Propositional modal provability logics like G and Grz have arithmetical interpretations where □φ can be read as ‘formula φ is provable in Peano Arithmetic’. These logics are decidable but are ...characterized by classes of Kripke frames which are not first‐order definable. By abstracting the aspects common to their characteristic axioms we define the notion of a formula generation map F(P) in one propositional variable. We then focus our attention on the properly displayable subset of all (first‐order definable) Sahlqvist modal logics. For any logic L from this subset, we consider the (provability) logic LF obtained by the addition of an axiom based upon a formula generation map F(P) so that LF = L + F(P). The class of such logics includes G and Grz. By appropriately modifying the right introduction rules for □, we give (not necessarily cut‐free) display calculi for every such logic. We define the pseudo‐displayable subset of these logics as those whose display calculi enjoy cut‐elimination for sequents of the form ⊤ ⊢ φ for any formula φ. We then show that for any provability logic LF having a conservative tense extension, there is a map f on formulae such that LF is pseudo‐displayable if and only if f maps theorems of LF to theorems of the underlying logic L and vice versa. By using a standard renaming technique we can guarantee that there is a polynomial‐time translation from LF into L. All proofs are purely syntactic and show the versatility of display calculi since similar results using traditional Gentzen calculi are not possible for as broad a range of logics and require further conditions. Our maps generalize previously known maps from G into K4. An application of our results gives an O(n.log n)3) translation from the (‘second order’) provability logic Grz into a decidable subset of first‐order logic. Since each of our logics L is a Sahlqvist logic, it is first‐order definable, and hence each L has a translation into first‐order logic. Our results therefore show that all pseudo‐displayable logics LF are ‘essentially first‐order’ even though their characteristic axiom may not be first‐order definable.
We define display calculi for nominal tense logics extending the minimal nominal tense logic (MNTL) by addition of primitive axioms. To do so, we use the natural translation ofMNTL into the minimal ...tense logic of inequality (L≠) which is known to be properly displayable by application of Kracht's results. The rules of the display calculus δMNTL for MNTL mimic those of the display calculus δL≠ for L≠. We show that every MNTL‐valid formula admits a cut‐free derivation in δMNTL. We also show that a restricted display calculus δ−MNTL, is not only complete for MNTL, but that it enjoys cut‐elimination for arbitrary sequents. Finally, we give a weak Sahlqvist‐type theorem for two semantically defined extensions of MNTL. Using Kracht's techniques we obtain sound and complete display calculi for these two extensions based upon δMNTL and δ−MNTL respectively. The display calculi based upon δMNTL enjoy cut‐elimination for valid formulae only, but those based upon δ−MNTL enjoy cut‐elimination for arbitrary sequents.
1. Artichoke tuber tissue contained RNA polymerase activity bound to the chromatin and in the supernatant after chromatin sedimentation. 2. The activity in the supernatant, the soluble polymerase, ...was fractionated into polymerases I and II by DEAE-cellulose chromatography, and the properties of each activity were determined. 3. The proportions of chromatin-bound and soluble activities varied with growth of the tissue, and there was a correlation between chromatin-bound activity and RNA accumulation. 4. The properties of the solubilized chromatin activity were compared with those of the soluble activity, and the relationship between these two activities is discussed.
Horizontal dislocation of the patella Gore, D R
JAMA : the journal of the American Medical Association,
11/1970, Letnik:
214, Številka:
6
Journal Article
A series of 21 trawls conducted by USNS BARTLETT in 3411-5060 m water depths in the Venezuela Basin during October to December 1981 produced about 100 specimens of polychelid lobsters of the abyssal ...genus Willemoesia. Abundances were highly disparate, with over 90 specimens of W. indica Alcock 1901 and 9 specimens of W. forceps A. Milne Edwards 1880. Neither species showed clear preference for a particular abyssal sediment, although W. forceps was not collected from turbidite substrata. Because turbidite sediments tend to be found deeper than sediments of hemipelagic or pelagic carbonate origin, the depth range in the Venezuela Basin of W. indica (3422-5060 m) is greater than that of W. forceps (3411-4064 m). Willemoesia forceps is widely distributed in the eastern and western North Atlantic and was previously known from the Caribbean Sea. Willemoesia indica was previously known from a very small series of specimens from the Bay of Bengal, and the Venezuela Basin records and collections substantially increase its known distribution and the material available for study. Because the range of morphological variation within the genus Willemoesia is not yet known, owing to paucity of specimens in the 8 known species, the taxonomic validity of several species within the genus remains uncertain.
In vivo studies on frog mesenteric arterioles (4) indicate that segmental differences in the response of microvessels to physical and chemical stimuli can be explained simply in terms of the ...length-tension characteristics of vascular smooth muscle at different points along the vascular tree. Studies on single, isolated arterioles in vitro were initiated to examine more closely the validity of this explanation for regional response differences. This paper reports some of the results. First-, second-, and third-order arterioles (18-60 micron i.d.) were dissected from hamster cheek pouches. The vessels were cannulated with a modified Burg microperfusion system, and their mechanical properties studied using the methods described by Duling and Gore. Vessels were activated in four stages with K+ and norepinephrine. During activation, transmural pressures were adjusted to minimize vascular smooth-muscle shortening. Active pressure-diameter curves were recorded while adjusting transmural pressure through the range 5 to 400 cm H20 in 5-25 cm steps. Vessel dimensions were measured with a videomicrometer. Passive curves were obtained after equilibration overnight in Ca2+-free medium. The vessels were then fixed and prepared for histologic sectioning, and measurements of vessel-wall composition were made. The Laplace relationship was used to construct length-tension diagrams, and the histologic data were used to normalize the dimensional data to smooth-muscle lengths. Maximum active tension of second-order arterioles (1,170 dynes/cm) was two times previous values reported by Gore et al. This was due presumably to refinements in techniques and dissection procedures. Maximum active stress averaged 3.9 X 10(+6) dynes/cm2 for second-order arterioles. This number is identical to data obtained from hog carotid strips by Dillon et al.
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