The Equation f(X) = f(Y) in Rational Functions X = X(t), Y = Y(t)

We determine all the complex polynomials f(X) such that, for two suitable distinct, nonconstant rational functions g(t) and h(t), the equality f(g(t)) = f(h(t)) holds. This extends former results of Tverberg, and is a contribution to the more general question of determining the polynomials f(X) over a number field K such that f(X) – has at least two distinct K-rational roots for infinitely many K.     

The limit space Cc(X,Y) and the connected components of X and Y

Let X and Y be limit spaces (in the sense of FISCHER). For f ? C(X, Y), let [f] denote the subset of C(X, Y), where the maps take the connected components of X into those of Y quite analogously to f. The subspace [f] of the continuous convergence space C_c(X, Y) is written as a product II C_c(X_i, Y_k(i)), where X_i runs through the components of X and Y_k(i) always is the component of Y which contains the set f(X_i). Sufficient conditions for the representation C_c(X, Y) = Σ [f] are given (in terms of the spaces X and Y). Some applications on limit homeomorphism groups are included.     

The exponential Lebesgue-Nagell equation X 2 + P 2m = Y n

Let p be an odd prime. In this paper, a complete classification of all positive integer solutions (x, y, m, n) of the equation x ²+p ^2m = y ⁿ , gcd(x, y) = 1, n > 2, is given. As a consequence, we solve the equation for certain interesting cases.     

Gruppen mit RelationenX 3=1, (XY)3=1

Ohne Zusammenfassung     

微分方程X=Q（X,Y）,Y=P（X）的极限环的存在性

ФИЛИППОВ在文（１）中，利用变换Ｌｉｅｎａｒｄ方程ｄｘ／ｄｙ＝ｙ－Ｆ（ｘ），ｄｙ／ｄｔ＝－ｇ（ｘ）在左右两平面上的轨线新方程在右半平面内的积分线的方法，得到了在一定条件下，方程（１）存在极限环的结论，本文应用文（１）的方法，对类型更为广泛的方程ｄｘ／ｄｙ＝Ｑ（ｘ，ｙ），ｄｙ／ｄｔ＝Ｐ（ｘ）进行了探讨，得到了（２）存在稳定极限环的充分条件。     

关于(X(+)Y)1的凸性

本文给出k-严格凸、(局部)k一致圆定义的几个等价形式.利用等价形式,讨论了(X(+)X)1的k-严格凸及(局部)k一致圆性.     

On solutions to min (X,{\text{ Y}})\mathop = \limits^d aX and min (X,{\text{ Y}})\mathop = \limits^d aX\mathop = \limits^d bY

Suppose that the minimum of a pair of independent non-negative random variables X and y has the same distribution, up to a scale factor, as the first of the two random variables. The restricted class of possible distributions for X and Y is identified. If in addition it is required that X and Y have distributions only differing by a scale factor, it is shown under mild regularity conditions that X and Y have Weibull distributions.     

Formes bilinéaires hankéliennes compactes surH 2(X)×H 2(Y)

Sans résumé     

Scalable and Systolic Architecture for Computing Double Exponentiation Over GF(2 m )

Double-exponentiation is a crucial arithmetic operation for many cryptographic protocols. Several efficient double-exponentiation algorithms based on systolic architecture have been proposed. However, systolic architectures require large circuit space, thus increasing the cost of the protocol. This would be a drawback when designing circuits in systems requiring low cost and low power consumption. However, some cost savings can be attained by compromising speed, as in portable devices and many embedded systems. This study proposes a scalable and systolic AB ² and a scalable and systolic A × B, which are the core circuit modules of double-exponentiation. A scalable and systolic double-exponentiation can thus be obtained based on the proposed scalable AB ² and A × B architecture. Embedded system engineers may specify a target double-exponentiation with appropriate scaling systolic circuits. The proposed circuit has lower circuit space/cost and low time/propagation than other circuits.     

Hereditary order convexity inL(X,Y)

LetX be a topological vector space,Y an ordered topological vector space andL(X,Y) the space of all linear and continuous mappings fromX intoY. The hereditary order-convex cover [K] ^h of a subsetK ofL(X,Y) is defined by [K] ^h ={A∈L(X,Y):Ax∈[Kx] for allx∈X}, where[Kx] is the order-convex ofKx. In this paper we study the hereditary order-convex cover of a subset ofL(X,Y). We show how this cover can be constructed in specific cases and investigate its structural and topological properties. Our results extend to the spaceL(X,Y) some of the known properties of the convex hull of subsets ofX ^*.     

Restoration of the norm and order in finite-dimensional spaces X and Y from the space L(X,Y) of operators

Novosibirsk Electrical Engineering Institute of Communications. Translated from Matematicheskie Zametki, Vol. 56, No. 5, pp. 108–116, November, 1994.     

Varieties with P3 = 3 and q = dim(X)

We prove that if X is a complex projective variety with P₃(X) = 3 and q(X) = dim(X), then X is birational to a bidouble cover of A(X). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computation of the homology ofΩ(X∨Y)

Summary We compute the homology of Ω(X∨Y) (the loop space of the wedge of the spaces X and Y), in terms of the homogies of ΩX and ΩY. To do this we use the fact that our problem is equivalent to the computation of the homology of the free product of two topological groups in terms of the homologies of the topological groups. We establish a multiple Kunneth formula with coefficients over a Dedekind domain, which is used to prove a Kunneth like formula involves homologies over a Dedekind domain and generalizes similar results with integral or field coefficients. Over a principal ideal domain the formula for a free product is made more specific. Entrata in Redazione il 31 maggio 1978.