estimating the parameters of 3 p weibull distribution using particle swarm optimization the weibull distribution is used lifetime distributions in reliability engineering the estimation of the parameters of this distribution is essential maximum likelihood ml estimation is a common method for parameter estimation the working principle of ml estimation based on maximizing the likelihood function we used particle swarm optimization as parameter estimation tool in 3 p weibull weibull distribution plays an important role in failure distribution modeling in reliability studies and the estimation of its parameters is essential in the most real applications maximum likelihood ml estimation is a common method which is usually used to elaborate on the parameter estimation the maximizing likelihood function formed for the parameter estimation of a three parameter 3 p weibull distribution is a quite difficult problem hence the heuristic approaches must be used to discover good solutions particle swarm optimization pso is a population based heuristic optimization technique developed from swarm intelligence the performance of pso greatly depends on its control parameters such as inertia weight and acceleration coefficients slightly different parameter settings may direct to very different performance this paper gives a comprehensive investigation of different pso variants according to inertia weight procedures acceleration coefficients particle size and search space in the parameter estimation problem of 3 p weibull distribution three explanatory numerical examples are given to show that pso approach variants exhibit a rapid convergence to the maximum value of the likelihood function in less iteration provides accurate estimates and pso method is satisfactory for the parameter estimation of the 3 p weibull distribution

slope inequality for families of curves over surfaces in this paper we investigate the general notion of the slope for families of curves f x rightarrow y the main result is an answer to the above question when dim y 2 and we prove a lower bound for this new slope in this case over fields of any characteristic both the notion and the slope inequality are compatible with the theory for dim y 0 1 in a very natural way and this gives a strong evidence that the slope for an n fold fibration of curves f x rightarrow y may be k x y n mathrm ch n 1 f omega x y rather than the usual stability methods the whole proof of the slope inequality here is based on a completely new method using characteristic p 0 geometry a simpler version of this method yields a new proof of the slope inequality when dim y 1

surfaces of general type with p_g q 1 k 2 8 and bicanonical map of degree 2 we classify the minimal algebraic surfaces of general type with pg q 1 k 2 8 and bicanonical map of degree 2 it will turn out that they are isogenous to a product of curves i e if s is such a surface then there exist two smooth curves c f and a finite group g acting freely on c x f such that s c x f g we describe the c f and g that occur in particular the curve c is a hyperelliptic bielliptic curve of genus 3 and the bicanonical map of s is composed with the involution induced on s by r x id c x f c x f where is the hyperelliptic involution of c in this way we obtain three families of surfaces with pg q 1 k 2 8 which yield the first known examples of surfaces with these invariants we compute their dimension and we show that they are three generically smooth irreducible components of the moduli space m of surfaces with p g q 1 k 2 8 moreover we give an alternative description of these surfaces as double covers of the plane recovering a construction proposed by du val

finite hilbert stability of bi canonical curves we prove that a generic canonically or bicanonically embedded smooth curve has semistable mth hilbert points for all m 2 we also prove that a generic bicanonically embedded smooth curve has stable mth hilbert points for all m 3 in the canonical case this is accomplished by proving finite hilbert semistability of special singular curves with mathbb g m action namely the canonically embedded balanced ribbon and the canonically embedded balanced doublea2k 1 curve in the bicanonical case we prove finite hilbert stability of special hyperelliptic curves namely wiman curves finally we give examples of canonically embedded smooth curves whose mth hilbert points are non semistable for low values of m but become semistable past a definite threshold

on nonlinear weighted errors in variables parameter estimation problem in the three parameter weibull model this paper is concerned with the three parameter weibull distribution which is widely used as a model in reliability and lifetime studies in practice the weibull model parameters are not known in advance and must be estimated from a random sample difficulties in applying the method of maximum likelihood to three parameter weibull models have led to a variety of alternative approaches in the literature in this paper we consider the nonlinear weighted errors in variables eiv fitting approach as a main result two theorems on the existence of the eiv estimate are obtained an illustrative example is also included

the existence of positive solutions and oscillation of solutions of higher order difference equations with forcing terms sufficient conditions are established for the existence of positive solutions and oscilla tion of all bounded solutions of the neutral difference equation ap zn can l t qnf zn k hn n no where a is the forward difference operator azn xn l xn i and k are integers c i is a real number and qn and hn are real sequences it is also shown that some of these sufficient conditions are necemary 1998 elsevier science ltd all rights reserved

hyperelliptic szpiro inequality we generalize the classical szpiro inequality to the case of a semistable family of hyperelliptic curves we show that for a semistable symplectic lefschetz fibration of hyperelliptic curves of genus g the number n of nonseparating vanishing cycles and the number d of singular fibers satisfy the inequality n 4g 2 d

