Ninul Anatoly Sergeevich - web-site http://NinulAS.narod.ru/english.html
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========================================================================== The author does not have commercial interests and any profit from the location here of his works in the indicated fields. These interests are purely scientific.
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Discussed in the web-site can be problems devoted to different divisions of mathematics, theoretical physics and mathematical chemistry from the fields indicated below. For this reason of especial interest for the author are opinions, remarks and suggestions concerning the contents of his published scientific monographs and the given web-site. Namely, they are.

1. The book by A. S. Ninul, "Tensor Trigonometry. Theory and applications.", with this new math subject and with studied in it a number of fundamental questions and problems of algebra, geometry and theoretical physics, was issued by "Mir Publishing House" (Moscow) in October 2004. Besides, this book contains a large Appendix "Trigonometric motion models in non-Euclidean geometries and in theory of relativity".
2. To the end of 2020, the author prepared its updated English version, and in January 2021 the "Fizmatlit Publishing House" (Moscow) issued it as the English monograph Ninul A. S. "Tensor Trigonometry." in its paper and digital forms, where in particular, in the frame of last Ch.10A, the study of the differential geometry of world lines in Minkowskian space-time was carried out by the author to its logical end.
3. The book by A. S. Ninul, "Optimization of Objective Functions: Analytics. Numerical methods. Design of experiments." was issued by "Fizmatlit Publishing House" (Moscow) in May 2009. The author hopes that in it he considered in natural and logical order all basic methods of search and identification of the extremum for evolutional objective functions on the basis of their genetic interconnection (up to mathematical programming) with the filling up of "blind spots" encountered in literature. This book also completed the investigation of some extremal problems considered earlier in the book "Tensor Trigonometry". So, for instance, Ch.4 contains the derivation of complete (extremal in essence) requirements to the coefficients of a real algebraic equation of degree n for the reality, including positivity, of all its roots, what is the solution to the problem posed by the great Descartes and partially solved by him.

At the end, last two books contain own "Physical-Mathematical Kunstkammers", which includes a number of questions and tasks connected with problems discussed in these monographs (math analysis, algebra, geometry and physics).
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In a paper form, all these books can be looked through in large scientific libraries – Russian and foreign. For instance, the book "Tensor Trigonometry. Theory and Applications." – M.: MIR, 2004 is presented in EU in the most known mathematical library Zentral Universitätsbibliothek Göttingen as the monograph “Tenzornaja Trigonometrija - teorija i prilozenija.” – Ninul A. S. (Moscow, Mir, 2004) with link.

In a digital form, these books, as the author's pdf files, are presented, for instance, in the main Russian digital servers Elibrary.ru and Rusneb.ru, in the electronic library of MSU's Mech-Math Faculty (the sections Geometry and Optimization), in a number of other scientific e-libraries of Russia and CIS, and also in Google books, Internet Archive with Open Library, English E-books Directory (Tensor Analysis), etc..

