Let p be a prime. For any finite p-group G, the deep transfers T H,G ' : H / H ' → G ' / G " from the maximal subgroups H of index (G:H) = p in G to the derived subgroup G ' are introduced as an ...Let p be a prime. For any finite p-group G, the deep transfers T H,G ' : H / H ' → G ' / G " from the maximal subgroups H of index (G:H) = p in G to the derived subgroup G ' are introduced as an innovative tool for identifying G uniquely by means of the family of kernels ùd(G) =(ker(T H,G ')) (G: H) = p. For all finite 3-groups G of coclass cc(G) = 1, the family ùd(G) is determined explicitly. The results are applied to the Galois groups G =Gal(F3 (∞)/ F) of the Hilbert 3-class towers of all real quadratic fields F = Q(√d) with fundamental discriminants d > 1, 3-class group Cl3(F) □ C3 × C3, and total 3-principalization in each of their four unramified cyclic cubic extensions E/F. A systematic statistical evaluation is given for the complete range 1 d 7, and a few exceptional cases are pointed out for 1 d 8.展开更多
Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are...Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are determined by abelian type invariants of p-class groups C1pE of unramified extensions E/F with degree [E : F] = pn-1. Illustrated by the most extensive numerical results available currently, the transfer kernels (TE, F) of the p-class extensions TE, F : C1pF → C1pE from F to unramified cyclic degree-p extensions E/F are shown to be capable of narrowing down the number of contestants significantly. By determining the isomorphism type of the maximal subgroups S G of all 3-groups G with coclass cc(G) = 1, and establishing a general theorem on the connection between the p-class towers of a number field F and of an unramified abelian p-extension E/F, we are able to provide a theoretical proof of the realization of certain 3-groups S with maximal class by 3-tower groups of dihedral fields E with degree 6, which could not be realized up to now.展开更多
The emergence of the middle class was closely related to the appearance of industrial society and its consequential constant changes in the social structure. Karl Marx and other theorists in the same camp were among t...The emergence of the middle class was closely related to the appearance of industrial society and its consequential constant changes in the social structure. Karl Marx and other theorists in the same camp were among the earliest scholars who discussed that topic. For a quite long period of time, the debate was mainly focused on the characteristics of the “new middle class.” The middle class, however, has undergone a categorical transformation from the old to the new middle-class, and furthermore, this transformation itself has signified the transition in social patterns from industrial to post-industrial society as well as economic globalization, both of which have contributed to the growth and global expansion of the middle class, having thus fundamentally renovated the middle class.展开更多
The main purpose of this article is to define the super characteristic classes on a super vector bundle over a superspace. As an application, we propose the examples of Riemann-Roch type formula. We also introduce the...The main purpose of this article is to define the super characteristic classes on a super vector bundle over a superspace. As an application, we propose the examples of Riemann-Roch type formula. We also introduce the helicity group and cohomology with respect to coefficient of the helicity group. As an application, we propose the examples of Gauss-Bonnet type formula.展开更多
Robust quadratic dissipative control for a class of linear multi-variable systems with parameter uncertainties is considered, where the uncertainties are expressed in a linear fractional form.For the nominal system wi...Robust quadratic dissipative control for a class of linear multi-variable systems with parameter uncertainties is considered, where the uncertainties are expressed in a linear fractional form.For the nominal system without uncertainties, the equivalence between quadratic dissipativeness and positive realness is established, and conditions are derived for linear systems to be quadratic dissipative. As for uncertain systems, it is shown that the robust quadratic dissipative control problem for the uncertain system can be reduced to the corresponding problem for a related system without uncertainties. The control problem concerned can be solved using LMI approach. The results of the paper unify existing results on H∞ control and positive real control and provide a more flexible and less conservative control design method.展开更多
Space images play an important role in the Earth study as they bring the main information received from the Space Flyer Units (SFU) to help researchers. Space images’ deciphering gives the opportunity to study the te...Space images play an important role in the Earth study as they bring the main information received from the Space Flyer Units (SFU) to help researchers. Space images’ deciphering gives the opportunity to study the territory and to plot different maps. On the basis of the space image obtained from Landsat 5TM (30 m resolution, 01.09.2012 year), we managed to get a picture of the modern relief of the northern part of Inder lake. When comparing the space image with topographic maps of 1985, we succeeded to identify the dynamics of landforms change on the studied area, what has been shown on the drawn map of the relief of the Inder salt dome uplift. 14 classes, corresponding to a particular type of terrain or to a landscape complex, have been distinguished on the studied area. Inder salt dome uplift is a paradynamic conjugation, consisting of highly karsted Inder Mountains corresponding to large diapir uplift, and of the Inder Lake having a large ellipsoidal shape. Geomorphologically, the investigated territory is located on the left bank of Zhaiyk River, and presents a salt dome uplift in the form of a plateau-like hill raised above the surrounding surface from 12 to 40 m. The maximum height reaches 42.5 m (g. Suatbaytau). The crest of the Inder salt dome is composed of Low Permian sediments (rock salt with anhydrite, potassiummagnesium salts), and has an area of about 210 km2. Inder lake’s basin is represented by a tectonic depression, which is the local basis of erosion and is a drainage place of the Inder uplift karstic water. The lake area is 150 km2. Depending on the climatic conditions, the water level can vary.展开更多
文摘Let p be a prime. For any finite p-group G, the deep transfers T H,G ' : H / H ' → G ' / G " from the maximal subgroups H of index (G:H) = p in G to the derived subgroup G ' are introduced as an innovative tool for identifying G uniquely by means of the family of kernels ùd(G) =(ker(T H,G ')) (G: H) = p. For all finite 3-groups G of coclass cc(G) = 1, the family ùd(G) is determined explicitly. The results are applied to the Galois groups G =Gal(F3 (∞)/ F) of the Hilbert 3-class towers of all real quadratic fields F = Q(√d) with fundamental discriminants d > 1, 3-class group Cl3(F) □ C3 × C3, and total 3-principalization in each of their four unramified cyclic cubic extensions E/F. A systematic statistical evaluation is given for the complete range 1 d 7, and a few exceptional cases are pointed out for 1 d 8.
