Motzkin decomposition of closed convex sets via truncation

A nonempty set F is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set C with a closed convex cone D. In that case, the sets C and D are called compact and conic components of F. This paper provides new characterizations of the Motzkin decomposable sets involving truncations of F (i.e., intersections of FF with closed halfspaces), when F contains no lines, and truncations of the intersection F̂ of F with the orthogonal complement of the lineality of F, otherwise. In particular, it is shown that a nonempty closed convex set F is Motzkin decomposable if and only if there exists a hyperplane H parallel to the lineality of F such that one of the truncations of F̂ induced by H is compact whereas the other one is a union of closed halflines emanating from H. Thus, any Motzkin decomposable set F can be expressed as F=C+D, where the compact component C is a truncation of F̂. These Motzkin decompositions are said to be of type T when F contains no lines, i.e., when C is a truncation of F. The minimality of this type of decompositions is also discussed.

On the stability of the Motzkin representation of closed convex sets

A set is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set with a closed convex cone. This paper analyzes the continuity properties of the set-valued mapping associating to each couple (C,D) formed by a compact convex set C and a closed convex cone D its Minkowski sum C + D. The continuity properties of other related mappings are also analyzed.

The Zeros of Riemann Zeta Partial Sums Yield Solutions to f(x) + f(2x) + · · · + f(nx) = 0

This paper proves that every zero of any n th , n ≥ 2, partial sum of the Riemann zeta function provides a vector space of basic solutions of the functional equation f(x)+f(2x)+⋯+f(nx)=0,x∈R . The continuity of the solutions depends on the sign of the real part of each zero.

A note on the real projection of the zeros of partial sums of Riemann zeta function

This paper proves that the real projection of each simple zero of any partial sum of the Riemann zeta function ζn(s):=∑nk=11ks,n>2 , is an accumulation point of the set {Res : ζ n (s) = 0}.

Computing the zeros of the partial sums of the Riemann zeta function

In this paper, we introduce a formula for the exact number of zeros of every partial sum of the Riemann zeta function inside infinitely many rectangles of the critical strips where they are situated.

(Table 1) Neutral and phenolic organohalogen compounds in blubber samples of ringed seals (Pusa hispida) from East Greenland

We report on the comparative bioaccumulation, biotransformation and/or biomagnification from East Greenland ringed seal (Pusa hispida) blubber to polar bear (Ursus maritimus) tissues (adipose, liver and brain) of various classes and congeners of persistent chlorinated and brominated contaminants and metabolic by-products: polychlorinated biphenyls (PCBs), chlordanes (CHLs), hydroxyl (OH-) and methylsulfonyl (MeSO2-) PCBs, polybrominated biphenyls (PBBs), OH-PBBs, polybrominated diphenyl ether (PBDE) and hexabromocyclododecane (HBCD) flame retardants and OH- and methoxyl (MeO-) PBDEs, 2,2-dichloro-bis(4-chlorophenyl)ethene (p,p'-DDE), 3-MeSO2-p,p'-DDE, pentachlorophenol (PCP) and 4-OH-heptachlorostyrene (4-OH-HpCS). We detected all of the investigated contaminants in ringed seal blubber with high frequency, the main diet of East Greenland bears, with the exception of OH-PCBs and 4-OH-HpCS, which indicated that these phenolic contaminants were likely of metabolic origin and formed in the bears from accumulated PCBs and octachlorostyrene (OCS), respectively, rather than being bioaccumulated from a seal blubber diet. For all of the detectable sum of classes or individual organohalogens, in general, the ringed seal to polar bear mean BMFs for SumPCBs, p,p'-DDE, SumCHLs, SumMeSO2-PCBs, 3-MeSO2-p,p'-DDE, PCP, SumPBDEs, total-(alpha)-HBCD, SumOH-PBDEs, SumMeO-PBDEs and SumOH-PBBs indicated that these organohalogens bioaccumulate, and in some cases there was tissue-specific biomagnification, e.g., BMFs for bear adipose and liver ranged from 2 to 570. The blood-brain barrier appeared to be effective in minimizing brain accumulation as BMFs were <= 1 in the brain, with the exception of SumOH-PBBs (mean BMF = 93±54). Unlike OH-PCB metabolites, OH-PBDEs in the bear tissues appeared to be mainly accumulated from the seal blubber rather than being metabolic formed from PBDEs in the bears. In vitro PBDE depletion assays using polar bear hepatic microsomes, wherein the rate of oxidative metabolism of PBDE congeners was very slow, supported the probability that accumulation from seals is the main source of OH-PBDEs in the bear tissues. Our findings demonstrated from ringed seal to polar bears that organohalogen biotransformation, bioaccumulation and/or biomagnification varied widely and depended on the contaminant in question. Our results show the increasing complexity of bioaccumulated and in some cases biomagnified, chlorinated and brominated contaminants and/or metabolites from the diet may be a contributing stress factor in the health of East Greenland polar bears.

