On the General Theory of Functions

For the purposes of mathematics the general notion of logic \u27propositional function\u27 may be used to define a concept which we may wish to regard as a mathematical function. The term function will be restricted to entities which satisfy the conditions imposed. These conditions may be regarded as axioms. They imply certain elementary properties of functions which we may call theorems, although it seems legitimate to raise the question: Are these propositions in logic or mathematics? The symbolism, and methodology are those of mathematics. The significance is so broad that the subject as a whole may be regarded as at least meta-mathematical if not entirely in the domain of logic. It will be assumed that there is a theory of classes, and certain properties of classes essential to the development of the theory of functions will be stated as need for them arises

Evaluation of spatial/temporal sources of variation in Nekton catch and the efficacy of stratified sampling in the Chesapeake Bay : final report for CBSAC V to Chesapeake Bay Stock Assessment Committee and the National Marine Fisheries Service, NOAA

Collections were made January through December 1988 using a 30 1 semiballoon trawl at 48 stations randomly selected each month, using equal allocation, from twelve geographical strata superimposed on a sampling frame of 16,730 possible stations uniformly distributed throughout water~ 12 feet deep in the Virginia mainstem Chesapeake Bay. The twelve geographical strata superimposed on the spatial sampling frame divided it into longitudinally-equal Upper, Middle and Lower Regions, each subdivided into four cross-bay regions, an Eastern Shore Littoral (12-30\u27), a Western Shore Littoral (12-30\u27), a Central Plain (30- 42\u27), and Deeps(\u3e 42 1 )

On the Characterization of the Algebra of Four Fundamental Boolean Functions

Let 0 and 1 denote the null and unit elements of a Boolean algebra B. The following four functions with argument in B and values in B are of fundamental importance in Boolean algebra. They are: the null function, defined by 0x = 0; the unit function, defined by 1x = 1; the identity function j, defined by jx = x, and the complementary function c, defined by the rule, ex is the complement of x. These four functions, 0, 1, j, c, form a tri-operational algebra in the sense of Karl Menger

Reproduction, Age And Growth, And Movements Of The Gulf Butterfish Peprilus-Burti

Collections were made for gulf butterfish Peprilus burti along a cross-shelf transect at depths of 5-100 m in the Gulf of Mexico off Texas from October 1977 to July 1980. Butterfish mature at 100-160 mm fork length as they approach age I. Spawning occurs primarily from September through May, but length frequencies indicate it concentrates, or is most successful, in distinct Winter (late January-mid-May) and Fall (early September-late October) periods that coincide with downcoast, alongshore currents (toward Mexico). Gonad data and persistence of small fish indicate spawning in winter, but at a low level. Spawning probably occurs offshore and upcoast toward the northcentral Gulf. Surface currents of the cyclonic shelf gyre probably transport eggs/larvae inshore and downcoast to recruit to the bottom in water 5-27 m deep, used as nurseries by butterfish when they are 2-5 months old. Butterfish disperse offshore as they mature and congregate in 36-100 m depths when they are 9-12 months old. They average 130-146 mm in fork length at age I in the northwestern Gulf, but 120-124 mm at age I and about 170 mm at age II in the northcentral Gulf. Estimates for the von Bertalanffy growth parameters L-infinity, K, and t0 were 164 mm, 1.99/year, and -0.20 years, respectively, for pooled northwestern Gulf Winter cohorts and 141 mm, 2.69/year, and -0.06 years, respectively, for pooled Fall cohorts. Somatic growth ceases as spawning approaches in the northwestern Gulf, but fish from the northcentral Gulf show large annual size increments. Butterfish reach about 200 mm in fork length, the largest ones occurring in the northcentral Gulf. Apparent maximum ages are 1-1.5 years in the northwestern Gulf, and 2-2.5 years in the northcentral Gulf. Differences in population attributes suggest complete mortality at age I in the northwestern Gulf or some unknown combination of an offshore and permanent contranatant spawning or postspawning emigration of adults to the northcentral Gulf. The genus Peprilus shows zoogeographic differences in population dynamics near Cape Hatteras, North Carolina

