Invariant-preserving Petri net reduction and conditions for invariant-existence

The use of invariants is an important tool for analysis of distributed and concurrent systems modeled by Petri nets. For a large practical system, the computation of desired invariants by the existing techniques is a time-consuming task. This paper proposes a theoretical foundation for simplified computation of desired invariants. We provide invariant-preserving Petri net reduction rules followed by the conditions for the existence of invariants in various well-structured nets. If an invariant exists, it can be found directly from the net structure using the formulas derived, or by applying the existing techniques on the reduced net.

Lyapunov-like conditions for the existence of zeno behavior in hybrid and lagrangian hybrid systems

Lyapunov-like conditions that utilize generalizations of energy and barrier functions certifying Zeno behavior near Zeno equilibria are presented. To better illustrate these conditions, we will study them in the context of Lagrangian hybrid systems. Through the observation that Lagrangian hybrid systems with isolated Zeno equilibria must have a onedimensional configuration space, we utilize our Lyapunov-like conditions to obtain easily verifiable necessary and sufficient conditions for the existence of Zeno behavior in systems of this form. © 2007 IEEE.

Sufficient Conditions for the Existence of Bound States in a Potential without Spherical Symmetry

We give in this paper several suffieient conditions for the existence of negative energy bound states in a purely attractive potential without spherical symmetry. These conditions generalize the condition obtained recently by K. Chadan and A. Martin (C. R. Acad. Sci. Paris290 (1980), 151), and can ensure the existence of n bound states. For the spherically symmetric case, one gets simple formulae which are also new.

SUFFICIENT CONDITIONS ON DIFFUSIVITY FOR THE EXISTENCE AND NONEXISTENCE OF STABLE EQUILIBRIA WITH NONLINEAR FLUX ON THE BOUNDARY

A reaction-diffusion equation with variable diffusivity and non-linear flux boundary condition is considered. The goal is to give sufficient conditions on the diffusivity function for nonexistence and also for existence of nonconstant stable stationary solutions. Applications are given for the main result of nonexistence.

Human science, or, Phrenology : its principles, proofs, faculties, organs, temperaments, combinations, conditions, teachings, philosophies, etc., etc. : as applied to health, its values, laws, functions, organs, means, preservation, restoration, etc. : mental philosophy, human and self improvement, civilization, home, country, commerce, rights, duties, ethics, etc. : God, His existence, attributes, laws, worship, natural theology, etc. : immortality, its evidences, conditions, relations to time, rewards, punishments, sin, faith, prayer, etc. : intellect, memory, juvenile and self education, literature, mental discipline, the senses, sciences, arts, avocations, a perfect life, etc., etc., etc. /

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Sufficient conditions for the existence of heteroclinic solutions for Phi-Laplacian differential equations

In this paper we consider the second order discontinuous equation in the real line, (a(t)φ(u′(t)))′ = f(t,u(t),u′(t)), a.e.t∈R, u(-∞) = ν⁻, u(+∞)=ν⁺, with φ an increasing homeomorphism such that φ(0)=0 and φ(R)=R, a∈C(R,R\{0})∩C¹(R,R) with a(t)>0, or a(t)<0, for t∈R, f:R³→R a L¹-Carathéodory function and ν⁻,ν⁺∈R such that ν⁻<ν⁺. We point out that the existence of heteroclinic solutions is obtained without asymptotic or growth assumptions on the nonlinearities φ and f. Moreover, as far as we know, this result is even new when φ(y)=y, that is, for equation (a(t)u′(t))′=f(t,u(t),u′(t)), a.e.t∈R.

Influence of oxidation and reduction conditions upon the morphology of silica-supported polycrystalline silver catalysts

The effect of oxidation and reduction conditions upon the morphology of polycrystalline silver catalysts has been investigated by means of in situ Fourier-transform infrared (FTIR) spectroscopy. Characterization of the sample was achieved by inspection of the νas(COO) band profile of adsorbed formate, recorded after dosing with formic acid at ambient temperature. Evidence was obtained for the existence of a silver surface reconstructed by the presence of subsurface oxygen in addition to the conventional family of Ag(111) and Ag(110) crystal faces. Oxidation at 773 K facilitated the reconstruction of silver planes due to the formation of subsurface oxygen species. Prolonged oxygen treatment at 773 K also caused particle fragmentation as a consequence of excessive oxygen penetration of the silver catalyst at defect sites. It was also deduced that the presence of oxygen in the gas phase stabilized the growth of silver planes which could form stronger bonds with oxygen. In contrast, high-temperature thermal treatment in vacuum induced significant sintering of the silver catalyst. Reduction at 773 K resulted in substantial quantities of dissolved hydrogen (and probably hydroxy species) in the bulk silver structure. Furthermore, enhanced defect formation in the catalyst was also noted, as evidenced by the increased concentration of formate species associated with oxygen-reconstructed silver faces.

