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This note gives the correct form of a result (Theorem 2, p. 478) published recently in [Math. Slovaca 60 (2010), 471–484].

The main objective of this paper is to construct a new sequence of operators involving Apostol-Genocchi polynomials based on certain parameters. We investigate the rate of convergence of the operators given in this paper using second-order modulus of continuity and Voronovskaja type approximation theorem. Moreover, we find weighted approximation result of the given operators. Finally, we derive the Kantorovich variant of the given operators and discussed the approximation results.

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.

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, 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 functionalϕλwhenλ 2R of functions belong to the classSLkconnected withk-Fibonacci numbers. The main purpose of this paper is to obtain sharp bounds forϕλbothλ 2R andλ 2C.

In this paper, we develop the theory of a class of casual differential equations on a time scale. An existence theorem for casual differential equations on a time scale is given under mixed Lipschitz and compactness conditions by the fixed point theorem in Banach algebra due to Dhage. Some fundamental differential inequalities on a time scale are also presented which are utilized to investigate the existence of extremal solutions. The comparison principle on casual differential equations on a time scale is established. Our results in this paper extend and improve some well-known results.

In this paper, the global exponential stability and periodicity are investigated for delayed neural network models with continuous coefficients and piecewise constant delay of generalized type. The sufficient condition for the existence and uniqueness of periodic solutions of the model is established by applying Banach’s fixed point theorem and the successive approximations method. By constructing suitable differential inequalities with generalized piecewise constant delay, some sufficient conditions for the global exponential stability of the model are obtained. Typical numerical examples with simulations are utilized to illustrate the validity and improvement in less conservatism of the theoretical results. This paper ends with a brief conclusion.

In this paper, by using lower bounds for linear forms in logarithms of algebraic numbers and the theory of continued fractions, we find all Fibonacci numbers that appear in generalized Pell sequences. Some interesting estimations involving generalized Pell numbers, that we believe are of independent interest, are also deduced. This paper continues a previous work that searched for Fibonacci numbers in the Pell sequence.

The authors developed in a recent paper natural dualities for finitely generated quasivarieties of Sugihara algebras. They thereby identified the admissibility algebras for these quasivarieties which, via the Test Spaces Method devised by Cabrer et al., give access to a viable method for studying admissible rules within relevance logic, specifically for extensions of the deductive system R-mingle.This paper builds on the work already done on the theory of natural dualities for Sugihara algebras. Its purpose is to provide an integrated suite of multisorted duality theorems of a uniform type, encompassing finitely generated quasivarieties and varieties of both Sugihara algebras and Sugihara monoids, and embracing both the odd and the even cases. The overarching theoretical framework of multisorted duality theory developed here leads on to amenable representations of free algebras. More widely, it provides a springboard to further applications.

In this paper, we consider the wavelet estimators of a nonparametric regression model based on widely orthant dependent random errors. The moment consistency and the completely consistency for wavelet estimators under some more mild moment conditions are investigated. The results obtained in the paper improve and extend the corresponding ones for dependent random variables. Finally, we provide a numerical simulation to verify the validity of our results.

The aim of this paper is to discuss the existence of mild solutions for a class of semilinear stochastic partial differential equation with nonlocal initial conditions and noncompact semigroups in a real separable Hilbert space. Combined with the theory of stochastic analysis and operator semigroups, a generalized Darbo’s fixed point theorem and a new estimation technique of the measure of noncompactness, we obtained the existence of mild solutions under the situation that the nonlinear term and nonlocal function satisfy some appropriate local growth conditions and a noncompactness measure condition. In addition, the condition of uniformly continuity of the nonlinearity is not required and also the strong restriction on the constants in the condition of noncompactness measure is completely deleted in this paper. An example to illustrate the feasibility of the main results is also given.

In this paper, the complete convergence for the weighted sums of arrays of rowwise extended negatively dependent (END, for short) random variables is established under some mild conditions. In addition, the Marcinkiewicz-Zygmund type strong law of large numbers for arrays of rowwise END random variables is also obtained. The result obtained in the paper generalizes and improves some corresponding ones for independent random variables and some dependent random variables in some extent. By using the complete convergence that we established, we further study the complete consistency for the weighted estimator in a nonparametric regression model based on END errors.

