奇数阶中立型方程的比较定理与非振动性

建立了一个判别奇数阶中立型时滞微分方程方程非振动性的比较定理。它把中立型时滞微分方程的非振动判别，化为对应的中立型时滞微分不等式存在有界正确的判别。并举例说明了这个比较定理的应用。     

一类具有分布时滞的三阶中立型微分方程的振动性

为丰富三阶中立型微分方程的振动性理论研究,针对一类具有分布时滞的三阶中立型微分方程,利用Riccati变换和一元二次不等式,给出了该类具有分布时滞的三阶中立型微分方程一切解振动或收敛于零的充分条件,得到了新的振动准则.     

一类中立型泛函微分方程的振动性

研究了一类既有超前量又有滞后量的一阶中立型管函微分方程的振动性,给出了其解振动的几个充分性条件,所得结论推广和改进了现有文献的部分结果。     

中立型分段常变量微分方程解的振动性

通过构造差分方程的振动解，研究了一类二阶中立型分段常变量微分方程解的振动性，得到几个振动判据。     

中立型随机时滞微分方程截断Milstein数值解的强收敛性

研究非线性系数的Milstein中立型随机时滞微分方程数值解的收敛性问题。将截断思想和Milstein数值格式结合,对有高度非线性系数的中立型随机时滞微分方程,构建了截断Milstein数值格式。在局部Lipschitz条件及Khasminskii条件下,证明了中立型随机时滞微分方程截断Milstein数值解Lp强收敛于精确解。针对一个具体的中立型随机时滞微分方程,使用数值模拟验证了结论的正确性。     

具有正负系数的一阶中立型时滞微分方程的振动性

得到了具有正负系数的一阶中立型时滞微分方程一切解振动的新的充分条件∫∞t0[P(s)-Q(s-τ+δ)]exp(1)/(μ)∫∞t0u[P(u)-Q(u-τ+δ)]duds=∞.应用此条件得到了这类方程振动的一些较弱的充分条件.     

非线性中立型时滞随机微分方程数值解的指数稳定性

在非线性中立型时滞随机微分方程数值解的指数稳定性问题中,一般是将方程中的漂移项系数和扩散项系数分开设置增长性限制条件。为了降低对每个系数增长的限制,将非线性中立型时滞随机微分方程中的漂移项系数和扩散项系数联合考虑,即将两系数的限制在一个式子中,给出了非线性中立型时滞随机微分方程Euler-Maruyama(EM)方法数值解指数稳定性的一类充分性条件。结果显示,在给定的充分性条件下,对于任意初值,运用EM方法得到的非线性中立型时滞随机微分方程的数值解都是几乎处处渐近指数稳定的。     

具强迫力的一阶中立型微分方程的振动性

考虑具强迫力的一阶中立型微分方程ｄ／ｄｔ「ｘ（ｔ）－Ｒ（ｔ）ｘ（ｔ－τ）」＋Ｐ（ｔ）ｘ（ｔ－σ）＝ｆ（ｔ），ｔ≥ｔ０这里０≤Ｒ（ｔ）〈Ｃ〈１，Ｃ为正常数，得到了方程的所有解都振动的一个充分条件。     

一类二阶中立型微分方程有界解的振动性

研究具有正负系数的二阶中立型微分方程,建立了方程的有界解振动的一个充要条件以及解的振动性.     

一阶中立型时滞微分方程的振动性

研究一阶中立型微分方程ｄ／ｄｔ「ｘ（ｔ）＝ｐ（ｔ）ｘ（ｔ－ｒ（ｔ））」＋ｑ）ｔ）ｘ（ｔ－σ（ｔ））＝０,ｔ≥ｔ０,（Ｅ）其中ｐ（ｔ）,ｑ（ｔ）,ｒ（ｔ）,σ（ｔ）是「ｔ０,∞）上的非负连续函数,得到了方程（Ｅ）所有解振动的充分性判据,所得结果包含或改进了已有文献的相关结果。     

ESTIMATION OF ORIGINAL GRAVITY BY REFRACTOMETER

Empirical equations have been determined so that Original Gravity, Percentage Alcohol by volume and Residual Gravity can be calculated from the Refractometer Scale Reading and Present Gravity of beer. The equations have been derived from 258 ales and lagers covering a range of Original Gravities from 32 excess degrees (circa 9°P) to 82 excess degrees (circa 20°P). Subsequent testing of the equations suggest that they are applicable to a wide range of beers. The accuracy and precision of these equations are sufficient to permit their use in normal quality control operations. The 95% confidence limits for Original Gravity, Percentage Alcohol by volume and Residual Gravity are, ±1·8 excess degrees, ±0·30 percent and ±0·45 excess degrees, respectively. A nomograph has been constructed from the equations to reduce the need for calculation.     

