Band 71, Heft 4

A quasi-decomposition of a Hilbert algebra A is a pair ( C , D ) of its subalgebras such that (i) every element a ∈ A is a meet c ∧ d with c ∈ C , d ∈ D , where c and d are compatible (i.e., c → d = c → ( c ∧ d )), and (ii) d → c = c (then c is uniquely defined). Quasi-decompositions are intimately related to the so-called triple construction of Hilbert algebras, which we reinterpret as a construction of quasidirect products. We show that it can be viewed as a generalization of the semidirect product construction, that quasidirect products has a certain universal property and that they can be characterised in terms of short exact sequences. We also discuss four classes of Hilbert algebras and give for each of them conditions on a quasi-decomposition of an arbitrary Hilbert algebra A under which A belongs to this class.

When an algebraic logic based on a poset instead of a lattice is investigated then there is a natural problem how to introduce implication to be everywhere defined and satisfying (left) adjointness with conjunction. We have already studied this problem for the logic of quantum mechanics which is based on an orthomodular poset or the logic of quantum effects based on a so-called effect algebra which is only partial and need not be lattice-ordered. For this, we introduced the so-called operator residuation where the values of implication and conjunction need not be elements of the underlying poset, but only certain subsets of it. However, this approach can be generalized for posets satisfying more general conditions. If these posets are even finite, we can focus on maximal or minimal elements of the corresponding subsets and the formulas for the mentioned operators can be essentially simplified. This is shown in the present paper where all theorems are explained by corresponding examples.

In the paper, we solve a problem proposed by Schinzel and Bednarek: A monic polynomial f ( x ) 2 – 1 with deg( f ) ≥ 3 is not a product of factors of degree one.

In a recent paper, Sokół et al. [ Applications of k-Fibonacci numbers for the starlike analytic functions , Hacet. J. Math. Stat. 44(1) (2015), 121{127] obtained an upper bound for the Fekete-Szegö functional ϕ λ when λ 2 R of functions belong to the class SL k connected with k -Fibonacci numbers. The main purpose of this paper is to obtain sharp bounds for ϕ λ both λ 2 R and λ 2 C.

The elementary Reinhardt domain associated to multi-index k = ( k 1 , …, k n ) ∈ ℤ n is defined by ℋ(k):={z∈Dn:zk is defined and |zk|<1}.$$\mathcal{H}(\mathbf{k}):=\{z\in\mathbb{D}^n: z^{\mathbf{k}}\ \text{is defined and}\ |z^{\mathbf{k}}|<1\}.$$ In this paper, we study the mapping properties of the associated Bergman projection on L p spaces and L p Sobolev spaces of order ≥ 1.

We introduce lemniscate-like constants by “twisting” the standard series expansions of the classical lemniscate constants via harmonic-type factors in the summand. Closed-form evaluations for these constants are established, and are then utilized to construct alternate proofs of summation formulae obtained recently via coefficient-extraction techniques applied to Kummer’s classical hypergeometric identity.

A class of second-order neutral delay differential equations is considered. New oscillation criteria are established to complement and improve some known results in the literature. Two examples are given to support our results.

This paper deals with the oscillation of second-order nonlinear retarded difference equations. We present some new oscillation criteria via comparison with first-order equations whose oscillatory behavior are known. The results are generalized to be applicable to different kinds of neutral equations. An example is also given to demonstrate the applicability of the obtained conditions.

The de la Vallée Poussin inequality is a handy tool for the investigation of disconjugacy, and hence, for the oscillation/nonoscillation of differential equations. The results in this paper are extensions of former those of Hartman and Wintner [Quart. Appl. Math. 13 (1955), 330–332] to the impulsive differential equations. Although the inequality first appeared in such an early date for ordinary differential equations, its improved version for differential equations under impulse effect never has been occurred in the literature. In the present study, first, we state and prove a de la Vallée Poussin inequality for impulsive differential equations, then we give some corollaries on disconjugacy. We also mention some open problems and finally, present some examples that support our findings.

In this paper, we define a particular class of Fourier Integral Operators (FIO for short). These FIO turn out to be bounded on the spaces S (ℝ n ) of rapidly decreasing functions (or Schwartz space) and S ′ (ℝ n ) of temperate distributions. Results about the composition of FIO with its L 2 -adjoint are proved. These allow to obtain results about the continuity on the Sobolev Spaces.

