Exact sequences of fuzzy linear maps

In this paper we study various properties of the fuzzy linear maps over the fuzzy quotient spaces. In particular we obtain some exact sequences of the fuzzy linear maps over the fuzzy quotient spaces.

The notions of vague fields and vague vector spaces with member- ship and non-membership function values taking in unit interval of real numbers are introduced, which generalize the existing notions of fuzzy field , fuzzy vector spaces, and studied various properties.

Pseudo-topological spaces (i.e. limit spaces) were defined by Fischer in 1959. In this paper the theory of fuzzy pseudo-topological spaces is applied to vector spaces. We introduce the concept of boundedness in fuzzy pseudo-topological vector spaces.

In this paper, we study the existence and uniqueness of solutions and controllability for the semilinear fuzzy integrodifferential equations in n-dimension fuzzy vector space \((E_N)^n\) by using the Banach fixed point theorem.KeywordsControllabilitysemilinear fuzzy integrodifferential equationsn-dimension fuzzy vector space

Fuzzy vector spaces under triangular norms

In this article, a wireless access in vehicular environments based localization technology is proposed to supplement the gaps of output frequency for global position system, saving dedicated localization facility. A subcarrier-based reflection filter is used to mitigate multipath effect. A fuzzy vector space and its fuzzy distance of normalized received signal strength indication sequence are formulated to solve the scarce variability problem of the position feature while offsetting common hardware errors and traffic noises. Based on them, the vehicle coordinates are calculated through integrating position feature with fuzzy distance, precise and stable result is achieved. Experiments confirmed its constant centimeter-level accuracy error, millisecond-level execute time as well as ignorable effects of grid size, speed, traffic, and weather. Performances meet the requirements of enforcement, autopilot, and navigation.

Mapping properties that preserve convergence in measure on finite measure spaces

\n Dada uma aplicação f: B -> A entre duas C*-álgebras, o cone dessa aplicação, Cf, é o conjunto formado pelos pares (b,g) pertencentes à soma direta da C*-álgebra B com o cone CA tais que f(b) = g(0), sendo CA o cone de A. Neste trabalho estudamos o funtor determinado pela associação da sequência exata curta 0 -> SA -> Cf -> B -> 0 para cada *-homomorfismo f: B -> A, e demonstramos que esse funtor é exato. Caracterizamos as aplicações de conexão associadas à sequência exata 0 -> SA -> Cf -> B -> 0, mostrando que a aplicação do índice é dada por tAK1(f) e que a aplicação exponencial é dada por bAK0(f), sendo tA o isomorfismo entre K1(A) e K0(SA) e bA a aplicação de Bott. Por fim, usando que toda sequência exata curta de C*-álgebras pode ser vista na forma 0 -> Ker f -> B -> A -> 0, mostramos que as aplicações de conexão d1 e d0 associadas a cada sequência exata curta podem ser dadas por dn = Kn+1(j)-1 Kn+1(i) hn, em que j é a inclusão do núcleo de f em Cf, i é a inclusão da suspensão SA também em Cf, hn = bA e h1 = tA .\n

<p>In this paper, the fuzzy counterparts of the collineations defined in classical projective spaces are defined in a 3-dimensional fuzzy projective space derived from a 4-dimensional fuzzy vector space. The properties of fuzzy projective space $ (\lambda, \mathcal{S}) $ left invariant under the fuzzy collineations are characterized depending on the membership degrees of the given fuzzy projective space and also depending on the pointwise invariant of the lines. Moreover, some relations between membership degrees of the fuzzy projective space are presented according to which are of the base point, base line, and base plane invariant under a fuzzy collineation. Specifically, when all membership degrees of $ (\lambda, \mathcal{S}) $ are distinct, the base point, base line, and base plane of $ (\lambda, \mathcal{S}) $ are invariant under the fuzzy collineation $ \bar{f} $. Conversely, if none of the base point, base line, or base plane remain invariant, then the system becomes crisp in $ (\lambda, \mathcal{S}) $. Additionally, some relations between the membership degrees of the fuzzy projective space, concerning the invariance of the base point, base line, and base plane, are presented.</p>

In this paper we investigate some situations in connection with two exact sequences of fuzzy linear maps. Also we obtain a generalization of the work [Theorem4] of Pan [5], and we study the analogies of The Four Lemma and The Five Lemma of homological algebra. Finally we obtain a special exact sequence.

This study considers four means of defining differential operators for extracting local aspects of shape in ill-specified environments: fuzzy differentiation as kernel smoothing; differentiation in the sense of weak or generalized derivatives; differentiation for fuzzy functions between normed spaces; and fuzzy differentiation for mappings between fuzzy manifolds. More consideration is given to the last, norm-free approach, which involves the notions of an abstract fuzzy topological vector space, fuzzy differentiation between fuzzy topological vector spaces, fuzzy atlases, and tangent vectors of fuzzy manifolds.

A given R-module is called a right np-injective module if for any non-nilpotent element of , and any right R-homomorphism can be extended to , if is np-injective, then is a right np-injective ring. A given ring is called right weakly np-injective if for each non-nilpotent element of , there exists a positive integer such that any right R-homomorphism can be extended to . A given ring is a right weakly np-injective ring, if . In the matrix ring, we poved that is right np-injective, for some , if is right Weakly np-injective. So, We extended many of the known properties and characterizations of right np-injective rings and modules. Finally, the main result in np-injective module found that the R-module is np-injective module if and only if for any the short exact sequence of R-modules, is also a short exact sequence, where and .

In a preceding article~[7] the authors and Tran Ngoc Nam constructed a minimal injective resolution of the mod 2 cohomology of a Thom spectrum. A Segal conjecture type theorem for this spectrum was proved. In this paper one shows that the above mentioned resolutions can be realized topologically. In fact there exists a family of cofibrations inducing short exact sequences in mod 2 cohomology. The resolutions above are obtained by splicing together these short exact sequences. Thus the injective resolutions are realizable in the best possible sense. In fact our construction appears to be in some sense an injective closure of one of Takayasu. It strongly suggests that one can construct geometrically (not only homotopically) certain dual Brown-Gitler spectra.

Let $m \ge 2$ be an integer. By using $m$ submodules of a given module, we construct a certain exact sequence, which is a well known short exact sequence when $m=2$. As an application, we compute a minimal projective resolution of the Jacobson radical of

We investigate some situations in connection with two exact sequences of fuzzy linear maps.