Š. Schwarz in his paper [SCHWARZ, Š.:Zur Theorie der Halbgruppen, Sborník prác Prírodovedeckej fakulty Slovenskej univerzity v Bratislave, Vol. VI, Bratislava, 1943, 64 pp.] proved the existence of maximal subgroups in periodic semigroups and a decade later he brought into play the maximal subsemigroups and thus he embodied the idempotents in the structural description of semigroups [SCHWARZ, Š.:Contribution to the theory of torsion semigroups, Czechoslovak Math. J.3(1) (1953), 7–21]. Later in his papers he showed that a proper description of these structural elements can be used to (re)prove many useful and important results in algebra and number theory. The present paper gives a survey of selected results scattered throughout the literature where an semigroup approach based on tools like idempotent, maximal subgroup or maximal subsemigroup either led to a new insight into the substance of the known results or helped to discover new approach to solve problems. Special attention will be given to some disregarded historical connections between semigroup and ring theory.

In this paper a general fixed point theorem for mappings with a new type of common limit range property satisfying a mixed implicit relation is proved. In the last part of the paper, as application, some fixed point results for mappings satisfying contractive conditions of integral type and for φ-contractive mappings are obtained.

The symbol 𝓢 c (X) denotes the hyperspace of all nontrivial convergent sequences in a Hausdorff space X. This hyperspace is endowed with the Vietoris topology. In the current paper, we compare the cellularity, the tightness, the extent, the dispersion character, the net weight, the i-weight, the π-weight, the π-character, the pseudocharacter and the Lindelöf number of 𝓢 c (X) with the corresponding cardinal function of X. We also answer a question posed by the authors in a previous paper.

In this paper, we introduce and investigate the following subclass 1 + 1 γ z f ′ ( z ) + λ z 2 f ″ ( z ) λ z f ′ ( z ) + ( 1 − λ ) f ( z ) − 1 ≺ φ ( z ) 0 ≤ λ ≤ 1 , γ ∈ C ∖ { 0 } $$\begin{array}{} \displaystyle 1+\frac{1}{\gamma }\left( \frac{zf'(z)+\lambda z^{2}f''(z)}{\lambda zf'(z)+(1-\lambda )f(z)}-1\right) \prec \varphi (z)\qquad\left( 0\leq \lambda \leq 1,\gamma \in \mathbb{C} \smallsetminus \{0\}\right) \end{array} $$ of analytic functions, φ is an analytic function with positive real part in the unit disk 𝔻, satisfying φ (0) = 1, φ '(0) > 0, and φ (𝔻) is symmetric with respect to the real axis. We obtain the upper bound of the second Hankel determinant | a2a4− a 3 2 $\begin{array}{} a^2_3 \end{array} $ | for functions belonging to the this class is studied using Toeplitz determinants. The results, which are presented in this paper, would generalize those in related works of several earlier authors.

The purpose of this paper is to study the notion of a ψ-porosity point and ψ-porosity topology, generated by it analogously to the porosity topology on the real line. The paper includes a necessary and sufficient conditions under which two ψ-porous topologies generated by two functions ψ 1 and ψ 2 are equal. The condition is formulated in terms of the behavior of two sequences of sets A k = { x ∈ ( 0 , ∞ ) : ψ 1 ( x ) < 1 k ψ 2 ( x ) } and B k = { x ∈ ( 0 , ∞ ) : ψ 2 ( x ) < 1 k ψ 1 ( x ) } . $\begin{array}{} A_k=\{x\in(0,\infty)\colon\psi_1(x) \lt \frac{1}{k}\psi_2(x)\} \text{ and } B_k=\{x\in(0,\infty)\colon\psi_2(x) \lt \frac{1}{k}\psi_1(x)\}. \end{array}$

Let 𝓜(Ω, μ) denote the algebra of all scalar-valued measurable functions on a measure space (Ω, μ). Let B ⊂ 𝓜(Ω, μ) be a set of finitely supported measurable functions such that the essential range of each f ∈ B is a subset of {0,1}. The main result of this paper shows that for any p ∈ (0, ∞), B has strict p-negative type when viewed as a metric subspace of L p (Ω, μ) if and only if B is an affinely independent subset of 𝓜(Ω, μ) (when 𝓜(Ω, μ) is considered as a real vector space). It follows that every two-valued (Schauder) basis of L p (Ω, μ) has strict p-negative type. For instance, for each p ∈ (0, ∞), the system of Walsh functions in L p [0,1] is seen to have strict p-negative type. The techniques developed in this paper also provide a systematic way to construct, for any p ∈ (2, ∞), subsets of L p (Ω, μ) that have p-negative type but not q-negative type for any q > p. Such sets preclude the existence of certain types of isometry into L p -spaces.

