastest convergence factor so that the spectral radius of the iteration matrix is minimized. In particular, we obtain iterative algorithms for the matrix equation AXB=C, the Sylvester equation, and the Kalman–Yakubovich equation. We give numerical experiments of the proposed algorithm to illustrate its applicability, effectiveness, and efficiency.

Single stitch Open interval appendectomy; when and why

Appendicitis is a very common cause of acute abdomen. Most of the patient admit in surgical emergency. Diagnosis usually made clinically, sonography sometimes may be helpful. Regarding management there is still controversy exists. Developed country usually performed laparoscopy appendectomy while in developing country surgical management is still in debate. Different surgeons have different opinion either emergency open or laparoscopy appendectomy or interval appendectomy. Even in open appendectomy there is still debate between classical procedure vs small incision. This study favors single stitch surgery rather than classical and laparoscopy appendectomy. this case study supports even better cosmetic and outcome than laparoscopy appendectomy.

The equivalence Vitali cover integral with Lebesgue integral

Collection interval v is called Vitali Cover measiu’able set up A ⊂ R, if for every number ε > 0 and x ∈ A is an open interval Ix ∈ v so that x ∈ Ix and μ(Ix ) < ε. By utilizing Vitali Cover can be constructed of a type of integral type, hereinafter referred Riemaim Vitali Cover integral. A Function A function is said to Lebesgue integrable if and only if there is a continuous function so that F absolutely continuous on [a,b] and F′(x) = f(x) almost everywhere in [a,b]. By using the properties of Vitali Cover can be shown that both types of the above integral are equivalent

S-shaped bifurcations in a two-dimensional Hamiltonian system

We study the solutions to the following Dirichlet boundary problem: d 2x(t) dt2 + λ f(x(t)) = 0, where x ∈ R, t ∈ R, λ ∈ R+, with boundary conditions: x(0) = x(1) = A ∈ R. Especially we focus on varying the parameters λ and A in the case where the phase plane representation of the equation contains a saddle loop filled with a period annulus surrounding a center. We introduce the concept of mixed solutions which take on values above and below x = A, generalizing the concept of the well-studied positive solutions. This leads to a generalization of the so-called period function for a period annulus. We derive expansions of these functions and formulas for the derivatives of these generalized period functions. The main result is that under generic conditions on f(x) so-called S-shaped bifurcations of mixed solutions occur. As a consequence there exists an open interval for sufficiently small A for which λ can be found such that three solutions of the same mixed type exist. We show how these concepts relate to the simplest possible case f(x) = x(x + 1) where despite its simple form difficult open problems remain.

Are professional forecasters Bayesian?

I investigate how professional forecasters update their uncertainty forecasts of output and inflation in response to macroeconomic news. I obtain a measure of individual uncertainty from the density forecasts of the Survey of Professional Forecasters for the United States (US-SPF) and the Euro area (ECB-SPF) and use it to test the prediction of Bayesian learning that uncertainty should decline as the forecast date nears the target date. Empirically, I find that the prediction is occasionally violated, in particular when forecasters experience unexpected news in the most recent data release, and following quarters in which they produce narrow density forecasts. The evidence indicates also significant heterogeneity in the updating behavior of forecasters in response to changes in these variables. In addition, I propose a method to solve the problem of the truncation of the density forecasts that occurs when a significant amount of probability is assigned to the open intervals.

Breakdown of Liesegang precipitation bands in a simplified fast reaction limit of the Keller\u2013Rubinow model

We study solutions to the integral equation ω(x)=Γ-x2∫01K(θ)H(ω(xθ))dθ\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} \\omega (x) = \\Gamma - x^2 \\int \\nolimits _{0}^1 K(\\theta ) \\, H(\\omega (x\\theta )) \\, \\mathrm {d}\\theta \\end{aligned}$$\\end{document}where Gamma >0, K is a weakly degenerate kernel satisfying, among other properties, K(theta ) sim k , (1-theta )^sigma as theta rightarrow 1 for constants k>0 and sigma in (0, log _2 3 -1), H denotes the Heaviside function, and x in [0,infty ). This equation arises from a reaction-diffusion equation describing Liesegang precipitation band patterns under certain simplifying assumptions. We argue that the integral equation is an analytically tractable paradigm for the clustering of precipitation rings observed in the full model. This problem is nontrivial as the right hand side fails a Lipschitz condition so that classical contraction mapping arguments do not apply. Our results are the following. Solutions to the integral equation, which initially feature a sequence of relatively open intervals on which omega is positive (“rings”) or negative (“gaps”) break down beyond a finite interval [0,x^*] in one of two possible ways. Either the sequence of rings accumulates at x^* (“non-degenerate breakdown”) or the solution cannot be continued past one of its zeroes at all (“degenerate breakdown”). Moreover, we show that degenerate breakdown is possible within the class of kernels considered. Finally, we prove existence of generalized solutions which extend the integral equation past the point of breakdown.

