1. Mark D. Kats ( born in 1937, higher education) is an applied mathematician, doctor of science, academician of Ukrainian Production Engineering Academy and Ukrainian Academy of Ecological Sciences, corresponding member of International Academy of Computer Sciences and Systems. Donetskaya St. 37/24, Severodonetsk Lugansk region 349940 Ukraine, Tel.: (380-6452)-3-08-75, E-mail: root@ixt.lg.ua (Kats M.D.).

2. Name of the project is "Development of a new composite material in collaboration with development engineering company."

3. Application field of the offer.

Development of new composite materials (alloys, rubbers, plastics, catalysts, mixtures of medicine preparations, commercial dyes and pigments, etc.) having specified combination of physical and chemical (consumptive) properties. Implementation of the project will enable to produce a material with specified combination of consumptive properties at minimum expenses and, on completion of the work, to prepare an application for a patent.

4. Description of the offer.

Taking into account that the problem of development of new composite materials is very actual, correct methods of its solution are missing for the time being, and development of new materials (alloys, rubbers, plastics, catalysts, mixtures of medicine preparations, commercial dyes and pigments, etc.) is invariant to their purpose and production method on the methodics plane, the following mathematical formulation of the problem has been proposed.

Given:

- Investigation domain P of input variables X space, defined by experts as ranges of possible values of each of M components of the mixture and parameters of technology for processing of the mixture to material;

- Requirements for material in form of domain of output variables [Y] space , determined by ranges of allowable values of each of t output variables [Yj]. IT IS NECESSARY:

- to select subset N from a set of possible components M (N<M), to determine optimum ratios of selected components and conditions for processing of mixture to material having specified combination of physical and chemical properties [Y].

In order to solve this problem, methodology of experimental investigation based on artificial intelligence philosophy, incorporating ideas of single-factor experiment, multidimensional purposeful random search and new methods of identification (mosaic portrait method) and suboptimization (logic programming method) has been mathematically substantiated and successfully proved in practice.

Its use enables to obtain four informative mathematical models at minimum expenses for experimental investigations using new methods of mathematical simulation.

Relations between each couple of input and output variables is described by means of the first model obtained on the basis of findings of active one-dimensional experiment.

These relations are objective (model construction procedure is formalized and does not depend on the expert ideas), robust (resistant to omission of column vectors of some unessential variables) and, as a rule, untrivial because the model is constructed taking into account a context of the problem (influence of other input variables).

Relations between complex output variable Y and each of input variables are described using the second model obtained on the basis of findings of active one-dimensional experiment and subsequent random search.

These relations are objective, robust and always untrivial, because procedure of output variables vector compression to a generalized criterion , unlike the known methods, is formalized and does not depend on the expert ideas.

The third model (mosaic) obtained by mosaic portrait method is used to reduce the system under study to its system's properties.

The essence of the mosaic portrait method is

- Transfer from continual (numerical) scales used for measurement of input and output parameters to discrete scales of names.

(Vector Y compression to a generalized criterion measured using discrete scales is formalized - it takes two values: Y=1 - "good" if all special criteria Yj meet specified constraints, and Y=0 -"bad" if even one of them does not meet these constraints.

A posteriori information about the behavior of relation between a complex output variable and each of input variables obtained using the second model is used as initial information required for transfer to discrete scales when measuring input variables.)

- Organization of a formalized procedure, polynomial in terms of computer time, enabling to find combinations of names of input variables subranges, which are found in the experimental data table only in case of experiments with output variable values belonging to one class of the objective function (for example, 1) and are not found in an experiment with other values (0). These combinations are interpreted as formal, non-conflicting on the basis of these experimental data of hypothesis, explaining the cause of output variable values difference.

Informative model is obtained by means of mosaic portrait method. This models carries a large scope of new untrivial information, unknown previously, about relation between physical and chemical (consumptive) properties of a material being developed and its composition and production technology.

The fourth model (logic one) obtained using logic programming is a solution of a stated problem in form of descriptions of a great number of areas of output variables space Ri, each description being interpreted as recommendation on mixture composition and technology for its processing to material having specified properties (Y=[Y]).

The logic programmatic method is based on the known axiom of algebra of logic about the truth of compound propositions: a compound proposition is true if it is formed of simple true propositions and false if it contains even one false proposition. If hypotheses of "good" class of mosaic model are interpreted as simple true propositions and those of "bad" class as simple false propositions, a compound proposition Ri of rank m (m - dimensional representation of input variables vector), obtained by combining the propositions of "good" class and containing no one proposition of "bad" class, may be interpreted as a description of the domain of input variables space predetermined by corresponding values of subranges of all mixture components and parameters of technology for processing of mixture to material. This domain corresponds to the domain of specified physical and chemical (consumptive) properties in the space output variables space.

