on a conjecture concerning integral real roots of certain cubic polynomials abstract in this paper we determine all the rational pairs x n such that f n x 3 x 3 7 10 n x 2 2 6 n 2 11 n 8 x 4 n 3 6 n 2 10 n 24 0 it follows that for each positive integer n 5 there is no integer solution x for the polynomial this confirms a conjecture of li et al concerning the uniqueness of a class of optimal graphs in the study of an extremal graph theory problem

on the existence of weak solutions for quasilinear parabolic initial boundary value problems structure conditions on a strongly nonlinear operator a u are given under whichthe initial dirichlet boundary value problem for has weak solutions

completeness and unbiased estimation for sum quota sampling abstract most statistical methodology in use today is designed for sampling schemes or experimental designs in which the sample size or number of data points is regarded as a fixed preset parameter this is in part for mathematical convenience but is also suggested by the intuition that sampling is restricted by a total cost of data collection and that the cost of sampling remains the same from unit to unit the cost of sampling however may vary from unit to unit and the costs may be unknown before the sample is taken if so the objective of taking a sample of preset cost may force one to sample sequentially until achieving the preset cost and then stop that is the objective of taking a sample of fixed size may be turned against itself if the cost of sampling varies from unit to unit a cost may be monetary or general in character motivated by the possibility of a quota for costs consider the sampling scheme in which random variables xi are sampled sequentially until the sum of the associated non

signless laplacians of finite graphs we survey properties of spectra of signless laplacians of graphs and discuss possibilities for developing a spectral theory of graphs based on this matrix for regular graphs the whole existing theory of spectra of the adjacency matrix and of the laplacian matrix transfers directly to the signless laplacian and so we consider arbitrary graphs with special emphasis on the non regular case the results which we survey old and new are of two types a results obtained by applying to the signless laplacian the same reasoning as for corresponding results concerning the adjacency matrix b results obtained indirectly via line graphs among other things we present eigenvalue bounds for several graph invariants an interpretation of the coefficients of the characteristic polynomial a theorem on powers of the signless laplacian and some remarks on star complements

spectra of signed graphs with two eigenvalues abstract in this paper we study connected signed graphs with 2 eigenvalues from several theoretical and computational perspectives we give some basic results concerning the eigenvalues and cyclic structure of such signed graphs in particular we complete the list of those that are 3 or 4 regular there is a natural relation between signed graphs and systems of lines in a euclidean space that are pairwise orthogonal or at fixed angle with a special role of those with 2 eigenvalues in this context we derive a relative bound for the number of such lines an extension of the similar bound related to unsigned graphs we also determine all such graphs whose negative eigenvalue in not less than 2 except for so called exceptional signed graphs using the computer search we determine those with at most 10 vertices several constructions are given and the possible spectra of those with at most 30 vertices are listed

on products and line graphs of signed graphs their eigenvalues and energy abstract in this article we examine the adjacency and laplacian matrices and their eigenvalues and energies of the general product non complete extended p sum or neps of signed graphs we express the adjacency matrix of the product in terms of the kronecker matrix product and the eigenvalues and energy of the product in terms of those of the factor graphs for the cartesian product we characterize balance and compute expressions for the laplacian eigenvalues and laplacian energy we give exact results for those signed planar cylindrical and toroidal grids which are cartesian products of signed paths and cycles we also treat the eigenvalues and energy of the line graphs of signed graphs and the laplacian eigenvalues and laplacian energy in the regular case with application to the line graphs of signed grids that are cartesian products and to the line graphs of all positive and all negative complete graphs

on the laplacian coefficients of signed graphs abstract let g be a signed graph where g is its underlying graph and its sign function defined on edges of g a signed graph the subgraph of is its signed tu subgraph if the signed graph induced by the vertices of consists of trees and or unbalanced unicyclic signed graphs let l d g a be the laplacian of in this paper we express the coefficient of the laplacian characteristic polynomial of based on the signed tu subgraphs of and establish the relation between the laplacian characteristic polynomial of a signed graph with adjacency characteristic polynomials of its signed line graph and signed subdivision graph as an application we identify the signed unicyclic graphs having extremal coefficients of the laplacian characteristic polynomial

bias properties of budget constrained simulations this paper addresses the bias characteristics of estimators produced from monte carlo simulations if the computer time allocated to the simulation is t then nt the number of replications completed by time t is a renewal process the simulation implications of a known exact expression for the expected value of a sample mean based on nt replications are explored and a similar exact expression for a sample mean based on nt 1 replications is derived bias expansions for a sample mean based on nt or nt 1 replications are obtained the bias in the sample mean based on nt replications is at most of order o1 t under suitable moment conditions the bias decreases at a much faster rate than o1 t on the other hand the estimator based on nt 1 replications has bias of order 1 t the exact expressions also lead to simple and totally unbiased estimators using taylor series the bias expansions of a general function of means based on nt or nt 1 replications are determined the leading terms in these expansions are of order 1 t although the coefficients are different based on these expansions a tin style adjusted estimator is proposed to reduce the bias these expansions are specialized to the case of ratio estimation in regenerative simulation due to a cancellation effect the ratio estimator based on nt 1 cycles is biased only to order o1 t providing confirmation and reinterpretation of a result of m meketon and p heidelberger

