The article proposes a method for constructing non-standard theories based on terms from partially existing sequences of elements. The method is illustrated by the example of the theory of monoids. ...Predicates and terms from non-standard sequences, 2023, udc: 510.65 msc: 03H05 Key words: monoid, term, ideal, category, isomorphizm, insignificant extension of the theory, non-standard theory
The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a ...convenient and short way of replacing axiom systems is shown. With such a replacement, the main idea of the system of axioms of the given mathematical theory immediately becomes clear. The reasons for using number systems in mathematics are also shown.
We study weakly perturbed integrodifferential equations with degenerate kernel in Banach spaces and establish conditions for the bifurcation of solutions of weakly perturbed integrodifferential ...equations in Banach spaces at the point
ε
= 0. A convergent iterative procedure is proposed for the determination of solutions in the form of series
∑
i
=
1
+
∞
ε
i
z
i
t
in powers of
ε
..
We consider weakly nonlinear Fredholm integral equations with degenerate kernel in Banach spaces and establish a necessary condition and sufficient conditions for the existence of solutions of ...equations of this kind. The convergent iterative procedures are proposed for the construction either of a single solution or of at least one possible solution.
Bounded Solutions of Evolutionary Equations Boichuk, O. A.; Zhuravl’ov, V. P.; Pokutnyi, O. O.
Ukrainian mathematical journal,
06/2018, Letnik:
70, Številka:
1
Journal Article
Recenzirano
We study the problems of existence and representations of the solutions bounded on the entire axis for both linear and nonlinear differential equations with unbounded operator coefficients in the ...Fréchet and Banach spaces under the condition of exponential dichotomy on the semiaxes of the corresponding homogeneous equation.
Precision drift tube chambers with a sense wire positioning accuracy of better than
20
μm
are under construction for the ATLAS muon spectrometer. 70% of the 88 large chambers for the outermost layer ...of the central part of the spectrometer have been assembled. Measurements during chamber construction of the positions of the sense wires and of the sensors for the optical alignment monitoring system demonstrate that the requirements for the mechanical precision of the chambers are fulfilled.
PDF
