Volume 28, Issue 1

A progressive iterative approximation technique for rational least squares fitting curves is developed. The format is interesting in CAGD (Computer Aided Geometric Design) and improves the recent algorithms. An improved chord method for the root finding based on rational operators is also presented.

In this paper, we study (non-Abelian) extensions of a given hom-Lie color algebra and provide a geometrical interpretation of extensions. In particular, we characterize an extension of a hom-Lie color algebra 𝔤{\mathfrak{g}} by another hom-Lie color algebra 𝔥{\mathfrak{h}} and discuss the case where 𝔥{\mathfrak{h}} has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, curvature and the Bianchi identity for possible extensions in differential geometry. Moreover, we find a cohomological obstruction to the existence of extensions of hom-Lie color algebras, i.e., we show that in order to have an extendible hom-Lie color algebra, there should exist a trivial member of the third cohomology.

Effective sufficient conditions are given for the unique solvability of the Cauchy problem for linear systems of generalized ordinary differential equations with singularities.

Sufficient conditions for the existence and uniqueness of a classical solution to a nonlocal problem for a system of Sobolev-type differential equations with integral condition are established. By introducing a new unknown function, we reduce the considered problem to an equivalent problem consisting of a nonlocal problem for the system of hyperbolic equations of second order with a functional parameter and an integral relation. We propose the algorithm for finding an approximate solution to the investigated problem and prove its convergence.

We prove that a completely regular locale L is realcompact if and only if the “remainder” β⁢L∖L{\beta L\smallsetminus L} is the join of the zero-sublocales of β⁢L{\beta L} that miss L . This extends a result of Mrówka which characterizes realcompact spaces in terms of their remainders in Stone–Čech compactifications. We prove that β⁢L∖L{\beta L\smallsetminus L} is Lindelöf if and only if L is of countable type, where the latter is defined for locales exactly as for spaces, subject to replacing subspaces with sublocales.

The purpose of the present paper is to obtain the degree of approximation in terms of a Lipschitz type maximal function for the Kantorovich type modification of Jakimovski–Leviatan operators based on multiple Appell polynomials. Also, we study the rate of approximation of these operators in a weighted space of polynomial growth and for functions having a derivative of bounded variation. A Voronvskaja type theorem is obtained. Further, we illustrate the convergence of these operators for certain functions through tables and figures using the Maple algorithm and, by a numerical example, we show that our Kantorovich type operator involving multiple Appell polynomials yields a better rate of convergence than the Durrmeyer type Jakimovski Leviatan operators based on Appell polynomials introduced by Karaisa (2016).

In this paper, we show some refinements of generalized numerical radius inequalities involving the Young and Heinz inequality. In particular, we present wpp⁢(A1*⁢T1⁢B1,…,An*⁢Tn⁢Bn)≤n1-1r21r⁢∥∑i=1n[Bi*⁢f2⁢(|Ti|)⁢Bi]r⁢p+[Ai*⁢g2⁢(|Ti*|)⁢Ai]r⁢p∥1r-inf∥x∥=1⁡η⁢(x),w_{p}^{p}(A_{1}^{*}T_{1}B_{1},\dots,A_{n}^{*}T_{n}B_{n})\leq\frac{n^{1-\frac{1% }{r}}}{2^{\frac{1}{r}}}\bigg{\|}\sum_{i=1}^{n}[B_{i}^{*}f^{2}(|T_{i}|)B_{i}]^{% rp}+[A_{i}^{*}g^{2}(|T_{i}^{*}|)A_{i}]^{rp}\bigg{\|}^{\frac{1}{r}}-\inf_{\|x\|% =1}\eta(x), where Ti,Ai,Bi∈𝔹⁢(ℋ){T_{i},A_{i},B_{i}\in\mathbb{B}(\mathscr{H})}(1≤i≤n){(1\leq i\leq n)}, f and g are nonnegative continuous functions on [0,∞){[0,\infty)} satisfying f⁢(t)⁢g⁢(t)=t{f(t)g(t)=t} for all t∈[0,∞){t\in[0,\infty)}, p,r≥1{p,r\geq 1}, N∈ℕ{N\in\mathbb{N}}, and η(x)=12∑i=1n∑j=1N(〈(Ai*⁢g2⁢(|Ti*|)⁢Ai)p⁢x,x〉2j-1-kj⁢〈(Bi*⁢f2⁢(|Ti|)⁢Bi)p⁢x,x〉kj2j\displaystyle\eta(x)=\frac{1}{2}\sum_{i=1}^{n}\sum_{j=1}^{N}\Bigl{(}\sqrt[2^{j% }]{\big{\langle}(A_{i}^{*}g^{2}(|T_{i}^{*}|)A_{i})^{p}x,x\big{\rangle}^{2^{j-1% }-k_{j}}\big{\langle}(B_{i}^{*}f^{2}(|T_{i}|)B_{i})^{p}x,x\big{\rangle}^{k_{j}}}-〈(Bi*⁢f2⁢(|Ti|)⁢Bi)p⁢x,x〉kj+1⁢〈(Ai*⁢g2⁢(|Ti*|)⁢Ai)p⁢x,x〉2j-1-kj-12j)2.\displaystyle -\sqrt[2^{j}]{\big{\langle}(B_{i}^{*}f^{2}(|T_{i}|)B_{i}% )^{p}x,x\big{\rangle}^{k_{j}+1}\big{\langle}(A_{i}^{*}g^{2}(|T_{i}^{*}|)A_{i})% ^{p}x,x\big{\rangle}^{2^{j-1}-k_{j}-1}}\,\Big{)}^{2}.

