optimal multi way number partitioning the np hard number partitioning problem is to separate a multiset s of n positive integers into k subsets such that the largest sum of the integers assigned to any subset is minimized the classic application is scheduling a set of n jobs with different runtimes on k identical machines such that the makespan the elapsed time to complete the schedule is minimized the two way number partitioning decision problem is one of the original 21 problems that richard karp proved np complete it is also one of garey and johnson s six fundamental np complete problems and the only one based on numbers this article explores algorithms for solving multi way number partitioning problems optimally we explore previous algorithms as well as our own algorithms which fall into three categories sequential number partitioning snp a branch and bound algorithm binary search improved bin completion bsibc a bin packing algorithm and cached iterative weakening ciw an iterative weakening algorithm we show experimentally that for large random numbers snp and ciw are state of the art algorithms depending on the values of n and k both algorithms outperform the previous state of the art by up to seven orders of magnitude in terms of runtime

note on numerical solution of the fredholm singular integro differential equation with cauchy kernel by using taylor series expansion and galerkin method abstract we study the paper of maleknejad and arzhang 2006 with taylor series expansion and galerkin method for fredholm singular integro differential equation with cauchy kernel we point out a basic error in the paper due to the basic error our observations reveal that generally the suggested method should not be considered for a fredholm singular integro differential equation with cauchy kernel

a survey of public key cryptosystems we give an overview of the most important public key cryptosystems and discuss the difficult task of evaluating the merit of such systems

on quadratic integral equation of fractional orders abstract we present an existence theorem for a nonlinear quadratic integral equations of fractional orders arising in the queuing theory and biology in the banach space of real functions defined and continuous on a bounded and closed interval the concept of measure of noncompactness and a fixed point theorem due to darbo are the main tool in carrying out our proof

monotonic solutions of a class of quadratic integral equations of volterra type using the technique associated with measures of noncompactness we prove the existence of monotonic solutions of a class of quadratic integral equation of volterra type in the banach space of real functions defined and continuous on a bounded and closed interval

a knapsack based probabilistic encryption scheme knapsack based cryptosystems had been viewed as the most attractive and the most promising asymmetric cryptographic algorithms for a long time due to their np completeness nature and high speed in encryption decryption unfortunately most of them are broken for the low density feature of the underlying knapsack problems in this paper we investigate a new easy compact knapsack problem and propose a novel knapsack based probabilistic public key cryptosystem in which the cipher text is non linear with the plaintext for properly chosen parameters the underlying knapsack problem enjoys a high density larger than 1 06 in the worst case hence it is secure against the low density subset sum attacks our scheme can also defeat other potential attacks such as the brute force attacks and the simultaneous diophantine approximation attack compared with previous knapsack based cryptosystems our scheme is efficient and practical

on quadratic integral equations in orlicz spaces abstract in this paper we study the quadratic integral equation of the form x t g t x t a b k t s f s x s d s several existence theorems for a e monotonic solutions in orlicz spaces are proved for strongly nonlinear functions f the presented method of the proof can be easily extended to different classes of solutions

a new approach to the theory of functional integral equations of fractional order abstract the aim of the paper is to present a new approach to the theory of functional integral equations of fractional order that approach depends on converting of the mentioned equations to the form of functional integral equations of volterra stieltjes type it turns out that the study of functional integral equations of volterra stieltjes type is more convenient and effective than the study of functional integral equations of fractional order an example illustrating our approach is also discussed

monotonic solutions of a perturbed quadratic fractional integral equation abstract we present an existence theorem for monotonic solutions of a perturbed quadratic fractional integral equation in c 0 1 the concept of a measure of noncompactness and a fixed point theorem due to darbo are the main tools in carrying out our proof finally we give an example for indicating the natural realizations of our abstract result presented in the paper

a new efficient method for cases of the singular integral equation of the first kind various cases of cauchy type singular integral equation of the first kind occur rather frequently in mathematical physics and possess very unusual properties these equations are usually difficult to solve analytically and it is required to obtain approximate solutions this paper investigates the numerical solution of various cases of cauchy type singular integral equations using reproducing kernel hilbert space rkhs method the solution u x is represented in the form of a series in the reproducing kernel space afterwards the n term approximate solution u n x is obtained and it is proved to converge to the exact solution u x the major advantage of the method is that it can produce good globally smooth approximate solutions moreover in this paper an efficient error estimation of the rkhs method is introduced finally numerical experiments show that our reproducing kernel method is efficient

