In this article, we study generating sets of the complete semigroups of binary relations defined by X-semilattices of unions of the class Σ<sub>8</sub>(X, 5). Found uniquely irreducible generating set for...In this article, we study generating sets of the complete semigroups of binary relations defined by X-semilattices of unions of the class Σ<sub>8</sub>(X, 5). Found uniquely irreducible generating set for the given semigroups and when X is finite set formulas for calculating the number of elements in generating sets are derived.展开更多
Difficulties encountered in studying generators of semigroup of binary relations defined by a complete X -semilattice of unions D arise because of the fact that they are not regular as a rule, which makes their invest...Difficulties encountered in studying generators of semigroup of binary relations defined by a complete X -semilattice of unions D arise because of the fact that they are not regular as a rule, which makes their investigation problematic. In this work, for special D, it has been seen that the semigroup , which are defined by semilattice D, can be generated by the set .展开更多
New algorithm for optimizing technological parameters of soft magnetic composites has been derived on the base of topological structure of the power loss characteristics. In optimization magnitudes obeying scaling, it...New algorithm for optimizing technological parameters of soft magnetic composites has been derived on the base of topological structure of the power loss characteristics. In optimization magnitudes obeying scaling, it happens that one has to consider binary relations between the magnitudes having different dimensions. From mathematical point of view, in general case such a procedure is not permissible. However, in a case of the system obeying the scaling law it is so. It has been shown that in such systems, the binary relations of magnitudes of different dimensions is correct and has mathematical meaning which is important for practical use of scaling in optimization processes. The derived structure of the set of all power loss characteristics in soft magnetic composite enables us to derive a formal pseudo-state equation of Soft Magnetic Composites. This equation constitutes a relation of the hardening temperature, the compaction pressure and a parameter characterizing the power loss characteristic. Finally, the pseudo-state equation improves the algorithm for designing the best values of technological parameters.展开更多
In this paper we give a full description of idempotent elements of the semigroup BX (D), which are defined by semilattices of the class ∑1 (X, 10). For the case where X is a finite set we derive formulas by means of ...In this paper we give a full description of idempotent elements of the semigroup BX (D), which are defined by semilattices of the class ∑1 (X, 10). For the case where X is a finite set we derive formulas by means of which we can calculate the numbers of idempotent elements of the respective semigroup.展开更多
In this paper, we take Q16 subsemilattice of D and we will calculate the number of right unit, idempotent and regular elements α of BX (Q16) satisfied that V (D, α) = Q16 for a finite set X. Also we will give a form...In this paper, we take Q16 subsemilattice of D and we will calculate the number of right unit, idempotent and regular elements α of BX (Q16) satisfied that V (D, α) = Q16 for a finite set X. Also we will give a formula for calculate idempotent and regular elements of BX (Q) defined by an X-semilattice of unions D.展开更多
In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly r...In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.展开更多
Convex cones are closely related to preference relations and play an important role in optimization.Corresponding to any convex cone,a binary relation can be defined,but the reverse is not true.Therefore,many binary r...Convex cones are closely related to preference relations and play an important role in optimization.Corresponding to any convex cone,a binary relation can be defined,but the reverse is not true.Therefore,many binary relations are discarded in the optimization.This paper is an attempt to define or prove the prerequisites for using convex coradiant sets(coradiants for simplicity)instead of convex cones so that more binary relations can be used in optimization and nonlinear analysis.展开更多
