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1.
B. M. Zupnik 《Theoretical and Mathematical Physics》2008,157(2):1550-1564
We consider the superspace of D=3, N=5 supersymmetry using SO(5)/U(2) harmonic coordinates. Three analytic N=5 gauge superfields depend on three vector and six harmonic bosonic coordinates and also on six Grassmann coordinates. Decomposing
these superfields in Grassmann and harmonic coordinates yields infinite-dimensional supermultiplets including a three-dimensional
gauge Chern-Simons field and auxiliary bosonic and fermionic fields carrying SO(5) vector indices. The superfield action of this theory is invariant with respect to the D=3, N=6 conformal supersymmetry realized on N=5 superfields.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 2, pp. 217–234, November, 2008. 相似文献
2.
B. M. Zupnik 《Theoretical and Mathematical Physics》1998,116(2):964-977
A modification of the harmonic superfield formalism in D=4, N=2 supergravity is considered using an additional condition of
covariance under the background supersymmetry with a central charge (B-covariance).
Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 116, No. 2, pp. 288–304, August. 1998. 相似文献
3.
We consider the theory of hypermultiplets in arbitrary representations of arbitrary semisimple gauge groups coupled to gauge
superfields. Using the N=2 harmonic superspace formulation of these models, we find the general structure of the holomorphic
effective action depending on the gauge superfield with values in the Cartan subalgebra of the gauge algebra. We find explicit
expressions for the effective actions in the cases where the hypermultiplets are in the fundamental and adjoint representations
of SU(n), SO(n), and Sp(2n).
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 122, No. 3, pp. 444–455, April, 2000. 相似文献
4.
5.
Given a graph G, a (k;a,b,c)-star in G is a subgraph isomorphic to a star K1,3 with a central vertex of degree k and three leaves of degrees a, b and c in G. The main result of the paper is:
Every planar graph G of minimum degree at least 3 contains a (k;a,b,c)-star with a≤ b≤ c and (i) k = 3, a≤ 10, or (ii) k = 4, a = 4, 4≤ b≤ 10, or (iii) k = 4, a = 5, 5≤ b≤ 9, or (iv) k = 4, 6≤ a≤ 7, 6≤ b≤ 8, or (v) k = 5, 4≤ a≤ 5, 5≤ b≤ 6 and 5≤ c≤ 7, or (vi) k = 5 and a = b = c = 6. 相似文献
6.
We consider the =2 supersymmetric massive Yang-Mills field theory formulated in the =2 harmonic superspace. We present various gauge-invariant forms of writing the mass term in the action (in particular, using
the Stueckelberg superfield), which result in dual formulations of the theory. We develop a gaugeinvariant and explicitly
supersymmetric scheme of the loop expansion of the superfield effective action beyond the mass shell. In the framework of
this scheme, we calculate gauge-invariant and explicitly =2 supersymmetric one-loop counterterms including new counterterms depending on the Stueckelberg superfield. We analyze the
component structure of one of these counterterms.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 22–40, October, 2008. 相似文献
7.
We show that the N=3 harmonic superfield equations of motion are invariant with respect to the fourth supersymmetry. We also use the SU(3) harmonics to analyze a more flexible form of superfield constraints for the Abelian N=4 vector multiplet and its N=3 decomposition. An unusual alternative representation of the N=4 supersymmetry is realized on infinite multiplets of analytic superfields in the N=3 harmonic superspace. An integer-valued parameter playing the role of a discrete coordinate parameterizes U(1) charges of superfields in these multiplets. Each superfield term of the N=3 Yang–Mills action has an infinite-dimensional N=4 generalization. The gauge group of this model contains an infinite number of superfield parameters. 相似文献
8.
