stochastic analysis of a modified first fit decreasing packing we make a stochastic analysis of a modified version mffd of first fit decreasing in which each bin is closed after it receives its first fallback item consider a probability measure on 0 1 and independent random variables x1 xn distributed according to let rn rx1 xn be the number of unit size bins that mffd needs to pack items of size x1 xn we prove that c limn ern n exists and that the random variable rn nc n converges in distribution the main tools are deterministic inequalities concerning mffd that might be of independent interest

reciprocal transformations of two component hyperbolic systems and their invariants abstract criteria for the equivalence under reciprocal transformations of two component hyperbolic systems are established in terms of reciprocal invariants these results are applied to a 1 1 dimensional isentropic gasdynamics system to determine reciprocal equivalence to the canonical system with a polytropic gas law the four parameter model pressure density relations for which this reciprocal equivalence holds are parameterized in terms of the lagrangian signal speed

operations on fuzzy ideals in this paper we give suitable definitions of the operations of l fuzzy ideals in a ring as intersection addition multiplication and residual division and we prove some fundamental properties of the operations analogous to those that hold for the operations of ordinary ideals see 3

multidimensional optimal bin packing with items of random size consider a probability measure on 0 1 d and independent random variables x 1 x n distributed according to let vn vnx 1 x n resp rn rnx 1 x n be the minimal number of unit size d dimensional bins needed to pack items of size x 1 x n in the vector packing resp rectangular packing problem for a large class of distributions we characterize v limn vn n and r limn rn n

fuzzy primary representations of fuzzy ideals abstract let r be a commutative ring with identity and let a be a fuzzy ideal of r then a is said to have a fuzzy primary representation if a is the intersection of a finite number of fuzzy primary ideals we show that every fuzzy ideal a of r such that a 0 1 has a fuzzy primary representation if and only if r is artinian we show that uniqueness properties for reduced primary representations of ideals in the usual sense carry over to fuzzy ideals

exact solutions for water infiltration with an arbitrary surface flux or nonlinear solute adsorption several authors have now used the backlund transformation to linearize richard s equation and so obtain analytical solutions for infiltration and redistribution processes for the linearizable class of diffusivities and hydraulic conductivities after transformation a convection diffusion equation is obtained to date all the analytical results making use of the backlund transform have been based on a specified constant flux that is assumed to exist at the surface boundary we generalize the previous work by removing this restriction and obtain a general solution for an arbitrary temporal variation in surface flux the solution contains a function that is specified by a volterra integral equation in practice the volterra equation must be evaluated numerically this task is accomplished using a relatively straightforward algorithm the analytical results for infiltration can be applied to the process of solute transport subject to a nonlinear adsorption isotherm since these two phenomena are equivalent under another mapping our new analytical results therefore also apply to this class of solute transport processes the general form of the adsorption isotherm for which exact results can be obtained is derived this isotherm appears capable of representing a relatively large family of physically relevant cases although this topic remains open for future investigation

on fuzzy ideals of a ring 1 abstract the aim of this paper is to study fuzzy ideals of a ring to characterise regular rings and noetherian rings by fuzzy ideals and to determine all fuzzy prime ideals of the ring z of integers

some distributions that allow perfect packing a probability distribution on 0 1 allows perfect packing if n items of size x 1 x n independent and identically distributed according to can be packed in unit size bins in such a way that the expected wasted space is o n a large class of distributions that allow perfect packing is exhibited as a corollary the intervals a b for which the uniform distribution on a b allows perfect packing are determined

fuzzy maximal radical and primary ideals of a ring we introduce the concepts of fuzzy maximal ideal the fuzzy radical of a fuzzy ideal and fuzzy primary ideal of a ring we show that a fuzzy left right ideal a of a ring r is a fuzzy maximal ideal if and only a 0 1 and a x r a x a 0 is a maximal left right ideal of r we also show that a fuzzy ideal a of a commutative ring r with unity is a fuzzy primary ideal of r if and only a 0 1 a is two valued and a is a primary ideal of r