In this paper, we establish some Fejér-type inequalities for convex functions. They complement the results from the previous recent paper [Dragomir, S. S.—Milošević, D. S.——Sándor, J.: On some refinements of Hadamard’s inequalities and applications, Univ. Belgrad. Publ. Elek. Fak. Sci. Math. 4 (1993), 3–10].

Let D ∈ ℤ and let C D be the set of all monic cubic polynomials x 3 + ax 2 + bx + c ∈ ℤ[x] with the discriminant equal to D. Along the line of our preceding papers, the following Theorem has been proved: If D is square-free and 3 ∤ h(−3D) where h(−3D) is the class number of Q ( − 3 D ) , $\mathbb Q(\sqrt {-3D}),$ then all polynomials in C D have the same type of factorization over the Galois field 𝔽 p where p is a prime, p > 3. In this paper, we prove the validity of the above implication also for primes 2 and 3.

The main aim of this paper is to present some theorems in order to guarantee existence and uniqueness of best proximity points under rational contractivity conditions using very general test functions. To illustrate the variety of possible test functions, we include some examples of pairs of functions which are included in innovative papers published in the last years. As a consequence, we prove that our results unify and extend some recent results in this field.

The paper concerns interesting problems related to the field of Complex Analysis, in particular Nevanlinna theory of meromorphic functions. The author have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a value or small function. The results of this paper are generalizations of some problems studied in [BOUSSAF, K.—ESCASSUT, A.—OJEDA, J.: Complex meromorphic functions f′P′(f), g′P′(g) sharing a small function, Indag. Math. (N.S.) 24 (2013), 15–41] and in [DYAVANAL, R. S.: Uniqueness and value-sharing of differential polynomials of meromorphic functions, J. Math. Anal. Appl. 374 (2011), 335–345].

In this paper, the authors study oscillatory and asymptotic behavior of solutions of a class of nonlinear third order neutral differential equations with positive and negative coefficients of the form (E) ( a ( t ) ( b ( t ) ( y ( t ) + p ( t ) y ( σ ( t ) ) ) ′ ) ′ ) ′ + q ( t ) G ( y ( α ( t ) ) ) − h ( t ) H ( y ( β ( t ) ) ) = 0 $$\begin{equation*}(a(t)(b(t)(y(t)+p(t)y(\sigma(t)))^{\prime})^{\prime})^{\prime} +q(t)G(y(\alpha(t)))-h(t)H(y(\beta(t)))=0 \tag{E}\end{equation*}$$ for 0 ⩽ p(t) ⩽ p 1 p 2 ⩽ p(t) ⩽ 0. The results in this paper generalize the results of [LI, T.—ZHANG, C.—XING, G.: Oscillation of third-order neutral delay differential equations, Abstr. Appl. Anal. 2012 (2012), Article ID 569201] and various results in the literature. We establish new conditions which guarantees that every solutions of (E) either oscillatory or converges to zero. Examples are considered to illustrate the main results.

Let G be a finite group. In this paper we give a new necessary condition for two real G-modules to be Smith equivalent if G has a normal Sylow 2-subgroup. We show that the condition is also sufficient under certain hypotheses. By results on the Smith equivalence obtained in this paper, the primary Smith sets are not subgroups of the real representation rings for various Oliver groups with normal Sylow 2-subgroups.

In this paper we are concerned with the existence of infinitely many homoclinic solutions for the following second order non-autonomous Hamiltonian systems u ¨ t − L t u t + ∇ W t , u t = 0 $$ \ddot u\left( t \right) - L\left( t \right)u\left( t \right) + \nabla W\left( {t,u\left( t \right)} \right) = 0$$ (HS) where t ∈ ℝ, L ∈ C(ℝ, ℝ n 2 ) is a symmetric and positive definite matrix for all t ∈ ℝ, W ∈ C 1(ℝ × ℝ n , ℝ) and ∇W(t,u) is the gradient of W at u. The novelty of this paper is that, assuming that L meets some coercive condition and the potential W is of the form W(t, u) = W 1(t, u) + W2(t, u), for the first time we show that (HS) possesses two different sequences of infinitely many homoclinic solutions via the Fountain theorem and the dual Fountain theorem such that the corresponding energy functional of (HS) goes to infinity and zero, respectively. Some recent results in the literature are generalized and significantly improved.

