DANZER-GRüNBAUM'S THEOREM REVISITED

In this paper we prove some stronger versions of Danzer-Grünbaum's theorem including the following stability-type result. For 0 < α < 14π/27 the maximum number of vertices of a convex polyhedron in E ³ such that all angles between adjacent edges are bounded from above by α is 8. One of the main tools is the spherical geometry version of Pál's theorem. This revised version was published online in August 2006 with corrections to the Cover Date.     

ON A THEOREM OF CHUI

Let f∈C_(2π) and let α_0/2+sum from k=1 to ∞ (a_k coskx+b_k sinkx) (1)be its Fourier series. Denote by S_n(f, x) the n-th partial sumof series (1) and by ω(f,δ) the modulus of continuity of functionf(x). For each q0, the Euler (E, q)-mean of series (1) is     

AN ELEMENTARY PROOF OF A THEOREM OF LEE

§ 1. Introduction Now we recall some basic notions and results in whitenoise analysis. Let S (R) (reop. S' (R)) denote the Sehwarz space of test functions (rosp. tempered distributions). Let A denoto tho self-adjoint operator-d~2/dt~2+1+t~2 in L~2(R).     

A BIFURCATION THEOREM OF SETCONTRACTIVE MAPS

In this paper, the global result on bifurcation given by P. H. Rabinowitz is extended tostrictly set-contractive maps and condensing maps.     

BCKLUND TRANSFORMATION OF NONLINEAR EVOLUTION EQUATIONS

Using Lax pair and looking for the gauge transformation,we obtain the B(?)cklundtransformation in another form(sometimes it is called Darboux transformation)for some nonlinearevolution equations.We shall see that it is more convenient to use this form of B(?)cklundtransformation.     

A NOTE ON A CHARACTERIZATION THEOREM OF STRAUSS

Assume that B is a compact subset on the real axis containing at least n+1 points,C(B) the normed linear space of all continuous functions defined on B,with Chebyshevnorm‖·‖,and G=span(g_1,…,g_n) an n-dimensional subspace of C(B).LetG_R={g=sum from j=1 to n a_jg_j:v(x)≤g(x)≤u(x),q_i≤sum from j=1 to n d_(ij)a_j≤p_i for i=1,…,l}where u,v are extended real-valued functions on B subject to -∞≤v(x)相似文献   

DISCRETE ANALOGUES OF A THEOREM OF WINTNER AND HARTMAN

１ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｓｅｃｏｎｄｏｒｄｅｒｏｒｄｉｎａｒｙｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｘ″＋ｑ（ｔ）ｘ＝０，ｔ≥０．（１．１）ＳｕｐｐｏｓｅｔｈａｔＱ（ｔ）＝∫＋∞ｔｑ（ｓ）ｄｓ（１．２）ｃｏｎｖｅｒｇｅｓ（ｐｏ...     

A NOTE ON TB THEOREM OF DAVID-JOURNE-SEMMES

David, Journe and Semmes proved the Tb theorem for para-accreclive funclions and showed this theo-rem is optimal in certain sense. In this note, we give a technical proof of Tb theorem for pseado-accretivefunctions. Our result still holds for para-accreting functions.     

A GENERALIZATION OF CLARKE''''S FIXED POINT THEOREM

ＡＧＥＮＥＲＡＬＩＺＡＴＩＯＮＯＦＣＬＡＲＫＥ＇ＳＦＩＸＥＤＰＯＩＮＴＴＨＥＯＲＥＭＳＯＮＧＷＥＮＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｐｒｏｐｏｓｅｓａｆｏｒｍａｌｌｙｓｔｒｏｎｇｅｒｓｅｔ－ｖａｌｕｅｄＣｌａｒｋｅ＇ｓｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒ...     

A GENERALIZATION OF GAUSS-KUZMIN-LE′VY THEOREM

We prove a generalized Gauss-Kuzmin-L′evy theorem for the generalized Gauss transformation Tp(x) = {p/x}.In addition, we give an estimate for the constant that appears in the theorem.     

A GENERALIZATION OF GLOBALLY TOPOLOGICAL LINEARIZATION THEOREM

In this paper, the globally topological linearization theorem of a certain system is given which generalizes the known result.     

A NOTE ON A STRONG UNIQUENESS THEOREM OF SITRAUSS

In this paper we present a correction of the proof of u strong uniqueness theorem given by H. Struuss [1] in 1992 on approximation by reciprocals of functions uf an n-dimensional space (u,…un) satisfying coefficient constraints.     

A NOTE ON A TRANSFERENCE THEOREM OF THE SYSTEMS OF LINEAR CONGRUENCES

<正> Let p be a prime number. Let a_(ij)(1≤i≤t,1≤j≤s) be a set of st integers.Weuse the notations x=max(1, |x|), p_1=[(p-1)/2], p_2=[p/2], and (a)_p to denote the integer satisfying (a)_p=a(mod p),-p_1≤(a)_p≤p_2. Consider the dual of linear congruences     

ON A GENERALIZATION OF A THEOREM OF ERDŐS AND FUCHS

Sárközy generalized a theorem of Erds and Fuchs by considering sums of.....     

A NOTE ON A STRONG UNIQUENESS THEOREM OF STRAUSS

In this paper we present a correction of the proofofa strong uniqueness theorem given by H.Strauss in1992 on approximation by reciprocals of functions of an n-dimensional space span (u_1,…,u_n) satisfyingcoefficient constraints.     

A GENERAL VERSION OF KALTON'S CLOSED GRAPH THEOREM

ＡＧＥＮＥＲＡＬＶＥＲＳＩＯＮＯＦＫＡＬＴＯＮ＇ＳＣＬＯＳＥＤＧＲＡＰＨＴＨＥＯＲＥＭＱｉｕＪｉｎｇｈｕｉ（丘京辉）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｕｚｈｏｕＵｎｉｖｅｒｓｔｉｙ，Ｓｕｚｈｏｕ２１５００６，Ｃｈｉｎａ．）Ａｂｓｔｒ...     

A THEOREM ON THE CONTINUITIES OF STOCHASTIC PROCESSES

If a stochastic process X_t is continuous in probability,then the points of discontinuityin γ-th mean constitute a set of lst category.     

A FIXED POINT THEOREM OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

In this paper we generalize a theorem of Goebel and Kirk,prove thatif X is a 2UR space,then each asymptotically nonexpansive mapping of none-mpty bounded closed convex subset of X into itself has a fixed point.     

CONVEXITY THEOREM OF PARAMETRIC TRIANGULAR BZIER SURFACES

The author introduces twist vectors of control nets of parametric triangular Bèziersurfaces.With twist vectors and other geometric magnitudes,a sufficient condition forparametric triangular Bèzier surfaces to be convex is offered.Incidently,a necessary andsufficient condition for triangular Bèzier surfaces of parametric form to degenerate to thatof functional form is given.A less stringent sufficient condition is proposed for quadraticBèzier surfaces to be convex.     

EXTENSION OF LAI-ROBBINS-WEI''''S THEOREM

A theorem of Lai,Robbins and Wei is extended To a more general form to contain all theknown results in the literature about the strong consistency of the lest squares estimates of theprogression coefficients in linear models with nonrandom regressors,and improvement is made onsome of these results.