A note on θ(g, g′)-continuity in generalized topological spaces

The concept of θ(g, g′)-continuity was introduced by Császár [1]. In this paper, we investigate characterizations for θ(g, g′)-continuous functions and introduce the concept of weak θ(g, g′)-continuity, and study characterizations for weak θ(g, g′)-continuity and the relationships among θ(g, g′)-continuity, weak (g, g′)-continuity and weak θ(g, g′)-continuity.     

唯一g(x)-clean环

本文研究了唯一g(x)-clean环的性质与结构.利用g(x)-clean环的方法,得到了唯一g(x)-clean环与g(x)-clean环的关系,唯一g(x)-clean环与一类特殊的生成环的等价条件,以及斜Hurwitz级数环的g(x)-clean性,推广了g(x)-clean环的研究结果.     

Smallest g -supersolution with constraint

In this paper the existence and uniqueness of the smallest g-supersolution for BSDE is discussed in the case without Lipschitz condition imposing on both constraint function and drift coefficient in the different method from the one with Lipschitz condition. Then by considering (ξ, g) as a parameter of BSDE, and (ξ ^α, g ^α) as a class of parameters for BSDE, where α belongs to a set , for every there exists a pair of solution {Y ^a, Z^a} for the BSDE, the properties of which is also a solution for some BSDE is studied. This result may be used to discuss optimal problems with recursive utility. This work was supported by NSFC (79790130)     

条件g-期望的矩不等式

找到了几个使条件g-期望的矩不等式在一般意义下成立的关于g和g-期望的充分条件.     

Group Divisible Designs with Block Size Four and Group Type gum1 with Minimum m

In this paper, we continue to investigate the spectrum for {4}-GDDs of type g^u m¹ with m as small as possible. We determine, for each admissible pair (g,u), the minimum values of m for which a {4}-GDD of type g^um¹ exists with four possible exceptions.Gennian Ge-Researcher supported by NSFC Grant 10471127.Alan C. H. Ling-Researcher supported by an ARO grant 19-01-1-0406 and a DOE grant.classification Primary 05B05     

On complex manifolds polarized by an ample line bundle of sectional genus q ( X ) + 2

Let (X,L) be a polarized manifold with dim X = n. In this paper, we classify (X,L) with n = 3, , and g(L)=q(X) + 2. Moreover we also classify (X,L) with , g(L)=q(x) + 2, and . Received February 12, 1999     

A note on a P ≠ NP result for a restricted class of real machines

For a class of real machines using only linear functionals as computations and equality-tests, we show that the classes P and NP differ.     

Minimal and Harmonic Unit Vector Fields in and Its Dual Space

 The complex two-plane Grassmannian carries a K?hler structure J and also a quaternionic K?hler structure ?. For we consider the classes of connected real hypersurfaces (M, g) with normal bundle such that and are invariant under the action of the shape operator. We prove that the corresponding unit Hopf vector fields on these hypersurfaces always define minimal immersions of (M, g), and harmonic maps from (M, g), into the unit tangent sphere bundle with Sasaki metric . The radial unit vector fields corresponding to the tubular hypersurfaces are also minimal and harmonic. Similar results hold for the dual space .     

Isomorphism classes of elliptic and hyperelliptic curves over finite fields

We give the number and representatives of isomorphism classes of hyperelliptic curves of genus g defined over finite fields , g=1,2,3. These results have applications to hyperelliptic curve cryptography.     

Truncated Transversal Designs: A New Lower Bound on the Number of Idempotent MOLS of Side n

A truncated transversal design TTD of type g^km¹ is a {k, k+1}-GDD of type g^km¹ in which each point on the group of size m lies only in blocks of size k+1. Thus a TTD of type g^km¹ is equivalent to a transversal design TD (k, g) having m disjoint parallel classes of blocks. We employ a new construction developed by the author (1993, J. Combin. Des.1, 15–26) to show that if g₁<g₂ and if there exists a TD (k, g₁) and a TD (k+1, g₂), then there exists a TTD of type (g₁g₂)^km¹ for any 0m(g₂ div g₁) g²₁. As a corollary, we obtain a new lower bound on the number of mutually orthogonal idempotent latin squares of side g: if g₁<g₂ and there exist r MOLS of side g₁ and r+1 MOLS of side g₂ , then N(1 ^g₁g₂)r.     

