All Lambda-Designs With λ = 2 p are Type-1

A-design is a family B ₁,B ₂,...,B _v of subsets of X={1, 2,..., v} such that B _i B _j = for all i jand not all B _i are of the same size. Ryser's andWoodall's -design conjecture states thateach -design can be obtained from a symmetricblock design by a certain complementation procedure. Our mainresult is that the conjecture is true when is twice a prime number.     

On the convergence of Fourier series in the metric ofL 1

L ¹ .      

Subsets with Restricted Movement

Let G be a finite permutation group on a set with no fixed points in and let m and k be integers with 0 < m < k. For a finite subset of the movement of is defined as move() = max_gG| ^g \ |. Suppose further that G is not a 2-group and that p is the least odd prime dividing |G| and move() m for all k-element subsets of . Then either || k + m or k (7m – 5) / 2, || (9m – 3)/2. Moreover when || > k + m, then move() m for every subset of .     

Stabilization of solutions of certain parabolic equations and systems

This paper concerns the investigation of the stabilization of solutions of the Cauchy problem for a system of equations of the form u/t = u + f_i(u, v); v/t = v + F₂(u, v). It is proved that under certain assumptions the behavior of solutions as t is determined by mutual arrangement of the set of initial conditions {(u, v): u = f₁(x), v =f ₂(x), xRⁿ} and the trajectories of the system of ordinary differential equations du/dt = F₁(u, v), dv/dt = F₂(u, v). The question of stabilization of the solutions of a single quasilinear parabolic equation is also considered.Translated from Matematicheskie Zametki, Vol. 3, No. 1, pp. 85–92, January, 1968.     

On contiguity of probability measures corresponding to semimartingales

, (ⁿ), - (P ⁿ ), P ⁿ (A ⁿ )>0P ⁿ (A ⁿ )0,n. [15] - , . , P ⁿ P ⁿ T ⁿ T ⁿ .     

On the order of approximation to functions ofH p (R) (0<p≦1) by certain means of Fourier integrals

H ^P (R ₊ ² ) — R ₊ ² ={zC: Imz>0} ^p (R) — H ^p (R ₊ ² ). P ^k (f,x) — ë- — ,W ^k (f,x) — — R ^k, (f,x) — f H (R) (. §1,1)–3)); _k (, f) _p — - . , fH ^p (R) 0<p1,kN; (1+)^–1<p1, 0<<,kN.     

Sukzessive Minima mit und ohne Nebenbedingungen

Given semi-normsf andg on ⁿ and a real number >0. Then the successive minima off under the constraintg are defined by _j : = inf {: there existj linear independent vectors inZ ⁿ withf andg}. The main theorem of this paper (Lagrange multiplier theorem) states that the successive minima of a certainnorm h on ⁿ (without constraints) coincide with the _j 's up to bounded factors. Moreover, this norm is constructed explicitly. Using Minkowski's wellknown theorem on successive minima and our result certain inequalities on simultaneous Diophantine approximations are derived.     

Bounds on the subdominant eigenvalue involving group inverse with applications to graphs

Let A be an n × n symmetric, irreducible, and nonnegative matrix whose eigenvalues are ₁₂ ... _n. In this paper we derive several lower and upper bounds, in particular on ₂ and _n , but also, indirectly, on . The bounds are in terms of the diagonal entries of the group generalized inverse, Q ^#, of the singular and irreducible M-matrix Q = ₁ I – A. Our starting point is a spectral resolution for Q ^#. We consider the case of equality in some of these inequalities and we apply our results to the algebraic connectivity of undirected graphs, where now Q becomes L, the Laplacian of the graph. In case the graph is a tree we find a graph-theoretic interpretation for the entries of L ^# and we also sharpen an upper bound on the algebraic connectivity of a tree, which is due to Fiedler and which involves only the diagonal entries of L, by exploiting the diagonal entries of L ^#.     

A condition for nonnegativity of an operator related to the Dirichlet operator

Let L₀ be a positive definite closed linear operator with domain of definition D(L₀) dense in the Hilbert space H; let(, ₁, ₂) be the positive boundary value space of the operator L₀ such that the restriction of L ₀ ^* to ker ₂ is the Friedrichs extension of the operator L₀. We establish a test for nonnegativity of an operator T of the form Ty=L ₀ ^* y+^*(₁–C)y, y D(T)= ker(₂+), where :H and C: are respectively a compact operator and a bounded nonnegative operator.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 32, 1990, pp. 30–33.     

A Foliation of the Space of Conjugacy Classes of Representations of a Surface Group

Let be the fundamental group of a closed orientable surface of genus g 1, and let R(, G)/G be the space of conjugacy classes of representations of into a connected real reductive Lie group G. Motivated by the theory of geometric quantization, we define a map ¯ on R(, G)/G and investigate whether the fibres of ¯ are isotropic with respect to the natural symplectic structure on R(, G)/G. If g = 2 and G = SU(2), then the foliation given by the fibres of ¯ is equivalent to a real polarization defined by Weitsman, and we reprove his result that the fibres are isotropic in this case. If g = 1 then the fibres of ¯ are also isotropic, but we give an example to show that in general they are not.     

