Showing papers in "Israel Journal of Mathematics in 1967"
TL;DR: In this paper, it is shown that if ZFM is consistent then it is consistent with every sentence φ whose consistency is proved by Cohen's forcing method with a set of conditions of cardinality < k.
Abstract: Let ZFM be the set theory ZF together with an axiom which asserts the existence of a measurable cardinal. It is shown that if ZFM is consistent then ZFM is consistent with every sentence φ whose consistency is proved by Cohen’s forcing method with a set of conditions of cardinality
258 citations
TL;DR: In this article, it is proved that an infinite dimensional subspace of m is complemented in m if and only if it is isomorphic to tom, i.e., it is a isomorphic subspace.
Abstract: It is proved that an infinite dimensional subspace ofm is complemented inm if and only if it is isomorphic tom.
82 citations
TL;DR: Asymptotic formulas with remainder estimates for spectral functions of general elliptic operators are derived in this paper, based on asymptotics of resolvent kernels in the complex plane.
Abstract: Asymptotic formulas with remainder estimates are derived for spectral functions of general elliptic operators. The estimates are based on asymptotic expansion of resolvent kernels in the complex plane.
68 citations
TL;DR: In this paper, an examination of relationship between two neighborhood systems (relative to two linear topologies) of extreme points yields a unified approach to some known and new results, among which are Bessaga-Pelczynski's theorem on closed bounded convex subsets of separable conjugate Banach spaces.
Abstract: An examination of relationship between two neighborhood systems (relative to two linear topologies) of extreme points yields a unified approach to some known and new results, among which are Bessaga-Pelczynski’s theorem on closed bounded convex subsets of separable conjugate Banach spaces and Ryll-Nardzewski’s fixed point theorem.
47 citations
TL;DR: In this article, it was shown that for each complete theory T, the nomberh of homogeneous models of T of powerm is a non-increasing function of uncountabel cardinals.
Abstract: It is shown that, For each complete theoryT, the nomberh
T(m) of homogeneous models ofT of powerm is a non-increasing function of uncountabel cardinalsm Moreover, ifh
T(ℵ0)≦ℵ0, then the functionh
T is also non-increasing ℵ0 to ℵ1.
35 citations
TL;DR: In this paper, a functional method using differentiable mappings is used to construct exceptional sets (such as Helson sets and sets of multiplicity) by means of a functional algorithm using a differentiable mapping.
Abstract: Various exceptional sets (such as Helson sets and sets of multiplicity) are constructed by means of a functional method using differentiable mappings.
32 citations
TL;DR: In this article, it was shown that if a certain set in ℝ n has the property that in some unsymmetric norm each point in this set has a unique farthest point in the set, then it consists of exactly one point.
Abstract: If a certain set in ℝ n has the property, that in some unsymmetric norm each point in ℝ n has a unique farthest point in this set, then it consists of exactly one point
28 citations
TL;DR: In this paper, it was shown that a ℵ1-categorical theory has only a countable number of nonisomorphic countable models, and that such a theory has no non-isomorphic models at all.
Abstract: Countable models of ℵ1-categorical theories are classified. It is shown that such a theory has only a countable number of nonisomorphic countable models.
24 citations
TL;DR: In this article, some inequalities concerning the Ito stochastic integral and solutions of different equations are obtained. But these inequalities are not applicable to the case of stochastically different equations.
Abstract: Some inequalities concerning the Ito stochastic integral and solutions of stochastic different equations are obtained.
23 citations
TL;DR: In this article, the fixed points of a continuous function or a homeomorphism of Bn are investigated, and the set of sets which can be found in the fixed point of such a function is investigated.
Abstract: The sets which can be the fixed points of a continuous function or a homeomorphism ofB
n are investigated.
16 citations
TL;DR: In this article, the extreme points of the closed unit ball of a simplex and a Banach space were characterized, where the latter is a special case of the simplex with the supremum norm.
Abstract: IfK a simplex andX a Banach space thenA(K, X) denotes the space of affine continuous functions fromK toX with the supremum norm. The extreme points of the closed unit ball ofA(K, X) are characterized,X being supposed to satisfy certain conditions. This characterization is used to investigate the extreme compact operators from a Banach spaceX to the spaceA(K)=A(K, (− ∞, ∞)).