Magnetic trajectories corresponding to Killing magnetic fields in a three-dimensional warped product

The aim of this paper is to investigate Killing magnetic trajectories of varying electrically charged particles in a three-dimensional warped product [Formula: see text] with positive warping function [Formula: see text], where [Formula: see text] is an open interval in [Formula: see text] equipped with an induced semi-Euclidean metric on [Formula: see text]. First, Killing vector fields on [Formula: see text] are characterized and it is observed that lifts to [Formula: see text] of Killing vector fields tangent to [Formula: see text] are also Killing on [Formula: see text]. Now, any Killing vector field on [Formula: see text] corresponds to a Killing magnetic field on [Formula: see text]. Magnetic trajectories (also known as magnetic curves) of charged particles which move under the influence of Lorentz force generated by Killing magnetic fields on [Formula: see text] are obtained in both Riemannian and Lorentzian cases. Moreover, some examples are exhibited with pictures determining Killing magnetic trajectories in hyperbolic [Formula: see text]-space [Formula: see text] modeled by the Riemannian warped product [Formula: see text]. Furthermore, some examples of spacelike, timelike and lightlike Killing magnetic trajectories are given with their possible graphs in the Lorentzian warped product [Formula: see text].

Multiple Solutions for Partial Discrete Dirichlet Problems Involving the p-Laplacian

Due to the applications in many fields, there is great interest in studying partial difference equations involving functions with two or more discrete variables. In this paper, we deal with the existence of infinitely many solutions for a partial discrete Dirichlet boundary value problem with the p-Laplacian by using critical point theory. Moreover, under appropriate assumptions on the nonlinear term, we determine open intervals of the parameter such that at least two positive solutions and an unbounded sequence of positive solutions are obtained by using the maximum principle. We also show two examples to illustrate our results.

Almost sure Assouad-like dimensions of complementary sets

Given a non-negative, decreasing sequence a with sum 1, we consider all the closed subsets of [0, 1] such that the lengths of their complementary open intervals are given by the terms of a. These are the so-called complementary sets, or rearrangements of the Cantor set, constructed from a . In this paper we determine the almost sure value of the $$\varPhi $$ -dimension of these sets given a natural model of randomness. The $$\varPhi $$ -dimensions are intermediate Assouad-like dimensions which include the Assouad and quasi-Assouad dimensions as special cases. The answers depend on the size of $$\varPhi ,$$ with one size behaving almost surely like the Assouad dimensions of the associated Cantor set and the other, like the quasi-Assouad dimensions. These results are new even for the Assouad dimensions.

The nature of the open birth interval distribution

Background: The open birth interval -- the time since the woman’s latest birth -- is closely correlated to the usual fertility measures, but it adds important information from the age of the woman’s youngest child, with its implications for her freedom from domestic roles. Studies of the open interval by age and parity can elucidate the transitions in reproductive behavior that women experience over time. Methods: 249 surveys of married women in 75 countries in the DHS series provide information on the open interval by age and parity, and by the fertility measures of the total fertility rate (TFR), the general fertility rate (GFR), and children ever born (CEB), with time trends. Stata 15 and the “R” software were used, and a two-parameter equation was employed to model the distribution. Results: The distribution of women by the open interval follows a downward curve from birth to 20 years; it varies across countries and over time only by its starting level and the steepness of the curve. Declines in the shortest intervals soon after birth reflect recent fertility declines. Variations are large by both age and parity, but in quite different patterns. Past modeling analyses demonstrate the effects of female and spouse mortality, declining fecundability, contraceptive use, and reduced sexual exposure. Both period and cohort effects can impact the curve. The open interval distribution is modelled in an equation with two parameters and calculated for the latest surveys in the 75 countries. Conclusions: The time since a woman’s birth is easily captured with a single question in successive surveys. Changes in the open interval distribution serve as sensitive indicators of recent fertility changes, and the dynamics of reproductive behavior across women’s life stages are captured in new ways, as gauged by age and parity trends in the distributions.

On the Integral of Diffusion Process on Interval with Unattainable Edges Boundaries: Semi-Markov Approach

A one-dimension semi-Markov process of diffusion type is considered. A range of values of this process is an open finite interval. It is supposed to have unattainable edges. The integral of this process as a function of time is studied. The invariance principle for this integral is proved.

