Generalized Taylor’s formula

Odibat, Zaid; Shawagfeh, Nabil

doi:10.1016/j.amc.2006.07.102

Cited by 664 publications

(343 citation statements)

References 4 publications

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“…When proportional abundance is applied to prey use by species, the niche width can be calculated as: (2) where B ' is Hurlbert's niche width, p j is the proportion of individuals using prey item j, and a j is the proportion of the total prey items utilized consisting of prey item j. Variance of the estimate was calculated using the delta method (Krebs 1999). As described by Seber (1973), Smith (1982), and Krebs (1999), the delta method is a standard method for deriving standard errors based on the Taylor expansion (Odibat & Shawagfeh 2007).…”

Section: Discussionmentioning

confidence: 99%

Food habits of Pacific cod and walleye pollock in the northern Gulf of Alaska

Urban¹

2012

Mar. Ecol. Prog. Ser.

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Seasonal variations in the diets of Pacific cod Gadus macrocephalus and walleye pollock Theragra chalcogramma were examined from fish collected during 5 sampling periods from August 1998 to June 1999 in the Kodiak Island area in the Gulf of Alaska. Both species were shown to be generalist predators, eating a wide variety of fish and invertebrates. Pollock, which are limited to pelagic prey, can be considered more specialized than cod. Cod consumed 78 prey items, and pollock consumed 45 prey items, with 28 items shared by both species. Individual pollock, however, typically concentrated on a single prey item, while individual cod stomachs contained a wider variety of prey. The principal prey of Pacific cod was Tanner crab Chionoecetes bairdi, comprising > 28% of the cod diet by weight. The most common prey item for walleye pollock was the euphausiid Thysanoessa. Over the 5 sampling periods, the prey evenness and niche width occupied by the 2 species were similar, but seasonal differences were evident.

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Section: Discussionmentioning

confidence: 99%

Food habits of Pacific cod and walleye pollock in the northern Gulf of Alaska

Urban¹

2012

Mar. Ecol. Prog. Ser.

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“…Then The generalized mean value theorem and another property are defined in the following Remark [40]. …”

Section: Appendixmentioning

confidence: 99%

Dynamics of Salmonella Infection

Rihan¹

2017

Current Topics in Salmonella and Salmonellosis

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In this chapter, we propose a mathematical epidemic model, with integer and fractional order to describe the dynamics of Salmonella infection in animal herds. We investigate the qualitative behaviors of such model and find the conditions that guarantee the asymptotic stability of disease-free and endemic steady states. To assess the severity of the outbreak, as well as the strength of the medical and/or behavioral interventions necessary for control, we estimate basic reproduction number R 0 . This threshold parameter specifies the average number of secondary infections caused by one infected individual during his/her entire infectious period at the start of an outbreak. We also provide an unconditionally stable implicit scheme for the fractional-order epidemic model. The theoretical and computational results give insight into the modelers and infectious disease specialists.

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“…Assuming the formula holds for m, If T = R and c = 0, then we obtain the expression from [21], If T = R, then we obtain an equivalent formula to that in [33], …”

Section: Taylor Theoremsmentioning

confidence: 99%

“…For further works, see [4], [8], [27], [33], [36], [38], [41] and [42]. This section is dedicated to constructing a time scale analogue of the expression obtained in [21].…”

Section: Taylor Theoremsmentioning

confidence: 99%

Fractional calculus on time scales with Taylor’s theorem

Williams

2012

fcaa

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We present a definition of the Riemann-Liouville fractional calculus for arbitrary time scales through the use of time scales power functions, unifying a number of theories including continuum, discrete and fractional calculus. Basic properties of the theory are introduced including integrability conditions and index laws. Special emphasis is given to extending Taylor's theorem to incorporate our theory.MSC 2010 : Primary 26A33, Secondary 39A12

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Generalized Taylor’s formula

Cited by 664 publications

References 4 publications

Food habits of Pacific cod and walleye pollock in the northern Gulf of Alaska

Food habits of Pacific cod and walleye pollock in the northern Gulf of Alaska

Dynamics of Salmonella Infection

Fractional calculus on time scales with Taylor’s theorem

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