Limit Formula Research Articles

A dose-response relationship found between the Ten Steps to Successful Breastfeeding indicators and in-hospital exclusive breastfeeding in US hospitals.

In-hospital exclusive breastfeeding (EBF) is associated with longer breastfeeding durations, yet only 64% of US newborns are EBF for 7 days. The Ten Steps to Successful Breastfeeding (Ten Steps) are a set of evidenced-based maternity practices shown to improve breastfeeding outcomes; these were updated in 2018. Using hospital-level data from the 2018 Maternity Practices in Infant Nutrition and Care Survey (n = 2045 hospitals), we examined the prevalence of implementation of Ten Steps indicators (each step and total number of steps implemented). Using linear regression, we also examined the association between the steps and EBF prevalence adjusted for hospital characteristics and all other steps. Discharge support was not included in the models since it primarily occurs after hospital discharge. The most frequently implemented step was the provision of prenatal breastfeeding education (95.6%). Steps with low implementation included rooming-in (18.9%), facility policies supportive of breastfeeding (23.4%), and limited formula supplementation (28.2%). After adjusting for hospital characteristics and all other steps, limited formula supplementation (difference = 14.4: 95% confidence interval [CI]: 12.6, 16.1), prenatal breastfeeding education (difference = 7.0; 95% CI: 3.3, 10.8), responsive feeding (difference = 6.3; 95% CI: 3.7, 9.0), care right after birth (skin-to-skin; difference = 5.8; 95% CI: 4.2, 7.4), and rooming-in (difference = 2.4; 95% CI: 0.4, 4.6) were associated with higher in-hospital EBF prevalence. We found a dose-response relationship between the number of steps implemented and in-hospital EBF prevalence. Increased implementation of the updated Ten Steps may improve EBF and infant and maternal health outcomes.

An automatic quadrature method for semi-infinite integrals of exponentially decaying functions and its Matlab code

For the integral of a function f over a semi-infinite interval [0,∞) with f(x) decaying exponentially as x→∞, an automatic quadrature scheme is constructed and implemented in Matlab. Three limit formulae of Clenshaw–Curtis-type rules in our recent work (Numerical Algorithms, vol.90, 2022, pp.3–30) are exploited that converge fast for analytic functions. Each formula is expressed by a weighted infinite sum of function values at nodes and so its truncated finite sum is used. The best of the three formulae in accuracy is used as an approximation whose error is estimated with other two formulae and no additional function evaluations, since nodes of the other formulae are included in those of the best one. Numerical results indicate that our automatic scheme is better in performance than the QUADPACK routine for several types of test integrals. Particularly, it copes quite well with oscillatory integrals including the sinusoidal function and/or the Bessel function that are known to be difficult to approximate.

A Kronecker limit formula for indefinite zeta functions

We prove an analogue of Kronecker’s second limit formula for a continuous family of “indefinite zeta functions”. Indefinite zeta functions were introduced in the author’s previous paper as Mellin transforms of indefinite theta functions, as defined by Zwegers. Our formula is valid in dimension g=2 at s=1 or s=0. For a choice of parameters obeying a certain symmetry, an indefinite zeta function is a differenced ray class zeta function of a real quadratic field, and its special value at s=0 was conjectured by Stark to be a logarithm of an algebraic unit. Our formula also permits practical high-precision computation of Stark ray class invariants.

Numerical study on the blocking effect of skin on Flash-Ball Impact and damage assessment

To explore the response law of non-lethal large-size kinetic energy projectiles to blunt attack on skin tissue, and to evaluate the skin injury characteristics of the attacked personnel and the use safety of kinetic energy projectiles. Based on the LS-DYNA simulation software, a three-layer skin simulation model and a Flash-Ball rubber bullet model are established, and the force-time and deformation-time biomechanical corridors of the Flash-Ball rubber bullet impacting human skin tissue are obtained. The corridor curve and the energy transfer and diffusion are analyzed and compared. The safety evaluation of the damage caused by the rubber bullet shooting a human body at different distances is carried out using the empirical formula of the penetration limit. Finally, the safe shooting distance is obtained. The results show that the model used in the simulation has a good correlation with the experimental data, its biomechanical corridor characteristics are different from those of conventional vehicle impact and small-size projectile response characteristics. The energy transfer and action time of medium and low-speed impact may cause greater damage. The fat layer is the largest energy absorption unit. The minimum safe shooting distance to ensure skin tissue from penetrating damage is 15.8 m, and the limit specific kinetic energy of skin damage is 7.88 J/cm2. This study can be extended to the study of biomechanical response law and safety evaluation under the impact of the same type of large kinetic energy projectile, which provides an important theoretical reference for the police to use large kinetic energy projectiles to conduct safe shooting in peacekeeping operations.

