boundary integral equations for the scattering of electromagnetic waves by a homogeneous chiral obstacle the time harmonic scattering of electromagnetic waves by a homogeneous chiral media are considered herein the scattering problem is reduced using bohren s decomposition to an equivalent boundary integral equation which is shown to be uniquely solvable except for a discrete set of values of electromagnetic parameters of the scatterer it should be noted that the boundary integral operators appearing in this equation are the same as for a dielectric scatterer and hence their mapping properties are well known

a relaxation method for constructing a beltrami flow in a bounded domain it is shown that a time dependent equation generates a beltrami flow or a force free field at time t from non beltrami initial data in an arbitrary bounded domain in three dimensions the generated beltrami flow has a zero normal component on the boundary and its helicity is equal to a prescribed value the existence and uniqueness of a solution to the equation are guaranteed globally in time and no finite time singularity occurs

on the vanishing viscosity limit for the 3d navier stokes equations with a slip boundary condition where and below and denote the div and curl operators respectively n is the outward normal and is the unit tangential vector of the investigation of vanishing viscosity limit of solutions of the navier stokes equations both in the two and three spacial dimensional cases is a classical issue there are two related questions arising from here one is how to describe the inviscid limiting behavior of the navier stokes equation and the other is that does the euler equation can be approximated by the navier stokes equations in the case that the solution to the this research is supported in part by zheng ge ru foundation and hong kong rgc earmarked research grants cuhk 4028 04p cuhk 4040 02p and cuhk 4279 00p

low frequency behavior of solutions to electromagnetic scattering problems in chiral media this paper deals with the low frequency scattering problem by a conducting object in a chiral medium using boundary integral equation methods we obtain the limit of the scattered field solution of the drude born fedorov equations as frequency tends to zero making use of a hodge decomposition of the tangent fields shows that the asymptotics strongly depend on the topological properties of the domains under consideration the asymptotic expansion s dependence on the chirality parameter is shown completely

on linear volterra equations in banach spaces abstract in this paper we present the basic theory for a class of volterra differential integral equations of convolution type in banach spaces we show that existence of resolvent operator for such an equation is equivalent to its wellposedness and we obtain a hille yosida theorem unfortunately this result is not easy to apply and therefore it is important to have peturbation theorems available we present a result of this type which also contains an existence theorem and show by means of several examples that it cannot be improved

approximate controllability results for analytic resolvent integro differential inclusions in hilbert spaces abstractin this work we consider a nonlinear resolvent integro differential evolution inclusions in hilbert spaces this paper deals with the approximate controllability for nonlinear resolvent integro differential inclusions in hilbert spaces we use bohnenblust karlin s fixed point theorem to establish a set of sufficient conditions for the approximate controllability for nonlinear resolvent integro differential inclusions in hilbert spaces further we extend the result to study the approximate controllability concept with non local conditions an example is presented to demonstrate the obtained theory

on a selfadjoint realization of curl in exterior domains the first order vectorial operator curl occurs in many areas of applications e g in electrodynamics fluid mechanics hydrodynamics magnetohydrodynamics and elasticity theory it is the purpose of this note to discuss a particular instance of curl where a domain can be given to curl so that it becomes a selfadjoint operator the particular domain of selfadjointness under consideration is singled out by its relevance in applications to establish this operator we initially consider curl as an operator curl c read restricted to in l2 defined by curl c c l2 l2 0 1

helicity is the only integral invariant of volume preserving transformations we prove that any regular integral invariant of volume preserving transformations is equivalent to the helicity specifically given a functional i defined on exact divergence free vector fields of class c 1 on a compact 3 manifold that is associated with a well behaved integral kernel we prove that i is invariant under arbitrary volume preserving diffeomorphisms if and only if it is a function of the helicity

asymptotic massey products induced currents and borromean torus links we introduce a class of currents which allows a new and very explicit form for the massey product of a third order link as a line integral the explicit form permits the introduction of an asymptotic massey product analogous to that introduced previously for gauss s integral by v arnold the average third order asymptotic massey product is shown to be equal to berger s third order helicity for divergence free vector fields in linked tori

a new description of force free magnetic fields the moses curl eigenfunctions are used to describe linear force free magnetic fields enabling a proof that such fields are defined entirely by the value of their curl transform on the unit hemisphere in transform space this change of viewpoint suggests an orderly approach to the exploration and classification of the properties of such fields which is briefly sketched the simplest force free fields defined on zero one and two dimensional sets on the transform sphere are exhibited and the possibility of fields with fractal support sets suggested connections with other mathematical descriptions are pointed out as well as several promising directions for further exploration all results apply equally well to the description of the trkalian subset of beltrami fields in fluid dynamics