optimal bin packing of items of sizes uniformly distributed over 0 1 consider n independent random variables uniformly distributed over 0 1 and consider the minimum number bk of unit size bins needed to pack these items under the restriction that no bin can accept more than k items we prove that eb2 eb3 is of order n but in sharp contrast we show that eb3 ebn is of a smaller order

fuzzy prime ideals of a ring abstract this paper characterizes all fuzzy prime ideals p of an arbitrary ring r we show that a nonconstant fuzzy ideal p of r is prime if and only if p0 x r p x p 0 is a prime ideal of r p is two valued and p 0 1 examples are given showing that p0 is a prime ideal is not sufficient for p to be a fuzzy prime ideal and that p0 may be a prime ideal of r with the image of p being of arbitrary finite cardinality or being countably infinite

perfect packing theorems and the average case behavior of optimal and online bin packing we consider the one dimensional bin packing problem under the discrete uniform distributions u j k 1 leq j leq k 1 in which the bin capacity is k and item sizes are chosen uniformly from the set 1 2 ldots j note that for 0 u j k leq 1 this is a discrete version of the previously studied continuous uniform distribution u 0 u where the bin capacity is 1 and item sizes are chosen uniformly from the interval 0 u we show that the average case performance of heuristics can differ substantially between the two types of distributions in particular there is an online algorithm that has constant expected wasted space under u j k for any j k with 1 leq j k 1 whereas no online algorithm can have o n 1 2 expected waste under u 0 u for any 0 u leq 1 our u j k result is an application of a general theorem of courcoubetis and weber that covers all discrete distributions under each such distribution the optimal expected waste for a random list of n items must be either theta n theta n 1 2 or o 1 depending on whether certain perfect packings exist the perfect packing theorem needed for the u j k distributions is an intriguing result of independent combinatorial interest and its proof is a cornerstone of the paper we also survey other recent results comparing the behavior of heuristics under discrete and continuous uniform distributions

fuzzy prime ideals of rings abstract the notions of fuzzy ideal and fuzzy prime ideal of a ring with truth values in a complete lattice satisfying the infinite meet distributive law are introduced which generalize the existing notions with truth values in the unit interval of real numbers a procedure to construct any fuzzy ideal from a family of ideals with certain conditions is established all fuzzy prime maximal ideals of a given ring are determined by establishing a one to one correspondence between fuzzy prime maximal ideals and the pairs p where p is a prime maximal ideal of the ring and is a prime element dual atom in the complete lattice

radicals of fuzzy ideals abstract there are several natural ways to fuzzify the concepts of prime ideal primary ideal the radical of an ideal and the primary representation of an ideal in a commutative ring in this paper we introduce some new approaches and compare them with known ones our main goal is to unify the various possible fuzzy primary representations of a fuzzy ideal to prepare the way for the study of fuzzy nonlinear systems of equations

group theoretic methods applied to burgers equation abstract in this study the group theoretic methods for calculating the solution of burgers equation with appropriate boundary and initial conditions is presented the application of a one parameter group reduces the number of independent variables by one and consequently the governing partial differential equation with the boundary and initial conditions to an ordinary differential equation with the appropriate corresponding conditions the obtained differential equation is solved analytically and the solution obtained in closed form for a specific choice of boundary condition

fuzzy ideals of artinian rings abstract the object of this paper is to study fuzzy ideals over artinian rings among others we prove that a ring with unity is left right artinian if and only if every fuzzy left right ideal of r is finite valued this gives a characterization of artinian rings in terms of fuzzy ideals mukherjee and sen 1987 proved that if every fuzzy ideal of a ring with unity is finite valued then the ring is noetherian we give an example to show that the converse of this theorem is not true we also show that certain results of pan 1987 are not true

