Open Interval Research Articles

Estimation of total fertility rate and birth averted due to contraception: regression approach

Fertility plays an important role in any demographic transition and total fertility rate (TFR) is one of the basic measurements of fertility. Absences of complete and reliable data, a large number of indirect techniques have been developed to estimate the demographic parameters with incomplete data. Some of these techniques are based on utilizing the data from stable population theory while others are based on the regression technique in which the parameters are estimated through regression equations between the dependent variable which is the TFR and the independent variables which is the socio economic well as demographic variables. The first method is based on the relationship between the Total fertility rate (TFR) and contraceptive prevalence rate for all women. By using this modified estimate of TFR, demographic analysis can easily calculate the birth averted for different regions as well as states also. In fact, provide reasonable estimates of births averted due to contraceptive use by national populations. The variables are CPR that about 51.2 percent variation in TFR can be explained by the first regression approach. The second is based on the relationship between total fertility rate (TFR) and Additive combination of CPR and proportion of currently married females having open birth interval. Using new predictor variable, the improved model explained about 55percent of the variation in TFR. The findings reveal that the values of TFR calculated by the present method are quite close to the observed values of the TFR without involving much computational complexities at different background characteristics. Estimates of births averted and the percent change in births in the absence of contraception, based on the two methods, are fairly consistent.

Constructing Groupings by Use of STATISTICA Software Package

STATISTICA software package for statistical analysis incorporates a wide range of advanced statistical methods. Quite often they are preceded by aggregating statistical survey data, which main component is their grouping. Although this phase of statistical data processing is relatively simple, the manual process of aggregation can be time-consuming given the need to process large data arrays, not mentioning a high probability of errors. Therefore, the all-purpose STATISTICA software package is a logical and reasonable tool for grouping of data. 
 The article shows the grouping algorithm in STATISTICA software package, with focus on setup when constructing tables of frequencies of discrete and continual characters. Various options of grouping are scrutinized, with providing examples of their visualization. 
 A large number of STATISTICA parameters offers ample opportunities for constructing user tables, but users often are not aware of these options or do not know how they can be applied. Yet, the apparently simple grouping process in STATISTICA software package can sometimes require the knowledge of fine mechanisms for its setup. The article gives a detailed description of the mechanisms for creating interval margins when applying the parameter “approximate number of intervals”.
 The standard algorithm for selection is analyzed, allowing a user to limit the number of groups in a grouping. STATISTICA allows for using a number of grouping parameters, enabling to produce more convenient results or filter them. Thus, setting the clicker for label field “Grouping” in the position “Integer Categories” (integer intervals (categories)) initiates the grouping only for integer values of a variable, by excluding the observations containing its fractional values.
 When only standard parameters are used, it will be impossible to form uneven or open intervals. This issue is out of focus in specialized literature and Internet sources. The article shows the algorithm for constructing open intervals by user-set conditions and the process of creating these conditions. This option allows for forming both closed and open intervals by solving all the problems in time of grouping. Because creating such conditions is time consuming, they should be preserved if they are required for further use.
 Setting up of STATISTICA software with missing data is analyzed. Its application will be advisable when a grouping for two or more variables is constructed. In this case, a separate sheet with a grouping is to be created in the worksheet for each variable.

Hodge–Dirac, Hodge-Laplacian and Hodge–Stokes operators in $L^p$ spaces on Lipschitz domains

