The finite dam II

1970 ◽  
Vol 7 (3) ◽  
pp. 599-616 ◽  
Author(s):  
P. B. M. Roes
Keyword(s):  
Time Intervals ◽  
Transient Behaviour ◽  
Continuous Release ◽  
Poisson Input ◽  
Excess Water ◽  
Starting Point ◽  
The Laplace Transform ◽  
Uniqueness Of The Solution ◽  
The One ◽  
Finite Dam

SummaryA weir of capacity K is considered in which the water inflow is a process with stationary independent increments. Unless the weir is empty, there is a continuous release of water at unit rate; if K is finite the weir may become full in which case the excess water overflows instantaneously. A weir for which K is infinite will be referred to as infinite dam. For the latter the transient behaviour is well known if the input possesses a second moment (cf. e.g., Prabhu [7]) and serves as the starting point for the present paper. This result is first extended to yield the Laplace transform (L.T.) of the trivariate Laplace-Stieltjes transform (L.S.T.) of the content v(t) at time t, the input X(t) in (0, t) and the total time d(t) in the interval (0, t) during which the dam is dry. (Incidentally, the last two quantities, for relevant time intervals, will be carried throughout.) Then we use a relation between the latter and the L.S.T. of the expected number of downward level y crossings of the v(t) process established in Roes [9]. Since the dam processes considered are Markov processes, we have therewith the L.S.T. of the renewal function of the renewal process imbedded at level y. From this, one finds the L.S.T.'s of first entrance and taboo first entrance times (for their definition see introduction). Next we calculate the first skip times for the infinite dam from the first entrance times and the L.T. of the L.S.T. of v(t). It is then a routine matter to determine the taboo first skip times. From the (taboo) first entrance and skip times we derive the first entrance times for the finite dam, which in turn lead to the renewal functions of the renewal processes imbedded in the finite dam content process v*(t) and hence to the transient behaviour of the finite dam.The advantage of the present approach over the one given in Roes [8] is that it is entirely probabilistic and avoids involved analytic arguments. As a result, the question of uniqueness of the solution does not arise, while more insight is obtained in the structure. The L.S.T. of several first entrance times and first skip times have been derived by Cohen [2] for compound Poisson input.

The finite dam II

1970 ◽  
Vol 7 (03) ◽  
pp. 599-616 ◽  
Author(s):  
P. B. M. Roes
Keyword(s):  
Time Intervals ◽  
Transient Behaviour ◽  
Continuous Release ◽  
Poisson Input ◽  
Excess Water ◽  
Starting Point ◽  
The Laplace Transform ◽  
Uniqueness Of The Solution ◽  
The One ◽  
Finite Dam

Summary A weir of capacity K is considered in which the water inflow is a process with stationary independent increments. Unless the weir is empty, there is a continuous release of water at unit rate; if K is finite the weir may become full in which case the excess water overflows instantaneously. A weir for which K is infinite will be referred to as infinite dam. For the latter the transient behaviour is well known if the input possesses a second moment (cf. e.g., Prabhu [7]) and serves as the starting point for the present paper. This result is first extended to yield the Laplace transform (L.T.) of the trivariate Laplace-Stieltjes transform (L.S.T.) of the content v(t) at time t, the input X(t) in (0, t) and the total time d(t) in the interval (0, t) during which the dam is dry. (Incidentally, the last two quantities, for relevant time intervals, will be carried throughout.) Then we use a relation between the latter and the L.S.T. of the expected number of downward level y crossings of the v(t) process established in Roes [9]. Since the dam processes considered are Markov processes, we have therewith the L.S.T. of the renewal function of the renewal process imbedded at level y. From this, one finds the L.S.T.'s of first entrance and taboo first entrance times (for their definition see introduction). Next we calculate the first skip times for the infinite dam from the first entrance times and the L.T. of the L.S.T. of v(t). It is then a routine matter to determine the taboo first skip times. From the (taboo) first entrance and skip times we derive the first entrance times for the finite dam, which in turn lead to the renewal functions of the renewal processes imbedded in the finite dam content process v*(t) and hence to the transient behaviour of the finite dam. The advantage of the present approach over the one given in Roes [8] is that it is entirely probabilistic and avoids involved analytic arguments. As a result, the question of uniqueness of the solution does not arise, while more insight is obtained in the structure. The L.S.T. of several first entrance times and first skip times have been derived by Cohen [2] for compound Poisson input.

The finite dam

1970 ◽  
Vol 7 (2) ◽  
pp. 316-326 ◽  
Author(s):  
P. B. M. Roes
Keyword(s):  
Continuous Release ◽  
Excess Water ◽  
Finite Dam

Denote by X(t) the total quantity of water flowing into a weir of capacity K in the interval (0, t). Unless the weir is empty, there is a continuous release of water at unit rate; if it becomes full, the excess water overflows instantaneously.