Environmental effects of thermal and radioactive discharges from nuclear power plants in the boreal brackish-water conditions of the northern Baltic Sea

During recent decades, thermal and radioactive discharges from nuclear power plants into the aquatic environment have become the subject of lively debate as an ecological concern. The target of this thesis was to summarize the large quantity of results obtained in extensive monitoring programmes and studies carried out in recipient sea areas off the Finnish nuclear power plants at Loviisa and Olkiluoto during more than four decades. The Loviisa NPP is located on the coast of the Gulf of Finland and Olkiluoto NPP on that of the Bothnian Sea. The state of the Gulf of Finland is clearly more eutrophic; the nutrient concentrations in the surface water are about 1½ 2 times higher at Loviisa than at Olkiluoto, and the total phosphorus concentrations still increased in both areas (even doubled at Loviisa) between the early 1970s and 2000. Thus, it is a challenge to distinguish the local effects of thermal discharges from the general eutrophication process of the Gulf of Finland. The salinity is generally low in the brackish-water conditions of the northern Baltic Sea, being however about 1 higher at Olkiluoto than at Loviisa (the salinity of surface water varying at the latter from near to 0 in early spring to 4 6 in late autumn). Thus, many marine and fresh-water organisms live in the Loviisa area close to their limit of existence, which makes the biota sensitive to any additional stress. The characteristics of the discharge areas of the two sites differ from each other in many respects: the discharge area at Loviisa is a semi-enclosed bay in the inner archipelago, where the exchange of water is limited, while the discharge area at Olkiluoto is more open, and the exchange of water with the open Bothnian Sea is more effective. The effects of the cooling water discharged from the power plants on the temperatures in the sea were most obvious in winter. The formation of a permanent ice cover in the discharge areas has been delayed in early winter, and the break-up of the ice occurs earlier in spring. The prolonging of the growing season and the disturbance of the overwintering time, in conditions where the biota has adjusted to a distinct rest period in winter, have been the most significant biological effects of the thermal pollution. The soft-bottom macrofauna at Loviisa has deteriorated to the point of almost total extinction at many sampling stations during the past 40 years. A similar decline has been reported for the whole eastern Gulf of Finland. However, the local eutrophication process seems to have contributed into the decline of the zoobenthos in the discharge area at Loviisa. Thermal discharges have increased the production of organic matter, which again has led to more organic bottom deposits. These have in turn increased the tendency of the isolated deeps to a depletion of oxygen, and this has further caused strong remobilization of phosphorus from the bottom sediments. Phytoplankton primary production and primary production capacity doubled in the whole area between the late 1960s and the late 1990s, but started to decrease a little at the beginning of this century. The focus of the production shifted from spring to mid- and late summer. The general rise in the level of primary production was mainly due to the increase in nutrient concentrations over the whole Gulf of Finland, but the thermal discharge contributed to a stronger increase of production in the discharge area compared to that in the intake area. The eutrophication of littoral vegetation in the discharge area has been the most obvious, unambiguous and significant biological effect of the heated water. Myriophyllum spicatum, Potamogeton perfoliatus and Potamogeton pectinatus, and vigorous growths of numerous filamentous algae as their epiphytes have strongly increased in the vicinity of the cooling water outlet, where they have formed dense populations in the littoral zone in late summer. However, the strongest increase of phytobenthos has extended only to a distance of about 1 km from the outlet, i.e., the changes in vegetation have been largest in those areas that remain ice-free in winter. Similar trends were also discernible at Olkiluoto, but to a clearly smaller extent, which was due to the definitely weaker level of background eutrophy and nutrient concentrations in the Bothnian Sea, and the differing local hydrographical and biological factors prevailing in the Olkiluoto area. The level of primary production has also increased at Olkiluoto, but has remained at a clearly lower level than at Loviisa. In spite of the analogous changes observed in the macrozoobenthos, the benthic fauna has remained strong and diversified in the Olkiluoto area. Small amounts of local discharge nuclides were regularly detected in environmental samples taken from the discharge areas: tritium in seawater samples, and activation products, such as 60Co, 58Co, 54Mn, 110mAg, 51Cr, in suspended particulate matter, bottom sediments and in several indicator organisms (e.g., periphyton and Fucus vesiculosus) that effectively accumulate radioactive substances from the medium. The tritium discharges and the consequent detection frequency and concentrations of tritium in seawater were higher at Loviisa, but the concentrations of the activation products were higher at Olkiluoto, where traces of local discharge nuclides were also observed over a clearly wider area, due to the better exchange of water than at Loviisa, where local discharge nuclides were only detected outside Hästholmsfjärden Bay quite rarely and in smaller amounts. At the farthest, an insignificant trace amount (0.2 Bq kg-1 d.w.) of 60Co originating from Olkiluoto was detected in Fucus at a distance of 137 km from the power plant. Discharge nuclides from the local nuclear power plants were almost exclusively detected at the lower trophic levels of the ecosystems. Traces of local discharge nuclides were very seldom detected in fish, and even then only in very low quantities. As a consequence of the reduced discharges, the concentrations of local discharge nuclides in the environment have decreased noticeably in recent years at both Loviisa and Olkiluoto. Although the concentrations in environmental samples, and above all, the discharge data, are presented as seemingly large numbers, the radiation doses caused by them to the population and to the biota are very low, practically insignificant. The effects of the thermal discharges have been more significant, at least to the wildlife in the discharge areas of the cooling water, although the area of impact has been relatively small. The results show that the nutrient level and the exchange of water in the discharge area of a nuclear power plant are of crucial importance.

