| 1. |
- Arnlind, Joakim, et al.
(författare)
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Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
- 2011
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 52:12, s. 123502-
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Tidskriftsartikel (refereegranskat)abstract
- As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]
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| 2. |
- Kurujyibwami, Celestin
(författare)
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Admissible transformations and the group classification of Schrödinger equations
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We study admissible transformations and solve group classification problems for various classes of linear and nonlinear Schrödinger equations with an arbitrary number n of space variables.The aim of the thesis is twofold. The first is the construction of the new theory of uniform seminormalized classes of differential equations and its application to solving group classification problems for these classes. Point transformations connecting two equations (source and target) from the class under study may have special properties of semi-normalization. This makes the group classification of that class using the algebraic method more involved. To extend this method we introduce the new notion of uniformly semi-normalized classes. Various types of uniform semi-normalization are studied: with respect to the corresponding equivalence group, with respect to a proper subgroup of the equivalence group as well as the corresponding types of weak uniform semi-normalization. An important kind of uniform semi-normalization is given by classes of homogeneous linear differential equations, which we call uniform semi-normalization with respect to linear superposition of solutions.The class of linear Schrödinger equations with complex potentials is of this type and its group classification can be effectively carried out within the framework of the uniform semi-normalization. Computing the equivalence groupoid and the equivalence group of this class, we show that it is uniformly seminormalized with respect to linear superposition of solutions. This allow us to apply the version of the algebraic method for uniformly semi-normalized classes and to reduce the group classification of this class to the classification of appropriate subalgebras of its equivalence algebra. To single out the classification cases, integers that are invariant under equivalence transformations are introduced. The complete group classification of linear Schrödinger equations is carried out for the cases n = 1 and n = 2.The second aim is to study group classification problem for classes of generalized nonlinear Schrödinger equations which are not uniformly semi-normalized. We find their equivalence groupoids and their equivalence groups and then conclude whether these classes are normalized or not. The most appealing classes are the class of nonlinear Schrödinger equations with potentials and modular nonlinearities and the class of generalized Schrödinger equations with complex-valued and, in general, coefficients of Laplacian term. Both these classes are not normalized. The first is partitioned into an infinite number of disjoint normalized subclasses of three kinds: logarithmic nonlinearity, power nonlinearity and general modular nonlinearity. The properties of the Lie invariance algebras of equations from each subclass are studied for arbitrary space dimension n, and the complete group classification is carried out for each subclass in dimension (1+2). The second class is successively reduced into subclasses until we reach the subclass of (1+1)-dimensional linear Schrödinger equations with variable mass, which also turns out to be non-normalized. We prove that this class is mapped by a family of point transformations to the class of (1+1)-dimensional linear Schrödinger equations with unique constant mass.
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| 3. |
- Brännmark, Cecilia, et al.
(författare)
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Mathematical modeling of white adipocyte exocytosis predicts adiponectin secretion and quantifies the rates of vesicle exo- and endocytosis
- 2017
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Ingår i: Journal of Biological Chemistry. - : AMER SOC BIOCHEMISTRY MOLECULAR BIOLOGY INC. - 0021-9258 .- 1083-351X. ; 292:49, s. 20032-20043
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Tidskriftsartikel (refereegranskat)abstract
- Adiponectin is a hormone secreted from white adipocytes and takes part in the regulation of several metabolic processes. Although the pathophysiological importance of adiponectin has been thoroughly investigated, the mechanisms controlling its release are only partly understood. We have recently shown that adiponectin is secreted via regulated exocytosis of adiponectin-containing vesicles, that adiponectin exocytosis is stimulated by cAMP-dependent mechanisms, and that Ca2+ and ATP augment the cAMP-triggered secretion. However, much remains to be discovered regarding the molecular and cellular regulation of adiponectin release. Here, we have used mathematical modeling to extract detailed information contained within our previously obtained high-resolution patch-clamp time-resolved capacitance recordings to produce the first model of adiponectin exocytosis/secretion that combines all mechanistic knowledge deduced from electrophysiological experimental series. This model demonstrates that our previous understanding of the role of intracellular ATP in the control of adiponectin exocytosis needs to be revised to include an additional ATP-dependent step. Validation of the model by introduction of data of secreted adiponectin yielded a very close resemblance between the simulations and experimental results. Moreover, we could show that Ca2+-dependent adiponectin endocytosis contributes to the measured capacitance signal, and we were able to predict the contribution of endocytosis to the measured exocytotic rate under different experimental conditions. In conclusion, using mathematical modeling of published and newly generated data, we have obtained estimates of adiponectin exo- and endocytosis rates, and we have predicted adiponectin secretion. We believe that our model should have multiple applications in the study of metabolic processes and hormonal control thereof.
