There exist several versions of discrete counterpart of continuity in the framework of finite chains, e.g., the smoothness, the divisibility, intermediate-value property and the 1-Lipschitz property. In this paper, we first discuss the relationships among the smoothness, divisibility, intermediate-value property and 1-Lipschitz property. Second, we present complete characterizations of divisible Associative aggregation operations on finite chains.

Micanorm-based logics with a weak form of associativity are introduced and their completeness results are addressed. More concretely, first the basic wa$_{t}$-uninorm logic \textbf{WA$_{\textbf{t}}$BUL} and its axiomatic extensions are introduced as $[0, t]$-continuous wa$_{t}$-uninorm analogues of the logics based the $[0, 1)$-continuous uninorms. Next algebraic structures characterizing the logics are introduced along with algebraic completeness results. Third, wa$_{t}$-uninorms are introduced as uninorms with weak $t$-associativity instead of associativity and associated properties are discussed. Finally, by virtue of Yang--style construction, it is verified that the logics based on wa$_{t}$-uninorms are complete on unit real interval $[0, 1]$, i.e., so called \emph{standard} complete.

The finite non-commutative and non-Associative algebraic structures are indeed one of the special structures for their probabilistic results in some branches of mathematics. For a given integer n ≥ 2, the nth-commutativity degree of a finite algebraic structure S, denoted by Pn(S), is the probability that for chosen randomly two elements x and y of S, the relator xny = yxn holds. This degree is specially a recognition tool in identifying such structures and studied for Associative algebraic structures during the years. In this paper, we study the nth-commutativity degree of two infinite classes of finite loops, which are non-commutative and non-Associative. Also by deriving explicit expressions for nth-commutativity degree of these loops, we will obtain best upper bounds for this probability.

Learning ability and memory duration are two inseparable factors which can increase the efficiency of a living organism during its lifetime. Trichgramma brassice Bezdenko (Hym.: Trichogrammatidae) is a biological control agent widely used against different pest species. This research was conducted to study the olfactory Associative learning ability and memory duration of T. brassicae under laboratory conditions. According to our results, T. brassicae showed olfactory learning ability in response to conditioned odors, and this learned olfactory stimuli lasted for 20 hours. In a second experiment, the effects of frequent experiences on the memory duration of females were studied. A direct relationship between frequent experiences and memory duration was observed. When exposed to a conditioned odor, wasps’ memory duration increased in response to the number of experiences. Memory was observed at 28 h after one extra conditioning. The duration of the Associative memory lasted 42 hours when 2 extra experiences were given, 50 hours after 3 experiences, and 58 hours after 4 extra conditioning experiences. Our results showed that T. brassicae can associate new odors to host existence, and they will show increased memory duration after multiple experiences.

Background: Regarding the adverse effects of sexual dysfunction in mental health of the menopause woman and their families, detecting related factors of sexual dysfunction in this period seems to be essential. This study aimed to determine the Associative factors of sexual dysfunction in menopause.Methods: This study was a cross sectional one. In this study simple random sampling was used to enroll 174 married women. Data were collected by questionnaires, through interviews and descriptive and inferential statistical methods, t-test, X2 and X2 mantel Hanszel test were used to analyze the data through SPSS software.Results: The relative frequency of sexual dysfunction in menopause is 72.4%, and the variables such as depression, spouse' relations quality and sexual knowledge were significantly associated with sexual dysfunctions. The findings also showed that no significant association exist between reproductive and personal characteristic such as spouses' age difference, marriage length, number of children and marriage status with sexual dysfunction in menopausal period.Conclusion: Sexual function can be affected by psychiatry disorders and lack of knowledge, regarding the creation of many psychological and community injuries following sexual dysfunction, therefore the role of health professionals in consulting and education is emphasized.