solving cauchy integral equations of the first kind by the adomian decomposition method a new approach is presented to resolve cauchy integral equations of the first kind in the general case by first considering a regularized integral equation and then transforming it into a canonical form suitable for applying the adomian decomposition method adm we obtain a decomposition solution f e of the regularized integral equation and prove the convergence of our new combined method as the regularization parameter e 1 the obtained solution is shown to be a sufficiently good approximate solution for the particular cauchy integral equation the proposed method has been tested for a variety of cauchy integral equations which are particularly important in engineering applications e g airfoil design etc

contact between spheres and general surfaces abstract this work presents a mathematical model to establish the weak form and tangent operator contributions due to contact between spherical surfaces and general surfaces normal and friction components are included such as dissipative actions the main concern herein is the proper consideration of the kinematics of the spherical surface and its influence on contact forces including the appropriate description of the spherical motion by gap functions in normal and tangential directions this leads to the possibility of dealing with complex kinematics of rolling or alternating rolling sliding of the spherical surface mapping its motion on another general surface to achieve that the model is based on rotational and translational degrees of freedom used to map the motion of contacting surfaces one may employ such strategy for interactions between spheres and rigid or flexible bodies modeled using finite element meshes as examples parameterizations of rigid and flexible surfaces are proposed and used practical applications are shown with usage of beam and shell finite elements experiencing contact interactions

on a perturbed quadratic fractional integral equation of abel type we present an existence theorem for monotonic solutions of a perturbed quadratic fractional integral equation in c 0 1 our equation contains the famous chandrasekhar integral equation as a special case the concept of the measure of noncompactness related to monotonicity introduced by j banas and l olszowy and a fixed point theorem due to darbo are the main tools in carrying out our proof moreover we give an example for indicating the natural realizations of our abstract result presented in this paper

a natural lattice basis problem with applications integer lattices have numerous important applications but some of them may have been overlooked because of the common assumption that a lattice basis is part of the problem instance this paper gives an application that requires finding a basis for a lattice defined in terms of linear constraints we show how to find such a basis efficiently

numerical evaluation of two dimensional cauchy principal value integrals a twelve point cubature formula has been constructed for the numerical evaluation of two dimensional real cauchy principal value cpv integrals some particular cases of this rule have been discussed and the truncation error associated with the rules have been analysed

on a transplant operator and explicit construction of cauchy type integral representations for p analytic functions we present a new technique for explicit construction of cauchy kernels and cauchy integral representations for a class of generalized analytic functions and p analytic functions

numerical solution of systems of cauchy singular integral equations with constant coefficients abstract this paper deals with the numerical solution of a class of systems of cauchy singular integral equations with constant coefficients the proposed procedure consists of two basic steps the first one is to consider a modified problem equivalent to the original one under suitable conditions the second one is to approximate its solution by means of a vector of polynomial functions such array is constructed by applying a quadrature type method based on gaussian rules that leads to solve a determined and well conditioned linear system the convergence and stability of the method are proved in weighted l 2 spaces some numerical tests are also shown

existence of fractional integral equation with hysteresis the existence of solutions to an integral equation of fractional order with hysteresis has been established a fixed point theorem due to schauder is the main tool in carrying out our proof

solvability of a nonlinear integral equation of volterra type the aim of this paper is to investigate a class of integral equation of volterra type and its solvability in the space of continuous and bounded functions on r the main tool used in our considerations is the technique associated with measures of noncompactness

a generalization of darbo s theorem with application to the solvability of systems of integral equations in this paper we give an extension of darbo s fixed point theorem associated with measures of noncompactness and present some results on the existence of coupled fixed points for a class of condensing operators in banach spaces moreover as an application we study the problem of existence of solutions for a general system of nonlinear integral equations

on a perturbed functional integral equation of urysohn type abstract we study the existence of monotonic solutions for a perturbed functional integral equation of urysohn type in the space of lebesgue integrable functions on an unbounded interval the technique associated with measures of noncompactness in both the weak and the strong sense and the darbo fixed point are the main tool to prove our main result

