A lower bound on the Chvátal-rank of Antiwebs

In [Holm, E., L. M. Torres and A. K. Wagler, On the Chvátal-rank of linear relaxations of the stable set polytope, International Transactions in Operational Research 17 (2010), pp. 827–849; Holm, E., L. M. Torres and A. K. Wagler, On the Chvátal-rank of Antiwebs, Electronic Notes in Discrete Mathematics 36 (2010), pp. 183–190] we study the Chvátal-rank of the edge constraint and the clique constraint stable set polytopes related to antiwebs. We present schemes for obtaining both upper and lower bounds. Moreover, we provide an algorithm to compute the exact values of the Chvátal-rank for all antiwebs with up to 5,000 nodes. Here we prove a lower bound as a closed formula and discuss some cases when this bound is tight.     

Lower bound for the area of an analytic curve inside a cube in the space ℂ n

The exact lower bound of the area of an analytic curve which lies inside a cube in the space and passes through its center is obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 145–148, January, 1993.     

A lower bound in Nehari’s theorem on the polydisc

By theorems of Ferguson and Lacey (d = 2) and Lacey and Terwilleger (d > 2), Nehari??s theorem (i.e., if H _?? is a bounded Hankel form on H ²(D ^d ) with analytic symbol ??, then there is a function ?? in L ^??(T ^d ) such that ?? is the Riesz projection of g4) is known to hold on the polydisc D ^d for d > 1. A method proposed in Helson??s last paper is used to show that the constant C _d in the estimate ??????_?? ?? C _d ??H _?? ?? grows at least exponentially with d; it follows that there is no analogue of Nehari??s theorem on the infinite-dimensional polydisc.     

A finite algorithm for finding the projection of a point onto the canonical simplex of ∝ n

An algorithm of successive location of the solution is developed for the problem of finding the projection of a point onto the canonical simplex in the Euclidean space ⁿ . This algorithm converges in a finite number of steps. Each iteration consists in finding the projection of a point onto an affine subspace and requires only explicit and very simple computations.     

A Weil–Petersson type metric on spaces of metric graphs

In this note, we discuss an analogue of the Weil–Petersson metric for spaces of metric graphs and some of its properties.     

A formula for the Bloch norm of a C 1-function on the unit ball of ℂ n

For a C ¹-function f on the unit ball ⊂ ℂ ⁿ we define the Bloch norm by , where is the invariant derivative of f, and then show that . Supported by MNZŽS Serbia, Project No. 144010.     

A class of normal weighted composition operators on the Fock space of ℂ n

This paper characterizes a class of normal weighted composition operators and their spectrum on the Fock space of Cⁿ.     

A new technique of integral representations in ℂ n

A new technique of integral representations in ? ⁿ , which is different from the well-known Henkin technique, is given. By means of this new technique, a new integral formula for smooth functions and a new integral representation of solutions of the ?-equations on strictly pseudoconvex domains in ? ⁿ are obtained. These new formulas are simpler than the classical ones, especially the solutions of the ?-equations admit simple uniform estimates. Moreover, this new technique can be further applied to arbitrary bounded domains in ? ⁿ so that all corresponding formulas are simplified.     

Zonal spherical function on the Lie ball in ℂn

In this paper, we give the explicit formula for the zonal spherical function on the Lie ball in ?ⁿ.     

On the injectivity of twisted spherical means on ℂ n

In this paper we study the injectivity and injectivity sets for the twisted spherical means on ℂ ⁿ . These results are then used to study the same problems on the reduced Hiesenberg group.     

The lattice point discrepancy of a body of revolution: Improving the lower bound by Soundararajan’s method

For a convex body in which is invariant under rotations around one coordinate axis and has a smooth boundary of bounded nonzero curvature, the lattice point discrepancy (number of integer points minus volume) of a linearly dilated copy is estimated from below. On the basis of a recent method of K. Soundararajan [16], an -bound is obtained that improves upon all earlier results of this kind.Dedicated to the memory of Professor Erich LamprechtThis revised electronic version of the Abstract includes the formulas that were missing in the previous electronic version published online in September 2004.     

A lower bound on the blow-up rate for the Davey–Stewartson system on the torus

We consider the hyperbolic–elliptic version of the Davey–Stewartson system with cubic nonlinearity posed on the two-dimensional torus. A natural setting for studying blow-up solutions for this equation takes place in H^s$H^s$, 1/2<s<1$1/2<s<1$. In this paper, we prove a lower bound on the blow-up rate for these regularities.     

A remark on the Gaussian lower bound for the Neumann heat kernel of the Laplace–Beltrami operator

We adapt in the present note the perturbation method introduced in Choulli and Kayser (Positivity 19(3):625–646, 2015) to get a lower Gaussian bound for the Neumann heat kernel of the Laplace–Beltrami operator on an open subset of a compact Riemannian manifold.     

An Ω(n 5/4) lower bound on the randomized complexity of graph properties

A decision tree algorithm determines whether an input graph withn nodes has a property by examining the entries of the graph's adjacency matrix and branching according to the information already gained. All graph properties which are monotone (not destroyed by the addition of edges) and nontrivial (holds for somes but not all graphs) have been shown to require (n ²) queries in the worst case.In this paper, we investigate the power of randomness in recognizing these properties by considering randomized decision tree algorithms in which coins may be flipped to determine the next entry to be examined. The complexity of a randomized algorithm is the expected number of entries that are examined in the worst case. The randomized complexity of a property is the minimum complexity of any randomized decision tree algorithm which computes the property. We improve Yao's lower bound on the randomized complexity of any nontrivial monotone graph property from (n log^1/12 n) to (n ^5/4).     

An Ω(n 4/3) lower bound on the randomized complexity of graph properties

We improve King's (n ^5/4) lower bound on the randomized decision tree complexity of monotone graph properties to (n ^4/3). The proof follows Yao's approach and improves it in a different direction from King's. At the heart of the proof are a duality argument combined with a new packing lemma for bipartite graphs.The paper was written while the author was a graduate student at the University of Chicago and was completed at M.I.T. The work was supported in part by NSF under GRANT number NSF 5-27561, the Air Force under Contract OSR-86-0076 and by DIMACS (Center for Discret Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center-NSF-STC88-09648.     

Bounded projections and duality on spaces of holomorphic functions in the unit ball ofℂ n

In this paper three Banach spacesA ₀(),A andA ¹() of functions holomorphic in the unit ballB of ⁿ are defined. We exhibit bounded projections fromC ₀(B) ontoA ₀(), fromL ¹(B) ontoA ¹(), and fromL(B) ontoA(). Using these projections, we show thatA ₀()* A ¹() andA ¹()* A().Supported in part by the National Natural Science Foundation of China.