colored group field theory random matrix models generalize to group field theories gft whose feynman graphs are dual to higher dimensional topological spaces the perturbative development of the usual gft s is rather involved combinatorially and plagued by topological singularities which we discuss in great detail in this paper thus very difficult to control and unsatisfactory

reduction of a nilpotent fuzzy matrix abstract a problem of reducing fuzzy matrices is considered and some results are obtained with regard to nilpotent matrices first reduction of irreflexive and transitive matrices is examined and then the results are applied to nilpotent matrices nilpotent matrices are matrices which represent acyclic graphs and the graphs are used to represent consistent systems the results are useful for simplification of various systems with fuzzy transitivity

a note on the power sequence of a fuzzy matrix abstract the properties of power sequence of an n n fuzzy matrix under some different pairs of fuzzy operations have been studied especially under min max composition the properties can be deduced from the results in this paper furthermore some results were established in the sense of max t composition when t is a commonly used product type triangular norm

convergence of the power sequence of a nearly monotone increasing fuzzy matrix abstract by introducing a new classification the essential role of the principal diagonal elements for the convergence of the power sequence of a fuzzy matrix a is exported at the level of a itself the established theorems cover those of monotone or nearly monotone increasing fuzzy matrices the convergence index of matrices of this type is always less than or equal to n the results can be considered to be a generalization of the results obtained by some authors on the one hand and on the other it is more important that the results have laid the foundation for studying the convergence and oscillation for power sequence of an arbitrary fuzzy matrix in general furthermore as a typical case which needs to be considered the necessary and sufficient conditions for an increasing fuzzy matrix a to have the property a n 1 a n a n 1 were established and the typical form was represented

szpilrajn s theorem on fuzzy orderings fuzzy relation matrices are considered and the well known szpilrajn theorem on orderings is generalized to fuzzy orderings zadeh has already shown a generalized theorem but another generalization is given in matrix form some interesting operations on fuzzy matrices are introduced and their properties are mentioned briefly the theorem is represented in terms of the matrix operations the operations have many properties and are useful in the various applications of fuzzy matrices or fuzzy relations

the 1 n expansion of tensor models beyond perturbation theory we analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor using a version of the loop vertex expansion which we call the mixed expansion we show that the cumulants write as explicit series in 1 n plus bounded rest terms the mixed expansion recasts the problem of determining the subleading corrections in 1 n into a simple combinatorial problem of counting trees decorated by a finite number of loop edges

multifactorial functions in fuzzy sets theory abstract the multifactorial function is a very important new concept which can be used to many aspects in fuzzy sets theory it appeared firstly in 5 where it was used to define fuzzy perturbation function and where the stability for the solutions of fuzzy relation equations by using fuzzy perturbation was studied in 6 by means of multifactorial functions multifactorial fuzzy sets and the multifactorial degree of nearness which are two new concepts too were given and they were used to multifactorial pattern recognition and clustering analysis with fuzzy characteristics in fact generally speaking most of the mathematical models dependent on several factors should use multifactorial functions especially fuzzy decision making fuzzy games fuzzy programming and fuzzy linear programming with several objective functions should here we study properties of multifactorial functions how to generate a new multifactorial function and we introduce in detail its applications in fuzzy pattern recognition fuzzy decision making fuzzy clustering fuzzy games and fuzzy programming etc

on nilpotency of matrices over antirings abstract an antiring is a semiring which is zerosumfree i e a b 0 implies a b 0 for any a b in this semiring in this paper we study the nilpotency of matrices over commutative antirings we first provide some properties and characterizations of the nilpotent matrices in terms of principal permanental minors main diagonals and permanental adjoint matrices when a family of matrices are simultaneously considered we establish some characterizations of the simultaneous nilpotence for a family of matrices

renormalization and hopf algebraic structure of the five dimensional quartic tensor field theory this paper is devoted to the study of renormalization of the quartic melonic tensor model in dimension rank five we review the perturbative renormalization and the computation of the one loop beta function confirming the asymptotic freedom of the model we then define the connes kreimer like hopf algebra describing the combinatorics of the renormalization of this model and we analyze in detail at one and two loop levels the hochschild cohomology allowing to write the combinatorial dyson schwinger equations feynman tensor graph hopf subalgebras are also exhibited

on nilpotent subsemigroups of the matrix semigroup over an antiring in this paper nilpotent subsemigroups in the matrix semigroup over a commutative antiring are discussed some basic properties and characterizations for the nilpotent subsemigroups are given and some equivalent conditions for the matrix semigroup over a commutative antiring to have a maximal nilpotent subsemigroup are obtained also the maximal nilpotent subsemigroups in the matrix semigroup are described

