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Using a generalized Riccati transformation, some new oscillation criteria of linear second order matrix differential system with damping are built by the method of integral average. These results are based on the information on a sequence of subintervals of 𝑡 0 , ∞).
Using the Cartan–Laptev invariant analytic method, an invariant affine normal (𝐸) is constructed, which is intrinsically connected with the distribution of hyperplane elements in the (𝑛 + 1)-dimensional affine space. For the normal (𝐸) we define a second kind normal and an invariant (𝑛 –...
In this paper, we show that every conjugacy class of the imprimitive complex reflection group 𝐺(𝑚, 1, 𝑛) can be represented by an admissible diagram. For this, we introduce a length function for elements of 𝐺(𝑚, 1, 𝑛) and study its properties. This then allows us to establish the admissible...
In this study, we obtain a Voronovskaja type asymptotic estimate for 𝑞-BBH operators. Second purpose of this paper is to obtain the monotonicity properties of 𝑞-BBH operators.
Weakly prime ideals in a commutative ring with non-zero identity have been introduced and studied in Anderson and Smith, Houston J. Math. 29: 831–840, 2003. Here we study the weakly primary ideals of a commutative ring. We define a proper ideal 𝑃 of 𝑅 to be weakly primary if 0 ≠ 𝑝𝑞 ∈ 𝑃 implies 𝑝...
We show that a norm version of Hardy's inequality holds in a variable exponent Sobolev space provided the maximal operator is bounded. Our proof uses recent local versions of the inequality for a fixed exponent. We give an example to show that our assumptions on the exponent are essentially...
We describe a method for proving the existence of a differential field over which two given differential subfields are linearly disjoint. In the affirmative case, they are linear disjoint over their intersection, which can be computed using characteristic sets. Our method is based on the...
We prove that there exist two absolutely negligible subsets A and B of the real line R , whose algebraic sum A + B is an absolutely nonmeasurable subset of R . We also obtain some generalization of this result and formulate a relative open problem for uncountable commutative groups.
The linear conjugation problem for the class of exponentially doubly quasi-periodic functions is considered, when the jump line is doublyperiodic and consist of open arcs. Effective solutions are obtained by means of a Cauchy type integral with Weierstrass kernel.
It is shown that the uniqueness property of probability invariant measures is preserved under the operation of Cartesian products. A similar question is investigated for inductive limits of nonzero ॣ -finite invariant measures.
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