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A conventional oil and gas well does not have a natural production capacity, which necessitates a hydraulic fracturing operation. The effectiveness of the fracturing directly impacts the economic benefit of a single well. Among the various parameters, including fracture spacing, fracture width, and conductivity, fracture half-length is one of the main influencing factors on the productivity of horizontal wells. For conventional homogeneous reservoirs, research mainly focuses on fracture patterns with equal fracture lengths. However, in actual production processes, due to mutual interference and the superimposition of drainage areas between fractures, the production distribution of each fracture is non-uniform. Typical fracture distribution patterns mainly include uniform, staggered, dumbbell, and spindle. While many believe that the dumbbell-shaped fracture distribution pattern has the best effect, there has been no quantitative study on the length of each fracture under the dumbbell-shaped pattern. Based on this, this paper proposes a modeling approach for function-shaped fracture distribution that takes advantage of the high production of edge fractures and the low output of middle fractures in horizontal wells. The influence of this approach on production capacity is studied. Constant, linear, and parabolic functions are used to establish the relationship between fracture position and fracture half-length, optimizing the fracture distribution function to achieve the best production effect. This method can guide the horizontal well fracture distribution in the block to maximize productivity. The results show that the parabolic function-shaped model is better than the linear function-shaped model and the constant function-shaped model is the least effective. The research presented in this paper offers a new idea for optimizing on-site fracturing plans. It utilizes mathematical expressions to describe the parameters that affect productivity, which provides valuable guidance for designing multi-stage fractured horizontal wells in the field. In the future, this research will be extended by exploring the optimal fracture distribution function under different formation conditions.

У статті наведено одержані результати проведених польових експериментальних випробувань модернізованої коренезбиральної машини МКК-6, яку обладнано комбінованою системою для очистки кормових буряків від різного роду забруднень при їх збиранні. На основі експериментальних результатів виведено рівняння регресії, які характеризують зміну загальної забрудненості вороху коренеплодів різними домішками та побудовано графічні залежності загальної забрудненості вороху кормових буряків, пошкоджень коренеплодів, забрудненості коренеплодів рослинними рештками і кількості налиплого ґрунту на поверхні тіла коренеплодів залежно від зміни кутової швидкості обертання гвинта та діаметра очисних пружних елементів. При аналізі залежностей виявлено, що загальна забрудненість вороху коренеплодів залежно від кутової швидкості обертання гвинта змінюється за параболічною функцією, яка має яскраво виражений оптимум. Також зв’ясовано, що основним фактором, який впливає на кількість налиплого ґрунту на поверхні тіла коренеплодів є діаметр очисних пружних елементів. При його збільшенні кількість налиплого ґрунту на поверхні тіла коренеплодів значно зменшується при всіх значеннях кутової швидкості обертання гвинта.

This paper deals with GPU computing of special mathematical functions that are used in Fractional Calculus. The graphics processing unit (GPU) has grown to be an integral part of nowadays’s mainstream computing structures. The special mathematical functions are an integral part of Fractional Calculus. This paper deals with a novel parallel approach for computing special mathematical functions used in Fractional Calculus. NVIDIA’s GPU hardware is used to speed up the parallel algorithm. A comparison of the sequential code, vectorized code and GPU code is performed. We have successfully reduced the computation time of special mathematical functions using the parallel computing capabilities of GPU.

In this paper we introduce a generalization of the Voigt functions and discuss their properties and applications. Some interesting explicit series representations, integrals and identities and their link to Jacobi,Laguerre and Hermite polynomials are obtained. The resulting formulas allow a considerable unification of various special results which appear in the literature. © 2019. Acad. Colomb. Cienc. Ex. Fis. Nat. Resumen En este artículo se introduce una generalización de las funciones de Voigt y se discuten sus propiedades y aplicaciones. Se obtienen representaciones explícitas de series, integrales e identidades y sus conexiones con los polinomios de Jacobi, Laguerre y Hermite. Las fórmulas resultantes permiten la unificación de algunos resultados especiales que aparecen en la literatura. © 2019. Acad. Colomb. Cienc. Ex. Fis. Nat.

