Type Formula Research Articles

Impact of venting, caloric density, and formula type on flow rates from bottle nipples

PurposeTo determine whether flow rate from the bottle nipple is impacted by a venting system, caloric density of the infant formula, or by milk type of the formula (i.e., standard cow's milk, hypoallergenic cow's milk, or soy protein). MethodFlow rates were tested of six nipple types with and without a venting system. Separately, five nipple types were tested for flow rate with formula at caloric densities of 20, 22, 24, and 30 calories per ounce. Then, two nipple types were tested with six infant formulas of different milk types. ResultsFor two nipple types, flow rate was faster with the venting system compared to without. For three of the nipple types, flow rate increased as caloric density increased. There were no significant differences in flow by milk type. ConclusionsVenting systems and caloric density may impact flow rate from the bottle nipple, but not consistently across nipple types.

A new diagonal and Toeplitz splitting preconditioning method for solving time-dependent Riesz space-fractional diffusion equations

The initial–boundary value problem of the Riesz space-fractional diffusions equation is an important class of equations arising in many application fields. In this paper, we apply the Grünwald–Letnikov type formulas to discretize the time-dependent Riesz space-fractional diffusion equations, and obtain a system of linear equations from the discretization results. A new diagonal and Toeplitz splitting (NDTS) iteration method is constructed for this linear system. Based on the NDTS iteration method, an NDTSτ preconditioner is proposed and the generalized minimal residual (GMRES) method combined with this preconditioner is applied to solve the linear system. We theoretically show that the eigenvalues of the NDTSτ preconditioned matrix are clustered. Numerical experiments illustrate the efficiency of the proposed method.

Comparison of Estimation of Glomerulus Filtration with MDRD and CKD-EPI Formula in Diabetes Mellitus Patients Type 2 in Bhayangkara Hospital Palembang

Patients with uncontrolled type 2 diabetes mellitus (DM) can be at risk of complications with the kidneys. The decrease in the condition of the kidneys impacts the ability of the glomerulus to filter. This study aims to compare the estimated glomerular filtration rate (eGFR) based on Creatinine Levels with MDRD and CKD-EPI Formulas. The research was conducted with a cross-sectional approach. The study was carried out from March to April 2021. The sample size of this study was 97 data points on Type 2 DM. The result shows the average eGFR values with the MDRD and CKD-EPI formulas in people with Type 2 DM were 97.85 ml/min/1.73 m2 and 85.67 ml/min/1.73 m2. From the Mann-Whitney test, the results obtained were p> α (0.05), p-value = 0.3498. There were differences in the eGFR values calculated by the MDRD and CKD-EPI formulas.

Multiphysics Simulation for the Performance of Tubular Solid Oxide Fuel Cells Operated on Coal Syngas

Solid oxide fuel cells (SOFCs) can be operated directly on coal syngas, but the various contaminants in coal syngas affect the performance and durability of the device. In the present study, three-dimensional multiphysics simulations were developed to investigate the performance degradation of tubular SOFCs operated on coal syngas. The numerical model includes charge conservation, species transport within the electrodes and the channels, and heat transfer within the device. These physical processes are coupled by the chemical/electrochemical reactions, which are represented by a Butler-Volmer type formula. Based on the thermodynamic database about impurities interaction with the Ni-YSZ composite anode, the contaminants are assumed to be adsorbed on the anode surface and form secondary phases. These formed phases affect the microstructural properties, electrical conductivity, and the number of active sites available for electrochemical reactions (i.e., hydrogen and carbon monoxide oxidation). During the cell operation, the contaminants diffuse from the fuel channel/anode interface to the anode/electrolyte interface, causing further irreversible degradation. The in-house developed multiphysics simulation is designed to be robust for prediction of interaction between anode materials with different types of contaminants (e.g., PH3, H2S, H2Se, AsH3, and user-defined). With the model parameters calibrated in the previous study, the performance of the tubular SOFCs with different levels/types of contaminants is predicted. The tolerance limits of the SOFC cell on single and multiple contaminants are also predicted with the simulations. Furthermore, the degradation resulted from Ni coarsening and redistribution, are also implemented into the model to mimic the performance of realistic SOFCs operating on coal syngas. The performance degradation investigation in this study provides guidance for experimental testing with syngas exposure, which is eventually beneficial to the cost reduction of the coal syngas clean-up technology.

