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Information × Registration Number 0214U006348, 0112U000374 , R & D reports Title Monogenic and hyperholomorphic functions in finite-dimensional algebras and their application to the boundary problems of mathematical physics popup.stage_title Head Gerus Oleg Fedorovych, Кандидат фізико-математичних наук Registration Date 11-03-2014 Organization Zhytomyr State University named after Ivan Franko popup.description2 We showed that only one among two commutative associative Banach wave algebras of the rank 2 exists and we described all wave basis in it. We state a criterium of monogenity of a function of double variable and we obtained a constuctive description of a double monogenic function of double variable through double differetiable functions of real variable. We described structure of basis elements of generalized Cayley-Dickson algebra. We introduced the notion of the left $A_t$-hyperholomorphic function and we worked out an algoritm for construction of that sort functions in a generalized Cayley-Dickson algebra. We carried out a consructive description of monogenic functions in a finite-dimentional semi-prime commutative algebra in terms of analytical functions of complex variable and we proved their differentiability in the Gateaux sense. We found a correct statement of the boundary problem for monogenic in the circle of the biharmonic plane functions with values in biharmonic algebra of Schwartz problem type associate with the main biharmonic problem which solved in the form of hypercomplex power serieses of biharmonic variable. We establisted dependence betwen coefficients of power series-solution and Fourier coefficients of boundary functions. We calculated in the explicit form the heat distribution of two-dimensional composition material disk-ring type associated by condition of ideal contact on condition that interior heat flow extends in the opposite to the real axis direction. We found an analytical dependeness of the tensor of effective conductivity of the disk-ring type composite on the radius of the interior circle of the componenta-insertion in form of a geometrical series by powers of the squared radius. We established the dependeness betwen the conductivities of components of the composite and their geometrical sizes on the assumption of constance of the tenzor of effective conductivity of the composite. We established sufficient conditions of the existence of quaternion singular Cauchy integral defined on a closed rectifiable regular surface in the space $R^3$ and we proved an upper estimate of its modulus of continuoity in terms of the modulus of continuity of the integrand. Product Description popup.authors Грищук Саргій Вікторович Плакса Сергій Анатолійович Пухтаєвич Роман Петрович Шпаківський Віталій Станіславович popup.nrat_date 2020-04-02 Close