In this study, we investigated the extent to which adolescents who spend time playing violent video games exhibit higher levels of aggressive behaviour when compared with those who do not. A large sample of British adolescent participants ( n = 1004) aged 14 and 15 years and an equal number of their carers were interviewed. Young people provided reports of their recent gaming experiences. Further, the violent contents of these games were coded using official EU and US ratings, and carers provided evaluations of their adolescents' aggressive behaviours in the past month. Following a preregistered analysis plan, multiple regression analyses tested the hypothesis that recent violent game play is linearly and positively related to carer assessments of aggressive behaviour. Results did not support this prediction, nor did they support the idea that the relationship between these factors follows a nonlinear parabolic function. There was no evidence for a critical tipping point relating violent game engagement to aggressive behaviour. Sensitivity and exploratory analyses indicated these null effects extended across multiple operationalizations of violent game engagement and when the focus was on another behavioural outcome, namely, prosocial behaviour. The discussion presents an interpretation of this pattern of effects in terms of both the ongoing scientific and policy debates around violent video games, and emerging standards for robust evidence-based policy concerning young people's technology use.

Clitellocephalus ophoni (Tuzet and Ormieres, 1956) Clopton, 2002, is one of the parasites of a common ground beetle species, Harpalus rufipes (De Geer, 1774), inhabiting practically the entire temperate zone of Eurasia. Photographs of 177 gamonts and 74 syzygies of C. ophoni from specimens of three populations of H. rufipes collected from the countryside near Dnipropetrovsk (Ukraine), were analyzed according to 15 linear characteristics and 18 indices for gamonts and 6 indices for syzygies. The coefficient of variation (CV) for the majority of linear parameters for gamonts ranged between 28.2-71.3%. Out of 15 linear parameters, only 6 showed a normal distribution; the others showed a statistically significant asymmetry (the maximum indicators on the histogram of distribution were inclined to the area of minimum value). The distribution of all 18 morphological indices diverged from the norm. Two maximum indicators were registered in the disposition of the widest point of the protomerite and deutomerite. The minimum CV was registered for the ratio of gamont length to the length of its deutomerite. The size ratios of the primite and satellite in the syzygies were more constant than the morphological indices for the gamonts. The sex of the host does not affect the length of the protomerite and deutomerite, but does affect their width, the disposition of the nucleus and the widest point of the deutomerite. The length of the protomerite and deutomerite relative to the length of the gamont is better described through linear functions, while their width has a nonlinear dynamic and is better described through parabolic function. The ratio of morphometric indices to total length of C. ophoni gamonts is also better described through nonlinear functions. The data obtained on the morphological variability of C. ophoni needs to be compared with the results for artificially infected individuals of other Harpalus species. Key words: Clitellocephalus ; Harpalus rufipes ; gregarine; morphometric characteristics; ratio of morphometric indices Received: September 23, 2015; Revised: November 30, 2015; Accepted: December 3, 2015; Published online: May 10, 2016

We study a class of nonlocal-diffusion equations with drifts, and derive a priori \(\Phi \)-Holder estimate for the solutions by using a purely probabilistic argument, where \(\Phi \) is an intrinsic scaling function for the equation.

This paper presents a corner-based image alignment algorithm based on the procedures of corner-based template matching and geometric parameter estimation. This algorithm consists of two stages: 1) training phase, and 2) matching phase. In the training phase, a corner detection algorithm is used to extract the corners. These corners are then used to build the pyramid images. In the matching phase, the corners are obtained using the same corner detection algorithm. The similarity measure is then determined by the differences of gradient vector between the corners obtained in the template image and the inspection image, respectively. A parabolic function is further applied to evaluate the geometric relationship between the template and the inspection images. Results show that the corner-based template matching outperforms the original edge-based template matching in efficiency, and both of them are robust against non-liner light changes. The accuracy and precision of the corner-based image alignment are competitive to that of edge-based image alignment under the same environment. In practice, the proposed algorithm demonstrates its precision, efficiency and robustness in image alignment for real world applications.