The Inequality 8pg < μ for Hypersurface Two-dimensional Isolated Double Points

The Milnor number μ and the geometric genus p_g of normal 2-dimensional double points are studied by using Zariski's canonical resolution. By using formulas due to E. HORIKAWA and H. LAUFER, we represent μ ? 8p_g in terms of the number of blowing-ups along ?¹ and the number l of ?even”? components in the resolution process. A key point of our arguments is the fact that if l is small then the resolution process is restricted very much. For rational double points and double points with p_a = 1, each classes are characterized by numerical invariants appearing in this resolution process. For the case p_a = 1, we can make our inequality sharper and can prove 12 · p_g ? 3 ≤ μ. This is an another proof of Xu-Yau's inequality for the singularity with p_a = 1 in our situation.     

On the number of equivalence classes of attracting dynamical systems

We study discrete dynamical systems of the kind h(x) = x + g(x), where g(x) is amonic irreducible polynomial with coefficients in the ring of integers of a p-adic field K. The dynamical systems of this kind, having attracting fixed points, can in a natural way be divided into equivalence classes, and we investigate whether something can be said about the number of those equivalence classes, for a certain degree of the polynomial g(x). The text was submitted by the authors in English.     

Weyl symbolic calculus on any Lie group

For any Lie groupG we extend the Weyl symbolic calculus to analytic symbol classes on the dual g^* of the Lie algebra g ofG.     

The smooth Banach submanifold B*(E, F) in B(E, F)

Let E,F be two Banach spaces,B(E,F),B+(E,F),Φ(E,F),SΦ(E,F) and R(E,F) be bounded linear,double splitting,Fredholm,semi-Frdholm and finite rank operators from E into F,respectively. Let Σ be any one of the following sets:{T ∈Φ(E,F):Index T=constant and dim N(T)=constant},{T ∈ SΦ(E,F):either dim N(T)=constant< ∞ or codim R(T)=constant< ∞} and {T ∈ R(E,F):Rank T=constant< ∞}. Then it is known that Σ is a smooth submanifold of B(E,F) with the tangent space TAΣ={B ∈ B(E,F):BN(A)-R(A) } for any A ∈Σ. However,for ...     

Existence,uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

For a bounded domain Ω ⊂ ℝ ⁿ , n ⩾ 3, we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system − Δu + u · ∇u + ∇p = f, div u = k, u _|aΩ = g with u ∈ L ^q , q ⩾ n, and very general data classes for f, k, g such that u may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of a series of papers by Frehse & Růžička, see e.g. Existence of regular solutions to the stationary Navier-Stokes equations, Math. Ann. 302 (1995), 669–717, where the existence of a weak solution which is locally regular is proved.      

Isochronous Centers and Isochronous Functions

Abstract We study isochronous centers of two classes of planar systems of ordinary differential equations.Forthe first class which is the Linard systems of the form =y-F(x),=-g(x) with a center at the origin, we provethat if g is isochronous(see Definiton 1.1),then the center is isochronous if and only if F≡0.For the secondclass which is the Hamiltonian systems of the form =-g(y),=f(x) with a center at the origin,we prove thatif f or g is isochronous,then the center is isochronous if and only if the other is also isochronous.     

Torsion classes of generalized Boolean algebras

Torsion classes and radical classes of lattice ordered groups have been investigated in several papers. The notions of torsion class and of radical class of generalized Boolean algebras are defined analogously. We denote by T _g and R _g the collections of all torsion classes or of all radical classes of generalized Boolean algebras, respectively. Both T _g and R _g are partially ordered by the class-theoretical inclusion. We deal with the relation between these partially ordered collection; as a consequence, we obtain that T _g is a Brouwerian lattice. W. C. Holland proved that each variety of lattice ordered groups is a torsion class. We show that an analogous result is valid for generalized Boolean algebras.     

On zeros of characters of finite groups

For a finite group G and a non-linear irreducible complex character χ of G write υ(χ) = {g ∈ G | χ(g) = 0}. In this paper, we study the finite non-solvable groups G such that υ(χ) consists of at most two conjugacy classes for all but one of the non-linear irreducible characters χ of G. In particular, we characterize a class of finite solvable groups which are closely related to the above-mentioned question and are called solvable φ-groups. As a corollary, we answer Research Problem 2 in [Y.Berkovich and L.Kazarin: Finite groups in which the zeros of every non-linear irreducible character are conjugate modulo its kernel. Houston J. Math. 24 (1998), 619–630.] posed by Y.Berkovich and L.Kazarin.     

On the law S ( S ( x , y ), T ( x , y )) = S ( x , y ) of fuzzy logic

Motivated by some functional models arising in fuzzy logic, when classical boolean relations between sets are generalized, we study the functional equation S(S(x, y), T(x, y)) = S(x, y), where S is a continuous t-conorm and T is a continuous t-norm. Some interesting methods for solving this type of equations are introduced.