This article discusses an economic game called
"The struggle for markets". We have generated a
mathematical model of quantum realization of this
game. For clarity, the algorithms are derived for
soft and hard quantum games for assessing the
impact of the degree of entanglement to work and
the result of the algorithm. There are step-by-step
instructions for the sequence of actions and
operations to create a quantum model of the game.
The aim is to assess the influence of the degree of
entanglement on work algorithms. Also, we
investigate the influence of quantum entanglement
on the win for two or more players. The article
gives a comparison with classical results
It is known that not every finite group can be
realized over the field of rational numbers as a
Galois group of some binomial. In this connection,
a more general question arises: suppose that there
is given a finite transitive subgroup G of the
symmetric group S on n symbols; Can this group G
be realized as a Galois group of some trinomial of
degree n over the field of rational numbers? In this
paper we prove that every transitive subgroup of
the group S can be realized in the form of the
Galois group of a certain trinomial of the degree n,
for the values n = 2, 3, 4. For n = 5 , 6 we give
examples that realize concrete Galois groups. In the
case n = 7, all the transitive subgroups of the group
S are realized, except possibly one group of the
isomorphic dihedral group D. Further calculations
will be directed to the realization of specific Galois
groups for n = 8, 9 ..., however, the number of
transitive subgroups of the group S for n = 8, 9 ...
grows very fast, so the larger the value of n, the
more difficult it is to realize not just everything but
the specific subgroup of the group S in the form of
a trinomial over Q
In some works, the feasibility of the use of fixed and
variable electromagnetic fields of different frequencies
and tension in the production technology of sunflower
oil are shown, but there is no theoretical justification.
The possibility of electromagnetic effects is associated
with the presence of polar molecules specific to organic
systems. Without prejudice to the role of polar groups
of terrestrial circuits, this work tries to address this
challenge more comprehensively. The reason for this is
the distinctive feature of the behavior of sunflower
during its flowering. This characteristic is that the
sunflower hat during the day changes its direction in
accordance with the direction of movement of the Sun
across the sky; so called "magnetism" of their
attraction. To justify this effect, we have analyzed the
essence of emitted photons, the Sun chemical
composition and structure arrangement of seeds in a
sunflower hat. Particles of light from the Sun represent
a stream of photons - a wide range of electromagnetic
waves of frequencies that exhibit and magnetic
properties. The article shows principal macro- and
micronutrients of sunflower raw materials and divides
them into groups of para- , dia- , and ferromagnetic
materials. In sunflower seeds, there are chemical
elements: diamagnetism-C, H, N, P, S, B, Cu, Zn, J;
paramagnetism-O, K, Ca, Mg, Mo, As and
ferromagnetic-iron (Fe). As there is resultant force of
the magnetic attraction between the sunflower hat and
magnetic flow of photons from the Sun, this effect
dominates the action of paramagnetics K2O ( -28.4
24.5%), CaO (7.6-17.0)%, MgO (12.3-17.9%),
magnetized in an external magnetic field in the
direction of the field. The presence of evident effect
demonstrates that it is possible to improve a number of
technological operations in the manufacture of
sunflower oil using electrical, magnetic or
electromagnetic fields
The steady increase in demand for isotopes requires the
development of methods to increase the efficiency of
isotope separation technologies. Methods of isotope
separation based on thermodynamic differences of
isotopic forms of the molecules don't require significant
investment, but characterized by a low rate of exchange.
It's known that the magnetic effect leads to a change the
vibrational frequency of the molecules, and therefore
their thermodynamic parameters. The change increases
the thermodynamic parameters, including the exchange
rate. The results of the experimental determination of the
thermal effect of dissolving the salts of NaCl, KCl,
CuSO4, sodium amalgam decomposition by distillate in
a magnetic field and without field were shown. Magnetic
interference can have a significant effect on the amalgam
exchange method which was shown by quantum and
mechanical analysis of the results
In this article, we consider the task of systematizing the axioms and postulates, directly or indirectly connected with the study of the cycles of varying length and nature, which constitute the absolute of the general theory of cycles
Statistical methods are based on the developed theory and demonstrated its usefulness in the sectors of the economy. However, the analysis of the situation in the application of statistical methods shows obvious distress, in which accumulated in our country's scientific potential is not used to the full. As practice shows, it is not enough to develop promising modern theory-based effective mathematical and instrumental methods of controlling. For using such methods in mass, it is necessary that they would be implemented. Management of innovations, i.e. innovation management, quite rightly is currently one of the most debated sections of the economy and the organization of production, of the entire economic science in general. However, the implementation of applied statistics and other statistical methods, more generally, mathematical and instrumental methods of controlling, has its own specifics. It is considered in the article. We have highlighted the developmental vulnerabilities - low scientific level of many individuals applying statistical methods, the lack of organizational structure of applied statistics as a field of applied activities and others. We regret to note that the very idea of the need to establish requirements for the methods of data analysis and project formulations such requirements remained outside the attention of those professionals who need them and were addressed. We have no adequate system of guidance for documents on concrete statistical methods performed on modern scientific level. According to the author, the desired future of applied statistics is reorganization according to the model of Metrology. We have analyzed the application of statistical methods as a specialty. The analysis of state standards on statistical methods and the causes of them blunders are given. We have discussed the status of documents for statistical methods for standardization and quality control.
