METHOD OF ASYMPTOTIC PARTIAL DECOMPOSITION OF DOMAIN

1998 ◽  
Vol 08 (01) ◽  
pp. 139-156 ◽  
Author(s):  
G. P. PANASENKO

A new method of partial decomposition of a domain is proposed for partial differential equations, depending on a small parameter. It is based on the information about the structure of the asymptotic solution in different parts of the domain. The principal idea of the method is to extract the subdomain of singular behavior of the solution and to simplify the problem in the subdomain of regular behavior of the solution. The special interface conditions are imposed on the common boundary of these partially decomposed subdomains. If, for example, the domain depends on the small parameter and some parts of the domain change their dimension after the passage to the limit, then the proposed method reduces the initial problem to the system of equations posed in the domains of different dimensions with the special interface conditions.

2015 ◽  
Vol 47 (3) ◽  
pp. 159-174
Author(s):  
Maciej Zych

Abstract The aim of this paper is the analysis of the names used on cartographic publications in Poland and the Czech Republic for transboundary geographical objects lying on the common boundary. After the analysis of the Czech and Polish topographic maps that are available on the national geoportals, maps of the divisions into natural regions, and toponymic databases (Polish the National Register of Geographical Names, and Czech Geonames – the Database of geographic names of the Czech Republic) it was established that 360 named geographic objects lie on this boundary. This number includes: 123 hydronyms (names of rivers and other streams), 224 oronyms (139 names of summits, 22 names of mountain passes, 35 names of mountain ranges and ridges, 15 names of highlands, plateaus and uplands, 7 names of mountain basins, valleys and depressions, 3 names of lowlands, and 3 names of rocks), 9 names of forests, 1 name of mountain meadow (alp), and 3 names of tracks. 212 of these objects (59%) have names in both languages – Polish and Czech, however, in 99 cases (47% of objects that have name in both Polish and Czech languages) the Polish and Czech toponyms entirely do not correspond to each other. From the remaining objects 67 (18%) have only the Czech name, and 81 (23%) only the Polish name. In some natural regions, the limits of their ranges set by the Czech and Polish geographers vary widely, for example a single region on one side of the boundary corresponds to two or more regions on other side of the boundary. In other cases illustrations of incorrectness are more sophisticated, like the river that has different course according to the Czech or Polish maps (stream regarded as a main watercourse in one country, which has its own name, in another country is considered as a tributary one with a different name). In the summary, it should be stated that in the large part of the Polish and Czech names of the geographical objects lying on the common boundary were drawn regardless of the names used in the neighboring country.


2020 ◽  
Vol 20 ◽  
Author(s):  
Andrzej Anderwald

One of the important tasks of the Church in the temporal order are concern for the work of creation and for man himself, and sometimes even the defense against threats of technical progress, conducted from any ethical and moral references. The concern for the common home is not only a domain of the Catholic Church. Similarly, other churches and Christian communities as well as other world religions reflect on the issues relating to the degradation of human and natural environment. Thus, the aim of these reflections is an attempt to recognize ecumenical impulses of the Pope in the context of integral ecology that takes into account the interlinkages between different dimensions of reality. Therefore, during the considerations will be presented firstly the papal diagnosis of the social and ecological crisis (1), then the proposals of actions aiming at the development of integral ecology (2) as well as an invitation to a dialogue resulting from the care for the common home (3). The main sources of the analysis undertaken are the two papal documents, namely the encyclical Laudato si’ (LS) and the post-synodal apostolic exhoration Querida Amazonia (QA).


Author(s):  
J. Pegna ◽  
F.-E. Wolter

Abstract Computer Aided Geometric Design of surfaces sometimes presents problems that were not envisioned by mathematicians in differential geometry. This paper presents mathematical results that pertain to the design of second order smooth blending surfaces. Second order smoothness normally requires that normal curvatures agree along all tangent directions at all points of the common boundary of two patches, called the linkage curve. The Linkage Curve Theorem proved here shows that, for the blend to be second order smooth when it is already first order smooth, it is sufficient that normal curvatures agree in one direction other than the tangent to a first order continuous linkage curve. This result is significant for it substantiates earlier works in computer aided geometric design. It also offers simple practical means of generating second order blends for it reduces the dimensionality of the problem to that of curve fairing, and is well adapted to a formulation of the blend surface using sweeps. From a theoretical viewpoint, it is remarkable that one can generate second order smooth blends with the assumption that the linkage curve is only first order smooth. This property may be helpful to the designer since linkage curves can be constructed from low order piecewise continuous curves.