Factor analysis of annual dynamics from 1879 to 2017 was carried out by the method of identification of stable regularities:maximum,minimum and average air temperature of Central England according to HadCET.The sample...Factor analysis of annual dynamics from 1879 to 2017 was carried out by the method of identification of stable regularities:maximum,minimum and average air temperature of Central England according to HadCET.The sample capacity was 139 rows.In factor analysis,time is excluded,and it acts only as a system-forming factor that ensures the relationship between the three parameters of climate and weather.Therefore,the adequacy of the dynamics models is taken into account in the diagonal cells of the correlation matrix.In addition to time,different lists of objects are possible in factor analysis.The coefficient of correlation variation,that is,a measure of the functional relationship between the parameters of the system(annual weather at the weather station in Central England)is 0.8230 for trends,0.8603 taking into account the annual dynamics of the four-membered model obtained from the computational capabilities of the software environment CurveExpert-1.40,and 0.9578 for the full up to the error of measurement wavelet analysis of the dynamics of the values of three factors.In all three methods of factor analysis,the meteorological parameter«average Annual temperature»was in the first place as the influencing variable,the«Maximum temperature»was in the second place,and the«Minimum temperature»was in the third place.As the dependent measure in these areas there are three kinds of temperature.The comparison shows that among the binary relations between the three temperatures,the average temperature on the maximum air temperature in the surface layer of the atmosphere has the greatest influence on the correlation coefficient 0.9765.At the same time,all six equations refer to strong connections,so there is a high quantum certainty between the three types of temperature.But when predicting the most meaningful essence showed the maximum temperature.展开更多
In this paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive fo...In this paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.展开更多
In the paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive for...In the paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.展开更多
In order to obtain some results in the theory of semigroups, the concept of regularity, introduced by J. V. Neumann for elements of rings, is useful. In this work, all regular elements of semigroup defined by semilatt...In order to obtain some results in the theory of semigroups, the concept of regularity, introduced by J. V. Neumann for elements of rings, is useful. In this work, all regular elements of semigroup defined by semilattices of the class ∑<sub>1</sub>(X,10)-I are studied. When X has finitely many elements, we have given the number of regular elements.展开更多
In this paper,we establish fixed point theorems for generalized nonlinear contractive mappings using the concept of w-distance in relational metric spaces.Thus we generalize the recent results of Senapati and Dey[J.Fi...In this paper,we establish fixed point theorems for generalized nonlinear contractive mappings using the concept of w-distance in relational metric spaces.Thus we generalize the recent results of Senapati and Dey[J.Fixed Point Theory Appl.19,2945-2961(2017)]and many other important results relevant to this literature.In order to revel the usefulness of such investigations,an application to first order periodic boundary value problem are given.Moreover,we furnish a non-trivial example to demonstrate the validity of our generalization over previous existing results.展开更多
The article is devoted to decision-making in the control and design of autonomous heat supply systems with tubular gas heaters.The results of mathematical modelling and optimization of tubular gas heaters(TGN)are know...The article is devoted to decision-making in the control and design of autonomous heat supply systems with tubular gas heaters.The results of mathematical modelling and optimization of tubular gas heaters(TGN)are known.Tubular gas heaters are an extension of the term“infrared tubular gas heaters”.The main elements are:a gas burner,a tubular heater inside which gas combustion products with air move,and a mechanical fan(supply or exhaust),which ensures the movement of the coolant inside the tubular part and its removal outside.There are a number of new technical solutions that expand the scope of tubular gas heaters,for example,tubular gas heaters on pellets.Mathematical models of tubular heaters on pellets and solutions to the problems of optimal design of tubular heaters of linear structure are known.Another possible structure of tubular gas heaters is heaters with recirculation of the heating gas-air medium.Optimisation of such pellet heaters has not been performed before,which determined the subject of this paper.The article is devoted to the presentation of the method of optimization of the design solution for tubular heaters taking into account recirculation under the existing constraints.The novelty of the optimization lies in the use of a quasi-two-dimensional mathematical model for the hydraulic circuit of the heater.An evolutionary search algorithm with binary choice functions is used for numerical search of solutions,for which convergence with probability 1 to the optimal solution is shown.The algorithm contains two consecutive functions:the function of so-lution generation and the function of solution selection.The function of solution generation is built largely independently of the content of the problem to be solved,while the function of selection is built in such a way that the resulting binary selection relation is completely determined by the requirement of finding the necessary solution.The resulting binary selection relation includes both the selection components of the available constraints and the basic optimiztion requirement.展开更多