convergence analysis of sinc collocation methods for nonlinear fredholm integral equations with a weakly singular kernel in this paper the efficient methods are proposed for solving nonlinear fredholm integral equations with a weakly singular kernel by using sinc approximation with the single exponential se and double exponential de transformations the methods are developed sinc approximation has considerable advantages approximation by sinc functions handles singularities in the problem and such approximations yield rapidly convergent schemes for solving the problem furthermore convergence of proposed methods is discussed by preparing the theorems which show exponential convergence and guarantee the applicability of those finally some numerical examples are presented to illustrate efficiency and accuracy of the numerical schemes

existence theorems for some quadratic integral equations using the theory of measures of noncompactness we prove a few existence theorems for some quadratic integral equations the class of quadratic integral equations considered below contains as a special case numerous integral equations encountered in the theories of radiative transfer and neutron transport and in the kinetic theory of gases in particular the well known chandrasekhar integral equation also belongs to this class

solving singular integral equations using gaussian quadrature and overdetermined system abstract gauss chebyshev quadrature and collocation at the zeros of the chebyshev polynomial of the first kind t n x and second kind u n x leads to an overdetermined system of linear algebraic equations the size of the coefficient matrix for the overdetermined system depends on the degrees of chebyshev polynomials used we show that we can get more accurate solution using t 4 n 4 x than other t n x the regularization method using generalized singular value decomposition is described and compared to gauss newton method for solving the overdetermined system of equations computational tests show that gsvd with an appropriate choice of regularization parameter gives better solution in solving singular integral equations

a digital signature scheme secure against adaptive chosen message attacks we present a digital signature scheme based on the computational difficulty of integer factorization the scheme possesses the novel property of being robust against an adaptive chosen message attack an adversary who receives signatures for messages of his choice where each message may be chosen in a way that depends on the signatures of previously chosen messages cannot later forge the signature of even a single additional message this may be somewhat surprising since in the folklore the properties of having forgery being equivalent to factoring and being invulnerable to an adaptive chosen message attack were considered to be contradictory more generally we show how to construct a signature scheme with such properties based on the existence of a claw free pair of permutations a potentially weaker assumption than the intractibility of integer factorization the new scheme is potentially practical signing and verifying signatures are reasonably fast and signatures are compact

nondecreasing solutions of a quadratic abel equation with supremum in the kernel we prove an existence theorem for a quadratic abel integral equation of the second kind with supremum in the kernel the quadratic integral equation studied below contains as a special case numerous integral equations encountered in the theory of radiative transfer and in the kinetic theory of gases we show that the singular quadratic integral equations with supremum has a monotonic solution in c 0 1 the concept of measure of noncompactness and a fixed point theorem due to darbo are the main tools in carrying out our proof

explicit solutions of cauchy singular integral equations with weighted carleman shift existence and uniqueness of solutions as well as their explicit representations are obtained for singular integral equations with weighted carleman shift which cannot be reduced to binomial boundary value problems

monotonic positive solution of a nonlinear quadratic functional integral equation abstract the existence of positive monotonic solutions in the class of continuous functions for some nonlinear quadratic integral equation have been studied in 4 5 6 7 8 here we are concerning with a nonlinear quadratic integral equation of volterra type and we shall prove the existence of at least one l 1 positive monotonic solution for that equation under caratheodory condition

an approximate numerical method for solving cauchy singular integral equations composed of multiple implicit parameter functions with unknown integral limits in contact mechanics abstract cauchy singular integral equations are widely used in physics and mathematics especially in solid contact mechanics the solution of cauchy singular integral equations composed of explicit functions has already been achieved in existing research however when dealing with the contact problem between two solid bodies with irregular surfaces described by implicit parametric functions difficulties arise when trying to solve the cauchy singular integral because it is composed of multiple implicit parameter functions moreover the integral limits are unknown and constrained by physical characteristics to solve this kind of problem an approximate calculation method with high accuracy will be provided in this paper specifically based on the quadrature method and taking the constraint function of the boundary as the convergence criterion both the integral limits satisfying the physical characteristics condition and the solution of the cauchy singular integral equations composed of multiple parameter functions can be derived by an iterative method finally five different examples are calculated using the new method and the absolute errors between the approximate values provided by the new method and the true values are analysed

