
TO D’ALEMBERTEULER PARADOX 
On arguing to readers some models grounded on the known theorem of KeppellaShejnsona from topology of fourdimensional varieties are offered, to the group theory of Galois, an algebraic number theory (group Tejta)  for a solution of the wellknown problem of hydrodynamics  Paradox of d’AlembertEuler. The given mathematical models are under construction on blanket “points” of a touch of this standing of hydrodynamics and the abovestated fields of mathematics. The lemma and the statement from which is stated follows that the Paradox reason “is covered” in a various denseness of substance  media and skew fields. 
Publishing date: January 3, 2015 

MATHEMATICAL LAWS FOR GEOGRAPHIC COORDINATES OF GEYSERS AND VOLCANOES 
On Earth, there are several valleys geysers, geographic coordinates are subject of interest laws. 
Publishing date: January 18, 2012 

MATEMATICAL LAWS FOR THE MASSES OF ATOMS AND ELEMENTARY PARTICLES 
With specific examples considered the formula by which we can write
the mass of any atom. We give similar formulas for the masses of elementary particles. 
Publishing date: January 10, 2012 

PHYSICAL AND GEOMETRIC EVALUATION OF THE POINCARE CONJECTURE 
Poincare conjecture assumes that: Every simply connected compact threedimensional manifold without boundary is homeomorphic to a threedimensional sphere. In the proof of the Poincare conjecture begin with an arbitrary Riemannian metric on a simply connected threedimensional manifold M and apply the Ricci flow with surgery. An important step is to prove that as a result of this process "thrown" everything. . This means that the original manifold M can be represented as a set of spherical space forms S3 / Ăi connected to each other handsets

Publishing date: March 19, 2011 

EXPONENT OF CIRCUMFERENCE AS THE PHASE TRAJECTORY OF NONLINEAR ITERATION RELATION. Etude 3. 
In this etude are determined criteria of equivalence of complex differential equation of first order and nonlinear iteration. Conditions, at which the points, corresponding to the decision of iterative relation, lay on the exponent of circumference, are determined. 
Publishing date: June 19, 2010 

EXPONENTS OF CIRCUMFERENCE AS PHASE CURVES OF NONLINEAR DYNAMICALLY SYSTEMS. 
At the investigation of dynamically systems for the determination of their integral parameters we recommend the introduction of complex parameter of wholeness and also finding and decision of complex differential equation, to which it satisfies. 
Publishing date: January 4, 2010 

BIFURCATIONS OF EXPONENT OF CIRCUMFERENCE. NUMBERS OF BASIN. 
Phase trajectories of linear dynamically systems are often represent closed cycles, near to the circumferences.Most typical nonlinear problem, yielding to analytically solving, is the problem of determining of dynamics of system, logarithms of which dynamic parameters are subordinated to lineal regularities. 
Publishing date: December 9, 2009 

QUADRATURE OF A CIRCLE. 
In the decision of a task the opportunity of construction of a circle, equal on the area is shown a square, that is “the quadrature of a circle” that has enabled to solve “a quadrature of a circle” with accuracy on eight signs on standard number π is solved, and to express length of a circle a direct piece 
Publishing date: October 21, 2009 

DEVELOPMENT OF COMPUTING MODELS OF SOCIAL PHENOMENA ON EXAMPLE OF FAMILY RELATIONS BY MEANS
OF DATA MINING 
The methodology and technologies of application of Data Mining tools at the analysis of social phenomena on an example of the analysis of family relations in divorced families are designed for the first time. The frame of the database is designed. The system of prediction of duration of a marriage for various cases is created. Multifactor computing models of a marriage that capable to approximate influence of the complex of the internal and external factors on duration of a marriage are constructed for the first time.