In this paper,we prove fixed point theorem for weakly contractive mappings using locally T-transitivity of binary relation and presenting an analogous version of Harjani and Sadarangani theorem involving more general ...In this paper,we prove fixed point theorem for weakly contractive mappings using locally T-transitivity of binary relation and presenting an analogous version of Harjani and Sadarangani theorem involving more general relation theoretic metrical notions.Our fixed point results under universal relation reduces to Harjani and Sadarangani[Nonlinear Anal.,71(2009),3403-3410]fixed point theorems.In this way we also generalize some of the recent fixed point theorems for weak contraction in the existing literature.展开更多
1 Introduction Advances in human genetics have facilitated the investigation of the genetic architecture underlying numerous complex traits.In particular,studies of quantitative expression trait loci(eQTL)have played ...1 Introduction Advances in human genetics have facilitated the investigation of the genetic architecture underlying numerous complex traits.In particular,studies of quantitative expression trait loci(eQTL)have played a pivotal role in elucidating how genetic variants influence gene expression across cell types.This progress has enabled the quantification of effect size for disease genetic risk loci and the construction of binary relational datasets linking diseases to their respective disease genes,such as Fantom5[1]and DisGeNET[2].展开更多
文摘In this article, we study generating sets of the complete semigroups of binary relations defined by X-semilattices of unions of the class Σ<sub>8</sub>(X, 5). Found uniquely irreducible generating set for the given semigroups and when X is finite set formulas for calculating the number of elements in generating sets are derived.
文摘Difficulties encountered in studying generators of semigroup of binary relations defined by a complete X -semilattice of unions D arise because of the fact that they are not regular as a rule, which makes their investigation problematic. In this work, for special D, it has been seen that the semigroup , which are defined by semilattice D, can be generated by the set .
基金supported by National Center of Science within the framework of research project Grant N N507 249940.
文摘New algorithm for optimizing technological parameters of soft magnetic composites has been derived on the base of topological structure of the power loss characteristics. In optimization magnitudes obeying scaling, it happens that one has to consider binary relations between the magnitudes having different dimensions. From mathematical point of view, in general case such a procedure is not permissible. However, in a case of the system obeying the scaling law it is so. It has been shown that in such systems, the binary relations of magnitudes of different dimensions is correct and has mathematical meaning which is important for practical use of scaling in optimization processes. The derived structure of the set of all power loss characteristics in soft magnetic composite enables us to derive a formal pseudo-state equation of Soft Magnetic Composites. This equation constitutes a relation of the hardening temperature, the compaction pressure and a parameter characterizing the power loss characteristic. Finally, the pseudo-state equation improves the algorithm for designing the best values of technological parameters.
文摘In this paper we give a full description of idempotent elements of the semigroup BX (D), which are defined by semilattices of the class ∑1 (X, 10). For the case where X is a finite set we derive formulas by means of which we can calculate the numbers of idempotent elements of the respective semigroup.
文摘In this paper, we take Q16 subsemilattice of D and we will calculate the number of right unit, idempotent and regular elements α of BX (Q16) satisfied that V (D, α) = Q16 for a finite set X. Also we will give a formula for calculate idempotent and regular elements of BX (Q) defined by an X-semilattice of unions D.
基金Supported by the National Natural Science Foundation of China(10861007)
文摘In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.
文摘Convex cones are closely related to preference relations and play an important role in optimization.Corresponding to any convex cone,a binary relation can be defined,but the reverse is not true.Therefore,many binary relations are discarded in the optimization.This paper is an attempt to define or prove the prerequisites for using convex coradiant sets(coradiants for simplicity)instead of convex cones so that more binary relations can be used in optimization and nonlinear analysis.