existence theorems for an integral equation of the chandrasekhar h equation with perturbation abstract we prove existence of positive solutions in thaces c 0 1 and c c 0 1 of an integral equation of the chandrasekhar h equation with perturbation

solvability of a functional integral equation of fractional order in the class of functions having limits at infinity abstract a functional integral equation of fractional order is investigated in the space of real functions which are defined continuous and bounded on the real half axis using the technique of measures of noncompactness and the fixed point theorem of darbo type we prove that the equation in question has solutions in the mentioned function space moreover a suitable choice of a measure of noncompactness enables us to prove that those solutions tend to limits at infinity an example illustrating our result is also given

on a class of urysohn stieljes quadratic integral equations and their applications abstract we investigate a class of nonlinear quadratic integral equation of urysohn stieltjes type such a class contains a number of classical nonlinear quadratic integral equations such as the chandrasekhar quadratic integral equation we consider the solvability of the equations in question in the space of continuous functions under very general assumptions several particular cases of the assumed hypotheses are discussed and numerous applications are indicated

study on existence of solutions for some nonlinear functional integral equations abstract using the technique of measures of noncompactness in banach algebra we employ abstract fixed point theorems such as darbo s theorem to study the existence solution in banach algebra c 0 a for some functional integral equations which include many key integral and functional equations that arise in nonlinear analysis

mortar based frictional contact formulation for higher order interpolations using the moving friction cone abstract finite element discretizations including contact usually apply the standard nts node to segment element thus a coupling with higher order solid elements leads to inconsistencies in the transmission of contact stresses one can circumvent this using the mortar method which includes a weak projection of the contact constraints in this paper we present a penalty formulation based on the mortar concept for two dimensional large deformation frictional contact the discretization of the contact surfaces contains quadratic approximations which can be used within a quadratic approximation of the solid elements to obtain a simple and efficient matrix formulation the moving friction cone algorithm is applied

on erdelyi kober type quadratic integral equation with linear modification of the argument abstract in this paper we study the existence of solutions for a nonlinear erdelyi kober fractional quadratic integral equations with linear modification of the argument the main tool used in our considerations is the technique associated to measures of noncompactness we compare our results with the ones obtained in recent papers finally we present some examples illustrating our results

a polynomial time algorithm for breaking the basic merkle hellman cryptosystem the merkle hellman cryptosystem is one of the two major public key cryptosystems proposed so far it is shown that the basic variant of this cryptosystem in which the elements of the public key are modular multiples of a superincreasing sequence is breakable in polynomial time

existence of solutions for a class of system of functional integral equation via measure of noncompactness abstract in this paper we give some generalization of darbo s fixed point theorem related to the measure of noncompactness and present some results on the existence of coupled fixed point theorem for a special class of operators in a banach space our results generalize and extend some comparable results in the literature also as an application we study the existence of solution for a class of the system of nonlinear functional integral equations finally an example illustrating the mentioned applicability is also included

on local attractivity and asymptotic stability of solutions of a quadratic volterra integral equation the existence of solutions of a nonlinear quadratic volterra integral equation is studied in our considerations we apply the technique of measures of noncompactness in conjunction with the classical schauder fixed point principle such an approach allows us to obtain a result on the existence of solutions of an equation in question which are uniformly locally attractive or asymptotically stable

on erdelyi kober fractional urysohn volterra quadratic integral equations a very general nonlinear singular integral equation is introduced namely u f 1 u f 2 u 0 s 1 k s a u s s 1 d s 0 1 0 and 0 1 the above equation is called erdelyi kober fractional urysohn volterra quadratic integral equation the main goal is to show that the above equation has solutions in c0 1 and these solutions are nonnegative and nondecreasing on 0 1 by means of a measure of noncompactness and darbo fixed point theorem we prove our main results in the end of the paper we give an example to show that our assumptions of our abstract results are rather easy to verify

normal singular cauchy integral operators with operator valued symbols abstract in this paper we characterize a class of normal isometric coisometric unitary hyponormal singular cauchy integral operators with operator valued or matrix valued symbols on vector valued or c n valued l 2 spaces