It is well known that the number of isolated singular points of a hypersurface of degree d in ℂPm does not exceed the Arnol’d number Am(d), which is defined in combinatorial terms. In the paper it is proved that if b
m−1
±
(d) are the inertia indices of the intersection form of a nonsingular hypersurface of degree d in ℂPm, then the inequality Am(d)<min{b
m−1
+
(d), b
m−1
−
(d)} holds if and only if (m−5)(d−2)≥18 and (m,d)≠(7,12). The table of the Arnol’d numbers for 3≤m≤14, 3≤d≤17 and for 3≤m≤14,
d=18, 19 is given. Bibliography: 6 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 180–190.
Translated by O. A. Ivanov and N. Yu. Netsvetev. 相似文献
9.
The classical equations of motion of the D=4, N=2 supersymmetric Yang–Mills (SYM) theory for Minkowski and Euclidean spaces are analyzed in harmonic superspace. We study dual superfield representations of equations and subsidiary conditions corresponding to classical SYM solutions with different symmetries. In particular, alternative superfield constructions of self-dual and static solutions are described in the framework of the harmonic approach. 相似文献
10.
A. Yu. Solynin 《Journal of Mathematical Sciences》1998,89(1):1031-1049
We study certain extremal problems concerning the capacity of a condenser and the harmonic measure of a compact set. In particular,
we answer in the negative Tamrazov's question on the minimum of the capacity of a condenser. We find the solution to Dubinin's
problem on the maximum of the harmonic measure of a boundary set in the family of domains containing no “long” segments of
given inclination. It is also shown that the segment [1-L, 1] has the maximal harmonic measure at the point z=0 among all
curves γ={z=z(t), 0≤t≤1}, z(0)=1, that lie in the unit disk and have given length L, 0<L<1. The proofs are based on Baernstein's
method of *-functions, Dubinin's dissymmetrization method, and the method of extremal metrics. Bibliography: 21 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 170–195. 相似文献
11.
Let {Xk} be a sequence of i.i.d. random variables with d.f. F(x). In the first part of the paper the weak convergence of the d.f.'s
Fn(x) of sums
is studied, where 0<α≤2, ank>0, 1≤k≤mn, and, as n→∞, bothmax
1≤k≤mna
nk→0 and
. It is shown that such convergence, with suitably chosen An's and necessarily stable limit laws, holds for all such arrays {αnk} provided it holds for the special case αnk=1/n, 1≤k≤n. Necessary and sufficient conditions for such convergence are classical. Conditions are given for the convergence
of the moments of the sequence {Fn(x)}, as well as for its convergence in mean. The second part of the paper deals with the almost sure convergence of sums
, where an≠0, bn>0, andmax
1≤k≤n ak/bn→0. The strong law is said to hold if there are constants An for which Sn→0 almost surely. Let N(0)=0 and N(x) equal the number of n≥1 for which bn/|an|<x if x>0. The main result is as follows. If the strong law holds,EN (|X1|)<∞. If
for some 0<p≤2, then the strong law holds with
if 1≤p≤2 and An=0 if 0<p<1. This extends the results of Heyde and of Jamison, Orey, and Pruitt. The strong law is shown to hold under various
conditions imposed on F(x), the coefficients an and bn, and the function N(x).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, 1993. 相似文献
12.
The general theme of this note is illustrated by the following theorem:Theorem 1.
Suppose K is a compact set in the complex plane and 0belongs to the boundary ∂K. Let A(K) denote the space of all functions f on K such that f is holo morphic in a neighborhood
of K and f(0) = 0.Also for any givenpositive integer m, let A(m, K) denote the space of all f such that f is holomorphic in a neighborhood of
K and f(0) =f′(0) = ... =f
(m)(0) = 0.Then A(m, K) is dense in A(K) under the supre mum norm on K provided that there exists a sector W = re
iθ; 0≤r≤ δ,α≤ θ≤ β
such that W ∩ K = 0. (This is the well- known Poincare’s external cone condition). We present various generalizations of this result in the context of higher dimensions replacing holomorphic with harmonic.
Dedicated to Prof. Ashoke Roy on his 62nd birthday 相似文献
13.
