scholarly journals Some inferences based on a mixture of power function and continuous logarithmic distribution

2020 ◽  
Vol 14 (1) ◽  
pp. 1116-1126
Author(s):  
Ahmed M. T. Abd El-Bar ◽  
Maria do Carmo S. Lima ◽  
M. Ahsanullah
Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1568
Author(s):  
Shaul K. Bar-Lev

Let F=Fθ:θ∈Θ⊂R be a family of probability distributions indexed by a parameter θ and let X1,⋯,Xn be i.i.d. r.v.’s with L(X1)=Fθ∈F. Then, F is said to be reproducible if for all θ∈Θ and n∈N, there exists a sequence (αn)n≥1 and a mapping gn:Θ→Θ,θ⟼gn(θ) such that L(αn∑i=1nXi)=Fgn(θ)∈F. In this paper, we prove that a natural exponential family F is reproducible iff it possesses a variance function which is a power function of its mean. Such a result generalizes that of Bar-Lev and Enis (1986, The Annals of Statistics) who proved a similar but partial statement under the assumption that F is steep as and under rather restricted constraints on the forms of αn and gn(θ). We show that such restrictions are not required. In addition, we examine various aspects of reproducibility, both theoretically and practically, and discuss the relationship between reproducibility, convolution and infinite divisibility. We suggest new avenues for characterizing other classes of families of distributions with respect to their reproducibility and convolution properties .


2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Haim Kalman

AbstractAny scientific behavior is best represented by nondimensional numbers. However, in many cases, for pneumatic conveying systems, dimensional equations are developed and used. In some cases, many of the nondimensional equations include Reynolds (Re) and Froude (Fr) numbers; they are usually defined for a limited range of materials and operating conditions. This study demonstrates that most of the relevant flow types, whether in horizontal or vertical pipes, can be better described by Re and Archimedes (Ar) numbers. Ar can also be used in hydraulic conveying systems. This paper presents many threshold velocities that are accurately defined by Re as a simple power function of Ar. Many particulate materials are considered by Ar, thereby linking them to a common behavior. Using various threshold velocities, a flow regime chart for horizontal conveying is presented in this paper.


1994 ◽  
Vol 1 (5) ◽  
pp. 459-467
Author(s):  
T. Buchukuri ◽  
D. Yanakidi

Abstract We investigate the solutions of boundary value problems of linear electroelasticity, having growth as a power function in the neighbourhood of infinity or in the neighbourhood of an isolated singular point. The number of linearly independent solutions of this type is established for homogeneous boundary value problems.


1966 ◽  
Vol 39 (6) ◽  
pp. 1261-1262
Author(s):  
S. S. Stevens ◽  
Miguelina Guirao
Keyword(s):  

Processes ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 1251
Author(s):  
Michael Vigdorowitsch ◽  
Alexander N. Pchelintsev ◽  
Liudmila E. Tsygankova

Using experimental data for the adsorption of phosphates out of wastewater on waste recycled bricks, published independently in MDPI Processes before (2020), this message re-visits the mathematical theory of the Freundlich adsorption model. It demonstrates how experimental data are to be deeper treated to model the saturation regime and to bridge a chasm between those areas where the data fit the Freundlich power function and where a saturation of surface adsorption centers occurs.


2021 ◽  
Author(s):  
Ryszard Mazurek

AbstractFor any commutative semigroup S and positive integer m the power function $$f: S \rightarrow S$$ f : S → S defined by $$f(x) = x^m$$ f ( x ) = x m is an endomorphism of S. We partly solve the Lesokhin–Oman problem of characterizing the commutative semigroups whose all endomorphisms are power functions. Namely, we prove that every endomorphism of a commutative monoid S is a power function if and only if S is a finite cyclic group, and that every endomorphism of a commutative ACCP-semigroup S with an idempotent is a power function if and only if S is a finite cyclic semigroup. Furthermore, we prove that every endomorphism of a nontrivial commutative atomic monoid S with 0, preserving 0 and 1, is a power function if and only if either S is a finite cyclic group with zero adjoined or S is a cyclic nilsemigroup with identity adjoined. We also prove that every endomorphism of a 2-generated commutative semigroup S without idempotents is a power function if and only if S is a subsemigroup of the infinite cyclic semigroup.


2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Huren Rong ◽  
Jingyu Gu ◽  
Miren Rong ◽  
Hong Liu ◽  
Jiayao Zhang ◽  
...  

In order to study the damage characteristics of the yellow sandstone containing pores under the freeze-thaw cycle, the uniaxial compression test of saturated water-stained yellow sandstones with different freeze-thaw cycles was carried out by rock servo press, the microstructure was qualitatively analyzed by Zeiss 508 stereo microscope, and the microdamage mechanism was quantitatively studied by using specific surface area and pore size analyzer. The mechanism of weakening mechanical properties of single-hole yellow sandstone was expounded from the perspective of microstructure. The results show the following. (1) The number of freeze-thaw cycles and single-pore diameter have significant effects on the strength and elastic modulus of the yellow sandstone; the more the freeze-thaw cycles and the larger the pore size, the lower the strength of the yellow sandstone. (2) The damage modes of the yellow sandstone containing pores under the freeze-thaw cycle are divided into five types, and the yellow sandstone with pores is divided into two areas: the periphery of the hole and the distance from the hole; as the number of freeze-thaw cycles increases, different regions show different microscopic damage patterns. (3) The damage degree of yellow sandstone is different with freeze-thaw cycle and pore size. Freeze-thaw not only affects the mechanical properties of yellow sandstone but also accelerates the damage process of pores. (4) The damage of the yellow sandstone by freeze-thaw is logarithmic function, and the damage of the yellow sandstone is a power function. The damage equation of the yellow sandstone with pores under the freezing and thawing is a log-power function nonlinear change law and presents a good correlation.


1987 ◽  
Vol 65 (11) ◽  
pp. 2690-2695 ◽  
Author(s):  
R. J. Larson

The rhizostome scyphomedusa Stomolophus meleagris swims continuously at speeds up to 15 cm∙s−1. Mean velocities increased as a power function of wet weight up to 70 g but were mostly constant thereafter. Bell pulsations ranged from 1.7 to 3.6 Hz. Reynolds numbers equalled 900 – 13 000. During activity, medusae consumed 0.05 mL O2∙h−1∙g WW−1 (1.2 mL O2∙h−1∙g DW−1), at 30 °C. Rates for inactive medusae were 50% less. The estimated cost of transport ranged from 2 J∙kg−1∙m−1 at 5 g to 1 J∙kg−1∙m−1 at 1 kg. These rates are comparable to those of fishes and about 1/50th that of planktonic crustaceans. These results were unexpected in light of the typical inefficiency (power output/power input) of jet swimming. However, S. meleagris has a very low respiration rate relative to crustaceans and fish, which probably compensated for low swimming efficiency.


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