This paper concerns Hodge–Dirac operators D_{{}^\Vert}=d+\underline{\delta} acting in L^p(\Omega, \Lambda) where \Omega is a bounded open subset of {\mathbb{R}}^n satisfying some kind of Lipschitz condition, \Lambda is the exterior algebra of {\mathbb{R}}^n , d is the exterior derivative acting on the de Rham complex of differential forms on \Omega , and \underline{\delta} is the interior derivative with tangential boundary conditions. In L^2(\Omega,\Lambda) , \underline{\delta} = {d}^* and D_{{}^\Vert} is self-adjoint, thus having bounded resolvents \{({\rm I}+itD_{{}^\Vert})^{-1}\}_{t\in{\mathbb{R}}} as well as a bounded functional calculus in L^2(\Omega,\Lambda) . We investigate the range of values p_H < p < p^H about p=2 for which D_{{}^\Vert} has bounded resolvents and a bounded holomorphic functional calculus in L^p(\Omega,\Lambda) . On domains which we call very weakly Lipschitz, we show that this is the same range of values as for which L^p(\Omega,\Lambda) has a Hodge (or Helmholz) decomposition, being an open interval that includes 2. The Hodge-Laplacian \Delta_{{{}^\Vert}} is the square of the Hodge–Dirac operator, i.e., -\Delta_{{}^\Vert}={D_{{}^\Vert}}^2 , so it also has a bounded functional calculus in L^p(\Omega,\Lambda) when p_H < p < p^H . But the Stokes operator with Hodge boundary conditions, which is the restriction of -\Delta_{{}^\Vert} to the subspace of divergence free vector fields in L^p(\Omega,\Lambda^1) with tangential boundary conditions, has a bounded holomorphic functional calculus for further values of p , namely for max \{1,{p_H}_S\} < p < p^H where {p_H}_S is the Sobolev exponent below p_H , given by 1/{{p_H}_S} =1/{p_H}+1/n , so that {{p_H}_S} < 2n/(n+2) . In 3 dimensions, {p_H}_S < 6/5 . We show also that for bounded strongly Lipschitz domains \Omega , p_H < 2n/(n+1) < 2n/(n-1) < p^H , in agreement with the known results that p_H < 4/3 < 4 < p^H in dimension 2, and p_H < 3/2 < 3 < p^H in dimension 3. In both dimensions 2 and 3, {p_H}_S<1 , implying that the Stokes operator has a bounded functional calculus in L^p(\Omega,\Lambda^1) when \Omega is strongly Lipschitz and 1 < p < p^H .

Idiopathic nephrotic syndrome and rituximab: may we predict circulating B lymphocytes recovery?

Rituximab (RTX) has been shown to be an efficient treatment for steroid-dependent nephrotic syndrome (SDNS). A long B cell depletion period seems to improve the duration of remission. This study reports the duration of B cell depletion after each RTX infusion in patients with nephrotic syndrome. We retrospectively report the data of 22 patients with a diagnosis of a SDNS or steroid-resistant nephrotic syndrome (SRNS) and a treatment with RTX in a single center. B cell depletion duration was compared to the first B cell depletion duration and to the previous B cell depletion duration in each patient. Twenty-two patients (5 girls) were included. Seventy-six periods of B cell depletions were compared to the first B cell depletion duration and to the preceding B cell depletion duration in the same patient. Total duration of B cell depletion was 26 (6-66) months. Individual post-RTX infusion B cell depletion duration was 5.1 (1.6-14) months. Median B cell depletion duration following the first RTX cure for children who had received 1 to 2 infusions at first cure was not statistically different of those who had received 3 to 4 infusions (p = 0.18). Comparing the B cell depletion induced by previous RTX courses and the following B cell depletion, 89.5% of patients had a similar duration within an open interval from 2months. Once the individual time interval until B cell recovery is determined, monitoring could be individualized by targeting the expected date of B cell recovery or by performing pre-emptive RTX injections.