By using a purely probabilistic argumentation, two theorems are proved. They simplify the existing methods of analysis for the M/G/1{M/G/1} queuing system by means of the supplementary variables method.

In the paper, we derive a formula of integration by parts for the left-sided Hilfer derivative. Moreover, we present a formula of such a type for the right-sided Hilfer derivative. These results generalize the well-known rules of integration by parts for the Riemann–Liouville and Caputo derivatives. Finally, we use these rules to investigate some boundary value problems involving mixed fractional derivatives.

The present paper deals with the Lie triple systems via Leibniz algebras. A perfect Lie algebra as a perfect Leibniz algebra and as a perfect Lie triple system is considered and the appropriate universal central extensions are studied. Using properties of Leibniz algebras, it is shown that the Lie triple system universal central extension is either the universal central extension of the Leibniz algebra or the universal central extension of the Lie algebra.

In this paper, we define accessibility on an iterated function system (IFS) and show that it provides a sufficient condition for the transitivity of this system and its corresponding skew product. Then, by means of a certain tool, we obtain the topologically mixing property. We also give some results about the ergodicity and stability of accessibility and, further, illustrate accessibility by some examples.

In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers and several integer sequences related to them have been studied. In the present paper, new sets of Bell–Sheffer polynomials are introduced. Connections with Bell numbers are shown.

The main goal of the present paper is to study some results concerning generalized derivations of prime rings with involution. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.

The nonlinear fractional differential equation with nonlocal fractional integro-differential boundary conditions in Banach spaces is studied, an existence result is obtained by using the method associated with the technique of measures of noncompactness and an appropriate fixed point theorem. An example is given to illustrate the theory.

Gabardo and Nashed studied nonuniform wavelets by using the theory of spectral pairs for which the translation set Λ={0,r/N}+2⁢ℤ{\Lambda=\{0,r/N\}+2\mathbb{Z}} is no longer a discrete subgroup of ℝ{\mathbb{R}} but a spectrum associated with a certain one-dimensional spectral pair. In this paper, we establish three sufficient conditions for the nonuniform wavelet system {ψj,λ⁢(x)=(2⁢N)j/2⁢ψ⁢((2⁢N)j⁢x-λ),j∈ℤ,λ∈Λ}{\{\psi_{j,\lambda}(x)=(2N)^{j/2}\psi((2N)^{j}x-\lambda),\,j\in\mathbb{Z},\,% \lambda\in\Lambda\}} to be a frame for L2⁢(ℝ){L^{2}(\mathbb{R})}. The proposed inequalities are stated in terms of Fourier transforms and hold without any decay assumptions on the generator of such a system.

We give some new characterizations of quasi-Frobenius rings. Namely, we prove that for a ring R , the following statements are equivalent: (1) R is a quasi-Frobenius ring, (2) M2⁢(R){M_{2}(R)} is right Johns and every closed left ideal of R is cyclic, (3) R is a left 2-simple injective left Kasch ring with ACC on left annihilators, (4) R is a left 2-injective semilocal ring such that R/Sl{R/S_{l}} is left Goldie, (5) R is a right YJ-injective right minannihilator ring with ACC on right annihilators.