Example of a solution for Dorodnitzyn’s limit formula

In the present paper, we show an example of a solution for Dorodnitzyn’s gaseous boundary layer limit formula. Oleinik’s no back-flow condition ensures the existence and uniqueness of solutions for the Prandtl equations in a rectangular domain R⊂R2. It also allowed us to find a limit formula for Dorodnitzyn’s stationary compressible boundary layer with constant total energy on a bounded convex domain in the plane R2. Under the same assumption, we can give an approximate solution u for the limit formula if |u|<<<1 such that: u(z)≅δ∗c∗z+625⋅12i0⋅4U23z4+o(z5),that corresponds to an approximate horizontal velocity component when a small parameter ϵ given by the quotient of the maximum height of the domain divided by its length tends to zero. Here, c>0, δ is the boundary layer’s height in Dorodnitzyn’s coordinates, U is the free-stream velocity at the upper boundary of the domain, and T0 is the absolute surface temperature.

KRONECKER LIMIT FUNCTIONS AND AN EXTENSION OF THE ROHRLICH–JENSEN FORMULA

Abstract In [20], Rohrlich proved a modular analog of Jensen’s formula. Under certain conditions, the Rohrlich–Jensen formula expresses an integral of the log-norm $\log \Vert f \Vert $ of a ${\mathrm {PSL}}(2,{\mathbb {Z}})$ modular form f in terms of the Dedekind Delta function evaluated at the divisor of f. In [2], the authors re-interpreted the Rohrlich–Jensen formula as evaluating a regularized inner product of $\log \Vert f \Vert $ and extended the result to compute a regularized inner product of $\log \Vert f \Vert $ with what amounts to powers of the Hauptmodul of $\mathrm {PSL}(2,{\mathbb {Z}})$ . In the present article, we revisit the Rohrlich–Jensen formula and prove that in the case of any Fuchsian group of the first kind with one cusp it can be viewed as a regularized inner product of special values of two Poincaré series, one of which is the Niebur–Poincaré series and the other is the resolvent kernel of the Laplacian. The regularized inner product can be seen as a type of Maass–Selberg relation. In this form, we develop a Rohrlich–Jensen formula associated with any Fuchsian group $\Gamma $ of the first kind with one cusp by employing a type of Kronecker limit formula associated with the resolvent kernel. We present two examples of our main result: First, when $\Gamma $ is the full modular group ${\mathrm {PSL}}(2,{\mathbb {Z}})$ , thus reproving the theorems from [2]; and second when $\Gamma $ is an Atkin–Lehner group $\Gamma _{0}(N)^+$ , where explicit computations of inner products are given for certain levels N when the quotient space $\overline {\Gamma _{0}(N)^+}\backslash \mathbb {H}$ has genus zero, one, and two.

Classification system for inter- and intra-module joints in non-sway steel MiC structures

The lack of guidelines for determining the rigidity of inter- and intra-module joints in corner-supported steel modular integrated construction (MiC) buildings can lead to unsafe or over-conservative designs. To address this issue, this study proposes a classification system for non-sway steel MiC buildings that covers both inter- and intra-module joints. First, the semi-rigidity of the joint regions in steel MiC buildings was clarified and the necessary degrees of freedom for joint classification were determined. Then a minimum substructure including one joint region was extracted from a steel MiC building, and its carrying capacity was determined as a simplified analytical model that considering the stiffnesses of both the inter- and intra-module joints. The simplified model was adopted to derive explicit formulas for the boundary limits of rigid/non-rigid inter- and intra-module joints, based on the criterion that the carrying capacity of the substructure with finite joint stiffnesses is 95% of that with rigid properties. Finally, the feasibility of the proposed classification system was verified by applying it to prototype MiC structures.