A consequence of the growth of rotation sets for families of diffeomorphisms of the torus

In this paper we consider $C^{\infty }$-generic families of area-preserving diffeomorphisms of the torus homotopic to the identity and their rotation sets. Let $f_{t}:\text{T}^{2}\rightarrow \text{T}^{2}$ be such a family, $\widetilde{f}_{t}:\mathbb{R}^{2}\rightarrow \mathbb{R}^{2}$ be a fixed family of lifts and $\unicode[STIX]{x1D70C}(\widetilde{f}_{t})$ be their rotation sets, which we assume to have interior for $t$ in a certain open interval $I$. We also assume that some rational point $(p/q,l/q)\in \unicode[STIX]{x2202}\unicode[STIX]{x1D70C}(\widetilde{f}_{\overline{t}})$ for a certain parameter $\overline{t}\in I$, and we want to understand the consequences of the following hypothesis: for all $t>\overline{t}$, $t\in I$, $(p/q,l/q)\in \text{int}(\unicode[STIX]{x1D70C}(\widetilde{f}_{t}))$. Under these very natural assumptions, we prove that there exists a $f_{\overline{t}}^{q}$-fixed hyperbolic saddle $P_{\overline{t}}$ such that its rotation vector is $(p/q,l/q)$. We also prove that there exists a sequence $t_{i}>\overline{t}$, $t_{i}\rightarrow \overline{t}$, such that if $P_{t}$ is the continuation of $P_{\overline{t}}$ with the parameter, then $W^{u}(\widetilde{P}_{t_{i}})$ (the unstable manifold) has quadratic tangencies with $W^{s}(\widetilde{P}_{t_{i}})+(c,d)$ (the stable manifold translated by $(c,d)$), where $\widetilde{P}_{t_{i}}$ is any lift of $P_{t_{i}}$ to the plane. In other words, $\widetilde{P}_{t_{i}}$ is a fixed point for $(\widetilde{f}_{t_{i}})^{q}-(p,l)$, and $(c,d)\neq (0,0)$ are certain integer vectors such that $W^{u}(\widetilde{P}_{\overline{t}})$ do not intersect $W^{s}(\widetilde{P}_{\overline{t}})+(c,d)$, and these tangencies become transverse as $t$ increases. We also prove that, for $t>\overline{t}$, $W^{u}(\widetilde{P}_{t})$ has transverse intersections with $W^{s}(\widetilde{P}_{t})+(a,b)$, for all integer vectors $(a,b)$, and thus one may consider that the tangencies above are associated to the birth of the heteroclinic intersections in the plane that do not exist for $t\leq \overline{t}$.

An indecomposable continuum as subpower Higson corona

In this paper, we study topological properties of the subpower Higson coronas of proper metric spaces and show that the subpower Higson corona of the half open interval with the usual metric is an indecomposable continuum. Continuous surjections from Higson-type coronas onto a Higson-type compactifications of the half open interval are also constructed.

Oscillatory Solutions of Some Autonomous Partial Differential Equations with a Parameter

We study a class of evolutionary partial differential equations depending on a parameter τ (stemming from the problems of groundwater flows). The existence of an open interval 𝒯0 of the parameter τ and of a function τ ⟼ Θ(τ), Θ: 𝒯0 ⟼(0, + ∞), is proved with the property that any nonzero global solution u:ℝ+ × Ω → ℝ of the equation cannot remain nonnegative (nonpositive) throughout the set J × Ω; where J ⊂ ℝ+ is any interval whose length is greater than Θ (τ). In other words, these solutions are globally oscillatory and Θ (τ) is the uniform oscillatory time. The interval 𝒯0 and the function Θ are explicitly determined.

Conceptualizing leakage and storage contributions from long open interval wells in regional deep basin flow models