monotonic solutions of a quadratic integral equation of volterra type abstract we study a nonlinear quadratic integral equation of volterra type in the banach space of real functions defined and continuous on a bounded and closed interval with the help of a suitable measure of noncompactness we show that the mentioned integral equation has monotonic solutions

volume integral equations for electromagnetic scattering in two dimensions we study the strongly singular volume integral equation that describes the scattering of time harmonic electromagnetic waves by a penetrable obstacle we consider the case of a cylindrical obstacle and fields invariant along the axis of the cylinder which allows the reduction to two dimensional problems with this simplification we can refine the analysis of the essential spectrum of the volume integral operator started in a previous paper costabel et al 2012 and obtain results for non smooth domains that were previously available only for smooth domains it turns out that in the transverse electric te case the magnetic contrast has no influence on the fredholm properties of the problem as a byproduct of the choice that exists between a vectorial and a scalar volume integral equation we discover new results about the symmetry of the spectrum of the double layer boundary integral operator on lipschitz domains

a nonlinear public key cryptosystem abstract a method for constructing a class of public key cryptosystems is described the method consists of composing a sequence of simple matrix transformations some linear and some nonlinear the nonlinear transformations may be as elementary as element wise squaring or cubing it should be possible to construct a variety of such codes using this basic method furthermore the implementation of these cryptosystems are generally quite simple in terms of coding and decoding

on a quadratic fractional hammerstein volterra integral equation with linear modification of the argument abstract we study the existence of monotonic solutions of a quadratic fractional hammerstein volterra integral equation with linear modification of the argument the quadratic integral equation studied below contains as a special case numerous integral equations encountered in the theory of radiative transfer and in the kinetic theory of gases we show that the quadratic fractional hammerstein volterra integral equation with linear modification of the argument has a monotonic solution in the banach space of all real functions defined and continuous on a bounded and closed interval the concept of measure of noncompactness and a fixed point theorem due to darbo are the main tools in carrying out our proof

improved cryptanalysis of a knapsack based probabilistic encryption scheme wang et al b wang q wu y hu information sciences 177 2007 proposed a knapsack based probabilistic encryption scheme with non binary coefficients which enjoys a high density larger than 1 06 in the worst case in this work we successfully attack this scheme by showing that a public key and a restriction on system parameters allow the attacker to recover a secret key in a cubic time complexity using modular equations this approach is much more efficient than the previous attack by youssef a m youssef information sciences 179 2009 in which lattice basis reductions are used recovering secret keys can be done within 4h and 4days when n 100 and 200 respectively a simple modification that helps resist known attacks is also discussed

on existence and local attractivity of solutions of a quadratic volterra integral equation of fractional order in the paper we study the existence of solutions of a nonlinear quadratic volterra integral equation of fractional order this equation is considered in the banach space of real functions defined continuous and bounded on an unbounded interval moreover we show that solutions of this integral equation are locally attractive

existence of solutions for a class of nonlinear volterra singular integral equations in this paper we prove some results concerning the existence of solutions for a large class of nonlinear volterra singular integral equations in the space c 0 1 consisting of real functions defined and continuous on the interval 0 1 the main tool used in the proof is the concept of a measure of noncompactness we also present some examples of nonlinear singular integral equations of volterra type to show the efficiency of our results moreover we compare our theory with the approach depending on the use of the theory of volterra stieltjes integral equations we also show that the results of the paper are applicable in the study of the so called fractional integral equations which are recently intensively investigated and find numerous applications in describing some real world problems

existence of solution for two dimensional nonlinear fractional integral equation by measure of noncompactness and iterative algorithm to solve it abstract in this article we establish the existence of solution for two dimensional nonlinear fractional integral equation using fixed point theorem and measure of noncompactness applicability of our results is shown by some examples and for validity of the proposed method we make an iterative algorithm by semi analytic technique that finds a closed form of the solution with an acceptable accuracy ability of the proposed method is granted by comparison with another method found in existing literature

