Lattice of Interval-Valued (∈,∈∨q)-Fuzzy LI-Ideals in Lattice Implication Algebras

In the present paper, the interval-valued (∈,∈∨q)-fuzzy LI-ideal theory in lattice implication algebras is further studied. Some new properties of interval-valued (∈,∈∨q)-fuzzy LI-ideals are given. Representation theorem of interval-valued (∈,∈∨q)-fuzzy LI-ideal which is generated by an interval-valued fuzzy set is established. It is proved that the set consisting of all interval-valued (∈,∈∨q)-fuzzy LI-ideals in a lattice implication algebra, under the partial order ?, forms a complete distributive lattice.     

R_0-代数的(∈, ∈ ∨ q_k)-模糊滤子格（英文）

The purpose of this paper is to further study the(∈,∈∨q_k)-fuzzy filter theory in R_0-algebras. Some new properties of(∈, ∈∨ q_k)-fuzzy filters are given. Representation theorem of(∈,∈∨q_k)-fuzzy filter which is generated by a fuzzy set is established. It is proved that the set consisting of all(∈, ∈∨q_k)-fuzzy filters on a given R_0-algebra, under the partial order, forms a complete distributive lattice.     

L-型模糊格蕴涵代数

This paper introduced the concept of L-fuzzy sub lattice implication algebra and discussed its properties. Proved that the intersection set of a family of L-fuzzy sub lattice implication algebras is a L-fuzzy sub lattice implication algebra, that a L-fuzzy sub set of a lattice implication algebra is a L-fuzzy sub lattice implication algebra if and only if its every cut set is a sub lattice implication algebra, and that the image and original image of a L-fuzzy sub lattice implication algebra under a lattice implication homomorphism are both L-fuzzy sub lattice implication algebras.     

GENERALIZED FUZZY FILTERS OF BL-ALGEBRAS

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered.In fact,this is a generalization of quasi-coincidence of a fuzzy point With a fuzzy set.By using this new idea,the notion of interval valued(∈,∈∨q)-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras,is defined,and related properties are investigated.In particular,the concept of a fuzzy subgroup with thresholds is extended to the concept of an interval valued fuzzy filter with thresholds in BL-algebras.     

A New View on Fuzzy Hypermodules

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy     

Redefined generalized fuzzy ideals of near-rings

With a new idea, we redefine generalized fuzzy subnear-rings(ideals) of a near- ring and investigate some of its related properties. Some new characterizations are given. In particular, we introduce the concepts of strong prime(or semiprime) (∈,∈∨q)-fuzzy ideals of near-rings, and discuss the relationship between strong prime(or semiprime) (∈,∈∨q)-fuzzy ideals and prime(or semiprime) (∈,∈∨q)-fuzzy ideals of near-rings.     

格蕴涵代数的LI-理想空间

In this paper,a topological space based on LI-ideals of a lattice implication algebra is constructed,and its topological properties,such as separability,compactness and connectedness are discussed.     

一个与Toda格相关的微分差分方程族及其反散射变换

By combined power evolution laws of the spectral parameter and the initial constants of integration,a new differential-difference hierarchy is presented from the Toda spectral problem.The hierarchy contains the classic Toda lattice equation,the nonisospectral Toda lattice equation and the mixed Toda lattice equation as reduced cases.The evolution of the scattering data in the inverse scattering transform is analyzed in detail and exact soliton solutions are computed through the corresponding inverse scattering transform.     

BCK代数的广义(∈,∈∨q)-模糊理想(英文)

In this paper, as a generalization of the notion of(∈, ∈∨ q)-fuzzy ideals, we introduced the notion of(∈, ∈∨ qδ)-fuzzy ideals and investigated their properties in BCKalgebras. Several equivalent characterizations of(∈, ∈∨ qδ)-fuzzy ideals are obtained and relations between(∈, ∈∨ qδ)-fuzzy ideals and ideals are discussed in BCK-algebras.     

完备一致空间的非标准特征

In This paper, we prove that the uniform space (X, ψ) is complete if and only if for every remote point p in *X, there exists a pseudo-metric d in the lattice set of ψ and a positive number r such that d(p, q) ≥ r for each q ∈ X.     

MTL-代数的区间值$(\in,\in \vee q)$-模糊滤子

The concepts of interval valued （∈,∈ ∨q）-fuzzy Boolean, MV - and G- filters in a MTL-algebra are introduced. The properties of these generalized fuzzy filters are studied and in particular, the relationships between these fuzzy filters in an MTL-algebra are investigated.     

