The Rates of Growth of the Galton–Watson Process in Varying Environments

1994 ◽  
Vol 26 (3) ◽  
pp. 698-714 ◽  
Author(s):  
J. C. D'Souza
Keyword(s):  
Infinite Number ◽  
Upper Bound ◽  
Sufficient Condition ◽  
Rate Of Growth ◽  
Varying Environments ◽  
Watson Process ◽  
Rates Of Growth

Let {Zn} be a supercritical Galton–Watson process in varying environments, and W be the limit of the non-negative martingale {Zn/EZn}. Under a condition which ensures that W is not identically equal to zero we give an upper bound on the possible rates of growth of the process on the set {W = 0}, and find a sufficient condition for the process to have only one rate of growth. We also give an example of a process whose offspring distributions have bounded pth moments, for some p > 1, and which has an infinite number of rates of growth.

The Rates of Growth of the Galton–Watson Process in Varying Environments

1994 ◽  
Vol 26 (03) ◽  
pp. 698-714
Author(s):  
J. C. D'Souza
Keyword(s):  
Infinite Number ◽  
Upper Bound ◽  
Sufficient Condition ◽  
Rate Of Growth ◽  
Varying Environments ◽  
Watson Process ◽  
Rates Of Growth

Let {Zn } be a supercritical Galton–Watson process in varying environments, and W be the limit of the non-negative martingale {Zn /EZ n }. Under a condition which ensures that W is not identically equal to zero we give an upper bound on the possible rates of growth of the process on the set {W = 0}, and find a sufficient condition for the process to have only one rate of growth. We also give an example of a process whose offspring distributions have bounded pth moments, for some p > 1, and which has an infinite number of rates of growth.

The extension of the Miles-Howard theorem to compressible fluids

1970 ◽  
Vol 43 (4) ◽  
pp. 833-836 ◽  
Author(s):  
G. Chimonas
Keyword(s):  
Growth Rate ◽  
Shear Flow ◽  
Upper Bound ◽  
Unstable Mode ◽  
Vertical Gradient ◽  
Flow Speed ◽  
Incompressible Fluids ◽  
Compressible Fluids ◽  
Sufficient Condition ◽  
Parallel Shear Flow

A statically stable, gravitationally stratified compressible fluid containing a parallel shear flow is examined for stability against infinitesimal adiabatic perturbations. It is found that the Miles–Howard theorem of incompressible fluids may be generalized to this system, so that n2 ≥ ¼U′2 throughout the flow is a sufficient condition for stability. Here n2 is the Brunt–Väissälä frequency and U’ is the vertical gradient of the flow speed. Howard's upper bound on the growth rate of an unstable mode also generalizes to this compressible system.

Nerve growth in a small applied electric field and the effects of pharmacological agents on rate and orientation

1990 ◽  
Vol 95 (4) ◽  
pp. 617-622
Author(s):  
C.D. McCaig
Keyword(s):  
Electric Field ◽  
Applied Electric Field ◽  
Ganglioside Gm1 ◽  
Normal Pattern ◽  
Pharmacological Agents ◽  
Rate Of Growth ◽  
Threefold Increase ◽  
Turning Behaviour ◽  
Rates Of Growth ◽  
Cyclase Activator

The rate of growth and orientation of embryonic Xenopus nerves exposed to pharmacological agents, to an applied electric field or to both simultaneously were studied. The adenyl cyclase activator forskolin (100 microM) induced a threefold increase in the rate of elongation, as did an electric field alone. Together, their effect in augmenting rate of growth was additive, but only at a concentration of 50 microM forskolin. The normal pattern of faster growth towards cathode than anode was not present in nerves treated with the lectin concanavalin A, which also inhibits normal turning behaviour towards the cathode. Nerve orientation towards the cathode and augmented rates of growth were found in the presence of forskolin or ganglioside GM1. It is suggested that a combined approach of drug treatment and an applied electric field may be useful in promoting nerve regeneration.

