nonlinear oblique boundary value problems for nonlinear elliptic equations on considere le probleme aux valeurs limites a derivee oblique non lineaire pour des equations uniformement elliptiques quasi lineaires et totalement non lineaires d ordre 2 les operateurs elliptiques satisfont des conditions de structure naturelle on donne des theoremes d existence pour les solutions

stochastic differential equations with reflecting boundary conditions on resout des equations differentielles stochastiques a conditions aux limites reflechissantes par une approche directe basee sur le probleme de skorokhod

trees with 4 or 5 distinct normalized laplacian eigenvalues abstract we develop a tool for locating eigenvalues of the normalized laplacian matrix of trees this is obtained by extending an algorithm designed for the adjacency matrix due to jacobs and trevisan 2011 as an application we study the multiplicity of normalized laplacian eigenvalues of small diameter trees our main result is the characterization of the trees that have 4 or 5 distinct normalized laplacian eigenvalues we also show that with a fixed diameter these trees are determined by their normalized laplacian spectrum

linear oblique derivative problems for the uniformly elliptic hamilton jacobi bellman equation on demontre la resolubilite et l unicite des problemes aux valeurs limites generaux et de dirichlet

regular graphs with four eigenvalues we study the connected regular graphs with four distinct eigenvalues properties and feasibility conditions of the eigenvalues are found several examples constructions and characterizations are given as well as some uniqueness and nonexistence results

viscoelastic taylor couette flow bifurcation analysis in the presence of symmetries the morphogenesis of secondary vortices is investigated for the axisymmetric flow of a viscoelastic fluid confined between two independently rotating infinitely long cylinders in the region near the onset of instability of the purely azimuthal couette flow the oldroyd b constitutive equation is used to model viscoelasticity three characteristic regions in the parameter space corresponding to three distinct solution families have been investigated where the onset of instability is due primarily to inertia both inertia and elasticity and exclusively elasticity respectively the secondary flow corresponds to a steady taylor vortex in the first case but to a time periodic one when elasticity becomes important hopf bifurcation degenerate hopf bifurcation theory in the presence of symmetries o 2 s 1 has been used to show the existence of two different time periodic solution families each following either one of two possible patterns the rotating wave or the standing wave through a computer aided nonlinear analysis all of the steady and time periodic bifurcating solutions are shown to be supercritical implying that one and only one is stable these results are consistent with the conclusions of time dependent numerical simulations which have demonstrated an exchange of stabilities from the rotating to the standing wave pattern emerging after the bifurcation as the elasticity of the fluid increases

nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints hamiltoniens sousquadratiques conditions aux limites infinies et donnees d explosion hamiltoniens superquadratiques formulation viscosite des conditions aux limites le probleme ergodique commande stochastique optimale avec contraintes d etat

pattern formation and bistability in flow between counterrotating cylinders abstract in the taykor coutte experiment on fluid flow counterrotating cylinders there is a bicritical point where the onset of instabilities to taylor vortex flow a steady state bifurcation and spiral vortex flow a hopf bifurcation meet the nonlinear mode interactions near this bicritical point are analyzed exploiting the role of symmetry in the bifurcation theory and with emphasis of the relevance to experiments for a range of raduis ratios 0 43 0 98 the mechanism of the pattern formation is elucidated and several new flow patterns and transitions are predicted including wavy vortices bistability hysteresis and up to 7 quasiperiodic flows

construction of low density parity check codes based on balanced incomplete block designs this correspondence presents a method for constructing structured regular low density parity check ldpc codes based on a special type of combinatoric designs known as balance incomplete block designs codes constructed by this method have girths at least 6 and they perform well with iterative decoding furthermore several classes of these codes are quasi cyclic and hence their encoding can be implemented with simple feedback shift registers

the dirichlet problem for nonlinear second order elliptic equations i monge ampegre equation on considere le probleme de dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture d un domaine borne dans r n avec une frontiere c

mean values of subsolutions of elliptic and parabolic equations abstract integral averages of weak subsolutions and supersolutions in rn of quasilinear elliptic and parabolic equations are investigated the important feature is that these integral averages are defined in terms of measures that reflect interesting geometric phenomena harnack type inequalities are established in terms of these integral averages author

local c 0 α estimates for viscosity solutions of neumann type boundary value problems abstract in this article we prove the local c 0 regularity and provide c 0 estimates for viscosity solutions of fully nonlinear possibly degenerate elliptic equations associated to linear or nonlinear neumann type boundary conditions the interest of these results comes from the fact that they are indeed regularity results and not only a priori estimates from the generality of the equations and boundary conditions we are able to handle and the possible degeneracy of the equations we are able to take into account in the case of linear boundary conditions