reproducing kernel method of solving singular integral equation with cosecant kernel in the paper a reproducing kernel method of solving singular integral equations sie with cosecant kernel is proposed for solving sie difficulties lie in its singular term in order to remove singular term of sie an equivalent transformation is made compared with known investigations its advantages are that the representation of exact solution is obtained in a reproducing kernel hilbert space and accuracy in numerical computation is higher on the other hand the representation of reproducing kernel becomes simple by improving the definition of traditional inner product and requirements for image space of operators are weakened comparing with traditional reproducing kernel method the final numerical experiments illustrate the method is efficient

non injective knapsack public key cryptosystems abstract two public key 0 1 knapsack cryptosystems are proposed that have so high a density and use so weak a modular multiplication as a trapdoor that known attacks can be avoided decryption is fairly slow and may produce more than one decipherment but all alternative decipherments can be found disambiguating protocols are needed to determine the correct decipherment it is suggested to use also redundancy for this purpose in the first system the initial knapsack is constructed from the powers of two which are multiplied by a constant and reduced with respect to a modulus to a specific range thus producing the easy knapsack then weak modular multiplication is used as a trapdoor transformation with respect to another modulus which is typically smaller than some or all of the elements of the easy knapsack the second knapsack is constructed iteratively from modularly injective or nearly injective components decryption of small components is based on look up tables the specific form of the proposal uses also one large non injective component which is generated and decrypted in a way that resembles superincrease

numerical solution for system of cauchy type singular integral equations with its error analysis in complex plane abstract in this paper the problem of finding numerical solution for a system of cauchy type singular integral equations of first kind with index zero is considered the analytic solution of such system is known but it is of limited use as it is a nontrivial task to use it practically due to the presence of singularity in the known solution itself therefore a residual based galerkin method is proposed with legendre polynomials as basis functions to find its numerical solution the proposed method converts the system of cauchy type singular integral equations into a system of linear algebraic equations which can be solved easily further hadamard conditions of well posedness are established for system of cauchy singular integral equations as well as for system of linear algebraic equations which is obtained as a result of approximation of system of singular integral equations with cauchy kernel the theoretical error bound is derived which can be used to obtain any desired accuracy in the approximate solution of system of cauchy singular integral equations the derived theoretical error bound is also validated with the help of numerical examples

existence of nondecreasing solutions of a quadratic integral equation of volterra type nondecreasing solutions of the quadratic integral equations is an interesting subject in the area of mathematics sciences and engineering using the theory of measures of noncompactness and applying a new method we prove the existence of nondecreasing solutions of a quadratic integral equation of volterra type in c i

monotonic solutions of a quadratic integral equation of fractional order abstract in the paper we indicate an error made in the proof of the main result of the paper m a darwish on quadratic integral equation of fractional orders j math anal appl 311 2005 112 119 moreover we provide correct proof of a slightly modified version of the mentioned result the main tool used in our proof is the technique associated with the hausdorff measure of noncompactness

on the congruence subgroup problem determination of the metaplectic kernel let f be a global field i e either a number field or a function field in one variable over a finite field and let oo be the set of its archimedean places let g be a finite non empty set of places of f containing oo let o o denote the ring of g integers of f let a denote the ring of g adeles i e the restricted direct product of the completions f v for r eg let f be an absolutely simple simply connected subgroup of sl defined over f recall that a subgroup f of c f is an g arithmetic subgroup if fnsl n o has finite index in f as well as in o fy f c sl n o an g arithmetic subgroup f is a congruence subgroup if there exists a non zero ideal a in o o g such that

on the quadratic integral equations and their applications the class of quadratic integral equations contains as a special case numerous integral equations encountered in the theory of radiative transfer the queuing theory the kinetic theory of gases and the theory of neutron transport as a pursuit of this in the following pages sufficient conditions are given for the existence of positive continuous solutions to some possibly singular quadratic integral equations meanwhile we prove the existence of maximal and minimal solutions of our problems the method used here depends on both schauder and schauder tychonoff fixed point principles unlike all previous contributions of the same type no assumptions in terms of the measure of noncompactness were imposed on the nonlinearity of the given functions as far as we know the approach presented in this paper in particular the discussion of the existence of maximal and minimal solutions to the quadratic integral equations was never applied in the field of the quadratic integral equations and so is new