Metzler/Zeta Correspondence

We present a formula for determinants on the Metzler matrices of digraphs. Furthermore, we introduce a walk-type zeta function with respect to this Metzler matrix of a finite torus graph and express its limit formula by using the integral expression.

Arithmetic properties of the Herglotz function

AbstractIn this paper we study two functionsF⁢(x){F(x)}andJ⁢(x){J(x)}, originally found by Herglotz in 1923 and later rediscovered and used by one of the authors in connection with the Kronecker limit formula for real quadratic fields. We discuss many interesting properties of these functions, including special values at rational or quadratic irrational arguments as rational linear combinations of dilogarithms and products of logarithms, functional equations coming from Hecke operators, and connections with Stark’s conjecture. We also discuss connections with 1-cocycles for the modular groupPSL⁡(2,ℤ){\operatorname{PSL}(2,\mathbb{Z})}.

Finding the Optimal Topology of an Approximating Neural Network

A large number of researchers spend a lot of time searching for the most efficient neural network to solve a given problem. The procedure of configuration, training, testing, and comparison for expected performance is applied to each experimental neural network. The configuration parameters—training methods, transfer functions, number of hidden layers, number of neurons, number of epochs, and tolerable error—have multiple possible values. Setting guidelines for appropriate parameter values would shorten the time required to create an efficient neural network, facilitate researchers, and provide a tool to improve the performance of automated neural network search methods. The task considered in this paper is related to the determination of upper bounds for the number of hidden layers and the number of neurons in them for approximating artificial neural networks trained with algorithms using the Jacobi matrix in the error function. The derived formulas for the upper limits of the number of hidden layers and the number of neurons in them are proved theoretically, and the presented experiments confirm their validity. They show that the search for an efficient neural network can focus below certain upper bounds, and above them, it becomes pointless. The formulas provide researchers with a useful auxiliary tool in the search for efficient neural networks with optimal topology. They are applicable to neural networks trained with methods such as Levenberg–Marquardt, Gauss–Newton, Bayesian regularization, scaled conjugate gradient, BFGS quasi-Newton, etc., which use the Jacobi matrix.

Exclusive Enteral Nutrition for the Treatment of Pediatric Crohn's Disease: The Patient Perspective.

Crohn's disease (CD) is a chronic, incurable and relapsing disease involving any part of the gastrointestinal tract and exclusive enteral nutrition (EEN) is first-line therapy. Few studies have examined the patient experience of EEN. The aim of this study was to assess the child' s experiences of EEN, to identify problematic themes and understand the child's mindset. Children with CD who previously completed EEN were recruited to complete a survey. All data were analyzed using Microsoft Excel and reported as N (%). Forty-four children (mean age 11.3 years) consented to participate. Sixty-eight percent of children reported limited formula flavors as the most challenging aspect and 68% of children identified 'support' to be important. This study highlights the psychological impact of chronic disease and its therapies on children. Providing adequate support is essential to insure EEN is successful. Further studies are required to determine psychological support strategies for children taking EEN.

Bourgain–Brezis–Mironescu–Maz’ya–Shaposhnikova limit formulae for fractional Sobolev spaces via interpolation and extrapolation

The real interpolation spaces between \(L^{p}({{\mathbb {R}}}^{n})\) and \({\dot{H}}^{t,p}({{\mathbb {R}}}^{n})\) (resp. \(H^{t,p}({{\mathbb {R}}}^{n})\)), \(t>0,\) are characterized in terms of fractional moduli of smoothness, and the underlying seminorms are shown to be “the correct” fractional generalization of the classical Gagliardo seminorms. This is confirmed by the fact that, using the new spaces combined with interpolation and extrapolation methods, we are able to extend the Bourgain–Brezis–Mironescu–Maz’ya–Shaposhnikova limit formulae, as well as the Bourgain–Brezis–Mironescu convergence theorem, to fractional Sobolev spaces. On the other hand, we disprove a conjecture of Brazke et al. (Bourgain–Brezis–Mironescu convergence via Triebel–Lizorkin spaces. https://arxiv.org/abs/2109.04159) suggesting fractional convergence results given in terms of classical Gagliardo seminorms. We also solve a problem proposed in Brazke et al. (Bourgain–Brezis–Mironescu convergence via Triebel–Lizorkin spaces. https://arxiv.org/abs/2109.04159) concerning sharp forms of the fractional Sobolev embedding.

