On the triplex substitution – combinatorial properties

If a substitution τ over a three-letter alphabet has a positively linear complexity, that is, $P_{\tau }(n)=C_{1}n+C_2$ ($n⩾1$) with $C_1,C_2⩾0$, there are only 4 possibilities: $P_{\tau }(n)=3$, $n+2$, $2n+1$ or 3n. The first three cases have been studied by many authors, but the case 3n remained unclear. This leads us to consider the triplex substitution $\sigma :a\mapsto ab$, $b\mapsto acb$, $c\mapsto acc$. Studying the factor structure of its fixed point, which is quite different from the other cases, we show that it is of complexity 3n. We remark that the triplex substitution is also a typical example of invertible substitution over a three-letter alphabet. To cite this article: B. Tan et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

NOTE – On Minimizing Symmetric Set Functions

u, v ) of nodes such that the star of v is a minimum cut separating u and v. Nagamochi and Ibaraki showed that the last two nodes of a ``max-back order' form such a pair and used this fact to develop an elegant min-cut algorithm. M. Queyranne extended this approach to minimize symmetric submodular functions. With the help of a short and simple proof, here we show that the same algorithm works for an even more general class of set functions. Received December 16, 1998     

Subdifferentials of Distance Functions, Approximations and Enlargements

In this work, we study some subdifferentials of the distance function to a nonempty nonconvex closed subset of a general Banach space. We relate them to the normal cone of the enlargements of the set which can be considered as regularizations of the set.     

On Deficient Values of Meromorphic Functions

I. Let f(z) be a meromorphic function of order p (O<ρ<∞) and T(γ,f) be the characteristic function. We use the standard notation of Nevanlinna theory. If ρ (γ) is a proximate order relative to T(γ, f) Levln, then by using ρ (γ) Valiron has introduced the following, for any complex nu-     

On a Class of Additive Functions

ＯｎａＣｌａｓｓｏｆＡｄｄｉｔｉｖｅＦｕｎｃｔｉｏｎｓＺｈａｉｗｅｎｇｕａｎｇ（翟文广）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＳｈａｎｄｏｎｇＵｎｉｖ．，Ｊｉｎａｎ，Ｓｈｏｎｄｏｎｇ，２５０１Ｏ０）ＣｏｍｍｕｎｉｃａｔｅｄｂｙＰａｎＣｈｅｎｇｂｉａｏＲｅｃｅｉ...     

On a Class of Univalent Functions

A sharp coefficient estimate,distortion theorem and the radius of convexityare determined for the class R(α,β,A,B)of function f(z)=z+sum from n=2 to∞a_nz~n satisfyingthe condition|f’(z)-1/Bf’(z)-[B+(A-B)(1-α)]|<βfor someα,β(0≤α<1,0<β≤1)and-1≤A相似文献   

On the Growth of Composite Entire Functions

ＯｎｔｈｅＧｒｏｗｔｈｏｆＣｏｍｐｏｓｉｔｅＥｎｔｉｒｅＦｕｎｃｔｉｏｎｓＱｉａｏＪｉａｎｙｏｎｇ（乔建永）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ，２００４３３）Ａｂｓｔｒａｃｔ：Ｌｅｔｆａｎ...     

On the Singular Direction of Entire Functions

In this paper, after defining a normal criterion with a parameter and a singular direction of an entire function corresponding to a normal criterion, we shall prove the following theorem.Theorem 1 Suppose that f(z) is a transcendental entire function. Then there exists a direction Δ: argz = θ0 (0≤0<2π) which is a singular direction of f(z) corresponding to every normal criterion with a parameter.From theorem 1 we deduce at once existence of some singular directions.     

On a Class of Fractal Interpolation Functions

ＯｎａＣｌａｓｏｆＦｒａｃｔａｌＩｎｔｅｒｐｏｌａｔｉｏｎＦｕｎｃｔｉｏｎｓＱｉａｎＸｉａｏｙｕａｎ（Ｉｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉｓ．，ＤａｌｉａｎＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ，１１６０２４）Ｋｅｙｗｏｒｄｓｉｔｅｒａｔｅｄｆｕｎ...     

