Quasi-Cauchy quotients and means

Let $$I\subset {\mathbb {R}}$$ I ⊂ R be an interval that is closed under addition, and $$ k\in {\mathbb {N}}$$ k ∈ N , $$k\ge 2\,$$ k ≥ 2 . For a function $$f:I\rightarrow \left( 0,\infty \right) $$ f : I → 0 , ∞ such that $$F\left( x\right) :=\frac{f\left( kx\right) }{ kf\left( x\right) }$$ F x : = f k x k f x is invertible in I, the k-variable function $$ M_{f}:I^{k}\rightarrow I,$$ M f : I k → I , $$\begin{aligned} M_{f}\left( x_{1},\ldots ,x_{k}\right) :=F^{-1}\left( \frac{f\left( x_{1}+\cdots +x_{k}\right) }{f\left( x_{1}\right) +\cdots +f\left( x_{k}\right) } \right) , \end{aligned}$$ M f x 1 , … , x k : = F - 1 f x 1 + ⋯ + x k f x 1 + ⋯ + f x k , is a premean in I, and it is referred to as a quasi Cauchy quotient of the additive type of generator f. Three classes of means of this type generated by the exponential, logarithmic, and power functions, are examined. The suitable quasi Cauchy quotients of the exponential types (for continuous additive, logarithmic, and power functions) are considered. When I is closed under multiplication, the quasi Cauchy quotient means of logarithmic and multiplicative type are studied. The equalities of premeans within each of these classes are discussed and some open problems are proposed.

Embryological Observations of Fruit Development in Mimosa pudica Linn.

The present papers deal with embryological studies of the fruit development in Mimosa pudica Linn.. Observations on seed coat development is of exotestal pattern and is of multiplicative type, Pericarp is differentiated into epicarp, mesocarp and endocarp were noted.

Means of expression of an alternative in the Khanty language

Introduction: the article is devoted to the identification of means of expression of an alternative in the Khanty language. An alternative is one of the varieties of multiplicative type of multiplicity of situations. The analysis of the semantic zone of alternativeness revealed lexical and morphological means through which this meaning is expressed. Objective: to identify means of expression of an alternative in the Khanty language and to identify the most expressive one. Research materials: the bilingual (Khanty-Russian) dictionaries of the Kazym, the Shuryshkar and the Eastern Khanty dialects, as well as examples from theoretical research on the Khanty language. Results and novelty of the research: the scientific novelty of the research is that for the first time a comprehensive study of the semantic zone of an alternative in the Khanty language was conducted. The analysis reveals lexical and morphological means by which this meaning is realized. The alternative subsystem contains three groups: lexical means with semantics of an alternative; word-forming means expressing the meaning of an alternative; paired adverbs expressing mutually directed action. In the components of the first group the meaning of an alternative is the least expressed and difficult determined; the second group contains verbs formed by the word500 forming suffix =i=/=ij= ~ = ĭ=/=ĭj= (they express the multiplicative type of multiplicity of situations including an alternative); the most clearly the meaning of an alternative is presented in the group with paired adverbs.

Retract Rationality and Algebraic Tori

For any prime number $p$ and field $k$, we characterize the $p$-retract rationality of an algebraic $k$-torus in terms of its character lattice. We show that a $k$-torus is retract rational if and only if it is $p$-retract rational for every prime $p$, and that the Noether problem for retract rationality for a group of multiplicative type $G$ has an affirmative answer for $G$ if and only if the Noether problem for $p$-retract rationality for $G$ has a positive answer for all $p$. For every finite set of primes $S$ we give examples of tori that are $p$-retract rational if and only if $p\notin S$.

Forecasting of Primary Energy Consumption Data in the United State: a comparison between ARIMA and Holter Winters Models

This research has a purpose to compare ARIMA Model and Holt-Winters Model based on MAE, RSS, MSE, and RMS criteria in predicting Primary Energy Consumption Total data in the US. The data from this research ranges from January 1973 to December 2016. This data will be processed by using R Software. Based on the results of data analysis that has been done, it is found that the model of Holt-Winters Additive type (MSE: 258350.1) is the most appropriate model in predicting Primary Energy Consumption Total data in the US. This model is more appropriate when compared with Holt-Winters Multiplicative type (MSE: 262260,4) and ARIMA Seasonal model (MSE: 723502,2).Paper ini dipresentasikan pada The 3th International Conference on Green Design and Manufacture 2017 (Krabi, Thailand, 29-30 April 2017), diunggah oleh Ansari Saleh Ahmar