文摘Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are determined by abelian type invariants of p-class groups C1pE of unramified extensions E/F with degree [E : F] = pn-1. Illustrated by the most extensive numerical results available currently, the transfer kernels (TE, F) of the p-class extensions TE, F : C1pF → C1pE from F to unramified cyclic degree-p extensions E/F are shown to be capable of narrowing down the number of contestants significantly. By determining the isomorphism type of the maximal subgroups S G of all 3-groups G with coclass cc(G) = 1, and establishing a general theorem on the connection between the p-class towers of a number field F and of an unramified abelian p-extension E/F, we are able to provide a theoretical proof of the realization of certain 3-groups S with maximal class by 3-tower groups of dihedral fields E with degree 6, which could not be realized up to now.
文摘The emergence of the middle class was closely related to the appearance of industrial society and its consequential constant changes in the social structure. Karl Marx and other theorists in the same camp were among the earliest scholars who discussed that topic. For a quite long period of time, the debate was mainly focused on the characteristics of the “new middle class.” The middle class, however, has undergone a categorical transformation from the old to the new middle-class, and furthermore, this transformation itself has signified the transition in social patterns from industrial to post-industrial society as well as economic globalization, both of which have contributed to the growth and global expansion of the middle class, having thus fundamentally renovated the middle class.
文摘The main purpose of this article is to define the super characteristic classes on a super vector bundle over a superspace. As an application, we propose the examples of Riemann-Roch type formula. We also introduce the helicity group and cohomology with respect to coefficient of the helicity group. As an application, we propose the examples of Gauss-Bonnet type formula.
文摘Robust quadratic dissipative control for a class of linear multi-variable systems with parameter uncertainties is considered, where the uncertainties are expressed in a linear fractional form.For the nominal system without uncertainties, the equivalence between quadratic dissipativeness and positive realness is established, and conditions are derived for linear systems to be quadratic dissipative. As for uncertain systems, it is shown that the robust quadratic dissipative control problem for the uncertain system can be reduced to the corresponding problem for a related system without uncertainties. The control problem concerned can be solved using LMI approach. The results of the paper unify existing results on H∞ control and positive real control and provide a more flexible and less conservative control design method.
文摘Space images play an important role in the Earth study as they bring the main information received from the Space Flyer Units (SFU) to help researchers. Space images’ deciphering gives the opportunity to study the territory and to plot different maps. On the basis of the space image obtained from Landsat 5TM (30 m resolution, 01.09.2012 year), we managed to get a picture of the modern relief of the northern part of Inder lake. When comparing the space image with topographic maps of 1985, we succeeded to identify the dynamics of landforms change on the studied area, what has been shown on the drawn map of the relief of the Inder salt dome uplift. 14 classes, corresponding to a particular type of terrain or to a landscape complex, have been distinguished on the studied area. Inder salt dome uplift is a paradynamic conjugation, consisting of highly karsted Inder Mountains corresponding to large diapir uplift, and of the Inder Lake having a large ellipsoidal shape. Geomorphologically, the investigated territory is located on the left bank of Zhaiyk River, and presents a salt dome uplift in the form of a plateau-like hill raised above the surrounding surface from 12 to 40 m. The maximum height reaches 42.5 m (g. Suatbaytau). The crest of the Inder salt dome is composed of Low Permian sediments (rock salt with anhydrite, potassiummagnesium salts), and has an area of about 210 km2. Inder lake’s basin is represented by a tectonic depression, which is the local basis of erosion and is a drainage place of the Inder uplift karstic water. The lake area is 150 km2. Depending on the climatic conditions, the water level can vary.
