the universal embedding for theu4 3 involution geometry abstract we prove that the universal embedding of the u 4 3 involution geometry is a known 70 dimensional module

some projective modules determined by sporadic geometries abstract we determine which known sporadic geometries have projective lefschetz modules an elementary lemma on local collapsibility greatly simplifies the task of verifying projectivity the modules are analyzed when possible in terms of projective covers of individual irreducibles

on a measure of noncompactness in the space of functions with tempered increments abstract based on a certain criterion for relative compactness in the space of functions with tempered increments we construct a formula expressing a set function in that space we prove that the mentioned function is a sublinear measure of noncompactness in the space in question moreover we show that with help of that measure of noncompactness we can obtain an existence result for a nonlinear quadratic integral equation of hammerstein type in the space of function satisfying the holder condition

the universal embedding for the involution geometry of co1 abstract a proof that the universal embedding for the 2 local involution geometry for co 1 over f 2 is 300 dimensional

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

universal presheaves on group geometries and modular representations abstract we extend the ideas of sheaf homology on buildings m a ronan and s d smith j algebra 96 1985 319 346 to more general geometries with transitive automorphism groups the main technical result is the construction of a universal extension of certain partial sheaves this guarantees a rich supply of sheaves on such geometries computation of zero homology then affords representations of the group we consider various applications of the technique for example to modular irreducibles for sporadic simple groups

a collection of subgroups for the generalized burnside ring abstract in this paper we will introduce a new collection of subgroups which induces a generalized burnside ring this collection arises from the normalizers of certain p radical subgroups

propagating sharp group homology decompositions a collection c of subgroups of a finite group g can give rise to three different standard formulas for the cohomology of g in terms of either the subgroups in c or their centralizers or their normalizers we give a short but systematic study of the relationship among such formulas for nine standard collections c of p subgroups obtaining some new formulas in the process to do this we exhibit some sufficient conditions on the poset c which imply comparison results

monte carlo analysis of the critical properties of the two dimensional randomly bond diluted ising model via wang landau algorithm abstract the influence of random bond dilution on the critical properties of the two dimensional ising model on a square lattice with periodic boundary conditions is presented using the monte carlo process with wang landau sampling the lattice linear size is l 20 140 and the concentration of the diluted bonds spans a wide range from weak to strong dilution namely q 0 05 0 1 0 2 0 3 0 4 the respective percolation limit for the square lattice is q c p e r c 0 5 its pure version q 0 has a second order phase transition with vanishing specific heat critical exponent an example of inapplicability of the harris criterion the main effort is focused on the temperature dependence of the specific heat and magnetic susceptibility to estimate the respective maximum values and subsequent pseudocritical temperatures for extracting the relative critical exponents we have also looked at the probability distribution of the susceptibility pseudocritical temperature and specific heat for assessing self averaging the study is carried out in the appropriately restricted but dominant energy subspaces by applying the finite size scaling analysis the critical exponents are estimated the specific heat exponent vanishes the correlation length exponent is equal to one and the critical exponents ratio retains its pure ising model value thus supporting the strong universality hypothesis

determining the density of states for classical statistical models a random walk algorithm to produce a flat histogram we describe an efficient monte carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models the density of states is modified at each step when the energy level is visited to produce a flat histogram by carefully controlling the modification factor we allow the density of states to converge to the true value very quickly even for large systems from the density of states at the end of the random walk we can estimate thermodynamic quantities such as internal energy and specific heat capacity by calculating canonical averages at any temperature using this method we not only can avoid repeating simulations at multiple temperatures but we can also estimate the free energy and entropy quantities that are not directly accessible by conventional monte carlo simulations this algorithm is especially useful for complex systems with a rough landscape since all possible energy levels are visited with the same probability as with the multicanonical monte carlo technique our method overcomes the tunneling barrier between coexisting phases at first order phase transitions in this paper we apply our algorithm to both first and second order phase transitions to demonstrate its efficiency and accuracy we obtained direct simulational estimates for the density of states for two dimensional ten state potts models on lattices up to 200 x 200 and ising models on lattices up to 256 x 256 our simulational results are compared to both exact solutions and existing numerical data obtained using other methods applying this approach to a three dimensional j spin glass model we estimate the internal energy and entropy at zero temperature and using a two dimensional random walk in energy and order parameter space we obtain the rough canonical distribution and energy landscape in order parameter space preliminary data suggest that the glass transition temperature is about 1 2 and that better estimates can be obtained with more extensive application of the method this simulational method is not restricted to energy space and can be used to calculate the density of states for any parameter by a random walk in the corresponding space

the subgroup structure and mod 2 cohomology of o nan s sporadic simple group this is the first of two papers in which we determine the mod 2 cohomology of the sporadic group o n of order 2 3 5 7 11 19 31 460 815 505 920 o n has 2 rank three and from the gorenstein harada theorem gh together with the results of amm fm m1 we which determine the mod 2 cohomology rings of j1 m12 g2 q d4 q with q odd there now remain only the chevalley groups u3 8 and sz 8 among the 2 rank three simple groups for which the mod 2 cohomology ring has not been determined in what follows we often use the atlas notation co