Publishing date: August 14, 2008 

AVOGADRO NUMBER AS a WORLD CONSTANT 
For construction model of discret form of ether and fomalisation of mechanism of its interections and cooperation on elementes of partical has been suggested quantum of quantitativequalitative change of order or numerical koefficent of a similarity “Avogadro number”, depending as a quant of bootstrap. 
Publishing date: March 22, 2004 

PHYSICAL EQUIVALENT of NUMBER ’PI’ and GEOMETRICAL EQUIVALENT of the FINESTRUCTURE CONSTANT ’alpha’. 
The number pi together with the finestructure constant a would give the opportunity to receive the important dimensionless fundamental constants, which it was not possible to receive in any other way. It is shown, that the constants a and pi would be constants of the same class. Within the framework of this class of constants the physical equivalent of number pi is found, and the number a2=7,49648184638205•103 or its inverse value a21 =133,395907639344 acts like it. This new constant has the status of the finestructure constant2. A geometrical equivalent of finestructure
constant pi is the number pi2= 1,83360822(13) which together with pi = 3,14159265358979… enables to receive simple numerical multipliers before the Dirac’s large numbers. 
Publishing date: November 10, 2003 

HARMONIC SEQUENCES 
The belonging of Fibonacci and Luke’s sequences to the generalized classes of numerical sequences and connection numerical invariants of the generalized sequences with a gold proportion is shown. The Fibonacci and Luke’s
numbers are examples of harmonic sequences. The Fibonacci and Luke’s constant of sequences or their numerical invariant is the gold proportion (O=1,618033). These sequences are special cases of the generalized algebraic sequence having recurrent property of this kind: a (n) =ka (n1) +a (n2) at k =1. If k > 1, constants of sequences are the numbers having properties close to properties of the gold proportion. The equations X±1/X= k allow to receive for sequences the large family numerical invariants, close on properties to the gold proportion having the recurrent ratio a (n) = ka (n1) ± a (n2). The example of a sequence having fractal triad structure is given. 
Publishing date: November 10, 2003 

PROBABILISTIC INTERPRETATION OF FERMA’S THEOREM. 
One should take into consideration that Ferma and Pascal were the pioneers of a new aria of mathematics – the theory of probability. They received the first evidence concerning this theory. It is quite natural to assume that “the most surprising” evidence which was not represented on the books could be probabilistic. In any case such an assumption should not be excluded. 
Publishing date: October 6, 2003 

COMMENTARY ABOUT FUNCTIONSCHARACTERISTICS OF MATTER. 
During many centuries scientific theoretical basis is created and founded by analysis of wellknown physical processes. This method of approach permitted to achieve great results but didn’t give any chances to solve all the problems before the science.
The author of this article tried to work out the method of calculations,founded not only on study of wellknown theories and physical processes,but on the creation of complex of functions
characteristics of matter. 
Publishing date: June 9, 2003 

DETERMINISTIC STRUCTURES WITH THE FINITE NUMBER OF CONDITIONS. POSSIBILITY OF COMPUTER REALIZATION. 
In the paper is presented the model of insulated deterministic dynamic structure with the finite number of conditions. It is shown that structures of such type have attractors in the form of stationary points or cycles. Maximum attractors of such structures are describing by mathematically models, equivalent
to the theory of finite groups. Different forms of presentations of under study structures dynamics are built. 
Publishing date: May 12, 2003 

NONSTANDARD ANALYSIS OF NONCLASSICAL MOTION TIME AND CHRONOMETRICS. AREAL MULTITUDES. 
During the International Mathematical Conference “Multidimensional Complex Analysis” (Krasnoyarsk, Russia, August 510, 2002) I made a poster report “Do the Hyperreal Numbers Exist in the QuantumRelative Universe?” The report was devoted to the extensive theme “NonStandard Analysis of NonClassical Motion”, and in particular, was concerned with the question of building
nonstandard theoretical time model and application of nonstandard mathematical approach to nonclassical physics (http://res.krasu.ru/nonstandard). The article offered below is the more detailed concretising of the results, presented there. The author expresses his gratitude towards the mathematicians and physicians, who gave personally or by email their critical and constructive comments to the stated problem. 
Publishing date: October 7, 2002 