In my web-site you can find the author's pdf files of these books. If something in their contents or proofs are not understand, then it is better to contact the author before he has finished his earthly journey. Electronic pdf files of both these books are exhibited with correction of all misprints and small inaccuracies, inevitable at forming such big works without a staff of helpers.
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In the case of interference on this large site, I advise to circle all the textual part with the mouse from below and then read or copy the text without problems, but better yet, download the web-page, for example, as a mht file.
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Given further are some results of the author's investigations discussed in his presented here monographs and the domains of his special interests in exact sciences.
1. Algebra and Theory of Exact Matrices:
- the general inequality for all average values (means) of a given set of positive numbers;
- a real algebraic equation of degree n, necessary and sufficient conditions presented to its coefficients for reality (in particular, positivity) of all roots;
- the limit method and the limit formulae for serial calculating the roots of a real algebraic equation and the eigen values of an nxn-matrix in case of their positivity;
- the scalar and matrix characteristic coefficients of an nxn-matrix (their structure properties and using in Linear Algebra and its applications);
- the fundamental relations for basic parameters of singularity of an nxn-matrix and the explicit form for its minimal annulling polynomial;
- the null-prime and null-normal singular nxn-matrices, their definition and properties;
- the affine and orthogonal (spherically and hyperbolically) quasi-inverse matrices and eigen projectors, i.e. 8 for real and 12 for complex nxn matrices, 4 for real and 6 for complex nxm-matrices (in total case), the Table of multiplication for all eigen projectors of a matrix;
- affine and orthogonal eigen reflectors;
- the quadratic geometric norms of nxn- and nxm-matrices (including hierarchical ones);
- trigonometric nature of commutativity and anticommutativity for nxn-matrices;
- the trigonometric spectrums of an nxn-matrix; the sine and cosine general inequalities;
- adequate and Hermitian analogies when the mathematical notions are complexificated.
2. Tensor Trigonometry – Euclidean, quasi-Euclidean and pseudo-Euclidean defined in Euclidean space of dimension n, in binary quasi-Euclidean and pseudo-Euclidean spaces of dimension (n+q), where q is an index for the binary spaces and (n+q) more or equal to 2 (two for trigonometry on a plane, a quasiplane, a pseudoplane including eigen ones):
- homogeneous transformations-motions in these 3 indicated spaces with objects in them (passive and active), namely Euclidean, quasi-Euclidean and pseudo-Euclidean, and their eigen non-commutative groups: Euclidean rotations with their Euclidean group, quasi-Euclidean rotations with their Special group, and pseudo-Euclidean rotations with their Lorentz group;
- the subgroup of secondary orthospherical rotations (as intersection of the last two groups in an universal base;
- projective and motive tensor angles and their tensor trigonometric functions;
- the middle reflector of a tensor angle;
- the united reflector tensor of quasi-Euclidean and pseudo-Euclidean binary spaces;
- tensors of principal spherical and hyperbolic rotations and deformations in general forms;
- tensors of principal spherical and hyperbolic rotations and deformations with their unity vector of directional cosines in elementary forms (only if q=1);
- the Special quart cycle from these tensor specific rotations and deformations;
- spherical-hyperbolic analogies - abstract and concrete (specific) ones, the angle or the number or the constant w=arsh1~0,881 as a hyperbolic analog of the number п/4=Arc tan1~0,785 and also their parallel representations by numeral power series;
- solution of a pseudo-Euclidean right triangle on a pseudoplane and in a pseudo-Euclidean space;
- a pseudo-Euclidean right triangle: complementary hyperbolic angles, infinite and zero combined right angle; functional connection of these complementary hyperbolic angles; application of the concrete (specific) sine-tangent analogy for inferring in an universal base of connections of spherical and hyperbolic angles on a quasiplane and a pseudoplane.
3. Non-Euclidean Geometries with constant radius +R, (+-)R or iR as spherical type and two associated complementary hyperbolic types:
- antipodal semi-parts of a spherical space and of two associated kinds of hyperbolic non-Euclidean spaces with their antipodal geometries;
- the flat projective tangent model inside of the trigonometric circle of radius R (identical to projective Beltrami-Klein model inside of the Cayley absolute of radius R) of the Minkowskian hyperboloid II and of the real-valued Lobachevsky-Bolyai n-dimensional surface with its constant R;