An inverse scattering problem for eigenparameter-dependent discrete Dirac system with Levinson formula

In this paper, we have considered an inverse scattering problem for discrete Dirac operator L with eigenparameter dependent boundary condition. At the outset, the Jost solution and the Jost function of L are given. Then the zeros of the Jost function and some properties of the scattering function are examined. After finding the scattering dataset and the main equation for the operator L, the uniqueness of the kernel, continuity of the scattering function and the appropriate Levinson type formula are obtained.

Three essays on Machin’s type formulas

We study three questions related to Machin’s type formulas. The first one gives all two terms Machin formulas where both arctangent functions are evaluated 2-integers, that is values of the form b/2a for some integers a and b. These formulas are computationally useful because multiplication or division by a power of two is a very fast operation for most computers. The second one presents a method for finding infinitely many formulas with N terms. In the particular case N=2 the method is quite useful. It recovers most known formulas, gives some new ones, and allows to prove, in an easy way, that there are two terms Machin formulas with Lehmer measure as small as desired. Finally, we correct an oversight from previous result and give all Machin’s type formulas with two terms involving arctangents of powers of the golden section.

Limiting Cases of the Black-Scholes Type Asymptotics of Call Option Pricing in the Generalised CRR Model

The article concerns the generalised Cox‑Ross‑Rubinstein (CRR) option pricing model with new formulas for changes in upper and lower stock prices. The formula for option pricing in this model, which is the Black‑Scholes type formula, and its asymptotics are presented. The aim of the paper is to analyse limiting cases of the obtained asymptotics using probability theory and later data from the Warsaw Stock Exchange. Empirical analyses of option pricing in the generalised CRR model confirm the calculated limits.

Solution Formula of Korteweg Type by Using Partial Fourier Transform Methods in Half-Space without Surface Tension

Solution Formula of Korteweg Type by Using Partial Fourier Transform Methods in Half-Space without Surface Tension

The topical application of different galenic formulations can alter the thermographic images of skin: Limitations for public thermal screening on infection control situations

To analyze whether the application of topical formulas as cosmetics or sunscreens could affect the skin thermographic readings in terms of infection control in pandemic situations. The temperature of the skin of the dorsal region of the back and the face of 20 volunteers was followed after the application of 6 different types of gels, sunscreens, and make-up under controlled temperature and humidity conditions. High-resolution thermographic images were analyzed to calculate the temperature of treated skin compared to skin free of topical products. The application of hydroalcoholic gel resulted in a mean drop of more than 2°C just after 1minute followed by organic sunscreens until 1.7°C. Recovery was observed progressively until minute 9. Color make-up type formulas, rich in iron oxide as well as sunscreens with mineral filters had little or no effect on the skin thermal response. It is possible to alter the skin temperature almost immediately by using hydroalcoholic gels and sunscreen cosmetics. So, it is possible to produce false negative data in the readings of patients screened thermically.

W/O/W type lotion formulation of “arum manis” mango (Mangifera indica L.) pell as antioxidant

Arum manis mango peel contains compounds, namely flavonoids. Flavonoid compounds act as natural antioxidants. The weakness of flavonoid compounds is that they are not stable to the influence of high temperature and light intensity, so that the arum manis mango peel extract is made in the form of lotion type W/O/W. This study aims to determine the physical characteristics and stability of the W/O/W type emulsion form optimum formula in double emulsion preparations and lotion preparations, determine the stability of W/O/W type lotion preparations during storage using the cycling test method and determine the IC50 value in the optimum formula. lotion preparation type W/O/W. The optimum formula for double emulsion type W/O/W is found in formula 5 with a ratio of primary emulsion: secondary emulsion (80%:20%) with span 80 (10%) and tween 20 (5%) concentrations while the optimum formula for lotion preparations found in formula 3 with a ratio of double emulsion type W/O/W: lotion base (80%:20%) with a concentration of stearic acid (5%), cetyl alcohol (2.5%) and glycerin (10%). In the antioxidant activity of lotion preparations, the IC50 value was 136.543 ppm and the stability test on the cycling test method had an unstable form.

