Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters

2014 ◽  
Vol 178 (1) ◽  
pp. 76-92 ◽  
Author(s):  
A. V. Pereskokov
2011 ◽  
Vol 36 (2) ◽  
pp. 251-266 ◽  
Author(s):  
Andrzej Rakowski ◽  
Piotr Rogowski

AbstractThis paper has two distinct parts. Section 1 includes general discussion of the phenomenon of "absolute pitch" (AP), and presentation of various concepts concerning definitions of "full", "partial" and "pseudo" AP. Sections 2-4 include presentation of the experiment concerning frequency range in which absolute pitch appears, and discussion of the experimental results. The experiment was performed with participation of 9 AP experts selected from the population of 250 music students as best scoring in the pitch-naming piano-tone screening tests. Each subject had to recognize chromas of 108 pure tones representing the chromatic musical scale of nine octaves from E0 to D#9. The series of 108 tones was presented to each subject 60 times in random order, diotically, with loudness level about 65 phon. Percentage of correct recognitions (PC) for each tone was computed. The frequency range for the existence of absolute pitch in pure tones, perceived by sensitive AP possessors stretches usually over 5 octaves from about 130.6 Hz (C3) to about 3.951 Hz (B7). However, it was noted that in a single case, the upper boundary of AP was 9.397 Hz (D9). The split-halves method was applied to estimate the reliability of the obtained results.


Author(s):  
Х.М. Хетагуров

Кленовники Северного Кавказа – особый тип лесных формаций. Особенность проявляется не только в структуре фитоценозов, но и в способах самовозобновления. Объект исследования – чистые и смешанные кленовники в нескольких урочищах РСО-Алания. Объекты расположены в различных условиях горного рельефа и на разной высоте над уровнем моря, от 1100 до 1900 м. Целью исследования является установление особенностей семенного возобновления кленовников, произрастающих в верхнем поясе распространения лесов на Северном Кавказе. Для достижения поставленной цели устанавливали время цветения и созревания семян по вертикальным поясам распространения кленовников. Обилие цветения и средний балл плодоношения устанавливали по В.Г. Капперу. Биометрические характеристики семян определяли по урочищам в трех повторностях. Учет подроста проводили на круговых учетных площадках по 10 м2, в соответствии с методикой А.В. Грязькина. Установлено, что цветение клена Траутфеттера начинается 10–14 мая и заканчивается в третьей декаде мая. Семена начинают созревать к концу августа – к началу сентября. Сроки опадения семян растянуты. Часть семян попадает на почву до начала листопада, поэтому они оказываются погребенными под опадом. Такие семена быстро теряют всхожесть, выпревают. Другая часть опадает вместе с листьями. Третья категория семян (самые легкие) держатся на деревьях до декабря и даже до весны. Естественное возобновление клена семенами под пологом материнского древостоя сильно затруднено из-за мощного травяного покрова. В древостое с сомкнутым пологом доля цветущих и плодоносящих деревьев составляет 2–3%, а средний балл плодоношения составляет 1,3. Освещенность на поверхности почвы не превышает 100 люкс, т. е. составляет 0,2–0,3% от освещенности на открытом месте; на высоте 1,3 м (над травостоем) освещенность несколько выше – от 1,2 до 1,6 тыс. люкс. Под пологом древостоя преобладает подрост вегетативного происхождения. У верхней границы кленового леса подрост семенного происхождения встречается в окнах, прогалинах и на открытых местах в количестве 430–630 экз./га. По высоте преобладает крупный подрост 50–60%, доля мелкого – 10–20%. The maple stands of the North Caucasus – a special type of forest formations. The peculiarity is manifested not only in the structure of phytocoenoses, but also in the ways of self-renewing. Object of research – pure and mixed maple stands in some areas of North Ossetia-Alania. The properties are located in various mountainous terrain and at different heights above sea level from 1100 to 1900 m. The aim of the study is to establish the characteristics of the seed the resumption of the maple stands growing in the upper belt of forests spread in the Northern Caucasus. To achieve this goal setting time of flowering and ripening of seeds on vertical zones distribution dominated. The abundance of flowering and the average score of fruiting was established by V.G. Capper. Biometric characteristics of the seeds was determined by the tracts in three replicates. Accounting for the undergrowth was carried out on a circular experimental plots at 10 m2, in accordance with the method of A.V. Grashkin. It is established that the flowering maple Trautvetter begins may 10–14 and ends in the third week of may. Seeds begin to ripen by late August – early September. The timing of subsidence of the stretched seed. Some of the seeds falls to the ground before the leaves, so they are trapped under the litter. These seeds quickly lose their germination, vypivaet. The other part falls along with the leaves. The third category of seeds (the light) stay on the trees until December and even till spring. Natural regeneration of maple seeds under the canopy of parent stand is very difficult due to the strong grass cover. In forest stands with dense canopy, proportion of flowering and fruit-bearing trees is 2–3%, and the average score of fruiting is 1.3. The illumination on the surface of the soil does not exceed 100 Lux, i. e. 0.2–0.3% of the light in the open, at a height of 1.3 m (on grass) the lighting is slightly higher, from 1.2 to 1.6 thousand Suite. Under the canopy of the forest the undergrowth is dominated by vegetative origin. At the upper boundary of the maple forest, saplings of seed origin occurs in Windows, clearings and open places in the number 430–630 ind./ha. In height dominated by large undergrowth of 50–60%, the share of small – 10–20%.