- the flat projective cotangent model outside of the trigonometric circle of radius R of the Minkowskian hyperboloid I and of some real-valued Minding-Beltrami n-dimensional surface with its constant R;
- the cylindrical projective tangent model onto the trigonometric projective cylinder of radius R and heights (+-)R  R of the Minkowskian hyperboloid I and of some real-valued Minding-Beltrami n-dimensional surface with its constant R;
- the flat projective sine model inside of the trigonometric circle of radius R of the hyperspheroid with its radius R;
- the contravariant Lobachevskian spherical angle of parallelism (П), connected with the hyperbolic angle of motion (g) in hyperbolic non-Euclidean geometries as g=arcoth(sin П)=arsinh(cot П) under the sine-cotangent analogy, but only in the universal base E1 (with exactness till orthospherical rotations of them), and connected with the spherical angle of principal motion (ф) in Lambert measure in spherical geometry as ф = п/2 – П in any admissible quasi-Cartesian base;
- the covariant angles of parallelism (g and ф), i.e., as also the angles of principal rotations in pseudo-Euclidean and quasi-Euclidean spaces, and as the angles in Lambert measures for principal motions in planimetries of both types non-Euclidean geometries with Lambertian sine-tangent analogy between angles g(ф) and ф(g), but only in any universal base E1 (with exactness till orthospherical rotations);
- universal, spherical and hyperbolic, covariant and contravariant angles of parallelism in non-Euclidean geometries;
- the natural hyperbolic equations of a tractrix (in only R-factor) in the Especial quasi-Euclidean plane and only with respect to its generating time-like hyperbola in a pseudoplane (with the same factor R), under specific vectorial sine-tangent or scalar cosine-secant analogy between their time-like hyperbolic and spherical angles-arguments;
- a tractrix as the hyperbolic analogue of a spherical curve "cycloid" but with only one cycle;
- the natural hyperbolic--orthospherical equations of a Beltrami pseudosphere (in only R-factor) in the Especial quasi-Euclidean space of index q=1 and with respect to its generating one-sheet hyperboloid of Minkowski -- with the common reflector tensor of their pseudo-Euclidean and Especial quasi-Euclidean enveloping spaces and hence with the common orthospherical admissible rotations;
- all these tractrices and pseudospheres as similar geometric objects of one factor R (as circles and spheres, hyperbolae and hyperboloids, catenaries and catenoids, etc.).
Note, in Chapter 6A of the English-language edition of the tensor trigonometry (January 2021), the author proposed to subdivide surfaces of constant Gaussian curvature into “perfect” and “imperfect” from the principle: whether a complete group of motions is given on the surface or it is absent. But, as can be seen from the context, from the point of view of the enveloping metric spaces, the former are “surfaces of constant radius”, but the latter are surfaces of constant curvature, but not of constant radius. It is at a constant surface radius-parameter that the geometric distances - movements are proportional to the changes in the angle of motion, determined by the rotational tensor trigonometry of the enclosing metric space. In the first case, we have a complete group of continuous motions, consisting of principal and orthospherical motions, relatively to the space reflector tensor. In the second case, for surfaces of revolution of constant curvature, we have only a subgroup of orthospherical rotations, but we do not have a complete group of continuous motions in addition with principal ones. From here, the hyperspheroid and hyperboloids of Minkowski are perfect surfaces of constant Gaussian curvature, while the Beltrami pseudosphere is not. The sphere is such, but only when a reflector tensor is specified, which determines for it a complete group of permissible motions. But then it turns into a hyperspheroid in the enveloping quasi-Euclidean space. The author believes that for high-level mathematicians - professionals, in principle, such detailed comments on this innovation in the book are not particularly required, since they increase the volume of the book, which sometimes violates its planned structure. Of course, this is not one such place in the book.
- n-dimensional isometry of a hyperboloid I of Minkowski and a pseudosphere of Beltrami;
- the infinitesimal Pythagorean theorems – Euclidean and pseudo-Euclidean on hyperboloids II and I;
- summing geodesic segments (motions) in non-Euclidean geometries (two- and multi-steps);
- the theorem about orthogonal representation of summing two principal motions, commutative in Euclidean and non-commutative in non-Euclidean geometries;
- polar representation of general rotations-motions (as principal and secondary orthospherical rotations), connection of the latter with rotation (or spherical shifting) of initial absolute base;