Local and post-local buckling behavior of welded square high-strength steel tubes with concrete-infilled restraints

Concrete-filled high-strength steel tubular members gain increasing popularity as the building height and bridge span increase. The slender sections and higher stress levels, however, make the high-strength steel plates more susceptible to local buckling. This paper reports an experimental and numerical investigation on local and post-local buckling behavior of welded square high-strength steel tubes with concrete-infilled restraints. Sixteen high-strength steel tubes with nominal yield strengths of 460, 500, and 550 MPa with concrete-infilled restraints were tested. The experimental results reveal that the post-buckling reserve strength of steel tubes with slender sections increases with the increase in plate slenderness regardless of steel grade. A total of 168 numerical models were subsequently established using the verified finite element method. Based on the finite element analysis results, the slenderness limits and effective width formula were proposed for both high-strength and normal-strength steel tubes with concrete-infilled restraints. Available test data of steel-only-loaded concrete-filled steel tubular specimens constitutes an experimental database to evaluate the reliability of the existing slenderness limits and effective width formulas. The comparison result shows that GB 50936, AS/NZS 2327, and AISC 360-16 overestimate the slenderness limits, while Song et al. underestimate the slenderness limit excessively. The proposed slenderness limit (λpl = 0.500) is more consistent with the experimental results with a reasonable conservative level. The mean ratio of predicted post-buckling strengths by the proposed effective width formula to experimental results is 0.94, with a standard deviation of 0.073. The proposed slenderness limit and effective width formula provide a more accurate prediction and, therefore, are recommended in design.

Effects of electric field on Rayleigh limit of nanoscale water droplets: molecular dynamics simulation

Nanoscale charged water droplets play a significant role in many physical processes, including cloud electrification and electrospray ionization, which have become one research focus. Generally, the maximum value of charge that a droplet can carry is called Rayleigh limit. Here, we investigate the effect of electric field (<0.5 V nm−1) on Rayleigh limit of nanoscale water droplets (r < 5 nm) by molecular dynamics simulation and theoretically qualitative analysis. In the simulation, Rayleigh limit of nanoscale water droplets under various electric fields is investigated based on optimal point charge water model by GROMACS package code. Our study demonstrates that electric field could affect Rayleigh limit by generating the induced charge, changing the surface tension and the droplet shape. Further, we propose the modified Rayleigh limit formula under electric field, with considering the potential energy of deformed charged droplet under strong electric field. The modified formula can qualitatively explain the abnormal trend that Rayleigh limit of nanoscale water droplet (r > 3 nm) decreases first and then increases with the electric field (<0.5 V nm−1) in the simulation.

High strength concrete prestressed bridges: Exposure conditions, mechanical properties, modified design equations, parametric study, and structural reliability

The majority of the current requirements for prestressed concrete were established based on the mechanical properties of normal strength concrete. However, with the more common use of High Strength Concretes (HSC) for bridges and structures, some of these requirements become conservative and require re-evaluation. The main objective of this research study was to modify the allowable stresses for HSC prestressed members and evaluate their impact on both structural design and reliability. An experimental program was developed and a statistical analysis was conducted to determine the effects of various field exposure conditions on the mechanical properties of HSC. Accordingly, property relationships and prediction formulas were proposed and compared to the current codes and standards. A parametric study was conducted to evaluate the economic impact of the modified stress limit formula on the design of typical HSC prestressed bridges, in terms of the maximum span lengths that can be achieved. Results revealed that the proposed modified design equation resulted in longer maximum spans in comparison with the current standards specifications, which would lead to cost reduction. Results also revealed that the majority of the prediction formulas used by codes and standards and suggested by various researchers overestimated the results obtained from this study and only the AASHTO LRFD Specifications and ACI 318 formulas provided conservative estimates. Furthermore, the safety of the proposed modified stress limit was evaluated by applying structural reliability theory and utilizing Monte-Carlo simulations..

