endotrivial modules for finite groups of lie type a in nondefining characteristic let g be a finite group such that mathop text sl nolimits n q subseteq g subseteq mathop text gl nolimits n q and z be a central subgroup of g in this paper we determine the group t g z consisting of the equivalence classes of endotrivial k g z modules where k is an algebraically closed field of characteristic p such that p does not divide q the results in this paper complete the classification of endotrivial modules for all finite groups of untwisted lie type a initiated earlier by the authors

general topology optimization method with continuous and discrete orientation design using isoparametric projection a general topology optimization method which is capable of simultaneous design of density and orientation of anisotropic material is proposed by introducing orientation design variables in addition to the density design variable in this work the cartesian components of the orientation vector are utilized as the orientation design variables the proposed method supports continuous orientation design which is out of the scope of discrete material optimization approaches as well as design using discrete angle sets the advantage of this approach is that vector element representation is less likely to fail into local optima because it depends less on designs of former steps especially compared with using the angle as a design variable continuous fiber angle optimization by providing a flexible path from one angle to another with relaxation of orientation design space an additional advantage is that it is compatible with various projection or filtering methods such as sensitivity filters and density filters because it is free from unphysical bound or discontinuity such as the one at theta 2 pi and theta 0 seen with direct angle representation one complication of cartesian component representation is the point wise quadratic bound of the design variables that is each pair of element values has to reside in a given circular bound to overcome this issue we propose an isoparametric projection method which transforms box bounds into circular bounds by a coordinate transformation with isoparametric shape functions without having the singular point that is seen at the origin with polar coordinate representation a new topology optimization method is built by taking advantage of the aforementioned features and modern topology optimization techniques several numerical examples are provided to demonstrate its capability copyright c 2014 john wiley sons ltd

penalty barrier multiplier methods for convex programming problems we study a class of methods for solving convex programs which are based on nonquadratic augmented lagrangians for which the penalty parameters are functions of the multipliers this gives rise to lagrangians which are nonlinear in the multipliers each augmented lagrangian is specified by a choice of a penalty function varphi and a penalty updating function pi the requirements on varphi are mild and allow for the inclusion of most of the previously suggested augmented lagrangians more importantly a new type of penalty barrier function having a logarithmic branch glued to a quadratic branch is introduced and used to construct an efficient algorithm convergence of the algorithms is proved for the case of pi being a sublinear function of the dual multipliers the algorithms are tested on large scale quadratically constrained problems arising in structural optimization

the classification of endo trivial modules this paper settles the classification of all endo trivial modules for a finite p group by treating the remaining case of a p group having maximal elementary abelian subgroups of rank 2 it is shown that the modules constructed by alperin using relative syzygies provide the complete list of endo trivial modules in this case

a retinex model based on absorbing markov chains the retinex algorithm developed by land and mccann provides an abstract model of the mechanism of color sensation in the human vision system at the basis of model lies the fact that the color appearance of a point does not depend only on its color value but rather on the comparison among itself and other pixels according to the model separately for each chromatic channel an image pixel receives suitably filtered information about the brightness of other image regions based on which its own brightness is eventually re scaled the original formulation land and mccann 1971 uses a path based sampling approach the information is transported by memoryless random walks starting from randomly chosen points along the path the information is filtered based on the brightness of the travelled regions by a specific path function computed through chains of ratios of pixel intensities such a function is path dependent and retains the value of the brightest point found along the path the overall correction to a pixel depends on the specific realizations of two sampling processes the starting point sampling process and the path sampling process as a consequence of the sampling this algorithm is known to be intrinsically noisy this draw back can be overcome by passing from the path sampling algorithm to the probabilistic representation of the corresponding diffusion process in this paper we start from the random path simulative model of retinex we respell the standard path based sampling process representation of the retinex model as formalized in provenzi et al 2005 and we show that despite the overall path dependence the model can be given a representation in terms of absorbing markov chains by means of the embedding into a suitable state space we derive the corresponding analytic model accounting for the combined effects of path function path sampling process and starting point sampling process finally we provide a numerical algorithm for working out its solution using such a model the output brightness of a pixel can be computed based on the solution of a simple sparse linear system we show that the output of the random walk sampling algorithm and the markov chain based algorithm agree to an extent that can be controlled by few model parameters we have found also that the markov chain based algorithm is more efficient than the basic random path sampling in obtaining noise free images those analytic probabilistic models and simulative models can be used as complementary tools for studying the retinex mechanism and for identifying and comparing variants

issues about retinex theory and contrast enhancement we present an interpretation of land s retinex theory that we show to be consistent with the original formulation the proposed model relies on the computation of the expectation value of a suitable random variable weighted with a kernel function thus the name kernel based retinex kbr for the corresponding algorithm kbr shares the same intrinsic characteristics of the original retinex it can reduce the effect of a color cast and enhance details in low key images but since it can only increase pixel intensities it is not able to enhance over exposed pictures comparing the analytical structure of kbr with that of a recent variational model of color image enhancement we are able to perform an analysis of the action of kbr on contrast showing the need to anti symmetrize its equation in order to produce a two sided contrast modification able to enhance both under and over exposed pictures the anti symmetrized kbr equations show clear correspondences with other existing color correction models in particular ace whose relationship with retinex has always been difficult to clarify finally from an image processing point of view we mention that both kbr and its antisymmetric version are free from the chromatic noise due to the use of paths in the original retinex implementation and that they can be suitably approximated in order to reduce their computational complexity from mathcal o n 2 to mathcal o n log n being n the number of input pixels

unipotent elements tilting modules and saturation the results in this paper were motivated by work of serre 19 where semisimplicity results for representations of arbitrary groups in positive characteristic were established a key ingredient in the arguments was the notion of saturation where one embeds a unipotent element of prime order of a simple algebraic group in a 1 dimensional unipotent subgroup one of our goals here is to show that saturation can be achieved rather generally and to establish a uniqueness result for the resulting unipotent subgroups as a by product we show for a simple algebraic group in good characteristic a unipotent element of prime order is contained in a particularly nice subgroup of type a1 and that the lie algebra of the ambient algebraic group usually affords a tilting module for this subgroup the tilting decompositions are applied to show that the centralizers of the unipotent element a corresponding 1 dimensional unipotent group and its lie algebra all coincide and are closely related to the centralizer of the a1 subgroup we also establish a convenient factorization of the centralizer of the unipotent element results for finite groups of lie type are also obtained

modified barrier functions theory and methods the nonlinear rescaling principle employs monotone and sufficiently smooth functions to transform the constraints and or the objective function into an equivalent problem the classical lagrangian which has important properties on the primal and the dual spaces the application of the nonlinear rescaling principle to constrained optimization problems leads to a class of modified barrier functions mbf s and mbf methods mbfm s being classical lagrangians cl s for an equivalent problem the mbf s combine the best properties of the cl s and classical barrier functions cbf s but at the same time are free of their most essential deficiencies due to the excellent mbf properties new characteristics of the dual pair convex programming problems have been found and the duality theory for nonconvex constrained optimization has been developed the mbfm have up to a superlinear rate of convergence and are to the classical barrier functions cbf s method as the multipliers method for augmented lagrangians is to the classical penalty function method based on the dual theory associated with mbf the method for the simultaneous solution of the dual pair convex programming problems with up to quadratic rates of convergence have been developed the application of the mbf to linear lp and quadratic qp programming leads to a new type of multipliers methods which have a much better rate of convergence under lower computational complexity at each step as compared to the cbf methods the numerical realization of the mbfm leads to the newton modified barrier method nmbm the excellent mbf properties allow us to discover that for any nondegenerate constrained optimization problem there exists a hot start from which the nmbm has a better rate of convergence a better complexity bound and is more stable than the interior point methods which are based on the classical barrier functions

simple endotrivial modules for quasi simple groups we investigate simple endotrivial modules of finite quasi simple groups and classify them in several important cases this is motivated by a recent result of robinson 41 showing that simple endotrivial modules of most groups come from quasi simple groups

a finite element analysis of optimal variable thickness sheets a quasi mixed finite element fe method for maximum stiffness of variable thickness sheets is analyzed the displacement is approximated with nine node lagrange quadrilateral elements and the thickness is approximated as elementwise constant one is guaranteed that the fe displacement solutions will converge in hh but in an example it is shown that in general one cannot expect any subsequence of the fe thickness solutions to converge in any l p omega norm however under a regularity and biaxiality assumption on the optimal stress field uniqueness of the optimal thickness function as well as convergence in l p omega 1 leq p infty of fe thickness solutions are proven

an axiomatic approach to image interpolation we discuss possible algorithms for interpolating data given in a set of curves and or points in the plane we propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations the absolute minimal lipschitz extension model amle is singled out and studied in more detail we show experiments suggesting a possible application the restoration of images with poor dynamic range

variational approach for the fusion of exposure bracketed pairs when taking pictures of a dark scene with artificial lighting ambient light is not sufficient for most cameras to obtain both accurate color and detail information the exposure bracketing feature usually available in many camera models enables the user to obtain a series of pictures taken in rapid succession with different exposure times the implicit idea is that the user picks the best image from this set but in many cases none of these images is good enough in general good brightness and color information are retained from longer exposure settings whereas sharp details are obtained from shorter ones in this paper we propose a variational method for automatically combining an exposure bracketed pair of images within a single picture that reflects the desired properties of each one we introduce an energy functional consisting of two terms one measuring the difference in edge information with the short exposure image and the other measuring the local color difference with a warped version of the long exposure image this method is able to handle camera and subject motion as well as noise and the results compare favorably with the state of the art

a new method for optimal truss topology design truss topology optimization formulated in terms of displacements and bar volumes results in a large nonconvex optimization problem for the case of maximization of stiffness for a prescribed volume this paper presents a new equivalent an unconstrained and convex minimization problem in displacements only where the function to be minimized is the sum of terms each of which is the maximum of two convex quadratic functions existence of solutions is proved as is the convergence of a nonsmooth steepest descent type algorithm for solving the topology optimization problem the algorithm is computationally attractive and has been tested on a large number of examples some of which are presented

a perceptually inspired variational framework for color enhancement basic phenomenology of human color vision has been widely taken as an inspiration to devise explicit color correction algorithms the behavior of these models in terms of significative image features such as e g contrast and dispersion can be difficult to characterize to cope with this we propose to use a variational formulation of color contrast enhancement that is inspired by the basic phenomenology of color perception in particular we devise a set of basic requirements to be fulfilled by an energy to be considered as perceptually inspired showing that there is an explicit class of functionals satisfying all of them we single out three explicit functionals that we consider of basic interest showing similarities and differences with existing models the minima of such functionals is computed using a gradient descent approach we also present a general methodology to reduce the computational cost of the algorithms under analysis from o n2 to o n logn being n the number of pixels of the input image

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

image editing with spatiograms transfer histogram equalization is a well known method for image contrast enhancement nevertheless as histograms do not include any information on the spatial repartition of colors their application to local image editing problems remains limited to cope with this lack of spatial information spatiograms have been recently proposed for tracking purposes a spatiogram is an image descriptor that combines a histogram with the mean and the variance of the position of each color in this paper we address the problem of local retouching of images by proposing a variational method for spatiogram transfer more precisely a reference spatiogram is used to modify the color value of a given region of interest of the processed image experiments on shadow removal and inpainting demonstrate the strength of the proposed approach

perceptual color correction through variational techniques in this paper we present a discussion about perceptual based color correction of digital images in the framework of variational techniques we propose a novel image functional whose minimization produces a perceptually inspired color enhanced version of the original the variational formulation permits a more flexible local control of contrast adjustment and attachment to data we show that a numerical implementation of the gradient descent technique applied to this energy functional coincides with the equation of automatic color enhancement ace a particular perceptual based model of color enhancement moreover we prove that a numerical approximation of the euler lagrange equation reduces the computational complexity of ace from o n2 to o nlogn where n is the total number of pixels in the image

optimal design of material properties and material distribution for multiple loading conditions an extension of recent work 1 on the simultaneous optimization of material and structure to address the design of structures under multiple loading conditions is presented material properties are represented in the most general form possible namely as elements of the unrestricted set of positive semi definite constitutive tensors of a linearly elastic continuum existence of solutions can be shown when the objective is a weighted average of compliances and a resource constraint measured as the 2 norm or the trace of the constitutive tensors is included the optimized material properties can be derived analytically the optimization of the layout of the material leads to a sizing problem of structural optimization involving a non linear non smooth elasticity analysis the computational solution of this problem is discussed and illustrated with examples

the classification of torsion endo trivial modules the main purpose of this paper is to show that if g is a finite p group which is not cyclic quaternion or semi dihedral then the group of endo trivial g modules is detected on restriction to elementary abelian p subgroups of rank 2 consequently the torsion subgroup of the group of endo trivial modules is trivial for any finite p group except in the known cases of cyclic quaternion and semi dihedral groups this requires a large amount of group cohomology recent bounds for the number of bocksteins in serre s theorem carlson s recent theorem expressing serre s theorem in terms of modules and finally the theory of varieties attached to modules a detection theorem for the torsion subgroup of the dade group of all endo permutation modules is deduced from the main theorem the structure of this torsion subgroup can then be fully described when p is odd using the results of bouc thevenaz

image fusion for enhanced visualization a variational approach we present a variational model to perform the fusion of an arbitrary number of images while preserving the salient information and enhancing the contrast for visualization we propose to use the structure tensor to simultaneously describe the geometry of all the inputs the basic idea is that the fused image should have a structure tensor which approximates the structure tensor obtained from the multiple inputs at the same time the fused image should appear natural and sharp to a human interpreter we therefore propose to combine the geometry merging of the inputs with perceptual enhancement and intensity correction this is performed through a minimization functional approach which implicitly takes into account a set of human vision characteristics

endotrivial modules for p solvable groups we determine the torsion subgroup of the group of endotrivial modules for a finite solvable group in characteristic p we also prove that our result would hold for p solvable groups provided a conjecture can be proved about the case of p nilpotent groups

on endotrivial modules for lie superalgebras abstract let g g 0 g 1 be a lie superalgebra over an algebraically closed field k of characteristic 0 an endotrivial g module m is a g supermodule such that hom k m m k ev p as g supermodules where k ev is the trivial module concentrated in degree 0 and p is a projective g supermodule in the stable module category these modules form a group under the operation of the tensor product we show that for an endotrivial module m the syzygies n m are also endotrivial and for certain lie superalgebras of particular interest we show that 1 k ev and the parity change functor actually generate the group of endotrivials additionally for a broader class of lie superalgebras for a fixed n we show that there are finitely many endotrivial modules of dimension n

bounds for decoupled design and analysis discretizations in topology optimization summary topology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution this paper discusses the relation between the number of design variables per element and the order of the elements used for analysis we derive that beyond a maximum number of design variables certain sets of material distributions cannot be discriminated based on the corresponding analysis results this makes the design description inefficient and the solution of the optimization problem non unique to prevent this we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing non uniqueness copyright 2016 the authors international journal for numerical methods in engineering published by john wiley sons ltd

a pde formalization of retinex theory in 1964 edwin h land formulated the retinex theory the first attempt to simulate and explain how the human visual system perceives color his theory and an extension the reset retinex were further formalized by land and mccann several retinex algorithms have been developed ever since these color constancy algorithms modify the rgb values at each pixel to give an estimate of the color sensation without a priori information on the illumination unfortunately the retinex land mccann original algorithm is both complex and not fully specified indeed this algorithm computes at each pixel an average of a very large set of paths on the image for this reason retinex has received several interpretations and implementations which among other aims attempt to tune down its excessive complexity in this paper it is proved that if the paths are assumed to be symmetric random walks the retinex solutions satisfy a discrete poisson equation this formalization yields an exact and fast implementation using only two ffts several experiments on color images illustrate the effectiveness of the retinex original theory

optimization of structure and material properties for solids composed of softening material an existing formulation for the prediction of the optimal material properties tensor for systems made of linear material is extended here to encompass design with nonlinear softening material the original model for the linear case was stated as a convex constrained nonlinear programming problem and this property is preserved in the extension the development is exemplified for the case of design for minimum global compliance an extremum problem formulation for elastostatics is incorporated into the design problem as a convenient way to model the structural analysis of general softening systems unlike the case for design with linear material in the nonlinear problem the form of the solution for optimal material properties and the associated stress fields as well evolve with increasing load computational results are presented for a two dimensional example problem in which a system is designed for different loads while parameters in the material model are held fixed

free material optimization with fundamental eigenfrequency constraints the goal of this paper is to formulate and solve free material optimization problems with constraints on the smallest eigenfrequency of the optimal structure a natural formulation of this problem as a linear semidefinite program turns out to be numerically intractable as an alternative we propose a new approach which is based on a nonlinear semidefinite low rank approximation of the semidefinite dual we introduce an algorithm based on this approach and analyze its convergence properties the article is concluded by numerical experiments proving the effectiveness of the new approach

gamut extension for cinema emerging display technologies are able to produce images with a much wider color gamut than those of conventional distribution gamuts for cinema and tv creating an opportunity for the development of gamut extension algorithms geas that exploit the full color potential of these new systems in this paper we present a novel gea implemented as a pde based optimization procedure related to visual perception models that performs gamut extension ge by taking into account the analysis of distortions in hue chroma and saturation user studies performed using a digital cinema projector under cinematic low ambient light large screen conditions show that the proposed algorithm outperforms the state of the art producing gamut extended images that are perceptually more faithful to the wide gamut ground truth as well as free of color artifacts and hue shifts we also show how currently available image quality metrics when applied to the ge problem provide results that do not correlate with users choices

free material design via semidefinite programming the multiload case with contact conditions free material design deals with the question of finding the stiffest structure with respect to one or more given loads which can be made when both the distribution of material and the material itself can freely vary the case of one single load has been discussed in several recent papers and an efficient numerical approach was presented in m kovara m zibulevsky and j zowe rairo model math anal numer 32 1998 pp 255 281 we attack here the multiload situation understood in the worst case sense which is of much more interest for applications but also significantly more challenging from both the theoretical and the numerical points of view after a series of transformation steps we reach a problem formulation for which we can prove existence of a solution a suitable discretization leads to a semidefinite programming problem for which modern polynomial time algorithms of interior point type are available a number of numerical examples demonstrate the efficiency of our approach

connected components of the category of elementary abelian p subgroups we determine the maximal number of conjugacy classes of maximal elementary abelian subgroups of rank 2 in a finite p group g for an odd prime p namely it is p if g has rank at least 3 and it is p 1 if g has rank 2 more precisely if g has rank 2 there are exactly 1 2 p 1 or possibly 3 classes for some 3 groups of maximal nilpotency class

stability of finite element models for distributed parameter optimization and topology design abstract we address a problem of numerical instability that is often encountered in finite element solutions of distributed parameter optimization and variable topology shape design problems we show that the cause of this problem is numerical rather than physical in nature we consider a two field distributed parameter optimization problem involving a design field and a response field and show that the optimization problem corresponds to a mixed variational problem an improper selection of the discrete function spaces for these two fields leads to grid scale anomalies in the numerical solutions to optimization problems similar to those that are sometimes encountered in mixed formulations of the stokes problem we present a theoretical framework to explain the cause of these anomalies and present stability conditions for discrete models the general theoretical framework is specialized to analyze the stability of specific optimization problems and stability results for various mixed finite element models are presented we propose patch tests that are useful in identifying unstable elements

a variational framework for retinex retinex theory addresses the problem of separating the illumination from the reflectance in a given image and thereby compensating for non uniform lighting this is in general an ill posed problem in this paper we propose a variational model for the retinex problem that unifies previous methods similar to previous algorithms it assumes spatial smoothness of the illumination field in addition knowledge of the limited dynamic range of the reflectance is used as a constraint in the recovery process a penalty term is also included exploiting a priori knowledge of the nature of the reflectance image the proposed formulation adopts a bayesian view point of the estimation problem which leads to an algebraic regularization term that contributes to better conditioning of the reconstruction problem based on the proposed variational model we show that the illumination estimation problem can be formulated as a quadratic programming optimization problem an efficient multi resolution algorithm is proposed it exploits the spatial correlation in the reflectance and illumination images applications of the algorithm to various color images yield promising results

material optimization in transverse electromagnetic scattering applications a class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed the idea behind the algorithm is similar to that of the sequential programming however in each major iteration a model is established on the basis of an appropriately parametrized material tensor the resulting nonlinear parametrization is treated on the level of the subproblem for which globally optimal solutions can be computed due to the block separability of the model although global optimization of nonconvex design problems is generally prohibitive a well chosen combination of analytic solutions along with standard global optimization techniques leads to a very efficient algorithm for most relevant material parametrizations a global convergence result for the overall algorithm is established the effectiveness of the approach in terms of both computation time and solution quality is demonstrated by numerical examples based on a two dimensional helmholtz equation inclu

endotrivial modules for the general linear group in a nondefining characteristic suppose that g is a finite group such that mathrm sl n q subseteq g subseteq mathrm gl n q and that z is a central subgroup of g let t g z be the abelian group of equivalence classes of endotrivial k g z modules where k is an algebraically closed field of characteristic p not dividing q we show that the torsion free rank of t g z is at most one and we determine t g z in the case that the sylow p subgroup of g is abelian and nontrivial the proofs for the torsion subgroup of t g z use the theory of young modules for mathrm gl n q and a new method due to balmer for computing the kernel of restrictions in the group of endotrivial modules

free material optimization via mathematical programming this paper deals with a central question of structural optimization which is formulated as the problem of finding the stiffest structure which can be made when both the distribution of material as well as the material itself can be freely varied we consider a general multi load formulation and include the possibility of unilateral contact the emphasis of the presentation is on numerical procedures for this type of problem and we show that the problems after discretization can be rewritten as mathematical programming problems of special form we propose iterative optimization algorithms based on penalty barrier methods and interior point methods and show a broad range of numerical examples that demonstrates the efficiency of our approach

contrast enhancement by nonlinear diffusion filtering to enhance the visual quality of an image that is degraded by uneven light an effective method is to estimate the illumination component and compress it some previous methods have either defects of halo artifacts or contrast loss in the enhanced image due to incorrect estimation in this paper we discuss this problem and propose a novel method to estimate the illumination the illumination is obtained by iteratively solving a nonlinear diffusion equation during the diffusion process surround suppression is embedded in the conductance function to specially enhance the diffusive strength in textural areas of the image the proposed estimation method has the following two merits 1 the boundary areas are preserved in the illumination and thus halo artifacts are prevented and 2 the textural details are preserved in the reflectance to not suffer from illumination compression which contributes to the contrast enhancement in the result experimental results show that the proposed algorithm achieves excellent performance in artifact removal and local contrast enhancement

p groups with maximal elementary abelian subgroups of rank 2 abstract let p be an odd prime number and g a finite p group we prove that if the rank of g is greater than p then g has no maximal elementary abelian subgroup of rank 2 it follows that if g has rank greater than p then the poset e g of elementary abelian subgroups of g of rank at least 2 is connected and the torsion free rank of the group of endotrivial kg modules is one for any field k of characteristic p we also verify the class breadth conjecture for the p groups g whose poset e g has more than one component

torsion free endotrivial modules let g be a finite group and let t g be the abelian group of equivalence classes of endotrivial kg modules where k is an algebraically closed field of characteristic p we investigate the torsion free part tf g of the group t g and look for generators of tf g we describe three methods for obtaining generators each of them only gives partial answers to the question but we obtain more precise results in some specific cases we also conjecture that tf g can be generated by modules belonging to the principal block and we prove the conjecture in some cases

the stable category and invertible modules for infinite groups abstract we construct a well behaved stable category of modules for a large class of infinite groups we then consider its picard group which is the group of invertible or endotrivial modules we show how this group can be calculated when the group acts on a tree with finite stabilisers

relative projectivity and relative endotrivial modules this dissertation is concerned with modular representation theory of finite groups and more precisely with the study of classes of representations which we shall term relative endotrivial modules given a prime number p a finite group g of order divisible by p we shall say that a kg module m is endotrivial relatively to the kg module v if its endomorphism algebra endk m is isomorphic as a kg module to a direct sum of a trivial module and another module which is projective relatively to v i e in short endk m k v projective more accurately in the first part of the text projectivity relative to kg modules is used to define groups of relative endotrivial modules which are obtained by replacing the notion of projectivity with that of relative projectivity in the definition of ordinary endotrivial modules however in order to achieve this goal we first need to develop the theory of projectivity relative to modules in particular with respect to standard group operations such as induction restriction and inflation then for finite groups having a cyclic sylow p subgroup using the structure of the group t g of endotrivial modules described in mt07 we give a complete classification of the groups of relative endotrivial modules we also study the case of groups that have a sylow p subgroup isomorphic to a klein group c2 c2 as well as the case of p nilpotent groups in a second part of the text it is shown how our new groups of relative endotrivial modules provide a natural context to generalise the dade group of a p group p to an arbitrary finite group the classification of endo permutation modules and the complete description of the structure of the dade group d p was completed in 2004 by s bouc with bou06 this adventure had started about 25 years earlier with the first papers and results by e dade in dad78a and dad78b in 1978 and the final classification was in fact achieved through the non effortless combined work of several co authors between 1998 and 2004 including s bouc j carlson n mazza and j thevenaz it is most interesting to note that crucial building pieces for this classification are indeed the endotrivial modules which are particular cases of endo permutation modules yet for an arbitrary finite group g no satisfying equivalent group structure to the dade group on a class of kg modules has been defined so far with the goal to fill this gap we turn the problem upside down in some sense and show how one can regard an endo permutation module as an endotrivial module of course not in the ordinary sense but in the relative sense this shall enable us to endow a set of isomorphism classes of endo p permutation modules with a group structure similar to that of the dade group we shall call this new group the generalised dade group of the group g explicitly compute its structure and show how it is closely related to that of the g stable points of the dade group of a sylow p subgroup of g

a wavelet perspective on variational perceptually inspired color enhancement the issue of perceptually inspired correction of color and contrast in digital images has been recently analyzed with the help of variational principles these techniques allowed building a general framework in which the action of many already existing algorithms can be more easily understood and compared in terms of intensification of local contrast and control of dispersion around the average intensity value in this paper we analyze this issue from the dual perspective of wavelet theory showing that it is possible to build energy functionals of wavelet coefficients that lead to a multilevel perceptually inspired color correction by computing the euler lagrange equations associated to the wavelet based functionals we were able to find an analytical formula for the modification of wavelet detail coefficients that overcomes the problem of an ad hoc selection based on empirical considerations besides these theoretical results the wavelet perspective provides the computational advantage of generating much faster algorithms in comparison with the spatial variational framework

a probabilistic method for image enhancement with simultaneous illumination and reflectance estimation in this paper a new probabilistic method for image enhancement is presented based on a simultaneous estimation of illumination and reflectance in the linear domain we show that the linear domain model can better represent prior information for better estimation of reflectance and illumination than the logarithmic domain a maximum a posteriori map formulation is employed with priors of both illumination and reflectance to estimate illumination and reflectance effectively an alternating direction method of multipliers is adopted to solve the map problem the experimental results show the satisfactory performance of the proposed method to obtain reflectance and illumination with visually pleasing enhanced results and a promising convergence rate compared with other testing methods the proposed method yields comparable or better results on both subjective and objective assessments

multidisciplinary free material optimization we present a mathematical framework for the so called multidisciplinary free material optimization mdfmo problems a branch of structural optimization in which the full material tensor is considered as a design variable we extend the original problem statement by a class of generic constraints depending either on the design or on the state variables among the examples are local stress or displacement constraints we show the existence of optimal solutions for this generalized free material optimization fmo problem and discuss convergent approximation schemes based on the finite element method

proximal operator of quotient functions with application to a feasibility problem in query optimization in this paper we determine the proximity functions of the sum and the maximum of componentwise reciprocal quotients of positive vectors for the sum of quotients denoted by q 1 the proximity function is just a componentwise shrinkage function which we call q shrinkage this is similar to the proximity function of the 1 norm which is given by componentwise soft shrinkage for the maximum of quotients q the proximal function can be computed by first order primal dual methods involving epigraphical projections the proximity functions of q 1 are applied to solve convex problems of the form argmin x q a x b subject to x 0 1 x 1 such problems are of interest in selectivity estimation for cost based query optimizers in database management systems