On Piecewise-Constant Approximation of Continuous Functions of n Variables in Integral Metrics

We consider the approximation by piecewise-constant functions for classes of functions of many variables defined by moduli of continuity of the form (₁, ..., _n ) = ₁(₁) + ... + _n ( _n ), where _i ( _i ) are ordinary moduli of continuity that depend on one variable. In the case where _i ( _i ) are convex upward, we obtain exact error estimates in the following cases: (i) in the integral metric L ₂ for (₁, ..., _n ) = ₁(₁) + ... + _n ( _n ); (ii) in the integral metric L _p (p 1) for (₁, ..., _n ) = c ₁₁ + ... + c _{n n} ; (iii) in the integral metric L _{(2, ..., 2, 2r)} (r = 2, 3, ...) for (₁, ..., _n ) = ₁(₁) + ... + _{n – 1}( _{n – 1}) + c _{n n} .     

Torsion tensor and critical metrics on contact (2n+1)-manifolds

Contact Riemannian manifolds (M, ,g) satisfying the condition (1) =0, where is the torsion introduced byChern andHamilton [6] and is the characteristic vector field, have interesting geometric properties (see [6], [9], [11]). In this paper we give a variational characterization of compact contact Riemannian manifolds which satisfy (1). Moreover we study the tangent sphere bundles (T ₁ M, , g), where (,g) is the standard contact Riemannian structure, which satisfy the condition (1); in particular in the 3-dimensional case we find a surprising result (see Corollary 5.3).Supported by funds of the M.U.R.S.T.     

Über den algorithmischen Nachweis von Ungleichungen I

We shall develop a method to prove inequalities in a unified manner. The idea is as follows: It is quite often possible to find a continuous functional : ⁿ , such that the left- and the right-hand side of a given inequality can be written in the form (u)(v) for suitable points,v=v(u). If one now constructs a map ^{n n} , which is functional increasing (i.e. for each x ⁿ (which is not a fixed point of ) the inequality (x)<((x)) should hold) one specially gets the chain (u)( u))( ²(u))... ⁿ (u)). Under quite general conditions one finds that the sequence { ⁿ (u)} _n converges tov=v(u). As a consequence one obtains the inequality (u)(v).     

Exact error bound of approximation by interpolating splines inL-metric on the classesW p r (1≦p

Корнейчук  Н. П. 《Analysis Mathematica》1977,3(2):109-117

Automorphismen und Modulraum galoisscher dreiblättriger Überlagerungen

The points of the modulus space M _g ² of compact hyperelliptic Riemann surfaces of genus^g g can be identified, with the PGL (2,)-orbits in the set of all subsets of ¹, which contain 2g+2 elements. The automorphism group Aut(X) of such a surface contains a canonical involution J, and Aut(X)/J is isomorphic to the finite subgroup of Aut(¹), whose elements permute the critical values of some twofold cover. In this paper we derive similar results for surfaces X, which admit a threefold Galois cover over ¹.

---

---

Herrn Prof. Dr. Dr. h.c. Karl Stein in Dankbarkeit gewidmet     

Sharp Nikolskii inequalities with exponential weights

w _a(x)=exp(–x^a), xR, a0. , N _n (a,p,q) — (2), _n P _nw_ap, CN_n(a,p, q)P_nw_aq. , — , {P _n}, .

---

---

This material is based upon research supported by the National Science Foundation under Grant No. DMS-84-19525, by the United States Information Agency under Senior Research Fulbright Grant No. 85-41612, and by the Hungarian Ministry of Education (first author). The work was started while the second author visited The Ohio State University between 1983 and 1985, and it was completed during the first author's visit to Hungary in 1985.     

Computation of Almost Split Sequences with Applications to Relatively Projective and Prinjective Modules

Let be an Artin algebra, let mod be the category of finitely generated -modules, and let Amod be a contravariantly finite and extension closed subcategory. For an indecomposable and not Ext-projective module CA, we compute the almost split sequence 0ABC0 in A from the almost split sequence 0DTrCEC0 in mod. Since the computation is particularly simple if the minimal right A-approximation of DTrC is indecomposable for all indecomposable and not Ext-projective CA, we manufacture subcategories A with the desired property using orthogonal subcategories. The method of orthogonal subcategories is applied to compute almost split sequences for relatively projective and prinjective modules.     

Asymptotic Formulae and Divisor Problems

We investigate the asymptotic behaviour of the summatory functions of _z(n, ), _k(n, ) z ⁽ⁿ⁾ and _k(n, ) z ⁽ⁿ⁾.     

Characterization theorem of generalized polynomial of best approximation having bounded coefficients

Let the set of generalized polynomials having bounded coefficients beK={p= _jg_j. _{j j j},j=1, 2, ...,n}, whereg ₁,g ₂, ...,g _n are linearly independent continuous functions defined on the interval [a, b], _j, _j are extended real numbers satisfying _j<+, _j>-, and _{j j}. Assume thatf is a continuous function defined on a compact setX [a, b]. This paper gives the characterization theorem forp being the best uniform approximation tof fromK, and points out that the characterization theorem can be applied in calculating the approximate solution of best approximation tof fromK.     

On the approximation by rational combinations of a class of functions

() [0,1] — {(n)} — , +. , f(x) [0,1] () , x ₁ ,x ₂ [0, 1], (₁)=(₂), f(x ₁ )=f(x ₂ ).