Effect of year and cutting on equations for estimating net energy of alfalfa forage.

The net energy of lactation (NEL) concentration of forages is important for formulating diets. The equations presently used to estimate NEL of alfalfa are based on limited data. Our objective was to determine whether a larger database would provide more relevant equations. One hundred eighty samples of alfalfa were taken over four cuttings and 2 yr, combined into 45 composites and analyzed for neutral detergent fiber, acid detergent fiber (ADF), and in vitro true digestibility. Finally, NEL values were estimated using neutral detergent fiber and in vitro true digestibility. Prediction equations were obtained by regressing NEL upon ADF concentration. Changes in NEL with age of alfalfa at harvest differed with year and cutting. Estimation of NEL would be more accurate with equations specific for cutting and year, but such an approach would be difficult to use in practice. When data were pooled across years, four cutting-specific equations were obtained; these had different intercepts and slopes and gave different NEL values for a given ADF content. Differences among estimates of NEL increased as ADF increased. Data were combined across years and cuttings to give an overall equation that was similar to published prediction equations. Compared with NEL values from the cutting-specific equations, the overall equation underestimated NEL for first cutting alfalfa and overestimated NEL of second cutting alfalfa. A lack of precision in estimating NEL could equate to 1.5 to 2.5 kg of milk/d. Cutting specific equations should be used to estimate the NEL of first- and second-cutting alfalfa; NEL of the third and fourth cuttings could be estimated using an overall equation.     

固液混装罐头食品固体中心冷点温度预测

本文探索了固液混装罐头食品的传热特性。应用CS—2型温度信息处理机测定了固液混装罐头食品的固体和汤汁中心冷点温度值。编了计算机程序,计算传热过程的参数j,f值。建立一系列的固体和汤汁冷点处的传热方程和确立罐头食品的固液传热比方程,可预测固体中心温度值,百分误差在允许范围内。本文提出的方法是一种较理想的预测固体中心温度方法,可供制订合理杀菌工艺条件之用。     

Additive Genetic Model with Groups and Relationships

From simple genetic assumptions, matrix expressions are derived for the first and second moments of a random vector of breeding values. Emphasis is on structure in these matrix representations that can be exploited computationally in a mixed model analysis. Also derived are mixed model equations corresponding to a model in which the random vector has nonnull mean. These equations are particularly advantageous for fitting a particular kind of animal model with groups and relationships.     

Invited review: Corrected milk: Reconsideration of common equations and milk energy estimates

Corrected milk equations were developed in attempts to bring milk weights to a standardized basis for comparison by expressing the weight and composition of milk as corrected to the energy content of milk of a specific composition. Expressed as milk weights familiar on farm and in commerce, this approach integrates energy contributions of the dissimilar components to make the mass units more comparable. Such values are applied in evaluating feed efficiency, lactation performance, and global milk production, as functional units for lifecycle assessments, and in translation of research results. Corrected milk equations are derived from equations relating milk gross energy to milk composition. First, a milk energy equation is used to calculate the energy value of the milk composition to correct to (e.g., 0.695 Mcal/kg for milk with 3.5% fat, 3.05% true protein, and 4.85% lactose). That energy value is divided into the energy equation to give the corrected milk equation. Confusion has arisen, as different equations purport to correct to the same milk composition; their differences are based on uses of different energy equations or divisors. Accuracy of corrected milk equations depends on the accuracy of the energy equations used to create them. Energy equations have evolved over time as different milk component analyses have become more available. Inclusion of multiple milk components more accurately predicts milk energy content than does fat content alone. Omission of components from an equation requires the assumption that their content in milk is constant or highly correlated with an included component. Neither of these assumptions is true. Milk energy equations evaluated on a small data set of measured milk values have demonstrated that equations that incorporate protein, fat, and lactose contents multiplied by the gross energy of each component more closely predict milk energy than equations containing fewer components or regression-derived equations. This provides a tentative recommendation for using energy equations that include the 3 main milk components and their gross energy multipliers for predicting milk energy and deriving corrected milk equations. Accuracy of energy equations is affected by the accuracy of gross energy values of individual components and variability of milk composition. Lactose has consistent reported gross energy values. In contrast, gross energy of milk fat and protein vary as their compositional profiles change. Future refinements could assess accuracy of milk fat and protein gross energy and whether that appreciably improves milk energy predictions. Fat gross energy has potential to be calculated using the milk fatty acid profile, although the influence on gross energy may be small. For research, direct reporting of milk energy values, rather than corrected milk, provides the most explicit, least manipulated form of the data. However, provision of corrected milk values in addition to information on components can serve to translate the energy information to a form familiar to and widely used in the field. When reporting corrected milk data, the corrected milk equation, citation for the energy equation used, and composition and energy contents of the corrected milk must be described to make clear what the values represent.     