Influence of sintering conditions and doping on the dielectric relaxation originating from the surface layer effects in CaCu3Ti4O12 ceramics

Detailed investigations into the dielectric dispersion phenomenon in the giant dielectric constant material CaCu3Ti4O12 (CCTO) around room temperature revealed the existence of two successive dielectric relaxations. In the temperature domain, a new dielectric relaxation was clearly observed around 250K, in addition to the well-investigated dielectric relaxation close to 100K. The effect of sintering and doping (La3+) on the strength of these dielectric relaxations were studied in detail. The sintering temperature as well as its duration was found to have tremendous influence on the dielectric relaxation that was encountered around 250 K. This Maxwell-Wagner (M-W) type of relaxation was found to be originating from the surface layer containing the Cu-rich phase, which was ascribed to the difference in the oxygen content between the surface and the interior of the sample. Interestingly, this particular additional relaxation was not observed in La2/3Cu3Ti4O12, a low dielectric constant member of the CCTO family, in which the segregation of Cu-rich phase on the surface was absent. Indeed the correlation between the new relaxation and the presence of Cu-rich phase in CCTO ceramics was further corroborated by the absence of the same after removing the top and bottom layers. (C) 2007 Elsevier Ltd. All rights reserved.

Formation and preservation of pedogenic carbonates in South India, links with paleo-monsoon and pedological conditions: Clues from Sr isotopes, U-Th series and REEs

The influence of the pedogenic and climatic contexts on the formation and preservation of pedogenic carbonates in a climosequence in the Western Ghats (Karnataka Plateau, South West India) has been studied. Along the climosequence, the current mean annual rainfall (MAR) varies within a 80 km transect from 6000 mm at the edge of the Plateau to 500 mm inland. Pedogenic carbonates occur in the MAR range of 500-1200 mm. In the semi-arid zone (MAR: 500-900 mm), carbonates occur (i) as rhick hardpan calcretes on pediment slopes and (ii) as nodular horizons in polygenic black soils (i.e. vertisols). In the sub-humid zone (MAR: 900-1500 mm), pedogenic carbonates are disseminated in the black soil matrices either as loose, irregular and friable nodules of millimetric size or as indurated botryoidal nodules of centimetric to pluricentimetric size. They also occur at the top layers of the saprolite either as disseminated pluricentimetric indurated nodules or carbonate-cemented lumps of centimetric to decimetric size. Chemical and isotopic (Sr-87/Sr-86) compositions of the carbonate fraction were determined after leaching with 0.25 N HCl. The corresponding residual fractions containing both primary minerals and authigenic clays were digested separately and analyzed. The trend defined by the Sr-87/Sr-86 signatures of both labile carbonate fractions and corresponding residual fractions indicates that a part of the labile carbonate fraction is genetically linked to the local soil composition. Considering the residual fraction of each sample as the most likely lithogenic source of Ca in carbonates, it is estimated that from 24% to 82% (55% on average) of Ca is derived from local bedrock weathering, leading to a consumption of an equivalent proportion of atmospheric CO2. These values indicate that climatic conditions were humid enough to allow silicate weathering: MAR at the time of carbonate formation likely ranged from 400 to 700 mm, which is 2- to 3-fold less than the current MAR at these locations. The Sr, U and Mg contents and the (U-234/U-238) activity ratio in the labile carbonate fraction help to understand the conditions of carbonate formation. The relatively high concentrations of Sr, U and Mg in black soil carbonates may indicate fast growth and accumulation compared to carbonates in saprolite, possibly due to a better confinement of the pore waters which is supported by their high (U-234/U-238) signatures, and/or to higher content of dissolved carbonates in the pore waters. The occurrence of Ce, Mn and Fe oxides in the cracks of carbonate reflects the existence of relatively humid periods after carbonate formation. The carbonate ages determined by the U-Th method range from 1.33 +/- 0.84 kyr to 7.5 +/- 2.7 kyr and to a cluster of five ages around 20 kyr, i.e. the Last Glacial Maximum period. The young occurrences are only located in the black soils, which therefore constitute sensitive environments for trapping and retaining atmospheric CO2 even on short time scales. The maximum age of carbonates depends on their location in the climatic gradient: from about 20 kyr for centimetric nodules at Mule Hole (MAR = 1100 mm/yr) to 200 kyr for the calcrete at Gundlupet (MAR = 700 mm/yr, Durand et al., 2007). The intensity of rainfall during wet periods would indeed control the lifetime of pedogenic carbonates and thus the duration of inorganic carbon storage in soils. (C) 2010 Elsevier Ltd. All rights reserved.