The finite dam

1970 ◽  
Vol 7 (02) ◽  
pp. 316-326 ◽  
Author(s):  
P. B. M. Roes
Keyword(s):  
Continuous Release ◽  
Excess Water ◽  
Finite Dam

Denote by X(t) the total quantity of water flowing into a weir of capacity K in the interval (0, t). Unless the weir is empty, there is a continuous release of water at unit rate; if it becomes full, the excess water overflows instantaneously.

scholarly journals Practices of sustainability and the enactment of their natures/cultures: Ecosystem services, rights of nature, and geoengineering

2021 ◽  
pp. 053901842199894
Author(s):  
Frank Adloff ◽  
Iris Hilbrich
Keyword(s):  
Ecosystem Services ◽  
Latin American ◽  
Social Systems ◽  
The Earth ◽  
Starting Point ◽  
Knowledge Cultures ◽  
Rights Of Nature ◽  
Value Of Nature ◽  
The One ◽  
And Control

Possible trajectories of sustainability are based on different concepts of nature. The article starts out from three trajectories of sustainability (modernization, transformation and control) and reconstructs one characteristic practice for each path with its specific conceptions of nature. The notion that nature provides human societies with relevant ecosystem services is typical of the path of modernization. Nature is reified and monetarized here, with regard to its utility for human societies. Practices of transformation, in contrast, emphasize the intrinsic ethical value of nature. This becomes particularly apparent in discourses on the rights of nature, whose starting point can be found in Latin American indigenous discourses, among others. Control practices such as geoengineering are based on earth-systemic conceptions of nature, in which no distinction is made between natural and social systems. The aim is to control the earth system as a whole in order for human societies to remain viable. Practices of sustainability thus show different ontological understandings of nature (dualistic or monistic) on the one hand and (implicit) ethics and sacralizations (anthropocentric or biocentric) on the other. The three reconstructed natures/cultures have different ontological and ethical affinities and conflict with each other. They are linked to very different knowledge cultures and life-worlds, which answer very differently to the question of what is of value in a society and in nature and how these values ought to be protected.

Ontology and Perception

2004 ◽  
Vol 5 (1) ◽  
pp. 43-58
Author(s):  
Jeffrey S. Galko ◽  
Keyword(s):  
Common Sense ◽  
The Other ◽  
Cognitive Capacity ◽  
Complex Environment ◽  
Starting Point ◽  
Ontological Question ◽  
The One ◽  
Bodies Of Water ◽  
The Relationship

The ontological question of what there is, from the perspective of common sense, is intricately bound to what can be perceived. The above observation, when combined with the fact that nouns within language can be divided between nouns that admit counting, such as ‘pen’ or ‘human’, and those that do not, such as ‘water’ or ‘gold’, provides the starting point for the following investigation into the foundations of our linguistic and conceptual phenomena. The purpose of this paper is to claim that such phenomena are facilitated by, on the one hand, an intricate cognitive capacity, and on the other by the complex environment within which we live. We are, in a sense, cognitively equipped to perceive discrete instances of matter such as bodies of water. This equipment is related to, but also differs from, that devoted to the perception of objects such as this computer. Behind this difference in cognitive equipment underlies a rich ontology, the beginnings of which lies in the distinction between matter and objects. The following paper is an attempt to make explicit the relationship between matter and objects and also provide a window to our cognition of such entities.

Radical Tense-Indexical Historicality and the De Se

KronoScope ◽  
2021 ◽  
Vol 21 (1) ◽  
pp. 7-27
Author(s):  
Carl Humphries
Keyword(s):  
Alternative View ◽  
The Past ◽  
Starting Point ◽  
De Se ◽  
Temporal Expressions ◽  
The Subject ◽  
The One ◽  
Self Reference ◽  
A Current ◽  
Shed Light

Abstract “Being is said in many ways,” claimed Aristotle, initiating a discussion about existential commitment that continues today. Might there not be reasons to say something similar about “having been,” or “having happened,” where these expressions denote something’s being located in the past? Moreover, if history – construed not only as an object of inquiry (actual events, etc.) but also as a way of casting light on certain matters – is primarily concerned with “things past,” then the question just posed also seems relevant to the question of what historical understanding amounts to. While the idea that ‘being’ may mean different things in different contexts has indisputable importance, the implications of other, past-temporal expressions are elusive. In what might any differences of substantive meaning encountered there consist? One starting point for responding – the one that provides the subject matter explored here – is furnished by the question of whether or not a certain way of addressing matters relating to the past permits or precludes forms of intelligibility that could be said to be ‘radically historical.’ After arguing that the existing options for addressing this issue remain unsatisfactory, I set out an alternative view of what it could mean to endorse or reject such an idea. This involves drawing distinctions and analogies connected with notions of temporal situatedness, human practicality and historicality, which are then linked to a further contrast between two ways of understanding the referential significance of what is involved when we self-ascribe a relation to a current situation in a manner construable as implying that we take ourselves to occupy a unique, yet circumstantially defined, perspective on that situation. As regards the latter, on one reading, the specific kind of indexically referring language we use – commonly labelled “de se” – is something whose rationale is exhausted by its practical utility as a communicative tool. On the other, it is viewed as capturing something of substantive importance about how we can be thought of as standing in relation to reality. I claim that this second reading, together with the line of thinking about self-identification and self-reference it helps foreground, can shed light on what it would mean to affirm or deny the possibility of radically historical forms of intelligibility – and thus also on what it could mean to ascribe a plurality of meanings to talk concerning things being ‘in the past.’

