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The paper presents the main results of the study of the cargo delivery control system in the Arctic zone. The authors hypothesized the need to generate information about the disadvantages of the cargo delivery control system in order to select and make effective decisions on changing this system. It is determined that the current control system has a number of problems that impede the management of cargo transportation, which require identification and updating of organizational and economic methods for their elimination due to the special interest in the Arctic at the current stage of its development. The study utilized the methods of applied sociology – the method of expert assessment with subsequent processing. A score scale with verbal characteristic was introduced, the use of which by expert respondents made it possible to quantify the significance of the disadvantages of the cargo delivery control system in the Arctic zone. The survey was conducted among experts from among forwarding operators carrying out specialized activities in the region, according to a pre-formed questionnaire. The results of the study show that the control quality is declining, as well as that the problems of controlling the cargo delivery to the Arctic zone are now quite relevant. The paper concludes on the need to develop organizational and economic methods to control the delivery of goods to the Arctic zone. Organizational and economic methods are proposed, in particular, the formation of a single transport operator of the Northern Supply Haul and a self-regulatory organization of forwarding operators.

We prove that : if f(x) is a measurable function, finite almost everywhere on [0,1] then there is a Schauder series, which converges unconditionally to f almost everywhere on [0,1] and for every ε > 0 there is a measurable set E contained in [0,1], with |E|> 1 −ε, such that for each f∈C(E) there is a Schauder series, which unconditionally converges to f in the uniform norm.

In the paper it is shown that there exists a function \\[U\\in L^1[0,1)^2\\], which is universal for all class \\[L^{p}[0,1)^2\\], \\[p\\in (0,1)\\], by rectangles and by spheres with respect to the double Walsh system in the sense of signs of Fourier coefficients.

It is shown that there exist such a function g ∈ L 1 [ 0 , 1 ] and a weight function 0 < μ ( x ) ≤ 1 that g is universal for the weighted space L μ 1 [ 0 , 1 ] with respect to signs of its Fourier–Walsh coefficients.

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) It is shown that there exist such a function ... and a weight function ... that g is universal for the weighted space ... with respect to signs of its Fourier–Walsh coefficients.

We will consider the behavior of Fourier-Walsh coeffcients after modifcation of functions. Note that Luzin's idea of modifcation of a function improving its properties (see [1]) was substantially developed later on. In 1939, Men'shov [2] proved the following fundamental theorem.

For any 0<\\epsilon <1,\\ p\\geq 1 and each function f\\in L^{p}[0,1] one can find a function g\\in L^{p}[0,1],\\ mes\\{x\\in \\lbrack 0,1] ;\\ g\\neq f\\}<\\epsilon , such that the sequence \\{|c_{k}(g)|,\\ k\\in spec(g)\\} is monotonically decreasing, where \\{c_{k}(g)\\} is\\ the sequence of Fourier-Walsh coefficients of the function g(x).

We call an element \\(U\\) conditionally universal for a sequential convergence space \\(\\mathbf{\\Omega}\\) with respect to a minimal system \\(\\{\\varphi_n\\}_{n=1}^\\infty\\) in a continuously and densely embedded Banach space \\(\\mathcal{X}\\hookrightarrow\\mathbf{\\Omega}\\) if the partial sums of its phase-modified Fourier series is dense in \\(\\mathbf{\\Omega}\\). We will call the element \\(U\\) almost universal if the change of phases (signs) needs to be performed only on a thin subset of Fourier coefficients. In this paper we prove the existence of an almost universal element under certain assumptions on the system \\(\\{\\varphi_n\\}_{n=1}^\\infty\\). We will call a function \\(U\\) asymptotically conditionally universal in a space \\(L^1(\\mathcal{M})\\) if the partial sums of its phase-modified Fourier series is dense in \\(L^1(F_m)\\) for an ever-growing sequence of subsets \\(F_m\\subset\\mathcal{M}\\) with asymptotically null complement. Here we prove the existence of such functions \\(U\\) under certain assumptions on the system \\(\\{\\varphi_n\\}_{n=1}^\\infty\\). Moreover, we show that every integrable function can be slightly modified to yield such a function \\(U\\). In particular, we establish the existence of almost universal functions for \\(L^p([0,1])\\), \\(p\\in(0,1)\\), and asymptotically conditionally universal functions for \\(L^1([0,1])\\), with respect to the trigonometric system.