maximal simultaneously nilpotent sets of matrices over antinegative semirings abstract we study the simultaneously nilpotent index of a simultaneously nilpotent set of matrices over an antinegative commutative semiring s we find an upper bound for this index and give some characterizations of the simultaneously nilpotent sets when this upper bound is met in the special case of antinegative semirings with all zero divisors nilpotent we also find a bound on the simultaneously nilpotent index for all nonmaximal simultaneously nilpotent sets of matrices and establish their cardinalities in case of a finite s

free sets and free subsemimodules in a semimodule abstract in this paper we investigate the free sets and the free subsemimodules in a semimodule over a commutative semiring s first we discuss some properties of the free sets and give a sufficient condition for a nonempty finite set to be free in a finitely generated free s semimodule and obtain a relation between free set and linear independent set in an s semimodule then we consider the free subsemimodules and prove that the rank of any free subsemimodule of a finitely generated s semimodule m does not exceed that of m also we give some equivalent descriptions for a commutative semiring s to have the property that all nonzero subsemimodules of any finitely generated free s semimodule are free partial results obtained in the paper develop and generalize the corresponding results for modules over rings and linear spaces over fields

fuzzy perturbation analysis part 2 undirectional perturbation abstract in this paper the stability of the solutions of fuzzy relation equations is discussed by the method of undirectional fuzzy perturbation first a general definition of fuzzy perturbation is given from this the concept of fuzzy perturbation equation is introduced and thus stability of the solutions is defined next the degree of stability of the solutions a kind of metric of the stability is advanced three ordered quotient sets are induced by use of the degree of stability these quotient sets have a well chained characteristic

the full ward takahashi identity for colored tensor models colored tensor models ctm is a random geometrical approach to quantum gravity we scrutinize the structure of the connected correlation functions of general ctm interactions and organize them by boundaries of feynman graphs for rank d interactions including but not restricted to all melonic varphi 4 vertices to wit solely those quartic vertices that can lead to dominant spherical contributions in the large n expansion the aforementioned boundary graphs are shown to be precisely all possibly disconnected vertex bipartite regularly edge d colored graphs the concept of ctm compatible boundary graph automorphism is introduced and an auxiliary graph calculus is developed with the aid of these constructs certain u invariance of the path integral measure is fully exploited in order to derive a strong ward takahashi identity for ctms with a symmetry breaking kinetic term for the rank 3 varphi 4 theory we get the exact integral like equation for the 2 point function similarly exact equations for higher multipoint functions can be readily obtained departing from this full ward takahashi identity our results hold for some group field theories as well altogether our non perturbative approach trades some graph theoretical methods for analytical ones we believe that these tools can be extended to tensorial syk models

on compositions of lattice matrices in this paper we give some properties of compositions of matrices whose elements belong to a distributive lattice we also construct an idempotent matrix from a given matrix and factor a matrix into a product of a square matrix and a rectangular matrix of the same dimension this square matrix has reflexivity and transitivity the main results obtained in this paper are generalizations of previous results on fuzzy matrices by ragab emam and hashimato

transitivity of generalized fuzzy matrices generalized fuzzy matrices are considered as matrices over a special type of semiring which is called a path algebra transitivity of generalized fuzzy matrices is defined and some properties of transitivity are shown especially properties of the composition of transitive fuzzy matrices representing transitive fuzzy relations are examined by introducing a third operation on the semiring with two operations the transitivity is closely related to metrics distances ultrametrics and so on

bases in semimodules over commutative semirings abstract in this paper the bases of a semimodule over a commutative semiring r are investigated some properties and characterizations of the bases are discussed and some equivalent conditions for a basis to be a free basis in a finitely generated free semimodule over r are given the different possible cardinalities for a basis in a finitely generated free semimodule over r are considered and some equivalent descriptions are obtained for a commutative semiring r satisfying the property that any two bases for a finitely generated free r semimodule have the same cardinality partial results obtained in the paper develop and generalize the corresponding results for commutative join semirings and for commutative zerosumfree semirings

parametric representation of covariant noncommutative qft models we extend the parametric representation of renormalizable non commutative quantum field theories to a class of theories which we call covariant because their power counting is definitely more difficult to obtain this class of theories is important since it includes gauge theories which should be relevant for the quantum hall effect

on the large n limit of schwinger dyson equations of a rank 3 tensor field theory we analyze in this paper the large n limit of the schwinger dyson equations in a rank 3 tensor quantum field theory which are derived with the help of ward takahashi identities in order to have a well defined large n limit appropriate scalings in powers of n for the various terms present in the action are explicitly found a perturbative check of our results is done up to second order in the coupling constant we analyze in this paper the large n limit of the schwinger dyson equations in a rank 3 tensor quantum field theory which are derived with the help of ward takahashi identities in order to have a well defined large n limit appropriate scalings in powers of n for the various terms present in the action are explicitly found a perturbative check of our results is done up to second order in the coupling constant

