共查询到20条相似文献,搜索用时 15 毫秒
1.
A. Polishchuk 《Journal of Mathematical Sciences》1997,84(5):1413-1444
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Translated from Matematicheskie Zametki, Vol. 46, No. 3, pp. 31–39, September, 1989. 相似文献
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Algebro-geometric sectors of solutions of the KP hierarchy are described in terms of τ-functions and vertex operators. Some useful identities involving theta functions and prime forms on Riemann surfaces are provided which are applied to obtain explicit solutions in the bilinear formalism. By using a dressing method for τ-functions the soliton dynamics against the background of quasiperiodic solutions is characterized. Furthermore, a formula for the soliton shifts in terms of prime forms on Riemann surfaces is obtained. 相似文献
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B. Plotkin 《Journal of Mathematical Sciences》2006,137(5):5049-5097
In every variety of algebras Θ, we can consider its logic and its algebraic geometry. In previous papers, geometry in equational
logic, i.e., equational geometry, has been studied. Here we describe an extension of this theory to first-order logic (FOL).
The algebraic sets in this geometry are determined by arbitrary sets of FOL formulas. The principal motivation of such a generalization
lies in the area of applications to knowledge science. In this paper, the FOL formulas are considered in the context of algebraic
logic. For this purpose, we define special Halmos categories. These categories in algebraic geometry related to FOL play the
same role as the category of free algebras Θ0 play in equational algebraic geometry. This paper consists of three parts. Section 1 is of introductory character. The first
part (Secs. 2–4) contains background on algebraic logic in the given variety of algebras Θ. The second part is devoted to
algebraic geometry related to FOL (Secs. 5–7). In the last part (Secs. 8–9), we consider applications of the previous material
to knowledge science.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 22, Algebra
and Geometry, 2004. 相似文献
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We use techniques from both real and complex algebraic geometry to study K-theoretic and related invariants of the algebra C(X) of continuous complex-valued functions on a compact Hausdorff topological space X. For example, we prove a parameterized version of a theorem by Joseph Gubeladze; we show that if M is a countable, abelian, cancellative, torsion-free, semi-normal monoid, and X is contractible, then every finitely generated projective module over C(X)[M] is free. The particular case gives a parameterized version of the celebrated theorem proved independently by Daniel Quillen and Andrei Suslin that finitely
generated projective modules over a polynomial ring over a field are free. The conjecture of Jonathan Rosenberg which predicts
the homotopy invariance of the negative algebraic K-theory of C(X) follows from the particular case . We also give algebraic conditions for a functor from commutative algebras to abelian groups to be homotopy invariant on
C
*-algebras, and for a homology theory of commutative algebras to vanish on C
*-algebras. These criteria have numerous applications. For example, the vanishing criterion applied to nil K-theory implies that commutative C
*-algebras are K-regular. As another application, we show that the familiar formulas of Hochschild–Kostant–Rosenberg and Loday–Quillen for
the algebraic Hochschild and cyclic homology of the coordinate ring of a smooth algebraic variety remain valid for the algebraic
Hochschild and cyclic homology of C(X). Applications to the conjectures of Beĭlinson-Soulé and Farrell–Jones are also given. 相似文献
9.
I. V. Cherednik 《Journal of Mathematical Sciences》1983,21(4):601-636
Algebraic (in the broad sense of the word) methods of the theory of solitons — the theory of differential equations related to the Korteweg-de Vries equation — are described for the example of two-dimensional, principal, chiral fields. 相似文献
10.