Furthermore, the methodology proposed is an algorithm of invention in the field of development of new materials and their production methods.

As descriptions of areas Ri are constructed using formalized procedure of logic programming by means of mosaic model containing a large scope of new untrivial, unknown previously information about relationship between input and output variables, many of them also provide new possibilities of material production.

If there is a prototype patent as an analogue when developing any material, its claim may be represented as a corresponding description of Ra. If for any Ri the value of even one output variable Yj is higher than that of a prototype, in this case the material (material production method) claim can be obtained using the following formalized procedure:

1) Limiting part of the claim is a general part of Ri and Ra descriptions.

2) Subject of invention is a novelty in order to increase Yj value...

3) Distinctive part of the claim is a part inherent only to Ri (logic difference Ri/Ra).

5. Advantage in comparison with analogues.

New materials development system using trial-and-error method, existing at present, does not meet any more up-to-date requirements: it requires more and more time and means and yields more and more modest results. Therefore the attempts to use various fundamental approaches allowing to predict physical and chemical properties of materials on the basis of solid-state physics knowledge, multifactor physical and chemical analysis, thermodynamic methods, etc. are quite natural. Unfortunately, the material science level, even in the most scientifically advanced field, i.e. metal science, is insufficient to develop a new material with specified properties. Moreover it is considered that realization of such an approach is a very remote future.

THE PROPOSED METHODOLOGY IS A RESULT OF STRATEGIC INVESTIGATION WHOSE OBJECT WAS TO ELABORATE A UNIVERSAL FORMALIZED PROCEDURE FOR DEVELOPMENT OF ANY COMPOSITE MATERIALS HAVING THE SPECIFIED COMBINATION OF CONSUMPTIVE (PHYSICAL AND CHEMICAL, BIOLOGICAL, ETC.) PROPERTIES.

Not only a new material with specified properties can be produced but also its essential distinction from the materials with similar purpose, protected by patents, can be provided using this methodology at minimum expenses for the material development. In fact the methodology is none other than algorithm of invention in the field of new composite materials development. Methodology of new composite materials development has no analogues.

6. Possible consumers are engineering companies engaged in development of new composite materials (construction materials, alloys, rubbers, plastics, ceramics, mixtures of medicine preparations, commercial dyes and pigments , catalysts, etc.).

7. There is a many year's experience in effective use of this methodology for production of materials having specified physical and chemical properties. For example, the following commercial dyes and pigments with specified physical and chemical (consumptive) properties have been developed at INSTITUTE OF CHEMICAL ENGINEERING AND INDUSTRIAL ECOLOGY (Rubezhnoye, Lugansk region, Ukraine, director Mr. A.Minin):

- Formula of commercial linear trans-quinacridone with improved color qualities and soft texture suitable for production of enamels and printing inks for polymers dyeing (pink quinacridone pigment C). Color identification tests have shown that in therms of dispersive ability in a binding agent, rheological characteristics and dyeing concentration it corresponds to an import analogue Hostaperm red …‡ (Hoechst, Germany), is warmer as to tint and more pure than the analogue.

- Liquid commercial form of dispersed yellow polyester dye 35-72" (analogue is resoling bright yellow C-6ƒ‹, Bayer). The color identification tests have shown that in terms of consumptive properties it corresponds to import analogues and ensures full absence of specks.

- Formula of commercial blue anthraquinone pigment. The color identification tests have shown that the recommended formula and production technology ensure reliably the specified consumptive properties as to yield, dispersity, dyeing concentration in enamel coating, dyeing concentration in oil coating, and specimens produced using the technology proposed are much better than those produced by existing technology.

- Formula and technology for production of liquid commercial form of bright scarlet dye for printing . Color identification test have shown that it has a high and uniform dispersity, sedimentation and aggregation resistance during long-term storage, fluidity and cold resistance. As to these characteristics the commercial form developed corresponds to the best foreign specimens.

The main theses of methodology and its some applications are given in [1-3].

1.M.D.Kats. Experiment planning when studying complex unlinear objects Chemical Industry, 1991, No.3, pp. 311-313

2. M.D.Kats at al. Development of technology for commercial quinacridone pigment production using logic programming method. Chemical Industry, 1981, No.7, pp.17-18

3. M.D.Kats at al. Use of logic programming method for optimization of dye application and standardization. Chemical Industry, 1983, No.1, pp.43-45

8. The methodology is based on mosaic portpait method. It is not protected by patent but the main part of an algorithm ensuring model completeness and polynomiality of computer time (realization time versus dimensionality of the problem) has not been published, and only the author is possessed of the software for its realization.