TL;DR: Mahlo used a method by which fixed points of an enumeration of regular cardinals were employed to get a hierarchy of "large cardinals" He also employed a second method which, in a certain sense, is much stronger than the first.
Abstract: Mahlo used a method by which fixed points of an enumeration of regular cardinals were employed to get a hierarchy of “large cardinals” He also employed a second method which, in a certain sense, is much stronger than the first Here the methods are investigated and generalized and the relations between them are clarified This stronger method turns out to be a kind of “least upper bound” to all “fixed-points operations” Possibilities of strengthening these processes in a natural way are pointed out
TL;DR: In this article, nonlinear least squares problems over convex sets in R n are treated by iterative methods which extend the classical Newton, gradient and steepest descent methods and the methods studied recently by Pereyra and the author.
Abstract: Nonlinear least squares problems over convex sets inR
n are treated here by iterative methods which extend the classical Newton, gradient and steepest descent methods and the methods studied recently by Pereyra and the author. Applications are given to nonlinear least squares problems under linear constraint, and to linear and nonlinear inequalities.
TL;DR: In this paper, the necessary and sufficient conditions on a sequence {μn} (n≧0) in order that it should possess the representation (1.2) wherea(t) is of bounded variation or the representation(1.3) wheref( t) ∈ L ∈ M[0, 1] orf(t), is essentially bounded.
Abstract: Let {λ
n} (n≧0) satisfy (1.1) we are considering the following problems: What are the necessary and sufficient conditions on a sequence {μn} (n≧0) in order that it should possess the representation (1.2) wherea(t) is of bounded variation or the representation (1.3) wheref(t) ∈L
M[0, 1] orf(t) is essentially bounded.
TL;DR: In this article, the problem of arranging a set in a circular symmetrical order has been studied and shown to be NP-hard under some additional assumptions under the assumption that the set (y) is arranged in a symmetric order.
Abstract: LetF(u, v) be a symmetric real function defined forα
TL;DR: Etude d algebres homogenes sur le cercle ayant les memes propriete, de calcul symbolique and de synthese speciale que l’algebre de Wiener as mentioned in this paper.
Abstract: Etude d’algebres homogenes sur le cercle ayant les memes propriete, de calcul symbolique et de synthese speciale que l’algebre de Wiener.
TL;DR: In this paper, a distortion theorem for holomorphic mappings of bounded domains of a Kahler manifold was proved, which depends essentially on the two Hermitian quadratic forms corresponding to the metric and to the Ricci tensor.
Abstract: Upper bounds for the Jacobian determinant by holomorphic mappings of bounded domainsD into itself were given first more then thirty years ago by Stefan Bergman by means of his theory of the kernel function ofD. In this paper a different method shall be developed and distortion theorems for holomorphic mappings of bounded domains of a Kahler manifoldM
n
into a Kahler manifoldM
0
shall be proved. The special casesM
n
=C
n
(unit sphere of C
n
) andM
n
=M
0
=|C
n
shall also be considered. The proof depends essentially on the two Hermitian quadratic forms corresponding to the metric and to the Ricci tensor. The manifolds must be of negative Ricci curvature and fulfil two conditions given in section 4.
TL;DR: In this article, the smallest positive integer p such that every connected (ordinary) graph of order p contains eitherr mutually adjacent lines ors mutually disjoint lines was defined. And it was shown that f′(r, s) =(r−1) (s−1)+2 unless r=2 and s ≠ 1, in which casef′(2,s)=3.
Abstract: For positive integersr ands, f′(r, s) is defined as the smallest positive integerp such that every connected (ordinary) graph of orderp contains eitherr mutually adjacent lines ors mutually disjoint lines. It is found thatf’(r,s) =(r−1) (s−1)+2 unlessr=2 and s ≠ 1, in which casef′(2,s)=3.
TL;DR: In this article, it was shown that all subfair casino functions are superadditive on the unit interval and that subfair games are sub-fair games with super-additive unit interval.
Abstract: It is shown that all subfair casino functions are superadditive on the unit interval.