On the Bounded Variation of Operator-Valued Functions

In[1],the Kothe nuclear sequence spaces are described and in[2]the characte-rization of the semi-nuclear and the barreled locally convex spaces by the boundedvariation of functions respectively.In this paper several kinds of bounded variationof operator-valued functions are studied. Let X and Y are Banach spaces,T(t):[0,1]→L(X,Y)be a operator-valued fun-ction.We called T(t)be uniformly bounded variation,if there exist a constantM>0,such that for any partition △:0=t_0相似文献   

On the Pseudo-Primeness of Meromorphic Functions of Infinite Order

In this paper the pseudo -primeness of meromorphic functions of infinite order is dissoussed in detail and quite a few result are obtained, which are improvments of that of Ozawa.     

On the computation of the Euler constant γ

The problem of the approximation to the Euler constant γ is considered. Some new formulas for the computation of Euler's constant are suggested. The problem of fast evaluation of γ is discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Mean–variance portfolio selection under a constant elasticity of variance model

This paper discusses a mean–variance portfolio selection problem under a constant elasticity of variance model. A backward stochastic Riccati equation is first considered. Then we relate the solution of the associated stochastic control problem to that of the backward stochastic Riccati equation. Finally, explicit expressions of the optimal portfolio strategy, the value function and the efficient frontier of the mean–variance problem are expressed in terms of the solution of the backward stochastic Riccati equation.     

On the Choquet Charge of δ-superharmonic Functions

Let u v be positive superharmonic functions in a general potential-theoretic setting, where these functions have a Choquet-type integral representation by minimal such functions with Choquet charges (i.e. representing measures) and , respectively. We show that on the contact set {u – v = 0} of the -superharmonic function u – v, if this set is properly interpreted as the set of those minimal superharmonic functions s which satisfy lim sup _{T s} v/u = 1 for the co-fine neighborhood filter T _s associated with s. In the setting of classical potential theory for Laplace's equation this result improves on results obtained by Fuglede in 1992.     

On the Irredundant Forms of Fuzzy Switching Functions

ＯｎｔｈｅＩｒｒｅｄｕｎｄａｎｔＦｏｒｍｓｏｆＦｕｚｚｙＳｗｉｔｃｈｉｎＦｕｎｃｔｉｏｎｓTXＯｎｔｈｅＩｒｒｅｄｕｎｄａｎｔＦｏｒｍｓｏｆＦｕｚｚｙＳｗｉｔｃｈｉｎｇＦｕｎｃｔｉｏｎｓＰｅｉＤａｏｗｕ（ＹａｎｃｈｅｎｇＴｅａｃｈｅｒｓＣｏｌｅｇｅ，...     

On the Convergence of ω1 Sequences of Real Functions

We study sets of points at which ω₁ sequences of real functions from a given class F converge. As F we consider continuous functions, first class of Baire, Borel measurable functions, functions with Baire property and Lebesgue measurable functions. Connections of those problem with additional set-theoretic axioms are discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Extensions of Zeta Functions – Examples and a Study of the Double Sine Functions

We discuss zeta extensions in the sense of Kurokawa and Wakayama, Proc. Japan Acad. 2002, for constructing new zeta functions from a given zeta function. This notion appeared when we introduced higher zeta functions such as higher Riemann zeta functions in Kurokawa et al., Kyushu Univ. Preprint, 2003, and a higher Selberg zeta functions in Kurokawa and Wakayama, Comm. Math. Phys., 2004. In this article, we first recall some explicit examples of such zeta extensions and give a conjecture about functional equations satisfied by higher zeta functions. We devote the second part to making a detailed study of the double sine functions which are treated in a framework of the zeta extensions.Mathematics Subject Classification (2000) 11M36.Partially supported by Grant-in-Aid for Scientific Research (B) No. 15340012, and by Grant-in-Aid for Exploratory Research No. 13874004. This is based on the talk at The 2002 Twente Conference on Lie Groups 16–18 Dec. University of Twente, Enschede, The Netherlands.     

On the Accurate Order of Approximatlon of Some Classes of Functions

1.Introduction. Let E_n(f)_([a,b])be the best approximation of degree n to f(x)∈C_([a,b]), w_k(f,δ)_([a,b]) is the k-th modulus of smoothness of f(x) in [a,b]. In 1914, S.Bernstein [1] proved that E_n(|x|)_([-1.1]) exists. Since then, S. Bernstein, S.Nikol'skii, M. Hasson and the author worked in this direction to     

On pseudoanalyticity of continuous functions with constant σ-extension

The theorem on pseudoanalyticity of continuous functions with constant -extension is proved; this is an analog of the well known results due to Bohr, Rademacher, Men'shov, and Trokhimchuk concerning the analyticity of functions with constant extension.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 459–465, April, 1993.