Composition of the Ichthyofauna Inhabiting the 110-Meter Contour of the Gulf of Mexico, Mississippi River to the Rio Grande

The ichthyofauna inhabiting the 110-m bathymetric contour from the Mississippi River to the Rio Grande was very diverse in comparison to the inshore fauna, although the number of species collected decreased off south Texas. A total of 69 species were identified, although only 3662 specimens were examined. Dominant taxa were the families Sparidae, Lutjanidae, Triglidae, Serranidae and Synodontidae with Stenotomus caprinus, Pristipomoides aquilonaris, Prionotus paralatus, Serranus atrobranchus, and Synodus joetens being the most abundant species. Faunal composition was very similar along the entire 110-m contour except for large changes in abundance of Stenotomus caprinus, Pristipomoides aquilonaris, and Serranus atrobranchus. Abundance of Stenotomus caprinus decreased greatly off south Texas whereas the converse was true for Pristipomoides aquilonaris and Serranus atrobranchus. The composition of the ichthyofauna at a depth of 110-m is similar to that found on the brown shrimp grounds of the northern Gulf of Mexico

A Comparison Of Calcified Structures For Aging Summer Flounder, Paralichthys Dentatus

Calcified structures of summer flounder, Paralichthys dentatus, were evaluated to identify the best age determination method. Scales, the currently preferred structure, were compared with opercular bones and to right and left whole and sectioned otoliths for ages 0 to 10. All structures showed concentric rings that were interpreted as annual; however structures differed greatly in the clarity of their presumed annual marks. Right and left otoliths generally gave the same age, although they differed in the clarity of marks. Sectioned otoliths, particularly right ones, were the best aging structure. Right sectioned otoliths consistently showed the clearest marks and had the highest confidence scores, lowest reading times, and highest agreement within and between readers, 97% and 96%, respectively. Left sectioned otoliths took twice as long to prepare and were more difficult to interpret than right sectioned otoliths. Whole otoliths were the second best structure and were adequate to age 4 or 5, after which sectioning greatly improved the clarity of marks. Scales were inferior to, and often did not give the same age readings as, whole and sectioned otoliths. Compared with otoliths, scales tended to overage at younger ages and to underage at older ages. Opercular bones were undesirable for aging summer flounder. They were often unclear and inconsistent, and they had the lowest confidence scores, the highest reading times, and only 46% within-reader agreement. A major source of disagreement in scale and otolith age readings was the presence of an early, presumably false, mark on some structures. We compare the formation of this early mark in summer flounder with early mark formation on otoliths of Atlantic croaker, a species,vith similar life history traits

Particle boards from Cyprus-grown trees

Following a visit to the Republic of Cyprus by a member of staff of the Tropical Products Institute, a request was received from the Forests Department of the Ministry of Agriculture and Natural Resources, to examine the wood from seven different species of locally-grown trees and assess the suitability of the wood for use in the manufacture of particle boards

Age, Growth, And Mortality Of Atlantic Croaker, Micropogonias-Undulatus, In The Chesapeake Bay-Region, With A Discussion Of Apparent Geographic Changes In Population-Dynamics

Atlantic croaker, Micropogonias undulatus, collected from commercial catches in Chesapeake Bay and in Virginia and North Carolina coastal waters during 1988-1991 (n=1,967) were aged from transverse otolith sections. Ages 1-8 were recorded, but eight-year-old fish were rare. Marginal increment analysis showed that for ages 1-7, annuli are formed once a year during the period April-May. Otolith age readings were precise: \u3e99% agreement within and between readers. Observed lengths-at-age were highly variable and growth rate decreased after the first year. Despite the high variability in sizes-at-age, observed lengths for ages 1-7 fit the von Bertalanffy growth model (r2=0.99; n=753) well. No differences in growth were found between sexes. Total annual instantaneous mortality (Z) estimated from maximum age and from a catch curve of Chesapeake Bay commercial catches ranged from 0.55 to 0.63. Our results do not indicate the existence of a group of larger, older Atlantic croaker in Chesapeake Bay compared with more southern waters and suggest that the hypothesis of a basically different population dynamics pattern for this species north and south of Cape Hatteras, North Carolina, should be reevaluated