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Let M_n stand for the Plancherel measure on Y_n, the set of Young diagrams with n boxes. A recent result of Stanley (arXiv:0807.0383) says that for certain functions G defined on the set Y of all Young diagrams, the average of G with respect to M_n depends on n polynomially. We propose two other proofs of this result together with a generalization to the Jack deformation of the Plancherel measure., Comment: Latex, 16 pp. Version 2: minor corrections, references added

O. Moreno and P.V. Kumar (IEEE Trans. Inform. Theory, vol.39, no.5, September 1993) showed how Deligne's theorem can be applied to coding theory. They studied certain subcodes of binary Reed-Muller codes and estimated the associated character sums over a field of q/sup 2/ elements. They obtained bounds of the order /spl Oscr/(q). The present paper shows that in one case one can improve the coefficient of q in the estimates. The author also shows that there is an error in Moreno and Kumar's argument and in some cases one needs need to replace a bound of the order /spl Oscr/(q) by a weaker bound of the order /spl Oscr/(q/sup 3/2/). >

In this note, we improve some results of Granville and Soundararajan on the distribution of values of the truncated random Euler product L ( 1 , X ; y ) : = ∏ p ⩽ y ( 1 − X ( p ) / p ) −1 , where the X ( p ) are independent random variables, taking the values ±1 with equal probability p / 2 ( p + 1 ) and 0 with probability 1 / ( p + 1 ) .

We determine the graphs with maximal spectral radius among the ones on n nodes with diameter D.

In § 11 of the above paper, the result is obtained that any polynomial scalar invariant under the group of orthogonal transformations of any number of 3 × 3 matrices is expressible as a polynomial in traces of products of the matrices. This result is in general valid only if all of the 3 × 3 matrices are symmetric. More generally, if the matrices may be non-symmetric, the argument given in the paper leads to the result that any polynomial scalar invariant under the group of orthogonal transformations is expressible as a polynomial in traces of products formed from the matrices and their transposes.

Most of the known continued fraction expansions of special functions are limit periodic. This means that the classical approximants S n (0) are normally not the best ones to use for approximations. In this paper we suggest a number of approximants S n (w n ) which converge faster. The estimation of the improvement and bounds for the error |f - Sn(wn)| (which we still call the truncation error) are mainly obtained by means of Thron's parabola sequence theorem and the oval sequence theorem.

We generalize and give a simple proof of a Theorem of Blasco. For a topological space X , C(X) denotes the algebra of real valued continuous functions on X under the operation (αf + gh)(x) := αf(x) + h(x)g(x) for each f, g, h ∈ C(X) and α ∈ R. An algebra A on X means a subalgebra of C(X) which contains the constant functions. By a ∗-algebra A on X we mean an algebra on X and all bounded functions in A separate points from the closed sets. Let A be an algebra on X and π : A −→ R be a (algebra) homomorphism and α be a cardinal number. π is said to be α-evaluating if for each subset B of A with cardinality at most α there exits xB ∈ X such that π(f) = f(xB) for each f ∈ B. If α = |N|(=the cardinal number of the set of the natural numbers N), the α-evaluating homomorphism is called countable evaluating. Let α be a cardinal number. Recall that a topological space X is called αLindelof if for each open cover U has a subcover V such that the cardinality of V is at most α. A lindelof space means a |N|-Lindelof space. The following theorem is given in [1] as one of the main results. Theorem 1. Let X be a completely regular Hausdorff space. Then X is Lindelof if and only if each countable evaluating homomorphism π on a ∗-algebra A on X is point evaluating. Received June 9, 2004; accepted June 30, 2004. Communicated by Bor-Luh Lin. 2000 Mathematics Subject Classification: Primary 54C35, 46E25.

Whitney [W2] proved that a function defined on a closed subset of R is the restriction of a Cm function if the limiting values of all mth divided differences form a continuous function. We show that Fefferman?s solution of Whitney?s problem for Rn [F, Th. 1] is equivalent to a variant of our conjecture in [BMP2] giving a criterion for Cm extension in terms of iterated limits of finite differences.

P. Lavrenko (t~) Institute of Macromolecular Compounds Russian Academy of Sciences 199004 St. Petersburg, Russia Here, ML is the shift factor (the ratio of M to the contour length L of the macromolecule) and ~b0 is the ~b value at T = 0. q~0 is equal to 2.870 x 1023 tool 1 in the limit of non-draining random coil [4]. To apply Eq. (4) to data on draining chain it is necessary to know the 9 value which is very sensitive to the draining effect. Namely, the 9 value decreases strongly with decrease of both the number of segments L / A in the chain and the reduced diameter d/A (Fig. 1). To choose the 9 value (with the known a one), Dondos and Staikos [1] have proposed (and this is the basis of the method) the relation between the Flory parameter 4~ and the exponent a

We are pleased to announce that the winner of the award for the Best Paper published in 2005 is Nathalie Delgehyr for the paper entitled `Microtubule nucleation and anchoring at the centrosome are independent processes linked by ninein function' ([Delgehyr et al., 2005][1]).[⇓][2] ![Figure][3

We present an algorithm to find a flat folding of a piece of paper, so that one complete straight cut on the folding creates any desired plane graph of cuts. The folds are based on the straight skeleton, which lines up the desired edges by folding along various bisectors; and a collection of perpendiculars that make the crease pattern foldable. We prove that the crease pattern is flat foldable by demonstrating a family of folded states with the desired properties.

As early as the 16th century, Simon Jacob, a German reckoning master, noticed that the worst case in computing the greatest common divisor of two numbers by the Euclidean algorithm occurs if these numbers are equimultiples of two consecutive members of the Fibonacci sequence.