- tensor-trigonometric interpretation as mathematically equivalent effects: (1) an orthospherical part of absolute rotation-motion and (2) a spherical Gauss-Bonnet deviation in hyperbolic (as an angular defect of Lambert) and in spherical (as angular excess of Garriot) non-Euclidean Geometries with expression of the latters in the form of multiplication of surface area into surface curvature – negative and positive;
- metric curvilinear spaces - Riemannian, quasi-Riemannian and pseudo-Riemannian as respectively infinitesimally Euclidean, quasi-Euclidean and pseudo-Euclidean ones;
- a reflector-tensor, a metric tensor and a quadratic metric as initial notions in the definition of all these metric spaces; orientational role of the reflector tensor.
4. Theory of Relativity:
- the mathematical principle of relativity and physical-mathematical isomorphism;
- the "affine-Euclidean" binary Lagrange space-time, imaging for velocities the Kleinian parabolic Geometry;
- parallel rotations-motions in "affine-Euclidean" Lagrange space-time as intermediate between spherical and hyperbolic rotations;
- the natural transition of Poincare in 1905 from the non-metric space-time of Lagrange to the relativistic homogeneous and isotropic space-time with complex pseudo-Euclidean metric and Lorentzian group of absolute rotations-motions;
- Euclidean and non-Euclidean representations of the subspace of physical velocities in the tangent projective models of parabolic (non-relativistic) and hyperbolic (relativistic) geometries;
- the instant hyperbolic angle g of relativistic collinear progressive physical motion of a material object in tensor, vector and scalar interpretations;
- the instant hyperbolic angle g and the induced orthospherical angle of relativistic non-collinear progressive physical motion of a material object in tensor, vector and scalar interpretations;
- the trigonometric tensors: a pseudo-orthogonal tensor of relativistic rotations-motions and a quasi-orthogonal tensor of relativistic deformations (the latter acts one-time and only in an universal base);
- tensor-trigonometric interpretations of relativistic effects: Einstein real dilation of time as consequence of rotational transformation and Lorentz seeming (apparent) contraction of extent as consequence of deformational transformation (of coordinates);
- a pair of accompanied relativistic effects to these main effects;
- the general laws of summing velocities (including the general formulae for secondary orthospherical rotation or shifting) in tensor, vector and scalar forms;
- the tensor-trigonometric models of relativistic kinematics and dynamics - relative and absolute;
- the trigonometric models of simplest relativistic motions - hyperbolic and pseudoscrewed;
- interpretation of hyperbolic motion (in pseudo-Euclidean space-time) as the motion along a time-like tractrix (in Special quasi-Euclidean space-time);
- proportional hyperbolically orthogonal tensors of a full impulse and a full energy, produced from the trigonometric dimensionless tensor of motion-rotation indicated above by multiplication it on the invariants mo•c and mo•c2;
- the last of them is known in relativistic physics as a tensor of energy-impulse; and on the contrary: the trigonometric dimensionless tensor of motion is produced as division of a tensor of energy-impulse by mo•c2;
- physical nature of absolute matter's motion at a 4-velocity of Poincare "c" along its world line, namely, with its proper impulse Po=mo•c and proper energy Eo=mo•c2 as a flow of its proper time to at a velocity "c" in the same direction of Minkowskian space-time; and on the contrary: a flow of its proper time as absolute matter's motion;
- the dynamic full characteristics of relative motion of matter in a specific base: a full impulse P=m•c, a full energy E=m•c2, - produced as consequence of hyperbolically orthogonal projection of absolute matter's motion onto the time-arrow ct;
- the relative impulse of matter's motion at a velocity v=c•thg in this specific base as hyperbolically orthogonal projection of the proper impulse into the space x3, namely, p=Po•shg=P•thg=mv and with the same direction cosines in the space x3 as for vectors v, shg, thg;
- the pseudo-Euclidean right triangle of impulses: Po (hypotenuse), P and p (cathetuses), - similar to the triangle, formed by the arrows of time cto and ct with the hyperbolic angle g between them;
- the pseudo-Euclidean Pythagorean Theorem for moduli of impulses: (iPo)2=(iP)2+p2, p2=P2-Po2, from which easily relativistic formulae m(v) and Einsteinian p2=(mv)2=(m2-mo2)•c2=(E2-Eo2)/c2 are resulted;
- the dynamic (at a 4-velocity "c") 4D pseudoanalogue of the 3D theory by Frenet-Serret in the Minkowskian space-time with interdependent local parameters of a world line's rotation with all of the current differential-geometric parameters of this world line until their order 3 at the maximal order of its embedding "4";
- tensor-trigonometric relativistic interpretations for Doppler effects and for an aberration, and also for the Thomas orthoprecession; the angular velocity of this orthoprecession and its connection with Coriolis acceleration of a material object at its non-collinear motion in the pseudo-Euclidean space-time of Minkowski.