Phosphorus components, trace metals and Ba excess of ODP Site 202-1237 sediments

We determined the sedimentary concentrations of phosphorus (P), barium (Ba), manganese (Mn), titanium (Ti), aluminum (Al), and uranium (U) for sediment samples from the southeast Pacific Nazca Ridge, Ocean Drilling Program Site 1237. This unique record extends to 31 Ma over 360 meters composite depth (mcd), recording depositional history as the site progressed eastward over its paleohistory. We sampled with a temporal resolution of ~0.2 m.y. throughout the sequence, equivalent to an average spacing of 1.63 m/sample. Concentrations of sequentially extracted components of P (oxide-associated, authigenic, organic, and detrital) increase toward the modern. Al/Ti ratios indicate that the background detrital source material is consistent with upper continental crust. U enrichment factors (U EFs) generally exceed crustal values and indicate slightly reducing environments. However, authigenic U precipitation can also be influenced by the organic carbon rain rate and may not be solely an indicator of redox conditions. Dramatic changes in Mn EFs at ~162 mcd, from values between 12 and 93 to values <12 after this depth, and a sharp color contact boundary lead us to believe that a paleoredox boundary from an oxygenated to a more reducing depositional environment occurred near this depth. Estimates of biogenic barite concentrations from a total sediment digestion technique (Ba excess) are greater than those from a barite extraction (Ba barite) for selected samples across the entire depth range. Applying a range of Ba/Ti ratios from different source materials to correct for detrital inputs does not change the lack of agreement with Ba barite concentrations. Reactive P (P reactive) concentrations (the sum of oxide-associated, authigenic, and organic P concentrations) increase toward the modern with values typically <12 µmol P/g from the base of our record through ~100 mcd, with a gradual increase to concentrations >15 µmol P/g. Ba excess follows the same general trends as Preactive, with concentrations <14 µmol Ba/g in the lower portion of the record to values >15 µmol Ba/g. Accumulation rate records of these proxies will be needed to infer paleoproductivity. P reactive/Ba excess ratios, an indicator of the relative burial of the nutrient P to organic carbon export, exhibit higher values, similar to modern, from the base of our record through ~180 mcd. The remainder of the record exhibits values lower than modern, indicating that organic carbon export to the sediments was higher relative to nutrient burial.

Growth, survival, gene expression, microbiota and tryptic activity during feeding of Scophthalmus maximus first feeding larvae with beta-glucan (MacroGard)

Reflecting the natural biology of mass spawning fish aquaculture production of fish larvae is often hampered by high and unpredictable mortality rates. The present study aimed to enhance larval performance and immunity via the oral administration of an immunomodulator, beta-glucan (MacroGard®) in turbot (Scophthalmus maximus). Rotifers (Brachionus plicatilis) were incubated with or without yeast beta-1,3/1,6-glucan in form of MacroGard® at a concentration of 0.5 g/L. Rotifers were fed to first feeding turbot larvae once a day. From day 13 dph onwards all tanks were additionally fed untreated Artemia sp. nauplii (1 nauplius ml/L). Daily mortality was monitored and larvae were sampled at 11 and 24 dph for expression of 30 genes, trypsin activity and size measurements. Along with the feeding of beta-glucan daily mortality was significantly reduced by ca. 15% and an alteration of the larval microbiota was observed. At 11 dph gene expression of trypsin and chymotrypsin was elevated in the MacroGard® fed fish, which resulted in heightened tryptic enzyme activity. No effect on genes encoding antioxidative proteins was observed, whilst the immune response was clearly modulated by beta-glucan. At 11 dph complement component c3 was elevated whilst cytokines, antimicrobial peptides, toll like receptor 3 and heat shock protein 70 were not affected. At the later time point (24 dph) an anti-inflammatory effect in form of a down-regulation of hsp 70, tnf-alpha and il-1beta was observed. We conclude that the administration of beta-glucan induced an immunomodulatory response and could be used as an effective measure to increase survival in rearing of turbot.