Algebraic geometry of Gaussian Bayesian networks 总被引:1,自引:0,他引:1
Conditional independence models in the Gaussian case are algebraic varieties in the cone of positive definite covariance matrices. We study these varieties in the case of Bayesian networks, with a view towards generalizing the recursive factorization theorem to situations with hidden variables. In the case when the underlying graph is a tree, we show that the vanishing ideal of the model is generated by the conditional independence statements implied by graph. We also show that the ideal of any Bayesian network is homogeneous with respect to a multigrading induced by a collection of upstream random variables. This has a number of important consequences for hidden variable models. Finally, we relate the ideals of Bayesian networks to a number of classical constructions in algebraic geometry including toric degenerations of the Grassmannian, matrix Schubert varieties, and secant varieties. 相似文献
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J. D. Zund 《Annali di Matematica Pura ed Applicata》1969,82(1):381-412
Summary The projective geometry of Lorentzian manifolds and the van der Waerden spinor calculus are shown to be closely related to
the geometry of complex binary quantics. This formalism is then applied to a detailed study of the Bel-Petrov classification
of vacuum Einstein-Lorentzian manifolds and the Lanczos spinor.
Dedicated in respect and admiration to Professor Dr. Donald Joseph Hansen
This research was partially supported by NSF Grant GP-7401.
Entrata in Redazione il 21 novembre 1968. 相似文献
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Nikolai Durov introduced the theory of generalized rings and schemes to study Arakelov geometry in an alternative algebraic framework, and introduced the residue field at the infinite place, 𝔽∞. We show an elementary algebraic approach to modules and algebras over this object, define prime congruences, show that the polynomial ring of n variables is of Krull dimension n, and derive a prime decomposition theorem for these primes. 相似文献
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In this paper we focus on the algebraic geometry of the variety of \(\ell \)-groups (i.e. lattice ordered abelian groups). In particular we study the role of the introduction of constants in functional spaces and \(\ell \)-polynomial spaces, which are themselves \(\ell \)-groups, evaluated over other \(\ell \)-groups. We use different tools and techniques, with an increasing level of abstraction, to describe properties of \(\ell \)-groups, topological spaces (with the Zariski topology) and a formal logic, all linked by the underlying theme of solutions of \(\ell \)-equations. 相似文献
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I. V. Cherednik 《Journal of Mathematical Sciences》1982,18(2):211-254
Algebraic methods, in the broad sense of the word, of the theory of solitons (the theory of nonlinear differential equations related to the Korteweg-de Vries equation) are described for the example of relativistically invariant, two-dimensional, principal chiral fields.Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 18, pp. 73–150, 1981. 相似文献
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The present paper deals with the algebro-geometric aspects of the eigenvector mapping for a free rigid body. The eigenvector mapping is regarded as a rational mapping to the complex projective plane from the product of the elliptic curves, one of which is the integral curve and the other the spectral curve. This is the space of the necessary data to determine the eigenvectors. The eigenvector mapping admits a factorisation through a Kummer surface, which is a double covering of the projective plane branched along a sextic curve associated with the dynamics. The key of the argument is the Cremona transformation of the projective plane and some elliptic fibrations of the Kummer surface. 相似文献
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B. Plotkin 《Vestnik St. Petersburg University: Mathematics》2013,46(1):35-42
The aim of the paper is to define the notion of isotypic algebras and to formulate a series of new problems related to this notion. 相似文献
19.
Let Xbe a projective variety (over Spec(K)) and f:X→G(r,v) a morphism to a Grassmannian, i.e. a pair (E,V) where E is a rank r vector bundle on V?HO(X,E) is a subspace spanning E with dim(V) = v. Here we study the differential properties of f and their relations to a sequence of quotient bundles E→E1→E2→of E called the derived bundles of (E,V). In the first 5 sections we study the case X a smooth curve, char(K) >0 (the case char(K) = 0, being due to D. Perkinson). Then we give a general duality theorem for the derived bundles when Xis any normal variety. 相似文献
20.
Martin E. Walter 《Proceedings of the American Mathematical Society》2003,131(7):2129-2131
Using a ``3 by 3 matrix trick' we show that multiplication (an algebraic structure) in a *-algebra is determined by the geometry of the *-algebra of the 3 by 3 matrices with entries from , . This is an example of an algebra-geometry duality which, we claim, has applications.