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

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

on a homotopy relation between the 2 local geometry and the bouc complex for the sporadic group co 3 we study the homotopy relation between the standard 2 local geometry and the bouc com plex for the sporadic group co3 we also give a result concerning the relative projectivity of the reduced lefschetz module l if g is a lie group in natural characteristic p then the tits building is the simplicial complex on the maximal parabolic subgroups of g the bouc complex jbp g j in this case the complex of unipotent radicals is the barycentric subdivision of the tits building in the 70 s and 80 s buekenhout 4 ronan and smith 11 and ronan and stroth 12 constructed various geometries for the sporadic simple groups in an attempt to generalize the tits buildings for lie groups also brown 5 quillen 10 bouc 6 and others were considering various collections of p subgroups related to group cohomology in his expository paper webb 16 noted the connections between the group geometries and the subgroup complexes and investigated the associated lefschetz modules and the corre sponding homology decompositions webb s paper contains speciflc calculations with details from various authors on geometries and subgroup complexes

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

a lattice theoretical construction of a gab of the suzuki sporadic simple group geometries that are almost buildings or gabs are buekenhout tits geometries z in which all rank two residual geometries are generalized polygons except that they need not satisfy the intersection property 2 sect 6 or 51 there exist two known examples of finite gabs with flagtransitive automorphism groups and the diagram of afline type arising from sporadic simple groups in s kantor constructed one of them from the lyons sims group the other was associated with the suzuki sporadic simple group suz and was constructed by ronan and smith s as a subgeometry of a geometry of the conway group co 1 which is fixed by some element of order 3 of co 1 it seems that these geometries deserve further studies because they are quotients of certain infinite buildings as is shown by a theorem of tits 12 the main purpose of this paper is to provide a non group theoretical description of the above gab associated with suz using natural notions with respect to the complex leech lattice for this purpose we give a new presentation of the complex leech lattice a for its usual definition using the ternary golay code see 11 or 10 5 8 61 since suz is a factor group of the automorphism group of the lattice 1 this gives another existence proof for suz the subsidiary aim of this paper is to provide explicit and elementary proofs for some fundamental properties of suz which are based only on this presentation of a the details are as follows let r be the ring z w where w 1 fl 2 we first consider some r submodule r in r4 the complex e lattice see 2 1 and define the complex leech lattice n as an r submodule of r3 198 0021 8693 88 3 00

on existence and asymptotic stability of solutions of a nonlinear integral equation we prove an existence theorem for a nonlinear integral equation being a volterra counterpart of an integral equation arising in the traffic theory the method used in the proof allows us to obtain additional characterization in terms of asymptotic stability of solutions of an equation in question

softening of first order transition in three dimensions by quenched disorder we study by extensive monte carlo simulations the effect of random bond dilution on the phase transition of the three dimensional four state potts model that is known to exhibit a strong first order transition in the pure case the phase diagram in the dilution temperature plane is determined from the peaks of the susceptibility for sufficiently large system sizes in the strongly disordered regime numerical evidence for softening to a second order transition induced by randomness is given here a large scale finite size scaling analysis made difficult due to strong crossover effects presumably caused by the percolation fixed point is performed

the radical 2 subgroups of some sporadic simple groups abstract the radical p subgroups of the monster the baby monster and the harada norton group hn for p 3 5 7 are determined up to conjugacy which completes the classification problem of odd radical subgroups for all sporadic simple groups together with m kitazume s yoshiara the radical subgroups of the fischer simple groups j algebra 255 2002 22 58 and the other works