Order ◽  
2021 ◽  
Author(s):  
Péter Vrana

AbstractGiven a commutative semiring with a compatible preorder satisfying a version of the Archimedean property, the asymptotic spectrum, as introduced by Strassen (J. reine angew. Math. 1988), is an essentially unique compact Hausdorff space together with a map from the semiring to the ring of continuous functions. Strassen’s theorem characterizes an asymptotic relaxation of the preorder that asymptotically compares large powers of the elements up to a subexponential factor as the pointwise partial order of the corresponding functions, realizing the asymptotic spectrum as the space of monotone semiring homomorphisms to the nonnegative real numbers. Such preordered semirings have found applications in complexity theory and information theory. We prove a generalization of this theorem to preordered semirings that satisfy a weaker polynomial growth condition. This weaker hypothesis does not ensure in itself that nonnegative real-valued monotone homomorphisms characterize the (appropriate modification of the) asymptotic preorder. We find a sufficient condition as well as an equivalent condition for this to hold. Under these conditions the asymptotic spectrum is a locally compact Hausdorff space satisfying a similar universal property as in Strassen’s work.


2019 ◽  
Vol 71 (1) ◽  
Author(s):  
Aki Ito ◽  
Takashi Tonegawa ◽  
Naoki Uchida ◽  
Yojiro Yamamoto ◽  
Daisuke Suetsugu ◽  
...  

Abstract We applied tomographic inversion and receiver function analysis to seismic data from ocean-bottom seismometers and land-based stations to understand the structure and its relationship with slow slip events off Boso, Japan. First, we delineated the upper boundary of the Philippine Sea Plate based on both the velocity structure and the locations of the low-angle thrust-faulting earthquakes. The upper boundary of the Philippine Sea Plate is distorted upward by a few kilometers between 140.5 and 141.0°E. We also determined the eastern edge of the Philippine Sea Plate based on the delineated upper boundary and the results of the receiver function analysis. The eastern edge has a northwest–southeast trend between the triple junction and 141.6°E, which changes to a north–south trend north of 34.7°N. The change in the subduction direction at 1–3 Ma might have resulted in the inflection of the eastern edge of the subducted Philippine Sea Plate. Second, we compared the subduction zone structure and hypocenter locations and the area of the Boso slow slip events. Most of the low-angle thrust-faulting earthquakes identified in this study occurred outside the areas of recurrent Boso slow slip events, which indicates that the slow slip area and regular low-angle thrust earthquakes are spatially separated in the offshore area. In addition, the slow slip areas are located only at the contact zone between the crustal parts of the North American Plate and the subducting Philippine Sea Plate. The localization of the slow slip events in the crust–crust contact zone off Boso is examined for the first time in this study. Finally, we detected a relatively low-velocity region in the mantle of the Philippine Sea Plate. The low-velocity mantle can be interpreted as serpentinized peridotite, which is also found in the Philippine Sea Plate prior to subduction. The serpentinized peridotite zone remains after the subduction of the Philippine Sea Plate and is likely distributed over a wide area along the subducted slab.


1998 ◽  
Vol 35 (2) ◽  
pp. 234-250 ◽  
Author(s):  
JF (Derick) Nixon ◽  
Nick Holl

A geothermal model is described that simulates simultaneous deposition, freezing, and thawing of mine tailings or sequentially placed layers of embankment soil. When layers of soil or mine tailings are placed during winter subfreezing conditions, frozen layers are formed in the soil profile that may persist with time. The following summer, warmer soil placement may not be sufficient to thaw out layers from the preceding winter. Remnant frozen soil layers may persist for many years or decades. The analysis is unique, as it involves a moving upper boundary and different surface snow cover functions applied in winter time. The model is calibrated based on two uranium mines in northern Saskatchewan. The Rabbit Lake scenario involves tailings growth to a height of 120 m over a period of 24 years. At Key Lake, tailings increase in height at a rate of 1.3 m/year. Good agreement between the observed position of frozen layers and those predicted by the model is obtained. Long-term predictions indicate that from 80 to 200 years would be required to thaw out the frozen layers formed during placement, assuming 1992 placement conditions continue. Deposition rates of 1.5-3 m/year give the largest amounts of frozen ground. The amount of frozen ground is sensitive to the assumed snow cover function during winter.Key words: geothermal, model, tailings, freezing, deposition.


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