The Lyapunov stability of the N-soliton solutions in the Lax hierarchy of the Benjamin-Ono equation

The Lyapunov stability is established for the N-soliton solutions in the Lax hierarchy of the Benjamin-Ono (BO) equation. We characterize the N-soliton profiles as critical points of certain Lyapunov functional. By using several results derived by the inverse scattering transform of the BO equation, we demonstarate the convexity of the Lyapunov functional when evaluated at the N-soliton profiles. From this fact, we deduce that the N-soliton solutions are energetically stable.Comment: To appear in Journa of Mathematical Physic

A novel multi-component generalization of the short pulse equation and its multisoliton solutions

We propose a novel multi-component system of nonlinear equations that generalizes the short pulse (SP) equation describing the propagation of ultra-short pulses in optical fibers. By means of the bilinear formalism combined with a hodograph transformation, we obtain its multi-soliton solutions in the form of a parametric representation. Notably, unlike the determinantal solutions of the SP equation, the proposed system is found to exhibit solutions expressed in terms of pfaffians. The proof of the solutions is performed within the framework of an elementary theory of determinants. The reduced 2-component system deserves a special consideration. In particular, we show by establishing a Lax pair that the system is completely integrable. The properties of solutions such as loop solitons and breathers are investigated in detail, confirming their solitonic behavior. A variant of the 2-component system is also discussed with its multisoliton solutions.Comment: Minor correction

Chris Vein: What Forensics Did for Me

ALUMNI CORNER: The forensic community is filled with alumni who will tout the benefits they received through their participation in intercollegiate speech and debate activities. As directors of forensics programs face battles for budgets and sometimes for their program’s very existence, having a collection of published testimonies about the positive influence of forensics can be a tremendous help. To that end, Speaker & Gavel is setting aside space in each issue for our alumni to talk about how forensics has helped them in their professional life. These are our alumni’s stories

REVITALISASI PENDIDIKAN KEWARGANEGARAAN MELALUI MODEL BELAJAR PRAKTIK BELAJAR KEWARGANEGARAAN (PROIECT CITIZEN)

In addition to civic knowledge, Project Citizen aims to foster the skills necessary for citizenship kewarganegaraan democracy. Various aspects of the program and student interaction with their classmates, government representatives, and non-governmental organisations at the time of intensive research on community problems allows the students have many opportunities to apply the intellectual skills and abilities to participate. Furthermore, through their participation in Project Citizen students have the opportunity to develop a variety of civic character of a democratic society such as the meaning of political values, political interests, political tolerance,commitment to the exercise democratic citizenship, commitment to civic responsibility, commitment to constitutionalism and the tendency to participate. The characteristics of these traits, which can be developed through Project Citizen,encourage responsible participation and effective by the citizens in a democracy which they run

Les peuplements d'éphémèroptères de plécoptères et de trichoptères des ruisseaux acides et non acides du massif vosgien : première approche

