scholarly journals II.—Investigation of an Expression for the Mean Temperature of a Stratum of Soil, in Terms of the Time of Year.

1862 ◽  
Vol 23 (1) ◽  
pp. 21-27
Author(s):  
Joseph D. Everett
Keyword(s):  
Harmonic Function ◽  
Harmonic Functions ◽  
Number Of Components ◽  
Mean Temperature ◽  
The Mean ◽  
Time Of Year

1. It is a well-known property of simple harmonic functions, that the sum of any two or more of them having the same period, is itself a simple harmonic function having the same period as its components. The same thing must be true of their mean, since this is equal to the sum divided by a constant; and it will still be true when the number of components is indefinitely great, and the mean becomes an integral.

MEAN VALUE PROPERTY OF HARMONIC FUNCTION ON THE HIGHER-DIMENSIONAL SIERPINSKI GASKET

Fractals ◽  
2020 ◽  
Vol 28 (05) ◽  
pp. 2050077
Author(s):  
YIPENG WU ◽  
ZHILONG CHEN ◽  
XIA ZHANG ◽  
XUDONG ZHAO
Keyword(s):  
Harmonic Function ◽  
Harmonic Functions ◽  
Sierpinski Gasket ◽  
Mean Value ◽  
Sierpiński Gasket ◽  
Mean Value Property ◽  
Average Value ◽  
Higher Dimensional ◽  
The Mean

Harmonic functions possess the mean value property, that is, the value of the function at any point is equal to the average value of the function in a domain that contain this point. It is a very attractive problem to look for analogous results in the fractal context. In this paper, we establish a similar results of the mean value property for the harmonic functions on the higher-dimensional Sierpinski gasket.

scholarly journals Some Remarks on Harmonic Functions in Minkowski Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 196
Author(s):  
Songting Yin
Keyword(s):  
Harmonic Function ◽  
Minkowski Space ◽  
Harmonic Functions ◽  
Mean Value ◽  
Mean Value Property ◽  
Minkowski Spaces ◽  
The Mean ◽  
Mean Value Formula

We prove that in Minkowski spaces, a harmonic function does not necessarily satisfy the mean value formula. Conversely, we also show that a function satisfying the mean value formula is not necessarily a harmonic function. Finally, we conclude that in a Minkowski space, if all harmonic functions have the mean value property or any function satisfying the mean value formula must be a harmonic function, then the Minkowski space is Euclidean.

1. Investigation of an Expression for the Mean Temperature of a Stratum of Soil, in terms of the time of year

1862 ◽  
Vol 4 ◽  
pp. 528-528
Author(s):  
J. D. Everett
Keyword(s):  
General Solution ◽  
Mean Temperature ◽  
The Mean ◽  
Time Of Year

In vol. xxii. of the Transactions of the Society, Prof. W. Thomson has given (after Fourier) the general solution of the problem of underground conduction, and he and Professor Everett have given methods more or less accurate of determining from observation the specific constants for any locality. These are mainly applied to the results of Principal Forbes's observations on the Calton Hill and other places near Edinburgh. (Trans., vol. xvi.)

scholarly journals On the existence of various bounded harmonic functions with given periods, II

1975 ◽  
Vol 56 ◽  
pp. 1-5
Author(s):  
Masaru Hara
Keyword(s):  
Riemann Surface ◽  
Harmonic Function ◽  
Harmonic Functions ◽  
Dirichlet Integral ◽  
Period Function ◽  
Boundedness Property ◽  
One Dimensional ◽  
Bounded Harmonic Functions

Given a harmonic function u on a Riemann surface R, we define a period functionfor every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.

scholarly journals On the mean value property of superharmonic and subharmonic functions

2006 ◽  
Vol 2006 ◽  
pp. 1-3
Author(s):  
Robert Dalmasso
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Subharmonic Functions ◽  
Mean Value Property ◽  
The Mean

We prove a converse of the mean value property for superharmonic and subharmonic functions. The case of harmonic functions was treated by Epstein and Schiffer.

scholarly journals First Benedicks Effect in Gas-Free Mercury, as Influenced by the Mean Temperature

Nature ◽  
1940 ◽  
Vol 145 (3665) ◽  
pp. 148-148
Author(s):  
C. BENEDICKS ◽  
P. SEDERHOLM
Keyword(s):  
Mean Temperature ◽  
The Mean

scholarly journals Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
M. T. Mustafa
Keyword(s):  
Harmonic Function ◽  
Riemannian Manifolds ◽  
Harmonic Functions ◽  
Horizontal Component ◽  
Harmonic Morphisms

For Riemannian manifoldsMandN, admitting a submersionϕwith compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians onMandN, we determine conditions under which a harmonic function onU=ϕ−1(V)⊂Mprojects down, via its horizontal component, to a harmonic function onV⊂N.