The q-Variation of Functions and Spectral Integration from Dominated Ergodic Estimates

For $1\leq q < \infty$, let $\mathfrak{M}_{q}\left( \mathbb{T}\right)$, (respectively, $\mathfrak{M}_{q}\left( \mathbb{R}\right) $) denote the Banach algebra consisting of the bounded complex-valued functions having uniformly bounded $q$-variation on the dyadic arcs of the unit circle, (respectively, on the dyadic intervals of the real line). Suppose that $(\Omega,\mu)$ is a $\sigma$-finite measure space, $1< p < \infty$, and $T:L^{p}(\mu)\rightarrow L^{p}(\mu)$ is a bounded, invertible, separation-preserving linear operator such that the two-sided ergodic means of the linear modulus of $T$ are uniformly bounded in norm. We show that there is a real number $q_{_{0}} > 1$ such that whenever $1\leq q < q_{_{0}}$, $T $ has a norm-continuous functional calculus associated with $\mathfrak{M}_{q}\left(\mathbb{T}\right) $. Our approach is rooted in a dominated ergodic theorem of Mart\{\i}n--Reyes and de la Torre which assigns $T$ a canonical family of bilateral $A_{p}$ weight sequences. We first establish the relevant multiplier properties of $\mathfrak{M}_{q}\left( \mathbb{R}\right) $ classes in weighted settings, transfer the outcome to $\mathfrak{M}_{q}\left(\mathbb{T}\right) $, and then apply the consequent $\mathfrak{M}_{q}\left(\mathbb{T}\right) $ multiplier theorem for weighted settings to the spectral decomposition of $T$. The desired $\mathfrak{M}_{q}\left(\mathbb{T}\right)$-functional calculus for $T$ then results from an extension criterion for spectral integration obtained in the general Banach space setting. The multiplier result for $\mathfrak{M}_{q}\left( \mathbb{R}\right) $ shown at the outset of this process expands the scope of the weighted Marcinkiewicz multiplier theorem from $q=1$ to appropriate values of $q > 1$     

有限群的$\Phi$-$\tau$-可补子群

假设$\tau$是一个子群算子, $H$是有限群$G$的一个$p$-子群. 令 $\bar{G}=G/H_{G}$且$\bar{H}=H/H_{G}$, 如果$\bar{G}$有一个次正规子群$\bar{T}$ 和一个包含于$\bar{H}$ 的$\tau$-子群$\bar{S}$满足$\bar{G}=\bar{H}\bar{T}$且$\bar{H}\cap\bar{T}\leq \bar{S}\Phi(\bar{H})$, 就称$H$是$G$的一个$\Phi$-$\tau$- 可补子群. 文章通过讨论群$G$的准素数子群的$\Phi$-$\tau$-可补性给出了超循环嵌入和$p$-幂零性的一些新的特征.     

参数函数$\epsilon$取边际值时的$GCF_\epsilon$集

Let ∈ :N → R be a parameter function satisfying the condition ∈(k) + k + 1 > 0and let T∈ :(0,1] →(0,1] be a transformation defined by T∈(x) =-1 +(k + 1)x1 + k-k∈x for x ∈(1k + 1,1k].Under the algorithm T∈,every x ∈(0,1] is attached an expansion,called generalized continued fraction(GCF∈) expansion with parameters by Schweiger.Define the sequence {kn(x)}n≥1of the partial quotients of x by k1(x) = ∈1/x∈ and kn(x) = k1(Tn-1∈(x)) for every n ≥ 2.Under the restriction-k-1 < ∈(k) <-k,define the set of non-recurring GCF∈expansions as F∈= {x ∈(0,1] :kn+1(x) > kn(x) for infinitely many n}.It has been proved by Schweiger that F∈has Lebesgue measure 0.In the present paper,we strengthen this result by showing that{dim H F∈≥12,when ∈(k) =-k-1 + ρ for a constant 0 < ρ < 1;1s+2≤ dimHF∈≤1s,when ∈(k) =-k-1 +1ksfor any s ≥ 1where dim H denotes the Hausdorff dimension.     

缺项算子矩阵的本性谱

Let =(A C X B)be a 2×2 operator matrix acting on the Hilbert space н( )κ.For given A ∈B (H),B ∈B(K)and C ∈B(K,H)the set Ux∈B(H,к)σe(Mx)is determined,where σe(T)denotes the essential spectrum.     