In this paper we consider certain groupoid-valued measures and their connections with quantum logic states. Let ∗ stand for the Łukasiewicz t-norm on [0, 1]2. Let us consider the operation ⋄ on [0, 1] by setting x ⋄ y = (x ⊥ ∗y ⊥)⊥ ∗ (x∗y)⊥, where x ⊥ = 1−x. Let us call the triple L = ([0, 1], ⋄, 1) the Łukasiewicz groupoid. Let B be a Boolean algebra. Denote by L(B) the set of all L-valued measures (L-valued states). We show as a main result of this paper that the family L(B) consists precisely of the union of classical real states and Z 2-valued states. With the help of this result we characterize the L-valued states on orthomodular posets. Since the orthomodular posets are often understood as “quantum logics” in the logico-algebraic foundation of quantum mechanics, our approach based on a fuzzy-logic notion actually select a special class of quantum states. As a matter of separate interest, we construct an orthomodular poset without any L-valued state.

In the paper, we study the uniqueness of meromorphic functions when certain nonlinear differential polynomials share a nonzero polynomial. The results of the paper improves two recent results due to [LI, X. M.—YI, H. X.: Uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a polynomial, Comput. Math. Appl. 62 (2011), 539–550].

The paper is sacrificed to discussing the property of some special subfamily F of the family of all permutations of ℕ, especially in the context of the fundamental properties of families C and D of the, so called, convergent and divergent permutations, in other words, permutations preserving or not preserving the convergence of the rearranged real series, respectively. Family F is the subgroup of the group G generated by C. In the paper we will prove, among others, that F ⊂ C−1 ◦ C and F \ (C ◦ C−1) ≠ ∅. So, in particular we have G ≠ C◦C−1. The family F is neither the subset nor superset of any of the families C, D and C−1. By using the permutations belonging to the family F we receive the strengthening of some Kronrod’s theorems (which are the generalizations of the Riemann Derangement Theorem).

In [RUSCHEWEYH, S.-SHEIL-SMALL, T.: Hadamard product of schlicht functions and the Poyla-Schoenberg conjecture, Comment. Math. Helv. 48 (1973), 119-135] the authors proved the P`olya-Schoenberg conjecture that the class of convex univalent functions is preserved under convolution, namely K ∗ K = K. They proved also that the class of starlike functions and the class of close-to-convex functions are closed under convolution with the class K. In this paper we consider similar convolution problems for some classes of functions. Especially we give a new applications of a result [SOKÓŁ, J.: Convolution and subordination in the convex hull of convex mappings, Appl. Math. Lett. 19 (2006), 303-306] on the subordinating relations in the convex hull of convex mappings under convolution. The paper deals with several ideas and techniques used in geometric function theory. Besides being an application to those results it provides interesting corollaries concerning special functions, regions and curves.

In this paper, the conditions of correct solvability are found for a class of the third order operator-differential equations whose principal part has multiple characteristics in the Sobolev type space with exponential weight. The estimations of the norms of intermediate derivative operators closely connected with the solvability conditions are carried out. Moreover, the connection between the weight exponent and the lower bound of the spectrum of the main operator involved in the principal part of the equation is determined in the results of the paper.

In this paper we prove an existence theorem for ordinary differential equations in Banach spaces. The main assumptions in our results, formulated in terms of the Kuratowski measure of noncompactness, are motivated by the paper [CONSTANTIN, A.: On Nagumo’s theorem, Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), 41-44].

With modest standing assumptions on a category C, it is shown that a Galois connection exists between subclasses of C-objects (on the one hand) and classes of epimorphisms of C (on the other). In this connection the following classes are in a one-to-one correspondence, which reverses inclusion: the epireflective classes of C-objects with the classes ε of epimorphisms which are pushout invariant, in the sense that, for each pushout diagram in which e ∈ ε, then it follows that n ∈ ε. The paper then examines some of the consequences of this result, and in so doing “revisits” the pushout invariance of the authors as it was discussed in a paper of some fifteen years ago.

In this paper, two new classes of harmonic univalent functions with varying arguments are defined by using planar harmonic convolution operator involving hypergeometric functions. Those classes are of special interest because they contain various classes of well-known harmonic univalent functions such as the classes of k-starlike and k-uniformly convex harmonic univalent functions. The main purpose of this paper is to investigate neighbourhoods of the classes in question.