An approach to simulation of dual drainage

1999 ◽  
Vol 39 (9) ◽  
pp. 95-103 ◽  
Author(s):  
S. Djordjević ◽  
D. Prodanović ◽  
Č. Maksimović
Keyword(s):  
Numerical Model ◽  
Model Development ◽  
Ground Level ◽  
Surface Flow ◽  
Surface Excess ◽  
Runoff Simulation ◽  
Sewer System ◽  
Excess Water ◽  
Flow Through ◽  
The One

The paper presents the development of the field of urban drainage modelling known as dual drainage - an approach to rainfaill runoff simulation in which the numerical model takes into account not only the flow through the sewer system, but also the flow on the surface. The steps in model development are described, and necessary data, assumptions used and operations to be performed using GIS are discussed. The numerical model simultaneously handles the full dynamic equations of flow through the sewer system and simplified equations of the surface flow. The surface excess water (due to the limited capacity of inlets or to the hydraulic head in the sewer system reaching the ground level) is routed to the neighbour subcatchment (not necessarily the one attached to the downstream network node), using surface retentions, if any.

A stochastic process whose successive intervals between events form a first order Markov chain — I

1968 ◽  
Vol 5 (03) ◽  
pp. 648-668
Author(s):  
D. G. Lampard
Keyword(s):  
Markov Chain ◽  
Point Processes ◽  
Electronic Device ◽  
Statistical Properties ◽  
Time Intervals ◽  
First Order ◽  
Stochastic Point Process ◽  
Order Markov Chain ◽  
The One ◽  
Stochastic Point Processes

In this paper we discuss a counter system whose output is a stochastic point process such that the time intervals between pairs of successive events form a first order Markov chain. Such processes may be regarded as next, in order of complexity, in a hierarchy of stochastic point processes, to “renewal” processes, which latter have been studied extensively. The main virtue of the particular system which is studied here is that virtually all its important statistical properties can be obtained in closed form and that it is physically realizable as an electronic device. As such it forms the basis for a laboratory generator whose output may be used for experimental work involving processes of this kind. Such statistical properties as the one and two-dimensional probability densities for the time intervals are considered in both the stationary and nonstationary state and also discussed are corresponding properties of the successive numbers arising in the stores of the counter system. In particular it is shown that the degree of coupling between successive time intervals may be adjusted in practice without altering the one dimensional probability density for the interval lengths. It is pointed out that operation of the counter system may also be regarded as a problem in queueing theory involving one server alternately serving two queues. A generalization of the counter system, whose inputs are normally a pair of statistically independent Poisson processes, to the case where one of the inputs is a renewal process is considered and leads to some interesting functional equations.

scholarly journals Retinomotor movements in the Antarctic fish Trematomus newnesi Boulenger submitted to different environmental light conditions

2007 ◽  
Vol 24 (2) ◽  
pp. 457-462 ◽  
Author(s):  
Lucélia Donatti ◽  
Edith Fanta
Keyword(s):  
Pigment Epithelium ◽  
Antarctic Fish ◽  
Constant Darkness ◽  
Time Intervals ◽  
Mean Values ◽  
Environmental Light ◽  
The Mean ◽  
The Difference ◽  
The One ◽  
The Antarctic

The Antarctic fish Trematomus newnesi (Boulenger, 1902) occurs from benthic to pelagic habitats, in seasonally and daily varied photic conditions that induce retinomotor movements. Fish were experimentally kept under constant darkness or light, and 12Light/12Dark for seven days. The retinomotor movement of the pigment epithelium was established through the pigment index, while that of the cones was calculated as the length of the myoid. The retinomotor movement of the pigment epithelium in T.newnesi,revealed that the adaptation to constant light occurred in the one hour of exposure, remaining constant for the next seven days. However, the adaptation to constant darkness, was slower. The difference between the mean values of the pigment indices in the time intervals of sampling was significant in the first hours of the experiment, and only after six hours they were not significant any more. The myoid of cones became elongated in darkness and contracted in light. In the experiments where T.newnesiwas exposed initially to 12 hours light followed by 12 hours darkness 12 was evidenced that the speed and intensity of the retinomotor movements was higher when darkness changed into light, than when light changed into darkness.

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