In this paper, we study the periodicity, the boundedness of the solutions, and the global asymptotic stability of the positive equilibrium of the system of p nonlinear difference equations xn+1(1)=A+xn−1(1)xn(p),xn+1(2)=A+xn−1(2)xn(p),…,xn+1(p−1)=A+xn−1(p−1)xn(p),xn+1(p)=A+xn−1(p)xn(p−1)$$\begin{equation*}x^{(1)}_{n+1}=A+\dfrac{x^{(1)}_{n-1}}{x^{(p)}_{n}},\quad x^{(2)}_{n+1}=A+\dfrac{x^{(2)}_{n-1}}{x^{(p)}_{n}},\quad\ldots,\quad x^{(p-1)}_{n+1}=A+\dfrac{x^{(p-1)}_{n-1}}{x^{(p)}_{n}},\quad x^{(p)}_{n+1}=A+\dfrac{x^{(p)}_{n-1}}{x^{(p-1)}_{n}} \end{equation*} $$ where n ∈ ℕ 0 , p ≥ 3 is an integer, A ∈ (0, +∞) and the initial conditions x−1(j)$x_{-1}^{(j)}$, x0(j)$x_{0}^{(j)}$, j = 1, 2, …, p are positive numbers.

In this paper, we introduce the notion of exponentially convex functions on time scales and then we establish Hermite-Hadamard type inequalities for this class of functions. As special case, we derive this double inequality in the context of classical notion of exponentially convex functions and convex functions. Moreover, we prove some new integral inequalities for n -times continuously differentiable functions with exponentially convex first Δ-derivative.

In this article, sufficient conditions are obtained so that every solution of the neutral difference equation Δm(yn−pnL(yn−s))+qnG(yn−k)=0,$$\begin{equation*}\Delta^{m}\big(y_n-p_n L(y_{n-s})\big) + q_nG(y_{n-k})=0, \end{equation*}$$ or every unbounded solution of Δm(yn−pnL(yn−s))+qnG(yn−k)−unH(yα(n))=0,n≥n0,$$\begin{equation*}\Delta^{m}\big(y_n-p_n L(y_{n-s})\big) + q_nG(y_{n-k})-u_nH(y_{\alpha(n)})=0,\quad n\geq n_0, \end{equation*}$$ oscillates, where m =2 is any integer, Δ is the forward difference operator given by Δ y n = y n +1 − y n ; Δ m y n = Δ(Δ m −1 y n ) and other parameters have their usual meaning. The non linear function L ∈ C (ℝ, ℝ) inside the operator Δ m includes the case L ( x ) = x . Different types of super linear and sub linear conditions are imposed on G to prevent the solution approaching zero or ±∞. Further, all the three possible cases, p n ≥ 0, p n ≤ 0 and p n changing sign, are considered. The results of this paper generalize and extend some known results.

In this paper, we introduce the sine extended odd Fréchet-G family of distributions, obtained from two well-established families of distributions of completely different nature: the sine-G and the extended odd Fréchet-G families. A particular focus is put on a very flexible member of this family defin ed with the Nadarajah-Haghighi distribution as a baseline, called the sine extended odd Fréchet Nadarajah-Haghighi distribution. For the theoretical part, the interesting mathematical properties of the family are investigated, including asymptotes, quantile function, linear representations and moments, with application to the introduced special member. Then, the inferential aspects of the sine extended odd Fréchet Nadarajah-Haghighi model are examined. In particular, the parameters are estimated by the maximum likelihood method. Two complementary cases are distinguished: the complete data case and the right censored data case, with the development of appropriate statistical tests. A simulation study is carried out to illustrate the convergence of the obtained estimates. Applications are given for three practicaldata sets, including one having the right censored property, illustrating the applicability of the proposed model.

In this paper, we introduce a new two-parameter lifetime distribution which is called extended Half-Logistic (EHL) distribution. Theoretical properties of this model including the hazard function, quantile function, asymptotic, extreme value, moments, conditional moments, mean residual life, mean past lifetime, residual entropy, cumulative residual entropy and order statistics are derived and studied in details. The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study. Finally, two real data sets are illustration the purposes.

This paper aims at producing numerical solutions of nonlinear parabolic PDEs with forcing term without any linearization. Since the linearization of nonlinear term leads to lose real features, without doing linearization, this paper focuses on capturing natural behaviour of the mechanism. Therefore we concentrate on analysis of the physical processes without losing their properties. To carry out this study, a backward differentiation formula in time and a spline method in space have been combined in leading to the discretized equation. This method leads to a very reliable alternative in solving the problem by conserving the physical properties of the nature. The efficiency of the present method are proved theoretically and illustrated by various numerical tests.

In a recent paper [JUKIĆ, D.: A necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set , J. Comput. Appl. Math. 375 (2020)], a new existence level was introduced and then was used to obtain a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set. In this paper, we determined that existence level for the residual sum of squares of the power-law regression with an unknown location parameter, and so we obtained a necessary and sufficient condition which guarantee the existence of the least squares estimate.

The category of MV-algebras is equivalent to the category of abelian lattice ordered groups with strong units. In this article we introduce the category of circled abelian groups and prove that the category of chain MV-algebras is isomorphic with the category of chain circled abelian groups. In the last section we show that the category of chain MV-algebras is a subcategory of abelian cyclically ordered groups.