the nonlinear oblique derivative problem for quasilinear elliptic equations on considere des problemes aux valeurs limites pour une equation elliptique quasilineaire d ordre 2 qu 0 dans ou est un domaine borne de r n n 2 et q est donne sur c 2 par qu x a ij x u x du x d ij u x a x u x du x

propagation algorithms for lexicographic ordering constraints finite domain constraint programming has been used with great success to tackle a wide variety of combinatorial problems in industry and academia to apply finite domain constraint programming to a problem it is modelled by a set of constraints on a set of decision variables a common modelling pattern is the use of matrices of decision variables the rows and or columns of these matrices are often symmetric leading to redundancy in a systematic search for solutions an effective method of breaking this symmetry is to constrain the assignments of the affected rows and columns to be ordered lexicographically this paper develops an incremental propagation algorithm gaclexleq that establishes generalised arc consistency on this constraint in o n operations where n is the length of the vectors furthermore this paper shows that decomposing gaclexleq into primitive constraints available in current finite domain constraint toolkits reduces the strength or increases the cost of constraint propagation also presented are extensions and modifications to the algorithm to handle strict lexicographic ordering detection of entailment and vectors of unequal length experimental results on a number of domains demonstrate the value of gaclexleq

strongly regular graphs with strongly regular decomposition the title refers to strongly regular graphs r which admit a partition x x of the vertex set such that each of the induced subgraphs r1 and l on x and x respectively is strongly regular a clique or a coclique a central role is played by the design d having point set x block set x and incidence given by adjacency in r if rl is a clique or a coclique and r is primitive d must be a quasisymmetric design if rl and r are both strongly regular d is a strongly regular design in the sense of d g higman 14 except possibly when r is the graph of a regular conference matrix conversely a quasisymmetric or strongly regular design with suitable parameters gives rise to a strongly regular graph with strongly regular decomposition moreover if r and rl are strongly regular with suitable parameters then r must be strongly regular too we give several examples and some nonexistence results we include a table of all feasible parameter sets up to 300 vertices for most of the cases in the table existence or nonexistence is settled some of the results in this paper are old due to m s shrikhande 17 w g bridges and m s shrikhande 3 and w h haemers 13 we mainly use eigenvalue techniques we need results on interlacing eigenvalues see 13 two sequences p1 2 p and u1 2 a

non axisymmetric subcritical bifurcations in viscoelastic taylor couette flow recently an account of the linear and nonlinear analysis of the viscoelastic taylor couette flow between independently rotating cylinders against axisymmetric disturbances was presented avgousti beris 1993 a however more recent linear stability analysis has shown that for the range of geometric and kinematic parameters studied and for high enough values of flow elasticity the critical instabilities are caused by non axisymmetric time dependent disturbances avgousti beris 1993 b in this work we calculate the bifurcating families corresponding to each one of the two possible non axisymmetric patterns emerging at the point of criticality namely the spirals and ribbons and determine their stability it is shown that for a narrow gap size for upper convected maxwell and oldroyd b fluids at least one of the non axisymmetric families bifurcates subcritically this result in conjunction with the theoretical analysis of hopf bifurcation in presence of symmetries golubitsky et al 1988 implies that neither of the bifurcating families is stable consequently there is a finite transition corresponding to infinitesimal changes of the flow parameters in the vicinity of the hopf bifurcation point although a change in the ratio of the deborah and reynolds numbers has not been found to qualitatively affect this behaviour calculations with a wider gap size have shown that both bifurcating families become supercritical there a ginzburg landau analysis shows that the ribbons are the stable pattern this behaviour is qualitatively similar to that seen for the newtonian fluid but for counterrotating cylinders albeit there spirals have been found to be stable golubitsky langford 1988

on the normalized laplacian energy and general randic index r 1 of graphs in this paper we consider the energy of a simple graph with respect to its normalized laplacian eigenvalues which we call the l energy over graphs of order n that contain no isolated vertices we characterize the graphs with minimal l energy of 2 and maximal l energy of 2 n 2 we provide upper and lower bounds for l energy based on its general randic index r 1 g we highlight known results for r 1 g most of which assume g is a tree we extend an upper bound of r 1 g known for trees to connected graphs we provide bounds on the l energy in terms of other parameters one of which is the energy with respect to the adjacency matrix finally we discuss the maximum change of l energy and r 1 g upon edge deletion