on existence of positive solutions and bounded oscillations for neutral difference equations abstract a criterion for the existence of a positive solution for the first order difference equation xn cxn m pnxn k 0 pn 0 is established results are also obtained for the oscillation and nonoscillation of solutions of a second order difference equation 2 xn cxn m pnxn k where the pn are either of constant sign or are oscillatory some of the results are sharp

severi inequality for varieties of maximal albanese dimension in this paper we prove the general severi inequality for varieties of maximal albanese dimension suppose that x is an n dimensional projective normal minimal and mathbb q gorenstein variety of general type in characteristic zero if x is of maximal albanese dimension then k n x ge 2 n chi omega x

fibred rational surfaces with extremal mordell weil lattices slope inequalities are given for fibred rational surfaces according as the clifford index of a general fibre for fibred rational surfaces of clifford index two the mordell weil lattices of maximal ranks are completely determined

existence results for special nonlinear total least squares problem in this paper we prove an existence theorem for a special nonlinear total least squares problem we show that the optimal parameters of the generalized logistic function exist in the sense of total least squares provided the data satisfy the chebyshev s inequality

oscillation theorems for forced neutral difference equations abstract some oscillation criteria are established for forced neutral difference equations of the form x n px n k q n x n f n and 2 x n px n k q n x n f n the results remain valid even when f n 0

fibered algebraic surfaces with low slope the background of this paper is the following conjecture on complex surfaces of general type let s be a smooth projective minimal surface of general type over ti with c 2 throughout the paper

oscillation of some nonlinear difference equations we investigate the oscillatory behavior of all solutions of a new class of first order nonlinear neutral difference equations several explicit oscillation criteria are established our main results are supported by illustrative examples

numerical methods for estimating parameters in nonlinear models with errors in the variables a numerically stable implementation of the gauss newton method for computing least squares estimates of parameters and variables in explicit nonlinear models with errors in the variables is proposed the algorithm uses only orthogonal transformations and exploits the special structure of the problem moreover a partially regularized marquardt like version is described that works with a reasonable overhead of arithmetic operations and storage compared to the error free case

zhang s conjecture and the effective bogomolov conjecture over function fields we prove the effective bogomolov conjecture and so the bogomolov conjecture over a function field of characteristic 0 by proving zhang s conjecture about certain invariants of metrized graphs in the function field case these conjectures were previously known to be true only for curves of good reduction for curves of genus at most 4 and a few other special cases we also either verify or improve the previous results we relate the invariants involved in zhang s conjecture to the tau constant of metrized graphs then we use and extend our previous results on the tau constant by proving another conjecture of zhang we obtain a new proof of the slope inequality for faltings heights on moduli space of curves

estimating the parameters of weibull distribution using simulated annealing algorithm weibull distribution plays an important role in failure distribution modeling in reliability studies it is a hard work to estimate the parameters of weibull distribution this distribution has three parameters but for simplicity a parameter is omitted and as a result the estimation of the others will be easily done when the three parameter distribution is of interest the estimation procedure will be quite boring maximum likelihood estimation is a good method which is usually used to elaborate on the parameter estimation the likelihood function formed for the parameter estimation of a three parameter weibull distribution is very hard to maximize many researchers have studied this maximization problem in this paper we have briefly discussed this problem and proposed a new approach based on the simulated algorithm to solve that

a second order nonlinear difference equation oscillation and asymptotic behavior discrete analogues are investigated for well known results on oscillation growth and asymptotic behavior of solutions of y q t y 0 for q t 0 and for q t 0 the analogue of atkinson s oscillation criterion is shown to be true for 2yn 1 qn yn 0 but the analogue for atkinson s nonoscillation criterion is shown to be false

oscillation theorems for neutral difference equations abstract oscillation criteria for first order difference equations of the form x n q n x n 0 and x n px n k q n x n f n are established here xn xn 1 xn is the forward difference operator 1 p is a real number and k are nonnegative integers qn fn are sequences of nonnegative real numbers and r r is continuous oscillation criteria for nonlinear difference equations of sublinear as well as superlinear type are also established

xiao s conjecture for general fibred surfaces we prove that the genus g the relative irregularity qf and the clifford index cf of a non isotrivial

the severi inequality k2 4χ for surfaces of maximal albanese dimension we prove the so called severi inequality stating that the invariants of a minimal smooth complex projective surface of maximal albanese dimension satisfy k 2 s ge4 chi s

