Introduction to finite fields and their applications: Preface

Fluctuation periodicity, generation separation, and the expression of larval competition

The potato tuberworm, Phthorimaea operculella Zeller, is a serious pest of the potato, Solanum tuberosum L., in subtropical and tropical production systems around the world. Knowledge of the temperature-dependent population growth potential is crucial for understanding population dynamics and implementing pest control strategies in different agro-ecological zones. The development, mortality of immature life stages, and reproduction of P. operculella were studied at constant temperatures ranging from 10 to 32°C. The theoretical developmental thresholds were 11, 13.5, and 11.8°C, and required incubation times were 65.3, 165.1, and 107.6 degree-days (DD) for the egg, larval, and pupal stages, respectively. The nonlinear shape of the temperature–development curve at low temperatures was well described by the modified four-parameter Sharpe & DeMichele model. The log-normal function was fitted to the normalized cumulative frequency distributions of developmental times for each life stage. Temperature effects on immature mortality were described by polynomial regressions. The optimal temperature for survival was within the range of 20–30°C. Temperature effects on adult senescence were described by the modified Sharpe & DeMichele model. A polynomial function was fitted to total fecundity and temperature. Fecundity was highest around 21°C. Age-related cumulative proportions of fecundity were well described by a Gamma function. Most eggs were laid within the first quarter of the female life span. The established functions were used to build a P. operculella population model, and life table parameters were simulated over a range of temperatures. Calculations gave good predictions when compared with published data. Populations increase within a temperature range of 10–35°C, with an optimum at 28–30°C.

https://bioone.org/journals/environmental-entomology/volume-33/issue-3/0046-225X-33.3.477/A-Temperature-Based-Simulation-Model-for-the-Potato-Tuberworm-Phthorimaea/10.1603/0046-225X-33.3.477.pdf

A Temperature-Based Simulation Model for the Potato Tuberworm, Phthorimaea operculella Zeller (Lepidoptera; Gelechiidae)

Foundations of stochastic development.

Tomato leafminer Tuta absoluta (Meyrick) is a major pest of tomato plants in South America. It was first recorded in the UK in 2009 where it has been subjected to eradication policies. The current work outlines T. absoluta development under various UK glasshouse temperatures. The optimum temperature for Tuta development ranged from 19–23 °C. At 19 °C, there was 52% survival of T. absoluta from egg to adult. As temperature increased (23 °C and above) development time of the moth would appear to decrease. Population development ceases between 7 and 10 °C. Only 17% of eggs hatched at 10 °C but no larvae developed through to adult moths. No eggs hatched when maintained at 7 °C. Under laboratory conditions the total lifespan of the moth was longest (72 days) at 13 °C and shortest (35 days) at both 23 and 25 °C. Development from egg to adult took 58 days at 13 °C; 37 days at 19 °C and 23 days at 25 °C. High mortality of larvae occurred under all temperatures tested. First instar larvae were exposed on the leaf surface for approximately 82 minutes before fully tunnelling into the leaf. Adult longevity was longest at 10 °C with moths living for 40 days and shortest at 19 °C where they survived for 16 days. Generally more males than females were produced. The potential of Tuta absoluta to establish populations within UK protected horticulture is discussed.

https://www.mdpi.com/2075-4450/4/2/185/pdf

Population Development of Tuta absoluta (Meyrick) (Lepidoptera: Gelechiidae) under Simulated UK Glasshouse Conditions

A stochastic model of a temperature-dependent population

Let A be a set of automorphisms of a finite group G. The structure of the near-ring C(A) of identity preserving functions which commute with every element of A is investigated.

The centralizer of a set of group automorphisms

The centralizer of a group endomorphism

For a finite ring R with identity and a finite unital /{-module V the set C(R; V) = {/: V-* V\f(av) = af(v) for all o e R, v e V) is the centralizer near-ring determined by R and V. Those rings R such that C(R; V) is a ring for every R-module V are characterized. Conditions are given under which C(R; V) is a semisimple ring. It is shown that if C(R; V) is a semisimple ring then C(R; V) » EndR(P"). 1. Preliminaries. Let G be a group and T a semigroup of endomorphisms of G. Then C(T; G) = {/: G -> G|/(0) = 0 and/(ya) = y/(a) for all y E T, a E G) is a near-ring under the operations of function addition and function composition, and is called the centralizer near-ring determined by T and G. Moreover, every near-ring with identity arises in this manner [6, p. 50]. It has been shown by Betsch [1] that N is a finite simple near-ring with identity if and only if there exists a finite group G and a fixed point free group of automorphisms T of G such that TV as C(T; G). The structure of C(T; G) for various G's and T's has been investigated in [2], [3] and [4]. Throughout this paper R will denote a finite ring with 1 and V a finite unital Ä-module. The corresponding centralizer near-ring is C(R; V) = {/: V-* V\f(rv) = rfiv) for all r E R, v E V). In dealing with C(R; V) we may assume, without loss of generality, that V is a faithful Ä-module, for we have C(R; V) = C(R; V) where Fis a faithful Ä-module, R = /?/Ann(F). In [5] we showed that if R is a finite simple ring then C(R; V) is a simple near-ring. This result is used to obtain the following generalization. Proposition. Let R be a finite semisimple ring and let V be a finite R-module. Then C(R; V) is a semisimple near-ring. Proof. We have R = Sx © • • • ©5, where each S¡ is a simple ring. Let e¡ denote the identity of S,. If V¡ = [v E V\e¡v = v) then V = Vx © • • • © V, and f(V¡) Ç V¡ for each / G C(R; V). Further, if f denotes the restriction of / to V¡ then the map <b: C(R; V)^> C(SX; Vx) © • • • ®C(S,; V,) given by <b(f) = (fv • ■ • >/<) is a near-ring homomorphism. The map is onto, for if </,, . . . ,/() is in C(SX; Vx) © ■ • ■ ©C(S,; Vf) extend each/, to all of V by/(ü, + • • • +vt) = fi(Vi). Then/= 2/ is an element of C(R; V) such that <f>(/) = </„ . . . ,/,>. To Received by the editors July 26, 1979 and, in revised form, October 30, 1979. AMS (MOS) subject classifications (1970). Primary 16A76, 16A44; Secondary 16A42, 16A48.

/pdf/centralizer-near-rings-that-are-endomorphism-rings-561aga056s.pdf

Centralizer near-rings that are endomorphism rings

It is known that structural matrix rings pro-vide a natural passage from complete matrix rings to upper and lower triangular matrix rings, and they often explain the peculiarities regarding certain properties of complete matrix rings on the one hand and of triangular matrix rings on the other hand. In this paper the concept of a set of matrix units in a ring associated with a quasi-order relation is introduced and used to provide an internal char-acterisation of structural matrix rings.

Kirby C. Smith

Papers

A stochastic model of a temperature-dependent population

The centralizer of a set of group automorphisms

The centralizer of a group endomorphism

Centralizer near-rings that are endomorphism rings

An internal characterisation of structural matrix rings