文摘Factor analysis of annual dynamics from 1879 to 2017 was carried out by the method of identification of stable regularities:maximum,minimum and average air temperature of Central England according to HadCET.The sample capacity was 139 rows.In factor analysis,time is excluded,and it acts only as a system-forming factor that ensures the relationship between the three parameters of climate and weather.Therefore,the adequacy of the dynamics models is taken into account in the diagonal cells of the correlation matrix.In addition to time,different lists of objects are possible in factor analysis.The coefficient of correlation variation,that is,a measure of the functional relationship between the parameters of the system(annual weather at the weather station in Central England)is 0.8230 for trends,0.8603 taking into account the annual dynamics of the four-membered model obtained from the computational capabilities of the software environment CurveExpert-1.40,and 0.9578 for the full up to the error of measurement wavelet analysis of the dynamics of the values of three factors.In all three methods of factor analysis,the meteorological parameter«average Annual temperature»was in the first place as the influencing variable,the«Maximum temperature»was in the second place,and the«Minimum temperature»was in the third place.As the dependent measure in these areas there are three kinds of temperature.The comparison shows that among the binary relations between the three temperatures,the average temperature on the maximum air temperature in the surface layer of the atmosphere has the greatest influence on the correlation coefficient 0.9765.At the same time,all six equations refer to strong connections,so there is a high quantum certainty between the three types of temperature.But when predicting the most meaningful essence showed the maximum temperature.
文摘In this paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.
文摘In the paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.
文摘In order to obtain some results in the theory of semigroups, the concept of regularity, introduced by J. V. Neumann for elements of rings, is useful. In this work, all regular elements of semigroup defined by semilattices of the class ∑<sub>1</sub>(X,10)-I are studied. When X has finitely many elements, we have given the number of regular elements.
文摘In this paper,we establish fixed point theorems for generalized nonlinear contractive mappings using the concept of w-distance in relational metric spaces.Thus we generalize the recent results of Senapati and Dey[J.Fixed Point Theory Appl.19,2945-2961(2017)]and many other important results relevant to this literature.In order to revel the usefulness of such investigations,an application to first order periodic boundary value problem are given.Moreover,we furnish a non-trivial example to demonstrate the validity of our generalization over previous existing results.
文摘The article is devoted to decision-making in the control and design of autonomous heat supply systems with tubular gas heaters.The results of mathematical modelling and optimization of tubular gas heaters(TGN)are known.Tubular gas heaters are an extension of the term“infrared tubular gas heaters”.The main elements are:a gas burner,a tubular heater inside which gas combustion products with air move,and a mechanical fan(supply or exhaust),which ensures the movement of the coolant inside the tubular part and its removal outside.There are a number of new technical solutions that expand the scope of tubular gas heaters,for example,tubular gas heaters on pellets.Mathematical models of tubular heaters on pellets and solutions to the problems of optimal design of tubular heaters of linear structure are known.Another possible structure of tubular gas heaters is heaters with recirculation of the heating gas-air medium.Optimisation of such pellet heaters has not been performed before,which determined the subject of this paper.The article is devoted to the presentation of the method of optimization of the design solution for tubular heaters taking into account recirculation under the existing constraints.The novelty of the optimization lies in the use of a quasi-two-dimensional mathematical model for the hydraulic circuit of the heater.An evolutionary search algorithm with binary choice functions is used for numerical search of solutions,for which convergence with probability 1 to the optimal solution is shown.The algorithm contains two consecutive functions:the function of so-lution generation and the function of solution selection.The function of solution generation is built largely independently of the content of the problem to be solved,while the function of selection is built in such a way that the resulting binary selection relation is completely determined by the requirement of finding the necessary solution.The resulting binary selection relation includes both the selection components of the available constraints and the basic optimiztion requirement.
文摘In this paper,we prove fixed point theorem for weakly contractive mappings using locally T-transitivity of binary relation and presenting an analogous version of Harjani and Sadarangani theorem involving more general relation theoretic metrical notions.Our fixed point results under universal relation reduces to Harjani and Sadarangani[Nonlinear Anal.,71(2009),3403-3410]fixed point theorems.In this way we also generalize some of the recent fixed point theorems for weak contraction in the existing literature.
基金supported by the National Natural Science Foundation of China(Grant Nos.62172318,62372349,62132015).
文摘1 Introduction Advances in human genetics have facilitated the investigation of the genetic architecture underlying numerous complex traits.In particular,studies of quantitative expression trait loci(eQTL)have played a pivotal role in elucidating how genetic variants influence gene expression across cell types.This progress has enabled the quantification of effect size for disease genetic risk loci and the construction of binary relational datasets linking diseases to their respective disease genes,such as Fantom5[1]and DisGeNET[2].