DO THE HYPERREAL NUMBERS EXIST IN THE QUANTUMRELATIVE UNIVERSE? 
Hyperreal numbers appear in Abraham Robinson’s nonstandard model of analysis as a result of extension of the field of real numbers, if the offence of the EudocksArchimed axiom is permitted. In other words, the hyperreal numbers  are a artificiallycreated abstract mathematical object, and if so, the question, stated in the title of this article, sounds at least strange.
In connection with this, it is necessary to explain what "existence" I mean, and why quantumrelative characteristics of the objective world are so important. 
Publishing date: September 2, 2002 

THE NEW FORMULAS TO CALCULATE PLANCK UNITS 
The new formulas to calculate Planck units are found. From the formulas follows that the constants lpl, tpl, mpl can be determined not only with the help of constants G, h, c, but also with application of others fundamental physical and cosmology constants. Formulas include universal superconstants hu, lu, tu, alfa, pi. Each group of the formulas gives practically identical values of the appropriate constant. The deviations are very insignificant and also are observed in the seventh  eighth digits that is connected to various accuracy of those constants by means of which Planck units are presented. 
Publishing date: March 20, 2002 

MATHEMATICAL FORMULAS FOR CALCULATION OF NEWTONIAN CONSTANT OF GRAVITATION G 
The global connection existing between fundamental physical constants is open [29]. On this basis Newtonian constant of gravitation G is explored. It is established that this constant is a compound constant and is comprising Planck`s constant h, speed of light c and other constants. 
Publishing date: January 9, 2002 

HOW MANY PHYSICAL
CONSTANTS ARE TRULY FUNDAMENTAL? 
To main fundamental constants scientists usually refer gravitational constant (G), Planck constant (h) and speed of light (c). These constant are considered to be independent. Researches have shown, that truly fundamental are not constants G, h, c, but quite other constants. 
Publishing date: January 9, 2002 

FORCE UNIVERSAL FORMULA 
The Constant G traditionally was reputed a very distant constant from electromagnetic constants.
Formulas which are shown above allow to
get row of new major results. Let’s consider some of them.
An amazing likeness exists in formulas of Coulomb law and Newton’s gravitation law. In the first one  charges, in the second one  the masses. Herewith the mathematical records of laws absolutely identical. In view of this most likely that these laws are the fragments of some universal fundamental force law. 
Publishing date: November 13, 2001 

CONNECTION OF NEWTONIAN CONSTANT OF GRAVITATION G AND PLANCK CONSTANT h 
The aim of our research is to define a tie of electrodynamics and gravitation and to define a tie of Newtonian constant of gravitation G and electromagnetic constants. Has been discovered a global tie between Newtonian constant of gravitation G and major fundamental physical constants and has been got mathematical equation for calculation of constant G. Has been found out that Newtonian constant of gravitation G includes in oneself Planck constant h. 
Publishing date: November 13, 2001 

A NEW PROBLEM OF FUNDAMENTAL PHYSICS 
At the end of the 20th century in physics one more problem has appeared, which till now was not designated among major fundamental physical problems. It goes about a problem of fundamental physical constants. It has grown naturally on the basis of a lot of research results in the field of elementary particles physics. Due to this direction of researches many new fundamental physical constants have appeared. They are already separated into a single class  "atomic and nuclear constants". It is necessary to note, that their quantity much more exceeds the quantity of all other constants taken together. 
Publishing date: October 22, 2001 

CALCULATION OF FUNDAMENTAL CONSTANTS: NEW ACCURATY VALUES OF CONSTANTS. 
New calculated values of important fundamental physical constants are shown below. They are received on the base of only four experimental constants c, h, a, R8 and Number. 
Publishing date: August 29, 2001 

UNEXPECTED CONECTION of THREE MAJOR CONSTANTS 
The simple and beautiful formula connecting major dimensionless constants is found: fine structure constant, number pi and gold ratio, following from numbers Fibonacci. 
Publishing date: August 17, 2001 