The Relative Growth of Parts in Palaemon Carcinus

1930 ◽  
Vol 7 (2) ◽  
pp. 165-174
Author(s):  
M. A. TAZELAAR
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Linear Measurements ◽  
Relative Growth ◽  
Male And Female ◽  
Relative Growth Rates ◽  
Rate Of Growth ◽  
The Difference ◽  
Rates Of Growth

Linear measurements of certain appendages and the carapace of P. carcinus were made and plotted in various ways. The following conclusions were drawn: 1. The cheliped shows heterogonic growth in both male and female, but more markedly in the male, the values of k being: male 1.8 and female 1.48 2. The pereiopods in both male and female are slightly heterogonic. The relative growth rates are graded from p3 to p5, that of p3 being slightly greater than that of p5 3. Of the ordinary pereiopods the rate of growth of p1 is the smallest in the male, but the largest in the female. 4. The difference between the rates of growth of p1 and p3 in male and female is greatest where the rate of growth in the heterogonic organ, the cheliped, is most excessive in the male. 5. The growth of the 3rd maxilliped is slightly negatively heterogonic, the value of k in the male being 0.93 and in the female 0.95. Hence there seems to be a correlation between the marked heterogony in the cheliped on the growth rate of neighbouring appendages. In those immediately posterior to the cheliped the growth rate is increased and in those anterior decreased.

scholarly journals Coefficient estimates of certain subclasses of analytic functions associated with Hohlov operator

2019 ◽  
pp. 2150021
Author(s):  
P. Gochhayat ◽  
A. Prajapati ◽  
A. K. Sahoo
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Gauss Hypergeometric Function ◽  
Open Unit ◽  
Sufficient Condition ◽  
Extremal Functions ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Coefficient Estimates ◽  
Extremal Value

A typical quandary in geometric functions theory is to study a functional composed of amalgamations of the coefficients of the pristine function. Conventionally, there is a parameter over which the extremal value of the functional is needed. The present paper deals with consequential functional of this type. By making use of Hohlov operator, a new subclass [Formula: see text] of analytic functions defined in the open unit disk is introduced. For both real and complex parameter, the sharp bounds for the Fekete–Szegö problems are found. An attempt has also been taken to found the sharp upper bound to the second and third Hankel determinant for functions belonging to this class. All the extremal functions are express in term of Gauss hypergeometric function and convolution. Finally, the sufficient condition for functions to be in [Formula: see text] is derived. Relevant connections of the new results with well-known ones are pointed out.

scholarly journals Mixed Moore Cayley Graphs

2017 ◽  
Vol 17 (03n04) ◽  
pp. 1741010
Author(s):  
GRAHAME ERSKINE
Keyword(s):  
Infinite Number ◽  
Upper Bound ◽  
Maximum Degree ◽  
Cayley Graphs ◽  
Computational Techniques ◽  
Elementary Group ◽  
Recent Interest ◽  
Mixed Graphs ◽  
Rule Out

The degree-diameter problem seeks to find the largest possible number of vertices in a graph having given diameter and given maximum degree. There has been much recent interest in the problem for mixed graphs, where we allow both undirected edges and directed arcs in the graph. For a diameter 2 graph with maximum undirected degree r and directed out-degree z, a straightforward counting argument yields an upper bound M(z, r, 2) = (z+r)2+z+1 for the order of the graph. Apart from the case r = 1, the only three known examples of mixed graphs attaining this bound are Cayley graphs, and there are an infinite number of feasible pairs (r, z) where the existence of mixed Moore graphs with these parameters is unknown. We use a combination of elementary group-theoretical arguments and computational techniques to rule out the existence of further examples of mixed Cayley graphs attaining the Moore bound for all orders up to 485.

Implications of rRNA Operon Copy Number and Ribosome Content in the Marine Oligotrophic Ultramicrobacterium Sphingomonassp. Strain RB2256

1998 ◽  
Vol 64 (11) ◽  
pp. 4433-4438 ◽  
Author(s):  
Fitri Fegatella ◽  
Julianne Lim ◽  
Staffan Kjelleberg ◽  
Ricardo Cavicchioli
Keyword(s):  
Growth Rate ◽  
Copy Number ◽  
Heterotrophic Bacteria ◽  
Single Copy ◽  
Rrna Operon ◽  
Limiting Factor ◽  
E Coli ◽  
Rate Of Growth ◽  
Rates Of Growth ◽  
Low Rate