Construction of general forms of ordinary generating functions for more families of numbers and multiple variables polynomials

The aim of this paper is to construct general forms of ordinary generating functions for special numbers and polynomials involving Fibonacci type numbers and polynomials, Lucas numbers and polynomials, Chebyshev polynomials, Sextet polynomials, Humbert-type numbers and polynomials, chain and anti-chain polynomials, rank polynomials of the lattices, length of any alphabet of words, partitions, and other graph polynomials. By applying the Euler transform and the Lambert series to these generating functions, many new identities and relations are derived. By using differential equations of these generating functions, some new recurrence relations for these polynomials are found. Moreover, general Binet's type formulas for these polynomials are given. Finally, some new classes of polynomials and their corresponding certain family of special numbers are investigated with the help of these generating functions.

Efficient computation of the overpartition function and applications

In this paper we develop a method to calculate the overpartition function efficiently using a Hardy-Rademacher-Ramanujan type formula, and we use this method to find many new Ramanujan-style congruences, whose existence is predicted by Treneer and a few of which were first discovered by Ryan, Scherr, Sirolli and Treneer.

Behavior of Lagrange‐Galerkin solutions to the Navier‐Stokes problem for small time increment

AbstractWe consider two kinds of numerical quadrature formulas of Gauss type and Newton‐Cotes type, which are required in the real computation of Lagrange–Galerkin scheme for the Navier–Stokes problem. The Lagrange–Galerkin scheme with numerical quadrature, which has been used practically but not fully analyzed, is proved to be convergent at least for Gauss type quadrature under a condition on the time increment. As for the scheme with Newton‐Cotes type quadrature, it has more smooth convergent property than that of Gauss type, whose reason is discussed.

Partial degeneration of finite gap solutions to the Korteweg–de Vries equation: soliton gas and scattering on elliptic backgrounds

We obtain Fredholm type formulas for partial degenerations of theta functions on (irreducible) nodal curves of arbitrary genus, with emphasis on nodal curves of genus one. An application is the study of ‘many-soliton’ solutions on an elliptic (cnoidal) background standing wave for the Korteweg–de Vries (KdV) equation starting from a formula that is reminiscent of the classical Kay–Moses formula for N-solitons. In particular, we represent such a solution as a sum of the following two terms: a ‘shifted’ elliptic (cnoidal) background wave and a Kay–Moses type determinant containing Jacobi theta functions for the solitonic content, which can be viewed as a collection of solitary disturbances on the cnoidal background. The expressions for the travelling (group) speed of these solitary disturbances, as well as for the interaction kernel describing the scattering of pairs of such solitary disturbances, are obtained explicitly in terms of Jacobi theta functions. We also show that genus N + 1 finite gap solutions with random initial phases converge in probability to the deterministic cnoidal wave solution as N bands degenerate to a nodal curve of genus one. Finally, we derive the nonlinear dispersion relations and the equation of states for the KdV soliton gas on the residual elliptic background.

Dispersive estimates for the Schrödinger equation with finite rank perturbations

In this paper, we investigate dispersive estimates for the time evolution of HamiltoniansH=−Δ+∑j=1N〈⋅,φj〉φjinRd,d≥1, where each φj satisfies certain smoothness and decay conditions. We show that, under a spectral assumption, there exists a constant C=C(N,d,φ1,…,φN)>0 such that‖e−itH‖L1−L∞≤Ct−d2,fort>0. As far as we are aware, this seems to provide the first study of L1−L∞ estimates for finite rank perturbations of the Laplacian in any dimension.We first deal with rank one perturbations (N=1). Then we turn to the general case. By using an Aronszajn-Krein type formula for finite rank perturbations, we reduce the problem to the rank one case and solve it in a unified manner. Moreover, we show that in some specific situations, the constant C(N,d,φ1,…,φN) grows polynomially in N. Finally, as an application, we are able to extend the results to N=∞ and deal with some trace class perturbations.

Multiphysics Simulation for the Performance of Tubular Solid Oxide Fuel Cells Operated on Coal Syngas