time domain green dyadics for temporally dispersive bi isotropic media time domain green dyadics for linear homogeneous temporally dispersive bi isotropic media are presented a complex time dependent electromagnetic field is introduced approximation to the complex field from an electric point dipole in an unbounded bi isotropic medium with respect to the slowly varying components second forerunner approximation is obtained numerical examples are presented surface integral equations for the tangential components of the electromagnetic fields are derived for two standard scattering problems

optimal linear combinations of multiple diagnostic biomarkers based on youden index in practice usually multiple biomarkers are measured on the same subject for disease diagnosis combining these biomarkers into a single score could improve diagnostic accuracy many researchers have addressed the problem of finding the optimal linear combination based on maximizing the area under roc curve auc actually such combined score might have less than optimal property at the diagnostic threshold in this paper we propose the idea of using youden index as an objective function for searching the optimal linear combination the combined score directly achieves the maximum overall correct classification rate at the diagnostic threshold corresponding to youden index in other words it is the optimal linear combination score for making the disease diagnosis we present both empirical and numerical searching methods for the optimal linear combination we carry out extensive simulation study to investigate the performance of the proposed methods additionally we empirically compare the optimal overall classification rates between the proposed combination based on youden index and the traditional one based on auc and demonstrate a significant gain in diagnostic accuracy for the proposed combination in the end we apply the proposed methods to a real data set

existence of knotted vortex tubes in steady euler flows we prove the existence of knotted and linked thin vortex tubes for steady solutions to the incompressible euler equation in mathbb r 3 more precisely given a finite collection of possibly linked and knotted disjoint thin tubes in mathbb r 3 we show that they can be transformed with a c m small diffeomorphism into a set of vortex tubes of a beltrami field that tends to zero at infinity the structure of the vortex lines in the tubes is extremely rich presenting a positive measure set of invariant tori and infinitely many periodic vortex lines the problem of the existence of steady knotted thin vortex tubes can be traced back to lord kelvin

on single integral equations for the transmission problem of acoustics the transmission problem namely scattering of time harmonic waves in a compressible fluid by a fluid inclusion with different material properties is usually formulated as a pair of coupled boundary integral equations over the interface s between the inclusion and the exterior fluid in this paper however we consider methods for solving the transmission problem using a single integral equation over s for a single unknown function in fact we derive four different integral equations using a hybrid of the direct green s theorem and indirect layer ansatz methods and give conditions for the unique solvability of each and for the subsequent construction of the solution to the transmission problem some of our single integral equations are fredholm integral equations of the second kind with weakly singular kernels thus these equations all of which appear to be new are attractive computationally

a priori estimates for a singular limit approximation of the constitutive laws for chiral media in the time domain abstract the equations for the evolution of electromagnetic fields in chiral media in the time domain are nonlocal in time in this work we study the validity of a singular limit local in time approximation for these nonlocal in time equations by estimating the size of the difference of the fields as predicted by both models in particular we establish an a priori estimate for this difference depending on the time horizon properties of the domain spatial properties of the initial data and the source terms and the chirality measure of the approximating model

optimal combinations of diagnostic tests based on auc summary when several diagnostic tests are available one can combine them to achieve better diagnostic accuracy this article considers the optimal linear combination that maximizes the area under the receiver operating characteristic curve auc the estimates of the combination s coefficients can be obtained via a nonparametric procedure however for estimating the auc associated with the estimated coefficients the apparent estimation by re substitution is too optimistic to adjust for the upward bias several methods are proposed among them the cross validation approach is especially advocated and an approximated cross validation is developed to reduce the computational cost furthermore these proposed methods can be applied for variable selection to select important diagnostic tests the proposed methods are examined through simulation studies and applications to three real examples

eigenfunctions of the curl operator in spherical coordinates the eigenfunctions of the curl operator are obtained by separation of variables in spherical coordinates making use of the spin weighted spherical harmonics it is shown that the eigenfunctions of the curl operator with vanishing divergence can be written in terms of a single scalar potential that satisfies the helmholtz equation it is also shown that these eigenfunctions give a complete basis for the divergenceless vector fields

strongly elliptic boundary integral equations for electromagnetic transmission problems we study a boundary integral equation method for transmission problems for strongly elliptic differential operators which yields a strongly elliptic system of pseudodifferential operators and which therefore can be used for numerical computations with galerkin s procedure the method is shown to work for the vector helmholtz equation in 3 with electromagnetic transmission conditions we propose a slightly modified system of boundary values in order for the corresponding bilinear form to be coercive over h 1 we analyse the boundary integral equations using the calculus of pseudodifferential operators here the concept of the principal symbol is used to derive existence and regularity results for the solution

eigenfunctions of the curl in cylindrical geometry eigenfunctions of the equation b b are found for finite cylindrical geometry with normal boundary condition b n 0 and nonaxisymmetric modes eim m 0 the vector field b can be represented by a scalar generating function of the chandrasekhar kendall type with radial bessel functions for the nondegenerate cases a general set of solutions can also be generated by transformation of variables a series solution in terms of radial bessel functions is found which has excellent convergence properties an 1 n4 and a robust method of locating eigenvalues is described

asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal initial conditions abstract of concern is a class of abstract semilinear integrodifferential equations with nonlocal initial conditions under some suitable hypotheses we establish some new theorems about the existence of asymptotically almost automorphic solutions to the integrodifferential equations moreover an example is given to illustrate our results

exponential stabilization of volterra integrodifferential equations in hilbert space we consider exponential stabilization of an abstract linear volterra integrodifferential equation in a hilbert space u e1au t e2 01k t s au s ds f t by a feedback control f t c0u t c1u t with bounded linear operators c0 and c1 of finite rank a is a positive semidefinite self adjoint unbounded operator k is nonnegative convex and decreasing with exponential decay k 0 being finite we introduce a concept of essential growth rate for resolvent operators similar to that for c0 semigroups and prove that the resolvent for the volterra equation has the same essential growth as the solution semigroup to u t e1au t e2k 0 e1u t f t stability can be checked by the location of poles and it is shown that exponential stabilization is possible with a decay rate of at most e2k 0 2e1 we apply our results to two problems concerning stabilization of motion of viscoelastic bodies

on the representation of inhomogeneous linear force free fields it is shown that there is a false assumption hidden in the description of a relaxed state with inhomogeneous boundary conditions as the vector sum of a potential field satisfying the boundary conditions and a sum of eigenfunctions of the associated eigenvalue problem expanded by certain coefficients in particular although the jensen and chu formula 1984 can provide the correct expansion coefficients it contains an implicit paradox in its derivation according to a general vector theorem the same paradox led chu et al 1999 to be concerned about a contradiction obtained by taking the curl of their magnetic field expansion which if permitted becomes inconsistent with a current normal to the surface the assumption that the curl can be commuted across an infinite sum of terms is the mechanism leading to these apparently paradoxical conclusions two mechanisms for resolving this apparent paradox are possible one of which will be described in some detail below and the other discussed further in a forthcoming more theoretical paper laurence et al 2000 the decomposition of the magnetic field above is valid with convergence in the mean squared sense but a decomposition of the current needs to be reinterpreted in terms of negative sobolev spaces to avoid this and remain in a more easily managable and familiar setting we derive the expansion coefficients in a way that involves the commuting of the inverse curl as opposed to the curl and the series the resulting series converges in a mean square sense when this is done the calculation can conform to the general vector theorem and a new gauge invariant expression for the coefficients is obtained however the consequence of the non commutability is nullified in the jensen and chu formula in both simply and multiply connected domains by the important extra requirement of a boundary condition on the vector potential eigenfunctions this excludes magnetic field eigenfunctions that carry flux but there remains a complete set for the expansion and all flux is carried by the potential field the two formulas are then identical on a different issue it is shown that if the general expansion is taken over a half space by combining positive and negative eigenvalue terms then the coefficients are anisotropic that is they are tensors except when evaluated at the first eigenvalue a specific example is presented to illustrate the situation and to validate the new method of deriving the coefficients

regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions the boundary integral equations bies in their original forms which govern the electromagnetic em wave scattering in three dimensional space contain at least a hypersingularity 1 r sup 3 or a cauchy singularity 1 r sup 2 usually both thus obtaining reliable numerical solutions using such equations requires considerable care especially when developing systematic numerical integration procedures for realistic problems regularized bies for the numerical computation of time harmonic em scattering fields due to arbitrarily shaped scatterers are introduced two regularization approaches utilizing an isolation method plus a mapping are presented to remove all singularities prior to numerical integration both approaches differ from all existing approaches to em scattering problems both work for integral equations initially containing either hypersingularities or cauchy singularities without the need to introduce surface divergences or other derivatives of the em fields on the boundary also neither approach is limited to flat surfaces nor flat element models of curved surfaces the muller linear combination of the electric and magnetic field integral equations efie and mfie is used to avoid the resonance difficulty that is usually associated with integral equation based formulations some preliminary numerical results for em scattering due to single and multiple dielectric spheres are presented and compared with analytical solutions

hyperbolic singular perturbations for integrodifferential equations we study the convergence of solutions email protected 2u t e u t e e 2a b u t e email protected 0 tk t s e 2a b u s e ds f t e t 0 u 0 e u 0 e u 0 e u 1 e to solutions ofw t bw t email protected 0 tk t s bw s ds f t t 0 w 0 w 0 when e 0 here a and b are linear unbounded operators in a banach space x k t is a linear bounded operator for each t 0 in x and f t e and f t are given x valued functions our result extends the studies in fattorini j diff eq 70 1987 1 for equations without the integral term and in liu proc am math soc 122 1994 791 for parabolic singular perturbation problems