signature of relations in mapping class groups and non holomorphic lefschetz fibrations we introduce the notion of signature for relations in mapping class groups and show that the signature of a lefschetz fibration over the 2 sphere is the sum of the signatures for basic relations contained in its monodromy combining explicit calculations of the signature cocycle with a technique of substituting positive relations we give some new examples of non holomorphic lefschetz fibrations of genus 3 4 and 5 which violate slope bounds for non hyperelliptic fibrations on algebraic surfaces of general type

relative noether inequality on fibered surfaces abstract we prove effective upper bounds on the global sections of nef line bundles of small generic degree over a fibered surface over a field of any characteristic it can be viewed as a relative version of the classical noether inequality for surfaces as a consequence we give a new proof of the slope inequality for fibered surface without using any stability method the treatment is essentially different from those of xiao cornalba harris and moriwaki we also study the geography problem of surfaces in positive characteristics and show that the severi inequality is true for surfaces of general type in positive characteristic whose albanese map is generically finite moreover the geography of surfaces with albanese fibrations is studied

on the algebraic fundamental group of surfaces with k 2 3x let s be a minimal complex surface of general type with q s 0 we prove the following statements concerning the algebraic fundamental groupalg 1 s assume that k 2 s 3 s then s has an irregularcover if and only if s has a free pencil of hyperelliptic curves of genus 3 with at least 4 double fibres if k 2 s 3 and s 1 then s has no irregularcover if k 2 3 s and s does not have any irregularcover then alg s 9 if alg s 9 then k 2 s 2 s 1

on abelian automorphism group of a surface of general type lets be a minimal surface of general type over k the canonical divisor ofs letg be an abelian automorphism group ofs ifk 2 140 then the order ofg is at most 52k 2 32 examples are also provided with an abelian automorphism group of order 12k 2 96 the automorphism groups for a complex algebraic curve of genusg 2 have been thoroughly studied by many authors including many recent ones in particular various bounds have been established for the order of such groups for example the order of the total automorphism group is 84 g 1 hu that of an abelian subgroup is 4g 4 n while the order of any automorphism is 4g 2 w see also ha it is an intriguing problem to generalise these bounds to higher dimensions for example for surfaces of general type it is well known that the automorphism groups are finite and the bound of the orders of these groups depends only on the chern numbers of the surface a in the attempts to such generalisations the order of abelian subgroups has a special importance due to jordan s theorem on group representations and its followers a bound on the order of abelian subgroups induces a bound on that of the whole automorphism group although bounds thus obtained are generally far from satisfactory in h s it is shown that for surfaces of general type the order of such an abelian subgroup is bounded by the square of the chern numbers times a constant the purpose of this article is to give a further analysis to the abelian case for surfaces of general type in proving that the order is bounded linearly by the chern numbers of the surface in good analogy with the case of curves more precisely our main result is the following

on the oscillation of solutions and existence of positive solutions of neutral difference equations abstract we obtain sufficient conditions for the oscillation of all solutions and existence of positive solutions of the neutral difference equation x n cx n m p n x n k 0 n 0 1 2 where c and p n are real numbers m and k are integers and p n m and k are nonnegative

estimating the parameters of 3 p weibull distribution through differential evolution the weibull distribution is used lifetime distributions in reliability engineering the estimation of the parameters of this distribution is essential maximum likelihood ml estimation is a common method for parameter estimation the working principle of ml estimation based on maximizing the likelihood function we used differential evolution algorithm as parameter estimation tool in 3 p weibull the weibull distribution is one of the most widely used lifetime distributions in reliability engineering and the estimation of the parameters of this distribution is essential in the most real applications maximum likelihood ml estimation is a common method which is usually used to elaborate on the parameter estimation the working principle of ml estimation method based on maximizing the established likelihood function and maximizing this function formed for the parameter estimation of a three parameter 3 p weibull distribution is a quite challenging problem in this paper this problem have been briefly discussed and an effective approach based on the differential evolution de algorithm operators is proposed in order to enhance the estimation accuracy with less system resources three explanatory numerical examples are given to show that de approach which requires significantly less cpu time and exhibits a rapid convergence to the maximum value of the likelihood function in less iterations provides accurate estimates and is satisfactory for the parameter estimation of the 3 p weibull distribution

family of curves with large unitary summand in the hodge bundle in this note we construct non isotrivial families of curves of genus g ge 2 where the rank of the unitary summand contained in the hodge bundle can be as large as 2g 1 3 and hence disprove xiao s conjecture for the unitary rank