critical behavior of the pure and random bond two dimensional triangular ising ferromagnet we investigate the effects of quenched bond randomness on the critical properties of the two dimensional ferromagnetic ising model embedded in a triangular lattice the system is studied in both the pure and disordered versions by the same efficient two stage wang landau method in the first part of our study we present the finite size scaling behavior of the pure model for which we calculate the critical amplitude of the specific heat s logarithmic expansion for the disordered system the numerical data and the relevant detailed finite size scaling analysis along the lines of the two well known scenarios logarithmic corrections versus weak universality strongly support the field theoretically predicted scenario of logarithmic corrections a particular interest is paid to the sample to sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality

the radical 2 subgroups of the sporadic simple groups j4 co2 and th for a finite group g and a prime divisor p of its order a nontrivial p subgroup r of g is called radical if o n r r with the poset p g b g of radical p subgroups of g with respect to inclusion we naturally p associate the simplicial complex of its chains denoted b g which is p known to be g homotopy equivalent to the complex associated with the poset of nontrivial p subgroups as well as that of nontrivial elementary abelian p subgroups of g see e g 5 6 6 the latter are important tools to investigate the structure of g concerning the prime p see e g 5 chap 6 thus the smaller complex b g has enough information to p understand behaviors of g on p the following fact a corollary of the borel tits theorem 5 6 8 4 shows the further importance of b g for a finite group of lie type p defined over a field in characteristic p the complex b g is the p barycentric subdivision of the building for g thus for an arbitrary finite group g we may think of the complex b g as a generalization of the p concept of buildings in fact as is observed in 14 for each sporadic simple group g of characteristic p type b g is homotopy equivalent to p some smaller simplicial complex previously constructed by an ad hoc method and referred to as a p local geometry of g this suggests the importance of examining minimal complexes which are homotopy equiva lent to b g for every specifically sporadic simple group g see also p the introduction of 17

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

some homotopy equivalences for sporadic geometries a previous work rsy90 established the projectivity of the reduced lefschetz modules of certain sporadic group geometries and the present paper continues that work in a wider context recent developments in sporadic group cohomology include some applications of rsy90 which in turn suggested treatment of a broader class of geometries recurring similarities in the proofs also led to a more unified treatment establishing the stronger result of homotopy equivalence of thep local geometry with the usual elementary poset ap g one equivalence method proceeds by means of a new closed set in a standard technique of quillen it was further observed that the larger list of simple groups now treated essentially coincides with those of characteristicp type suggesting another equivalence method via the poset bp g of radical or stubborn p subgroups in particular one finds that these sporadic groups satisfy an analogue of the borel tits theorem that normalizers ofp groups lie in simplex stabilizers still further intriguing coincidences remain to be explained

on some measures of noncompactness in the space of continuous functions abstract we consider some quantities in the space of functions continuous on a bounded interval which are related to monotonicity of functions based on those quantities we construct a few measures of noncompactness in the mentioned function space several properties of those measures are established among others it is shown that they are regular or partly regular measures and equivalent to the hausdorff measure of noncompactness

existence of solution of an infinite system of generalized fractional differential equations by darbo s fixed point theorem abstract in our manuscript the existence of solution of an infinite system of three point boundary value problem of generalized fractional derivative in the caputo sense has been discussed in the linear space c 0 1 c 0 we obtain existence result by employing darbo fixed point theorem using the hausdorff measure of noncompactness

the geometry and cohomology of the mathieu group m12 it is usually very complex to calculate the cohomology of a finite group g to date the most significant results have been on the symmetric and alternating groups n m m ma mu a m m the general linear groups over a finite field q1 and the extra special p groups q2 in the list above only the alternating groups and the gln f2 are simple indeed among the simple groups only a very few aside from those above have been understood it is probable that away from the characteristic p h psln fpn z q is available but even this is not obvious especially for q 2 and certainly we currently have no information on most of the families of groups of lie type for example g2 fq e6 fq e7 fq e8 fq or any of the sporadic groups but m11 and j1 about 15 years ago quillen introduced very powerful techniques that allowed for a much deeper understanding of group cohomology however it is also apparent that successful calculations over z p have only occurred when the group has a well behaved lattice of p elementary abelian subgroups formidable combinatorial problems arise in the general situation as well as necessarily complicated multiplicative relations for example the general calculation of h gln fp z p remains quite inaccessible and there has been only marginal progress since quillen s landmark results

effect of random impurities on fluctuation driven first order transitions we analyse the effect of quenched uncorrelated randomness coupling to the local energy density of a model consisting of n coupled two dimensional ising models for n 2 the pure model exhibits a fluctuation driven first order transition characterized by runaway renormalization group behaviour we show that the addition of weak randomness acts to stabilize these flows in such a way that the trajectories ultimately flow back towards the pure decoupled ising fixed point with the usual critical exponents apart from logarithmic corrections we also show by examples that in higher dimensions such transitions may either become continuous or remain first order in the presence of randomness