optimal differential energy watermarking of dct encoded images and video this paper proposes the differential energy watermarking dew algorithm for jpeg mpeg streams the dew algorithm embeds label bits by selectively discarding high frequency discrete cosine transform dct coefficients in certain image regions the performance of the proposed watermarking algorithm is evaluated by the robustness of the watermark the size of the watermark and the visual degradation the watermark introduces these performance factors are controlled by three parameters namely the maximal coarseness of the quantizer used in pre encoding the number of dct blocks used to embed a single watermark bit and the lowest dct coefficient that we permit to be discarded we follow a rigorous approach to optimizing the performance and choosing the correct parameter settings by developing a statistical model for the watermarking algorithm using this model we can derive the probability that a label bit cannot be embedded the resulting model can be used for instance for maximizing the robustness against re encoding and for selecting adequate error correcting codes for the label bit string

cryptanalysis of optimal differential energy watermarking dew and a modified robust scheme this work presents a cryptanalytic methodology of the well known optimal differential energy watermarking dew scheme the dew scheme divides the image into some disjoint regions each region containing two subregions in the dew scheme the watermark is a secret binary string where each individual bit information gets inserted in one of the regions by modifying the high frequency discrete cosine transform dct coefficients this modification creates a required energy difference between two subregions we modify these high frequency components so that this energy difference vanishes and in turn extraction of the watermark signal becomes impossible making the cryptanalysis successful further we improve the dew scheme by inserting the watermark information in low frequency components instead of high frequency components and propose an oblivious robust watermarking strategy that enables forensic tracking we present statistical justification toward the robustness of our modified scheme

linear combinations of multiple diagnostic markers abstract the receiver operating characteristic roc curve is a simple and meaningful measure to assess the usefulness of diagnostic markers to use the information carried by multiple markers we note that fisher s linear discriminant function provides a linear combination of markers to maximize the sensitivity over the entire specificity range uniformly under the multivariate normal distribution model with proportional covariance matrices with no restriction on covariance matrices we also provide a solution of the best linear combination of markers in the sense that the area under the roc curve of this combination is maximized among all possible linear combinations we illustrate both situations discussed in the article with a cancer clinical trial data

on state dependent delay partial neutral functional integro differential equations in this paper the existence of mild solutions for a class of abstract neutral integro differential equations with state dependent delay is studied

eigenfunctions of the curl in annular cylindrical and rectangular geometry a method for determining the eigenfunctions of the equation b b for finite cylindrical geometry with normal boundary condition b n 0 and nonaxisymmetric modes eim m 0 was given by morse j math phys 46 113511 2005 this method uses series solution of a chandrasekhar kendall astrophys j 126 157 1957 function here this method is generalized to include annular coaxial cylindrical geometry of finite length the method is also applied to the case of rectangular duct geometry with periodic z dependence for slender aspect ratios in the annular cylinder the eigenfunctions and eigenfields correspond to the rectangular duct the eigenfunctions for finite length rectangular boxes can also be obtained from the rectangular duct case the robust convergence properties an 1 n4 and simple eigenvalue equations from morse are retained in these other geometries

electromagnetic scattering by a homogeneous chiral obstacle boundary integral equations and low chirality approximations time harmonic electromagnetic waves are scattered by a homogeneous chiral obstacle the corresponding transmission problem is reduced to a pair of coupled integral equations over s where s is the interface between the obstacle and the surrounding medium this is done using a generalization of the stratton chu representation that is valid for chiral media the integral equations obtained are a generalization of those obtained by muller for a homogeneous dielectric obstacle finally we develop approximations for low chirality obstacles these approximations can be computed using simple modifications to existing codes for solving muller s equations

transient wave propagation in reciprocal bi isotropic media at oblique incidence in this paper a new wave splitting is suggested that simplifies the analysis of wave propagation in reciprocal bi isotropic media two different methods to solve the scattering problem are analyzed the invariant imbedding and the green function approach the medium is modeled by constitutive relations in the time domain time convolutions and the slab is assumed to be inhomogeneous with respect to the depth it is shown that the cross polarized contribution to the reflected field at normal incidence is zero for the general reciprocal inhomogeneous slab moreover the rotation and the attenuation of the wave front are calculated explicitly in the general inhomogeneous slab case special attention is paid to normal incidence and to the homogeneous semi infinite medium

nonlocal cauchy problem for analytic resolvent integrodifferential equations in banach spaces abstract in this paper we prove the existence of semi classical and mild solutions of nonlinear integrodifferential equations with nonlocal conditions in banach spaces the results are obtained by using the theory of analytic resolvents and schaefer s fixed point theorem