The nature of the open birth interval distribution.

Background: The open birth interval -- the time since the woman's latest birth -- is closely correlated to the usual fertility measures, but it adds important information from the age of the woman's youngest child, with its implications for her freedom from domestic roles. Studies of the open interval by age and parity can elucidate the transitions in reproductive behavior that women experience over time. Methods: 249 surveys of married women in 75 countries in the DHS series provide information on the open interval by age and parity, and by the fertility measures of the total fertility rate (TFR), the general fertility rate (GFR), and children ever born (CEB), with time trends. Stata 15 and the "R" software were used, and a two-parameter equation was employed to model the distribution. Results: The distribution of women by the open interval follows a downward curve from birth to 20 years; it varies across countries and over time only by its starting level and the steepness of the curve. Declines in the shortest intervals soon after birth reflect recent fertility declines. Variations are large by both age and parity, but in quite different patterns. Past modeling analyses demonstrate the effects of female and spouse mortality, declining fecundability, contraceptive use, and reduced sexual exposure. Both period and cohort effects can impact the curve. The open interval distribution is modelled in an equation with two parameters and calculated for the latest surveys in the 75 countries. Conclusions: The time since a woman's birth is easily captured with a single question in successive surveys. Changes in the open interval distribution serve as sensitive indicators of recent fertility changes, and the dynamics of reproductive behavior across women's life stages are captured in new ways, as gauged by age and parity trends in the distributions.

On relationships between the Pearson and the distance correlation coefficients

In this paper we show that for any fixed Pearson correlation coefficient strictly between −1 and 1, the distance correlation coefficient can take any value in the open unit interval (0,1).

The Effect of Inclination on the Stability of Foam Systems in Drilling and Well Operations

SummaryTo minimize fluid loss and the associated formation damage, foam is a preferred fluid to perform cleanout operations and reestablish communication with an open completion interval. Because of their high viscosity and structure, foams are suitable cleanout fluids when underbalanced well-cleanout operations are applied. Although several studies have been conducted to better understand foam-flow behavior and hydraulics, investigations performed on foam stability are very limited. Specifically, very little is known regarding the impact of wellbore inclination on the stability of foams. Unstable foams do not possess high viscosity, and as a result, they are not effective in cleanout operations, especially in inclined wellbores. Predicting the downhole instability of foam could reduce the number of drilling problems associated with excessive liquid drainage, such as temporary overbalance, formation damage, and wellbore instability. The objectives of this study are to investigate the effects of wellbore inclination on the stability of various types of foams and develop a method to account for the effect of inclination on foam stability in inclined wells.In this study, foam-drainage experiments were performed using a flow loop that consists of a foam-drainage-measurement section and pipe viscometers. To verify proper foam generation, foam viscosity was measured using pipe viscometers and compared with previous measurements. Drainage experiments were performed with aqueous, polymer-based, and oil-based foams in concentric annulus and pipe under pressurized conditions. Tests were also conducted in vertical and inclined orientations to examine the effect of wellbore inclination on the stability of foams. The foam-bubble structure was examined and monitored in real time using a microscopic camera to study bubble coarsening. The foam quality (i.e., gas volume fraction) was varied from 40 to 80%.Results show that the drainage rates in the pipe and annular section were approximately the same, indicating a minor effect of column geometry. More importantly, the drainage rate of foam in an inclined configuration was significantly higher than that observed in a vertical orientation. The inclination exacerbated foam drainage and instability substantially. The mechanisms of foam drainage are different in an inclined configuration. In inclined wellbores, drainage occurs not only axially but also laterally. As a result, the drained liquid quickly reaches a wellbore wall before reaching the bottom of foam column. Then, a layer of liquid forms on the low side of the wellbore. The liquid layer flows downward because of gravity and reaches the bottom of the test section without facing the major hydraulic resistance of the foam network. This phenomenon aggravates the drainage process considerably.Although foam-drainage experiments have been reported in the literature, there exists only limited information on the effects of geometry and inclination on foam drainage and stability. The information provided in this paper will help to account for the effect of inclination on foam stability and subsequently improve the performance of oilfield operations involving foam as the working fluid.

Algebraic Numbers of the form αT with α Algebraic and T Transcendental

Let α≠1 be a positive real number and let P(x) be a non-constant rational function with algebraic coefficients. In this paper, in particular, we prove that the set of algebraic numbers of the form αP(T), with T transcendental, is dense in some open interval of R.