Volume 62, Issue 5

Pseudo-BL-algebras are a noncommutative extention of BL-algebras. In this paper we consider polars in pseudo-BL-algebras and the class of complete pseudo-BL-algebras. In the final section, a version of the Cantor-Bernstein theorem will be proved.

With the help of a property of completely simple semigroups proved in this paper we give necessary and sufficient conditions for vertex-transitivity of Cayley digraphs of strong semilattices of completely simple semigroups.

The notion of weak relatively uniform convergence (wru-convergence, for short) on an abelian lattice ordered group G has been investigated in a previous authors’ article. In the present paper we deal with Cantor extension of G and completion of G with respect to a wru-convergence on G.

In this paper, we introduce the notion of a BO-algebra, and we prove that every BO-algebra is 0-commutative, and we show that BO-algebras, 0-commutative B-algebras, BM-algebras, p-semisimple BCI-algebras and abelian groups are logically equivalent.

Given two baric algebras (A 1, ω 1) and (A 2, ω 2) we describe a way to define a new baric algebra structure over the vector space A 1 ⊕ A 2, which we shall denote (A 1 ⋈ A 2, ω 1 ⋈ ω 2). We present some easy properties of this construction and we show that in the commutative and unital case it preserves indecomposability. Algebras of the form A 1 ⋈ A 2 in the associative, coutable-dimensional, zero-characteristic case are classified.

In this note we shall give characterisations for HNN extensions of non-cyclic polycyclic-by-finite groups with normal infinite cyclic associated subgroups to be residually finite, subgroup separable and conjugacy separable.

Some aspects of the theory of order and (D)-convergence in (ℓ)-groups with respect to ideals are investigated. Moreover some new Basic Matrix Theorems are proved.

By using the variant version of Mountain Pass Theorem, the existence of homoclinic solutions for a class of second-order Hamiltonian systems is obtained. The result obtained generalizes and improves some known works.

In this paper, we prove the existence and uniqueness of mild solution of a class of nonlinear fractional integrodifferential equations of neutral type with nonlocal conditions in a Banach space. New results are obtained by fixed point theorem.

We introduce the truncation method for solving a backward heat conduction problem with time-dependent coefficients. For this method, we give the stability analysis with new error estimates. Meanwhile, we investigate the roles of regularization parameters in these two methods. These estimates prove that our method is effective.

For a space X, let E k(X), E ks(X) and E k○ (X) denote respectively the set of Euler classes of oriented k-plane bundles over X, the set of Euler classes of stably trivial k-plane bundles over X and the spherical classes in H k(X; ℤ). We prove some general facts about the sets E k(X), E ks(X) and E k○ (X). We also compute these sets in the cases where X is a projective space, the Dold manifold P(m, 1) and obtain partial computations in the case that X is a product of spheres.

In this paper, we discuss precise asymptotics for a new kind of moment convergence of the moving-average process $$X_k = \sum\limits_{i = - \infty }^\infty {a_{i + k} \varepsilon _i }$$, k ≥1, where {ε i: −∞ < i < ∞} is a doubly infinite sequence of independent identically distributed random variables with mean zero and the finiteness of variance, {α i: −∞ < i < ∞} is an absolutely summable sequence of real numbers, i.e., $$\sum\limits_{i = - \infty }^\infty {\left| {a_i } \right| < \infty }$$.

Let {X n: n ≥ 1} be a strictly stationary sequence of positively associated random variables with mean zero and finite variance. Set $$S_n = \sum\limits_{k = 1}^n {X_k }$$, $$Mn = \mathop {\max }\limits_{k \leqslant n} \left| {S_k } \right|$$, n ≥ 1. Suppose that $$0 < \sigma ^2 = EX_1^2 + 2\sum\limits_{k = 2}^\infty {EX_1 X_k < \infty }$$. In this paper, we prove that if E|X 1|2+δ < for some δ ∈ (0, 1], and $$\sum\limits_{j = n + 1}^\infty {Cov\left( {X_1 ,X_j } \right) = O\left( {n^{ - \alpha } } \right)}$$ for some α > 1, then for any b > −1/2 $$\mathop {\lim }\limits_{\varepsilon \searrow 0} \varepsilon ^{2b + 1} \sum\limits_{n = 1}^\infty {\frac{{(\log \log n)^{b - 1/2} }} {{n^{3/2} \log n}}} E\left\{ {M_n - \sigma \varepsilon \sqrt {2n\log \log n} } \right\}_ + = \frac{{2^{ - 1/2 - b} E\left| N \right|^{2(b + 1)} }} {{(b + 1)(2b + 1)}}\sum\limits_{k = 0}^\infty {\frac{{( - 1)^k }} {{(2k + 1)^{2(b + 1)} }}}$$ and $$\mathop {\lim }\limits_{\varepsilon \nearrow \infty } \varepsilon ^{ - 2(b + 1)} \sum\limits_{n = 1}^\infty {\frac{{(\log \log n)^b }} {{n^{3/2} \log n}}E\left\{ {\sigma \varepsilon \sqrt {\frac{{\pi ^2 n}} {{8\log \log n}}} - M_n } \right\}} _ + = \frac{{\Gamma (b + 1/2)}} {{\sqrt 2 (b + 1)}}\sum\limits_{k = 0}^\infty {\frac{{( - 1)^k }} {{(2k + 1)^{2b + 2} }}} ,$$ where x + = max{x, 0}, N is a standard normal random variable, and Γ(·) is a Gamma function.

The class of functions that are ℓ-stable at some point is a generalization of the class of C 1,1 functions. In this paper we prove that the class of vector functions that are ℓ-stable at some point is closed under composition.