on the power sequence of a fuzzy matrix iii a detailed study on the power sequence of matrices of commonly used types abstract focusing on the behavior of the principal diagonal elements of ak a new classification has been introduced which is called circularly k dominating in turns out that the convergence index or the oscillating index of the power sequence of an n n fuzzy matrix of the circularly k dominating type is bounded by nk n k from above and if it is oscillating then the period index pa is a factor of k the fuzzy matrices of the 2 dominating type were discussed in detail it was shown that the 2 dominating type is a more general class than those have been discussed before and the results established for matrices of 2 dominating type is as good as the results obtained for controllable matrices therefore most commonly used types of fuzzy matrices can be examined under the framework of 2 dominating matrices and the convergence index or oscillating index can be estimated based on the results

controllable fuzzy matrices abstract controllable fuzzy matrices are defined several properties of controllable fuzzy matrices and nilpotent fuzzy matrices are studied we obtain an algorithm to judge whether a fuzzy matrix is controllable and reduce a controllable fuzzy matrix to canonical form the results presented generalize analogous results concerning strongly transitive fuzzy matrices and nilpotent fuzzy matrices known in the literature

on simultaneously nilpotent fuzzy matrices abstract nilpotent fuzzy matrices play a crucial role in the study of fuzzy matrices in this paper we shall extend the nilpotence to the notion of simultaneous nilpotence for a finite set of fuzzy matrices the notion of simultaneous nilpotence relates to the infinite products of a finite number of fuzzy matrices which converge to the zero matrix properties of the simultaneous nilpotence will be established in the study of consecutive powers of a fuzzy matrix a controllable fuzzy matrix can be characterized by an associated nilpotent fuzzy matrix in this paper we propose the notion of simultaneously controllable fuzzy matrices which can be thought of as a generalization of the notion of controllable fuzzy matrices similar to the nilpotent characterization for a controllable fuzzy matrix the simultaneously controllable fuzzy matrices can be characterized by a finite set of associated simultaneously nilpotent fuzzy matrices

the transitive closure convergence of powers and adjoint of generalized fuzzy matrices generalized fuzzy matrices are considered as matrices over a special type of semiring which is called an incline and their transitive closure powers determinant and adjoint matrices are studied an expression for the transitive closure of a matrix a as a sum of its powers and some su2cient conditions for powers of a matrix to converge are given if the incline is commutative a su2cient condition for nilpotency of a matrix is obtained namely the determinants of the principal submatrices of the matrix are all equal to zero element in addition it is proved that a n 1 is equal to the adjoint matrix of a if the matrix a satis5es a in

matrices over semirings introducing the concept of semi invertibility of square matrices over semirings some sufficient conditions for semi invertibility of square matrices over various kinds of semirings are obtained also a necessary and sufficient condition for semi invertibility of square matrices over semirings is obtained

eigenvalues and eigenvectors for matrices over distributive lattices abstract let l be a complete and completely distributive lattice a vector is said to be an eigenvector of a square matrix a over the lattice l if a for some l the elements are called the associated eigenvalues in this paper we characterize the eigenvalues and the eigenvectors and also the roots of the characteristic equation of a

on the finite amplitudes for open graphs in abelian dynamical colored boulatov ooguri models in the work ben geloun and bonzom 2011 int j theor phys 50 2819 it has been proved that the radiative corrections of the 2 point function in the su 2 boulatov tensor model generates a marginal in the renormalization group sense contribution of the form of a laplacian such a term which was missing in the initial boulatov model action should be added in that action before discussing the renormalization analysis of this model in this work by linearizing the group manifold we prove that the amplitudes associated with feynman graphs with external legs of the colored boulatov model over u 1 3 endowed with a laplacian dynamics are all convergent we conjecture that the same feature happens for the corresponding boulatov model over su 2 higher rank models are also discussed

invertible and nilpotent matrices over antirings abstract in this paper we characterize invertible matrices over an arbitrary commutative antiring s with 1 and find the structure of gl n s we find the number of nilpotent matrices over an entire commutative finite antiring we prove that every nilpotent n n matrix over an entire antiring can be written as a sum of log 2 n square zero matrices and also find the necessary number of square zero summands for an arbitrary trace zero matrix to be expressible as their sum