Anisotropic Elliptic Nonlinear Obstacle Problem with Weighted Variable Exponent

In this paper, we are concerned with a show the existence of a entropy solution to the obstacle problem associated with the equation of the type :$\begin{cases}Au+g(x,u,∇u) = f & {\rm in} & Ω \\ u=0 & {\rm on} & ∂Ω \end{cases}$where $\Omega$ is a bounded open subset of $\;\mathbb{R}^{N}$, $N\geq 2$, $A\,$ is an operator of Leray-Lions type acting from $\; W_{0}^{1,\overrightarrow{p}(.)} (\Omega,\ \overrightarrow{w}(.))\;$ into its dual $\; W_{0}^{-1,\overrightarrow{p}'(.)} (\Omega,\ \overrightarrow{w}^*(.))$ and $\,L^1\,-\,$deta. The nonlinear term $\;g\,$: $\Omega\times \mathbb{R}\times \mathbb{R}^{N}\longrightarrow \mathbb{R} $ satisfying only some growth condition.     

Compact and Loeb Hausdorff spaces in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathsf {ZF}$\end{document} and the axiom of choice for families of finite sets

Given a set X, $\mathsf {AC}^{\mathrm{fin}(X)}$ denotes the statement: “$[X]^{<\omega }\backslash \lbrace \varnothing \rbrace$ has a choice set” and $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )$ denotes the family of all closed subsets of the topological space $\mathbf {2}^{X}$ whose definition depends on a finite subset of X. We study the interrelations between the statements $\mathsf {AC}^{\mathrm{fin}(X)},$ $\mathsf {AC}^{\mathrm{fin}([X]^{<\omega })},$ $\mathsf {AC}^{\mathrm{fin} (F_{n}(X,2))},$ $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$ and “$\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$has a choice set”. We show:

• (i) $\mathsf {AC}^{\mathrm{fin}(X)}$ iff $\mathsf {AC}^{\mathrm{fin}([X]^{<\omega } )}$ iff $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set iff $\mathsf {AC}^{\mathrm{fin}(F_{n}(X,2))}$.
• (ii) $\mathsf {AC}_{\mathrm{fin}}$ ($\mathsf {AC}$ restricted to families of finite sets) iff for every set X, $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set.
• (iii) $\mathsf {AC}_{\mathrm{fin}}$ does not imply “$\mathcal {K}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set($\mathcal {K}(\mathbf {X})$ is the family of all closed subsets of the space $\mathbf {X}$)
• (iv) $\mathcal {K}(\mathbf {2}^{X})\backslash \lbrace \varnothing \rbrace$ implies $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$ but $\mathsf {AC}^{\mathrm{fin}(X)}$ does not imply $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$.

We also show that “For every setX, “$\mathcal {K}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$has a choice set” iff “for every setX, $\mathcal {K}\big (\mathbf {[0,1]}^{X}\big )\backslash \lbrace \varnothing \rbrace$has a choice set” iff “for every product$\mathbf {X}$of finite discrete spaces,$\mathcal {K}(\mathbf {X})\backslash \lbrace \varnothing \rbrace$ has a choice set”.     

一类上三角矩阵环$W_{n}(p, q)$的斜Armendariz性质

设α是环R的一个自同态,称环R是α-斜Armendariz环,如果在R[x;α]中,(∑_(i=0)~ma_ix~i)(∑_(j=0)~nb_jx~j)=0,那么a_ia~i(b_j)=0,其中0≤i≤m,0≤j≤n.设R是α-rigid环,则R上的上三角矩阵环的子环W_n(p,q)是α~—-斜Armendariz环.     

On a Littlewood-Paley type inequality

The following is proved: If is a function harmonic in the unit ball and if then the inequality

holds, where is the nontangential maximal function of This improves a recent result of Stoll. This inequality holds for polyharmonic and hyperbolically harmonic functions as well.

     

E-紧框架小波来自MRA的特征刻画

设E=■或■,■(x)∈L~2(R~2)且■_(jk)(x)=2■(E~jx-k),其中j∈Z,k∈Z~2.若{■_(jk)|jJ∈Z,k∈Z~2}构成L~2(R~2)的紧框架,则称■(x)为E-紧框架小波.本文给出E-紧框架小波是MRA E-紧框架小波的一个充要条件,即E紧框架小波■来自多尺度分析当且仅当线性空间F_■(ξ)的维数为0或1,其中F_■(ξ)=■(ξ)|j■1},■_j(ξ)={■((E~T)~j(ξ+2kπ))}_(k∈EZ~2,j■1。