This study deals with the analysis of relationship between 67 environmental indicators in geological environment and breast cancer mortality in Slovakia. Primary data comprises a database of 67 environmental indicators for groundwater and soils as a mean value for every Slovak municipality and the data on relative mortality from breast cancer for Slovak municipalities (about 2900) collected for the period of 22 years. The training neural network was used as a mathematical model for data analysis. The top 200 networks have identified 12 environmental indicators (8 for soils: pHKCl, carbonates, Ca, Mg, Na, Co, Sr and 4 for groundwater: Ba, SiO2, Zn, Fe) with high rate of influence. As the most influential environmental indicator was identified pHKCl in soil that should be within the range of acids, definitely under the neutral point. Most of environmental indicators were unambiguously identified as negative (Mg, Ca, Sr, carbonates, Ba, SiO2, Zn and Fe). These indicators should be at the lowest level of their concentration in related geological component. Three environmental indicators, Ce, Na and Co had parabolic function where certain essential concentration levels of these elements are presumed with protective effect on human health. For all influential indicators limit values with respect to the lowest mortality were proposed. The verification of achieved results was performed through regressive model of breast cancer mortality for 12 calculated influential environmental indicators for all municipalities in the Slovak Republic. The revealed difference between real mortality levels and the model values was found for 6 environmental indicators (pHKCl, Mg, Ca, Sr, Ba, Zn). Each executed limit has decreased breast cancer mortality for about 0.79 cases per 100,000 inhabitants.

The study was carried out in Serbian spruce (Picea omorika Panc/Purkyn?) plantations in the western Serbia. The paper presents results of the analysis of crown development. The following elements were analyzed: total tree height, height of the crown base, absolute and relative crown length, maximal crown diameter, coefficient of crown spreading and degree of crown girth. We discuss approaches to the modeling of tree crown growth and development, growing under favorable environmental and stand conditions, without anomalies in development. In order to establish the relationship between analyzed factors, regression analyses were applied. Data fitting was by the analytic method, by the implementation of Prodan?s functions of growth, linear and parabolic function. Received models can be used for the simulation of various growth and developing processes in forest.

Highway infrastructure elements, such as signs, guardrails, structures, and pavements, deteriorate over time because of weather, accidents, daily wear and tear, and other factors. To keep them functional and operational, the elements require periodic maintenance. In the absence of an optimization model that can optimally allocate the annual maintenance budget for needed maintenance, it is often difficult to secure adequate funding for such activities. A mathematical model is developed; it evaluates the condition of elements, considers a budget constraint, and suggests the optimal maintenance schedule over a specified period of time. A genetic algorithm has been used to solve the model. The model considers a parabolic function over time to represent deterioration of the elements as well as rehabilitation expenses. The extent of rehabilitation at a given time is considered as dependent on the present condition and amount of deterioration. Also, threshold values for level of deterioration are considered as a check for the minimum condition before rehabilitation is warranted. With inputs such as deterioration levels, rehabilitation costs, threshold deterioration levels, and annual budget, the model can give the optimum maintenance schedule of the elements over a specified time period as an output. The approach is illustrated through a numerical example.

微小重力下の凸状固液界面で半導体結晶を成長させる条件を調べるため、数値計算を行った。計算コードは境界適合座標系(BFC)法に基づいている。現在のコードは、エネルギー輸送方程式、渦度輸送方程式、流れ関数方程式、エネルギーバランス方程式のような、非定常的支配方程式を同時に解けるよう改良された。このコードを使って、色々な重力レベルで界面の位置と界面の形状変化の両方を追跡した。計算の信頼性を調べるため、地上実験を行った。これらの結果の比較から、数値的に得られた初期界面形状は、実験的に得られたものと良く一致することが明らかになった。界面形状変化の傾向を探るため、形状を放物関数でフィットし、2次項の比例係数を求めた。実験結果の傾向は数値計算で得られたものの約2倍の急勾配であった。しかし、計算した温度プロファイルは実験的に測定した温度と良く一致した。, In order to investigate conditions to grow semiconductor crystals with convex solid-liquid interface under microgravity, numerical calculations have been carried out. The caculation code is based on the Boundary Fitted Coordinate (BFC) method. The current code has been improved so as to simultaneously solve nonsteady governing equations, such as an energy transport equation, a vorticity transport equation, a stream function equation, and an energy balance equation. By using this code, both interface location and interface shape change are traced for various gravity levels. In order to investigate reliability of the calculation, a ground-based experiment is carried out. From the comparison of these results, it is clarified that the numerically obtained initial interface shape well agrees with the experimentally obtained one. In order to obtain the trend of the shape change, the shape is fitted by a parabolic function and a proportional coefficient of the second order term is obtained. The trend of the experimental result is about twice as steep as that obtained by calculation. However, calculated temperature profiles well agree with experimentally measured temperatures., 資料番号: AA0029300008, レポート番号: NASDA-TMR-000007E

