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72. Evolution equations governed by Lipschitz continuous non-autonomous forms
- Creator:
- Sani, Ahmed and Laasri, Hafida
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, sesquilinear form, non-autonomous evolution equation, maximal regularity, convex set, 13, and 51
- Language:
- English
- Description:
- We prove L2-maximal regularity of the linear non-autonomous evolutionary Cauchy problem \dot u(t) + A(t)u(t) = f(t){\text{ for a}}{\text{.e}}{\text{. }}t \in \left[ {0,T} \right],{\text{ }}u(0) = {u_0}, where the operator A(t) arises from a time depending sesquilinear form a(t, ·, ·) on a Hilbert space H with constant domain V. We prove the maximal regularity in H when these forms are time Lipschitz continuous. We proceed by approximating the problem using the frozen coefficient method developed by El-Mennaoui, Keyantuo, Laasri (2011), El-Mennaoui, Laasri (2013), and Laasri (2012). As a consequence, we obtain an invariance criterion for convex and closed sets of H., Ahmed Sani, Hafida Laasri., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
73. Existence theorems for nonlinear differential equations having trichotomy in Banach spaces
- Creator:
- Gomaa, Adel Mahmoud
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- mathematics, nonlinear differential equation, trichotomy, existence theorem, 13, and 51
- Language:
- English
- Description:
- We give existence theorems for weak and strong solutions with trichotomy of the nonlinear differential equation x(t)=L(t)x(t)+f(t,x(t)), t R where {L(t) in R}$ is a family of linear operators from a Banach space E into itself and f R E to E. By L(E) we denote the space of linear operators from E into itself. Furthermore, for a<b and d>0, we let C([-d,0],E) be the Banach space of continuous functions from [-d,0] into E and f^d [a,b] C([-d,0],E) E. Let L: [a,b] to L(E) be a strongly measurable and Bochner integrable operator on [a,b] and for t in [a,b] define tau_tx(s)=x(t+s) for each s in[-d,0]. We prove that, under certain conditions, the differential equation with delay x(t)=L(t)x(t)+f^d(t,tau_tx) if t in [a,b], Q has at least one weak solution and, under suitable assumptions, the differential equation (Q) has a solution. Next, under a generalization of the compactness assumptions, we show that the problem (Q) has a solution too., Adel Mahmoud Gomaa., and Seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
74. Exponential polynomial inequalities and monomial sum inequalities in p-Newton sequences
- Creator:
- Charles R Johnson, Marijuán, Carlos, Pisonero, Miriam, and Yeh, Michael
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, exponential polynomial, Newton inequality, Newton coefficients, p-Newton sequence, 13, and 51
- Language:
- English
- Description:
- We consider inequalities between sums of monomials that hold for all p-Newton sequences. This continues recent work in which inequalities between sums of two, two-term monomials were combinatorially characterized (via the indices involved). Our focus is on the case of sums of three, two-term monomials, but this is very much more complicated. We develop and use a theory of exponential polynomial inequalities to give a sufficient condition for general monomial sum inequalities, and use the sufficient condition in two ways. The sufficient condition is necessary in the case of sums of two monomials but is not known if it is for sums of more. A complete description of the desired inequalities is given for Newton sequences of less than 5 terms., Charles R. Johnson, Carlos Marijuán, Miriam Pisonero, Michael Yeh., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
75. Extensions of hom-Lie algebras in terms of cohomology
- Creator:
- Armakan, Abdoreza R and Farhangdoost, Mohammed Reza
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, hom-Lie algebras, cohomology of hom-Lie algebras, extensions of hom-Lie algebras, 13, and 51
- Language:
- English
- Description:
- We study (non-abelian) extensions of a given hom-Lie algebra and provide a geometrical interpretation of extensions, in particular, we characterize an extension of a hom-Lie algebra g by another hom-Lie algebra h and discuss the case where h has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, Maurer-Cartan formula, curvature and the Bianchi identity for the possible extensions in differential geometry. Moreover, we find a cohomological obstruction to the existence of extensions of hom-Lie algebras, i.e., we show that in order to have an extendible hom-Lie algebra, there should exist a trivial member of the third cohomology., Abdoreza R. Armakan, Mohammed Reza Farhangdoost., and Seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
76. Extremely primitive groups and linear spaces
- Creator:
- Guan, Haiyan and Zhou, Shenglin
- Format:
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- Type:
- model:article and TEXT
- Subject:
- matematika, permutace, lineární prostory, mathematics, permutations, linear spaces, automorphism, point-primitive automorphism group, extremely primitive permutation group, 13, and 51
- Language:
- English
- Description:
- A non-regular primitive permutation group is called extremely primitive if a point stabilizer acts primitively on each of its nontrivial orbits. Let S be a nontrivial finite regular linear space and G ≤ Aut(S). Suppose that G is extremely primitive on points and let rank(G) be the rank of G on points. We prove that rank(G) ≥ 4 with few exceptions. Moreover, we show that Soc(G) is neither a sporadic group nor an alternating group, and G = PSL(2, q) with q + 1 a Fermat prime if Soc(G) is a finite classical simple group., Haiyan Guan, Shenglin Zhou., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
77. Factorization of cp-rank-3 completely positive matrices
- Creator:
- J. H Brandts and Michal Křížek
- Format:
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- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, completely positive matrix, cp-rank, factorization, discrete maximum principle, 13, and 51
- Language:
- English
- Description:
- A symmetric positive semi-definite matrix A is called completely positive if there exists a matrix B with nonnegative entries such that A = BB^{\top }. If B is such a matrix with a minimal number p of columns, then p is called the cp-rank of A. In this paper we develop a finite and exact algorithm to factorize any matrix A of cp-rank 3. Failure of this algorithm implies that A does not have cp-rank 3. Our motivation stems from the question if there exist three nonnegative polynomials of degree at most four that vanish at the boundary of an interval and are orthonormal with respect to a certain inner product., Jan Brandts, Michal Křížek., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
78. Fermat test with Gaussian base and Gaussian pseudoprimes
- Creator:
- Grau, José María, Oller-Marcén, Antonio M, Rodríguez, Manuel, and Sadornil, Daniel
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- Gaussian integer, Fermat test, pseudoprime, 13, and 51
- Language:
- English
- Description:
- The structure of the group (\mathbb{Z}/n\mathbb{Z})* and Fermat’s little theorem are the basis for some of the best-known primality testing algorithms. Many related concepts arise: Euler’s totient function and Carmichael’s lambda function, Fermat pseudoprimes, Carmichael and cyclic numbers, Lehmer’s totient problem, Giuga’s conjecture, etc. In this paper, we present and study analogues to some of the previous concepts arising when we consider the underlying group G_{n}:=\left \{ a+bi\in \mathbb{Z}\left [ i\right ]:a^{2}+b^{2}\equiv 1\left ( mod n \right ) \right \}. In particular, we characterize Gaussian Carmichael numbers via a Korselt’s criterion and present their relation with Gaussian cyclic numbers. Finally, we present the relation between Gaussian Carmichael number and 1-Williams numbers for numbers n ≡ 3 (mod 4). There are also no known composite numbers less than 1018 in this family that are both pseudoprime to base 1 + 2i and 2-pseudoprime., José María Grau, Antonio M. Oller-Marcén, Manuel Rodríguez, Daniel Sadornil., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
79. Fiber product preserving bundle functors as modified vertical Weil functors
- Creator:
- Mikulski , Włodzimierz M.
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, Weil algebra, Weil functor, vertical Weil functor, Weil algebra bundle functor, modified Weil functor, modified vertical Weil functor, bundle functor, fiber product preserving bundle functor, natural transformation, 13, and 51
- Language:
- English
- Description:
- We introduce the concept of modified vertical Weil functors on the category \mathcal{F}\mathcal{M}_m of fibred manifolds with m-dimensional bases and their fibred maps with embeddings as base maps. Then we describe all fiber product preserving bundle functors on \mathcal{F}\mathcal{M}_m in terms of modified vertical Weil functors. The construction of modified vertical Weil functors is an (almost direct) generalization of the usual vertical Weil functor. Namely, in the construction of the usual vertical Weil functors, we replace the usual Weil functors T^{a} corresponding to Weil algebras A by the so called modified Weil functors T^{a} corresponding to Weil algebra bundle functors A on the category \mathcal{F}\mathcal{M}_m of m-dimensional manifolds and their embeddings., Włodzimierz M. Mikulski., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
80. Finitistic dimension and restricted injective dimension
- Creator:
- Wu, Dejun
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, finitistic dimension, restricted injective dimension, tilting module, 13, and 51
- Language:
- English
- Description:
- We study the relations between finitistic dimensions and restricted injective dimensions. Let R be a ring and T a left R-module with A = EndRT. If RT is selforthogonal, then we show that rid \left ( T_{A} \right )\leqslant findim(A_{A})\leqslant findim \left ( _{R}T \right )+rid\left ( T_{A} \right ). Moreover, if R is a left noetherian ring and T is a finitely generated left R-module with finite injective dimension, then rid \left ( T_{A} \right )\leqslant findim(A_{A})\leqslant fin.inj.dim \left ( _{R}R \right )+rid\left ( T_{A} \right ). Also we show by an example that the restricted injective dimensions of a module may be strictly smaller than the Gorenstein injective dimension., Dejun Wu., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public