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| 4. |
- Tkachev, Vladimir
(författare)
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Minimal cubic cones via Clifford algebras
- 2010
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Ingår i: Complex Analysis and Operator Theory. - : SP Birkhäuser Verlag Basel. - 1661-8254 .- 1661-8262. ; 4:3, s. 685-700
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we construct two infinite families of algebraic minimal cones in R n . The first family consists of minimal cubics given explicitly in terms of the Clifford systems. We show that the classes of congruent minimal cubics are in one to one correspondence with those of geometrically equivalent Clifford systems. As a byproduct, we prove that for any n ≥ 4, n ≠ 16k + 1, there is at least one minimal cone in R n given by an irreducible homogeneous cubic polynomial. The second family consists of minimal cones in R m 2 , m ≥ 2, defined by an irreducible homogeneous polynomial of degree m. These examples provide particular answers to the questions on algebraic minimal cones in R n posed by Wu-Yi Hsiang in the 1960s.
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| 5. |
- Asekritova, Irina, et al.
(författare)
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Distribution and Rearranement Estimates of the Maximal Functions and Interpolation
- 1997
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Ingår i: Studia Mathematica. - 0039-3223 .- 1730-6337. ; 124:2, s. 107-132
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Tidskriftsartikel (refereegranskat)abstract
- There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition. Analogous methods allow us to obtain K-functional formulas in terms of the maximal function for couples of weighted $L_p$-spaces.
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| 6. |
- Asekritova, Irina, et al.
(författare)
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Interpolation of Multiparameter Approximation Spaces
- 2004
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Ingår i: Journal of Approximation Theory. - : Elsevier. - 0021-9045 .- 1096-0430. ; 129:2, s. 182-206
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Tidskriftsartikel (refereegranskat)abstract
- We prove a general interpolation theorem for linear operators acting simultaneously in several approximation spaces which are defined by multiparametric approximation families. As a consequence, we obtain interpolation results for finite families of Besov spaces of various types including those determined by a given set of mixed differences.
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| 7. |
- Asekritova, Irina, et al.
(författare)
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Lions-Peetre Reiteration Formulas for Triples and Their Application
- 2001
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Ingår i: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 145:3, s. 219-254
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Tidskriftsartikel (refereegranskat)abstract
- We present, discuss and apply two reiteration theorems for triples of quasi-Banach function lattices. Some interpolation results for block-Lorentz spaces and triples of weighted Lp-spaces are proved. By using these results and a wavelet theory approach we calculate (θ,q)-spaces for triples of smooth function spaces (such as Besov spaces, Sobolev spaces, etc.). In contrast to the case of couples, for which even the scale of Besov spaces is not stable under interpolation, for triples we obtain stability in the frame of Besov spaces based on Lorentz spaces. Moreover, by using the results and ideas of this paper, we can extend the Stein–Weiss interpolation theorem known for Lp(μ)-spaces with change of measures to Lorentz spaces with change of measures. In particular, the results obtained show that for some problems in analysis the three-space real interpolation approach is really more useful than the usual real interpolation between couples.
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| 8. |
- Asekritova, Irina, et al.
(författare)
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Lizorkin-Freitag Formula for Several Weighted Lp Spaces and Vector-Valued Interpolation
- 2005
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Ingår i: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 170:3, s. 227-239
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Tidskriftsartikel (refereegranskat)abstract
- A complete description of the real interpolation space L=(Lp0(ω0),…,Lpn(ωn))θ⃗ ,q is given. An interesting feature of the result is that the whole measure space (Ω,μ) can be divided into disjoint pieces Ωi (i∈I) such that L is an lq sum of the restrictions of L to Ωi, and L on each Ωi is a result of interpolation of just two weighted Lp spaces. The proof is based on a generalization of some recent results of the first two authors concerning real interpolation of vector-valued spaces.
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| 9. |
- Asekritova, Irina, et al.
(författare)
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Real Interpolation of Vector-Valued Spaces in Non-Diagonal Case
- 2004
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Ingår i: Proceedings of the American Mathematical Society. - 0002-9939 .- 1088-6826. ; 133:6, s. 1665-1675
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that the formula where and is correct under the restrictions and It is also true if we suppose that and the spaces are functional Banach or quasi-Banach lattices on the same measure space
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| 10. |
- Asekritova, Irina, et al.
(författare)
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The Besikovitch Covering Theorem and Near Minimizers for the Couple (L2,BV)
- 2010
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Ingår i: Proceedings of the Estonian Academy of Sciences. - : Estonian Academy Publishers. - 1406-0086 .- 2228-0685 .- 1736-6046 .- 1736-7530. ; 59:1, s. 29-33
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Tidskriftsartikel (refereegranskat)abstract
- Let Ω be a rectangle in R2. A new algorithm for the construction of a near-minimizer for the couple (L2(Ω), BV(Ω)) is presented. The algorithm is based on the Besicovitch covering theorem and analysis of local approximations of the given function f ∈ L2(Ω).
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