AbstractDeep basin aquifers are increasingly used in water‐stressed areas, though their potential for sustainable development is inhibited by overlying aquitards and limited recharge rates. Long open interval wells (LOIWs)—wells uncased through multiple hydrostratigraphic units—are present in many confined aquifer systems and can be an important mechanism for deep basin aquifers to receive flow across aquitards. LOIWs are a major control on flow in the deep Cambrian–Ordovician sandstone aquifers of the upper Midwest, USA, providing a source of artificial leakage from shallow bedrock aquifers and equilibrating head within the sandstone aquifers despite differential pumpage. Conceptualizing and quantifying this anthropogenic flow has long been a challenge for groundwater flow modellers, particularly on a regional scale. Synoptic measurements of active production wells and well completion data for northeast Illinois form the basis for a transient, head‐specified MODFLOW model that determines mass balance contributions to the region and estimates LOIW leakage to the aquifers. Using this insight, transient LOIW leakage was simulated using transiently changing KV zones in a traditional, Q‐specified MODFLOW‐USG model, a novel approach that allows the KV in a cell containing a LOIW to change transiently by use of the time‐variant materials (TVM) package. With this modification, we achieved a consistent calibration through time, averaging 19.9 m root mean squared error. This model indicates that artificial leakage via LOIWs contributed a minimum of 10–13% of total flow to the sandstone aquifers through the entire history of pumping, up to 50% of flow around 1930. Removal from storage exceeds 40% of flow during peak withdrawals, much of this flow sourced from units other than the primary sandstone aquifers via LOIWs. As such, understanding the timing and magnitude of LOIW leakage is essential for predicting future water availability in deep basin aquifers.

On multiplicatively-additive iteration groups

Define on the set G:=mathbb R^+times mathbb R the operation (t,a)*(s,b)=(ts,tb+a). (G,*) is a non-commutative group with the neutral element (1, 0). We consider a non-commutative translation equation F(eta ,F(xi ,x))=F(eta *xi ,x), eta , xi in G, xin I, F(1,0)=mathrm{id}, where I is an open interval and F:Gtimes Irightarrow I is a continuous mapping. This equation can be written in the form: F((t,a),F((s,b),x))=F((ts,tb+a),x), t,s in mathbb R^+, xin I. For t=1 the family {F(t,a)} defines an additive iteration group, however for a=0 it defines a multiplicative iteration group. We show that if F(t, 0) for some tne 1 has exactly one fixed point x_t, (F(t,0)-mathrm{id})(x_t-mathrm{id})ge 0 and for an a>0 F(1,a)>mathrm {id}, then there exists a unique homeomorphism varphi :Irightarrow mathbb R such that F((s,b),x)=varphi ^{-1}(svarphi (x)+b) for sin mathbb R^+ and bin mathbb R.

The Problem of Selfish Parking

One of the models of discrete analog of the Renyi problem known as the “parking problem” has been considered. Let n and i be integers, n ≥ 0, and 0 ≤ i ≤ n–1. Open interval (i, i + 1), where i is a random variable taking values 0, 1, 2, …, and n–1 for all n ≥ 2 with equal probability, is placed on interval [0, n]. If n < 2, we say that the interval cannot be placed. After placing the first interval, two free intervals [0, i] and [i + 1, n] are formed, which are filled with intervals of unit length according to the same rule, independently of each other, etc. When the filling of [0, n] with unit intervals is completed, the distance between any two neighboring intervals does not exceed 1. Let Xn be the number of placed intervals. This paper analyzes the asymptotic behavior of moments of random variable Xn. Unlike the classical case, exact expressions for the first moments can be found.

L1-Uniqueness of the Fokker-Planck Equation on a Riemannian Manifold

In this paper, we obtain a necessary and sufficient condition for L∞-uniqueness of Sturm-Liouville operator $a(x)\frac {d^{2}}{dx^{2}} + b(x) \frac d{dx} -V$ on an open interval of $\mathbb {R}$, which is equivalent to the L1-uniqueness of the associated Fokker-Planck equation. For a general elliptic operator $\mathcal {L}^{V}:={\Delta } +b \cdot \nabla -V$ on a Riemannian manifold, we obtain sharp sufficient conditions for the L1-uniqueness of the Fokker-Planck equation associated with $\mathcal {L}^{V}$, via comparison with a one-dimensional Sturm-Liouville operator. Furthermore the L1-Liouville property is derived as a direct consequence of the L∞-uniqueness of $\mathcal {L}^{V}$.