a new kind of fuzzy relation equations based on inner transformation this paper mainly deals with a new kind of fuzzy relation equations based on inner transformation first the inner projection of a fuzzy relation and the inner transformation by a fuzzy relation are introduced and also what is a fuzzy relation equation based on inner transformation is described second the discriminative matrix and the discriminative vector are defined on the basis of them an approach of discriminating whether such a fuzzy relation equation has nonzero solution is obtained at last a procedure of solving such fuzzy relation equations is presented the solution set of a fuzzy relation equation based on inner transformation is not closed with respect to join and meet operations in general this shows that the traditional methods being used for solving email protected composite fuzzy relation equations cannot be applied into the study of this kind of fuzzy relation equations based on inner transformation

ward takahashi identities for the colored boulatov model ward takahashi wt identities of the colored boulatov model are derived using a generic unitary field transformation in a specific instance this generic transformation turns out to be a symmetry of the interaction so that particular classes of reduced wt identities for that symmetry are consequently identified and interpreted

parametric representation of rank d tensorial group field theory abelian models with kinetic term sum_s p_s mu we consider the parametric representation of the amplitudes of abelian models in the so called framework of rank d tensorial group field theory these models are called abelian because their elds live on

determinant theory for fuzzy matrices abstract we study determinant theory for fuzzy square matrices including some boolean matrices and consider the cayley hamilton theorem for these matrices we prove that det a adj a det a det adj a a where adj a denotes the adjoint matrix of a fuzzy matrix a

on nilpotency of generalized fuzzy matrices in this paper generalized fuzzy matrices are considered as matrices over a special type of semiring which is called path algebra some properties and characterizations for nilpotent generalized fuzzy matrices are established reduction of generalized fuzzy matrices is defined and some properties of reduction of nilpotent generalized fuzzy matrices are obtained partial results obtained in this paper generalize the corresponding ones on fuzzy matrices on lattice matrices and on incline matrices

determinant theory for d 01 lattice matrices abstract we study determinant theory for d01 lattice matrices and consider the cayley hamilton theorem for these matrices a distributive lattice l is said to be d01 lattice if 0 1 l and 0 x 1 for all x l we prove that det ab det a det b det aadj a det a det adj a a where adj a denotes the adjoint matrix of a d01 lattice matrice a

inversion of matrices over a commutative semiring it is a well known consequence of the elementary theory of vector spaces that if a and b are n by n matrices over a field or even a skew field such that ab 1 then ba 1 this result remains true for matrices over a commutative ring however it is not in general true for matrices over noncommutatives rings in this paper we show that if a and b are n by n matrices over a commutative semiring then the equation ab 1 implies ba 1 we give two proofs one algebraic in nature the other more combinatorial both proofs use a generalization of the familiar product law for determinants over a commutative semiring

linear operators strongly preserving r potent matrices over semirings abstract we consider the problem of characterizing those linear operators l on the matrices over a semiring such that l x is idempotent if and only if x is complete characterizations are obtained for many semirings including the nonnegative reals the nonnegative integers the two element boolean algebra and the fuzzy scalars

on simultaneously nilpotent antiring matrices antirings are an important type of semirings which generalize boolean algebra fuzzy algebra distributive lattice and incline in this paper we study the issue of nilpotent antiring matrices provide some properties and characterizations of the simultaneous nilpotence for a finite number of antiring matrices present some methods for calculating the simultaneously nilpotent index of a finite number of antiring matrices partial results obtained in this paper generalize and develop the corresponding ones on nilpotent antiring matrices and on simultaneously nilpotent fuzzy matrices lattice matrices

some classes of renormalizable tensor models we identify new families of renormalizable tensor models from anterior renormalizable tensor models via a mapping capable of reducing or increasing the rank of the theory without having an effect on the renormalizability property mainly a version of the rank 3 tensor model as defined by ben geloun and samary ann henri poincare 14 1599 2013 e print arxiv 1201 0176 hep th 10 1007 s00023 012 0225 5 and the grosse wulkenhaar model in 4d and 2d generate three different classes of renormalizable models the proof of the renormalizability is fully performed for the first reduced model the same procedure can be applied for the remaining cases interestingly we find that due to the peculiar behavior of anisotropic wave function renormalizations the rank 3 tensor model reduced to a matrix model generates a simple super renormalizable vector model

renormalizable models in rank d geq 2 tensorial group field theory classes of renormalizable models in the tensorial group field theory framework are investigated the rank d tensor fields are defined over d copies of a group manifold g d u 1 d or g d su 2 d with no symmetry and no gauge invariance assumed on the fields in particular we explore the space of renormalizable models endowed with a kinetic term corresponding to a sum of momenta of the form p 2a a in 0 1 this study is tailored for models equipped with laplacian dynamics on gd case a 1 but also for more exotic nonlocal models in quantum topology case 0 a 1 a generic model can be written dim g d phi k d a where k is the maximal valence of its interactions using a multi scale analysis for the generic situation we identify several classes of renormalizable actions including matrix model actions in this specific instance we find a tower of renormalizable matrix models parametrized by k geq 4 in a second part of this work we study the uv behavior of the models up to maximal valence of interaction k 6 all rank d geq 3 tensor models proved renormalizable are asymptotically free in the uv all matrix models with k 4 have a vanishing function at one loop and very likely reproduce the same feature of the grosse wulkenhaar model commun math phys 256 305 2005

