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232. Vector invariant ideals of abelian group algebras under the actions of the unitary groups and orthogonal groups

Creator:
Zeng, Lingli and Nan, Jizhu
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, vektorová algebra, mathematics, vector algebra, vector invariant ideal, group algebra, unitary group, orthogonal group, 13, and 51
Language:
English
Description:
Let F be a finite field of characteristic p and K a field which contains a primitive pth root of unity and char K ≠ p. Suppose that a classical group G acts on the F-vector space V. Then it can induce the actions on the vector space \left [ V\bigoplus V \right ] and on the group algebra K\left [ V\bigoplus V \right ], respectively. In this paper we determine the structure of G-invariant ideals of the group algebra K\left [ V\bigoplus V \right ], and establish the relationship between the invariant ideals of K[V] and the vector invariant ideals of K\left [ V\bigoplus V \right ], and establish the relationship between the invariant ideals of K[V] and the vector invariant ideals of K\left [ V\bigoplus V \right ], if G is a unitary group or orthogonal group. Combining the results obtained by Nan and Zeng (2013), we solve the problem of vector invariant ideals for all classical groups over finite fields., Lingli Zeng, Jizhu Nan., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

233. Víra ve zdravý rozum se ukázala neopodstatněnou

Creator:
Štefan Schwabik
Format:
print, bez média, and svazek
Type:
article, články, model:article, and TEXT
Subject:
Věda. Všeobecnosti. Základy vědy a kultury. Vědecká práce, Akademie věd České republiky, věda, výzkum a vývoj, matematika, science, research and development, mathematics, Česko, Czechia, 12, and 00
Language:
Czech
Description:
Štefan Schwabik.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

234. Volume comparison theorems for manifolds with radial curvature bounded

Creator:
Mao, Jing
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, radiální zakřivení, spherically symmetric manifolds, radial Ricci curvature, radial sectional curvature, volume comparison, 13, and 51
Language:
English
Description:
In this paper, for complete Riemannian manifolds with radial Ricci or sectional curvature bounded from below or above, respectively, with respect to some point, we prove several volume comparison theorems, which can be seen as extensions of already existing results. In fact, under this radial curvature assumption, the model space is the spherically symmetric manifold, which is also called the generalized space form, determined by the bound of the radial curvature, and moreover, volume comparisons are made between annulus or geodesic balls on the original manifold and those on the model space., Jing Mao., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

235. Weak- and strong-type inequality for the cone-like maximal operator in variable Lebesgue spaces

Creator:
Szarvas, Kristóf and Weisz, Ferenc
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, Lebesgueovy prostory, nerovnosti (matematika), mathematics, Lebesgue spaces, inequalities (mathematics), variable Lebesgue space maximal operator γ-rectangle Besicovitch’s covering theorem weak-type inequality strong-type inequality, maximal operator, γ-rectangle, Besicovitch’s covering theorem, weak-type inequality, strong-type inequality, 13, and 51
Language:
English
Description:
The classical Hardy-Littlewood maximal operator is bounded not only on the classical Lebesgue spaces Lp(Rd) (in the case p > 1), but (in the case when 1/p(·) is log-Hölder continuous and p- = inf{p(x): x\in Rd > 1) on the variable Lebesgue spaces Lp(·)(Rd), too. Furthermore, the classical Hardy-Littlewood maximal operator is of weak-type (1, 1). In the present note we generalize Besicovitch’s covering theorem for the so-called γ-rectangles. We introduce a general maximal operator Msγδ, and with the help of generalized Φ-functions, the strong- and weak-type inequalities will be proved for this maximal operator. Namely, if the exponent function 1/p(·) is log-Hölder continuous and p- ≥ s, where 1 ≤ s ≤ ∞ is arbitrary (or p- ≥ s), then the maximal operator Msγδ is bounded on the space Lp(·)(Rd) (or the maximal operator is of weak-type (p(·), p(·)))., Kristóf Szarvas, Ferenc Weisz., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

238. Yetter-Drinfeld-Long bimodules are modules

Creator:
Lu, Daowei and Wang, Shuanhong
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, Hopf algebra, Yetter-Drinfeld-Long bimodule, braided monoidal category, 13, and 51
Language:
English
Description:
Let H be a finite-dimensional bialgebra. In this paper, we prove that the category LR(H) of Yetter-Drinfeld-Long bimodules, introduced by F.Panaite, F.Van Oystaeyen (2008), is isomorphic to the Yetter-Drinfeld category H⊗H H⊗H YD over the tensor product bialgebra H H∗ as monoidal categories. Moreover if H is a finite-dimensional Hopf algebra with bijective antipode, the isomorphism is braided. Finally, as an application of this category isomorphism, we give two results., Daowei Lu, Shuanhong Wang., and Seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

240. Zákony zachování v moderních variačních teoriích: odkaz Emmy Noetherové

Creator:
Czudková, Lenka, Musilová, Jana, and Strouhalová, Jitka
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
Noether, Emmy, 1882-1935, variační metody, matematika, variational methods, mathematics, 6, and 53
Language:
Czech and English
Description:
Otázku, kde se berou zákony zachování hybnosti, momentu hybnosti, mechanické energie a dalších veličin, lze v rámci klasické mechaniky či teorie pole zodpovědět různými způsoby. Principiálně však zachovávající se veličiny souvisejí s operacemi symetrie daného problému. Tuto souvislost odhaluje pro případ teorií řídících se variačním principem teorém Emmy Noetherové z roku 1918, odvozený klasickým "souřadnicovým" způsobem užívajícím variací, tehdy ve variačním počtu obvyklým. Propracovaný moderní geometrický aparát fibrovaných variet a diferenciálních forem "kopírujících" jejich struktura je mnohem účinnějším prostředkem pro formulaci jak variačních teorií samotných, tak i jejich důsledků právě typu teorému Noetherové. Podstatu geometrického přístupu lze objasnit již na nejjednodušším případu - jednorozměrném pohybu klasické částice v mechanice., The question of the origin of conservation laws for the momentum, angular momentum, mechanical energy and other quantities in classical mechanics and classical field theories can be answered by various ways. Nevertheless, in principle the conserved quantities are connected with the symmetry of a problem under consideration. For variational theories such a connection was disclosed by the Emmy Noether theorem derived in 1918 by a classical "coordinate" procedure using variations, which was typical for the former calculus of variations. The elaborate modern geometrical formalism of fibred manifolds and differential forms adapted to their fibred structure is a much more effective tool not only for variational theories themselves but also for their consequences as the Noether theorem. The merit of the geometrical approach can be explained by the simplest example - a one-dimensional motion of a classical mechanical particle., Lenka Czudková, Jana Musilová, Jitka Strouhalová., and Obsahuje bibliografii
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public