Les peuplements d'Ephémèroptères, de Plécoptères et de Trichoptères de quatorze cours d'eau du massif vosgien granitique, ont été échantillonnés de mars 1988 à mars 1990. Les stations, au nombre de seize, ont été choisies en amont de toute agglomération et en dehors de zones d'activité agricole.Les mesures de pH, conductivité et aluminium total, ont établi que sept ruisseaux sont acides (pH moyens : 4,67-5,62), très faiblement minéralisés (conductivités moyennes : 17-21,5 µS/cm) et présentent des concentrations moyennes en aluminium total, comprises entre 221 et 387 µg/l.Les sept autres cours d'eau sont faiblement acides à neutres (pH moyens : 6,80-6,98), peu minéralisés (conductivité moyenne : 36-90 µS/cm) et montrent des concentrations moyennes eut aluminium variant de 41 à 78 µg/l.Seules 29 espèces ont été récoltées dans les ruisseaux acides alors que 93 l'ont été dans les cours d'eau non acides.Les Ephémèroptères se révèlent les plus sensibles aux conditions acides et disparaissent totalement. Parmi les Trichoptères, seuls les Polycentropodidae, les Rhyacophilidae et les Limnephilidae sont encore présents dans les ruisseaux acides. Alors que les Plécoptères Filipalpes sont bien représentés, certaines espèces étant même très abondantes, les Plécoptères Sétipalpes ne sont plus récoltés dans les cours d'eau acidifiés, à l'exception de Siphonoperla torrentium.Acidification of freshwaters has become a serious problem in certain parts of the Vosges Mountains (Northeastern France). Aquatic organisms at all major levels are affected by decreased pH. As the Ephemeroptera, Plecoptera and Trichoplera are a significant par of the macrobenthos in mountain streams, the objective of this preliminary study was to determine how the physico-chemical environment in acidified running waters affects the qualitative composition of mayflies, stoneflies and caddis-flies communities compared with non acidified streams and to evaluate the reliability and possible use of the taxonomic groups as indicators of the extent of acidification.A biological survey of fourteen streams was conducted in the Vosges mountains from March 1988 to March 1990. The areas investigated lie on granitic bed-rock and soils in the process of podzolisation. The sampling sites (sixteen), at altitudes of 600 to 1020 meters a.s.l. were located above built-in and agricultural areas thus avoiding organic pollution. The streams drain forested catchments regarded as sensitive to acid inputs and affected by forest decline. Silver fir (Abies alba), Norway spruce (Pecea abies) and European beech (Fagus sylvatica) are dominant.Larvae and pupae of Ephemeroptera, Plecoptera and Trichoptera were collected by band picking and Surber sampler (mesh aperture 350 µm). Adults were collected with an insert net by beating bushes and trees or sweeping low herbage near streams. A long-handled net was required for high-flying Ephemeroptera and Trichoptera. Organisms were preserved in 5 % formalin or 70 % ethanol.The pH was measured in the field using a specific glass electrode for low ionic solutions, compensated for temperature. Water samples were acidified for total aluminium analysis. Determination of aluminium was performed using an atomic absorption spectrophotometer equipped with a graphite furnace. Conductivity was measured in the laboratory al 20 °C.Determination of pH revealed that acidification occurred et seven sites (sampling sites n° 8 to 16). Six were strongly acidic (mean pH : 4.7-5.2) and one moderately acidic (mean pH : 5,6). In such streams mean total aluminium ranged from 221 µg/1 to 387 µg/1 and mean conductivity from 17,0 µS/cm to 21.5 µS/cm. Minimum pH and maximum aluminium values were recorded during snowmelt or rein event. In all these streams the fish population (Salmo trutta fario) has completely disappeared.Others streams (sampling sites n° 1 to 7) went from slightly acidic to neutral with a range pH between 6.8-7.0 and were characterized by average total aluminium varying from 41 µg/1 to 78 µg/l and average conductivity from 36 µS/cm to 90 µS/cm. These streams have been considered as reference for non acidified running waters.The number of species occurring in acidified streams contrasted markedly with those of the non acidified streams. Specific richness of Ephemeroptera, Plecoptera and Trichoptera are reduced in acidic waters. Only twenty-nine species were found in acidic streams, whereas a total of ninety-three species were collected in non acidic streams.EphemeropteraIn the reference streams, the Ephemeroptera fauna was rich and diverse with twenty taxa. Some species, for example Epeorus sylvicola, Baetis alpinus and B. rhodani were very common and widespread. In contrast, in acidic water only one species, Baetis vernus, was actually present (3 larvae).TrichopteraThirty-eight species of caddis flies were found in non acidic streams. Hydropsychidae (hydropsyche sp) Philopotamidae (Philopotamus ludificatus, P. montanus, Wormaldia sp) and Glossosomatidae (Glossosoma conformis, Agapetus sp) were the organisms most commonly present.In acidic streams, eleven species were food. Rhyacopyhilidae (Rhyacophlla obliterata, R. potamoides, R. praemorsa), Polycentropodidae (Plectrocnemia sp, P. conspersa) and Limnephilidae (Drusus annulatus, D. discolor, Caetopterygopsis maclachlani, Chaelopteryx villosa, Anitella sp) were among the most abundant taxa.PlecopteraIn acidic streams, taxonomic richness (17 species) was about 50% lower than those obtained in the non acidic streams. The common species Perla marginata, Perlodes microcephala and Isoperla oxylepis were not listed when pH was below 5.6. At the opposit, some species were dominant and very abundant. For example, Brachyptera seticornis, was dominant in April, Leuctra nigra in May, Siphonoperla torrentium in June and Leuctra cingulala in July.The sensitivity of organisms towards to acidification appeared to be different among these groupe of aquatic insects. Three types of responses can be distinguished in relation with pH and/or associated factors :- High sensitivity of Ephemeroptera, which have completely disappeared- High sensitivity of most Trichoptera families except the following : Polycentropodidae, Rhyacophilidae and Limnephilidae.- Tolerance of Plecoptera filipalpia which were sometimes very abundant, but disappearance of Plecoptera Setipalpia except for Siphonoperla torrentium.This analysis showed that many species of mayflies, stoneflies and caddis flies do not tolerate low pH (and/or) associated with low conductivity and elevated aluminium concentrations. Because the biological response is the result of present and post environmental situations, we suggest the use of these taxa as indicators of acidification in running waters, particularly when a restricted number of physico-chemical measurements is insufficient to appreciate the acidification level, as during low flow periods or during periodes of no acid stress.Nevertheless, to be considered as a useful indicator of pollution in general and acidification in particular, a taxa (species, genera or family) should be widespread, relatively abundant, present all the year round, very sensitive to the studied factor and easy or relatively easy to identity.For example, in unpolluted streams in the Vosges Mountains, Epeorus sylvicola, Perlodes microcephala, Hydropsyche sp, Philopotamus sp seem to fit these criteria.However, in evaluating aquatic organisms as indicators of pollutional conditions, great caution is necessary because knowledge of the ecological requirements of the species is essential, several ecologic conditions other than the presence of a pollutant may limit the distribution of certain species. For this reason, the benthic macrofauna of a more significant number of sites of different chemical and physical characteristics should be collected

On the First Crossing of Two Boundaries by an Order Statistics Risk Process

We derive a closed form expression for the probability that a non-decreasing, pure jump stochastic risk process with the order statistics (OS) property will not exit the strip between two non-decreasing, possibly discontinuous, time-dependent boundaries, within a finite time interval. The result yields new expressions for the ruin probability in the insurance and the dual risk models with dependence between the claim severities or capital gains respectively

Ullemar's formula for the Jacobian of the complex moment mapping

The complex moment sequence m(P) is assigned to a univalent polynomial P by the Cauchy transform of the P(D), where D is the unit disk. We establish the representation of the Jacobian det dm(P) in terms of roots of the derivative P'. Combining this result with the special decomposition for the Hurwitz determinants, we prove a formula for the Jacobian which was previously conjectured by C. Ullemar. As a consequence, we show that the boundary of the class of all locally univalent polynomials in $U$ is contained in the union of three irreducible algebraic surfaces.Comment: 14 pages, submitted for "Complex Variables. Theory and Application