fixed point method for solving nonlinear quadratic volterra integral equations we consider a paper of banas and sadarangani 2008 11 which deals with monotonicity properties of the superposition operator and their applications an application of the monotonicity properties is to study the solvability of a quadratic volterra integral equation in this paper we prepare an efficient numerical technique based on the fixed point method and quadrature rules to approximate a solution for quadratic volterra integral equation then convergence of numerical scheme is proved by some theorems and some numerical examples are given to show applicability and accuracy of the numerical method and guarantee the theoretical results

application of jacobi polynomials to approximate solution of a singular integral equation with cauchy kernel abstract in this paper exact solution of the characteristic equation with cauchy kernel on the interval 1 1 is presented next jacobi polynomials are used to derive approximate solutions of the characteristic and general cauchy type singular integral equations moreover estimations of errors of the approximated solutions are presented and proved

quadratic compact knapsack public key cryptosystem knapsack type cryptosystems were among the first public key cryptographic schemes to be invented their np completeness nature and the high speed in encryption decryption made them very attractive however these cryptosystems were shown to be vulnerable to the low density subset sum attacks or some key recovery attacks in this paper additive knapsack type public key cryptography is reconsidered we propose a knapsack type public key cryptosystem by introducing an easy quadratic compact knapsack problem the system uses the chinese remainder theorem to disguise the easy knapsack sequence the encryption function of the system is nonlinear about the message vector under the relinearization attack model the system enjoys a high density we show that the knapsack cryptosystem is secure against the low density subset sum attacks by observing that the underlying compact knapsack problem has exponentially many solutions it is shown that the proposed cryptosystem is also secure against some brute force attacks and some known key recovery attacks including the simultaneous diophantine approximation attack and the orthogonal lattice attack

monotonicity properties of the superposition operator and their applications we establish some properties of the superposition operator which are associated with monotonicity those properties are expressed in terms of the notion of degree of decrease or degree of increase an application of the obtained results to the study of solvability of a quadratic volterra integral equation is also derived

on a measure of noncompactness in the holder space ck γ ω and its application abstract in this article based on the concept of relative compactness in the holder space c k where k 0 0 1 and is a compact subset of r n we present a new measure of noncompactness on c k moreover as an application we study the existence of solution of a nonlinear integral equation in the holder space by applying darbo fixed point theorem

nystrom method for cauchy singular integral equations with negative index in this paper the authors propose a nystrom method to approximate the solutions of cauchy singular integral equations with constant coefficients having a negative index they consider the equations in spaces of continuous functions with weighted uniform norm they prove the stability and the convergence of the method and show some numerical tests that confirm the error estimates

global existence for nonlinear operator inclusions abstract we use fixed point theory for multivalued maps to obtain general existence principles for nonlinear operator inclusions our maps are either of upper semicontinuous or lower semicontinuous type

on the concept of existence and local attractivity of solutions for some quadratic volterra integral equation of fractional order in this paper we present some results on existence of solutions for a quadratic volterra integral equation of fractional order in two independent variables this equation is considered in the banach space of real functions defined continuous and bounded on an unbounded interval moreover we show that solutions of this integral equation are locally attractive an example is provided to illustrate the theory

numerical solution of variable order fractional nonlinear quadratic integro differential equations based on the sixth kind chebyshev collocation method abstract in this paper a sixth kind chebyshev collocation method will be considered for solving a class of variable order fractional nonlinear quadratic integro differential equations v ofnqides the operational matrix of variable order fractional derivative for sixth kind chebyshev polynomials is derived and then a collocation approach is employed to reduce the v ofnqide to a system of nonlinear algebraic equations convergence analysis of the proposed method is evaluated and the rate of convergence is established finally some numerical test examples are investigated to validate the accuracy and robustness of the proposed approach

a dynamic access control scheme based upon the knapsack problem abstract a new dynamic access control scheme for information protection systems is proposed in this paper the main idea of it is inspired by the concept of the trapdoor knapsack problem proposed by merkle and hellman since the knapsack problem is an np complete problem the security of access control is achieved henceforth our scheme associates each user with some user keys and each file with some file keys there is a positive integer set of s through a simple formula on keys and s the corresponding access privilege can be easily revealed in the protection system moreover by employing our scheme insertion or deletion of the user file can be processed effectively with only a few previously defined keys and locks required to be modified