Study of mathematical models applied to sorption isotherms of Argentinean black bean varieties

Moisture sorption isotherms of five commercial black bean varieties harvested in the province of Salta, Argentina, were measured. Statistical methodology was applied to compare their sorption characteristics and it was observed that the five varieties could be considered as belonging to a same group.

Different equations proposed in the literature were studied and it was found that the best adjustments were provided by the Oswin and the White and Eiring equations. The estimated isotherm equations are given.

Adjusting the equations to sorption data found in literature, the White and Eiring equation provided a reasonable adjustment for all of them.     

变系数二阶微分方程的稳定性

研究二阶微分方程ｘ（ｔ）＋ｐ（ｔ）ｘ（ｔ）＋ｑ（ｔ）ｘ（ｔ）＝０的稳定性问题,获得某些有用的充分性条件,结果可用于讨论不满足有关文献中假设条件的方程的稳定性问题。     

Prediction and evaluation of urine and urinary nitrogen and mineral excretion from dairy cattle

Urine excretion is a substantial factor in the amount of manure that needs to be managed, and urinary N can contribute to ammonia volatilization. Development and validation of prediction equations focusing on dietary factors to decrease urine and urinary nutrient excretion will provide information for managing urine and feces separately or for other future technologies. The objective of this study was to develop equations for prediction of urine excretion and excretion of urinary N, Na, and K and to evaluate both new and previously published prediction equations for estimation of urine and urinary nutrient excretion from lactating dairy cows. Data sets from metabolism studies conducted at Washington State University were compiled and evaluated for excretion of minerals. Urine excretion averaged 24.1 kg/d and urinary nitrogen excretion ranged from 63 to 499 g/d in the calibration data set. Regression equations were developed to predict urine excretion, urinary N excretion, and urinary Na and K excretion. Predictors used in the regression equations included milk yield, body weight, dietary crude protein percentage, milk urea nitrogen, and nutrient intakes. Previously published prediction equations were evaluated using data sets from Washington State University and the University of Wisconsin. Mean and linear biases were evaluated by determining the regression of residuals on predicted values. Evaluation and validation of prediction equations are important to develop equations that will more accurately estimate urine and urinary nitrogen excretion from lactating dairy cows.     

An Approach to Kinematic Design of Four-bar Sley Drive Mechanisms in Weaving

Abstract

An approach to design a four-bar linkage sley drive mechanism for a desired sley motion curve is introduced. Kinematic design equations are given and then the link lengths of the mechanism are determined. Sley angular displacement, angular velocity and angular acceleration are obtained by using kinematic analysis equations and the effects of time ratio, the angle β and the deviation of the transmission angle from 90° on sley motion are discussed. Finally, the angle β, the minimum transmission angle and the time ratio values that can be used for different weaving machine types are commented on.     

Thermal Process Calculations for Different z and jc Values Using a Hand-Held Calculator

Equations facilitating the calculation of F, or process time used in the design and evaluation of thermal processes for low-acid foods packaged in hermetically sealed containers for j, values of 0.4–2.3 and a z value of 10–26°F are presented. The relationships are based on the data presented by Hicks (1958) and Hayakawa (1970). The equations, although complex, can be efficiently used to calculate sterilization values and processing times using presently available programmable calculators. The equations were developed and tested so the maximum error in a calculated result will not be more than 5%.