Secret Worlds ◽  
2021 ◽  
pp. 53-84
Author(s):  
Martin Stevens

This chapter explores how vision is used by animals and the diversity in ways of seeing. It first details how colour vision works, focusing on the example of honeybees, which, like humans, are trichromatic and have good colour vision. Bees have a dedicated ultraviolet (UV) receptor, and then one for seeing shortwave (blue) and mediumwave (green) light. Other animals deviate more substantially, in that they have either more or fewer receptors used in colour vision, and hence different ‘dimensions’ of colour perception. The chapter then considers how jumping spiders use UV vision in identifying known or suitable prey species, as well as in mating. It also looks at polarisation vision in mantis shrimp. Mantis shrimp are bizarre in the number of receptors they have, each sensitive to different parts of the light spectrum. Finally, the chapter assesses how toads recognize prey from non-prey. The toad’s visual system acts as a ‘feature detector’ based on several stages of visual processing, producing a quick and appropriate response to a set of criteria that reliably encode objects of particular importance—in this case, food.


2007 ◽  
Vol 97 (4) ◽  
pp. 379-386 ◽  
Author(s):  
H.C. Zhang ◽  
G.X. Qiao

AbstractThe tribe Fordini is a fascinating group because of its complicated life history, primary host specificity and gall-forming characteristic. Different species produce galls with different morphology on different parts of the host plants. The EF-1α-based, COI-based and combined sequences-based phylogenetic trees with three algorithms MP, ML and Bayes all strongly suggest that Fordini is a monophyletic group with two clades corresponding to two subtribes, Fordina and Melaphidina, each also monophyletic. Some important morphological characters and primary host plants of aphids were mapped onto the phylogenetic tree to analyse the division of subtribes and to uncover at which level the aphids correspond to their primary hosts, Pistacia and Rhus. Results suggest that the division of subtribes in Fordini is closely related to host selection of aphids. The evolution of gall morphology and the probable driving force behind it in this tribe were also discussed. The Fordini aphids seem to have evolved towards a better ability to manipulate their host plant, induce strong sinks and gain high reproductive success. Galls in this tribe evolved mainly along two directions to attain this goal: (i) by enlarging the gall from small bag to spherical, even big cauliflower-like, and changing the galls' location or forming two galls in their life cycle (Fordina); (ii) by moving the gall position from midrib, petiole of the leaflet, and eventually to the common petiole of the compound leaf (Melaphidina).


1946 ◽  
Vol 24c (2) ◽  
pp. 26-38 ◽  
Author(s):  
Margaret Newton ◽  
T. Johnson

During the period 1919 to 1944, 65 physiologic races were identified from a total of 4543 isolates derived from uredial collections of Puccinia graminis Pers. var. Tritici Erikss. & Henn. Forty-nine races were obtained in the Prairie Provinces from a study of 3475 isolates; 40 in Eastern Canada from 1013 isolates, and 12 in British Columbia from 55 isolates. During this period, the predominant races have shown notable fluctuations in their prevalence. Races 36, 17, and 21 were the most common races until shortly after 1930 and were largely responsible for the severe rust losses suffered by Marquis and other common wheats during the decade preceding that year. Races 34 and 49 were collected frequently from 1927 to about 1935. All of these races diminished greatly in their prevalence between 1930 and 1936, whereas race 56, which was first collected in Canada in 1931, has become the predominant race since 1934. It was this race that played a major part in the stem rust epiphytotic of 1935. Another recent change in the racial population was a recrudescence in 1940 of race17, which for several previous years had been of minor importance. In 1941 this race challenged the pre-eminent position of race 56 but receded again in succeeding years to minor significance.The distribution of races is somewhat similar but not identical in different parts of Canada. Races 36 and 21 have been relatively more common in the Prairie Provinces than in Eastern Canada, while the contrary is true of race 38. Only about a dozen of the 65 races collected in Canada have thus far assumed much economic importance, a few others may be considered of minor significance, but at least two-thirds of the races have been found only occasionally and have, for reasons not fully understood, failed to gain even a limited distribution.A comparison of the number of physiologic races collected in Eastern Canada and the Prairie Provinces, respectively, has indicated a somewhat greater variety of physiologic races in the former region, a condition that may perhaps be explained by the presence of the common barberry in many localities in Eastern Canada.