We describe four different types of N=(4, 4) twisted supermultiplets in the two-dimensional N=(2, 2) superspace ℝ(1,1|2,2). All these multiplets are represented by a pair of chiral and twisted chiral superfields and differ in the transformation
properties under an extra hidden N=(2, 2) supersymmetry. The sigma-model N=(2, 2) superfield Lagrangians for each type of
the N=(4, 4) twisted supermultiplet are real functions subjected to some differential constraints implied by the hidden supersymmetry.
We prove that the general sigma-model action including all types of N=(4, 4) twisted multiplets and invariant under the N=(4,
4) supersymmetry reduces to a sum of sigma-model actions for separate types. An interaction between the multiplets of different
sorts is possible only through the appropriate mass terms and only for those multiplets that belong to the same “self-dual”
pair.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 1, pp. 66–86, October, 2005. 相似文献
14.
B. M. Zupnik 《Theoretical and Mathematical Physics》2006,147(2):670-686
We consider quantum supergroups that arise in nonanticommutative deformations of the N=(1/2, 1/2) and N=(1, 1) four-dimensional
Euclidean supersymmetric theories. Twist operators in the corresponding superspaces and deformed superfield algebras contain
left spinor generators. We show that nonanticommutative *-products of superfields transform covariantly under the deformed
supersymmetries. This covariance guarantees the invariance of the deformed superfield actions of models involving *-products
of superfields.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 270–289, May, 2006. 相似文献
15.
Let ρ be a triangulation of a polygonal domain D⊂R2 with vertices V={vi:l≤i≤Nv} and RSk(D, ρ)={u∈Ck(D): ≠ T∈ρ, u/T is a rational function}. The purpose of this paper is to study the existence and construction of Cμ-rational spline functions on any triangulation ρ for CAGD. The Hermite problem Hμ(V,U)={find u∈U: Dαu(vi)=Dαf(vi),|α|≤μ} is solved by the generalized wedge function method in rational spline function family, i.e. U=RSμ. this solution needs only the knowledge of partial derivatives of order≤μ at vi. The explicit repesentations of all Cμ-GWF(generalized wedge functions)and the interpolating operator with degree of precision at least 2μ+1 for any triangulation
are given. 相似文献
16.
Bruno Bosbach 《Semigroup Forum》1980,20(1):299-317
O. CallS:=(S,·,∩) a d-semigroup ifS satisfies the axioms (A1) (S,·) is a semigroup, (A2) (S,∩) is a semilattice (A3), (S,·,∩) is a semiring, (A4) a ≤b⇒bε aS
∩ Sa. Call tεS positive if ÅaεS: ta ≥a≤at. Let S+ denote the set {t‖t positive}. Every d-semigroup is closed under sup and (s,·,∪) is a semiring, (S, ∩, ∪) is a distributive
lattice. Denote by D□X the implication s=Xai⇒x□s□y=X(x□ai□y) where □ε{·,∩,∪} and Xε{∪,∩}. CallS continuous ifS satisfies all D□X. The theory of d-semigroups (divisibility-semigroups) was established in [3], [4], [5], and is continued
here by some contributions to the theory of continuous d-semigroups the main results of which are the two propositions: (1)
LetS be a d-semigroup with 1. ThenS satisfies D□X iffS
+ satisfies this axiom. (2) LetS be continuous. Then (S,·) is commutative. Obviously Proposition (2) is an improvement of Iwasawa's theorem concerning conditionally
complete lattice ordered groups.
Klaus Wagner zum 70. Geburtstag gewidmet 相似文献
Zur Theorie der Stetigen Teilbarkeitshalbgruppen
Klaus Wagner zum 70. Geburtstag gewidmet 相似文献
17.
L. Yu. Kolotilina 《Journal of Mathematical Sciences》2006,137(3):4801-4814
The paper presents new upper and lower bounds for the Perron root of a nonnegative matrix in terms of the simple circuits
of length not exceeding k and the simple paths of length k, 1 ≤ k ≤ n, in the directed graph of the matrix. For each k, 1
≤ k ≤ n, these bounds are intermediate between the circuit bounds and the path-dependent bounds suggested previously, and
for k = 1 and k = n they reduce to the corresponding path-dependent bounds and the circuit bounds, respectively. Bibliography:
5 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 69–93. 相似文献
18.
