Solid weak BCC-algebras

We characterize weak BCC-algebras in which the identity $(xy)z=(xz)y$ is satisfied only in the case when elements $x,y$ belong to the same branch

Properties of Bipolar Fuzzy Hypergraphs

In this article, we apply the concept of bipolar fuzzy sets to hypergraphs and investigate some properties of bipolar fuzzy hypergraphs. We introduce the notion of $A-$ tempered bipolar fuzzy hypergraphs and present some of their properties. We also present application examples of bipolar fuzzy hypergraphs

A description of n-ary semigroups polynomial-derived from integral domains

We provide a complete classification of the n-ary semigroup structures defined by polynomial functions over infinite commutative integral domains with identity, thus generalizing G{\l}azek and Gleichgewicht's classification of the corresponding ternary semigroups

Representations of Menger (2,n)(2,n)-semigroups by multiplace functions

Investigation of partial multiplace functions by algebraic methods plays an important role in modern mathematics were we consider various operations on sets of functions, which are naturally defined. The basic operation for $n$-place functions is an $(n+1)$-ary superposition $[ ]$, but there are some other naturally defined operations, which are also worth of consideration. In this paper we consider binary Mann's compositions \op{1},...,\op{n} for partial $n$-place functions, which have many important applications for the study of binary and $n$-ary operations. We present methods of representations of such algebras by $n$-place functions and find an abstract characterization of the set of $n$-place functions closed with respect to the set-theoretic inclusion

Associative polynomial functions over bounded distributive lattices

The associativity property, usually defined for binary functions, can be generalized to functions of a given fixed arity n>=1 as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case of polynomial functions over bounded distributive lattices and present explicit descriptions of the corresponding associative functions. We also show that, in this case, both generalizations of associativity are essentially the same.Comment: Final versio

Representations of (2,n)(2,n)-semigroups by multiplace functions

We describe the representations of $(2,n)$-semigroups, i.e. groupoids with $n$ binary associative operations, by partial $n$-place functions and prove that any such representation is a union of some family of representations induced by Schein's determining pairs.Comment: 17 page

Nuclear Tetrahedral Symmetry: Possibly Present Throughout the Periodic Table

More than half a century after the fundamental, spherical shell structure in nuclei has been established, theoretical predictions indicate that the shell-gaps comparable or even stronger than those at spherical shapes may exist. Group-theoretical analysis supported by realistic mean-field calculations indicate that the corresponding nuclei are characterized by the $T_d^D$ ('double-tetrahedral') group of symmetry, exact or approximate. The corresponding strong shell-gap structure is markedly enhanced by the existence of the 4-dimensional irreducible representations of the group in question and consequently it can be seen as a geometrical effect that does not depend on a particular realization of the mean-field. Possibilities of discovering the corresponding symmetry in experiment are discussed.Comment: 4 pages in LaTeX and 4 figures in eps forma

Characterizations of quasitrivial symmetric nondecreasing associative operations

We provide a description of the class of n-ary operations on an arbitrary chain that are quasitrivial, symmetric, nondecreasing, and associative. We also prove that associativity can be replaced with bisymmetry in the definition of this class. Finally we investigate the special situation where the chain is finite

Evaluation of thermal pattern distributions in racehorse saddles using infrared thermography

The impact of a rider’s and saddle’s mass on saddle thermal pattern distribution was evalu ated using infrared thermography (IRT). Eighteen racehorses were ridden by four riders with their own saddle. Images of the saddle panels were captured at each of six thermographic examinations. On each image, six regions of interest (ROIs) were marked on the saddle panels. The mean temperature for each ROI was extracted. To evaluate the influence of load on saddle fit, 4 indicators were used: ΔTmax (difference between the mean temperature of the warmest and coolest ROI); standard deviation of the mean temperature of the six ROIs; right/left; bridging/rocking and front/back thermal pattern indicator. Incorrect saddle fit was found in 25 measurements (23.1%) with ΔTmax greater than 2˚C. The relationships between rider and saddle fit as well as saddle fit and horse were significant (p<0.001). An average ΔTmax in rider A was significantly higher than in other riders (p<0.001). The right/left thermal pattern differed significantly from the optimal value for riders A and B; while the bridging/rocking thermal pattern differed significantly from this value for riders A, C and D (p<0.05). Front saddle thermal pattern was most frequent for rider A (41.5%), whereas back saddle thermal pattern was most frequent for rider C (85.7%). Measurement of the mean temperature in 6 ROIs on saddle panels after training was helpful in assessing the influence of rider and saddle mass on saddle fit. IRT offered a non-invasive, rapid and simple method for assessing load on thermal pattern distribution in race saddles.info:eu-repo/semantics/publishedVersio