fuzzy clustering method based on perturbation abstract based on the results obtained in the earlier paper 1 the fuzzy clustering method based on perturbation fcmbp is further studied and several important results are obtained first since the fuzzy similarity matrix equation x2 x is one of the most important basic components of the fcmbp approach the structure of the solutions of this matrix equation is investigated to express the solutions the concept of fuzzy equivalent standard form is proposed second the existence of the globally and locally optimal fuzzy equivalent matrices which are nearest to the given fuzzy similarity matrix is proved third an effective fuzzy clustering method based on the above results is proposed finally two examples which show that the result obtained by the fcmbp method is more accurate than that obtained by the transitive closure method are solved

continuity of the generalized spectral radius in max algebra abstract let be an induced matrix norm associated with a monotone norm on r n and be the collection of all nonempty closed and bounded subsets of n n nonnegative matrices under this matrix norm for the hausdorff metric h between and is given by h max sup a inf b a b sup b inf a a b the max algebra system consists of the set of nonnegative numbers with sum a b max a b and the standard product ab for a b 0 for n n nonnegative matrices a b their product is denoted by a b where a b ij max 1 k n a ik b kj for each the max algebra version of the generalized spectral radius of is limsup m sup a m a 1 m where m a 1 a 2 a m a i here a is the maximum circuit geometric mean in this paper we prove that the max algebra version of the generalized spectral radius is continuous on the hausdorff metric space h the notion of the max algebra version of simultaneous nilpotence of matrices is also proposed necessary and sufficient conditions for the max algebra version of simultaneous nilpotence of matrices are presented as well

on nilpotent matrices over antirings in this paper the nilpotent matrices over commutative antirings are characterized in terms of principal permanental minors main diagonals and permanental adjoint matrices and a necessary and sufficient condition for a nilpotent matrix over a commutative antiring which has a given nilpotent index is obtained also a method for calculating the nilpotent index of any nilpotent matrix over a commutative entire antiring is given

generalization of the bollobas riordan polynomial for tensor graphs tensor models are used nowadays for implementing a fundamental theory of quantum gravity we define here a polynomial t encoding the supplementary topological information this polynomial is a natural generalization of the bollobas riordan polynomial used to characterize matrix graphs and is different from the gur u polynomial r gur u ann henri poincare 11 565 2010 10 1007 s00023 010 0035 6 defined for a particular class of tensor graphs the colorable ones the polynomial t is defined for both colorable and non colorable graphs and it is proved to satisfy the deletion contraction relation a non trivial example of a non colorable graphs is analyzed

on nilpotent fuzzy matrices abstract in this paper we study the issue of nilpotent fuzzy matrices we first provide some properties of nilpotent fuzzy matrices in terms of eigenvalues when a finite number of fuzzy matrices are simultaneously considered we establish some characterizations of the simultaneous nilpotence for a finite number of fuzzy matrices on the other hand it is well known that the max min algebra is one kind of lattice we shall extend the results on simultaneous nilpotence to matrices on a bounded distributive lattice

a rank theorem for vandermonde matrices we show that certain matrices built from vandermonde matrices are of full rank this result plays a key role in the construction of the limit theory of generic polynomials

canonical form of a strongly transitive fuzzy matrix abstract several properties of so called strongly transitive fuzzy matrices are developed the canonical form of the strongly transitive fuzzy matrix is formulated and constructed the results presented generalize analogous results concerning max min transitive fuzzy matrices known in the literature

renormalisation of noncommutative ϕ 4 theory by multi scale analysis in this paper we give a much more efficient proof that the real euclidean 4 model on the four dimensional moyal plane is renormalisable to all orders we prove rigorous bounds on the propagator which complete the previous renormalisation proof based on renormalisation group equations for non local matrix models on the other hand our bounds permit a powerful multi scale analysis of the resulting ribbon graphs here the dual graphs play a particular role because the angular momentum conservation is conveniently represented in the dual picture choosing a spanning tree in the dual graph according to the scale attribution we prove that the summation over the loop angular momenta can be performed at no cost so that the power counting is reduced to the balance of the number of propagators versus the number of completely inner vertices in subgraphs of the dual graph