on the laplacian coefficients of acyclic graphs abstract let g be a graph of order n and let g k 0 n 1 k c k n k be the characteristic polynomial of its laplacian matrix zhou and gutman recently proved that among all trees of order n the kth coefficient ck is largest when the tree is a path and is smallest for stars a new proof and a strengthening of this result is provided a relation to the wiener index is discussed

strongly nonlinear parabolic equations with natural growth terms in orlicz spaces abstract we prove approximation and compactness results in inhomogeneous orlicz sobolev spaces and look at as an application the cauchy dirichlet equation u a u g x t u u f w 1 x e m where a is a leray lions operator having a growth not necessarily of polynomial type we also give a trace result allowing to deduce the continuity of the solutions with respect to time

spectral properties of complex unit gain graphs abstract a complex unit gain graph is a graph where each orientation of an edge is given a complex unit which is the inverse of the complex unit assigned to the opposite orientation we extend some fundamental concepts from spectral graph theory to complex unit gain graphs we define the adjacency incidence and laplacian matrices and study each of them the main results of the paper are eigenvalue bounds for the adjacency and laplacian matrices

variational inequalities in orlicz sobolev spaces on etudie l existence de solutions d inegalites variationnelles associees a des operateurs differentiels elliptiques

an improved estimator of the mean for a sequential binomial sampling plan for sampling bernoulli random variables a sequential sampling plan is considered that includes inverse sampling as a special case this plan is viewed as a random walk in two dimensions in a way that gives the distribution of the sample given the endpoint of the walk thus by the rao blackwell method an unbiased estimator based on the minimal sufiicient statistic is derived for the common bernoulli probability the techniques used apply in general to unbiased estimation when sampling sequentially at least conceptually and are also applied to a second class of sequential binomial sampling plans

renormalized solutions to nonlinear parabolic problems in generalized musielak orlicz spaces abstract we will present the proof of existence of renormalized solutions to a nonlinear parabolic problem t u div a d u f with right hand side f and initial data u 0 in l 1 the growth and coercivity conditions on the monotone vector field a are prescribed by a generalized n function m which is anisotropic and inhomogeneous with respect to the space variable in particular m does not have to satisfy an upper growth bound described by a 2 condition therefore we work with generalized musielak orlicz spaces which are not necessarily reflexive moreover we provide a weak sequential stability result for a more general problem t u div a d u f u f where is a monotone function with respect to the second variable and f is locally lipschitz continuous within the proof we use truncation methods young measure techniques the integration by parts formula and monotonicity arguments which have been adapted to nonreflexive musielak orlicz spaces

adaptive cluster sampling abstract in many real world sampling situations researchers would like to be able to adaptively increase sampling effort in the vicinity of observed values that are high or otherwise interesting this article describes sampling designs in which whenever an observed value of a selected unit satisfies a condition of interest additional units are added to the sample from the neighborhood of that unit if any of these additional units satisfies the condition still more units may be added sampling designs such as these in which the selection procedure is allowed to depend on observed values of the variable of interest are in contrast to conventional designs in which the entire selection of units to be included in the sample may be determined prior to making any observations because the adaptive selection procedure introduces biases into conventional estimators several estimators are given that are design unbiased for the population mean with the adaptive cluster designs of this article that is the

unbiased estimation when sampling from renewal processes the single sample and k sample random means cases summary suppose random variables are sampled sequentially until the sum of associated nonnegative random variables is greater than or equal to a predetermined constant when no distributional assumptions are made we derive uniform minimum variance unbiased estimators for functions which are u estimable in the fixed sample size case we also consider estimation for some special cases when distributional assumptions are made when estimating the mean and variance of random means it is often assumed that sample sizes are independent of populations selected for sampling and hence independent of the random means associated with the populations sampled when sampling from renewal processes sample size is dependent on the distribution of the population selected for sampling thus in addition to the single sample case we consider the k sample problem and the estimation of the expectation and variance of random means

on the laplacian coefficients of unicyclic graphs abstract let g be a graph of order n and let p g k 0 n 1 k c k n k be the characteristic polynomial of its laplacian matrix generalizing an approach of mohar on graph transformations we show that among all connected unicyclic graphs of order n the k th coefficient c k is largest when the graph is a cycle c n and smallest when the graph is the a s n with an additional edge between two of its pendent vertices a relation to the recently established laplacian like energy of a graph is discussed

on some class of nonlinear parabolic inequalities in orlicz spaces abstract the paper deals with the existence of solutions of some unilateral problems in the framework of orlicz spaces

spectral characterizations of signed lollipop graphs abstract let g be a signed graph where g is the underlying simple graph and e g is the sign function on the edges of g in this paper we consider the spectral characterization problem extended to the adjacency matrix and laplacian matrix of signed graphs after giving some basic results we study the spectral determination of signed lollipop graphs and we show that any signed lollipop graph is determined by the spectrum of its laplacian matrix

on the signless laplacian coefficients of unicyclic graphs let g be a graph of order n and let qg x i 0n 1 ipi g xn i be the characteristic polynomial of the signless laplacian of g let eg n respectively cg sn g 1 denote the unicyclic graph of order n obtained by a coalescence of a vertex in the cycle cg with an end vertex respectively the center of the path pn g 1 respectively the star sn g 1 it is proved that for k 2 n 1 as g varies over all unicyclic graphs of order n depending on k and n the maximum value of pk g is attained at g cn or e3 n and the minimum value is attained uniquely at g c4 sn 3 or c3 sn 2 except for the resolution of a conjecture on cubic polynomials the uniqueness issue for the maximization problem is also settled