Perilaku Pencarian Informasi Mahasiswa Melalui Media Sosial Instagram Sebagai Pemenuhan Pengetahuan Tentang Akademik dan Kemahasiswaan

Research Purpose. This study aims to determine the behavior of students seeking information through social media as a fulfillment of knowledge about academics and student affairs based on the theoretical model of Carol Kuhlthau, namely the information search process. In this model the information search process is divided into 6 stages, namely the initiation stage, the selection stage, the exploration stage, the preparation stage, the collection stage and the presentation stage. Methods. The method used is a quantitative method with a descriptive approach. The population of this researcher is followers of the Instagram account @liscarehimaka as many as 525 and the sampling technique uses simple random sampling which produces a sample of 84 respondents. Data Analysis. The data analysis method used is in the form of table analysis and category calculations with interval limit formulas. Result and Discussion. The results showed that the stages in searching for student information through social media Instagram as the fulfillment of knowledge about academics and student affairs were in the high category.Keywords: Information seeking behavior, knowledge, social media

Experimental investigation of effect of changing gap size in buckling restrained braces

This experimental study investigates the effect of changing the debonding gap between the core and the mortar filler on the global stability of BRBs using different cross-section restrained members. A total of eight mortar-filled BRBs were produced using a rectangular cross-section steel core and two different restraining members, a circular hollow cross-section (BRB-C series) and a square hollow cross-section (BRB-S series). In choosing the gap sizes, the gap limit formulas in the literature were considered. Not exceeding the limits of the gap, 2.8 mm, 5.6 mm, 8.4 mm, and 11.2 mm gaps were left as the multiples for the radius of inertia of the rectangular cross-section core in the BRBs. All specimens were subjected to displacement-controlled axial cyclic loading. As a result, failure modes, hysteretic performance, energy dissipation, and ductility were summarized and analysed for each specimen. The results showed that the specimens had a better structural performance with a 2.8-mm gap size, which is the radius of inertia of the core. Furthermore, the local buckling modes throughout the core increased in number as the size of the gap decreased, thus raising the members' axial load capacity and energy dissipation. It was concluded that the best structural behaviour of the tested series was provided with the smallest gap of 2.8 mm, better behaviour in energy dissipation may be obtained with smaller gap sizes. However, in this case, it is more likely to increase buckling at the gusset plates and cause local deformations with the end of the restraining members.

General Limit Formulae Involving Prime Numbers

Abstract Let p n be the n th prime number. In this note, we study strictly increasing sequences of positive integers A n such that the limit lim n →∞ (A 1 A 2 · · · A n )1 /pn = e holds. This limit formula is in fact a generalization of some previously known results. Furthermore, some other generalizations are established.

Exploring women’s exposure to marketing of commercial formula products: a qualitative marketing study from two sites in South Africa

ABSTRACT Background Regulating the marketing of commercial formula products is a long-term commitment required to protect breastfeeding. Marketing strategies of formula manufacturers, retailers and distributors evolve at a rapid rate. Objective The aim of this research was to describe exposure of pregnant women and mothers of young children in South Africa to marketing of commercial formula products, compared to international recommendations and national legislation. Methods Using mobile phone marketing diaries twenty participants in Cape Town and Johannesburg documented the formula marketing they were exposed to for one week. Ten mothers were interviewed to explore their perceptions towards marketing exposure in more depth. Results Women reported limited infant formula advertising, but an abundance of strategies used to market growing-up formula and powdered drinks for children over 36 months. Strategies included product packaging, in-store displays, online distribution channels and educational material about product ranges. Online strategies were reported, namely social media marketing (sponsored adverts and support groups), websites and mobile phone applications providing infant and young child feeding information and price discounts, print and TV advertisements, and competitions. Products for children over 36 months are cross-promoted with products prohibited to be advertised by national legislation. Conclusions South African women are being exposed to covert marketing of infant, follow-up, and growing-up formula. Explicit marketing of products for children over 36 months of age allows formula companies to provide messages about branding and use of commercial formula products to mothers. National legislation should be updated and effectively implemented to address changing marketing strategies.

Nonadiabatic Correction and Adiabatic Criteria of Noninteracting Quantum Dot Systems

We theoretically study nonadiabatic corrections for charge pumping in a noninteracting electron model of a single-level quantum dot. We derive a formula for the velocity limit of parameter driving to realize adiabatic pumping and illustrate its features in the wide-band limit. We discuss the effect of the nonadiabatic corrections in terms of a typical velocity limit, which is defined by averaging the velocity limits on the parameter contour. We also show that the typical velocity limit vanishes when the adiabaticity breakdown occurs in a quantum dot coupled to reservoirs with a band edge.