characterization of graphs with some normalized laplacian eigenvalue of multiplicity n 3 abstract graphs with few distinct eigenvalues have been investigated extensively in this paper we focus on a related problem characterizing graphs with some eigenvalue of large multiplicity specifically the normalized laplacian matrix of a graph is considered here let n 1 g and g be the second smallest normalized laplacian eigenvalue and the independence number of a graph g respectively as the main conclusions two families of n vertex connected graphs with some normalized laplacian eigenvalue of multiplicity n 3 are determined graphs with n 1 g 1 and graphs with n 1 g 1 and g 3 moreover it is proved that these graphs are determined by their normalized laplacian spectrum

graphs with three distinct eigenvalues and largest eigenvalue less than 8 abstract in this paper we consider graphs with three distinct eigenvalues and we characterize those with the largest eigenvalue less than 8 we also prove a simple result which gives an upper bound on the number of vertices of graphs with a given number of distinct eigenvalues in terms of the largest eigenvalue

a lattice based systematic recursive construction of quasi cyclic ldpc codes this paper presents a low complexity recursive and systematic method to construct good well structured low density parity check ldpc codes the method is based on a recursive application of a partial kronecker product operation on a given gamma x q q ges 3 a prime integer lattice l gamma x q the n 1 fold product of l gamma x q by itself denoted ln gamma x q represents a regular quasi cyclic qc ldpc code denoted see pdf of high rate and girth 6 the minimum distance of see pdf is equal to that of the core code see pdf introduced by l gamma x q the support of the minimum weight codewords in see pdf are characterized by the support of the same type of codewords in see pdf from performance perspective the constructed codes compete with the pseudorandom ldpc codes

the normalized laplacians on both k triangle graph and k quadrilateral graph with their applications abstract the k triangle graph tk g is obtained from a graph g by replacing each edge in g with k 1 parallel paths in which one is of length 1 and each of the rest k paths is of length 2 whereas the k quadrilateral graph qk g is obtained from g by replacing each edge in g with k 1 parallel paths in which one is of length 1 and each of the rest k paths is of length 3 in this paper we completely determine the normalized laplacian spectrum on tk g resp qk g for any connected graph g k 2 as applications the correlation between the degree kirchhoff index the kemeny s constant and the number of spanning trees of tk g resp qk g the r th iterative k triangle graph t r k g the r th iterative k quadrilateral graph q r k g and those of g are derived our results extend those main results obtained in xie et al 2016 and li and hou 2017

graphs whose normalized laplacian has three eigenvalues we give a combinatorial characterization of graphs whose normalized laplacian has three distinct eigenvalues strongly regular graphs and complete bipartite graphs are examples of such graphs but we also construct more exotic families of examples from conference graphs projective planes and certain quasi symmetric designs

a family of graphs that are determined by their normalized laplacian spectra abstract let f p q be the generalized friendship graph k 1 p k q on p q 1 vertices obtained by joining a vertex to all vertices of p disjoint copies of the complete graph k q on q vertices in this paper we prove that f p q is determined by its normalized laplacian spectrum if and only if q 2 or q 1 and p 2

the neumann problem for hessian equations in this paper we prove the existence of a classical solution to a neumann boundary value problem for hessian equations in uniformly convex domain the method depends upon the establishment of a priori derivative estimates up to second order so we give an affirmative answer to a conjecture of n trudinger in 1987

optimal complete diallel crosses summary optimality of complete diallel crosses in incomplete blocks is investigated optimal complete diallel crosses are characterized and such binary plans are derived using nested balanced incomplete block designs a table of optimal complete diallel crosses for up to 15 lines is also provided

crc handbook of combinatorial designs balanced incomplete block designs and t designs2 v k l designs of small orderbibds with small block sizet designs t 3steiner systemssymmetric designsresolvable and near resolvable designslatin squares mols and orthogonal arrayslatin squaresmutually orthogonal latin squares mols incomplete molsorthogonal arrays of index more than oneorthogonal arrays of strength more than twopairwise balanced designspbds and gdds the basicspbds recursive constructionspbd closurepairwise balanced designs as linear spacespbds and gdds of higher indexpbds frames and resolvabilityother combinatorial designsassociation schemesbalanced part ternary designsbalanced tournament designsbhaskar rao designscomplete mappings and sequencings of finite groupsconfigurationscostas arrayscoveringscycle systemsdifference familiesdifference matricesdifference sets abeliandifference sets nonabeliandifference triangle setsdirected designsd optimal matricesembedding partial quasigroupsequidistant permutation arraysfactorial designsfrequency squaresgeneralized quadranglesgraph decompositions and designsgraphical designshadamard matrices and designshall triple systemshowell designsmaximal sets of molsmendelsohn designsthe oberwolfach problemordered designs and perpendicular arraysorthogonal designsorthogonal main effect planspackingspartial geometriespartially balanced incomplete block designsquasigroupsquasi symmetric designs r l designsroom squaresself orthogonal latin squares sols sols with a symmetric orthogonal mate solssom sequences with zero autocorrelationskolem sequencesspherical t designsstarterstrades and defining sets t m s netstuscan squarest wise balanced designsuniformly resolvable designsvector space designsweighing matrices and conference matriceswhist tournamentsyouden designs generalizedyouden squaresapplicationscodescomputer science selected applicationsapplications of designs to cryptographyderandomizationoptimality and efficiency comparing block designsgroup testingscheduling a tournamentwinning the lotteryrelated mathematics and computational methodsfinite groups and designsnumber theory and finite fieldsgraphs and multigraphsfactorizations of graphsstrongly regular graphstwo graphsclassical geometriesprojective planes nondesarguesiancomputational methods in design theoryindex