ABSTRACT Sphingomonas sp. strain RB2256 is a representative of the dominant class of ultramicrobacteria that are present in marine oligotrophic waters. In this study we examined the rRNA copy number and ribosome content of RB2256 to identify factors that may be associated with the relatively low rate of growth exhibited by the organism. It was found that RB2256 contains a single copy of the rRNA operon, in contrast to Vibrio spp., which contain more than eight copies. The maximum number of ribosomes per cell was observed during mid-log phase; however, this maximum content was low compared to those of faster-growing, heterotrophic bacteria (approximately 8% of the maximum ribosome content of Escherichia coli with a growth rate of 1.5 h−1). The low number of ribosomes per cell appears to correlate with the low rate of growth (0.16 to 0.18 h−1) and the presence of a single copy of the rRNA operon. However, on the basis of cell volume, RB2256 appears to have a higher concentration of ribosomes than E. coli (approximately double that of E. coli with a growth rate of 1.5 h−1). Ribosome numbers reached maximum levels during mid-log-phase growth but decreased rapidly to 10% of maximum during late log phase through 7 days of starvation. The cells in late log phase and at the onset of starvation displayed an immediate response to a sudden addition of excess glucose (3 mM). This result demonstrates that a ribosome content 10% of maximum is sufficient to allow cells to immediately respond to nutrient upshift and achieve maximum rates of growth. These data indicate that the bulk of the ribosome pool is not required for protein synthesis and that ribosomes are not the limiting factor contributing to a low rate of growth. Our findings show that the regulation of ribosome content, the number of ribosomes per cell, and growth rate responses in RB2256 are fundamentally different from those characteristics in fast-growing heterotrophs like E. coliand that they may be characteristics typical of oligotrophic ultramicrobacteria.

scholarly journals Experiments in the Sea on Rate of Growth of some Crustacea Decapoda

1936 ◽  
Vol 20 (3) ◽  
pp. 673-689 ◽  
Author(s):  
J. H. Orton
Keyword(s):  
Carapace Width ◽  
Maximum Size ◽  
Rate Of Growth ◽  
Maximum Time ◽  
Experimental Apparatus ◽  
The Difference ◽  
Rates Of Growth

From experiments in the sea with wire cages and boxes with perforated zinc sides and tops more than 100 individuals of certain Crustacea which had grown inside the apparatus have been obtained at various subsequent dates.Minimal mean rates of growth are obtainable from the difference between maximum size at immediate entry and size at a given later date, and the approximate age by an allowance for age at entry plus the maximum time occupiable in the experimental apparatus. It was found that C. maenas spawned early in the year may attain a carapace width of 30 to 40 mm. by the following winter. In experiments extending over twelve months from July to July male C. maenas attained a carapace width of 43 to 53 mm. and females 37 mm. at an estimated maximum age of 15 months.

scholarly journals Normal Ranges of Upper Extremity Length, Circumference, and Rate of Growth in the Pediatric Population

Hand ◽  
2019 ◽  
Vol 15 (5) ◽  
pp. 713-721
Author(s):  
Tyler Edmond ◽  
Alexandra Laps ◽  
Alexandria L. Case ◽  
Nathan O’Hara ◽  
Joshua M. Abzug
Keyword(s):  
Upper Extremity ◽  
Normal Values ◽  
Pediatric Population ◽  
Upper Arm ◽  
Mean Values ◽  
Rate Of Growth ◽  
Normal Ranges ◽  
Rates Of Growth ◽  
Forearm Length ◽  
Age And Sex

Background: Upper extremity length and circumference abnormalities are present in a number of conditions in the pediatric population. In most cases, upper limb hypoplasia and hypertrophy are diagnosed when one limb appears substantially different from the other during physical examination. However, occasionally when this discrepancy exists, it can be difficult to determine which limb is the abnormal one. The purpose of this study was to establish normal values for upper extremity length, circumference, and rate of growth in children aged 0 to 17 years. Methods: In all, 377 participants had 4 measurements taken of each upper extremity: upper arm length, upper arm circumference, forearm length, and forearm circumference. Statistical analysis was performed to identify differences and rates of growth. Results: Mean values for arm and forearm length and circumference for each age, 0 to 17 years, were established. The determination of a child’s expected arm length is dependent on his or her height, age, and sex, while the calculation of a child’s expected forearm length depends on his or her weight, age, and sex. Male and female arms and forearms have similar growth rates of lengths and circumferences. No significant differences were found between right and left extremities for each of the 4 measurements taken. Conclusions: Contralateral limbs can be used for comparison of length and circumference of the arm and forearm in cases of unilateral upper extremity abnormality. The establishment of normal values for upper extremity length, circumference, and growth rate will be a useful diagnostic tool for upper extremity hypoplasia and hypertrophy.

Section II. The forecast in detail

2002 ◽  
Vol 180 ◽  
pp. 41-53
Keyword(s):  
Economic Growth ◽  
Rate Of Growth ◽  
Rates Of Growth

There is now mounting evidence to suggest that positive rates of growth have been restored early this year, but the recovery is likely to be somewhat slower than we had anticipated in January. Our early estimates of monthly GDP suggest that growth in the first quarter was 0.2 per cent. The pattern of monthly GDP suggests that the stagnation in economic growth which began in September last year continued into the first month of 2002, contributing to the weak rate of growth estimated for the first quarter.

Sign in / Sign up

Export Citation Format

Share Document