ANALYZING THE SMOOTH AND STRIATED SPACE IN PASAR CIPUTAT TANGERANG SELATAN

Striated is seen as a fixed space and carries a sense of border. On the other hand, smooth space is seen as continuous and open interval. However, both terms are always intermingling, at one point smooth can be striated and vice versa. A city can be seen as a striated (border) and as smooth space (urban sprawl). Looking at a strip near Pasar Ciputat, Tangerang Selatan, this paper investigates how space changes function and identity overtime. The strip becomes a good example of analyzing the smooth and striated space practiced in everyday life. This strip is heavily populated by street vendors who has ‘occupying schedule’ and continuously changes the patterns of occupation. They prefer to sell goods on the road instead of in the provided building. By midnight, the road is not accessible as the vendors closed off and sell their goods on the road. In the morning and afternoon, some vendors disappear and their former space has been used by other vendors to sell different goods. Through observation, urban morphological mapping and photographic analysis, this paper uncovers the fluid uses and meaning of the space.

Impact of Heterogeneity on Closed and Open Birth Intervals

Vast literature is available where modelling for duration between ith and (i + 1)th births has been done. Apart from other considerations these models assume that consecutive birth intervals are independently distributed. This assumption may be quite reasonable if the population of females is homogeneous with respect to fertility parameters involved in the model. However, if population is heterogeneous with respect to these parameters, then the consecutive intervals are likely to be dependent. The behaviour of closed and open birth intervals under the condition of heterogeneity in the population with respect to certain fertility parameters is investigated.

On Glowinski’s Open Question on the Alternating Direction Method of Multipliers

The alternating direction method of multipliers was proposed by Glowinski and Marrocco in 1974, and it has been widely used in a broad spectrum of areas, especially in some sparsity-driven application domains. In 1982, Fortin and Glowinski suggested to enlarge the range of the dual step size for updating the multiplier from 1 to the open interval of zero to the golden ratio, and this strategy immediately accelerates the convergence of alternating direction method of multipliers for most of its applications. Meanwhile, Glowinski raised the question of whether or not the range can be further enlarged to the open interval of zero to 2; this question remains open with nearly no progress in the past decades. In this paper, we answer this question affirmatively for the case where both the functions in the objective function are quadratic. Thus, Glowinski’s open question is partially answered. We further establish the global linear convergence of the alternating direction method of multipliers with this enlarged step size range for the quadratic programming under a tight condition.

On the Difference of Spectral Projections

For a semibounded self-adjoint operator T and a compact self-adjoint operator S acting on a complex separable Hilbert space of infinite dimension, we study the difference $$ D(\lambda ) := E_{(-\infty , \lambda )}(T+S) - E_{(-\infty , \lambda )}(T), \, \lambda \in \mathbb {R} $$ , of the spectral projections associated with the open interval $$ (-\infty , \lambda ) $$ . In the case when S is of rank one, we show that $$ D(\lambda ) $$ is unitarily equivalent to a block diagonal operator $$ \Gamma _{\lambda } \oplus 0 $$ , where $$ \Gamma _{\lambda } $$ is a bounded self-adjoint Hankel operator, for all $$ \lambda \in \mathbb {R} $$ except for at most countably many $$ \lambda $$ . If, more generally, S is compact, then we obtain that $$ D(\lambda ) $$ is unitarily equivalent to $$ \Gamma _{\lambda } + \Lambda _{\lambda } $$ for all $$ \lambda \in \mathbb {R} $$ except for at most countably many $$ \lambda $$ , where $$ \Gamma _{\lambda } $$ is a bounded self-adjoint Hankel operator and $$ \Lambda _{\lambda } $$ is a compact self-adjoint operator.

Slant Vector Fields on the Hypersurfaces

In the present paper, we introduce the concept of a slant vector field $$\chi$$ defined on a hypersurface S, as a generalization of the tangent vector field on S, and investigate the problem of its existence, uniqueness and integral curve. Among other things, we provide an integral equation and also a differential equation for the integral curve of $$\chi$$ , say $$\alpha$$ , defined on an open interval I containing 0 such that $$\alpha (0)=p$$ , where p is an arbitrary point of the hypersurface. At the end, we also investigate some special cases and some examples.