local representation and construction of beltrami fields ii solenoidal beltrami fields and ideal mhd equilibria abstract object of the present paper is the local theory of solution for steady ideal euler flows and ideal mhd equilibria the present analysis relies on the lie darboux theorem of differential geometry and the local theory of representation and construction of beltrami fields developed in sato and yamada 2019 a theorem for the construction of harmonic orthogonal coordinates is proved using such coordinates families of solenoidal beltrami fields with different topologies are obtained in analytic form existence of global solenoidal beltrami fields satisfying prescribed boundary conditions while preserving the local representation is considered it is shown that only singular solutions are admissible an explicit example is given in a spherical domain and a theorem on existence of singular solutions is proven local conditions for existence of solutions and local representation theorems are derived for generalized beltrami fields ideal mhd equilibria and general steady ideal euler flows the theory is applied to construct analytic examples

helical bifurcation and tearing mode in a plasma a description based on casimir foliation the relation between the helical bifurcation of a taylor relaxed state a beltrami equilibrium and a tearing mode is analyzed in a hamiltonian framework invoking an eulerian representation of the hamiltonian the symplectic operator defining a poisson bracket becomes non canonical i e the symplectic operator has a nontrivial cokernel dual to its nullspace foliating the phase space into level sets of casimir invariants a taylor relaxed state is an equilibrium point on a casimir helicity leaf changing the helicity equilibrium points may bifurcate to produce helical relaxed states a necessary and sufficient condition for bifurcation is derived tearing yields a helical perturbation on an unstable equilibrium producing a helical structure approximately similar to a helical relaxed state a slight discrepancy found between the helically bifurcated relaxed state and the linear tearing mode viewed as a perturbed singular equilibrium state is attributed to a casimir element named helical flux pertinent to a resonance singularity of the non canonical symplectic operator while the helical bifurcation can occur at discrete eigenvalues of the beltrami parameter the tearing mode being a singular eigenfunction exists for an arbitrary beltrami parameter bifurcated beltrami equilibria appearing on the same helicity leaf are isolated by the helical flux casimir foliation the obstacle preventing the tearing mode to develop in the ideal limit turns out to be the shielding current sheet on the resonant surface preventing the release of the potential energy when this current is dissipated by resistivity reconnection is allowed and tearing instability occurs the criterion for linear tearing instability of beltrami equilibria is shown to be directly related to the spectrum of the curl operator

eigenfunction expansions associated with the curl derivatives in cylindrical geometries completeness of chandrasekhar kendall eigenfunctions eigenfunctions of the curl derivatives are used in many different fields of theoretical physics for example in plasma physics an eigenfunction of curl represents a certain eigenstate of a plasma that has the force free property the present theory proves that the spectral resolution of the curl operator gives a complete eigenfunction expansion of a solenoidal vector field with homogeneous boundary and flux conditions useful decomposition theories and a previous abstract result math z 204 235 1990 are concisely summarized explicit eigenfunctions have been studied in cylindrical geometries chandrasekhar kendall functions astrophys j 126 457 1957 which are eigenfunctions of the curl derivatives in a cylindrical domain give an orthogonal complete basis of the hilbert space that is the orthogonal complement of the space of irrotational vector fields

on markovian kinetic equations zubarev s nonequilibrium statistical operator approach abstract generalized markovian kinetic equations obtained by the zubarev method of the nonequilibrium statistical operator nso are revised in a simple example of the spin s 1 2 coupled to its surroundings it is shown that these equations are incorrect because of an inadequate markovian approximation a correct procedure of building markovian equations of motion is constructed two different although equivalent methods the davies technique and the krylov bogoliubov mitropolsky averaging method are utilized

time dependent potential scattering in chiral media electromagnetic waves propagating in a homogeneous three dimensional unbounded chiral medium are considered we define a chiral operator and study potential scattering relative to this operator a spectral analysis of associated operators is obtained based on the plancherel theory of the fourier transform using the generalised eigenfunction expansion theory we give an integral representation of the solution a discussion of asymptotic equality of solutions is provided and the associated wave operator introduced

a special class in vanishing helicity ideal flows the derivation of a lagrangian invariant so called spirality is reviewed through the lagrangian coordinates the value of the spirality is fixed up to a gauge transformation the helicity conservation follows directly from this invariant among all ideal flows with zero helicity in a domain of flow frozen into the fluid motion a special class is introduced this special topological class has the possibility to transform its spirality to be identically zero everywhere in the domain for those simply connected domains of motion a necessary and a sufficient condition is presented for these zero spirality flows

combining multiple biomarkers linearly to maximize the partial area under the roc curve it is now common in clinical practice to make clinical decisions based on combinations of multiple biomarkers in this paper we propose new approaches for combining multiple biomarkers linearly to maximize the partial area under the receiver operating characteristic curve pauc the parametric and nonparametric methods that have been developed for this purpose have limitations when the biomarker values for populations with and without a given disease follow a multivariate normal distribution it is easy to implement our proposed parametric approach which adopts an alternative analytic expression of the pauc when normality assumptions are violated a kernel based approach is presented which handles multiple biomarkers simultaneously we evaluated the proposed as well as existing methods through simulations and discovered that when the covariance matrices for the disease and nondisease samples are disproportional traditional methods such as the logistic regression are more likely to fail to maximize the pauc while the proposed methods are more robust the proposed approaches are illustrated through application to a prostate cancer data set and a rank based leave one out cross validation procedure is proposed to obtain a realistic estimate of the pauc when there is no independent validation set available

