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.fiC. MIKUfiSKOVfiA, M. SEDLAfiCfiIK, The application of regression trees to modelling ozone concentration measured in selected regions, Mendel 2016, 241-248. [18] M. NOVfiAK, Some basic properties of EL-hyperstructures, European J. of Combin. 34(2013), 446-459. [19] M. NOVfiAK, n-ary hyperstructures constructed from binary quasi-orderer semigroups, An. Stiint. Univ. \Ovidius" Constanta Ser. Mat., 22(3), (2014), 147-168. [20] A. RAHNEMAI-BARGHI, The prime ideal theorem for distributive hy- perlattices, Ital. J. Pure Appl. Math., 10(2010), 75-78. [21] S. RASOULI, B. DAVVAZ, Lattice

of ortholattices via orthoposets. Formalized Mathematics, 13(1):189-197, 2005. [10] George Gr¨atzer. General Lattice Theory. Academic Press, New York, 1978. [11] George Gr¨atzer. Lattice Theory: Foundation. Birkh¨auser, 2011. [12] Eliza Niewiadomska and Adam Grabowski. Introduction to formal preference spaces. Formalized Mathematics, 21(3):223-233, 2013. doi:10.2478/forma-2013-0024. [13] G.C. Rao, R.K. Bandaru, and N. Rafi. Generalized almost distributive lattices - I. Southeast Asian Bulletin of Mathematics, 33:1175-1188, 2009. [14] U.M. Swamy and G.C. Rao. Almost

References [1] G. Birkhoff, Lattice theory (Amer. Math. Soc. Colloquium Pub., 1967). [2] G.C. Rao and G. Nanaji Rao, Dense elements in almost distributive lattices, South- east Asian Bull. Math. 27 (2004) 1081-1088. [3] G.C. Rao and M. Sambasiva Rao, Annihilator ideal in almost distributive lattices, Int. Math. Forum 4 (2009) 733-746. [4] G.C. Rao and M. Sambasiva Rao, Annulets in almost distributive lattices, Euro- pean. J. Pure and Applied Math. 2 (2009) 58-72. [5] G.C.Rao and S. Ravi Kumar, Normal almost distributive lattices, Southeast Asian Bull. Math. 32

References [1] Raymond Balbes and Philip Dwinger. Distributive Lattices . University of Missouri Press, 1975. [2] Grzegorz Bancerek. Filters - part I. Formalized Mathematics , 1(5):813-819, 1990. [3] Grzegorz Bancerek. Ideals. Formalized Mathematics , 5(2):149-156, 1996. [4] Grzegorz Bancerek. Complete lattices. Formalized Mathematics , 2(5):719-725, 1991. [5] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics , 1(1): 55-65, 1990. [6] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics , 1(1):153-164, 1990. [7

References Berent, I., Pinker, S., Tzelgov, J., Bibi, U., and Goldfarb, L. (2005). Computation of semantic number from morphological information. Journal of Memory and Language , 53 , 342-358. Bock, K., Butterfield, S., Cutler, A., Cutting, J. C., Eberhard, K. M., and Humphreys, K. R. (2006). Number agreement in British and American English: Disagreeing to agree collectively. Language , 82 (1), 64-113. Cable, S. (2014). Distributive numerals and distance distributivity in Tlingit (and beyond). Language , 90 (3

1 Introduction The foundation for the modern theory of skew lattice was laid by Jonathan Leech in 1989 [ 5 ]. Leech [ 6 , 7 ] showed that each right handed skew Boolean algebra can be embedded in to a generic skew Boolean algebra of partial functions from a given set in the co-domain { 0 ,1} . Heyting algebra is a relatively pseudo-complemented distributive lattice that arises from non-classical logic, and it is named after a Dutch mathematician Arend Heyting, it was introduced by G. Birkhoff [ 1 ] and was developed by H. B. Curry around the year 1963. While

R eferences [1] W.H. Cornish, Congruences on distributive pseudo-complemented lattices , Bull. Aust. Math. Soc. 8 (1973) 161–179. doi:10.1017/S0004972700042404 [2] T.S. Blyth, Ideals and filters of Pseudo-complemented semilattices , Proc. Edinburgh Math. Soc. 23 (1980) 301–316. doi:10.1017/S0013091500003850 [3] O. Frink, Pseudo-complements in semilattices , Duke Math. J. 29 (1962) 505–514. doi:10.1215/S0012-7094-62-02951-4 [4] G. Gratzer, General Lattice Theory (Academic Press, New York, 1978). [5] K.B. Lee, Equational class of distributive pseudo

R eferences [1] G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. Publ. XXV (Providence, 1967). [2] G. Gratzer, General Lattice Theory (Academic Press, New York, Sanfransisco, 1978). [3] G.C. Rao, Almost Distributive Lattices, Doctoral Thesis (1980), Dept. of Mathematics, Andhra University, Visakhapatnam. [4] G.C. Rao, N. Rafi and R.K. Bandaru, Closure operators in Almost Distributive Lattices , Int. Math. Forum 5 (19) (2010) 929–935. [5] G.C. Rao, N. Rafi and B. Ravikumar, On the prime filters of normal almost distributive lattices , South. Asian Bull


This article presents a relatively straightforward theoretical framework about distributive justice with applications. It draws on a few key concepts of Sociological Game Theory (SGT). SGT is presented briefly in section 2. Section 3 provides a spectrum of distributive cases concerning principles of equality, differentiation among recipients according to performance or contribution, status or authority, or need. Two general types of social organization of distributive judgment are distinguished and judgment procedures or algorithms are modeled in each type of social organization. Section 4 discusses briefly the larger moral landscapes of human judgment – how distribution may typically be combined with other value into consideration. The article suggests that Rawls, Elster, and Machado point in this direction. Finally, it is suggested that the SGT framework presented provides a useful point of departure to systematically link it and compare the Warsaw School of Fair Division, Rawls, and Elster, among others.


Heating of natural gas on the gas-distributive installations is carried out for prevention of creation of gas hydrates in gas pressure controller. There are a few methods of heating of natural gas: complete heating of gas and heating of gas pressure controller. The indicated methods have a row of failings, the delivered from which is possible at the use of vortex tube. Work of vortex tube consists of the simultaneous making of two streams: heated and frappe. The heated stream is used for a serve on a gas pressure controller which shuts out it freezing. Little price, insignificant sizes, absence of motive details helps to use a vortex tube for heating of natural gas on the gasdistributive installations.