Solid oxide fuel cells (SOFCs) can be operated directly on coal syngas, but the various contaminants in coal syngas affect the performance and durability of the device. In the present study, three-dimensional multiphysics simulations were developed to investigate the performance degradation of tubular SOFCs operated on coal syngas. The numerical model includes charge conservation, species transport within the electrodes/channels, and heat transfer within the device. These physical processes are coupled by the chemical/electrochemical reactions, which are represented by a Butler-Volmer type formula. Based on the thermodynamic database of impurity interactions with the Ni-YSZ composite anode, the contaminants are assumed to be adsorbed on the anode surface and form secondary phases. These formed phases affect the microstructural properties, electrical conductivity, and the number of active sites for electrochemical reactions. During the operation, the contaminants diffuse from the channel/anode interface to the anode/electrolyte interface, causing further irreversible degradation. The in-house developed multiphysics simulation is robust for prediction of interaction between anode materials with different types of contaminants (e.g., PH3, H2S, AsH3, etc.). With the calibrated model parameters, the performance of the tubular SOFCs with different levels/types of contaminants is predicted. The tolerance limits of the cells are also predicted. Furthermore, the degradation resulted from Ni redistribution, are also implemented into the model to mimic the performance of realistic SOFCs operating on coal syngas. The performance degradation investigation in this study provides guidance for experimental testing with syngas exposure, which is eventually beneficial to the cost reduction of the coal syngas clean-up technology.

Normalized Null hypersurfaces of Indefinite Kähler Manifolds

We study null hypersurfaces of indefinite Kähler manifolds and by taking the advantages of the almost complex structure $J$, we select a suitable rigging $\zeta$, which we call the $J-$rigging, on the null hypersurface. This suitable rigging enables us to build an associated Hermitian metric $\breve{g}$ on the ambient space and which is restricted into a non-degenerated metric $\widetilde{g}$ on the normalized null hypersurface. We derive Gauss-Weingarten type formulae for null hypersurface $M$ of an indefinite Kähler manifold $\overline{M}$ with a fixed closed Killing $J-$rigging for $M$. Later, we establish some relations linking the curvatures, null sectional curvatures, Ricci curvatures, scalar curvatures etc. of the ambient manifold and normalized null hypersurface.

Reliability Analysis on Stability of Armor Units for Foundation Mound of Composite Breakwaters

Probabilistic and deterministic analyses are implemented for the armor units of rubble foundation mound of composite breakwaters which is needed to protect the upright section against the scour of foundation mounds. By a little modification and incorporation of the previous empirical formulas that has commonly been applied to design the armor units of foundation mound, a new type formula of stability number has been suggested which is capable of taking into account slopes of foundation mounds, damage ratios of armor units, and incident wave numbers. The new proposed formula becomes mathematically identical with the previous empirical formula under the same conditions used in the developing process. Deterministic design have first been carried out to evaluate the minimum weights of armor units for several conditions associated with a typical section of composite breakwater. When the slopes of foundation mound become steepening and the incident wave numbers are increasing, the bigger armor units more than those from the previous empirical formula should be required. The opposite trends however are shown if the damage ratios is much more allowed. Meanwhile, the reliability analysis, which is one of probabilistic models, has been performed in order to quantitatively verify how the armor unit resulted from the deterministic design is stable. It has been confirmed that 1.2% of annual encounter probability of failure has been evaluated under the condition of 1% damage ratio of armor units for the design wave of 50 years return period. By additionally calculating the influence factors of the related random variables on the failure probability due to those uncertainties, it has been found that Hudson’s stability coefficient, significant wave height, and water depth above foundation mound have sequentially been given the impacts on failure regardless of the incident wave angles. Finally, sensitivity analysis has been interpreted with respect to the variations of random variables which are implicitly involved in the formula of stability number for armor units of foundation mound. Then, the probability of failure have been rapidly decreased as the water depth above foundation mound are deepening. However, it has been shown that the probability of failure have been increased according as the berm width of foundation mound are widening and wave periods become shortening.

THEOREMS OF LEGENDRE TYPE FOR OVERPARTITIONS

AbstractFormulas evaluating differences of integer partitions according to the parity of the parts are referred to as Legendre theorems. In this paper we give some formulas of Legendre type for overpartitions.

A proof of the fermionic theta coinvariant conjecture

Let (x1,…,xn,y1,…,yn) be a list of 2n commuting variables, (θ1,…,θn,ξ1,…,ξn) be a list of 2n anticommuting variables, and C[xn,yn]⊗∧{θn,ξn} be the algebra generated by these variables. D'Adderio, Iraci, and Vanden Wyngaerd introduced the Theta operators on the ring of symmetric functions and used them to conjecture a formula for the quadruply-graded Sn-isomorphism type of C[xn,yn]⊗∧{θn,ξn}/I where I is the ideal generated by Sn-invariants with vanishing constant term. We prove their conjecture in the ‘purely fermionic setting’ obtained by setting the commuting variables xi,yi equal to zero.