on a quaternionic maxwell equation for the time dependent electromagnetic field in a chiral medium maxwell s equations for the time dependent electromagnetic field in a homogeneous chiral medium are reduced to a single quaternionic equation its fundamental solution satisfying the causality principle is obtained which allows us to solve the time dependent chiral maxwell system with sources

resolvent operators for integral equations in a banach space conditions are given which ensure the existence of a resolvent operator for an integrodifferential equation in a banach space the resolvent operator is similar to an evolution operator for nonautonomous differential equations in a banach space as in the finite dimensional case this operator is used to obtain a variation of parameters formula which can be used to obtain results concerning the asymptotic behaviour of solutions and weak solutions

existence and regularity for a class of integrodifferential equations of parabolic type the method we use rests on the inversion of the formal laplace transform of r and allows one to analyze the regularity of the solution u problem 1 1 has been studied by several authors using various methods see for instance l 18 211 the laplace transform approach presented here has been used in s 7 9 14 153 in our previous papers s 7 93 we have in fact analyzed a more general situation while here we take full 36 0022 247x 85 3 00

numerical computation of the helical chandrasekhar kendall modes a new formulation is presented for numerically computing the helical chandrasekhar kendall modes in an axisymmetric torus it explicitly imposes b 0 and yields a standard matrix eigenvalue problem which can then be solved by standard matrix eigenvalue techniques numerical implementation and computational results are shown for an axisymmetric torus typical of reversed field pinch and spherical tokamak

on the statistical analysis of roc curves we introduce a new accuracy index for receiver operating characteristic roc curves namely the partial area under the binormal roc graph over any specified region of interest we propose a simple but general procedure based on a conventional analysis of variance for comparing accuracy indices derived from two or more different modalities the proposed method is related to and compared with existing methodology and is illustrated by results from an experiment on optimization of density and contrast yielded by multiform photographic images used for scintigraphy

estimating the error rate of a prediction rule improvement on cross validation abstract we construct a prediction rule on the basis of some data and then wish to estimate the error rate of this rule in classifying future observations cross validation provides a nearly unbiased estimate using only the original data cross validation turns out to be related closely to the bootstrap estimate of the error rate this article has two purposes to understand better the theoretical basis of the prediction problem and to investigate some related estimators which seem to offer considerably improved estimation in small samples

quaternionic factorization of the schrodinger operator and its applications to some first order systems of mathematical physics we show that an ample class of physically meaningful partial differential systems of first order such as the dirac equation with different one component potentials static maxwell s system and the system describing the force free magnetic fields are equivalent to a single quaternionic equation which in its turn reduces in general to a schrodinger equation with quaternionic potential and in some situations this last can be diagonalized the rich variety of methods developed for different problems corresponding to the schrodinger equation can be applied to the systems considered in the present work

positivity and regularity of hyperbolic volterra equations in banach spaces soit x un espace de banach a un operateur lineaire clos non borne dans x a domaine dense d a a l loc 1 r f c j x avec j 0 t et on considere l equation de volterra de type scalaire u t f t 0 t a t au d t j on etudie l existence la positivite la regularite et la compacite ainsi que l integrabilite de l operateur resolvant s t defini par s t x x 0 t a t as xd t 0 x d a pour deux classes particulieres de noyaux a et d operateurs a

combining predictors for classification using the area under the receiver operating characteristic curve no single biomarker for cancer is considered adequately sensitive and specific for cancer screening it is expected that the results of multiple markers will need to be combined in order to yield adequately accurate classification typically the objective function that is optimized for combining markers is the likelihood function in this article we consider an alternative objective function the area under the empirical receiver operating characteristic curve auc we note that it yields consistent estimates of parameters in a generalized linear model for the risk score but does not require specifying the link function like logistic regression it yields consistent estimation with case control or cohort data simulation studies suggest that auc based classification scores have performance comparable with logistic likelihood based scores when the logistic regression model holds analysis of data from a proteomics biomarker study shows that performance can be far superior to logistic regression derived scores when the logistic regression model does not hold model fitting by maximizing the auc rather than the likelihood should be considered when the goal is to derive a marker combination score for classification or prediction

an exterior boundary value problem for the maxwell equations with boundary data in a sobolev space we treat the time harmonic maxwell equations in an exterior domain with prescribed boundary data n e in the sobolev space of square integrable tangential fields with square integrable surface divergence by using boundary integral equation methods existence and uniqueness results are established furthermore we investigate the completeness of electric and magnetic dipoles distributed on an inner surface in this sobolev space