Ertürk, Mustafa (Balikesir Author), The amount of solar radiation falling on the surface of the earth is a very important data for engineers and scientists tomodel the solar energy systems and to design and carry out a performance analysis. Solar global radiation values can be estimated practically by employing parabolic monthly irradiation models (PMIMs). Following the establishing of the model parameters, average hourly global solar radiation values per month can be obtained for any given place. In this chapter, PMIMparameters are calculated for 34 cities in Turkey. Also, daily average global solar radiation values are determined by employing the measured data of 70 cities in Turkey and given in a parabolic function. The predictions are compared with the solar data available in literature for Turkey. According to annual average global solar radiation values, Turkey is divided into four regions, and a new comparison factor is introduced and called the global radiation comparison rate. This model can be applied to any specific location, where meteorological data are measured in the world. Thus, the calculation time will be reduced. It is expected that this study will be useful for designers and scientists working on solar energy systems.

We study the positive solutions of a heat equation on an infinite-dimensional state space using Hida's white noise analysis. We establish an integral representation theorem for generalized parabolic functions via so-called generalized Cameron-Martin densities, and we apply the representation formula in the study of the positive generalized parabolic functions on the white noise space.

This study presents a new frequency domain parameter, Parabolic Spectral Parameter (PSP), for the quantification of the glottal volume velocity waveform. PSP is based on fitting a parabolic function to the low-frequency part of a pitch-synchronously computed spectrum of the estimated glottal flow. PSP gives a single numerical value that describes how the spectral decay of an obtained glottal flow behaves with respect to a theoretical limit corresponding to maximal spectral decay. By analyzing speech signals of different phonation types the performance of the new parameter is compared to three commonly used time-based parameters and to one previously developed frequency domain method.

We have developed the lattice model for describing polypeptide chains in the presence of crowders. The influence of crowding confinement on the fibrillation kinetics of polypeptide chains is studied using this model. We observed the non-trivial behavior of the fibril formation time τfib that it decreases with the concentration of crowders if crowder sizes are large enough, but the growth is observed for crowders of small sizes. This allows us to explain the recent experimental observation on the dual effect of crowding particles on fibril growth of proteins that for a fixed crowder concentration the fibrillation kinetics is fastest at intermediate values of total surface of crowders. It becomes slow at either small or large coverages of cosolutes. It is shown that due to competition between the energetics and entropic effects, the dependence of τfib on the size of confined space is described by a parabolic function.

A regression study of Andrade, Krone, McAllister and Hildebrand equations with experimental data of viscosity of mixtures of triglycerides or free fatty acids and trichloroethylene, tetrachloroethylene and hexane was carried out. Temperature range studied was 278-313 K in steps of 5K. The results showed that the Hildebrand equation presents the best fit for all the viscosity data of the mixtures studied, tending towards a lineal or parabolic function of its parameters. Andrade and Krone equations presented acceptable fits for all mixtures studied except the fatty acids and hexane mixture. The McAllister equation was applicable only to mixtures with tetrachloroethylene.Se ha realizado el estudio de regresión de las ecuaciones de Andrade, Krone, McAllister e Hildebrand con datos experimentales de viscosidad de mezclas de triglicéridos o ácidos grasos libres con tricloroetileno, tetracloroetileno y hexano en el intervalo de temperaturas de 278 a 313 K cada 5 K. Los resultados obtenidos indican que el mejor ajuste de los datos experimentales de viscosidad lo presenta la ecuación de Hildebrand, buscándose una función lineal o parabólica con la fracción molar de sus dos parámetros. Las ecuaciones de Andrade y Krone presentan un ajuste aceptable para todas las mezclas estudiadas excepto para las de ácidos grasos en hexano y la ecuación de McAllister es únicamente aplicable a las mezclas con tetracloroetileno.

Four parabolic functions were derived separately for the first, the second, the third and the fourth tetrads of lanthanides in samples of leuco-granitic gneiss from Korea, and seawater from off the coasts of Shimane and Kochi prefectures, Japan. We conclude that relative lanthanide abundances in each of those samples are mathematically expressed by a set of four parabolic functions. The parabolic functions are applicable to the abundance ratio values as well as the values of aberration from the cusp-spanning lines. Both parabolic function systems are significant in different senses, but a set of four parabolas for “aberration” is convenient in visualizing the characteristics of lanthanide tetrad phenomenon observed for the sample. Difference in those characteristics can be interpreted to reflect uniquely the state of lanthanides present and/or the condition of genesis of the sample.