embedded models in three parameter distributions and their estimation summary two distinct problems can arise in maximum likelihood estimation in certain threeparameter problems one problem associated with the fitting of a threshold parameter occurs if the fitted distribution has to be very positively skewed this problem is well known however there is a second and unrelated difficulty which occurs quite often in practice and which arises when the distribution is not at all skew this problem is not so well understood it is shown in this paper that within the three parameter model there is an embedded twoparameter special case which corresponds to infinite parameter values in the original model the problem arises when this embedded model is the best fit to the data the problem is shown to be easily resolved by first carrying out a check to see whether the embedded model should be fitted instead of the three parameter model formal tests for this are discussed the gamma inverse gaussian log normal and weibull distributions are examples where the problem occurs numerical examples are provided for illustration

on the gonality and the slope of a fibered surface abstract let f x b be a locally non trivial relatively minimal fibration of curves of genus g 2 we obtain a lower bound of the slope f increasing with the gonality of the general fiber of f in particular we show that f 4 provided that f is non hyperelliptic and g 16

canonical class inequality for fibred spaces we establish the canonical class inequality for families of higher dimensional projective manifolds as an application we get a new inequality between the chern numbers of threefolds x with smooth families of minimal surfaces of general type over a curve c 1 3 x 18c 3 x

total least squares fitting michaelis menten enzyme kinetic model function the michaelis menten enzyme kinetic model f x a b ax b x a b 0 is widely used in biochemistry pharmacology biology and medical research given the data p i x i y i i 1 m m 3 we consider the total least squares tls problem for the michaelis menten model we show that it is possible that the tls estimate does not exist as the main result we show that the tls estimate exists if the data satisfy some natural conditions some numerical examples are included

relative bogomolov s inequality and the cone of positive divisors on the moduli space of stable curves an interesting point of the above theorem is that even if the weak positivity of disx y e at y is a global property on y it can be derived from the local assumption the goodness of xg and the semistability of eg this gives a great advantage to our applications in order to understand the intuition underlying the theorem let us consider a simulated case namely we suppose that f x y is a smooth surface fibred over a curve and the fiber is general bogomolov s instability theorem 1 says that if e is semistable then the codimension two cycle 2rc2 e r 1 cl e 2 has nonnegative degree so if we push it down to a codimension one cycle on y then one can rephrase bogomolov s theorem as saying that the semistability of ey implies the non negativity of disx y e

a characterization of certain shimura curves in the moduli stack of abelian varieties let f x y be a semistable family of complex abelian varieties over a curve y of genus g y and smooth over the com

oscillation of first order neutral functional differential equations abstract some new sufficient conditions are obtained for oscillation of a kind of neutral differential equations these conditions improve some recent results

a new inequality on the hodge number h 1 1 of algebraic surfaces we get a new inequality on the hodge number h 1 1 s of fibred algebraic complex surfaces s which is a generalization of an inequality of beauville our inequality implies the arakelov type inequalities due to arakelov faltings viehweg and zuo respectively

global asymptotic stability in a nonlinear nonautonomous difference equation with delays abstract in this paper some sufficient conditions are obtained for the global asymptotic stability of a nonlinear nonautonomous difference equation with delays and the works in 1 and the authors 2 are generalized

on the arakelov inequality in positive characteristic in this note we generalize the arakelov inequality in positive characteristic for non isotrivial semistable families of curves of g ge 2 which are liftable to w 2 k resp w k as a consequence we give an analogue of beauville s conjecture in positive characteristic there are at least 5 singular fibers for non isotrivial semistable families of curves of g ge 2 over mathbb p 1 which are liftable to w k

on nonlinear weighted least squares estimation of bass diffusion model the bass model is one of the most well known and widely used models of first purchase demand estimation of its parameters has been approached in the literature by various techniques the focus of this paper is on a nonlinear weighted least squares fitting approach as a main result two theorems on the existence of the least squares estimate are obtained one of them gives necessary and sufficient conditions which guarantee the existence of the least squares estimate some numerical experiments are given to illustrate the efficiency of our approach

a note on maximum likelihood estimation for regression models using grouped data summary the estimation of parameters for a class of regression models using grouped or censored data is considered it is shown that with a simple reparameterization some commonly used distributions such as the normal and extreme value result in a log likelihood which is concave with respect to the transformed parameters apart from its theoretical implications for the existence and uniqueness of maximum likelihood estimates this result suggests minor changes to some commonly used algorithms for maximum likelihood estimation from grouped data two simple examples are given

generalized clifford severi inequality and the volume of irregular varieties we give a sharp lower bound for the self intersection of a nef line bundle l on an irregular variety x in terms of its continuous global sections and the albanese dimension of x which we call the generalized clifford severi inequality we also extend the result to nef vector bundles and give a slope inequality for fibered irregular varieties as a by product we obtain a lower bound for the volume of irregular varieties when x is of maximal albanese dimension the bound is vol x 2n chi omega x and it is sharp