polchinski s exact renormalisation group for tensorial theories gausian universality and power counting in this paper we use the exact renormalisation in the context of tensor models and group field theories as a byproduct we rederive gausian universality for random tensors and provide a general power counting for abelian tensorial field theories with a closure constraint leading us to a only five renormalisable theories

on transitivity of generalized fuzzy matrices abstract in this paper generalized fuzzy matrices are considered as matrices over a special type of semiring which is called path algebra some elementary properties and characterizations for transitive generalized fuzzy matrices are established and transitivity of powers of a generalized fuzzy matrix is discussed also the transitive closure of a generalized fuzzy matrix is considered and some properties of the transitive closures are obtained partial results obtained in this paper generalize the corresponding ones on nilpotent matrices and on matrices with periods

on nilpotent incline matrices inclines are additively idempotent semirings in which products are less than or equal to either factor thus they generalize boolean algebra fuzzy algebra and distributive lattice this paper studies the nilpotent incline matrices in detail it is proved that an incline matrix is nilpotent if and only if it has index and the zero vector is its unique standard eigenvector the nilpotent matrices over an incline without nilpotent elements are characterized in terms of principal minors main diagonals nilpotent indices and adjoint matrices also some properties of the reduction of nilpotent matrices over an additively residuated incline without nilpotent elements are established the results obtained here generalize the corresponding ones on fuzzy matrices and lattice matrices shown in the references

a note on the sequence of consecutive powers of a nonnegative matrix in max algebra abstract in this note we shall consider the sequence of consecutive powers in max algebra of a nonnegative matrix with each element less than or equal to 1 the notion of asymptotic period is defined to study the limiting behavior of this sequence a simple and effective characterization for the asymptotic period of the sequence is given

eigenvectors in bottleneck algebra abstract let b be a nonempty linearly ordered set without maximum and minimum and max min a vector x is said to be an eigenvector of a square matrix a if a x x the aim of the present paper is to characterize the eigenvectors by means of the associated graph of the matrix and to give bounds for the set of all eigenvectors we define the lower and the upper basic eigenvectors and derive efficient methods for computing them

bubble divergences from twisted cohomology we consider a class of lattice topological field theories among which are the weak coupling limit of 2d yang mills theory and 3d riemannian quantum gravity whose dynamical variables are flat discrete connections with compact structure group on a cell 2 complex in these models it is known that the path integral measure is ill defined because of a phenomenon known as bubble divergences in this paper we extend recent results of the authors to the cases where these divergences cannot be understood in terms of cellular cohomology we introduce in its place the relevant twisted cohomology and use it to compute the divergence degree of the partition function we also relate its dominant part to the reidemeister torsion of the complex thereby generalizing previous results of barrett and naish guzman the main limitation to our approach is the presence of singularities in the representation variety of the fundamental group of the complex we illustrate this issue in the well known case of two dimensional manifolds

feynman diagrams of generalized matrix models and the associated manifolds in dimension four the problem of constructing a quantum theory of gravity has been tackled with very different strategies most of which rely on the interplay between ideas from physics and from advanced mathematics on the mathematical side a central role is played by combinatorial topology often used to recover the space time manifold from the other structures involved an extremely attractive possibility is that of encoding all possible space times as specific feynman diagrams of a suitable field theory in this work we analyze how exactly one can associate combinatorial four manifolds with the feynman diagrams of certain tensor theories

simultaneously controllable fuzzy matrices let f be a set of n x n fuzzy matrices f is called simultaneously controllable if there exists a permutation matrix p such that for each a e f c c i j p a p t satisfies c i j c j i for i j where is the max min composition in this paper the necessary and sufficient conditions for a set of n x n fuzzy matrices to be simultaneously controllable will be established a constructive algorithm which can determine a simultaneously controllable set of n x n fuzzy matrices is presented as well

on the nilpotent matrices over d01 lattice abstract in this paper we study nilpotent matrices over d 01 lattice a distributive lattice l is said to be d 01 lattice if 0 1 l and 0 x 1 for all x l a necessary and sufficient condition for a d 01 lattice matrix a to be a nilpotent matrix will be given we also establish some important properties of nilpotent matrices

tensor models and 3 ary algebras tensor models are the generalization of matrix models and are studied as models of quantum gravity in general dimensions in this paper i discuss the algebraic structure in the fuzzy space interpretation of the tensor models which have a tensor with three indices as its only dynamical variable the algebraic structure is studied mainly from the perspective of 3 ary algebras it is shown that the tensor models have algebraic expressions and that their symmetries are represented by 3 ary algebras it is also shown that the 3 ary algebras of coordinates which appear in the nonassociative fuzzy flat spacetimes corresponding to a certain class of configurations with gaussian functions in the tensor models form lie triple systems and the associated lie algebras are shown to agree with those of the snyder s noncommutative spacetimes the poincare transformations of the coordinates on the fuzzy flat spacetimes are shown to be generated by 3 ary algebras