Conversations with a witness to a violent episode of hostage-taking lead the author to reflect on the importance of understanding the role of unconscious identifications in conducting group debriefings with trauma survivors. Individuals with discordant identifications, identifications which run counter to the usual experience, present special challenges to leaders of critical-incident stress debriefings. Such identifications reveal much about the dynamics of calling to the helping professions and caring within them, and may serve a parabolic function, revealing aspects of God and community otherwise hidden.

Improvement of the CAD process to design the shape of crown restorations of a 6 die was carried out by including the bite data of the antagonistic tooth in addition to the data measured in the previous paper. Initially, the position adjustment of the crown data with the bite data in the centric occlusion was attempted. After fixation of the crown data to a suitable position, modulation of the occlusal surface by the functionally generated path (FGP) data was carried out. To connect between the end of the crown data and the margin, a parabolic function was used instead of the B-Spline function used in the previous paper. As a result, the data points were connected more smoothly. Thus, CAD data which were composed of the die data, the crown data, and the connecting data were accomplished. They will be used as the basic data to CAM.

In this paper, we consider the following type of non-local (pseudo-differential) operators $\LL $ on $\R^d$: $$ \LL u(x) =\frac12 \sum_{i, j=1}^d \frac{\partial}{\partial x_i} (a_{ij}(x) \frac{\partial}{\partial x_j}) + \lim_{\eps \downarrow 0} \int_{\{y\in \R^d: |y-x|>\eps\}} (u(y)-u(x)) J(x, y) dy, $$ where $A(x)=(a_{ij}(x))_{1\leq i, j\leq d}$ is a measurable $d\times d$ matrix-valued function on $\R^d$ that is uniform elliptic and bounded and $J$ is a symmetric measurable non-trivial non-negative kernel on $\R^d\times \R^d$ satisfying certain conditions. Corresponding to $\LL$ is a symmetric strong Markov process $X$ on $\R^d$ that has both the diffusion component and pure jump component. We establish a priori H��lder estimate for bounded parabolic functions of $\LL$ and parabolic Harnack principle for positive parabolic functions of $\LL$. Moreover, two-sided sharp heat kernel estimates are derived for such operator $\LL$ and jump-diffusion $X$. In particular, our results apply to the mixture of symmetric diffusion of uniformly elliptic divergence form operator and mixed stable-like processes on $\R^d$. To establish these results, we employ methods from both probability theory and analysis., 32 pages

Materials in the langasite family are of current interest for both bulk wave and surface wave devices. Piano-convex Y-cut bulk wave resonators have been built and tested on overtones 1 through 9 using LGS (langasite; La/sub 3/Ga/sub 5/SiO/sub 14/), LGN (langanite; La/sub 3/Ga/sub 5.5/Nb/sub 0.5/O/sub 14/), and LGT (langatate; La/sub 3/Ga/sub 5.5/Ta/sub 5.5/O/sub 14/). Frequencies and motional inductances are compared with calculated values, with good agreement except for the motional inductance of LGT. For all three materials, frequency variation is an essentially parabolic function of temperature. For LGN and LGT, reported values of the Q-frequency product are significantly above the classical limit for AT-cut quartz. A maximum 4 f value of 25.6/spl times/10/sup 6/, where frequency is in megahertz;, was observed for an LGT resonator; for an unplated resonator, 29.2/spl times/10/sup 6/ was measured. Still higher values are believed possible.

The inverse relationship between length of service and labour turnover is a consistent finding in the literature. This paper demonstrates by a longitudinal cohort analysis of 40,816 British Rail workers recruited during 1979-1980, the increased accuracy and sensitivity obtained by concentrating separately on quits and dismissals.Comparisons between quit rates and dismissal rates during the first ten months of employment pointed to the following major results: (1) quit rates and dismissal rates are better explained by nonlinear functions rather than by a linear one; (2) quits are best described by a parabolic function whereas dismissals are best described by a nearly inverse 'U'-shaped function; and (3) nonlinear patterns of quit rates and dismissal rates remained consistent for 1979 and 1980, although the unemployment levels, quit rates and dismissal rates in 1979 differed substantially from those in 1980.