We discuss a new system of "Six Sigma" for implementation advanced mathematical and instrumental methods of controlling
In various applications, it is necessary to analyze
several expert orderings, i.e. clustered rankings
objects of examination. These areas include
technical studies, ecology, management, economics,
sociology, forecasting, etc. The objects can be some
samples of products, technologies, mathematical
models, projects, job applicants and others. In the
construction of the final opinion of the commission
of experts, it is important to find clustered ranking
that averages responses of experts. This article
describes a number of methods for clustered
rankings averaging, among which there is the
method of Kemeny median calculation, based on the
use of Kemeny distance. This article focuses on the
computing side of the final ranking among the
expert opinions problem by means of median
Kemeny calculation. There are currently no exact
algorithms for finding the set of all Kemeny
medians for a given number of permutations
(rankings without connections), only exhaustive
search. However, there are various approaches to
search for a part or all medians, which are analyzed
in this study. Zhikharev's heuristic algorithms serve
as a good tool to study the set of all Kemeny
medians: identifying any connections in mutual
locations of the medians in relation to the
aggregated expert opinions set (a variety of expert
answers permutations). Litvak offers one precise
and one heuristic approaches to calculate the median
among all possible sets of solutions. This article
introduces the necessary concepts, analyzes the
advantages of median Kemeny among other possible searches of expert orderings. It identifies
the comparative strengths and weaknesses of
examined computational ways
We consider the hypothesis of the origin of mass of the observed matter from electromagnetic field interacting with streams of preons. The interaction between preons and the scalar and vector potentials of the electromagnetic fields acquire mass, which leads to a massive scalar and vector bosons. The described mechanism of mass generation is different from the well-known Higgs mechanism associated with the spontaneous breaking of the electroweak symmetry, for which at the moment is finding a suitable scalar boson
Partially ordered set is a basic concept of modern settheoretic
mathematics. The problem of linear set
ordering with given binary relations is well-known.
Every partial order over a finite set can be linearly
ordered, but not every binary relation over this set can
be linearly ordered as well. Up to now, there is no
known formula for calculating the number of partial
orders over a given finite set. It appears that there is a
formula for calculating linearly ordered binary
relations over a finite set. This article is concerned
with derivation of this formula. The fact from work of
G.N. Titov [9] that a binary relation over a finite set is
linearly ordered if and only if any diagonal block,
derived from the binary relation matrix as a result of
setting main diagonal elements to zero, contains at
least one zero row (diagonal block of matrix means
any matrix composed of elements at the crossings of
rows and columns of a given matrix with the same
numbers), plays a key role in process of corroboration.
The main conclusion of the article is a theorem that
allows to find the number of linearly ordered binary
relations over a set of n elements using the formula. A
recurrence formula for the number of linearly ordered
(irreflexive) binary relations over a finite set of n
elements, provided in the lemma, was derived as well
The relationship of Mathematical Statistics (wider -
Mathematical methods of research) and history is
multifaceted. In our opinion, the history of
mathematical statistics is an integral part of this
mathematical discipline. We have given a review of
our works on the history of statistical methods. The
role of mathematical statistics for the history is very
important. In this article, we restrict ourselves to the
questions of chronology. For centuries, the
chronology is considered as a part of applied
mathematics. The main problem is that the whole
"common" concept of the Russian and the World
history as a whole presented in textbooks was faked
by the opponents of Russia after the collapse of the
global Empire (Russian kingdom) in the early 17th
century - 400 years ago. The stories about historical
events are the information weapon. It was used by
the new rulers to suppress the resistance of the
vanquished. A new mathematical and statistical
chronology of general and Russian history, which
was built by a scientific team led by Academician
Fomenko, has been helpful for the discussion about
the current economic and political problems of
relations between Russia and the West in the XXI
century. In our opinion, the new chronology of the
World and Russian history should be one of the
foundations of state-patriotic ideology and deriving
practical solutions. The purpose of this article is to
give the initial idea of the new chronology from this
point of view