asymptotic methods in the probabilistic analysis of sequencing and packing heuristics recently there has been considerable interest in the average case performance of heuristics this paper pursues that interest where it concerns sequencing and packing problems in particular we survey the methods that have been used to obtain formal probabilistic analyses of heuristics for makespan scheduling and one dimensional bin packing in so doing we present many of the key results in these research areas

optimal bin packing with items of random sizes iii consider a probability measure mu on 0 1 and independent random variables x 1 cdots x n distributed according to mu let q n q n x 1 cdots x n be the minimum number of unit size bins needed to pack items of size x 1 cdots x n let c mu lim n to infty e q n n in this paper it is proved that the random variable q n nc mu sqrt n converges in distribution the limit is identified as a distribution of the supremum of a certain gaussian process canonically attached to mu

fuzzy commutative algebra and intersection equations abstract in this paper we discuss the status of fuzzy commutative algebra as it applies to intersection equations we give an up to date account of the theory of nonlinear systems of intersection equations of l singletons the concept of an algebraic l variety is presented in order to bring fuzzy commutative algebra to bear on the solution of such intersection equations

analytical solution to transient richards equation with realistic water profiles for vertical infiltration and parameter estimation a general analytical model for one dimensional transient vertical infiltration is presented the model is based on a combination of the brooks and corey soil water retention function and a generalized hydraulic conductivity function this leads to power law diffusivity and convective term for which the exponents are functions of the inverse of the pore size distribution index accordingly the proposed analytical solution covers many existing realistic models in the literature the general form of the analytical solution is simple and it expresses implicitly the depth as function of water content and time it can be used to model infiltration through semi infinite dry soils with prescribed water content or flux boundary conditions some mathematical expressions of practical importance are also derived the general form solution is useful for comparison between models validation of numerical solutions and for better understanding the effect of some hydraulic parameters based on the analytical expression a complete inverse procedure which allows the estimation of the hydraulic parameters from water content measurements is presented

application of a reciprocal transformation to a two phase stefan problem a reciprocal transformation is employed to reduce a two phase stefan problem in nonlinear heat conduction to a form which admits a class of exact solutions analogous to the classical newmann solution

dual bin packing with items of random sizes given a collection of items and a number of unit size bins the dual bin packing problem requires finding the largest number of items that can be packed in these bins in our stochastic model the item sizesx1 x n are independent identically distributed according to a given probability measure denote byn n n n x1 x n the largest number of these items that can be packed in an bins where 0 a 1 is a constant we show thatb limn e n n n exists and that the random variable n n nb sqrt n converges in distribution the limit is identified as the distribution of the supremum of a certain gaussian process cannonically attached to

reciprocal auto backlund transformations invariant backlund transformations of reciprocal type are derived for a class of n 1 th order conservation laws a new auto backlund transformation for the harry dym equation is presented as a special case of the analysis

on the exactly solvable equation s_t beta s gamma 2 s_x _x alpha beta s gamma 2 s_x occurring in two phase flow in porous media the symmetry approach of fokas j math phys 21 1980 pp 1318 1325 is used to show that the most general equation of the form s t g s s xx f s s x dg ds ne 0 which is exactly solvable is equivalent to the equation s t beta s gamma 2 s x x alpha beta s gamma 2 s x this equation is then mapped to the linear heat equation through a series of backlund transformations the above result is used to solve an initial boundary value problem modeling the process of waterflooding i e the displacement of oil initially in a porous reservoir by continuously injected water

on line bin packing with items of random size consider an i i d sequence of random variables x1 xn distributed according to a given distribution on 0 1 let c be the asymptotic optimal packing ratio i e c limn etn n where tn is the minimum number of unit size bins needed to pack x1 xn we prove the existence of an on line algorithm dependent on that packs x1 xn in nc on1 2log n3 4 bins

r primary l representations of l ideals we examine the basic properties of prime l ideals primary l ideals and r radicals of l ideals where l is a completely distributive lattice we determine to what extent every l ideal has an r primary l representation