This article examines the spatial relationships between avatars (i.e., graphical identities or icons) over time in a 2-dimensional online chat environment. The Spatial Distance Analysis Program (SDAP) was developed to measure the distance between avatars in a specially designed Palace environment. Correlations between distance and interpersonal communication constructs of (1) conversational appropriateness, (2) social attraction, and (3) uncertainty reduction indicate that distance effects are significant in an online environment. Specifically, it was found that general conversational appropriateness mediated between uncertainty reduction and specific conversational appropriateness for individuals who moved closer together and farther apart over time, respectively. Furthermore, the relationship between social attraction and distance indicated a significant positive parabolic function; that social attraction (i.e., liking) decreased at middle distances and increased at low and high distances. This finding suggests that there are three interpersonal distance zones in online communication.

We study the positive parabolic functions of the Ornstein-Uhlenbeck operator on an abstract Wiener space $E$ using the approach developed by Dynkin. This involves first proving a characterization of the entrance space of the corresponding Ornstein-Uhlenbeck semigroup and deriving an integral representation for an arbitrary entrance law in terms of extreme ones. It is shown that the Cameron-Martin densities are extreme parabolic functions, but that if $\dim E = \infty$, not every positive parabolic function has an integral representation in terms of those (which is in contrast to the finite-dimensional case). Furthermore, conditions for a parabolic function to be representable in terms of Cameron-Martin densities are proved.

This paper gives the background to the seismic torsional provisions of the New Zealand Loadings Code. These provisions attempt to deal with three effects: accidental eccentricity, torsional ground motion, and coupling between torsional and translational modes. The first two effects lead to an effective eccentricity of one-tenth of the width of a building, while the third leads to a parabolic function of the calculated eccentricity: this was obtained by applying existing results for torsional amplification to a number of typical building structures.

Our purpose is the forecast of the global radiation. As a first step we try to determine the global radiation as function of other predictable parameters. First the daily average values of the relative global radiation was considered as parabolic function of the cloud coverage obtained from METEOSAT images, an empirical formula was determined for calculation of the relative global radiation from the cloud amount. The correct this formula the cloud coverage and ground based visibility data were used. The value of the multiple correlation coefficient presenting the accuracy of the new formula was 0.96 for Budapest, and 0.93 for region of Hungary. This fact indicates that we have a sufficiently correct formula for calculation of the global radiation.

An analysis of over 40,000 eye fixations made by college students during reading indicates that the frequency of immediately refixating a word following an initial eye fixation on it varies with the location of that fixation. The refixation frequency is lowest near the center of the word, positively accelerating with distance from the center. The data are well fit by a parabolic function. Assuming that refixation frequency is related to the frequency of successful word identification, the observed curvilinear relation results naturally from models that postulate a linear decrease in visual information with retinal eccentricity. A single letter difference in fixation location in a word can make a sizeable difference in the likelihood of refixating that word. The effects of word length and cultural frequency on the frequency of refixating are also examined.

The orbital chemical shift of N.M.R., which measures the weight of non-s states in the chemical bond, can be related directly to the ionicity for tellurium compounds. In a molecular picture of the solid neglecting d states, the shift is a parabolic function of the number of p-electrons in the valence band. This number depends simply on the ionicity for tellurium bonds and can be modified by change in the local symmetry, especially by amorphization.

In 35,680 fetuses of women who had prenatal cytogenetic diagnosis done upon amniotic fluid specimens obtained during 2nd trimester amniocentesis and in whom there was no increased cytogenetic risk except for age, there was no statistically significant evidence for an increase of 47,+21 at any paternal age after adjustment for maternal age. The ratio of observed-to-expected numbers in fathers less than 30 years old was 1.0 and in fathers 40 years or older was 0.9 when compared with numbers derived from maternal-age-specific rates in men 30-39 years old. The ratio was 1.1 for those younger than 34 years when compared with rates in fathers aged 34-39 years old. Only for men 55 years or older was there any, even suggestive, increase. The ratio was roughly 1.5 (9 observed to about 6 expected). This was not statistically significant, and moreover, the increase such as it was, was in men married to women 37-42 years old. Regression analyses using several additive parental age models introducing a parabolic function for paternal age, failed to reveal any paternal age contribution.