Here one should at least briefly argue the position of the author, which he stated in the discussion Ch. 9A. In it, the mathematical description of relativistic motions of an object was subdivided into real ones (locally at the place of events) and observable ones (at a remote place of their fixation), with a significant difference in the potential of the gravitational field in these places. In GTR by Albert Einstein, this mathematical description is maid according to the changing values of the metric tensor of space-time formed by the gravitational field and inertia of the object (G-field). But an observable motion is accepted as a real motion in all further conclusions. This is a positivist point of view, coming from the views of Ernst Mach in his work: “Die Mechanik in ihrer Entwickelung historisch-kritisch dargestellt. – 1904”. In GTR, a straight line is the trajectory of a ray of light, since on a cosmic scale there is really nothing to tie it to. This idea came from the creators of non-Euclidean geometry, and Karl Gauss even tried to test it. Therefore, the gravitational effect on moving photons from cosmic objects bends not only their path, but also the physical and mathematical space-time itself of GTR. The main contradictions in this approach are the following.
-The real and remotely fixed descriptions of one motion must inevitably differ, since at the place of observation the gravitational field is completely different, that is, information about the real motion reaches the external observer through the gravitational lens.
-In a curved pseudo-Riemannian space-time of GTR, there is no complete group of motions, and, therefore, there is no uniqueness of motions mapping in various coordinate bases.
- Electrically and magnetically curved rays of light are not considered straight lines and do not bend the space-teme. So, a ray of light is bent not only in a gravitational field, but also under the influence of fields created by electric charges and magnetic dipoles. Due to the fact that the absolute electric and magnetic permeabilities are many orders of magnitude higher than the gravitational constant in similar CGS units, then these ray curvatures are observed even in terrestrial conditions in media with a variable refractive index.
- More widely, in GTR, there is no answer to the cardinal question: why should space-time be curved in a gravitational field, but not curved in other physical fields?
- From here, as before, there is the incompatibility of GTR and Quantum Mechanics, acting according to Pole Dirac in the Minkowski space-time.
- There is inevitable violation of the fundamental Law of conservation of energy-momentum of matter and field, according to Amalia Noether's Theorem, due to the curvature of space-time with violation of its isotropy and homogeneity. This also gives rise to theoretical temptations for the production of matter and energy from nothing as a modern kind of perpetuum mobile.
- According to general relativity, in a gravitational field, spatial material objects should also be bent (for example, cosmological ones) without the influence of any forces of nature. And else many-many others …
But there is another way: to revive the basic physical and mathematical space-time of Hermann Minkowski (originally discovered by Henri Poincaré) to describe precisely the local real relativistic motion, including in the gravitational field. This idea belongs to Nathan Rosen. But the observed description of the remote motion must be carried out taking into account the distortion of material information about it when passing through a gravitational field changed in the force of the impact. A number of such approaches, gradually eliminating contradictions in general relativity, have been done a lot, starting with the well-known works of Nathan Rosen, an assistant to Einstein himself at the Princeton University. In these works, all known general relativistic effects are interpreted flawlessly too and also up to the 1st order in the gravitational constant. With the same precision, it is theoretically possible to implement the complete approach. For example, a real relativistic motion is described in the 4-dimensional space-time of Minkowski (taking into account STR, as well as the refraction of photons – gravitational and optical); the same, but observable motion is described in a 4-dimensional pseudo-Riemannian space-time embedded in a Minkowski space-time with a higher dimension, i.e., as a result, while maintaining the homogeneity and isotropy of the basis space-time.
5. Formal Complex Analysis:
- formal analyticity of nonholomorphic functions (complex and real) of complex conjugate arguments (one-dimensional and many-dimensional);
- formal differentiation and integration;
- formal power series and completeness of a differential.
6. Differential Analysis and Methods of Optimization for evolutionary Objective Functions:
- analytic optimization for functions in a scalar variable;
- analytic unconditional optimization for functions in a vector variable;
- analytical conditional optimization for the function in a vector variable - either depended on some parameters or restricted by some connections equations;
- analytical conditional optimization limit methods with big and small parameters, connected between them;
- the exact characteristic (secular) equation for conventional eigenvalues of a Hesse matrix of a function of 2nd order under linear connected its arguments;
- in passing: isoparametric polynomials (including the mirror ones), differential invariants of the order 2 and higher for flat curves y(x), x(y);
- solution of the Newton problem about the relationship between the coefficients of direct and inverse power series, which is also equivalent to the problem of the relationship between derivatives of any order for direct and inverse to it analytic function;