self averaging distribution of pseudocritical temperatures and finite size scaling in critical disordered systems we evaluate by monte carlo simulations various singular thermodynamic quantities x for ensembles of quenched random ising and ashkin teller models the measurements are taken at t c and we study how the distributions p x and in particular their relative squared width r x over the ensemble depend on the system size l the ashkin teller model was studied in the regime where bond randomness is irrelevant and we found weak self averaging r x ensuremath sim l ensuremath alpha ensuremath nu ensuremath rightarrow 0 where ensuremath alpha l0 and ensuremath nu are the exponents of the pure model fixed point governing the transition for the site dilute ising model on a cubic lattice known to be governed by a random fixed point we find that r x tends to a constant as predicted by aharony and harris we tested whether this constant is universal however this constant is different for canonical and grand canonical disorder we identify the pseudocritical temperature of each sample i t c i l as the temperature at which the susceptibility reaches its maximal value ensuremath chi mathrm max the distribution of these sample dependent t c i l was investigated we found that its variance scales as ensuremath delta t c l 2 ensuremath sim l ensuremath 2 ensuremath nu our previously proposed finite size scaling ansatz for disordered systems was tested and found to hold we did observe deviations from a single function which imply that sample dependent scaling functions are needed these deviations are however relatively small and hence to obtain a fixed statistical error it may be more computationally efficient to measure ensuremath chi mathrm max than the commonly used ensuremath chi t c ensuremath infty

critical behavior of the two dimensional spin diluted ising model via the equilibrium ensemble approach the equilibrium ensemble approach to disordered systems is used to investigate the critical behavior of the two dimensional ising model in the presence of quenched random site dilution the numerical transfer matrix technique in semi infinite strips of finite width together with phenomenological renormalization and conformal invariance is particularly suited to putting the equilibrium ensemble approach to work a method by which to extract with great precision the critical temperature of the model is proposed and applied a more systematic finite size scaling analysis than in previous numerical studies has been performed a parallel investigation along the lines of the two main scenarios currently under discussion namely the logarithmic corrections scenario with critical exponents fixed in the ising universality class versus the weak universality scenario critical exponents varying with the degree of disorder is carried out in interpreting our data maximum care is constantly taken to be open to both possibilities a critical discussion shows that an unambiguous discrimination between the two scenarios is still not possible on the basis of the available finite size data s1063 651x 99 16110 5

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

radical 2 subgroups of the monster and the baby monster the radical 2 subgroups of the monster and the baby monster are determined up to conjugacy which completes the classification problem of radical 2 subgroups for all sporadic simple groups

the cohomology of the mclaughlin group and some associated groups the group of order 27 syl2 m22 h seems quite remarkable being the sylow 2 subgroup of three of the sporadics m22 m23 mcl as well as the simple group of lie type psu 4 3 also it is a particularly nice index two subgroup of syl2 ly we are interested in determining the mod 2 cohomology of these groups and throughout this note all cohomology groups will be taken with f2 coe cients so the coe cients will generally be suppressed we use the standard atlas see co notation we have already determined the rings h m22 h h am2 and h m23 h h m in this article we determine the rings h psu4 3 h h and h mcl h h

scaling analysis of the site diluted ising model in two dimensions a combination of recent numerical and theoretical advances are applied to analyze the scaling behavior of the site diluted ising model in two dimensions paying special attention to the implications for multiplicative logarithmic corrections the analysis focuses primarily on the odd sector of the model i e that associated with magnetic exponents and in particular on its lee yang zeros which are determined to high accuracy scaling relations are used to connect to the even thermal sector and a first analysis of the density of zeros yields information on the specific heat and its corrections the analysis is fully supportive of the strong scaling hypothesis and of the scaling relations for logarithmic corrections

a family of measures of noncompactness in the holder space cn γ r and its application to some fractional differential equations and numerical methods abstract in this paper we prove the existence of solutions for the following fractional boundary value problem c d u t f t u t n n 1 0 t u 0 0 u 0 0 u n 0 0 lim t c d 1 u t u the considerations of this paper are based on the concept of a new family of measures of noncompactness in the space of functions c n r satisfying the holder condition and a fixed point theorem of darbo type we also provide an illustrative example in support of our existence theorems finally to credibility we apply successive approximation and homotopy perturbation method to find solution of the above problem with high accuracy

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