Let D be a domain in R x n × R t 1 R_x^n \, \times \, R_t^1 and ∂ p D {\partial _p}D be the parabolic boundary of D. Suppose ∂ p D {\partial _p}D is composed of two parts B and S: B is given locally by t = τ t = \tau and S is given locally by the graph of x n = f ( x 1 , x 2 , ⋯ , x n − 1 , t ) {x_n} = f({x_1},{x_2}, \cdots ,{x_{n - 1}},t) where f is Lip 1 with respect to the local space variables and Lip 1 2 \tfrac {1} {2} with respect to the universal time variable. Let σ \sigma be the n-dimensional Hausdorff measure in R n + 1 {R^{n + 1}} and σ ′ \sigma ’ be the ( n − 1 ) (n - 1) -dimensional Hausdorff measure in R n {\textbf {R}^n} . And let d m ( E ) = d σ ( E ∩ B ) + d σ ′ × d t ( E ∩ S ) dm(E) = d\sigma (E \cap B) + d{\sigma ’} \times dt(E \cap S) for E ⊆ ∂ p D E \subseteq {\partial _p}D . We study (i) the relation between the parabolic measure on ∂ p D {\partial _p}D and the measure dm on ∂ p D {\partial _p}D and (ii) the boundary behavior of subparabolic functions on D.

In this paper we will deal with quasidiffusions X=(Xt)t^0 on [0, 1) assuming that 0 is a reflecting regular boundary, 1 is an accessible or entrance boundary and X is killed as soon as it hits the boundary 1. We shall give a Martin representation of space-time-excessive functions for X. This includes in particular a representation of all parabolic functions f(x, t) satisfying a certain integrability condition by minimal ones (see Theorem 2 below). We shall show that the set of minimal points of space-time Martin boundary is homeomorphic to (0, oo[; in particular the minimal parabolic functions form a one-parameter family (kt) (re(0, oo]). If z

The “thermal effectiveness-transfer unit” charts developed by the authors, for multipass exchangers, assume that the overall heat transfer coefficient varies as a parabolic function of temperature; their use can lead to greater accuracy in calculating heat transfer areas. Les auteurs ont construit des chartes ďefficacite thermique pour des echangeurs a passe multiple. Ils ont suppose que le coefficient global de transfert de chaleur varie ďune facon parabolique avec la temperature. Ľemploi de ses chartes peut conduire a une plus grande precision pour le calcul des surfaces ďechange de chaleur.

Data are presented which indicate that the forces of attraction between influenza virus and chicken erythrocytes are governed by an orderly mechanism which effects a proportional distribution of virus between erythrocytes and suspending fluid. For a unit mass of erythrocytes, the ratio of combined (sorbed) virus to free (unsorbed) virus is sufficiently constant over a wide range of virus concentrations to indicate compliance with the laws of mass action, or, perhaps, with the laws of simple adsorption; however, the ratio of combined (sorbed) virus to free (unsorbed) virus appears to be a parabolic function of the total quantity of virus.

Sodium oleate reacts progressively with human red cells at pH 7. By progressive is meant a reaction which is not adequately described as reversible or irreversible; such reactions cannot be stopped once they are under way, and are probably associated with a more or less stable "internal" lysin phase at the cell surfaces. The uptake of the lysin and the effect of dilution on the uptake can be studied by converting sodium oleate into the radioactive form, sodium oleate-I131. The uptake is a parabolic function of the lysin initially present in the system, and the effect of a tenfold dilution of systems in which red cells have remained in contact with the lysin for 2 minutes is to reduce the lysin taken up at the cell surfaces twofold. The lysin rapidly forms a relatively stable layer at the cell interfaces, and this layer is little affected by the dilution of the system as a whole.

1. This report deals with a study of the amount of regeneration in the carapace of Daphnia magna.2. The amount of regeneration during any adult instar is a parabolic function of the area of the wound during that instar and may be expressed by the equation [see equation in PDF file] where y is the amount of regeneration; x, the area of the wound; and a and k constants.3. The amount of regeneration during any adult instar decreases with the age of the animal.4. The amount of regeneration during adult instars is independent of the temperature.5. The amount of regeneration during any adult instar decreases with the age of the wound but to a greater extent than when the age of the animal alone is considered.6. These results have been discussed with reference to those secured by others for relatively complex structures.

