共查询到20条相似文献,搜索用时 31 毫秒
1.
A. T. Filippov 《Theoretical and Mathematical Physics》2010,163(3):753-767
We propose new models of the “affine” theory of gravity in multidimensional space-times with symmetric connections. We use
and develop ideas of Weyl, Eddington, and Einstein, in particular, Einstein’s proposed method for obtaining the geometry using
the Hamilton principle. More specifically, the connection coefficients are determined using a “geometric” Lagrangian that
is an arbitrary function of the generalized (nonsymmetric) Ricci curvature tensor (and, possibly, other fundamental tensors)
expressed in terms of the connection coefficients regarded as independent variables. Such a theory supplements the standard
Einstein theory with dark energy (the cosmological constant, in the first approximation), a neutral massive (or tachyonic)
meson, and massive (or tachyonic) scalar fields. These fields couple only to gravity and can generate dark matter and/or inflation.
The new field masses (real or imaginary) have a geometric origin and must appear in any concrete model. The concrete choice
of the Lagrangian determines further details of the theory, for example, the nature of the fields that can describe massive
particles, tachyons, or even “phantoms.” In “natural” geometric theories, dark energy must also arise. The basic parameters
of the theory (cosmological constant, mass, possible dimensionless constants) are theoretically indeterminate, but in the
framework of modern “multiverse” ideas, this is more a virtue than a defect. We consider further extensions of the affine
models and in more detail discuss approximate effective (“physical”) Lagrangians that can be applied to the cosmology of the
early Universe. 相似文献
2.
E. D. Livshits 《Proceedings of the Steklov Institute of Mathematics》2011,272(1):107-118
We discuss new models of an “affine” theory of gravity in multidimensional space-times with symmetric connections. We use and develop ideas of Weyl, Eddington, and Einstein, in particular, Einstein’s proposal to specify the space-time
geometry by the use of the Hamilton principle. More specifically, the connection coefficients are determined using a “geometric”
Lagrangian that is an arbitrary function of the generalized (nonsymmetric) Ricci curvature tensor (and, possibly, of other
fundamental tensors) expressed in terms of the connection coefficients regarded as independent variables. Such a theory supplements
the standard Einstein gravity with dark energy (the cosmological constant, in the first approximation), a neutral massive
(or tachyonic) vector field (vecton), and massive (or tachyonic) scalar fields. These fields couple only to gravity and can generate dark matter and/or inflation.
The new field masses (real or imaginary) have a geometric origin and must appear in any concrete model. The concrete choice
of the geometric Lagrangian determines further details of the theory, for example, the nature of the vector and scalar fields
that can describe massive particles, tachyons, or even “phantoms.” In “natural” geometric theories, which are discussed here,
dark energy must also arise. We mainly focus on intricate relations between geometry and dynamics while only very briefly
considering approximate cosmological models inspired by the geometric approach. 相似文献
3.
We prove a preservation theorem for limit steps of countable support iterations of proper forcing notions whose particular
cases are preservations of the following properties on limit steps: “no random reals are added”, “μ(Random(V))≠1”, “no dominating reals are added”, “Cohen(V) is not comeager”. Consequently, countable support iterations of σ-centered forcing notions do not add random reals.
The work was supported by BRF of Israel Academy of Sciences and by grant GA SAV 365 of Slovak Academy of Sciences. 相似文献
4.
5.
The model of a domain wall (“thick brane”) in a noncompact five-dimensional space-time with asymmetric geometries of AdS type
aside the brane is proposed. This model is generated by fermion self-interaction in the presence of gravity. Asymmetric geometries
in the bulk are provided by a space defect in the scalar field potential and the related defect of cosmological constant.
The possibility of localization of scalar modes on such “thick branes” is studied. Bibliography: 21 titles. 相似文献
6.