rank inequalities and separation algorithms for packing designs and sparse triple systems combinatorial designs find numerous applications in computer science and are closely related to problems in coding theory packing designs correspond to codes with constant weight 4 sparse partial steiner triple systems 4 sparse pstss correspond to erasure resilient codes that are useful in handling failures in large disk arrays chee colbourn ling discrete appl math to appear hellerstein gibson karp katz paterson algorithmica 12 1994 182 208 the study of polytopes associated with combinatorial problems has proven to be important for both algorithms and theory but only recently the study of design polytopes has been pursued moura math appl 368 1996 227 254 moura ph d thesis university of toronto 1999 moura proc seventh annu european symp prague 1999 lecture notes in computer science vol 1643 springer berlin 1999 pp 462 475 wengrzik master s thesis universitat berlin 1995 zehendner doctoral thesis universitat augsburg 1986 in this article we study polytopes associated with t v k packing designs and with m sparse pstss subpacking and l sparseness inequalities are introduced and studied they can be regarded as rank inequalities for the independence systems associated with these designs conditions under which subpacking inequalities define facets are derived in particular those which define facets for pstss are determined for m 4 the l sparseness inequalities with 2 l m are proven to induce facets for the m sparse psts polytope this proof uses extremal families of pstss known as erdos configurations separation algorithms for these inequalities are proposed we incorporate some of the sparseness inequalities in a polyhedral algorithm and determine maximal 4 sparse psts v v 16 an upper bound on the size of m sparse pstss is presented

which graphs are determined by their spectrum for almost all graphs the answer to the question in the title is still unknown here we survey the cases for which the answer is known not only the adjacency matrix but also other types of matrices such as the laplacian matrix are considered

the dirichlet problem for nonlinear second order elliptic equations ii complex monge ampere and uniformaly elliptic equations on considere le probleme de dirichlet pour des equations elliptiques non lineaires d ordre 2 pour une fonction reelle dans un domaine borne de r n a frontiere lisse

low density parity check codes from transversal designs with improved stopping set distributions this paper examines the construction of low density parity check ldpc codes from transversal designs based on sets of mutually orthogonal latin squares mols by transferring the concept of configurations in combinatorial designs to the level of latin squares we thoroughly investigate the occurrence and avoidance of stopping sets for the arising codes stopping sets are known to determine the decoding performance over the binary erasure channel and should be avoided for small sizes based on large sets of simple structured mols we derive powerful constraints for the choice of suitable subsets leading to improved stopping set distributions for the corresponding codes we focus on ldpc codes with column weight 4 but the results are also applicable for the construction of codes with higher column weights finally we show that a subclass of the presented codes has quasi cyclic structure which allows low complexity encoding

the neumann problem for equations of monge ampere type we prove the existence of a classical solution to a neumann type problem for nonlinear elliptic equations of monge ampere type the methods depend upon the establishment of a priori derivative estimates up to order two and yield a sharp result for the equation of prescribed gauss curvature we also present applications to asymptotic problems which approach the non unique case and maximum principles for linear equations of aleksandrov bakelman type

a construction method for optimally universal hash families and its consequences for the existence of rbibds we introduce a method for constructing optimally universal hash families and equivalently rbibds as a consequence of our construction we obtain minimal optimally universal hash families if the cardinalities of the universe and the range are powers of the same prime a corollary of this result is that the necessary conditions for the existence of an rbibd with parameters v k namely v 0 mod k and v 1 0 mod k 1 are sufficient if v and k are powers of the same prime as an application of our construction we show that the k maxcut algorithm of hofmeister and lefmann a combinatorial design approach to maxcut random struct algorithms 9 1996 163 173 can be implemented such that it has a polynomial running time in the case that the number of vertices and k are powers of the same prime