on the powers of matrices in bottleneck fuzzy algebra abstract powers of square matrices under the operations max and min are studied we show that the powers of a given matrix stabilize if and only if its orbits stabilize for each starting vector and prove a necessary and sufficient condition for this property using the associated graphs of the matrix applications of the obtained results to several special classes of matrices including circulants are given

the 1 n expansion of tensor models with two symmetric tensors it is well known that tensor models for a tensor with no symmetry admit a 1 n expansion dominated by melonic graphs this result relies crucially on identifying jackets which are globally defined ribbon graphs embedded in the tensor graph in contrast no result of this kind has so far been established for symmetric tensors because global jackets do not exist in this paper we introduce a new approach to the 1 n expansion in tensor models adapted to symmetric tensors in particular we do not use any global structure like the jackets we prove that for any rank d a tensor model with two symmetric tensors and interactions the complete graph k d 1 admits a 1 n expansion dominated by melonic graphs

convergence of powers of controllable fuzzy matrices abstract convergence of powers of controllable fuzzy matrices is considered it is shown that they oscillate with period equal to 2 in general some equalities and sequences of inequalities about powers of controllable fuzzy matrices are obtained using these general results we improve some results known in the literature

canonical form of a transitive fuzzy matrix some properties of a transitive fuzzy matrix are examined and the canonical form of the transitive matrix is given using the properties as a special case an open problem concerning idempotent matrices of kim and roush is solved in our results a nilpotent matrix and a symmetric matrix play an important role we decompose a transitive matrix into the sum of a nilpotent matrix and a symmetric matrix then we obtain a canonical form of the transitive matrix

on the asymptotic period of powers of a fuzzy matrix in our prior study we have examined in depth the notion of an asymptotic period of the power sequence of an nxn fuzzy matrix with max archimedean t norms and established a characterization for the power sequence of an nxn fuzzy matrix with an asymptotic period using analytical decomposition methods in this paper by using graph theoretical tools we further give an alternative proof for this characterization with the notion of an asymptotic period using graph theoretical tools we additionally show a new characterization for the limit behaviour and then derive some results for the power sequence of an nxn fuzzy matrix with an asymptotic period

multi orientable group field theory group field theories gfts are quantum field theories over group manifolds they can be seen as a generalization of matrix models gft feynman graphs are tensor graphs generalizing ribbon graphs or combinatorial maps these graphs are not always dual to manifolds in order to simplify the topological structure of these various singularities colored gft was recently introduced and intensively studied we propose here a different simplification of gft which we call multi orientable gft we study the relation between multi orientable gft feynman graphs and colorable graphs we prove that tadfaces and some generalized tadpoles are absent some feynman amplitude computations are performed a few remarks on the renormalizability of both multi orientable and colorable gft are made a generalization from three dimensional to four dimensional theories is also proposed

on the stability of takagi sugeno fuzzy systems with time varying uncertainties this paper studies the problems of stability analysis of takagi sugeno free fuzzy systems with time varying uncertainties in our prior study we represented the time varying uncertainty incurred in characteristic interval matrices in terms of the stability of takagi sugeno free fuzzy systems with consequent parameter uncertainties based on mayer s convergent theorem for powers of single interval matrix and its generalization we further proposed some sufficient conditions for the takagi sugeno free fuzzy system with time varying uncertainties to be globally asymptotically stable in this paper we propose the notion of simultaneously nilpotent interval matrices to investigate the takagi sugeno free fuzzy system with time varying uncertainties to be strongly stable within steps where relates to the dimension of interval matrices moreover a unique situation for the deterministic takagi sugeno free fuzzy system to be strongly stable within steps is derived as well where relates to the dimension of characteristic matrices for the deterministic takagi sugeno free fuzzy system

fuzzy clustering methods based on perturbation the fuzzy clustering method as it is known to us transforms a fuzzy similarity matrix r into a fuzzy equivalent matrix r t r which is the transmission closure of r in this paper we put forward a new fuzzy clustering method using the idea to find a fuzzy equivalent matrix r which is closest to r by a certain distance in general the distance between r and r is much less than the distance between r and r which means that the lack of fidelity that is brought about by clustering according to r is much less than the lack of fidelity by r

determinantal identities over commutative semirings abstract we present a development of determinantal identities over commutative semirings this includes a generalization of the cauchy binet and laplace theorems as well as results on compound matrices and adjoints it is further shown that laplace s theorem is a special case of the grade s adjoint identity