Short-term spectral analysis of ODP Hole 114-704B

Short-term spectral analysis was carried out on geochemical logging data from ODP Site 704. The FFT was used to compute the amplitude spectra of short-term overlapping segments to produce depth-period-amplitude spectrograms of the logging data. The spectrograms provided a means of evaluating the significance of the observed periodic components. The periodic components that were consistently present and prominent across a given record interval were considered to be significant. Changes in the spectrogram characteristics seem to reflect changes in either lithology, sedimentation rates, or hiatuses and may therefore provide useful information to aid in stratigraphic and paleoenvironmental studies. The dominant periodicity during the late Pleistocene and Brunhes Chron (0.97 to 0.47 Ma) was determined to be > 100,000 yr whereas the upper Matuyama Chron was dominated by the 41,000-yr periodicity. These periodicities suggest that the sedimentation patterns within the upper Matuyama Chron (0.98-1.78 Ma) were influenced by the Milankovitch obliquity cycle and those within the latest Matuyama-Brunhes Chron (<0.98 Ma) by the eccentricity cycle. The Brunhes/Matuyama boundary therefore represents a major discontinuity. Periodicities observed within the lower Matuyama and the upper Gauss Chron did not correlate with any of the periodicities within the Milankovitch frequency bands.

(Table 1) Composition of organic matter in bottom sediments from the Kuril-Kamchatka Trench

From results of analyses of sediment samples collected on a profile crossing the Kuril-Kamchatka Trench distribution of organic D, N. carbohydrates, lipids and humic substances was established, as well as nature of their relationship with amorphous silica and clay fraction. Sum of the main biochemical groups of organic matter in the surface layer of sediments (0-1 cm) from the Kuril-Kamchatka Trench amounts to about 15%; neogenetic forms not encountered in living organisms make up 85% of organic matter. Among such forms 26% comprise humic substances formed during initial stages of polymerization of decomposition products of biochemical macromolecules.

Abundance and biomass of mesozooplankton collected in front of the Danube Delta in May and October 1978

The Gurile Dunarii 1978 dataset contains zooplankton data collected in May and October 1978 in 14 station allong 3 transect in front of the Danube Delta (45°05' - 44°45'N, 30°02'- 29°27'E). Zooplankton sampling was undertaken at 14 stations where samples were collected using a Juday closing net in the 0-10, 10-20, 20-30, 30-40 and 40-50m layer (depending also on the water masses). The dataset includes samples analysed for mesozooplankton species composition and abundance. Sampling volume was estimated by multiplying the mouth area with the wire length. Taxon-specific mesozooplankton abundance was count under microscope. Total abundance is the sum of the counted individuals. Total biomass Fodder, Rotifera , Ctenophora and Noctiluca was estimated using a tabel with wet weight for each species an stage.

Chemistry of very young basalts from ODP Hole 106-648B

Basalts in Hole 648B, located in the rift valley of the Mid-Atlantic Ridge at 23°N in crust estimated to be less than 100,000 years old, are mainly fresh, but small amounts of secondary phases are found on fracture surfaces and in alteration halos within the rocks. The halos are defined by dark bands 1-4 mm thick that have developed parallel to fracture surfaces or pillow margins and which in some cases have migrated some centimeters into the rock. The dark bands are the principal locus of secondary phases. The secondary phases are olive-green and yellow protoceladonites, of composition and structure intermediate between celadonite and iron-rich saponite, red (Mn-poor) to opaque (Mn-rich) iron oxyhydroxides, mixtures of protoceladonite and iron oxyhydroxide, and rare manganese oxides. These phases occur mainly as linings or fillings of open spaces in the basalt within the dark bands. Sulfides and intersertal glass are the only primary phases that can be seen to have been altered. Where dark bands have migrated into the rock, the rock behind the advancing band is almost devoid of secondary phases, implying redissolution. The potassium and magnesium in the secondary phases could have been supplied from ambient seawater. The aluminum in the protoceladonites must have been derived from local reaction of intergranular glass. The source of iron and silica could have been intergranular glass or low temperature mineralizing solutions of the type responsible for the formation of deposits of manganese oxides and iron oxyhydroxides and silicates on the seafloor.

Prevalence of mixed neuropathologies in autopsied older adults and associations with clinical disease progression

Thesis (Ph.D.)--University of Washington, 2016-06

Certain observations concerning the effects of epistasis on complex traits and the evolution of genomes.

Thesis (Ph.D.)--University of Washington, 2016-05