In this paper we introduce generalized or vector-valued Orlicz-Lorentz sequence spaces l p,q,M (X) on Banach space X with the help of an Orlicz function M and for different positive indices p and q. We study their structural properties and investigate cross and topological duals of these spaces. Moreover these spaces are generalizations of vector-valued Orlicz sequence spaces l M (X) for p = q and also Lorentz sequence spaces for M(x) = x q for q ≥ 1. Lastly we prove that the operator ideals defined with the help of scalar valued sequence spaces l p,q,M and additive s-numbers are quasi-Banach operator ideals for p < q and Banach operator ideals for p ≥ q. The results of this paper are more general than the work of earlier mathematicians, say A. Pietsch, M. Kato, L. R. Acharya, etc.

The paper concerns the density points with respect to the sequences of intervals tending to zero in the family of Lebesgue measurable sets. It shows that for some sequences analogue of the Lebesgue density theorem holds. Simultaneously, this paper presents proof of theorem that for any sequence of intervals tending to zero a relevant operator ϕJ generates a topology. It is almost but not exactly the same result as in the category aspect presented in [WIERTELAK, R.: A generalization of density topology with respect to category, Real Anal. Exchange 32 (2006/2007), 273–286]. Therefore this paper is a continuation of the previous research concerning similarities and differences between measure and category.

In this paper, by using a fixed-point theorem in cones to study the boundary value problem for a class of quadratic mixed type of delay differential equations with eigenvalue, the sufficient condition of existence of their solutions is derived. The main results in this paper are the generalization and improvement of those existing ones.

A sequential implicit function theorem for the method of chords was proved in the paper cited in the title. In this paper we add to this theorem a statement regarding the Lipschitz continuity of the mapping involved together with a sketch of proof.

In the paper, we study eight properties of partial algebras most of which are related to diagonality. For each of the properties, we give sufficient conditions under which this property is preserved by powers of partial algebras. In the paper, we study eight properties of partial algebras most of which are related to diagonality. For each of the properties, we give sufficient conditions under which this property is preserved by powers of partial algebras.

In this paper, some properties of prime elements, pseudoprime elements, irreducible elements and coatoms in posets are investigated. We show that the four kinds of elements are equivalent to each other in finite Boolean posets. Furthermore, we demonstrate that every element of a finite Boolean poset can be represented by one kind of them. The example presented in this paper indicates that this result may not hold in every finite poset, but all the irreducible elements are proved to be contained in each order generating set. Finally, the multiplicative auxiliary relation on posets and the notion of arithmetic poset are introduced, and some properties about them are generalized to posets.

In this paper we study q-subharmonic and q-plurisubharmonic functions in ℂn. Next as an application, we give the notion of q-convex domains in ℂn which is an extension of weakly q-convex domains introduced and investigated in [10]. In the end of the paper we show that the q-convexity is the local property and give some examples about q-convex domains.

The present paper deals with continuous extreme-like selections for the Vietoris hyperspace of countably compact spaces. Several new results and applications are established, along with some known results which are obtained under minimal hypotheses. The paper contains also a number of examples clarifying the role of countable compactness.

Orthocomplemented difference lattices (ODLs) are orthocomplemented lattices endowed with an additional operation of “abstract symmetric difference”. In studying ODLs as universal algebras or instances of quantum logics, several results have been obtained (see the references at the end of this paper where the explicite link with orthomodularity is discussed, too). Since the ODLs are “nearly Boolean”, a natural question arises whether there are “nearly Boolean rings” associated with ODLs. In this paper we find such an association — we introduce some difference ring-like algebras (the DRAs) that allow for a natural one-to-one correspondence with the ODLs. The DRAs are defined by only a few rather plausible axioms. The axioms guarantee, among others, that a DRA is a group and that the association with ODLs agrees, for the subrings of DRAs, with the famous Stone (Boolean ring) correspondence.

A structure on terms of faster convergent series is studied in the paper. Necessary and sufficient conditions for the existence of faster convergent series with different types of terms are found. A faster convergence criteria for certain Kummer’s series is proved in this paper.

There are two definitions of Γ-semigroups and investigations for both of them in the bibliography. The definition given by Sen in 1981, and the definition given by Sen and Saha in 1986. In this paper we show the way we pass from ordered semigroups to ordered Γ-semigroups no matter which one of the two definitions we use. Moreover we show that, exactly as in ordered semigroups, in many results of ordered Γ-semigroups points do not play any essential role, but the sets, which shows their pointless character. Under the methodology using in this paper, all the results of ordered semigroups can be transferred into ordered Γ-semigroups.