S. Shelah 《Israel Journal of Mathematics》1981,38(4):315-334
We prove that the Souslin Hypothesis does not imply “every Aron. (=Aronszajn) tree is special”. For this end we introduce
variants of the notion “special Aron. tree”. We also introduce a limit of forcings bigger than the inverse limit, and prove
it preserves properness and related notions not less than inverse limit, and the proof is easier in some respects.
The result was announced in [9].
The author thanks Uri Avraham for detecting many errors. 相似文献
7.
In the example of dust matter, it is shown that a gravitational attractive force does not lead to the formation of “black
holes” in the relativistic theory of gravity. It is proved that in the absence of matter, the gravitational field is also
absent. Therefore, a vacuum is not a source of a gravitational field. The mechanism of energy production in the process of
the accumulation of matter into massive objects is discussed. 相似文献
8.
In the relativistic theory of gravity, we analyze the solution for a static spherically symmetrical body in detail. Comparing
this solution with the Schwarzschild solution in general relativity, we find that they are essentially different in the domain
near the Schwarzschild sphere. This difference eliminates the possibility of a collapse leading to the formation of “black
holes.”
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 1, pp. 4–24, October, 1999. 相似文献
9.
F. B. Pakovich 《Journal of Mathematical Sciences》2009,158(1):148-154
In this paper, in the context of the “dessins d’enfants” theory, we give a combinatorial criterion for a plane tree to cover
a tree from the classes of “chains” or “stars.” We also discuss some applications of this result that are related to the arithmetical
theory of torsion on curves.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 6, pp. 207–215, 2007. 相似文献
10.
Maciej Paluszyński Hrvoje Šikić Guido Weiss Shaoliang Xiao 《Journal of Geometric Analysis》2001,11(2):311-342
A tight frame wavelet ψ is an L
2(ℝ) function such that {ψ jk(x)} = {2j/2
ψ(2
j
x −k), j, k ∈ ℤ},is a tight frame for L
2 (ℝ).We introduce a class of “generalized low pass filters” that allows us to define (and construct) the subclass of MRA tight
frame wavelets. This leads us to an associated class of “generalized scaling functions” that are not necessarily obtained
from a multiresolution analysis. We study several properties of these classes of “generalized” wavelets, scaling functions
and filters (such as their multipliers and their connectivity). We also compare our approach with those recently obtained
by other authors. 相似文献
11.
Flemming Tops?e 《Journal of Global Optimization》2009,43(4):553-564
Inspired by previous work on information theoretical optimization problems, the basics of an axiomatic theory of certain special
two-person zero-sum games is developed. One of the players, “Observer”, is imagined to have a “mind”, the other, “Nature”,
not. These ideas lead to un-symmetric modeling as the two players are treated quite differently. Basic concavity- and convexity
results as well as a general minimax theorem are derived from the axioms. 相似文献
12.
Alessio Moretti 《Logica Universalis》2009,3(1):19-57
Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic
(both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”,
“permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s
“logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic
oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a “deontic hexagon” as being the geometrical
representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie
73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter,
Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic
internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic
has appeared, that is “n-opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m” (m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper,
by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s
unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”,
“deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities
is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra),
whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional
very regular solid).
相似文献
13.
K. S. Banerjee 《Annals of the Institute of Statistical Mathematics》1974,26(1):447-454
Summary Dey [3] has suggested a spring balance weighing design in preference to “repeated designs”, and later, Kulshreshtha and Dey
[5] have suggested yet one more weighing design which, they say, would be preferred to “repeated designs” and to those suggested
in [3], provided one is interested in estimating the weights of some of the objects with increased precision at the cost of
precision for others. It has been shown here that, while the above findings may be true in some situations, one might, in
a given problem, prefer “repeated designs” to those suggested in [3] and [5].
NSF Grant No. GP-28312 and GP-36562. 相似文献
14.