The “Thermal effectiveness-Transfer unit” charts developed by the authors, for the countercurrent heat exchanger, assume that the overall heat transfer coefficient varies as a parabolic function of temperature; their use can lead to greater accuracy in calculating heat transfer areas. Les auteurs ont construit des chartes d'efficacite ther-mique pour un echangeur de chaleur a contre-courant. Ils ont suppose que le coefficient global de transfert de chaleur varie d'une facon parabolique avec la temperature. L'emploi de ces chartes peut conduire a une plus grande precision pour le calcul des surfaces d'echange de chaleur.

IN a recent article which appeared in this Journal, Robert Legan' challenged an earlier study made by Howard Bonham, Jr.2 on the projection of the Dow Jones Industrial Average (DJIA) in 1970. Bonham's study had concluded, with pertinent reservations, that the overall growth rate of the stock price may be "topping out." Legan claimed that the semi-logarithmic and the parabolic functions he used in the investigation fitted the past trend of the DJIA better than the parabolic function used by Bonham and that Bonham's conclusion may be premature, if not incorrect, because Bonham used the yearly closing price of the DJIA instead of its yearly range. Legan's criticism on the Bonham finding in general and Legan's methodological framework in particular can be challenged on the basis of the inappropriate use of statistical techniques. In addition, Legan's refutation of the random walk hypothesis can be questioned on the basis of his misunderstanding of the hypothesis. This note (1) questions the statistical concepts and methods employed by Legan, (2) suggests the probabilistic confidence attached to his projections are non sequitur in nature, and (3) points out that he failed to show any concrete basis on which to refute the random walk hypothesis.

It is well known that the zero function is the only non-negative parabolic function (i.e., solution of the heat equation) on R n ×(0,T) which vanishes continuously on R n ×{0} (cf. [2, Part 1, Chap. XVI], [6, Chap. VIII]). In this paper, considering the Huygens property of minimal parabolic functions (see Proposition 2), we shall show the following generalization of the above result

A series of aliphatic amides of amphotericin B have been synthesized. The structure of the derivatives which were obtained has been established by mass spectrometry. Their biological properties: inhibition of growth of Saccharomyces cerevisiae and hemolytic activity have been determined. The quantitative relationships between the activity of amides of amphotericin B against S. cerevisiae and their lipophilicity can be expressed by a parabolic function, whereas that between hemolytic activity and lipophilicity--by polynominal expression of fourth degree.

A high-precision y=x2 generator based on a partial segmentation of a parabolic function is described. The overall accuracy of 0.01% has been achieved using two segments only.

The spaces H α p \mathcal {H}_\alpha ^p of parabolic Bessel potentials were introduced by B. F. Jones and R. J. Bagby. We prove a Sobolev-type imbedding theorem for H α p 1 , p 2 \mathcal {H}_\alpha ^{{p_1},{p_2}} (multinormed versions of H α p \mathcal {H}_\alpha ^p ) when α \alpha is a positive integer k, 1 > p 1 1 > {p_1} , p 2 > ∞ {p_2} > \infty . In particular this theorem holds for W 2 l , l p W_{2l,l}^p , since H 2 l p ≡ W 2 l , l p \mathcal {H}_{2l}^p \equiv W_{2l,l}^p . We use the concepts of parabolic Riesz transforms and half-time derivatives introduced by us elsewhere.

A method is described for generating a precisely phase‐controlled linear FM pulse of large time‐bandwidth product T⋅W=N by digitally phase‐modulating a square‐wave carrier at frequency fo with phase jumps of magnitude π/m, where design parameters N and m are powers of 2. A parabolic function generator, which sequentially computes the square of the number of clock input pulses, furnishes modulation orders and is basically comprised of 2s+1 flip‐flops (where 2s=m⋅N). Frequency of input pulses is m⋅W, where sweep bandwidth W has to be chosen smaller than 2fo/1+m. Phase quantization noise takes the place of “linearity” and “stability” concepts in analog linear FM generators, and its power can be controlled by design parameter m, with a reduction of 6 dB for each doubling of the value of m. Bandpass‐filtering of the output‐modulated signal gives, in many cases, a satisfactory signal‐to‐quantization noise ratio, even with m=2. [The system described was developed by the author and H. W. K. Kelly, now of Admiralt...