2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Shahla Afsharpaiman ◽  
Musa Zare ◽  
Masoud Yasemi ◽  
Tannaz Jamialahmadi ◽  
Amirhossein Sahebkar

Background. The keratorefractive surgeries (KRS) are one of the most common ocular surgeries. One of the dangerous complications of these surgeries is infectious keratitis (IK), which is the second cause of blindness after cataract surgery. The purpose of this study was to estimate the prevalence of IK after KRS in different parts of the world. Methods. In order to obtain relevant studies, all national and international databases including IranMedex, SID, Magiran, IranDoc, Medlib, ScienceDirect, PubMed, Scopus, Cochrane, Embase, Web of Science, and Google Scholar were searched using standard keywords. Results. IK prevalence after KRS was 0.000496% (0.000145% for the left eye and 0.000149% for the right eye). IK prevalence after KRS in the United States, Europe, and Asia was 0.000667%, 0.000473%, and 0.000045%, respectively, in all of which the common microorganisms were Staphylococci. Meta-regression showed no significant association between IK after KRS and either sample size or publication year of the studies. IK prevalence after KRS in the right eye was more than that in the left one. Also, the probability of IK incidence after LASIK surgery was more than PRK and LASEK. In the evaluation of continents, IK after KRS in the United States was more frequent compared with Europe and Asia. Conclusions. This study provided data as to the overall prevalence of IK following KRS and its variations according to the types of eye, surgery, pathogenic microorganism, and geographical location.


The author remarks, that Mr. Ware’s observations with regard to short-sightedness, being in general merely the consequence of habit acquired at an early age, is conformable with his own experience in general, and that he himself is a particular instance of natural long-sightedness gradually converted into confirmed short sight. He very well remembers first learning to read, at the common age of four or five years, and that at that time he could see the usual inscriptions across a wide church; but that at the age of nine or ten years he could no longer distinguish the same letters at the same distance, without the assistance of a watch-glass, which has the effect of one slightly concave. In a few years more the same glass was not sufficiently powerful; but yet his degree of short-sightedness was so inconsiderable, that he yielded to the dissuasion of his friends from using the common concave glasses till he was upwards of thirty years of age, when No. 2 was barely sufficient; and he very shortly had recourse to No. 3. In the course of a few years an increase of the defect rendered it necessary for him to employ glasses still deeper, and his sight soon required No. 5, where it has remained stationary to the present time. From the progress which Sir Charles Blagden has observed in his own short-sightedness, he is of opinion that it would have been accelerated by an earlier use of concave glasses, and might have been retarded, or perhaps prevented altogether, by attention to read and write with his book or paper as far distant as might be from his eyes. In this communication he takes the same opportunity of adding an experiment made many years since on the subject of vision, with a view to decide how far the similarity of the images received by the two eyes contribute to the impression made on the mind, that they arise from only one object. In the house where he then resided, was a marble surface ornamented with fluting, in alternate ridges and concavities. When his eyes were directed to these, at the distance of nine inches, they could be seen with perfect distinctness. When the optic axes were directed to a point at some distance behind, the ridges seen by one eye became confounded with the impression of concavities made upon the other, and occasioned the uneasy sensation usual in squinting. But when the eyes were directed to a point still more distant, the impression of one ridge on the right eye corresponded with that made with an adjacent ridge upon the left eye, so that the fluting then appeared distinct and single as at first, but the object appeared at double its real distance, and apparently magnified in that proportion. Though the different parts of the fluting were of the same form, their colours were not exactly alike, and this occasioned some degree of confusion when attention was paid to this degree of dissimilarity.


1986 ◽  
Vol 104 (3-4) ◽  
pp. 261-277 ◽  
Author(s):  
F.-O. Speck

SynopsisVarious physical problems in diffraction theory lead us to study modifications of the Sommerfeld half-plane problem governed by two proper elliptic partial differential equations in complementary ℝ3 half-spaces Ω± and we allow different boundary or transmission conditions on two half-planes, which together form the common boundary of Ω±.


Sign in / Sign up

Export Citation Format

Share Document