on generalized fuzzy matrices with periods in this paper generalized fuzzy matrices are considered as matrices over a special type of semiring which is called path algebra some properties and characterizations for generalized fuzzy matrices with periods are established and an expression for the transitive closure of a generalized fuzzy matrix with a period as a sum of its powers is shown reduction of generalized fuzzy matrices is defined and some properties for reduction of generalized fuzzy matrices with periods are obtained also the structure of all standard eigenvectors for a generalized fuzzy matrix with a period is determined

convergence of products of fuzzy matrices convergence of powers of a fuzzy matrix has been studied in the literature in this paper we shall extend the scope to the products of a finite number of fuzzy matrices we shall demonstrate that the outcomes of products of fuzzy matrices will be more complicated than the cases of powers of a fuzzy matrix two notions of convergence are established weak convergence and strong convergence the main results to guarantee the weak convergence of products of fuzzy matrices are due to the concepts of transitive and compact properties of fuzzy matrices which can be viewed as a generalization of the transitive and compact properties of a fuzzy matrix sufficient conditions similar to the pinching theorem in calculus are given as well for strong convergence

on nilpotent matrices over distributive lattices abstract in this paper nilpotent matrices over distributive lattices are considered some properties and characterizations for nilpotent matrices are established and in particular a necessary and sufficient condition for an n n nilpotent matrix to have the nilpotent index n is given also some properties of the reduction of a nilpotent matrix are obtained partial results obtained in this paper are results on nilpotent fuzzy matrices by h hashimoto

continuous point symmetries in group field theories we discuss the notion of symmetries in non local field theories characterized by integro differential equations of motion from a geometric perspective we then focus on group field theory gft models of quantum gravity and provide a general analysis of their continuous point symmetry transformations including the generalized conservation laws following from them

convergence of powers of s transitive fuzzy matrices abstract natural powers via max min multiplication of s transitive fuzzy matrices are considered it is shown that they oscillate with period equal to 2 this is an extension of the convergence property concerning max min transitive fuzzy matrices

on the powers of matrices over a distributive lattice abstract in this paper the index and the period for a lattice matrix are estimated some necessary and sufficent conditions for the convergence of the powers of a lattice matrix are obtained also some equivalent conditions for a nilpotent lattice matrix are discussed

convergence of powers of a fuzzy transitive matrix convergence of powers of a fuzzy transitive matrix is considered and some conditions for convergence are given under the max min operation on fuzzy matrices a fuzzy transitive matrix is a matrix which represents a fuzzy transitive relation and has many interesting properties the conditions for convergence of fuzzy matrices are examined under a special operation which is essential to reduction of fuzzy matrices or fuzzy systems given results show graph theoretic properties of fuzzy matrices and are useful when we consider convergence of systems represented by fuzzy matrices

parametric representation of noncommutative field theory in this paper we investigate the schwinger parametric representation for the feynman amplitudes of the recently discovered renormalizable phi 4 4 quantum field theory on the moyal non commutative mathbb r 4 space this representation involves new hyperbolic polynomials which are the non commutative analogs of the usual kirchoff or symanzik polynomials of commutative field theory but contain richer topological information

on the oscillating power sequence of a fuzzy matrix abstract the properties of an oscillating power sequence of an n n fuzzy matrix have been studied the necessary and sufficient conditions have been established for a power sequence to be oscillatory furthermore the oscillation index was detailed to some degree especially for some typical boolean matrices it is also shown that the period index set of the power sequences of fuzzy matrices of order n is not bounded from above by a power of n for all integers n

power counting theorem for non local matrix models and renormalisation solving the exact renormalisation group equation a la wilson polchinski perturbatively we derive a power counting theorem for general matrix models with arbitrarily non local propagators the power counting degree is determined by two scaling dimensions of the cut off propagator and various topological data of ribbon graphs as a necessary condition for the renormalisability of a model the two scaling dimensions have to be large enough relative to the dimension of the underlying space in order to have a renormalisable model one needs additional locality properties typically arising from orthogonal polynomials which relate the relevant and marginal interaction coefficients to a finite number of base couplings the main application of our power counting theorem is the renormalisation of field theories on noncommutative d in matrix formulation

renormalization of tensorial group field theories abelian u 1 models in four dimensions we tackle the issue of renormalizability for tensorial group field theories tgft including gauge invariance conditions with the rigorous tool of multi scale analysis to prepare the ground for applications to quantum gravity models in the process we define the appropriate generalization of some key qft notions including connectedness locality and contraction of high subgraphs we also define a new notion of wick ordering corresponding to the subtraction of maximal melonic tadpoles we then consider the simplest examples of dynamical 4 dimensional tgft with gauge invariance conditions for the abelian u 1 case we prove that they are super renormalizable for any polynomial interaction