- analytic optimization for real nonholomorphic functions in complex conjugate or mixed variables with the use of operations of the formal complex analysis;
- one dimensional numerical methods of optimization of the orders 0, 1 and 2;
- iterative optimization techniques;
- one dimensional Newton’s method of 2-nd order and its difference analogues;
- multi-dimensional analytical-numerical optimization of the orders 0, 1 and 2;
- coordinate-wise Seidel method of 0th order;
- gradient Cauchy method of 1st order with a given step;
- modification by the speedy descent or ascent method of 1st order;
- quadratic method of incomplete 2nd order with a calculated step;
- modification by the speedy descent or ascent method of incomplete 2nd order;
- multi-dimensional Newton's method of 2-nd order with a calculated step;
- modification by the speedy descent or ascent method of 2nd order;
- independence of the efficiency of both second-order methods on the initially selected scales along the axes or from the dimensions of the parameters;
- multi-dimensional analytical- numerical conditional optimization of the orders 0, 1 and 2;
- normal projection methods of the orders 1 and 2;
- connected methods with big and small parameters (the first of these is the Courant penalty functions method);
- multi-dimensional planned-calculational optimization methods of the 1st, incomplete and complete 2nd orders based on the selected plan of the location of the argument points to calculate the values of the function in them and on the finite difference method to estimate the first and second partial derivatives of the objective function;
- adequacy criterion for planning-difference models;
- multi-dimensional planned-experimental optimization methods of the 1st, incomplete and complete 2nd orders; in general, this is more well-known under name “Design of experiments on the factor space”, when optimization of some objective scalar function of response is realized through searching for optimal values of the influencing significant factors (in the case of a normal distribution of the random error of finding values of this function of response under exact given values of its factors-arguments;
- planned-experimental optimization of some function of response of the orders: 1st (Box method of the speedy descent or ascent), incomplete 2nd (quadratic method) and 2nd (Box-Wilson method); exact formulae and values for all accompanying parameters of the Box-Wilson plan;
- adequacy criterion for planning-experimental models;
- genesis of all these optimization methods and their consecutive interrelation.
7. Mathematical Chemistry:
- mathematical modelling of chemical reactions, the general kinetic function;
- modelling of a chemical reaction of one mono- and one polyfunctional substances - the last with all initially identical-active functional groups and with reduction of their activity (step by step);
- kinetic curves as plots of functions and as functionals (including the functions of response in planned-experimental optimization of some chemical reaction parameters);
- kinetic isotherms and isochrones, their theory and applications;
- the direct and indirect kinetics;
- the kinetic of 3D curing of a thermosetting plastics or elastomers (composites) in isothermal and isochronous temperature regimes; the characteristic temperature of 3D structuring;
- torsional indirect curing kinetics (by Lewis-Gillham method) due to the change in the shear modulus, according to the periods of free torsional oscillations; and due to fluctuations of the zero point during structuring, calculating the decrement of oscillations through the ratio of successive angular sectors of oscillations clockwise and counterclockwise.
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Below the author sets out his position on the related issues regarding own scientific publications.
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N.B.! Exceptional copyright, initial E-manuscripts, initial files of articles, originals of imposition forms with designs of these books belong only to the author himself. However, the author's desire consists in that the indicated materials can be used now and when the author, as any man, will no longer exist, i.e., always, but with pure scientific aims, and also that these books can be distributed without restrictions, for instance, through electronic and other libraries. It stands to reason that for true scientists there exists a certain rule: any using or citing original parts of works in their publications must be referred to the places where they were adopted from. Any camouflage of other people's results with their presentation in another form and without reference to the original is doubly categorically unacceptable. In these monographs the author tried honestly to cite the works of all predecessors which were known to him or at least the educational literature on the theme because he is delicate in such question. If anyone thinks that some analogical ideas have been placed before in other authors publications, I ask him to inform about this on the site or in my e-mail. Sometimes even brilliant thoughts were similar and close in time. Very typical examples are polyphonic stories of the originations and formation of non-Euclidean geometry and theory of relativity. At least for the current 2021, the author, during the time after the publication of his books, did not receive any such comments either on this site or in his E-mail. However, the author is aware of examples of explicit and camouflaged plagiarisms of some of his mathematical fragments or formulae and even the book as a whole. These plagiarisms were published both by little-known publishers and by a very well-known mathematical publisher. This web-site, in particular, serves as a vehicle for justifying the priority by the author now and by others in the future.
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Further you can see active references to different parts of my web-site:

Invitation book

Compact English version of this web-site

Large Russian version of this web-site
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Pdf file of the book Ninul A. S. “Tensor Trigonometry. Theory and Applications.” – Moscow: MIR, 2004, 336p. (Russian e-book, format А5)

Pdf file of the book Ninul A. S. “Tensor Trigonometry. Theory and Applications.” – Moscow: MIR, 2004, 336p. (Russian p-book, format А5)

Pdf file of the book Ninul A. S. “Tensor Trigonometry.” – Moscow: Fizmatlit, 2021, 320p. (English e-book, format A4)

Pdf file of the book Ninul A. S. “Tensor Trigonometry.” – Moscow: Publisher Fizmatlit, 2021, 320p. (English p-book, format B5)

Comments: Some Novelties in_the_book Tensor Trigonometry with exposition and development of this new subject of Mathematics
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Pdf file of the book Ninul A. S. "Optimization of Objective Functions: Analytics. Numerical Methods. Design of Experiments.” – Moscow: Fizmatlit, 2009, 336p. (Russian e-book, format A5)

Pdf file of the book Ninul A. S. "Optimization of Objective Functions: Analytics. Numerical Methods. Design of Experiments.” – Moscow: Fizmatlit, 2009, 336p. (Russian p-book, format A5)
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6 math articles of the author on the topics of the books “Tensor Trigonometry” and "Optimization of Objective Functions” non-published before in soviet academic math journals without “affiliation” (in the Soviet years 1982-1989)
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MCCME – Moscow Center for continuous mathematical education

pdf file of the book Ninul A. S. “Tensor Trigonometry. Theory and Applications.” – M.: MIR, 2004 (in Russian). – in E-library of MCCME (since 17.04.2006)
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E-Library of the Moscow State University, Mechanical-Mathematical Faculty

pdf file of the book Ninul A. S. “Tensor Trigonometry. Theory and Applications.” – M.: MIR, 2004. – in this E-library since 28.08.2007.

pdf file of the book Ninul A. S. “Tensor Trigonometry.” – M.: Fizmatlit, 2021. – in this E-library since 20.08.2021.

pdf file of the book Ninul A. S. "Optimization of Objective Functions: Analytics. Numerical Methods. Design of Experiments.” – M.: Fizmatlit, 2009. – in this E-library since 26.11.2010.
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Jpg compressed file of Front Cover of book Нинул А. С. "Тензорная тригонометрия" (drag with the mouse from the screen)
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Jpg compressed file of Front Cover of book Ninul A. S. “Tensor Trigonometry” (drag with the mouse from the screen)
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Jpg compressed file of Front Cover of book Нинул А. С. "Оптимизация целевых функций" (drag with the mouse from the screen)
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Small photoalbum
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P.S.: My Russian professional web-site in Chemical fields
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