Mean Temperature Difference Charts for Air Coolers

1983 ◽  
Vol 105 (3) ◽  
pp. 592-597 ◽  
Author(s):  
A. Pignotti ◽  
G. O. Cordero
Keyword(s):  
Heat Transfer ◽  
Heat Capacity ◽  
Temperature Difference ◽  
Optimization Technique ◽  
Independent Variables ◽  
Mean Temperature ◽  
Air Cooler ◽  
The Mean ◽  
The One ◽  
Water Ratio

Computer generated graphs are presented for the mean temperature difference in typical air cooler configurations, covering the combinations of numbers of passes and rows per pass of industrial interest. Two sets of independent variables are included in the graphs: the conventional one (heat capacity water ratio and cold fluid effectiveness), and the one required in an optimization technique of widespread use (hot fluid effectiveness and the number of heat transfer units). Flow arrangements with side-by-side and over-and-under passes, frequently found in actual practice, are discussed through examples.

THE TEMPERATURES OF SURFACE FIRES IN JACK PINE BARREN: I. THE VARIATION IN TEMPERATURE WITH TIME

1966 ◽  
Vol 44 (10) ◽  
pp. 1285-1292 ◽  
Author(s):  
David W. Smith ◽  
John H. Sparling
Keyword(s):  
Jack Pine ◽  
Maximum Temperature ◽  
Surface Fires ◽  
Mean Temperature ◽  
The Mean ◽  
Maximum Temperatures

The temperatures of 18 fires in an open jack pine barren near Timmins, Ontario, have been recorded. The maximum temperature recorded was 545 °C, although in other determinations fire temperatures in excess of 1000 °C were reached. The mean temperature of all fires was 340.6 ± 133.2 °C. Three fires at 230, 345, and 545 °C were considered in detail.The maximum temperature of a fire was normally recorded at heights of 5 cm or 10 cm above the surface. Maximum temperatures of hotter fires usually occurred at greater heights than cooler ones. Duration and the temperature ("intensity") of the fire are important aspects of fire studies.

Implicit LES for Shaped-Hole Film Cooling Flow

2017 ◽  
Author(s):  
Todd A. Oliver ◽  
Joshua B. Anderson ◽  
David G. Bogard ◽  
Robert D. Moser ◽  
Gregory Laskowski
Keyword(s):  
Film Cooling ◽  
Density Ratio ◽  
Vortex Pair ◽  
Cooling Flow ◽  
Blowing Ratio ◽  
Eddy Simulation ◽  
Mean Temperature ◽  
Cooling Hole ◽  
The Mean ◽  
Adiabatic Effectiveness

Results of a recent joint experimental and computational investigation of the flow through a plenum-fed 7-7-7 shaped film cooling hole are presented. In particular, we compare the measured adiabatic effectiveness and mean temperature against implicit large eddy simulation (iLES) for blowing ratio approximately 2, density ratio 1.6, and Reynolds number 6000. The results overall show reasonable agreement between the iLES and the experimental results for the adiabatic effectiveness and gross features of the mean temperature field. Notable discrepancies include the centerline adiabatic effectiveness near the hole, where the iLES under-predicts the measurements by Δη ≈ 0.05, and the near-wall temperature, where the simulation results show features not present in the measurements. After showing this comparison, the iLES results are used to examine features that were not measured in the experiments, including the in-hole flow and the dominant fluxes in the mean internal energy equation downstream of the hole. Key findings include that the flow near the entrance to the hole is highly turbulent and that there is a large region of backflow near the exit of the hole. Further, the well-known counter-rotating vortex pair downstream of the hole is observed. Finally, the typical gradient diffusion hypothesis for the Reynolds heat flux is evaluated and found to be incorrect.

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