Emmanuel Schenck 《Annales Henri Poincare》2009,10(4):711-747
We study a toy model for “partially open” wave-mechanical system, like for instance a dielectric micro-cavity, in the semiclassical
limit where ray dynamics is applicable. Our model is a quantized map on the 2-dimensional torus, with an additional damping
at each time step, resulting in a subunitary propagator, or “damped quantum map”. We obtain analogues of Weyl’s laws for such
maps in the semiclassical limit, and draw some more precise estimates when the classical dynamics is chaotic.
Submitted: October 16, 2008. Accepted: April 3, 2009. 相似文献
15.
We prove a generalization of the Krasnosel’ski theorem on star-shaped sets. Usingd-segments inn-dimensional Minkowski spaces instead of usual segments, the notions “d-visibility” and “d-star-shapedness” are introduced. Our main aim is to give necessary and sufficient conditions ford-star-shapedness in finite-dimensional normed spaces. 相似文献
16.
Rade T. Živaljević 《Discrete and Computational Geometry》2009,41(1):135-161
This paper lays the foundation for a theory of combinatorial groupoids that allows us to use concepts like “holonomy”, “parallel transport”, “bundles”, “combinatorial curvature”, etc. in the context
of simplicial (polyhedral) complexes, posets, graphs, polytopes and other combinatorial objects. We introduce a new, holonomy-type
invariant for cubical complexes, leading to a combinatorial “Theorema Egregium” for cubical complexes that are non-embeddable
into cubical lattices. Parallel transport of Hom-complexes and maps is used as a tool to extend Babson–Kozlov–Lovász graph coloring results to more general statements about
nondegenerate maps (colorings) of simplicial complexes and graphs.
The author was supported by grants 144014 and 144026 of the Serbian Ministry of Science and Technology. 相似文献
17.
We describe a tower of spaces whose inverse limit is a “fiberwise completion” of a fibrationE →B, and study the resulting spectral sequence converging to the homotopy groups of the space of lifts of a mapX →B. This is used to give a proof of the “generalized Sullivan conjecture”.
All three authors were supported in part by the National Science Foundation. 相似文献
18.
Ivan Chajda 《Central European Journal of Mathematics》2011,9(5):1185-1191
We introduce two unary operators G and H on a relatively pseudocomplemented lattice which form an algebraic axiomatization of the tense quantifiers “it is always
going to be the case that” and “it has always been the case that”. Their axiomatization is an extended version for the classical
logic and it is in accordance with these operators on many-valued Łukasiewicz logic. Finally, we get a general construction
of these tense operators on complete relatively pseudocomplemented lattice which is a power lattice via the so-called frame. 相似文献
19.
Masaaki Sibuya 《Annals of the Institute of Statistical Mathematics》1979,31(1):373-390
Summary In this paper we introduce and study new probability distributions named “digamma” and “trigamma” defined on the set of all
positive integers. They are obtained as limits of the zero-truncated Type B3 generalized hypergeometric distributions (inverse
Pólya-Eggenberger or negative binomial beta distributions), and also by compounding the logarithmic series distributions.
The family of digamma distributions has the logarithmic series as a limit and the trigamma as another limit. The trigamma
distributions are very close to the zeta (Zipf) distributions. Thus, our new distributions are useful as substitutes of the
logarithmic series when the observed frequency data have such a long tail that cannot be fitted by the latter distributions.
In the beginning sections we summarize properties of the Type B3 generalized hypergeometric distributions. It is emphasized
that the distributions are obtained by compounding a Poisson distribution by “gamma product-ratio” distributions. 相似文献
20.
Martin Šmíd 《Annals of Operations Research》2009,165(1):29-45
In the present paper, the approximate computation of a multistage stochastic programming problem (MSSPP) is studied. First,
the MSSPP and its discretization are defined. Second, the expected loss caused by the usage of the “approximate” solution
instead of the “exact” one is studied. Third, new results concerning approximate computation of expectations are presented.
Finally, the main results of the paper—an upper bound of the expected loss and an estimate of the convergence rate of the
expected loss—are stated. 相似文献