TL;DR: In this article, the authors show that a finite group G is isomorphic to PSL (2,p,p>3) if G is non-solvable, contains more than one class of conjugate elements of orderp, and satisfies an additional condition.
Abstract: LetG be a finite group, containing a self-centralizing subgroup of prime orderp. IfG is non-solvable, contains more than one class of conjugate elements of orderp, and satisfies an additional condition, thenG is isomorphic toPSL (2,p),p>3.
TL;DR: In this paper, a treatment preserving the main features of the controversial treatment in the author's doctoral dissertation is newly derived from a model for negotiation and play that is more elaborate than most such models.
Abstract: For the special case of games with linearly transferable utility, a treatment preserving the main features of the controversial treatment in the author’s doctoral dissertation is newly derived from a model for negotiation and play that is more elaborate than most such models. The crucial point of the derivation is that the author’s special bargaining theory is not needed; the usual Zeuthen-Nash-Harsanyi bargaining theory gives the same result. The main novelty in the model that makes this possible is the replacement of customary informal uses of ‘enforceable agreements’ by explicit contract law. The problems of contract law for cooperative games seem to be very complex, and the present work makes only a bare beginning on them. A characteristic function and value are derived.
TL;DR: In this article, the authors define functions which permit the solution of a special hyperbolic system to be expressed as a quadrature of its initial data over the initial surface.
Abstract: Functions are defined which permit the solution of a special hyperbolic system to be expressed as a quadrature of its initial data over the initial surface.
TL;DR: In this article, the authors define functions which permit the solution of a special hyperbolic system to be expressed as a quadratur of its initial data over the initial surface.
Abstract: Functions are defined which permit the solution of a special hyperbolic system to be expressed as a quadratur of its initial data over the initial surface.
TL;DR: In this paper, a linear topological space is said to have the circle property if every power series with coefficients in it has a circle of convergence, and every complete locally convex or locally bounded space has this property, but not a certain class of F-spaces including the space of all random variables on a non-atomic probability space.
Abstract: A linear topological space is said to have the circle property if every power series with coefficients in it has a circle of convergence Every complete locally convex or locally bounded space has the circle property, but not a certain class ofF-spaces including the space of all random variables on a non-atomic probability space, endowed with the topology of convergence in probability
TL;DR: Considering a vortex line as a C 3 curve in E 3, the equations governing the flow of a steady, compressible gas are expressed in the intrinsic form as discussed by the authors, and these intrinsic relations are applied to derive some geometric properties of rotational motions.
Abstract: Considering a vortex line as aC 3 curve inE 3, equations governing the flow of a steady, compressible gas are expressed in the intrinsic form. These intrinsic relations are applied to derive some geometric properties of rotational motions, and to study a class of flows whose vortex lines form a family of helices on right circular cylinders.
TL;DR: In this paper, a sufficient condition for analytic iterations to be conformal and univalent inz ∈ D, whereD is a given domain and for sufficiently small |a | is established.
Abstract: In this paper we study some mapping properties of analytic iterationsW(a, z). Our purpose is to establish a sufficient condition forW(a, z) to be conformal and univalent inz forz ∈D, whereD is a given domain and for sufficiently small |a |. To this end we consider the differential equationϱW(a, z)/ϱa=L[W(a, z)] with the conditionW(O, z)=z. A sufficient condition for the solutionW(a, z) of this system to be conformal and univalent inD for |a | 0), and to satisfy the iteration equation, is established.
TL;DR: In this article, it is shown that if M is a compact metric space, and A ⊂ M an arc, while M/A is an arc having A/A as an end-point, then M is an arcs, a triod, some sin (1/x)-curve, or some sin curve with an arc attached at one point.
Abstract: By a sin (1/x)-curve is meant a metric continuum that is a 1-1 continuous image of the disjoint union of an arc and a semi-open interval that has the image of the arc as continuum of convergence. It is shown that ifM is a compact metric space,A ⊂M an arc, whileM/A is an arc havingA/A as an end-point, thenM is an arc, a triod, some sin (1/x)-curve, or some sin (1/x)-curve with an arc attached at one point, or some sin (1/x)-curve with two arcs attached. The case of shrinking finitely many arcs is also considered in an attaching theorem.