the technique of volterra stieltjes integral equations in the application to infinite systems of nonlinear integral equations of fractional orders our study in this paper concerns the infinite systems of nonlinear integral equations of volterra stieltjes type we show that some assumptions imposed on terms of the mentioned systems guarantee the solvability of those systems in the space c i c 0 with i 0 1 and c 0 being the classical sequence space as a particular and very important case of the investigated systems of nonlinear volterra stieltjes integral equations we obtain infinite systems of nonlinear integral equations of fractional orders thus the approach applied in the paper enables us to obtain rather general results concerning the existence of solutions of infinite systems of nonlinear fractional integral equations

numerical treatment of solving singular integral equations by using sinc approximations abstract in this paper we propose numerical treatment for singular integral equations the methods are developed by means of the sinc approximation with smoothing transformations such approximation is an effective technique against the singularities of the equations and achieves exponential convergence therefore the methods improve conventional results where only polynomial convergence have been reported the resulting algebraic system is solved by least squares approximation and leap frog algorithm estimation of errors of the approximate solution is presented some experimental tests are presented to show the efficient of the proposed methods

numerical solution of various cases of cauchy type singular integral equation abstract in this paper a robust but very simple numerical method is developed to solve various cases of cauchy type singular integral equation for this first bernstein polynomials are defined which are used for approximation of solution of the given singular integral equation then numerical method is introduced by using bernstein polynomials this ultimately leads to solution of a system of linear algebraic equations examples are illustrated to demonstrate simplicity of proposed method results are also compared with those present in literature to claim better efficiency of the method introduced

an unbiased nitsche s formulation of large deformation frictional contact and self contact in this paper we propose an extension of nitsche s method for frictional contact in large elastic deformations in fact we develop an unbiased strategy in which no asymmetry is considered between contact surfaces conversely to the master slave strategy this enables to take into account within the same formalism contact of two elastic bodies as well as self contact we provide a numerical study of the performance and robustness of the method

optimal quadrature formulas for cauchy type singular integrals in sobolev space in the present paper in l 2 m 1 1 space the optimal quadrature formula is constructed for approximate calculation of the cauchy type singular integral explicit formulas for the optimal coefficients are obtained

polygonal finite element methods for contact impact problems on non conformal meshes in this paper a polygonal finite element method is presented for large deformation frictionless dynamic contact impact problems with non conformal meshes the geometry and interfaces of the problem are modeled independent of the background mesh based on the level set method to produce polygonal elements at the intersection of the interface with the regular fe mesh various polygonal shape functions are employed to investigate the capability of polygonal fem technique in modeling frictionless contact impact problems the contact constraints are imposed between polygonal elements produced along the contact surface through the node to surface contact algorithm several contact impact problems are modeled using various polygonal interpolation functions including the wachspress interpolation functions the metric coordinate shape functions the natural neighbor based functions and the mean value coordinate functions to demonstrate the efficiency of proposed technique in modeling contact impact problems

cryptanalytic attacks on the multiplicative knapsack cryptosystem and on shamir s fast signature scheme the basic merkle hellman additive trapdoor knapsack public key cryptosystem was recently shown to be insecure and attacks have also been developed on stronger variants of it such as the graham shamir system and the iterated knapsack cryptosystem it is shown that some simple variants of another merkle hellman system the multiplicative knapsack cryptosystem are insecure it is also shown that the shamir fast signature scheme can be broken quickly similar attacks can also be used to break the schobi massey authentication scheme these attacks have not been rigorously proved to succeed but heuristic arguments and empirical evidence indicate that they work on systems of practical size

solvability of volterra stieltjes operator integral equations and their applications abstract we investigate a class of operator integral equations of volterra stieltjes type and we study the solvability of those equations in the space of continuous functions equations in question create a generalization of numerous integral equations considered in nonlinear analysis the main tool used in our considerations is the technique associated with measures of noncompactness we show the applicability of our existence result in the study of a few integral equations of volterra type

boundedly connected sets and the distance to the intersection of two sets abstract we prove that if x d is a metric space c is a closed subset of x and x x then the distance of x to r s agrees with the maximum of the distances of x to r and s for every closed subsets r s c such that c r s if and only if c is x boundedly connected