Coverage of the whole space

Consider an inhomogeneous germ-grain model with spherical grains whose radii depend on their positions through a rate function, possibly perturbed by a random noise. We find the critical rate function that separates the cases when the germ-grain model covers the whole space with a positive probability and when the total coverage occurs with probability zero.

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Dividend Problems with a Barrier Strategy in the Dual Risk Model until Bankruptcy

Journal of Applied Mathematics ◽

10.1155/2014/184098 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 2

Author(s):

Donghai Liu ◽

Zaiming Liu

Keyword(s):

Risk Model ◽

Rate Function ◽

Explicit Solutions ◽

Positive Probability ◽

Barrier Strategy ◽

Numerical Examples ◽

Dividend Payments ◽

Dual Risk Model ◽

Probability Of Bankruptcy ◽

Bankruptcy Rate

The paper studies the dual risk model with a barrier strategy under the concept of bankruptcy, in which one has a positive probability to continue business despite temporary negative surplus. Integrodifferential equations for the expectation of the discounted dividend payments and the probability of bankruptcy are derived. Moreover, when the gain size distribution is exponential, explicit solutions for the expected dividend payments and the bankruptcy probability are obtained for constant bankruptcy rate function. It also provided some numerical examples to illustrate the applications of the explicit solutions.

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Borehole gravity drift correction: A new approach

Geophysics ◽

10.1190/1.1442412 ◽

1988 ◽

Vol 53 (10) ◽

pp. 1343-1346

Author(s):

Kent A. Pennybaker

Keyword(s):

Random Noise ◽

Correction Method ◽

Rate Function ◽

Quality Data ◽

Frequency Noise ◽

Gradual Change ◽

Random Errors ◽

Drift Correction ◽

Pass Filter ◽

Low Pass Filter

Gravity meter drift is the gradual change in the gravity reading over time; this change is unrelated to actual gravity changes. Drift is caused by creep in the gravity meter mechanism and by external influences which produce a change in the physical properties of the gravity element. Previous methods of drift correction for the LaCoste and Romberg borehole gravity meter are either linear random noise filters or nonlinear techniques relying upon the judgement of an interpreter for filtering. The method presented in this paper responds to the nonlinearity of the drift signal while retaining the ability to filter out the noise. The drift rate function is defined by repeat readings, which are integrated to yield a drift correction. The drift correction data’s Fourier transform has a sharp amplitude break between the drift signal and the noise. A low‐pass filter removes the higher frequency noise, resulting in a smoothed drift correction. This drift correction method, which attenuates random errors while retaining the characteristic drift signal, works well with a variety of drift patterns and leads to consistently better quality data.

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Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

Journal of Applied Probability ◽

10.1017/s0021900200003119 ◽

2007 ◽

Vol 44 (02) ◽

pp. 492-505

Author(s):

M. Molina ◽

M. Mota ◽

A. Ramos

Keyword(s):

Branching Process ◽

Branching Processes ◽

Sufficient Conditions ◽

Positive Probability ◽

Limit Laws ◽

Bisexual Branching Processes ◽

Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

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A method for direct measurement of specimen noise in HREM images

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100148125 ◽

1993 ◽

Vol 51 ◽

pp. 458-459

Author(s):

Sidnei Paciornik ◽

Roar Kilaas ◽

Ulrich Dahmen ◽

Michael Adrian O'Keefe

Keyword(s):

Random Noise ◽

Image Interpretation ◽

Thin Foil ◽

High Resolution Electron Microscopy ◽

Black Dot ◽

Atomic Column ◽

Amorphous Oxide ◽

Resolution Electron ◽

Imaging Conditions ◽

Image Simulations

High resolution electron microscopy (HREM) is a primary tool for studying the atomic structure of defects in crystals. However, the quantitative analysis of defect structures is often seriously limited by specimen noise due to contamination or oxide layers on the surfaces of a thin foil.For simple monatomic structures such as fcc or bcc metals observed in directions where the crystal projects into well-separated atomic columns, HREM image interpretation is relatively simple: under weak phase object, Scherzer imaging conditions, each atomic column is imaged as a black dot. Variations in intensity and position of individual image dots can be due to variations in composition or location of atomic columns. Unfortunately, both types of variation may also arise from random noise superimposed on the periodic image due to an amorphous oxide or contamination film on the surfaces of the thin foil. For example, image simulations have shown that a layer of amorphous oxide (random noise) on the surfaces of a thin foil of perfect crystalline Si can lead to significant shifts in image intensities and centroid positions for individual atomic columns.

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CIScoSI Study [Children Immunization Status and cases of Systemic Illness]

Medical & Clinical Research ◽

10.33140/mcr.03.03.02 ◽

2018 ◽

Vol 3 (3) ◽

Keyword(s):

Infectious Diseases ◽

East Asia ◽

Pediatric Patients ◽

Severe Disease ◽

Tertiary Care ◽

Immunization Coverage ◽

South East Asia ◽

Immunization Status ◽

Tertiary Care Hospitals ◽

Total Coverage

To determine the immunization status of pediatric patients under age of 5 years visiting pediatric department of tertiary care hospitals in South East Asia. The aim of this study was to appreciate the awareness and implementation of vaccination in pediatric patients who came into pediatric outpatient Department with presenting complain other than routine vaccination. we can also know the count of patients who do not complete their vaccination after birth. we can differentiate between vaccinated and unvaccinated patients and incidence of severe disease in both groups. Immunization is a protective process which makes a person resistant to the harmful diseases prevailing in the community, typically by vaccine administration either orally or intravenously. It is proven for controlling and eliminating many threatening diseases from the community. WHO report that licensed vaccines are available for the prevention of many infectious diseases. After the implementation of effective immunization the rate of many infectious diseases have declined in many countries of the world. South-East Asia is far behind in the immunization coverage. An estimated total coverage is 56%-88% for a fully immunized child, which is variable between countries. Also the coverage is highest for BCG and lowest for Polio.

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