combining several screening tests optimality of the risk score the development of biomarkers for cancer screening is an active area of research while several biomarkers exist none is sufficiently sensitive and specific on its own for population screening it is likely that successful screening programs will require combinations of multiple markers we consider how to combine multiple disease markers for optimal performance of a screening program we show that the risk score defined as the probability of disease given data on multiple markers is the optimal function in the sense that the receiver operating characteristic roc curve is maximized at every point arguments draw on the neyman pearson lemma this contrasts with the corresponding optimality result of classic decision theory which is set in a bayesian framework and is based on minimizing an expected loss function associated with decision errors ours is an optimality result defined from a strictly frequentist point of view and does not rely on the notion of associating costs with misclassifications the implication for data analysis is that binary regression methods can be used to yield appropriate relative weightings of different biomarkers at least in large samples we propose some modifications to standard binary regression methods for application to the disease screening problem a flexible biologically motivated simulation model for cancer biomarkers is presented and we evaluate our methods by application to it an application to real data concerning two ovarian cancer biomarkers is also presented our results are equally relevant to the more general medical diagnostic testing problem where results of multiple tests or predictors are combined to yield a composite diagnostic test moreover our methods justify the development of clinical prediction scores based on binary regression

on the existence of force free magnetic fields with small nonconstant α in exterior domains the existence of force free magnetic fields in the exterior domain of some compact simply connected surface s is proved via an iteration scheme the iteration starts with an arbitrary exterior vacuum field which contains flux tubes originating and ending on s at one cross section of such a flux tube with s an arbitrary function is prescribed for small values of in the holder norm 1 0 1 the iteration is shown to converge to a force free field with the prescribed values of in a flux tube which is close to the vacuum flux tube and 0 outside the force free field is close in the holder norm 1 to the starting vacuum field in particular it has the same field line topology the same boundary values on s and satisfies the same decay conditions in spatial infinity it is in general three dimensional and requires no continuous symmetries

moduli spaces of vortex knots for an exact fluid flow the moduli spaces s d of non isotopic vortex knots are introduced for the ideal fluid flows in invariant domains d the analogous moduli spaces of the magnetic fields b knots are defined we derive and investigate new exact fluid flows and analogous plasma equilibria satisfying the beltrami equation which have nested invariant balls b k 3 with radii rk k 1 k the first flow is z axisymmetric the other ones do not possess any rotational symmetries the axisymmetric flow has an invariant plane z 0 due to an involutive symmetry of the flow its vortex knots in the invariant half spaces z 0 and z 0 are equivalent it is demonstrated that the moduli space x1d4ae 3 for the derived fluid flow in 3 is naturally isomorphic to the set of all rational numbers p q in the interval j 1 0 25 q m 1 0 5847 where q is the safety factor for the fluid flow in the first invariant ball b 1 3 it is shown that all values of the safety factor q belong to a small interval of length l 0

linear stochastic degenerate sobolev equations and applications in this paper a general class of linear stochastic degenerate sobolev equations with additive noise is considered this class of systems is the infinite dimensional analogue of linear descriptor systems in finite dimensions under appropriate assumptions the mild and strong well posedness for the initial value problem are studied using elements of the semigroup theory and properties of the stochastic convolution the final value problem is also examined and it is proved that this is uniquely strongly solvable and the solution is continuously dependent on the final data based on the results of the forward and backward problem the conditions for the exact controllability are investigated for a special but important class of these equations the abstract results are illustrated by applications in complex media electromagnetics in the one dimensional stochastic dirac equation in the non relativistic limit and in a potential application in input output analysis in economics

blow up criterion for 3d viscous liquid gas two phase flow model abstract this work deals with the blow up criterion for the strong solution to the three dimensional viscous liquid gas two phase flow model in terms of the l 1 0 t l norm of the gradient of the velocity with two types of boundary conditions the dirichlet boundary condition and the navier slip boundary condition there is no extra restriction on viscosity coefficients the result also applies to the whole space case

overestimation of the receiver operating characteristic curve for logistic regression logistic regression is often used to find a linear combination of covariates which best discriminates between two groups or populations the roc receiver operating characteristic curve is a good way of assessing the performance of the resulting score but using the same data both to fit the score and to calculate its roc leads to an over optimistic estimate of the performance which the score would give if it were to be validated on a sample of future cases the paper studies the extent of this overestimation and suggests a shrinkage correction for the roc curve itself and for the area under the curve the correction is consistent with efron s formula for the bias in the error rate of a binary prediction rule two medical examples are discussed

on woltjer s variational principle for force free fields the existence of minimizers for woltjer s variational principle is established and that the minimizers are force free fields this method has the nature of a constructive implicit function theorem and handles successfully the nonconvex constraint of constant total helicity domains of arbitrary connectivity are allowed as well as nonhomogeneous boundary conditions and periods