W.M. Priestly 《Semigroup Forum》1998,56(3):301-322
t , for t ≥ 0, be a strongly continuous Markovian semigroup acting on C(X), where X is a compact Hausdorf space, and let D
denote the domain of its infinitesimal generator Z. Suppose D contains a (perhaps finite) family of functions f separating
the points of X and satisfying Zf2 = 2fZf. If either
(1) there exists δ > 0 such that (Tt f)2∈ D if 0 ≤ t ≤δ for each f in this family; or
(1′) for some core D′ of Z, g ∈ D′ implies g2∈ D, then the underlying Markoff process on X is deterministic. That is, there exists a semiflow — a semigroup (under composition)
of continuous functions φt from X into X — such that Ttf(x) = f(φt (x)). If the domain D should be an algebra then conditions (1) and (1′) hold trivially. Conversely, if we have a separating
family satisfying Zf2 = 2fZf then each of these conditions implies that D is an algebra. It is an open question as to whether these conditions
are redundant. If the functions φt are homeomorphisms from X onto X, then of course we have a Markovian group induced by a flow. This result is obtained by
first providing general results about the null-space N of the (function-valued) positive semidefinite quadratic form defined
by < f, g > = Z(fg) - fZg - gZf. The set N can be defined for any generator Z of a strongly continuous Markovian semigroup
and is equivalently given by
N = {f ∈ D| f2∈ D and Zf2 = 2fZf}
= {f ∈ D| Tt(f2)-(Ttf)2 is o(t2) in C(X)}.
In the general case N is an algebra closed under composition with any C1-function φ from the reals to the reals, and Z(φ[f]) = (Zf)φ′[f] if f ∈ N. This "chain rule" on N (on which Z must act as
a derivation) is a special case of a theorem for C2-functions φ which holds more generally for all f in d, viz.,
Z(φ[f] = (Zf) φ′[f] + ? <f, f> φ″[f],
Provided Z is a local operator and D is an algebra. In this case the form < f, g > itself enjoys the relation
< φ[f], ψ[g] > = φ′ [f] ψ′[g] < f, g >,
for C2functions φ and ψ. Some of the results and their proofs continue to hold when the setting is switched from the commutative
C*-algebra C(X) to a general (noncommutative) C*-algebra A. In the norm continuous case we obtain a sharp characterization
of Markovian semigroups that are groups: Let Tt = etz , defined for t ≥ 0, be a Markovian semigroup acting on a C*-algebra A that is norm continuous, i.e., ||Tt - I|| ⇒ 0 as t ⇒ 0 +. Assume Z(a2) = a(Za) + (Za) a for some (perhaps finite) set of self-adjoint elements a that generate a Jordan algebra dense among the
self-adjoint elements of A. The etz , -∞ < t < ∞, is a group of Markovian operators. 相似文献
19.
§1IntroductionInthispaper,weconsiderthelargetimebehaviorofaproblem,ut=Δu+up,x∈RN+,t>0,-ux1=uq,x1=0,t>0,u(x,0)=u0(x),x∈RN+,(... 相似文献
20.
Bui Xuan Hai 《Journal of Mathematical Sciences》1997,83(5):617-625
For any (noncommutative) skew field T, the lattice of subgroups of the special linear group Λ=SL(n,T) that contain the subgroup
Δ=SD(n,T) of diagonal matrices (with Dieudonné determinants equal to 1) is studied. It is established that for any subgroup
H, Δ≤H≤Λ, there exists a uniquely determined unital net σ such that Λ(σ)≤H≤N(σ), where Λ(σ) is the net subgroup associated
with the net σ and N(σ) is its normalizer in Λ. Bibliography: 11 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 91–103.
Translated by Bui Xuan Hai. 相似文献