Maximal Operators: Scales, Curvature and the Fractal Dimension

The spherical maximal operator $$Af(x) = \mathop {sup}\limits_{t > 0} \left| {{A_t}f(x)} \right| = \mathop {sup}\limits_{t > 0} \left| \int{f(x - ty)d\sigma (y)} \right|$$ where σ is the surface measure on the unit sphere, is a classical object that appears in a variety of contexts in harmonic analysis, geometric measure theory, partial differential equation and geometric combinatorics. We establish Lp bounds for the Stein spherical maximal operator in the setting of compactly supported Borel measures μ, ν satisfying natural local size assumptions $$\mu (B(x,r)) \leqslant C{r {{s_\mu }}},v(B(x,r)) \leqslant C{r {{s_v}}}$$ . Taking the supremum over all t > 0 is not in general possible for reasons that are fundamental to the fractal setting, but we can obtain single scale (t ∈ [a, b] ⊂ (0,∞)) results. The range of possible Lp exponents is, in general, a bounded open interval where the upper endpoint is closely tied with the local smoothing estimates for Fourier Integral Operators. In the process, we establish L2(μ) → L2(ν) bounds for the convolution operator Tλf(x) = λ * (fμ), where λ is a tempered distribution satisfying a suitable Fourier decay condition. More generally, we establish a transference mechanism which yields Lp(μ) → Lp(ν) bounds for a large class of operators satisfying suitable Lp-Sobolev bounds. This allows us to effectively study the dimension of a blowup set ({x: Tf(x) = ∞}) for a wide class of operators, including the solution operator for the classical wave equation. Some of the results established in this paper have already been used to study a variety of Falconer type problems in geometric measure theory.

Effects of Intraborehole Flow on Purging and Sampling Long-Screened or Open Wells.

Hydraulic head differences across the screened or open interval of a well significantly influence the sampled water mixture. Sample bias can occur due to an insufficient pumping rate and/or due to native groundwater displacement by intraborehole flow (IBF). Proper understanding of the sampled water mixture is crucial for accurate interpretation of environmental tracers and groundwater chemistry data, and hence groundwater characterization. This paper uses numerical modeling to quantify sample bias caused by IBF in an un-pumped high-yield well, and the influence of pumping rate and heterogeneity on the volume of pumpage required to purge an IBF plume. The results show that (1) the pumping rate must be at least an order of magnitude greater than the IBF rate to achieve permeability-weighted yield, (2) purge volume was 2.2 to 20.6 times larger than the IBF plume volume, with the ratio depending on plume location relative to hydraulic conductivity and head distributions, and (3) after an example 1000-day un-pumped period, purging required removal of at least three orders of magnitude more water than the common practice of three to five well volumes. These results highlight the importance of knowing the borehole flow regime to identify IBF inflow and outflow zones, estimate IBF rates, and to develop a strategic sampling approach.

Special multiply Einstein warped products with an affine connection

The aim of this paper is to study special multiply Einstein warped products having an affine connection. Let [Formula: see text] be a multiply warped product such that [Formula: see text] is an open interval, [Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text] for every [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] an affine connection on [Formula: see text] We compute the warping functions that make [Formula: see text] an Einstein space in the following cases: (a) [Formula: see text] is a semi-symmetric metric/non-metric connection and all the fibers are Ricci flat. (b) [Formula: see text] is a quarter-symmetric metric/non-metric connection and all the fibers are Ricci flat.

Local Exact Controllability to the Trajectories of the Cahn–Hilliard Equation

In this paper we prove the local exact controllability to the trajectories of the Cahn–Hilliard equation, which is a nonlinear fourth-order parabolic equation, by means of a control supported on an interior open interval. To prove this result we derive a Carleman estimate that allows us to conclude, thanks to a duality argument, the null controllability of the linearized equation around a given solution. Then, we apply a local inversion theorem to extend the control result to the nonlinear equation.