In this paper we prove some general theorems on the existence of continuous order-preserving functions on topological spaces with a continuous preorder. We use the concepts of network and netweight to prove new continuous representation theorems and we establish our main results for topological spaces that are countable unions of subspaces. Some results in the literature on path-connected, locally connected and separably connected spaces are shown to be consequences of the general theorems proved in the paper. Finally, we prove a continuous representation theorem for hereditarily separable spaces.

In two earlier papers [GAVRILUŢ, A.: A Gould type integral with respect to a multisubmeasure, Math. Slovaca 58 (2008), 1–20] and [Gavriluţ, A.: On some properties of the Gould type integral with respect to a multisubmeasure, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 52 (2006), 177–194], we defined and studied a Gould type integral for a real valued, bounded function with respect to a multisubmeasure having finite variation. In this paper, we introduce and study the properties of a Gould type integral in the general setting: the function may be unbounded and the variation of the multisubmeasure may be infinite.

Many algebras arising in logic have a lattice structure with intervals being equipped with antitone involutions. It has been proved in [CHK1] that these lattices are in a one-to-one correspondence with so-called basic algebras. In the recent papers [BOTUR, M.—HALAŠ, R.: Finite commutative basic algebras are MV-algebras, J. Mult.-Valued Logic Soft Comput. (To appear)]. and [BOTUR, M.—HALAŠ, R.: Complete commutative basic algebras, Order 24 (2007), 89–105] we have proved that every finite commutative basic algebra is an MV-algebra, and that every complete commutative basic algebra is a subdirect product of chains. The paper solves in negative the open question posed in [BOTUR, M.—HALAŠ, R.: Complete commutative basic algebras, Order 24 (2007), 89–105] whether every commutative basic algebra on the interval [0, 1] of the reals has to be an MV-algebra.

In this paper we define the notion of relative subalgebra of an MV-algebra A. A particular case of this notion is the notion of interval subalgebra of A; this has been already studied in the literature. Applying these notions, two new categories denoted as r and int are introduced. In both cases the objects are MV-algebras, but the homomorphisms are defined by means of relative subalgebras or by interval subalgebras, respectively. The relations occurring between these categories and the category of all MV-algebras with usual homomorphisms are investigated. The main results of the paper deal with one-generated free MV-algebras in the variety generated by the finite chains S i, i ⩽ p (p varying over the set of all positive integers) and their relations to certain relative subalgebras of the cyclic free MV-algebra.

We consider the problem of making statistical inference about the mean of a normal distribution based on a random sample of quantized (digitized) observations. This problem arises, for example, in a measurement process with errors drawn from a normal distribution and with a measurement device or process with a known resolution, such as the resolution of an analog-to-digital converter or another digital instrument. In this paper we investigate the effect of quantization on subsequent statistical inference about the true mean. If the standard deviation of the measurement error is large with respect to the resolution of the indicating measurement device, the effect of quantization (digitization) diminishes and standard statistical inference is still valid. Hence, in this paper we consider situations where the standard deviation of the measurement error is relatively small. By Monte Carlo simulations we compare small sample properties of the interval estimators of the mean based on standard approach (i.e. by ignoring the fact that the measurements have been quantized) with some recently suggested methods, including the interval estimators based on maximum likelihood approach and the fiducial approach. The paper extends the original study by Hannig et al. (2007).

In this paper, sufficient conditions are obtained, so that the second order neutral delay differential equation $$ (r(t)(y(t) - p(t)y(t - \tau ))')' + q(t)G(y(h(t)) = f(t) $$ has a positive and bounded solution, where q, h, f ∈ C ([0, ∞), ℝ) such that q(t) ≥ 0, but ≢ 0, h(t) ≤ t, h(t) → ∞ as t → ∞, r ∈ C (1) ([0, ∞), (0, ∞)), p ∈ C (2) [0, ∞), ℝ), G ∈ C(ℝ, ℝ) and τ ∈ ℝ+. In our work r(t) ≡ 1 is admissible and neither we assume G is non-decreasing, xG(x) > 0 for x ≠ 0, nor we take G is Lipschitzian. Hence the results of this paper improve many recent results.