regularity of solutions of evolution integrodifferential equations with deviating argument abstract in this paper we prove the existence of mild and classical solutions of delay integrodifferential equation and delay integrodifferential evolution equations with nonlocal condition in banach spaces the regularity solutions of integrodifferential evolution equations interconnected with viscoelastic material is derived to guarantee the stabilization the results are established by using the resolvent operators and the fixed point principles finally an example is given to show the potential of the proposed techniques

boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle time harmonic electromagnetic waves are scattered by a homogeneous dielectric obstacle the corresponding electromagnetic transmission problem is reduced to a single integral equation over s for a single unknown tangential vector field where s is the interface between the obstacle and the surrounding medium in fact several different integral equations are derived and analysed including two previously known equations due to e marx and j r mautz and two new singular integral equations mautz s equation is shown to be uniquely solvable at all frequencies a new uniquely solvable singular integral equation is also found the paper also includes a review of methods using pairs of coupled integral equations over s it is these methods that are usually used in practice although single integral equations seem to offer some computational advantages

analytic resolvent operators for integral equations in banach space on etudie l equation integrodifferentielle x t a 0 x t 0 t b t s x s ds f t t 0 x 0 x 0 ed a x et l equation integrale x t 0 t a t s x s ds f t dans un espace de banach x les operateurs a a 0 b t et a t sont des operateurs clos sur x a domaine dense

linear combinations of biomarkers to improve diagnostic accuracy with three ordinal diagnostic categories many researchers have addressed the problem of finding the optimal linear combination of biomarkers to maximize the area under receiver operating characteristic roc curves for scenarios with binary disease status in practice many disease processes such as alzheimer can be naturally classified into three diagnostic categories such as normal mild cognitive impairment and alzheimer s disease ad and for such diseases the volume under the roc surface vus is the most commonly used index of diagnostic accuracy in this article we propose a few parametric and nonparametric approaches to address the problem of finding the optimal linear combination to maximize the vus we carried out simulation studies to investigate the performance of the proposed methods we apply all of the investigated approaches to a real data set from a cohort study in early stage ad copyright 2012 john wiley sons ltd

local representation and construction of beltrami fields abstract a beltrami field is an eigenvector of the curl operator beltrami fields describe steady flows in fluid dynamics and force free magnetic fields in plasma turbulence by application of the lie darboux theorem of differential geometry we prove a local representation theorem for beltrami fields we find that locally a beltrami field has a standard form amenable to an arnold beltrami childress flow with two of the parameters set to zero furthermore a beltrami flow admits two local invariants a coordinate representing the physical plane of the flow and an angular momentum like quantity in the direction across the plane as a consequence of the theorem we derive a method to construct beltrami fields with given proportionality factor this method based on the solution of the eikonal equation guarantees the existence of beltrami fields for any orthogonal coordinate system such that at least two scale factors are equal we construct several solenoidal and non solenoidal beltrami fields with both homogeneous and inhomogeneous proportionality factors

vortex knots for the spheromak fluid flow and their moduli spaces abstract new exact solutions to the euler hydrodynamics equations are constructed a method for the study of vortex knots is developed for a special class of ideal fluid flows the axisymmetric ones satisfying the beltrami equation curl v x v x the method is based on a construction of the moduli spaces of vortex knots s r 3 applying the method to the spheromak fluid flow we demonstrate that only those torus knots k p q are realized as vortex knots for which p q belongs to the interval i 1 0 5 m 1 0 8252 we prove that each torus knot k p q with 1 2 p q 1 2 is realized on countably many invariant tori t 2 r 3 while torus knots with 1 2 p q m 1 are realized only on finitely many tori the moduli spaces of vortex knots s m b a 3 m 1 2 are constructed for the spheromak fluid flows inside a ball b a 3 of radius a

on linear combinations of biomarkers to improve diagnostic accuracy we consider combining multiple biomarkers to improve diagnostic accuracy su and liu derived the linear combinations that maximize the area under the receiver operating characteristic roc curves these linear combinations however may have unsatisfactory low sensitivity over a certain range of desired specificity in this paper we consider maximizing sensitivity over a range of specificity we first present a simpler proof for su and liu s main theorem and further investigate some other optimal properties of their linear combinations we then derive alternative linear combinations that have higher sensitivity over a range of high or low specificity the methods are illustrated using data from a study evaluating biomarkers for coronary heart disease

on the ideal compressible magnetohydrodynamic equations abstract in this paper we consider the short time strong solutions to the ideal compressible magnetohydrodynamic equations with initial vacuum where the velocity field satisfies the navier slip condition inspired by kato and lax s idea we use the contraction mapping argument to prove the local existence moreover under the navier slip condition we establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of l norm of the deformation tensor d u

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed