atmospheric data analysis with the i variability diagram method hint to fractional brownian motion like phenomena for the inner structure of clouds abstract a method to sort out short range correlations and decorrelations in meteorology physical data is introduced an i variability diagram statistical method is used on liquid water cloud content taken from the astex 92 program data set the i 1 2 cases are treated here the subsequent points are found to be embedded in polygons for which the inertial axes are calculated and are shown to have non trivial values such findings are similar to those found in biological and financial data sequences this suggests ways of modeling inner cloud structure and possibly alter meteorological fields using fractional brownian motion type constraints

representation type of hecke algebras of type a in this paper we provide a complete classification of the representation type for the blocks for the hecke algebra of type a stated in terms of combinatorical data the computation of the complexity of young modules is a key component in the proof of this classification result

a cramer rule for least norm solutions of consistent linear equations abstract the least euclidean norm solution of a consistent linear equation ax b is given a determinantal form which reduces to cramer s rule if a is nonsingular

structure and perimeters of percolation clusters site percolation clusters are simulated at the percolation threshold on the square lattice an algorithm for walks around each cluster is used to obtain information on its fractal geometry the fractal dimensionality of the external perimeter is found to depend on the size of adsorbent particles used to measure it if the vacant perimeter sites have only nearest neighbour connectivity then the perimeter has dimension de 1 37 or 0 03 instead of that of the hull dh 1 75 the authors also measured the mass of internal dangling sites surrounded by the backbone s blobs singly and doubly connected sites the number of blobs and the average linear distance between entry into the exit from a blob

a cramer rule for the least norm least squared error solution of inconsistent linear equations abstract a recent cramer rule for obtaining the least norm solution of a consistent system of linear equations ax b is shown to also provide the least squared error solution in the inconsistent case i e the solution a b where a is the moore penrose inverse of a

the ordinary quiver of a weight three block of the symmetric group is bipartite abstract suppose f is a field of characteristic p 5 and that b is a p block of the symmetric group s n of defect 3 we prove that the ext 1 quiver of b is bipartite with the bipartition being described in a simple way using the leg lengths of p hooks of partitions

generalized inverses of morphisms with kernels abstract let x y be a morphism with kernel k x in an additive category with an involution then has a moore penrose inverse with respect to iff is invertible in this case 1 if x y then has a group inverse iff has a cokernel x k and 2 is invertible in this case 2 1

on vertices of simple modules for symmetric groups of small degrees abstract we present some algorithmic methods for the computation of vertices of indecomposable and simple modules over group algebras in prime characteristic furthermore we apply these to the simple modules of the symmetric groups and determine the vertices of all simple modules of the symmetric groups of degree at most 14 and 15 in characteristic 2 and 3 respectively with one exception

the moore penrose inverse of a morphism with factorization abstract given an m by n matrix a of rank r over a field with an involutory automorphism it is well known that a has a moore penrose inverse if and only if rank a a r rank aa by use of the full rank factorization theorem this result may be restated in the category of finite matrices as follows if a 1 r a 2 is an epic monic factorization of a m n through r then a has a moore penrose inverse if and only if a a 1 r a 2 and a 1 r a 2 a are respectively epic monic factorizations of a a n n and aa m m through r this characterization of the existence of moore penrose inverses is extended to arbitrary morphisms with epic monic factorizations

hecke algebras of classical type and their representation type the purpose of this article is to determine the representation type for all of the hecke algebras of classical type to do this we combine methods from our previous work which is used to obtain information on their gabriel quivers and recent advances in the theory of finite dimensional algebras the principal computation is for hecke algebras of type b with two parameters then we show that the representation type of hecke algebras is governed by their poincare polynomials

searching for more general weight conjectures using the symmetric group as an example abstract let k be a field of characteristic p and let s n be the symmetric group of degree n assume that n p let a be the centralizer in ks n of ks n 1 we find all simple a modules and relate the number of non projective simple a modules to p local information

donovan s conjecture blocks with abelian defect groups and discrete valuation rings we give a reduction to quasisimple groups for donovan s conjecture for blocks with abelian defect groups defined with respect to a suitable discrete valuation ring mathcal o consequences are that donovan s conjecture holds for mathcal o blocks with abelian defect groups for the prime two and that using recent work of farrell and kessar for arbitrary primes donovan s conjecture for mathcal o blocks with abelian defect groups reduces to bounding the cartan invariants of blocks of quasisimple groups in terms of the defect a result of independent interest is that in general i e for arbitrary defect groups donovan s conjecture for mathcal o blocks is a consequence of conjectures predicting bounds on the mathcal o frobenius number and on the cartan invariants as was proved by kessar for blocks defined over an algebraically closed field

generalized invertibility of hankel and toeplitz matrices abstract a result for the computation of the moore penrose inverse of hankel matrices over the field of the complex numbers is given by heinig and rost in this note some methods of characterizing and computing generalized inverses of hankel and toeplitz matrices over fields and over rings with the extended rao condition are presented the results were obtained by combining classical theory on the special structure of those classes of matrices with recent theory on generalized invertibility

the moore penrose inverse of von neumann regular matrices over a ring abstract necessary and sufficient conditions are given in order that a von neumann regular matrix a over an arbitrary ring and also the matrices arising in certain factorizations of a be moore penrose invertible

the heights of irreducible brauer characters in 2 blocks of the symmetric groups abstract we prove that there exists a unique irreducible brauer character of height zero in any 2 blocks of the symmetric group this generalizes the theorem of p fong and g d james that the dimension of every non trivial 2 modular simple module of the symmetric group is even

sectional rank and cohomology abstract donovan s conjecture implies a bound on the dimensions of cohomology groups in terms of the size of a sylow p subgroup and we give a proof of a stronger bound in terms of sectional p rank for dim h 1 g v we also prove a reduction theorem for higher cohomology

on equivalences between blocks of group algebras reduction to the simple components abstract a conjecture of michel broue states that if d is an abelian sylow p subgroup of a finite group g and h n g d then the principal blocks of g and h are rickard equivalent the structure of groups with abelian sylow p subgroups as determined by p fong and m e harris raises the following question assuming that broue s conjecture holds for the simple components of g under what conditions does it hold for g itself due to the structure of g this problem requires mainly the lifting of rickard complexes to p extensions of the simple components and the construction of complexes over wreath products we give here these reduction steps which may be regarded as a clifford theory of tilting complexes

drazin moore penrose invertibility in rings abstract characterizations are given for elements in an arbitrary ring with involution having a group inverse and a moore penrose inverse that are equal and the difference between these elements and ep elements is explained the results are also generalized to elements for which a power has a moore penrose inverse and a group inverse that are equal as an application we consider the ring of square matrices of order m over a projective free ring r with involution such that r m is a module of finite length providing a new characterization for range hermitian matrices over the complexes

self organizing criticality in cloud formation abstract starting from the phenomenology of cloud formation we derive a cellular automaton model which turns out to have a strong resemblance to percolation based growth models projections of thereby produced clusters show a realistic fractal dimension of the perimeter but only at or near the critical percolation threshold pc a mechanism based on the continuity equation is proposed and numerically tested which possibly explains why the atmosphere acts in fact near its critical threshold during cloud formation self organizing criticality numerically this is achieved by a feedback of the number of active sites on the occupation concentration p

three dimensional turbulent diffusion versus critical phenomena the critical exponent nu of the correlated or coherent length of a turbulent cluster has been related to the minimal fractal dimension dmin of multifractal isotropic turbulence the relationship has turned out to be nu dmin 3 2 for the homogeneous case dmin 3 and hence nu 1 2 the so called mean field approach of the theory of critical phenomena for dmin approximately 2 36 the well known turbulent value nu approximately 0 63 this result allows one to classify this case as the critical phenomenon of the so called thermal class of universality transition to the percolation class of universality nu approximately 0 9 is determined by the boundary conditions

symmetric group blocks of small defect has a specht module s and a p modular irreducible module d the decomposition number s d is de ned to be the composition multiplicity of d in s the following facts areknown about blocks of weight w a if w 0 or 1 then all the decomposition numbers of the block are 0 or 1 b if w 2 and p 2 then all the decomposition numbers of the block are 0 or 1 s2 c if w 4 then some decomposition numbers of a block can be greater than 1 even if p w moreover if w 0 1 or 2 then there is a known method for determining the decompositionnumbers r the situation for the case w 3 is still not properly understood in particular thedecomposition number s 2p 2 2p 2 p 1 1 d 3p 3 2p 1 is yet to be determined for p 5 this is just one of a collection of decomposition numbers forweight 3 which we are unable to evaluate our investigation of blocks of weight 3 grew out of an attempt to improve upon the earlier resultsof martin and russell mr by explicitly calculating the decomposition numbers this led us todiscover various errors and omissions in mr which place in doubt the claim made there that whenp w all the decomposition numbers are 0 or 1 note incidentally that if the decompositionnumbers for a given block are known to be 0 or 1 then the decomposition numbers can in principle be determined by applying schaper s theorem sch jm1 2 basic resultsby using a result of brundan and kleshchev we are able to improve upon the presentation ofseveral of the basic techniques used in s1 s2 mr for estimating decomposition numbers in orderto state these results recall that the diagram of a partition is the set of nodes i j 1 j

source algebras of blocks sources of simple modules and a conjecture of feit abstract we verify a finiteness conjecture of feit on sources of simple modules over group algebras for various classes of finite groups related to the symmetric groups

signed young modules and simple specht modules abstract by a result of hemmer every simple specht module of a finite symmetric group over a field of odd characteristic is a signed young module while specht modules are parametrized by partitions indecomposable signed young modules are parametrized by certain pairs of partitions the main result of this article establishes the signed young module labels of simple specht modules along the way we prove a number of results concerning indecomposable signed young modules that are of independent interest in particular we determine the label of the indecomposable signed young module obtained by tensoring a given indecomposable signed young module with the sign representation as consequences we obtain the green vertices green correspondents cohomological varieties and complexities of all simple specht modules and a class of simple modules of symmetric groups and extend the results of gill on periodic young modules to periodic indecomposable signed young modules

on donovan s conjecture abstract this article contains reduction theorems for some weaker variants of donovan s conjecture which supposes that for every finite group d of prime order p there are only finitely many morita equivalence classes of p blocks of finite groups having defect groups isomorphic to d i when restricting the conjecture to the case of abelian defect groups it can be reduced to only considering p blocks of a class of groups that are close to being direct products of simple groups ii when restricting the conjecture to the case of principal blocks of finite groups having an abelian sylow p subgroup it can be reduced to only considering p blocks of simple groups a weaker version of donovan s conjecture would suppose that there are only finitely many cartan matrices of p blocks of finite groups with defect group isomorphic to a given one iii this conjecture can be reduced to only considering p blocks of quasisimple groups with centers having orders prime to p

specht modules in the auslander reiten quiver abstract let a be a symmetric algebra over an algebraically closed field we study the position of indecomposable a modules with small socles or heads in auslander reiten components of tree class a we apply the results to specht modules when a is a block of a group algebra of a symmetric group in particular we show that if the block has weight 2 then all specht modules are quasi simple that is they lie at the ends of their components

spreading of percolation in three and four dimensions the authors present monte carlo simulations of the spreading of bond percolation on three and four dimensional simple hyper cubic lattices the algorithm is the same as that applied previously in two dimensions with the spreading proceeding from a hyperplane they find the spreading dimension to be d 1 82 or 0 02 three dimensional and d 1 88 or 0 03 four dimensional also they obtain values of the percolation probability and of the static exponents with errors at least comparable to the best values from the literature

generalized inverses of hankel and toeplitz mosaic matrices abstract hankel and toeplitz mosaic matrices are block matrices with hankel or toeplitz blocks respectively it is shown that hankel and toeplitz mosaic matrices possess reflexive generalized inverses which are bezoutians furthermore the bezoutian structure of the moore penrose and group inverses is investigated

2 blocks with minimal nonabelian defect groups abstract we study numerical invariants of 2 blocks with minimal nonabelian defect groups these groups were classified by redei see redei 1947 41 if the defect group is also metacyclic then the block invariants are known see sambale 43 in the remaining cases there are only two infinite families of interesting defect groups in all other cases the blocks are nilpotent we prove brauer s k b conjecture and olsson s conjecture for all 2 blocks with minimal nonabelian defect groups for one of the two families we also show that alperin s weight conjecture and dade s conjecture are satisfied this paper is a part of the author s phd thesis

topological loop intermittency in the three dimensional turbulence a new topological or loop type of intermittency is studied in three dimensional turbulence the spectral or fracton dimension ds 7 4 7 1 95 for this turbulence i e all states are localized this intermittency is different both from kolmogorov type unlocalized since ds 2 and from alexander orbach type strong localized helical fractons with ds 43 the corresponding energy spectral exponent is obtained to be equal to 1 7 1 65 these results are in good agreement with recent numerical spectral dimension and laboratory turbulent energy spectrum data the anomaly in the experimentally observed fractal dimension of clouds surface d 2 35 can be also explained in the framework of this intermittency phenomenon the results have been obtained by a renormalization of the noise like 1k energy spectrum in isotropic incompressible turbulence with taking into account of spontaneous parity breaking by virtual pairs of helical excitations

symmetric morphisms and the existence of moore penrose inverses abstract let x y be a morphism of an additive category with an involution then has a moore penrose inverse with respect to iff is invertible for some annihilator n x of iff there exists an object z and morphisms x z z z z y such that 2 and 1 z and 1 z are invertible in this case 1 1 z 1 1 z 1

martin s conjecture holds for weight 3 blocks of symmetric groups abstract we prove that martin s conjecture holds for weight 3 blocks of symmetric group algebras that if these blocks have abelian defect group then their projective indecomposable modules have a common radical length 7

towards donovan s conjecture for abelian defect groups abstract we define a new invariant for a p block of a finite group the strong frobenius number which we use to address the problem of reducing donovan s conjecture to normal subgroups of index p as an application we use the strong frobenius number to complete the proof of donovan s conjecture for 2 blocks with abelian defect groups of rank at most 4 and for 2 blocks with abelian defect groups of order at most 64

2 blocks with abelian defect groups we give a classification up to morita equivalence of 2 blocks of quasi simple groups with abelian defect groups as a consequence we show that donovan s conjecture holds for elementary abelian 2 groups and that the entries of the cartan matrices are bounded in terms of the defect for arbitrary abelian 2 groups we also show that a block with defect groups of the form c2m c2m for m 2 has one of two morita equivalence types and hence is morita equivalent to the brauer correspondent block of the normaliser of a defect group this completes the analysis of the morita equivalence types of 2 blocks with abelian defect groups of rank 2 from which we conclude that donovan s conjecture holds for such 2 groups a further application is the completion of the determination of the number of irreducible characters in a block with abelian defect groups of order 16 the proof uses the classification of finite simple groups

group and moore penrose invertability of bezoutians abstract a characterization of the group and moore penrose inverse of bezoutians generalized bezoutians and related matrices is presented the results are obtained by combining specific factorizations in the literature with recent theory on generalized inverses

modular lie powers and the solomon descent algebra let v be an r dimensional vector space over an infinite field f of prime characteristic p and let l n v denote the nth homogeneous component of the free lie algebra on v we study the structure of l n v as a module for the general linear group gl r f when n pk and k is not divisible by p and where r n our main result is an explicit 1 1 correspondence multiplicity preserving between the indecomposable direct summands of l k v and the indecomposable direct summands of l n v which are not isomorphic to direct summands of v n our approach uses idempotents of the solomon descent algebras and in addition a correspondence theorem for permutation modules of symmetric groups

adjustment matrices for weight three blocks of iwahori hecke algebras abstract we compute the adjustment matrices for weight 3 blocks of iwahori hecke algebras of type a in characteristic 2 or 3 this enables all the decomposition numbers for weight 3 blocks to be calculated

the quasihereditary structure of the auslander dlab ringel algebra abstract given an arbitrary algebra a we may associate to it a special endomorphism algebra r a introduced by auslander dlab and ringel constructed a heredity chain for r a proving that every algebra a has an associated highest weight theory in this paper we investigate the quasihereditary structure of r a using an axiomatic approach

james s conjecture holds for weight four blocks of iwahori hecke algebras abstract james s conjecture suggests that in certain cases the decomposition numbers for the iwahori hecke algebra of the symmetric group over a field of prime characteristic and in particular the decomposition numbers for the symmetric group itself coincide with the decomposition numbers for a corresponding iwahori hecke algebra defined over c and hence can be computed using the llt algorithm we prove this conjecture for blocks of weight 4

equivalent blocks of finite general linear groups in non describing characteristic abstract j chuang r kessar and j rickard have proved broue s abelian defect group conjecture for many symmetric groups we adapt the ideas of kessar and chuang towards finite general linear groups represented over non describing characteristic we then describe morita equivalences between certain p blocks of gl n q with defect group c p c p as q varies see theorem 2 here p and q are coprime this generalizes work of s koshitani and m hyoue who proved the same result for principal blocks of gl n q when p 3 1 in a different way

the derived categories of some blocks of symmetric groups and a conjecture of broue abstract a well known conjecture of broue in the representation theory of finite groups involves equivalences of derived categories of blocks the aim of this paper is to verify this conjecture for defect 2 blocks of symmetric groups actually we prove for these blocks a refinement of broue s conjecture due to rickard

defect 3 blocks of symmetric group algebras abstract in this paper we study if the following properties are present in defect 3 blocks of symmetric group algebras k g n where k has characteristic p 5 the ext quiver is bipartite the p i m s have a common loewy length 7 we obtain a criteria for a defect 3 block b of k g n to inherit these properties from a defect 3 block b of k g n 1 with which it forms a 3 1 pair we also verify that the principal blocks of k g n 3 p n 4 p 1 have these properties

group and moore penrose inverses of regular morphisms with kernel and cokernel abstract let y be a morphism with kernel k x and cokernel y l in an additive category c 1 if x y then has a group inverse iff is invertible and is regular 2 if c has an involution then has a moore penrose inverse with respect to iff and are invertible and is regular

cartan matrices and morita equivalence for blocks of the symmetric groups theorem 1 the blocks of the symmetric groups with a given weight w 0 over a field of characteristic p can be collected into families according to the shapes of their cores each family consists of morita equivalent blocks the number of such families is at most flf 1 i l w 1 11 and each family contains a block of some g where n is less than or equal to p2 p 1 2 w 1 2 4 wp

simplified model for fractal dimension of clouds abstract projections of three dimensional random percolation clusters onto a two dimensional plane give roughly the same fractal dimension 1 3 for the perimeter versus area relation as lovejoy s observation of real clouds and cellular automata simulations of nagel and raschke

weights of multipartitions and representations of ariki koike algebras abstract we consider representations of the ariki koike algebra a q deformation of the group algebra of the complex reflection group c r s n the representations of this algebra are naturally indexed by multipartitions of n and for each multipartition we define a non negative integer called the weight of we prove some basic properties of this weight function and examine blocks of small weight

concentration gradient approach to continuum percolation in two dimensions the author has investigated percolation properties of a system of overlapping discs randomly distributed with a gradient of concentration fractal properties and critical exponents of this system appear to be identical to their counterparts on a lattice this is in agreement with the universality of critical exponents of percolation the concentration gradient approach permits a precise calculation of the percolation threshold corresponding to a critical area fraction of 0 6766 or 0 0005 he has investigated the part of the external perimeter of the percolation cluster which is accessible to discs of various sizes the fractal dimension of this accessible perimeter is found to decrease abruptly as a function of the radius of invading discs from 1 75 or 0 02 to 1 35 or 0 02

the irreducible representations of the alternating group which remain irreducible in characteristic p let p be an odd prime and an the alternating group of degree n we determine which ordinary irreducible representations of u n remain irreducible in characteristic p verifying the author s conjecture from 2010 given the preparatory work done in 2010 our task is to determine which self conjugate partitions label specht modules for the symmetric group in characteristic p having exactly two composition factors this is accomplished through the use of the robinson brundan kleshchev i restriction functors together with known results on decomposition numbers for the symmetric group and additional results on the mullineux map and homomorphisms between specht modules

decomposition numbers for weight three blocks of symmetric groups and iwahori hecke algebras let f be a field q a non zero element of f and h n h f q g n the iwahori hecke algebra of the symmetric group g n if b is a block of h n of e weight 3 and the characteristic of f is at least 5 we prove that the decomposition numbers for b are all at most 1 in particular the decomposition numbers for a p block of g n of defect 3 are all at most 1

completing a matrix when certain entries of its inverse are specified abstract suppose a a 11 a 12 a 21 a 22 is an n n matrix where a 11 has order p q if a is nonsingular let a 1 have the transposed partitioning b 11 b 12 b 21 b 22 first we show that the nullities of a 11 and b 22 are equal the remainder of our paper deals with the following completion problem suppose m 1 m 2 n 1 n 2 are nonnegative integers such that m 1 m 2 n 1 n 2 n 0

general runner removal and the mullineux map abstract we prove a new runner removal theorem for q decomposition numbers of the level 1 fock space of type a e 1 1 generalising earlier theorems of james mathas and the author by combining this with another theorem relating to the mullineux map we show that the problem of finding all q decomposition numbers indexed by partitions of a given weight is a finite computation

on young modules of defect 2 blocks of symmetric group algebras abstract in this paper we obtain the ordinary characters and module structures of the young modules of defect 2 blocks of symmetric group algebras we also study how these modules induce and restrict in a 2 1 pair

weight two blocks of iwahori hecke algebras of type b abstract in the representation theory of iwahori hecke algebras of type a and in particular for representations of symmetric groups the notion of the weight of a block introduced by james plays a central role richards determined the decomposition numbers for blocks of weight 2 and here the same task is undertaken for weight two blocks of iwahori hecke algebras of type b using the author s own definition of the weight of a bipartition

scopes reduction and morita equivalence classes of blocks in finite classical groups ii abstract we extend our work of j algebra 230 2000 378 423 on unipotent blocks of classical groups to blocks of orthogonal groups containing characters labelled by degenerate symbols we also show that for classical groups in the linear prime case there are only finitely many morita types of unipotent blocks with a given defect group