In the second paragraph on page 30 [ 1 ], we wrote ‘Making a critical point precritical decreases the number of points about which we have to worry’. Indeed, we stopped worrying about these points so much, that we forgot to mention them in several statements. This includes Lemma 3.13, Theorem 3.14 and the Main Theorem. Thus, the possibility of critical points being precritical (not only sinking or recurrent) has to be added to those statements. In particular, the Main Theorem should read as follows.

The metric $D_{\alpha}(q,q')$ on the set $Q$ of particle locations of a homogeneous Poisson process on $\mathbb{R}^d$ , defined as the infimum of $(\sum_i |q_i - q_{i+1}|^{\alpha})^{1/\alpha}$ over sequences in $Q$ starting with $q$ and ending with $q'$ (where $|·|$ denotes Euclidean distance) has nontrivial geodesics when $\alpha>1$. The cases $1< \alpha

Let X/Q be a smooth projective (but not necessariy geometrically irreducible) variety, and let χ be a flat proper model of X over Z. Then the image of the map $${{K'}_{*}}(\chi ) \otimes Q \to {{K'}_{*}}(X) \otimes Q = {{K}_{*}}(X) \otimes Q $$ (1) is independent of the model χ.

The determination of plotting positions on probability graph paper so that the associated weighted least squares estimators of the scale parameter and the percentiles of a continuous distribution have certain properties is discussed. Necessary and sufficient conditions are given for an invariant optimal plot for percentile estimation. Also discussed is the derivation of ordered plotting positions.

A set A of integers is said to be an asymptotic basis of order h if every sufficiently large integer can be represented as a sum of h (not necessarily instinct) elements of A. In a recent paper [ENJ, Erdos and Nathanson prove the following interesting result.

An existence theorem is proved for closed convex surfaces whose principal radii of curvature regarded as functions of the unit normal vectorn satisfy the equation $$R_1 R_2 + \Phi (R_1 + R_2 ,R_1 ,R_2 ,n) + c \cdot n = \varphi (n),$$ wheree is an unknown constant vector being sought along with the surface. This equation has been studied by Miranda, who proved a variety of existence and uniqueness theorems about its solutions. The results obtained lead to a certain simplification in the hypotheses imposed on the functions Φ andϕ in these theorems.

In this technical note, we give a short proof based on some standard results in convex analysis of some important characterization results listed in Theorems 3 and 4 of Benson [Benson, H.P., 2006. Fractional programming with convex quadratic forms and functions. European Journal of Operational Research]. Actually our result is slightly more general since we do not specify the nonempty convex set X. For clarity we use the same notation for the different equivalent optimization problems as done in Benson (2006).

We begin this story with the Greeks and their fascination with the challeng of constructing regular convex polygons–that is, polygons with all sides of the same length and all interior angles equal. We refer to such N-sided polygons as regular convex N-gons, and we may suppress the word “regular” or the word “convex” if no confusion would result. The Greeks wanted to construct these polygons using what we call Euclidean tools, namely, an unmarked straight edge and a compass.

Volume I.- Biographical Note.- The Impact of Stieltjes' Work on Continued Fractions and Orthogonal Polynomials.- Number Theory.- The Stieltjes Integral, the Concept that Transformed Analysis.- On the History of the Function $$ M(x)/\sqrt {x} $$ Since Stieltjes.- xuvres Completes * Tome I.- On a Uniform Function (Translation).- Bibliography of T. J. Stieltjes.- xuvres Completes Tome II.- Investigations on Continued Fractions (Translation).- Bibliography of T. J. Stieltjes.

A curve is called regular if its derivative is never zero. We associate to any regular curve x(t) on the unit two-dimensional sphere a moving frame f(t) = [x(t), T(t), N(t)] t whose row vectors are x(t), its unit tangent vector \({\rm T}(t)=\dot{\rm x}(t)/|\dot{\rm x}(t)|\) and its righthanded normal N(t) = x(t) × T(t). Thus f(t) is a curve in the three-dimensional rotation group S0(3). It satisfies the Frenet-Serret equations

Geometric partitioning and its applications by P. K. Agarwal On the convex hull of the integer points in a disc by A. Balog and I. Barany Horizon theorems for lines and polygons by M. Bern, D. Eppstein, P. Plassmann, and F. Yao On the perimeter of a point set in the plane by V. Capolyeas and J. Pach Lines in space--A collection of results by H. Edelsbrunner Singularities of minimal surfaces and networks and related extremal problems in Minkowski space by Z. Furedi, J. C. Lagarias, and F. Morgan Wu-Ritt characteristic sets and their complexity by G. Gallo and B. Mishra Algorithms in real algebraic geometry and applications to computational geometry by J. Heintz, T. Recio, and M.-F. Roy Ehrhart polynomials of convex polytopes, $h$-vectors of simplicial complexes, and nonsingular projective toric varieties by T. Hibi Unimodular fans, linear codes, and toric manifolds by P. Kleinschmidt, N. Schwartz, and B. Sturmfels New results for simplicial spherical polytopes by P. Kleinschmidt and Z. Smilansky Rational-function-valued valuations on polyhedra by J. Lawrence Winding numbers and the generalized lower-bound conjecture by C. W. Lee Computing the center of planar point sets by J. Matousek Finite quotients of infinite universal polytopes by P. McMullen and E. Schulte The universality theorem on the oriented matroid stratification of the space of real matrices by N. Mnev The densest double-lattice packing of a convex polygon by D. M. Mount Arrangements in topology by P. Orlik Notes on geometric graph theory by J. Pach Recent progress on the complexity of the decision problem for the reals by J. Renegar Sweeping arrangements of curves by J. Snoeyink and J. Hershberger On geometric permutations and the Katchalski-Lewis conjecture on partial transversals for translates by H. Tverberg Invariant-theoretic computation in projective geometry by N. L. White.